Econometric Analysis of the Real Estate Market and Investment [1 ed.] 0415241812, 9780415241816, 9780203164396

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Econometric analysis of the real estate market and investment This book provides an economic and econometric analysis of real estate investment and real estate market behaviour. The author examines fluctuations in the real estate business to reveal the mechanisms governing the interaction between real estate and other sectors of the economy. Addressing new developments in financial and economic research, the workings of the real estate market are analysed through theory and the use of econometric models, with real cases demonstrating the applications. The methodology and theoretical developments in the book are universal to the professions of economics, econometrics and finance, but it is the first time that many of them have been applied to real estate research, particularly in book-length format. The author draws upon literature of the business cycle, the efficient market hypothesis and rational expectations, while applying and discussing econometric methods that include those used for investigating trends and cycles, decomposition of trends and cycles, common trends and common cycles, and univariate and multivariate shock persistence profiles. This book should prove to be valuable reading for financial economists and econometricians, real estate researchers and doctoral students and researchers working in finance with a focus on financial markets. Peijie Wang teaches in finance and investment at UMIST and University of Manchester. He has extensive research experience and has published widely in finance, real estate, economics and econometrics.

Econometric analysis of the real estate market and investment Peijie Wang

London and New York

First published 2001 by Routledge 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2005. “ To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.” © 2001 Peijie Wang All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Wang, Peijie, 1956– Econometric analysis of the real estate market and investment / Peijie Wang. p. cm. Includes bibliographical references and index. 1. Real estate investment – Great Britain – Econometric models. 2. Commercial real estate – Great Britain – Econometric models. 3. Real estate business – Great Britain – Econometric models. 4. Business cycles – Great Britain – Econometric models.I. Title. HD596 W36 2001 332.63′24′015195–dc21 00–47057 ISBN 0-203-16439-3 Master e-book ISBN

ISBN 0-203-25852-5 (Adobe e-Reader Format) ISBN 0-415-24181-2 (Print Edition)

Contents List of figures

vii

List of tables

viii

List of abbreviations and variables Preface

PART I Preliminaries 1 Background

xi xiii

1

2

2 Real estate and the economy: preliminary statistics

15

3 Theories of dynamics

31

PART II The dynamic behaviour of economic and financial time series

48

4 Trends, cycles and persistence

52

5 A unified representation of economic fluctuations and dynamics

64

PART III The dynamic behaviour of real estate

80

6 Recapturing market information from appraisal-based real estate indices

81

7 Real estate’s response to shocks

95

8 Price discovery and study of real estate market efficiency

116

9 Cyclical fluctuations in the real estate market

125

10 Summary

Bibliography

140

146

Index of names

159

Subject index

165

Figures 1.1 Investment in property by life assurance companies

9

1.2 Investment in property by general insurance companies

10

1.3 Investment in property by pension funds

11

1.4 Real estate by sector

12

1.5 Overall performance comparison, 1977 Quarter 2–1993 Quarter 2

13

2.1 Relevant time series variables

28-30

3.1 The development of business cycle theory

37

4.1 The effect of a shock to the stochastic trend process

55

4.2 The effect of a shock to the deterministic trend process

56

6.1 Smoothing in the appraisal-based index – original and unsmoothed JLW quarterly indices against FTAP

90

6.2 Smoothing in the appraisal-based index – original and unsmoothed IPD monthly indices against FTAP

91

7.1 Persistence in real estate market and other economic activities 98– levels 101 7.2 Persistence in real estate market and other economic activities 102– first difference 105 9.1 Coherence and phase – an example (GDP with lagged GDP)

136

9.2 Coherence and phase – real estate with other variables

138

Tables 1.1

UK Insurance company (long-term) asset structures

6

1.2

UK Insurance company (general) asset structures

7

1.3

UK Pension funds structures

8

1.4

Overall performance comparison: 1977 Quarter 2–1993 Quarter 13 2, quarterly data

2.1 (a)

Property’s correlations with selected economic variables: 1977 19 Quarter 2–1993 Quarter 2 JLW – first difference filter (rates of change analysis)

2.1 (b)

Property’s correlations with selected economic variables: 1977 Quarter 2–1993 Quarter 2 JLW–Hodrick–Prescott filter

2.2 (a)

Property’s correlations with selected economic variables: 1977 21 Quarter 2–1993 Quarter 2 HPK – first difference filter (rates of change analysis)

2.2 (b)

Property”s correlations with selected economic variables: 1977 22 Quarter 2–1993 Quarter 2 HPK–Hodrick–Prescott filter

2.3

Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 JLW – Johansen procedure

23

2.4

Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 JLW – ADF statistic

24

2.5

Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 HPK – Johansen procedure

25

2.6

Cointegration of real estate with selected economic variables:

25

20

1977 Quarter 2–1993 Quarter 2 HPK – ADF statistic 6.1

Summary statistics – MF-Shilling method, JLW index

87

6.2

Summary statistics – MF-Shilling method, IPD index

89

6.3

Summary statistics – implied cointegration, JLW

92

6.4

Summary statistics – implied cointegration, IPD

93

6.5

Unsmoothing of the JLW index

93

6.6

Unsmoothing of the IPD index

94

7.1

Transitory components in shocks

106

7.2

Multivariate persistence Vk (with unsmoothed JLW index)

110

7.3

Multivariate persistence Vk (with original JLW index)

110

7.4

Multivariate persistence Vk (with fully-unsmoothed JLW index) 111

7.5

Summary statistics for the money growth model

112

7.6

Multivariate persistence Vk, monetary shocks decomposed

112

7.7

Multivariate persistence Vk, summary of monetary and nonmonetary shocks

113

8.1

Unit root test, Perron’s (1993) model

119

8.2

Cointegration, long-run and short-term relationship, unsmoothed JLW and FTAP

121

8.3

Cointegration, long-run and short-term relationship, original JLW and FTAP

122

9.1

Serial correlation in individual series

127

9.2

Feature (cycles) tests: JLW has a feature involving other variables (with unsmoothed JLW index)

127

9.3

Feature (cycles) tests: other variables have a feature involving JLW (with unsmoothed JLW index)

128

9.4

Feature (cycles) tests: JLW has a feature involving other variables (with the original JLW index)

128

9.5

Feature (cycles) tests: other variables have a feature involving JLW (with original JLW index)

129

9.6

Cointegration and common cycles

130

9.7

Common features tests – coincident common cycles using IV method

132

9.8

Common features tests. Phase-shifting common cycles using IV 133 method (two lags)

9.9

Common features tests. Phase-shifting common cycles using IV 134 method (four lags)

Abbreviations and variables ADF

augmented Dickey–Fuller

AIC

Akaike information criterion

AMEX

American Stock Exchange

APT

arbitrage pricing theory

ARIMA

autoregressive integrated moving average

CAPM

capital asset pricing model

CAR

cumulative abnormal returns

CC

coincident indicator

CO

construction output on new work

CSO

Central Statistical Office

CV

coefficient of variance

DF

Dickey–Fuller

DS

difference stationary

DWG

indicator of fixed investment in dwellings

DYMIMIC

dynamic multiple indicator, multiple cause

ECM

error correction mechanism

EMH

efficient market hypothesis

FTA

Financial Times actuary all-share index

FTAP

property company sector of FTA

GARCH

generalised autoregressive conditional heteroscedaticity

GDP

gross domestic product

GLT

gilts

GMM

generalised method of moments

GNP

gross national product

HFX

Halifax Building Society house price index

HP

Hodrick and Prescott

HPK

Hillier Parker property market return

index IPD

Investment Property Databank

JLW

Jones Lang Wootten property total return index

LG

lagging indicator

LL

longer leading indicator

M0

narrowly defined money

M4

broad money supply

MNG

manufacturing sector

NCREIF

National Council of Real Estate Investment Fiduciaries

NO

construction new orders

NPT

number of property transactions

NTW

Nationwide Building Society house price index

NYSE

New York Stock Exchange

ONS

Office for National Statistics

PDN

industrial production

REH

rational expectations hypothesis

REIT

real estate investment trust

RESA

stock under construction

RESC

change in stock under construction

RMSE

root mean squared errors

SC

Schwartz’s criterion

SL

shorter leading indicator

SUR

seemingly unrelated regression

SVC

services sector

TS

trend stationary

UER

unemployment rate

VAR

vector autoregressive

Preface This book is on the economic and econometric analysis of real estate investment and real estate market behaviour in the UK. Issues of fluctuations in real estate and its dynamics are addressed and examined, to reveal the mechanisms governing the interactions between real estate and the other sectors in the economy, and to study the ways in which real estate influences and is influenced by the economy. The term ‘real estate’ is used throughout the book to mean commercial real estate as in the US, or commercial property as in the UK. The book covers theories of economic fluctuations and dynamic analysis, econometric approaches to investigating economic fluctuations and dynamics, and an empirical study on fluctuations and dynamics in the real estate market and investment. Its methodology and theoretical developments are universal to the economics profession, including econometrics and finance. Most methods in the book are either new in general or new to real estate research. The empirical part is the applications of the theories and econometric methodologies. The book addresses new developments in financial and economic research, as well as some relevant traditional ideas in finance. The book analyses and explains how the real estate market works with the theories and models, and demonstrates the applications with real cases. It would also be a helpful reference book and tool, helping researchers in their studies and projects with useful methods and procedures, together with their relevance to real estate research. The intended audience includes: economists and econometricians who have an interest in real estate or who are interested in applying theories to real problems; real estate researchers and teachers who are keen to learn the new developments in financial econometrics and the ever-growing literature in the area; doctorate students researching real estate; and researchers working in finance with a focus on financial markets. It is assumed that the reader has the basic knowledge in econometrics up to univariate and multivariate regression, ARIMA (autoregressive integrated moving average) models and Box-Jenkins analysis, and the VAR (vector autoregression) model. In finance and investment areas, the reader is assumed to have knowledge in fundamentals of corporate finance, financial markets and investment. There are many excellent textbooks available, e.g., Econometric Analysis by Greene (1993), Time Series Analysis by Hamilton (1994), Unit Roots, Cointegration, and Structural Change by Maddala and Kim (1998), and Introduction to Econometrics by Maddala (1992), for basic econometrics and time series analysis. With regard to finance and investment, there are Capital Markets by Fabozzi and Modigliani (1996), Financial Institutions and Markets by Kolb and Rodriguez (1996), Corporate Finance by Ross, Westerfield and Jaffe (1996), Financial Theory and Corporate Policy by Copeland and Weston (1992), Financial Management by Brigham, Gapenski and Ehrhardt (1999), and Investments by Sharpe, Alexander and Bailey (1998). On the other hand, the book introduces and discusses a number of econometric models

and methodologies which are currently scattered in the literature and yet to be included and integrated in single books. The book is divided into three parts and consists of 10 chapters. After an introduction to the background, current research and the literature in real estate in Chapter 1, a straight forward and descriptive statistical analysis of the real estate market and performance is provided in Chapter 2, in relation to relevant sectors or activities in the economy. Real estate is analysed in levels and in changes, examining both short-term and long-run relationships. Chapter 3 discusses three related theories with common attributes of dynamics: the efficient market hypothesis, rational expectations, and business cycle theory. The discussion leads to empirical examinations of real estate market behaviour in later chapters. It has been revealed that fluctuations in real estate are linked to the economic environment in a variety of ways. This constitutes the theme and framework for this book. It has been made clear that further scrutiny is required to gain insights into the crucial relationships and underlying mechanism in the real estate market. This is achieved by utilising and developing more constructive economic and econometric models and analytical techniques pertinent to the research. In Chapter 4, time series attributes of cycles, trends and persistence are discussed in both univariate and multivariate circumstances. It covers decomposition of time series into cycles and trends; the effects of shocks, e.g., transitory and permanent effects of shocks; and monetary and real shocks. Attention has been paid to their implications. Chapter 5 presents a framework for modelling and analysing economic fluctuations and dynamics. It incorporates common trends and common cycles and analyses common trends and common cycles at the same time. Phase-shifting common cycles in a nonstationary system are further explored. In these two chapters, which form Part II of the book, econometric models and analytical approaches are presented, extended and developed. Fluctuations and dynamic behaviour in real estate investment markets are prominently exhibited in cycles, trends, their response to shocks and common factors among them. Consequently, econometric modelling approaches reflecting these time series attributes and characteristics are explored with statistical explanations and with economic sense. This part has, in many ways, extended the current literature in the study of economic dynamics and developed the econometric modelling framework and strategies which will be utilised to make empirical inquiry into real estate markets. Chapter 6 is the first step of empirical research in the book. It discusses the smoothing issues in real estate indices and proposes two multivariate approaches to unsmoothing the appraisal-based real estate indices. It then applies these procedures to the UK real estate indices of LaSalle (formerly Jones Lang Wootten) and Investment Property Databank, to be used in following chapters. Chapter 7 investigates the persistence patterns in the real estate market, and examines the impact of shocks in other economic and financial variables on the real estate market. In addition, the effects of monetary and non-monetary shocks on the real estate market are also studied. In Chapter 8, the price discovery mechanism in direct and indirect real estate investment markets is investigated. The analysis takes into account both long-run and short-term relationships between these two investments. Moreover, it has further examined asymmetry in indirect real estate investment and direct real estate investment. In Chapter 9, both coincident and phaseshifting common cycles are examined in the economy involving real estate. Common cycle analysis on its own is an extension of common trend analysis. But common cycles

differ from common trends in that the phase matters in the former, therefore analysis is more complicated, and sometimes, rather difficult. When these attributes and trend-cycle behaviour are investigated together in a dynamic system, as proposed in Chapter 5, the study of this chapter is a further advancement of the previous two chapters, especially Chapter 7. These four chapters in Part III are an empirical study of the dynamic behaviour of real estate. Investigations are carried out on important issues pertinent to revealing the nature and the mechanism of fluctuations and dynamic behaviour in real estate markets, their close relation to other sectors in the economy. The book emphasises that real estate is an integrated part of the economy and is treated and examined accordingly throughout the research. Finally, Chapter 10 is a summary of the book.

Part I Preliminaries This book is on the economic and econometric analysis of commercial real estate investment and commercial real estate market behaviour in the UK. Throughout the book, the term ’real estate’ refers to commercial real estate as in the US and commercial property in the UK for abbreviation. Part I is an introduction to research in the book. It contains preliminary analysis of UK real estate markets and discusses the research theme and framework of the book. Chapter 1 outlines the background of research in this book and the current state of research in the area. An initial analysis of UK real estate investment and markets and real estate performance over the last two decades is carried out to present a general picture of UK real estate markets and the players. This, together with a literature review on the contemporary research in the area, forms the background of research in the book, and advocates and supports why research in this book is required. Broad descriptive statistics are estimated and reported in Chapter 2, to gain more intuitive understanding of the real estate market and its relationship with the other sectors in the economy. In particular, this chapter examines the links between the real estate market and a large number of the real sectors of the economy and financial markets, in both the short term and the long run. Chapter 3 set out the research framework and methodologies for the book. Three closely-related theories of dynamics, drawn from studies of business cycle, the rational expectations hypothesis, and the efficient market hypothesis, are discussed with specific reference to real estate.

1 Background This book studies real estate market behaviour in the UK in an economic and econometric analytical framework. The book will examine patterns of real estate market fluctuations, and reveal its relationship with the economy. In particular, it will investigate the ways in which real estate influences, and is influenced by, the other sectors of the economy, and identify the sources and mechanism of shock transmission in the real estate market. As part of this approach, economic and econometric models will be developed to study real estate fluctuations and dynamics in both the short term and the long run and in a multivariate environment. Topics including common cycles and common trends, sources and persistence of shocks, and cointegration, error correction and market efficiency will be covered. Research in this book is motivated by the need for a reconsideration of real estate market behaviour which, until recently, has generally been viewed as different and distinctive from other financial markets. This separation has failed to develop satisfactory explanations, and arises from a lack of economic studies on the UK real estate market utilising modern finance and economic theory. The research will investigate real estate market behaviour in three related areas: the efficient market hypothesis; rational expectations; and business cycle theory. These three theories, with specific reference to real estate market, eventually lead to Real Estate Dynamics – the theme of this book. Real estate dynamics provides economic and econometric modelling for, and explanations of real estate’s cyclical movement. It deals with the underlying mechanism which, in this book, is to be theoretically derived and empirically tested.

Current research in real estate Most real estate research has been carried out differently and distinctively, compared with other research are as in finance or economic science in general. Research in real estate has been largely professional. However, the last decade has witnessed the reorientation of the study on real estate from professional towards academic and from surveying and valuation towards finance and economics. Accompanying these trends are the development and use of real estate performance indices in con-formity with stock market research; the analysis of real estate market efficiency in a modern investment analysis framework; the study of real estate market behaviour, expectations and rationality; and the investigation of the cause and nature of the real estate cycle with business cycle theories. The studies are sometimes sporadic but encouraging.

Econometric analysis of the real estate market and investment

3

Most studies have been documented in America. The operation and institutional structures of the American real estate market are by no means the same as in Britain. However, the implications and methodology of such studies should be useful elsewhere. Reviewing literature in real estate research, Fisher and Webb (1992) have summarised six current issues in the analysis of commercial real estate, three of them closely related with economic and financial theories. They are: • The macroeconomic and other factors affecting returns, which emphasises APT (arbitrage pricing theory); • Risk and return characteristics of commercialreal estate. Most recent studies challenge the traditional view that real estate outperforms other financial assets. Fisher and Webb claim this could have resulted from either the use of performance measures that are not really comparable with other financial markets, or the use of incorrect measures of risk; and • Commercial market rental index. Again, one of the major difficulties with estimating the returns on commercial real estate is the lack of transaction data. A tremendous step towards improving the ability to monitor real estate market would be achieved by the development of an index of effective market rental rates. In fact, the interwoven research topics can be broadened and categorised as following: real estate in institutional portfolios; risk, return and performance comparisons; the derivation of transaction-driven data or indices; tests on real estate market efficiency; behaviour of real estate market and prices; and analysis of the real estate cycle. Most of the studies rely on a reliable measurement of real estate prices and performance. Webb, Miles and Guilkey (1992) generate a transaction-driven commercial real estate return series to determine whether the reliance on appraised values in the estimation of real estate returns is the source of the reported underpricing of real estate relative to shares, bonds and government securities when analysed in the traditional mean-variance point of view, an equilibrium pricing model such as the CAPM (capital asset pricing model), or a Markowitz efficient portfolio. While they find that the transaction-driven real estate returns have greater variance than appraisal-based returns for individual properties, most of the individual real estate risk is idiosyncratic and diversified away at the portfolio levels, which makes them claim that real estate continues to be a dominant asset class even when represented with transaction driven indices. In a sense, this suggests that smoothing in real estate return indices is, in fact, not a big issue at the portfolio level – a finding similar to Wang (1995a, 1995b) which allege that the weight of real estate in a three asset portfolio is not sensitive to the degree of unsmoothing applied to the appraisal based index. Similar research is conducted by Miles et al. (1990) who inquire why commercial real estate only makes up a relatively small percentage of most institutional portfolios, even though the existing literature has consistently reported attractive risk-return characteristics that would suggest much larger allocations. This discrepancy has been explained by a perceived lack of comparability between return series calculated for real estate and those calculated for other asset classes. They make adjustments, using sales data from real estate that help comprise the NCREIF/FRC (National Council of Real Estate Investment Fiduciaries/Frank Russell Company) index, to generate a ‘transactiondriven’ commercial real estate return series. They find that: risk adjusted real estate

Background

4

returns of the transactionbased series are more consistent with other asset classes than the appraisal-based returns; real estate investment still presents an attractive diversification opportunity for shares, bonds and government security portfolios; and real estate is not a homogeneous asset, advising there is a need for further research on the performance of subcategories within this broad asset class. Liu et al. (1990) investigate the consequences of several imperfections associated with real estate markets on pricing and optimal investor portfolios in a CAPM context. CAPM assumptions are relaxed to recognise illiquidity and segmented market structure, and that illiquidity reduces the extent to which investors hold real estate in their portfolios. Chan et al. (1990) employ a multi-factor arbitrage pricing model using prespecified macroeconomic factors to analyse monthly returns on equity REITs (real estate investment trusts) which are not appraisal based. Their findings are, when a single factor CAPM model is used, excess returns still seem to exist as in the case of appraisal based returns; when a five factor APT model is utilised, the evidence of excess returns disappears; and real estate is not seen to be a hedge against inflation. The relationship between stock market and real estate market returns is examined by Gyourko and Keim (1992). They analyse the risks and returns of real estate related firms traded on NYSE (NewYork Stock Exchange) andAMEX (American Stock Exchange), and the relation between real estate share portfolio returns and returns on a standard appraisal-based index. It has been found that lagged values of traded real estate portfolio returns can predict returns on the appraisal-based index after controlling for persistence in the appraised series. The stock market reflects the information on the real estate market that is later imbedded in infrequent real estate appraisal. Empirical tests on real estate market efficiency can be found in Guntermann and Norrbin (1991), who use a dynamic multiple indicator, multiple cause (DYMIMIC) model to test market efficiency; in Case and Shiller (1989), McIntosh and Henderson (1989), Rayburn et al. (1987), and Gau (1984), who adopt a forecasting approach; and in Guntermann and Smith (1987) and Linneman (1986), who employ a traditional financial analysis approach. These studies generally find some evidence of market inefficiency, but the results are more or less mixed. A recent study on real estate market efficiency and rational expectations is by Tegene and Kuchler (1993). The methodology employed is cointegration tests on present value models, as proposed by Campbell and Shiller (1987). They conduct tests for the contribution of speculative bubbles to farmland prices. These tests are carried out under the hypothesis that farmland investors rationally form expectations. They infer whether farmland prices are determined by market fundamentals – discounted returns from the highest economic land use, or whether rumours about farmland price movements are selffulfilling. They find little to reject the hypothesis that market fundamentals determine farmland prices. Tegene and Kuchler (1991) also use Campbell and Shiller’s present value models to test the way in which the expectations are formed, and the implications of the present value model. They find, combined with rational expectations, the present value hypothesis is strongly rejected, while combined with adaptive expectations, the hypothesis is accepted. In the UK,Wang and Matysiak (1994) investigate the regional patterns in commercial real estate rent fluctuations and movement. Their study confirms that there is regional

Econometric analysis of the real estate market and investment

5

segment, and London and the Southeast lead other regions in rent adjustments. Following Wang and Matysiak (1994) and Matysiak and Wang (1995), Campeau (1994) examines the geographical patterns and the relationships between unsecuritised real estate investment and securitised real estate investment, by investigating the valuation process and the data generating process underlying these investments. Barkham and Geltner (1995), in a Granger causality framework, find a long-run price discovery mechanism to link direct investment in real estate and investment in real estate company shares. Similar findings have also been documented in Lizieri and Satchell (1997) and Wang et al. (1997). In real estate index research, Blundell and Ward (1987) were the first to address the issue of smoothing and pioneered an approach to correcting for smoothing in the appraisal based real estate indices. Valuation accuracy is discussed in Lizieri and Venmore-Rowland (1991, 1993), and Matysiak and Wang (1995), among others. The diversification potentials of real estate in multi-asset portfolios are studied by MacGregor and Nanthakumaran (1992), confirming US studies that real estate is a dominant asset class for diversification. It can be seen from the above review that tremendous efforts have been made in real estate research, and significant results and findings have been achieved in recent years. However, frontiers remain and the task is as large and hard as before. Price and return dynamics has yet to be examined thoroughly in a rigorous economic and econometric analytical framework. Specifically, factors which influence real estate performance and the ways in which they influence and are influenced by real estate performance have yet to be inspected; the mechanism of adjustments between real estate and other sectors in the economy has yet to be probed; and the patterns of real estate in response to shocks of a different nature have yet to be observed. This book is, therefore, a timely project in the course of search for knowledge, understanding, and solutions.

Real estate investment and markets Institutions The institutions are the main investors in the real estate market with their real estate holdings amounting to £53 billion at the end of 1993, according to Financial Statistics. It would then be helpful to look into asset structures of the institutions, especially their real estate holdings over time as they control a majority of total real estate investment. Callender and Key (1996) estimate that about 45 per cent of commercial real estate in the UK is held by ‘investors’, and roughly half of this is held by institutions. Of the remaining 55 per cent, not all is owner-occupied In addition to direct investment in real property, the institutions also have substantial equity holdings in real estate companies as will be seen in the next section for real estate company analysis. The post-war period has witnessed rapid growth of real property in the economy, in volume as well as proportion. After the real estate boom in the 1950s and early 1960s, a period of strong direct institutional investment ran from the mid-1960s through to 1981 when the institutions had over 20 per cent of their assets in property. This was largely fuelled by the hypothesis that real estate was a hedge against inflation.

Background

6

Soon after the real estate mini-boom of 1979 to 1981, the institutions began to realise then that it was difficult to engage in asset allocations when real estate was involved, due to its illiquidity compared with other financial investment, e.g. equities, corporate bonds and gilts. Many insurance companies and pension funds started rethinking and taking the view that, on detailed analysis of volatility, liquidity and returns, real estate was less attractive in the medium and longer term than equities. The fact that the institutions had too much real estate at the wrong price resulted in the gradual reduction of their real estate holdings since 1981, in order to have more flexibility in portfolio management and to improve performance. The structural change in real estate finance also contributed to the decline of institutional investment in real estate during the 1980s. Bank lending to real estate companies fuelled the expansion of a new generation of entrepreneurial developers and a largely debt financed development boom took off in this period. The level of bank lending to real estate companies rose dramatically in the second half of the 1980s, from around £8 billion in 1986 to over £40 billion in 1991. The effect of the removal of constraints on international investment which enabled a massive inflow of funds into UK real estate market contributed to the reduced significance of institutional investment. Detailed information on the asset structure of institutions is provided in Tables 1.1 to 1.3. The analysis at disaggregated level for insurance companies provides a clearer

Table 1.1 UK Insurance company (long-term) asset structures Year 1970

1975

1980

1985

1990

1993

Govt securities

Equities Bonds Mortgages

Land and property

Others

Total

3533

3202

2511

2332

1692

513

13781

26

23

18

17

12

4

100

6269

5062

2783

3016

4350

1863

23342

27

22

12

13

19

8

100

15469

16596

2061

3424

12362

3786

53746

29

31

4

6

2

7

100

32915

54673

4960

4268

20162

26

43

4

3

16

35892

100130

13306

6883

34828

16

43

6

3

15

66659

166291

28015

8071

30684

19

47

8

2

9

11189 128167 9

100

40275 232314 17

100

53763 353491 15

Sources: British Association of Insurers, Office for National Statistics: Financial Statistics Note: First line for each year shows value (£ million, current market value, second line shows percentage)

100

Econometric analysis of the real estate market and investment

7

Table 1.2 UK Insurance company (general) asset structures Year Govt securities Equities Bonds Mortgages 1970

1975

1980

1985

1990

1993

Land and Others Total property

273

443

194

92

106

562

1671

16

27

12

6

6

34

100

1082

963

316

182

437

1566

4548

24

21

7

4

10

34

100

3279

2638

720

296

1280

29

23

6

3

11

6381

6264

1763

381

1595

31

30

9

2

8

8198

10251

3047

1854

3288

19

23

7

4

7

16942

10378

5009

1014

2059

28

17

8

2

3

3302 11516 29

100

4332 20716 21

100

17578 44216 40

100

24636 60068 41

100

Sources: British Association of Insurers, Office for National Statistics: Financial Statistics Note: First line for each year shows value (£ million, current market value, second line shows percentage)

picture as life and general insurance companies operate differently. Quite plausibly, insurance companies with a long-term nature hold larger proportions of land and real estate than their non long- term counterparts. The size of the assets of long-term insurance companies is far larger than that of general insurance firms. Due, in part, to legislative changes, pension funds have been growing rapidly and exceeded the insurance funds in mid 1980s to become the largest sector in institutional investment. The percentage of the assets allocated to real estate and land by pension funds is about twothirds of that by long-term insurance companies. Figures 1.1 to 1.3 depict changes in institutional real estate and equity holdings over the last two decades. The drop in real estate holdings by institutions, measured in percentage terms, is actually attributed to the rapid growth of their investment in equities. Not until 1990 did real estate experience decline in values, when it was most hit by the recession. At the peak in 1980, real estate accounted for 23 per cent of the total assets held by long-term insurance companies and valued at £12.4 billion; by the end of 1993, the proportion of real estate dropped to 9 per cent, despite the fact that the value of real estate has more than doubled and was worth £30.7 billion. The biggest investment made by long-term insurance companies is in equities, which accounted for nearly half of the total assets at the end of 1993 and has increased ten fold in value since 1980. Regarding pension funds, the patterns were similar to that of long-term insurance companies. The only difference is that equities had an even larger share amongst total assets. The asset

Background

8

Table 1.3 UK Pension funds structures Year 1970

1975

1980

1985

1990

1993

Govt Equities Bonds securities

Loans and mortgages

Land and Property

Property Others unit trust

Total

1422

3886

1099

274

645

120

139

7836

18

50

14

4

8

2

2

100

2573

8207

–

249

1946

327

148

14467

18

57

–

2

14

2

1

100

12034

29375

–

271

8170

1460

1208

54712

22

54

–

1

15

3

2

100

28631

99842

2536

376

13190

2257

18

63

2

0

8

1

33414

189607

7748

258

26363

1656

11

63

3

0

9

1

37939

266480

7489

262

20240

1804

10

68

2

0

5

1

3974 157376 3

100

18580 302670 6

100

29549 390017 8

100

Sources: Office for National Statistics: Financial Statistics Note: First line for each year shows value (£ million, current market value, second line shows percentage)

structure of general insurance companies began to differ from that of their long-term counterparts from the 1970. The proportion of both equities and real estate holdings declined in the last 20 years, with real estate accounting for only 3 per cent in 1993. Conceivably, these companies invested heavily in gilts, the bonds issued by the UK government and are regarded to stand for riskless investment. No comprehensive separate figures for insurance companies and pension funds’ disaggregate real estate by sector are available. Nevertheless, data and samples from real estate research and consulting agencies could be representative. e.g., IPD (Investment Property Databank) provide their fund structures separately for insurance companies and pension funds. According to IPD and Figure 1.4, at the end of December of 1992, the allocations to retail, office and industrial properties were 41 per cent, 44 per cent and 15 per cent respectively. IPD data bank comprises 157 funds at the end of 1991 with the values of these funds amounting to over £31 billion, covering more than 17,000 individual properties. The funds in IPD’s databank make up half of the institutional real estate holdings, and is the largest information collection on UK investment real estate, sponsored by six major firms of chartered surveyors. Historically, the retail sector has increased from about 30 per cent of total real estate in 1981 to over 40 per cent in 1992. A large decline took place in the office sector, hit severely by the last recession. The proportion of office real estate dropped from 56 per cent in 1981 to 44 per cent in 1992, but the pre-recession figure in 1988 was still as high as 52 per cent. The portion of

Econometric analysis of the real estate market and investment

9

industrial real estate was relatively small and less than 15 per cent during all the time. Changes in IPD’s sectoral allocation during the last recession reflect a

Figure 1.1 Investment in property by life assurance companies. Source: Office for National Statistics Financial Statistics pattern consistent with changes in capital values and rental growth in all sectors. Real estate companies Real estate companies are one of the major players in the real estate market, may be only second to the institutions. They are actively engaged in real estate development, investment and trading. The activities of big companies usually cover all of these three aspects, while the small ones are mostly involved in trading only. For example, Land Securities, British Land and MEPC groups all have a diverse portfolio of offices, shopping centres, out of town retail, food superstores, industrial and warehouse buildings in the UK, invest in all kinds of commercial properties, and are additionally involved in real estate trading and development. According to market capitalisations the top ten real estate companies in mid 1994, in addition to Land Securities, MEPC and British Land, were Hammerson, Slough Estate, Capital Shop Ctrs, Great Portland, Brixton, Burford, and Bradford. These ten companies accounted for 58 per cent of the total market capitalisations within the real estate company sector listed on the London Stock Exchange, and they had a market share larger than there maining 80 companies. As a result, analysis of the accounts of two or three of these major companies is helpful in providing a general picture of their financial structures, activities and related parties. The overall performance of the real estate

Background

10

company sector as measured in total returns on its share index (the combination of gain in share prices and dividends) will be examined later in this section as against other investment alternatives. Real estate companies, as described above, develop, invest in, and deal with

Figure 1.2 Investment in property by general insurance companies. Source: Office for National Statistics Financial Statistics properties. Real estate company shares are thus a surrogate for real estate (Isaac 1994). They also provide a channel for investment in real estate for the investors who either lack large financial resources, or management skills to invest in real estate directly. To invest in real estate company shares allows people to ‘buy’ real estate piecemeal – some thousand pounds against a whole real estate worth millions of pounds. In addition, real estate company shares are, just like any other stock market investment, highly liquid, and normally can be traded many times in a single day, in contrast with real property trading which can take several months to complete a transaction. Due to these factors, real estate company shares are financial vehicles providing a medium for indirect investment in real estate. This indirect investment, while enjoying liquidity and divisibility, should reflect the performance of the underlying real estate in some way. The value of a real estate company’s shares bear some relationship to the value of the real estate it owns and the income it derives from real estate operations, but the link is not so straightforward. First, real estate company shares are stock market investment. They will fluctuate on the market, depending on the value of real estate owned, but the stock market will also tend to discount expected economic and financial events before they happen, while valuations may lag the events. Therefore, real estate company shares may lead real estate in time sequence. Expressed in econometric terms, the former may Granger-cause the latter,

Econometric analysis of the real estate market and investment

11

although the true cause and effect are more likely to be the other way round. Nevertheless, the two sharply dissimilar types of investments inevitably exhibit differential performance. This is particularly true in timing of returns and cash flows. This means that the two investments have little short-term resemblance, as reported in a number of studies. Second, real

Figure 1.3 Investment in property by pension funds. Source: Office for National Statistics Financial Statistics estate companies are geared, and the effect of gearing is higher volatility in real estate company shares. Third, dividend policy tends to induce additional volatility with regard to uncertainty in the timing and amount of cash flows, as observed empirically. Fourth, tax regimes also affect the profit and performance. While real estate company shareholders are double taxed on the one hand, they do enjoy a corporate tax shield on the other due to the leverage or gearing which is typically high in real estate companies. The combined effects could benefit or disfavour investors, depending on the individual companies and investor utilities. Performance assessment The overall performance of real estate company shares, the institutional real estate investment, and general stock market investment is depicted in Figure 1.5. Descriptive financial figures are reported in Table 1.4. From Table 1.4, it can be seen that the real estate company sector share index, represented by FTAP (Financial Times actuary all-share index’s real estate sector), has the highest coefficient of variance (CV), a number dividing the variance by the rate of

Background

12

return, thus a rough measure of excess returns required for bearing additional risk. Although CV is not recommended as a measure for ranking investment opportunities due to a number of defects, it does provide a means to link return to risk or a risk adjusted return, and it is all that is needed for the moment. Compared with the FTA all share index, it has a lower return and higher volatility, and seems to be inferior to the general stock market investment. The real estate investment has a much lower standard deviation, 2.71 for the JLW (Jones Lang Wootten)

Figure 1.4 Real estate by sector Source: IPD property index and 3.94 for the HPK (Hillier Parker) property index. However the comparison of real estate company shares with real estate investment is not readily applicable due to possible smoothing in the valuation- based real estate performance index. The difference also exists between the two indices for real estate investment–the CV of the JLW is 0.95 and that of the HPK is 1.18. The HPK index, based on hypothetical properties, is claimed to react to market movement briskly, which is reflected in its higher CV. Even so, according to the HPK, real estate still has a relatively

Econometric analysis of the real estate market and investment

13

low volatility, and is preferred to the investment in real estate company shares in terms of CV, even if the FTAP figure is adjusted down for the effect of gearing. In fact, degearing is unlikely to change much in CV, when both variance and rate of return become lower. One of the interesting points displayed by Figure 1.5 is that real estate and real estate company shares tend to move closely in the short to medium term. Since 1990 real estate company shares, in line with real estate, have dropped considerably with possible over reaction to their underlying operations, while the general stock market investment, measured by the FTA all- share index, has kept growing. It

Figure 1.5 Overall performance comparison, 1977 Quarter 2–1993 Quarter 2. Sources: Jones Lang Wotton, Hillier Parker

Table 1.4 Overall performance comparison: 1977 Quarter 2–1993 Quarter 2, quarterly data JLW

HPK

FTAP

FTA

GLT

r

2.85

3.33

3.51

4.93

3.48

σ

2.71

3.94

12.17

9.64

6.69

CV

0.95

1.18

3.46

1.95

1.92

then seems reasonable to model real estate with real estate company shares. But this stance should only be taken with caution and more enquiries are needed to reach a satisfactory conclusion.

Background

14

Organisation of the book The book is organised as follows. Part 1 is the preliminaries of research of the book. It first outlines background of research in this book and the current state of research in the area. It is then devoted to the general discussion on real estate investment and the market, and of descriptive statistics for real estate and the economy. These would generally present a picture of various facets for real estate with its performance in relation to economic fluctuations, in aggregate as well as in specific but pertinent sectors. The purpose is to reveal that fluctuations in real estate are linked to its economic environment in a variety of ways; and research methodologies and contents in the later parts of this book reflect these views. These analyses, together with the review on the recent developments in the real estate research literature, outline the issues and set the framework for advanced studies in the subsequent parts of this book. Part 2 will study the issue of economic fluctuations in real estate research. Econometric models and analytical approaches will be presented, extended and developed. To match the characteristics of real estate revealed and the views expressed in Part 1, the methodology and approaches to studying real estate will be used to examine real estate in an integrated economic system implied by the multivariate time series modelling strategy. In particular, this part will study fluctuations and the dynamic behaviour in real estate investment markets in terms of cycles, trends, their response to shocks, and the common factors which real estate shares with other economic and financial sectors in both the short and long run. This part attempts to advance the current literature in the study of economic dynamics and develop the econometric modelling framework and strategies which will be utilised to make an empirical inquiry into UK real estate markets. Part 3 will study the dynamic behaviour of real estate in the UK empirically. This part will extend real estate research to such areas outlined in part I which are either new or remain important and unsolved, and apply both existing econometric approaches and the approaches developed in the previous chapters to the inquiries. Issues of real estate fluctuations and dynamics in both the short term and the long run, with specific reference to cycles, market efficiency and expectations, will be studied in detail. The last chapter will summarise the book and highlight the findings.

2 Real estate and the economy Preliminary statistics In recent years, a small number of researchers have adopted regressional analysis in levels between direct real estate investment performance and real estate company shares. Although the results challenge the early perception or judgement that the performance of real estate has little relationship with that of other financial market investments, and thus cannot be explained by or predicted via the latter, the results are somewhat mixed. This type of approach is motivated by the search for an easy way to describe and explain real estate performance and real estate market behaviour in the absence of reliable transaction-driven market data. However, analysis has been restricted to the stock market arena. There are no reasons, nor evidence, to support the idea that real estate company shares should necessarily behave similar to real estate. First, the investment undertaken by real estate companies rather small portion of total investment in commercial real estate. Second, real estate companies’ assets are geared which, along with company management, accounting policies and taxation, would cause a big variation in performance. And third, real estate investment, though a financial investment as well, is by little means a stock market bustle; rather, it is more interacted with the economic activities in the real sectors. The purpose of this chapter is to provide a straightforward and descriptive statistical analysis of real estate performance, in relation to relevant sectors or activities. The time series data sets used are: • House prices, drawn from the Halifax Building Society House Price Index (HFX) and the Nationwide Building Society House Price Index (NTW); • Indicators of fixed investment in dwellings (DWG); • Number of property transactions (NPT); • Construction output (CO) and new orders1 (NO), two new series standing for stock under construction (RESA) and the change in stock under construction2 (RESC) being created; • The cyclical indicators including longer el ading (LL), shorter leading (SL), coincident (CC), and lagging indicators (LG). The graphs of these indicators (except cyclical indicatiors) are shown in Figure A2.1 in the appendix to this chapter. It can be observed that they display similar patterns as real estate, suggesting that there might exist some kinds of relationships between real estate and these indicators. There are two types of relationships, those of long-run nature and those of short term characteristics, will be of general interest here. These two types of relationships in economic and financial terms will be reflected and distinguished in their time series

Econometric analysis of the real estate market and investment

16

characteristics too, and the latter are employed only to serve as useful analytical tools for the former. Long-run characteristics in economics and finance are usually associated with nonstationarity in time series and called trends. Whereas short-term fluctuations are stationary time series and called cycles. Economic time series can be viewed as combinations of these components of trends and cycles. However, there are two different kinds of trends and non-stationarity, and they behave rather differently. One view on economic time series is that economic variables can be decomposed into a secular or growth component and a cyclical component. The secular component is assumed not to fluctuate much over the short term but rather move slowly and smoothly relative to the cyclical component, and is therefore called deterministic trend. Stationarity is achieved via detrending of time series by regression on time, with the residuals being cycles, and the time series is accordingly a trend stationary (TS) process. The other kind of trend, in contrast to the deterministic trend, has no tendency to return to a deterministic trend path. Stationarity in such time series is achieved by taking difference operations, and the time series is difference stationary (DS). Though both DS and TS time series are nonstationary prior to transformation, their behaviour is different. Consequently, the behaviour of economic and financial activities, depending on which kind of time series they subscribe to, differs too. Typically, a shock to a TS series would have a one-off effect but no permanent effect on the time series; or, in other word, no permanent effect on the economic activity levels. Whereas a shock to a DS series would permanently change the path of the time series; or permanently move the activity to a different level, either higher or a lower level. Details of these two types of non-stationarity will be discussed in Chapter 3 in the section on business cycles. Each activities behaviour is, therefore, analysed in levels and in changes, examining both short-term and long-run relationships. In the long run, variables’ current positions are derived either via the accumulation of past innovations,3 fea tured by difference stationary, or from the deterministic trends over a long period, featured by trend stationary. The tests on long-run relationships between two non-stationary series, are referred to as cointegration analysis. With regard to the short-term behaviour, previous studies usually restrict themselves to analyses in rates of returns or changes in prices. This implicitly presumes a stochastic trend or random walk stance. While the line between DS and TS is not clear cut, it is worthwhile to tackle the associations between series in a TS manner. This is achieved via a HP filter, 4 named after Hodrick and Prescott (1980). The conventional rate of return approach amounts to a first difference filter which permits the least low frequency (equivalent to long cycles) components to pass through, the linear filter permits the most, and the HP filter stands in between. Depending on the values chosen for the parameters with a HP filter, the series after the filtering would contain the highest frequency components plus the wanted lower frequency components. Compared with first difference filters, HP filters retain some medium cycles. That means the relationships between HP filtered data are concerned with short and medium terms. In the following, the statistics from applying the HP filter and the first difference filter for stationary series are reported, along with the analysis in levels for non stationary series in the long run. The compilation methodology of cyclical indicators means they are detrended and, presumably, stationary. So the relationship between cyclical indicators and other data

Real estate and the economy

17

series associated with economic activity levels will not be considered. Only those series showing movements around their trend values, which could either be obtained via HP filters or by taking first differences, may have meaningful comparisons with cyclical indicators. Cyclical indicators are the composite of several series and are compiled to show consistent timing relationships with peaks and troughs in the growth of overall economic activity. There are four of them in general use. A longer leading index indicates turning points in activity about thirteen months in advance; a shorter leading index indicates turning points about five months in advance; a coincident index generally moves in line with the business cycles; and a lagging index displays turning points about twelve months after they took place, and hence is completely useless operationally. Construction is by all means relevant to real estate development. The relationships may not be clear using conventional statistical methods and simple measures of construction activity such as indicators for output and new orders, due to the timing differences. There are time lags and leads in these two indicators with reference to real estate development, which weakens a probable statistical relationship linking real estate to either of them individually. Conceive each of the three variables adjust to the other two’s activities, then there may exist a stronger, nevertheless, complicated relationship among them dynamically. In this concern, two series have been created standing for the stock of uncompleted orders and the change in stock of uncompleted orders. Two methods are used to generate the series as follows: (a) Cointegration regression, with the cointegration residuals in the statistical term as the change in stock in the economic term, and the accumulation of residuals in the statistical term as the stock the economic term; and (b) The change in stock is the subtraction of output from new orders, then the stock is the accumulation of the former. This method is much more straight forward to show the economic sense of numerical operations, although it is less precise as it in fact imposes an untested but reasonable restriction on the cointegration vector, i.e., the cointegration vector is [1, 1]. The correlation between real estate performance and the selected economic variables is reported with both lags and leads. For reasons explained previously, the analysis of relationships in levels involves neither lags and leads,5 nor cyclical indicators. The cyclical indicators are stationary by construction, so their relationship with real estate is only examined in the difference but not in levels.

The short term As discussed before, the short term is referred to stationary time series or processes. The correlation statistic is usually used as an indicator about the short-term relationship between two stationary time series. For the reason that real estate may lag or lead other sectors, and therefore a contemporary correlation may not be sufficient to reveal the relationship, the correlations up to four periods of lags and leads are reported in Table 2.1A and Table 2.1B.With the quarterly data used in this book, these statistics span over a whole year period in both directions. Analysis of any longer period lags or leads seems redundant for the short term.

Econometric analysis of the real estate market and investment

18

The correlation of up to four periods of lags and leads is reported in Tables 2.1 and 2.2. In Table 2.1 in which real estate is represented by the JLW series, the correlation is calculated for original and unsmoothed6 indices respectively. The figures maintain the previous claims that real estate performance has little correlation with gilts and ordinary shares – two financial assets often quoted for comparison. None of the correlation in lags, leads and contemporaneous is significant at the five per cent level for both the original and unsmoothed real estate indices. However, the shares of one particular sector, real estate companies, have significant contemporaneous correlation with both real estate indices, and significant correlation at one and two lags with the original real estate index, at the five per cent level. Nonetheless, more significant correlation is to be found in the real sectors. The first set of these is housing or residential real estate. Real estate performance has correlation with the changes in the Halifax Building Society house price index at the one per cent significance level all the way through three leads to four lags, measured by the original real estate index; and the correlation is significant at the one per cent level from lag 2 to lead 3 in means of the unsmoothed real estate index. The biggest correlation occurs at lag 1. With regard to the Nationwide Building Society house price index, the situation is broadly the same except that the significance level for the unsmoothed JLW index is mostly the five per cent rather than the one per cent level; and the contemporaneous correlation is the largest, suggesting more or less the same timing and movement in residential and commercial real estate markets. The second set is construction activities. The two series from the ONS (Office for National Statistics, formerly CSO – Central Statistical Office) are construction output on new work and new orders. A derived series through the difference operation between output and new orders is used to represent the changes in the stock of uncompleted new orders. While real estate performance seems to have correlation with construction output on new work at lead 2, it lacks any correlation with construction new orders, no matter whether it is estimated with the original or the unsmoothed real estate index. But impressively, the derived series of the changes in the stock of uncompleted new orders has a strong relation with real estate and the results suggest that either they move coincidentally or possibly with one period lag in the changes in the stock of uncompleted new orders, implying the adjustment mechanism in construction process in relation to real estate operations. Finally, real estate is compared to aggregated economic cyclical indicators. The correlation structure between real estate and the longer leading index indicates that real estate moves most likely one or two period behind the longer leading index, i.e., about seven to ten months in advance of the reference cycle. This is consistent with the results for the shorter leading index and the real estate index, as real estate leads the shorter leading index for one period, about eight months in advance of the reference cycle. Again, real estate leads the coincident index for three to four periods, about ten months in advance. The HPK index is claimed to be a market indicator. The Hillier Parker property index represents values and rents of hypothetical properties and hence attempts to capture current market conditions, while JLW and IPD are portfolio based indices representing achieved values and net income. Accordingly, the HPK index seems to be able to catch up real estate market movement, so the unsmoothing process is not required. The results from using the Hillier Parker property index, as reported in Tables 2.2A and 2.2B, are, however, consistent with that from the JLW series. Two of the most quoted financial asset series – the GLT and the FTA, remain uncorrelated with the HPK. The

Real estate and the economy

19

Table2.1.A Property’s correlations with selected economic variables: 1977 Quarter 2–193 Quarter 2 JLW – first difference filter (rates of change analysis) ρ4 CO

ρ3

ρ2

ρ1

ρ0

0.0 0.0 0.0 0.0 0.28 0.3 0.2 0.0 0.2 0.1 06, 13 57, 56 1,* 34 38, 87 61, 59 ** NO –0.1 –0.0 –0. 0.0 0.0 0.0 0.0 0.0 0.1 0.0 20, 59 063, 16 36, 94 72, 65 00, 75 DWG –0.0 0.1 0.1 0.25 0.0 –0.0 –0.0 –0.1 0.1 0.2 20, 26 65, 5* 98, 08 53, 54 62, 55* NPT –0.1 –0.1 0.0 0.2 0.0 0.0 0.0 –0.0 –0.1 –0.2 62, 15 93, 52* 55, 02 02, 44 81, 53* HFX

ρ–1

ρ–2

ρ–3

0.0 –0.1 0.1 0.1 0.1 62, 31 83, 91 37, 0.1 20, 0.1 44, 0.2 01,

0.0 75 0.0 49 0.3 88 ** 0.6 20 ** 0.2 62*

0.1 20, 0.1 40, 0.1 85,

0.0 64 0.0 57 0.0 63

ρ–4 0.0 0.25 38 1,*

0.2 0.1 05, 76 0.0 0.0 82, 01 0.0 –0.0 47, 78

0.2 27

0.0 –0.0 54, 89 0.1 0.1 49, 40 0.0 0.0 64, 54

0.2 0.2 0.4 0.4 0.5 0.4 0.6 0.4 0.6 0.4 0.8 0.7 0.4 0.6 0.25 0.5 0.1 78,* 44 66 62 64, 38 34 61 78, 71 11, 99, 83 46, 7* 16,** 94 ,** ** ** ** ,** ** ** ** ** ** ** ** NTW 0.2 0.2 0.3 0.3 0.5 0.3 0.5 0.2 0.5 0.3 0.5 0.5 0.2 0.4 0.1 0.27 –0.0 30, 19 95, 40 37 95 04, 48 76, 66 47, 49, 88 70, 92 1,* 12 ** ** ,** ** ** ** ** ** ** * ** GLT –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.0 0.1 0.1 0.0 –0.0 0.0 0.0 0.0 0.0 79, 76 94, 18 95, 07 89, 01 10, 22 07, 67 83, 79 75, 60 86, 95 FTA –0.0 –0.1 –0.0 –0.0 –0.1 –0.1 –0.0 0.1 –0.0 –0.0 0.0 0.0 0.0 0.0 0.1 0.1 –0.0 –0.1 73, 17 88, 61 35, 10 02, 22 15, 38 49, 16 92, 05 74, 84 45, 82 FTAP 0.0 0.0 0.0 –0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.1 0.2 0.1 0.1 –0.0 0.0 –0.0 88, 81 30, 24 40, 61 68, 00 93,* 55* 13,* 73 97,* 35 38, 53 55, 35 RESC 0.2 0.2 0.31 0.2 0.3 0.2 0.4 0.3 0.5 0.2 0.5 0.2 0.4 0.2 0.4 0.2 0.33 0.1 15, 01 6,* 58* 92, 71* 88, 42 10, 96* 10, 83* 58, 18 34, 09 8,** 00 ** ** ** ** ** ** ** LL –0.1 0.0 0.0 0.1 0.1 0.2 0.2 0.2 0.4 0.4 0.5 0.3 0.5 0.29 0.5 0.2 0.45 0.1 85, 55 03, 99 77, 34 91,* 55* 67, 06 52, 18* 67, 2* 33, 26 0,** 89 ** ** ** ** ** SL 0.46 0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0.2 0.4 0.0 0.3 0.1 0.25 –0.0 0.1 –0.0 6,** 03* 21, 43 72, 44 97, 28 75, 50* 43, 78 60, 43 5,* 20 09, 30 ** ** ** ** ** ** ** ** ** LG 0.60 0.2 0.4 0.1 0.3 0.0 0.1 –0.0 –0.0 –0.1 –0.1 –0.2 –0.2 –0.2 –0.3 –0.29 –0.43 –0.26 1,** 51* 92, 27 32, 09 61, 74 21, 81 94, 57 99,* 44 92, 4* 1,** 4* ** ** ** CC 0.65 0.3 0.63 0.3 0.6 0.2 0.4 0.1 0.3 0.0 0.2 –0.0 0.0 –0.0 –0.0 –0.1 –0.1 –0.1 5**, 48** 8,** 15* 05, 64* 98, 42 49,** 42 02, 29 79, 57 23, 30 36, 73 ** Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively. * significant at 5% level, ** significant at 1% level. Left hand side for original index, right hand side for unsmoothed index. ρ–i – property lags i periods, ρj – property leads j periods.

Econometric analysis of the real estate market and investment

20

Table 2.1.B Property’s correlations with selected economic variables: 1977 Quarter 2–1993 Quarter 2 JLW–Hodrick–Prescott filter ρ4

ρ3

CO

0.069

0.162

NO

–0.267

DWG

ρ1

ρ0

ρ–1

ρ–2

0.284*

0.325**

0.314*

0.255*

0.255*

–0.160*

0.004

0.153

0.257*

0.322* 0.335** 0.355**

–0.010

0.180

0.212

0.181

0.280*

0.283*

0.245

0.217 0.263*

NPT

–0.327**

–0.163

–0.119

–0.123

–0.091

0.189

0.276*

0.306* 0.423**

HFX

–0.223

–0.005

0.209

0.419** 0.636**

0.827**

0.835**

0.667** 0.418**

NTW

0.005

0.216

0.400**

GLT

–0.289*

–0.302*

–0.277*

–0.217

–0.051

0.137

FTA

–0.135

–0.164

–0.164

–0.102

–0.045

FTAP

–0.139

–0.169

–0.081

0.058

RESC

–0.300*

–0.252*

–0.193

–0.094

LL

ρ2

0.473** 0.524** 0.500** 0.416**

ρ–3

ρ–4

0.246 0.268* 0.246

0.251*

0.013

0.216

0.239

0.261

0.011

0.049

0.041 –0.066

0.232

0.311*

0.276*

0.163

0.106

–0.001

0.092

0.131

0.167

0.129

–0.573** –0.577** –0.524** –0.446** –0.255*

–0.042

0.201 0.390** 0.514**

SL

–0.225

–0.095

0.046

0.198 0.328** 0.367** 0.427** 0.384** 0.325**

LG

0.485**

0.624**

0.675**

0.649** 0.545** 0.371**

CC

0.125

0.290*

0.434**

0.506** 0.497** 0.435** 0.359**

0.184

–0.016 –0.171 0.267*

0.173

Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively * significant at 5% level, ** significant at 1% level. ρ–i - property lags i periods, ρj - property leads j periods.

contemporaneous correlation with the FTAP is now more significant and the correlation structure is more or less the same as exhibited by the JLW. The correlation with construction output and new orders becomes even less significant, while the correlation with the derived series RESC is again confirmed with the contemporaneous coefficient being the largest. The fact that commercial real estate has strong correlation with residential real estate is further proved via the use of the HPK index. The analysis of the HPK index with cyclical indicators also suggests that real estate has an eight to ten months lead on the reference cycle. The above analysis has a number of implications. First, real estate is congruously integrated into the economy and its performance is closely related to, and at least partially explainable by, some of the economic activities. Therefore it might be possible for the real estate profession to develop and use more plausible forecasting techniques, the immediate effects of which would be to smooth out the seemingly damaging fluctuations in the real estate market in the future. Second, real estate’s comovement with the construction industry is better seen via the changes in the stock of uncompleted new orders. It is a dynamic and joint adjustment between construction new orders and output

Real estate and the economy

21

to the overall performance in the real estate market. Thirdly, commercial and residential properties have similar timing or the former might lag the latter for one period, possibly due to the effect from interest rates. Finally, the necessity for unsmoothing the real estate index has been evident through examination of the correlation structures: the original real estate index, whenever correlated with other variables, has significant correlation at too many leads and lags, unreasonably implying that real estate responds very reluctantly to information disseminated in the economy and the market.

Table2.2.A Property’s correlations with selected economic variables: 1977 Quarter 2–1993 Quarter 2 HPK – first difference filter (rates of change analysis) ρ4

ρ3

ρ2

ρ1

ρ0

ρ–1

ρ–2

ρ–3

ρ–4

CO

–0.053

0.130

0.206

0.154

0.222

0.136

0.214

0.216

0.230

NO

–0.084

–0.095

0.094

–0.055

0.176

–0.000

0.198

0.149

0.129

DWG

0.029

0.007

0.072

0.058

0.203

0.146

0.115

0.173

0.154

NPT

–0.071

0.028

0.022

0.005

0.069

0.050

0.100

0.123

0.150

HFX

0.439** 0.603** 0.690** 0.730** 0.760** 0.749** 0.692**

0.615**

0.498**

NTW

0.358** 0.471** 0.582** 0.527** 0.594** 0.572** 0.556**

0.516**

0.382**

GLT

–0.177 –0.292* –0.253*

–0.161

–0.008

0.076

0.027

0.021

0.139

FTA

–0.053

–0.143

–0.092

–0.144

–0.013

0.058

0.079

0.070

0.105

FTAP

0.058

0.075

0.148

0.231 0.362**

0.253*

0.304*

0.232

0.160

RESC

0.208

0.266* 0.394** 0.399** 0.516** 0.469** 0.508**

0.425**

0.367**

0.240 0.410** 0.525** 0.557** 0.543**

0.519**

0.450**

SL

0.442** 0.545** 0.597** 0.628** 0.623** 0.497** 0.393**

0.303*

0.160

LG

0.551** 0.424**

CC

0.693** 0.672** 0.594** 0.481** 0.376**

LL

–0.079

0.094

0.285*

0.113

–0.044

–0.176 –0.279* –0.373** –0.428** 0.253*

0.129

0.003

–0.123

Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively * significant at 5% level, ** significant at 1% level. ρ–i – property lags i periods, ρj – property leads j periods.

The long run When a long-run relationship exists between two or more non-stationary (more exactly I (1)) time series, their linear combinations are stationary. Such a relationship is called cointegration, and can be examined in several ways. Two most frequently used methods are the Johansen procedure and Engle–Granger two-step method. While the former directly tests for the cointegration relationship in a dynamic environment, the latter

Econometric analysis of the real estate market and investment

22

Table 2.2.B Property’s correlations with selected economic variables: 1977 Quarter 2–1993 Quarter 2 HPK – Hodrick – Prescott filter ρ4

ρ3

ρ2

ρ1

ρ0

ρ–1

ρ–2

ρ–3

ρ–4

CO

–0.060

0.093

0.200

0.247

0.297*

0.305* 0.351** 0.380** 0.389**

NO

–0.263*

–0.182

–0.003

0.046

0.233

0.250* 0.376** 0.407** 0.360**

DWG

–0.048

0.073

0.201

NPT

–0.380**

–0.220

–0.120

HFX

0.092

0.353**

0.540**

0.643** 0.685** 0.678** 0.583** 0.429**

0.230

NTW

0.185

0.384**

0.526**

0.540** 0.541** 0.520** 0.437**

0.069

GLT

–0.408** –0.431** –0.361**

FTA

–0.146

–0.228

–0.245

FTAP

–0.086

–0.089

0.002

RESC

–0.264

–0.247*

–0.152

LL

0.306* 0.432** 0.406** 0.363** 0.371** 0.349** –0.044

0.089

0.209

0.289* 0.382** 0.491**

0.285*

–0.216

0.016

0.145

0.215

0.275* 0.349**

–0.274*

–0.144

–0.049

0.036

0.093

0.147

0.169 0.335** 0.335** 0.344**

0.303*

0.228

0.185

0.177

–0.111

0.013

0.059

0.148

–0.661** –0.651** –0.595** –0.444**

–0.222

0.136

0.223 0.408** 0.541**

SL

–0.304

–0.188*

–0.058

0.106

0.295* 0.391** 0.456** 0.492** 0.469**

LG

0.544**

0.649**

0.699**

0.661** 0.558** 0.383**

0.013

–0.162

CC

0.091

0.280*

0.421**

0.495** 0.525** 0.506** 0.460** 0.394**

0.300*

0.202

Critical value equals 0.25 and 0.325 at 5% and 1% significant levels respectively * significant at 5% level, ** significant at 1% level. ρ–i – property lags i periods, ρj – property leads j periods.

achieves the same objective in two separate but simple steps. The first step is to run a regression of one time series on the other, then the second step tests whether the residual is stationary with the DF (Dickey–Fuller) andADF (augmented Dickey–Fuller) statistics (cf Dickey and Fuller 1979 and 1981). The DF and ADF tests were originally designed to check the presence of unit roots in individual time series. When applied to two time series, a stationary residual, or rejection of a unit root in the residual, implies a cointegration relationship or a long-run relationship between the two time series. The Johansen procedure (cf Johansen 1988 and Johansen and Juselius 1990) and the ADF statistic are adopted for the analysis in levels, or the long-run relationships. Tables 2.3 to 2.6 present these results. The ADF is relatively easy to interpret for unit root tests, so it is adopted in spite of the availability of other unit root test procedures which are equally uncomplicated to use. The lag length is determined by the Akaike information criterion (AIC) and the residuals are checked to be white noise using the Ljung-Box Q* statistic. In the ADF test, all the statistics from lag 0 (the DF statistic) to lag 4 are reported with † indicating those with optimal lag length. The reasons for presenting the ADF statistic at all lags instead of only at the ‘optimal lag length’is that the AIC is a rather subjective criterion to penalize a model which has too many lags. Other criteria would give a different guideline on lag length choice. For example, another commonly

Real estate and the economy

23

used criterion, Schwarz’s criterion (SC), favours shorter lag lengths compared with the AIC. It should not be surprising that real estate moves in pace with construction and housing in the long run, though such kind of inquiry has not been widely documented previously. These findings are mainly attributable to the adoption of the new method, as the derived series for the stock of uncompleted construction new orders has the most significant and definitive cointegration with real estate. Both the trace value and the maximum eigenvalue are much higher than their 95 per cent critical values, for both the JLW and HPK indices, which are 19.169 and 18.594 for the JLW, and 25.252 and 20.247 for the HPK respectively. The evidence is further confirmed by the ADF statistic, which is–3.597 for the JLW and –3.735 for the HPK, being significant at the 5 per cent level to reject the null of a unit root in the residual,or no cointegration between the two series. Regarding the long-run relationship between commercial and residential properties, the Johansen procedure suggests that a cointegration vector does exist. From Table 2.3, it can be seen that the JLW is cointegrated with both the HFX and NTW indices, and from Table 2.5, the results show that the HPK is cointegrated with these two housing price indices. However, while the ADF statistic supports the existence of a cointegration relation between the JLW and both the HFX and the NTW,

Table 2.3 Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 JLW – Johansen procedure –T · ln(1 – )

–T · Σ ln(1 – )

CO

8.650

11.223

NO

10.012

12.365

14.017*

15.632**

NPT

8.847

9.262

HFX

21.935**

24.993**

NTW

13.360*

19.714**

GLT

7.710

7.758

FTA

14.204**

14.482*

FTAP

11.889

14.518*

RESA

18.594**

19.169**

DWG

max (0.95) = 14.069, max (0.90)=12.071; trace (0.95) =15.410, *reject H0: no cointegration with 90% critical value ** reject H0: no cointegration with 95% critical value

trace

(0.90) = 13.325

it suggests that the HPK series only has cointegration relation with the HFX. Another interesting point is that the real estate performance index does not only cointegrate with the real estate company share index FTAP, it also does so with the all-share index FTA, when assessed with the Johansen procedure. This would, therefore, play down the

Econometric analysis of the real estate market and investment

24

importance of studies of the price discovery between real estate and real estate company shares as the all share index FTA appears to play the same role as the real estate company sector index. The results for the long-run relationship between real estate and two simple construction series are mixed. The HPK index’s cointegration with construction output is established by applying both the Johansen procedure and the ADF statistics, but its cointegration with construction new orders is only confirmed by the Johansen procedure. For the JLW index, the long-run relationship with the construction output is only confirmed by the ADF statistics. The same pattern applies to the total investment in dwellings and the number of property transactions. To sum up, the analysis in levels reveals additional information and presents further insights than those from the analysis in differences. The stock under construction evidently adjusts to real estate performance, and the two variables move together in the long run. The other construction and real estate related variables, such as house prices,real estate transactions and the investment in dwelling also prove relevant in the studies on real estate from the view of economic analysis and modelling. The long-run analysis has important implications. First of all, the relationship of real estate with other sectors in the economy in the long run is stronger than that in the short term. It is because that real estate investment has long-run attribute, its short-term changes and swings are not so far as to reflect the underlying fundamentals as other financial investments. When considered in the long run, real estate and other sectors in the economy are likely to be driven by the same or relevant fundamentals and, consequently, they may not move apart far away

Table 2.4 Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 JLW – ADF statistic DF

ADF(1)

ADF(2)

ADF(3)

ADF(4)

CO

–0.418

–2.598

–3.034*†

–2.561

–3.098*

NO

–0.867

–2.518

–3.583**†

–2.600

–3.207*

DWG

–1.197

–1.869

–1.993

–2.390

–3.122*†

NPT

–1.370

–2.071

–1.671

–2.427

–3.995**†

HFX

–2.234

–2.992*†

–2.304

–2.669

–3.305*

NTW

–1.859

–2.689†

–2.097

–2.195

–2.940*

GLT

–0.904

–1.487†

–2.034

–2.378

–2.542

FTA

–0.866

–2.577

–2.848†

–2.362

–3.001*

FTAP

–2.121

–2.338†

–2.302

–2.618

–2.451

RESA

–2.628

–3.439**

–3.597**†

–2.739

–3.533**

* reject H0: a unit root with 90% critical value, ** reject H0 with 95% critical value. (for critical values cf Engle andYoo (1987) and Banerjee et al.(1993)) † indicates optimal lag length

Real estate and the economy

25

Table 2.5 Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 HPK – Johansen procedure –T · ln(1 – )

–T · Σ ln(1 – )

CO

10.044

15.245**

NO

11.634

14.013*

DWG

8.217

10.625

NPT

7.207

8.760

HFX

11.832

18.264**

NTW

13.859*

19.328**

GLT

7.258

7.333

FTA

13.822*

13.901*

FTAP

15.236**

18.923**

RESA

20.247**

25.252**

max (0.95) = 14.069, max (0.90)=12.071; trace (0.95) =15.410, *reject H0: no cointegration with 90% critical value ** reject H0: no cointegration with 95% critical value

trace

(0.90) = 13.325

as in the short term. Second, real estate is more closely related with the real sector of the economy than with the financial sector. Real estate is not a purely financial market investment. It is, in the meantime, an investment in production, trading, work, and storage spaces and capacity, so it shares similarity and possibly the same fundamentals with the real sector more than with the financial sector of the economy. Third, among the real sectors, construction has the strongest relationship with real estate in the long run, especially when viewed with the stock of uncompleted construction new orders. It is, in analogue to the shortterm analysis, the results of a dynamic and joint adjustment between construction

Table 2.6 Cointegration of real estate with selected economic variables: 1977 Quarter 2–1993 Quarter 2 HPK – ADF statistic DF

ADF(1)

ADF(2)

ADF(3)

ADF(4)

CO

–0.778

–1.591

–2.148

–2.974*†

–3.291**

NO

–0.884

–1.747

–2.128

–3.056*†

–3.305**

DWG

–1.278

–1.329

–1.478

–2.303

–3.220**†

NPT

–1.081

–2.028

–2.026

–3.163*

–4.128**†

HFX

–2.514

–3.404**†

–3.146*

–2.810

–3.517**

Econometric analysis of the real estate market and investment

26

NTW

–1.833

–2.259†

–1.882

–1.834

–2.006

GLT

–1.365

–0.745†

–1.098

–1.838

–2.587

FTA

–0.774

–1.409

–2.100

–3.046*†

–3.583**

FTAP

–2.084

–2.018†

–1.961

–2.315

–2.239

RESA

–2.363

–2.286

–2.673

–3.735**†

–4.144**

* reject H0: a unit root with 90% critical value, ** reject H0 with 95% critical value. † indicates optimal lag length

new orders and output to the overall performance in the real estate market, an sometimes can possibly be called ‘construction reacts to property’ as in Tsolacos (1995). Finally, a strong relationship found in the short term between commercial and residential properties can be extended to the long run as well.

Notes 1 The difference in the coverage of value of new orders and value of output. Contractors’s output is defined as the amount chargeable to customers for building and civil engineering work. It includes the value of work done on their own initiative on buildings such as dwellings or offices for eventual sale or lease, of work done by their own operatives on the construction and maintenance of their own premises, and of goods made by the contractors themselves and used in the work. The value of output on new work excludes repair and maintenance. Though the output on new work and new orders have the same classification, the site value and architects’ or consultants’ fees are excluded from the value of the order, resulting in smaller figures for new orders than output on new work on average. Reflecting this difference, a discount has been taken on output on new work to make the statistical data more consistent in estimations. 2 Output and orders are regarded as construction flows; an annual figure would normally be as big as four times of a quarterly one. Stock of uncompleted new orders would have the same level whether the data are annual or quarterly. Usually the value of stock of uncompleted new orders at its peak would roughly have the same magnitude as that of new orders received in a period of twelve months, or of the output on new work. This is merely to give a rough idea about the relative values of the two variables – it is not bound to hold by any theoretical or practical reason. 3 Let xt and yt be two simple random walk processes, i.e. xt = xt–1 + 1,t,yt = yt–1+ 2,t then the relation between the irrates of change, i.e., ∆xt and yt, would be that between 1,t and ∆2,t, only relevant in the current period. If one intends to inquire into the relationships in their levels, as xt = xt–1 + 1,t = xt–2 + 1,t + 1,t–1 = … = 1,t + 1,t–1+…+ 1,1,y1,t = y1,t–1 + 2,t = … = 2,t + 2,t–1 + … + 2,1, then all of their past innovations are involved. Thus it is termed ‘in the long run’. 4 Hodrick–Prescott (HP) filters. The operation of the HP filters is to solve the following optimisation problem

subject to

Real estate and the economy

27

The smaller the parameter , the smoother the trend path. When = 0, the trend path is a straight line, i.e., the zero frequency component has been filtered out. The HP filter gradually filters out more lower frequency components/cycles as increases. A HP filter with bigger would trace the time series closer in the period. The selection of the smoothing parameter is usually arbitrary. Judgement would be made on the individual time series. 5 According to Engle and Granger (1987), if time series xt,yt and zt are all I(1) process, and if xt is cointegrated with yt and zt respectively, then yt and zt are cointegrated as well. As an I(1) series is cointegrated with its own lagged series with vector [1, –1], it follows that, e.g., if xt is cointegrated with yt, then xt–1 will also be cointegrated with yt. Denoting zt = xt–1 confirms this. 6 The unsmoothed index is derived using a procedure developed in Chapter 6.

Econometric analysis of the real estate market and investment

Appendix

Figure 2.1 Relevant time series variables

28

Real estate and the economy

29

Econometric analysis of the real estate market and investment

30

3 Theories of dynamics In the previous two chapters, descriptive analysis and broad statistical figures have been provided, and the changing patterns of real estate and the role played by the institutions and real estate companies analysed. Together with a review of the literature, it has been revealed that the fluctuations in real estate are linked to the economic environment in a variety of ways. Moreover, there is a need to address issues in real estate research, and in particular, to reconsider real estate market behaviour utilising modern finance and economic theory. The research theme of the book, as proposed, is to investigate real estate market behaviour in three related areas: the market efficient hypothesis; rational expectations; and business cycle theory. The three theories are closely related and have common attributes of dynamics. This chapter, therefore, will study these theories of dynamics and their relevance to real estate market behaviour. Dynamic theories are drawn from studies of the business cycle, the rational expectations hypothesis, and the efficient market hypothesis. Each of the three literatures is comprehensive and could make a single volume in its own right. However, the purpose here is to apply existing work to real estate research, not to develop theory. Nevertheless, because real estate data and behaviour are unique, the results and implications of the empirical investigations in this book may shed light on the theory, as any literature exclusive of evidence in this important sector of the economy is incomplete. Moreover, real estate is probably one of the most suited areas to link the three theories – for them to be jointly and critically scrutinised in a way that has rarely been attempted before. In this regard, there are no consensus, no ready body of techniques and approaches, hence such an analysis is no easy task but rather a challenging one. In the following discussion, the three theories are presented and discussed with regard to the development, econometric testing procedures and implications and, in particular, their relevance to real estate research.

Market efficiency Market efficiency is always one of the central issues in financial market studies, and real estate is no exception. A number of factors may make the real estate market appear less efficient that other financial markets. These include high transaction costs, long lags between deciding to take and actually completing a transaction, and illiquidity. The situation is further complicated by the fact that there are no reliable real estate indices available for assessing performance. Real estate indices, unlike transaction-driven indices in financial markets, are usually appraisal or valuation based. Studying real estate market efficiency is not only important but also difficult Therefore, the efficient market hypothesis, models and procedures for testing the hypothesis, and the implications in the real estate market will be addressed in the following.

Econometric analysis of the real estate market and investment

32

Definitions The study of efficient markets is one of the single most important subjects in finance and investment, being closely associated with expectations formation and price fluctuations. Emerging from stock market analysis, the history of the efficient market hypothesis could be traced back at least to the 1920s. In modern times, Fama (1970) is generally credited as presenting a scholarly abstraction of the efficient market hypothesis (EMH). According to his definition, there are three types of efficient market, depending on the extent of information reflected in the market: 1. Weak form. A market is said to be weak form efficient if there is no relationship between past price changes and future price changes, i.e., the price changes are independent. No trading rules can be developed to make abnormal returns based on the past history of an asset’s prices or returns. 2. Semi-strong form. Semi-strong form EMH states that no abnormal returns can be made by developing a trading rule based on publicly available information. The semi-strong form encompasses the weak form since past history is publicly available. Public information also includes non market information, e.g. economic news, company accounts, and stock splits. 3. Strong form. Strong form EMH extends the information set to including all information, no matter whether it is public or private. No trading rules can be developed to make abnormal returns based on all available information. Strong form EMH implies semi-strong EMH which, in turn, implies weak form EMH. An efficient market should not be confused with a perfect market. A market is said perfect if the following conditions hold: 1. The market is informationally efficient, i.e., information is costless and it is received simultaneously by all individuals; 2. The market is frictionless. There are no transactions costs or taxes, assets are perfectly divisible and marketable. There are no regulatory constraints; 3. There is perfect competition in product and securities markets. In the product market, all producers supply goods and services at the minimum average costs; and in the securities market, agents are price takers. 4. All market participants are rational, maximising their expected utility. The above assumptions set the conditions for the capital market to be allocationaly and operationally efficient, in that prices would be set to equate the marginal rates of return for all producers and savers. The concept of the efficient market is less restrictive. Imperfect competition in the product market would imply capital market imperfection; nevertheless the stock market could still determine security prices which fully reflect all public available information and would be set to equal the present value of a stream of expected future returns. Consequently the stock market could still be efficient in the presence of imperfection. A general statement of the efficient market hypothesis says that security prices fully reflect all available information. A precondition for this strong form hypothesis is that information and trading costs, the costs of getting prices to reflect information, are always zero, as Grossman and Stiglitz (1980) suggest. A less restrictive but more rational version of the efficient market hypothesis by Jensen (1978) states that prices reflect

Theories of dynamics

33

information to the point where the marginal benefits of acting on information do not exceed the marginal costs. There have been many difficulties and problems in testing the EMH in the 20 years since the theory emerged. In his 1991 review of the efficient capital market literature, Fama re-divides the work on market efficiency into three new categories. Instead of weak form tests, which are only concerned with the forecast power of past returns, the first category now covers the more general area of tests for return predictability, which also includes forecasting returns with variables such as dividend yields and interest rates. Since market efficiency would always go hand in hand with equilibrium pricing models, the predictability also regards the cross sectional predictability of returns, i.e., tests of asset pricing models and anomalies discovered in the tests. For the second and third categories, Fama proposes changes in title, rather than coverage. The semi-strong form tests are now replaced by a common title, event studies. The strong form tests now becomes the tests for private information. Tests of the efficient market hypothesis Tests for return predictability (weak form hypothesis) The basic weak form test is to examine whether the return process follows a random walk: Xt = c + Xt–1 + t (3.1) or Rt = c +

t

(3.2) where Xt is return, price or the index, Rt is the rate of return, c is a constant and t is the serially uncorrelated residual. With Fama’s 1991 version of tests for the efficient market hypothesis, the first category incorporates statistical tests of return predictability which includes tests of independence between current and past returns, other forecasting variables, volatility tests and seasonality in returns, along with cross sectional return predictability. The tests for the predictability from past returns often amount to tests on autocorrelation in the return series. Market efficiency implies the returns follow a random walk, and residuals are white noise. Since returns are unpredictable, then the best forecast of returns is the historical mean. Other forecasting variables used for testing the efficient market hypothesis are dividend yields (D/P) and the price earnings ratio (P/E). Therefore, the tests would include the sevariables in equations (3.1) and (3.2). Research by Shiller (1984) and Fama and French (1988) suggests that D/P explain small fractions of stock returns for horizons up to 5 years. Campbell and Shiller (1988a) observe that P/E helps forecast returns with a certain reliability. The predictability of share returns from D/P or P/E is not itself evidence for or against market efficiency. In an efficient market, the predicting power of D/P says that prices are high relative to dividends when discount rates and expected

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returns are low, and vice versa. On the otherhand, with the existence of irrational bubbles, low D/P ratios signal irrationally high share prices that will move back toward fundamental values. Initially, these variables were included in regressional equations to reject the random walk hypothesis if they could help forecast returns. Controversially, the test results did not necessarily rule out market efficiency. Nevertheless, analysis of this kind helps understand market operating mechanisms. Recent developments in one of the most prominent areas of econometrics, the time varying volatility of financial time series, has provided a fresh tool in GARCH (generalised autoregressive conditional heteroscedasticity) modelling (Bollerslev 1987) for tests on volatility and seasonality. Earlier studies on volatility tested whether the expected returns are constant or vary over time. With GARCH, various relationships between returns and volatility can be explicitly expressed and tested, and the changing returns over time do not necessarily mean market inefficiency as traditionally suggested, as long as they do not help exploit excess returns. In many cases, it has been revealed that the stock market is even more volatile than previously perceived. The variance (the second moment) is changing over time and serially correlated even where the returns (the first moment) are constant with white noise innovations. Seasonal patterns have also been found to be more significant in the second moment than in the first moment. Such evidence would lead to the rejection of the efficient market hypothesis in some of the cases which had earlier supported it. Cross-sectional predictability considers asset pricing models and anomalies and could be termed as testing the efficient market hypothesis and asset pricing models simultaneously.The most widely adopted asset pricing model,which has also been most critically attacked, is the Sharpe–Lintner–Black (SLB) single factor model in which the cross sectional expected returns are sufficiently explained by the market , the slope in the simple regression of the return of an asset on that of the market portfolio.The multifactor asset pricing models of Merton and Ross are the generalisations of SLB, recognising the limitations in the latter. The most popular approach amongst all the multifactor models is Ross’s (1976) arbitrage pricing theory (APT), which uses the statistical technique of factor analysis to extract the common factors in returns to test whether expected returns are explained by the cross sections of the factor loadings of asset returns on the factors. The multifactor version of asset pricing models are, in fact, an ideal state which can be made closer to, but never reached.On the other front of advancing asset pricing models, consumption-based asset pricing models (Rubinstein 1976, Lucas 1978, Breeden 1979) study an asset’s consumption which is the slope in the regression of its returns on the growth rate of per capita consumption. The model abstracts all the elements in hedge shifts in consumption and portfolio opportunities that can appear in multi factor model with one factor relationship between expected returns and the consumption . The empirical tests on the consumption based asset pricing models often involve time series and cross section predictions. Again, the advances in statistical and econometric techniques in last ten years,particularly the generalised method of moments (GMM) proposed by Hansen (1982), have made significant contributions to the studies. One of the earliest studies of this kind is Hansen and Singleton (1982), which jointly tests the time series and cross-sectional predictions of the consumption-based model.

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Event studies (semi-strong form hypothesis) This category is concerned with tests of the adjustment of prices to public announcements. Obviously, some issues usually belonging to the semi-strong form hypothesis have been moved to the first category by Fama’s recent reviews, making Fama’s definitions and boundaries for the first two forms of market efficiency even more ambiguous. However, as the title suggests, the tests mainly involve the investigation of price movements around the time of an announcement, i.e., when information is made public, to see when the expected price adjustment takes place, and the investigation of the potential for above verage risk adjusted rates of return assuming an investor acquired or disposed some set of securities after an announcement was made public. The question is whether such an investor has enjoyed above verage risk adjusted profits compared with those from buy-and-hold policy after transaction costs. The tests in this category are usually to examine the abnormal returns (AR) and cumulative abnormal returns (CAR) before and after an event occurs, and to observe the pattern: (3.3) (3.4)

where Rt is the true return, and is the expected return (derived from an asset pricing model). If the market is efficient and the price responds and adjusts to the event quickly, only the AR immediately after the announcement or occurrence of the event would be positive (for good news) or negative (for bad news). All other ARs should be close to zero. The pattern of CAR, from equation (3.4), should show a sharp jump immediately after the event, and the curve should be flat before and after the jump. A survey of methods and models used in event studies can be found in Armitage (1995). Various events to be studied include stock splits (Fama et al. 1969), new issues (Ibbotson 1975, Ibbotson and Jaffe 1975, and Loughran and Ritter 1995), earnings announcements (Ball and Brown 1968, and Bernard and Thomas 1990), announcement of accounting changes (Kaplan and Roll 1972, and Biddle and Lindahl 1982), and macroeconomic events (Chen 1991, and Chen et al. 1986). Some others are concerned with anomalies and seasonality. Among them are the book value of equity (BE) to the market value of equity (ME) ratio (Fama and French 1992), the size effect (Banz 1981, and Dimson and Marsh 1986), price earnings ratio and returns (Ball 1978), the impact of annual rebalancing, the January effect and other calendar effects (Ariel 1987, 1990, Kleim 1988, Lakonishok and Smidt 1988, Reinganum 1983, and Ritter 1988). The acceptance of market efficiency in this category would imply that asset prices move swiftly to adjust to new information and investors cannot make abnormal returns by acting after the announcements and the events. As with the first category of tests, the evidence for and against the EMH is mixed. However, most studies on the EMH come out of this category.

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Tests for private information (the strong form hypothesis) The tests in this category investigate whether asset prices fully reflect all information, public and private. The title, as well as the definition, is superfluous, as all information other than private has been studied in the first two categories. This form of hypothesis is extremely rigid, requiring that asset prices adjust swiftly to new public information, but also that no groups have monopolistic access to specific information which they can capitalise upon. This implies that all information is available to all investors at the same time. The tests in this category examine the performance of different groups of investors to investigate whether any identifiable group has consistently had above average riskadjusted returns. Such results would either indicate they have monopolistic access to important information or they consistently have the ability to act on public information before other investors can, which would suggest the market is not adjusting asset prices to all new information swiftly. Issues examined include insider trading (Jaffe 1974, Finnerty 1976, and Seyhun 1986), security analysis (Black 1973, Hulbert 1990, and Liu et al. 1990) and professional port-folio management (Jensen 1968, Grossman and Stiglitz 1980, Ippolito 1989, and Elton et al. 1993). The results from most studies are, as one can image, mixed. The efficient market hypothesis in a real estate context Real estate company sector share prices, like other security prices, behave more or less in a random walk manner, which at least supports a weak form efficient market hypothesis. Real estate investment itself, as represented by various real estate price and performance indices, has severe autocorrelation which means that the direct real estate investment market is not, even at the lowest level, efficient. However due to the appraisal based nature of most real estate price and performance indices which attributes to a large part of autocorrelation, the predictable component may be smaller than that inferred from the indices. But in a common sense, most practitioners and academics in real estate research do not accept that the indices should be corrected for smoothing to the point when the return or price becomes unpredictable. If the return or price is predictable, it may still be difficult to exploit any regularities because of (a) high transaction costs and, (b) long lags between deciding to act and actually completing a transaction. In such a situation, there is no difference between acting on information and not acting on information, thus there are no incentives for taking advantage of getting information. The other reason might be the confidence in the accuracy of prediction which is not only measured with some statistical criteria such as MSEs (mean squared errors) or RMSEs (root mean squared errors), but more fundamentally, in relative magnitude with trading costs. With the same predicted return and its standard deviation, the larger the trading costs, the fewer the actions taken on receipt of information. The immediate consequence of fewer actions on information is that real estate remains predictable to a certain extent. As autoregrassive and moving average components in residuals are the major sources of fluctuation or cyclical movement, the connection between real estate market efficiency and real estate cycle is apparently observed in this way. With the development in real estate research, prediction techniques and transaction procedures, the costs of information and the transaction costs

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would be gradually reduced, with the real estate market becoming more mature than it is now and fluctuations being hampered out to a larger extent.

Business cycle theory (theories of output and price fluctuations) It has been observed that real estate displays striking cyclical patterns. It may be one of the most turbulent sectors in the economy in this sense, against some findings of relatively low variance in its returns, which takes on the issues from a different perspective. Cycles and poor performance were evident in the recession of the early 1990s which witnessed a much sharper downturn in real estate than in any other sectors. With some previous research having reported and described cycles, it is now necessary to bring real estate into a theoretical analytical framework, not only to show the phenomenon of cycles, but to link the real estate cycle with other economic activities, and furthermore, to reveal the underlying mechanisms

Figure 3.1 The development of business cycle theory governing the process of cycles. As one of the dynamic theories mentioned at the beginning of this chapter, business cycle theory is presented and discussed in the following.

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The development of the theory Business cycles are periodic, but irregular up and down movements in economic activity, measured by fluctuations in real GDP and other economic variables, which can be decomposed into two elements: the trend, and the deviation from the trend. To identify business cycles, attention has focused on deviation from the trend, since this gives a direct measure of the uneven pace of economic activities, being separated from their underlying trend growth path. A business cycle is identified as a sequence of four phases: contraction, trough, expansion, and peak. Business cycle theory has developed in three strands: Keynesian business cycle theory, monetary business cycle (MBC) theory, and real business cycle (RBC) theory. Figure 3.1 shows the development of business cycle theories and the links between them. MBC and RBC are equilibrium business theories and have dominated the business cycle literature since the 1970s. Equilibrium theories regard short-term deviation of output from trend to be consistent with a state of equilibrium. RBC and MBC models view the cycle as the result of propagation of a series of random shocks. The MBC theory emphasizes the monetary aspects of shocks, while RBC theory highlights the importance of real shocks. Within the monetary tradition, the theory differs between that of the monetarists who consider the observed component of the monetary shocks causes the fluctuation, and the new classical (NC) model, developed by Lucas (1975), Barro (1976) and Sargent and Wallace (1975, 1976), argues that what matters is the unanticipated changes in monetary growth. As disequilibrium theory, Keynesian models treat rigidity or frictions in the economy, such as sticky wages and prices, as the cause of disequilibrium and cycles which are generated via mechanisms of multiplier-accelerator interaction (Haberler 1946, Hansen 1957, Fischer 1977). While Keynesian theory does not rule out real shocks as the source of business cycle, it typically attributes cyclical deviations to aggregate demand shocks. In the development of business cycle theory, Lucas’ monetary business cycle (MBC) model has played an important role in reviving business cycle research in the 1970s and marks a major changes from the Keynesian approach to business cycle modelling which regards the cycles as an essential disequilibrium phenomenon. Subsequently, the MBC approach has evolved into the real business cycle (RBC) which emphasizes the importance of real shocks (Kydland and Prescott 1982). The widespread rejection of MBC, due to its reliance on implausible claims of information deficiencies, resulted in the proliferation of research on RBCin the 1980s. RBC theory retains the rational expectations hypothesis (REH), but asserts that real shocks, in particular technological shocks, are the major source of the impulses. Both MBC and RBC focus on key intertemporal relationships. Towards the end of the 1980s, the RBC approach was broadened to make use of dynamic recursive techniques to solve agent optimisation problems subject to market clearing conditions, in a general model of economic growth. The most influential early contributions to the RBC literature are those of Kydland and Prescott (1982) and Long and Plosser (1983). They retain the MBC approach and rational expectations hypothesis, while assuming that all information concerning the path of the general price level is publicly and costlessly available. The signal extraction problem that

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is a key ingredient of the MBC models is thus discarded and, consequently, the unanticipated temporary monetary shocks are of no importance. The rejection of MBC models means that the RBC approach has to look at the real economy for both disturbances and the propagation mechanism. Kydland and Prescott’s (1982) ‘Time to build’ paper modifies the neoclassical growth model to permit the capital utilisation rate to vary. The effect of this modification is to increase the amplitude of the aggregate fluctuation predicted by theory as the equilibrium response to technological shocks. The treatment of the current value of leisure and the past history of leisure allows the intertemporal substitution of leisure and multiperiods are required to build new capital goods. The technology parameter is subject to a stochastic process with two components, permanent and temporary. Productivity is assumed to be observable by agents, but it is observed with noise. Economic agents are unable to judge whether the technology shock is permanent or temporary. The permanent component is highly persistent, and shocks are therefore autocorrelated. When the technology parameter grows smoothly, steady state growth prevails; but when it is stochastic, cycles take place. Kydland and Prescott (1988) further extend the analysis to cover policy issues and assert that public finance considerations are not the principal factor driving the cycle and, thus, that abstracting from them at this stage is warranted. Only when we have considerable confidence in a theory of business cycle fluctuations would the application of public finance theory to the question of stabilisation be warranted. Such an extension is straightforward in theory, but carrying it out will be difficult and will require ingenuity. Long and Plosser (1983) adopt a highly restrictive formulation assuming rational expectations, complete current information, no long-lived commodities, no frictions or adjustment costs, no government, no money, and no serial correlation in the shocks. The focus is on intertemporal consumer preferences and production processes. There is persistence in the effects of changes in wealth, since they alter the demand for goods over time. The production possibility hypothesis also allows for intra- and inter-temporal substitutions. Business cycle equilibrium is preferred to non-business cycle alternatives since agents are willing to take risks to achieve higher expected returns. Input output relationships propagate the effects of output shocks both forward in time and across sectors. Other prominent contributions to business cycle theory can be found in Nelson and Plosser (1982), King and Plosser (1984), Barro (1977, 1978), McCallum (1983, 1986, 1989), and King et al. (1991). Early work is mostly attributable to Fisher (1925), Frisch (1933), Friedman (1957), and Solow (1957). On the empirical side, Eichenbaum and Singleton (1986) investigate the postwar US business cycles via equilibrium business cycle theories, to examine whether the empirical evidence for the US supports the view that the business cycle is not a monetary phenomenon. Sims (1980) compares the interwar and postwar business cycles with a time series approach. Davidson and Mackinnon (1981, 1982) carry the studies on alternative business cycle theories through non-nested hypothesis tests. The econometric issues in equilibrium business cycle models are tackled by Singleton (1988), who analyses the nature and sources of secular, cyclical, and seasonal fluctuations, the econometric implications of prefiltering to remove some of these components from aggregate time series, and the methods for solving nonlinear, dynamic stochastic business cycle models. Nelson and Plosser (1982) is among the first papers to study trends and random walks in macroeconomic time series which is akin to

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the unit root tests applied later, and formally investigated by Perron (1988) from the then new approach, the Dickey–Fuller procedure. Sims’s (1980, 1982, 1986) main contributions to econometric analysis of business cycle theory are his vector autorregressive process which has been applied to business cycle research by himself and adopted by many researchers. The cause of economic fluctuations The basic model of the real business cycle is represented by the following formulation which maximises a lifetime utility function with rational expectations (3.5)

where 0 < < 1is the discount factor, ct+j(>= 0) is consumption in period t + j,lt+j(>=0)=l– nt+j is leisure in period j, and nt+j is hours of work in period t+j. The expected life time utility function, U, is the sum of all (discounted) future utility function, u, which is a function of consumption ct+j and leisure lt+j in each period. Furthermore, U is concerned with the optimal path of future consumption and leisure. Output is in the form of a production function yt = ztf (nt, kt) (3.6) where yt is the output, kt is the capital stock, nt is labour or hours of work as above, and zt is the technology shock at time t, a random process with a mean value of unity. Equations (3.5) and (3.6) are simple in appearance. However, there are very limited functional forms for u and f so that the closed form solutions for kt, ct and nt can be derived. Several authors, including Long and Plosser (1983), have consequently used the combination which specifies u in a log-linear form and f as a Cobb–Douglas function u(ct, 1–nt)= log ct + (1– ) log(1–nt) (3.7) (3.8) Equilibrium requires: yt = ct + [kt+1 – (1– )kt] (3.9) Assuming capital is written off within each period, i.e., = 1 in equation (3.9), from equations (3.8) and (3.9), the following relationship is derived: (3.10) These specifications would lead to the explicit expressions for ct and kt+1

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(3.11) (3.12) The logarithm of kt would follow a stochastic process of the form (3.13) The process for kt is dynamically stable, where since |1 – α| < 1. log kt+1 is a first order autoregressive process if log zt is serial uncorrelated. If the zt process is itself a first order autoregressive process of the form log zt = ρ log zt–1 + t (3.14) where

t

is white noise, then log kt+1 would be a second order autoregressive process (3.15)

The second order autoregressive process also applies to other crucial quantity variables including log ct and log yt. Taking the logarithm of ct in (3.9) would yield (3.16)

This simple special case of the prototype where RBCmodel suggests that withAR(1) technology shocks, important quantity variables would have the time series properties of AR(2) process. Since (1–α) < 1 and ρ 1, an unanticipated increase would be reinforced by other positive changes in the future, and the series would continue to diverge from its pre-shock expected level. There are two customary versions for the measurement of persistence. One is the polynomial of the Wold moving average representation evaluated at L = 1, and its variants, by Campbell and Mankiw (1987a, 1987b). The other is known as Cochrane’s

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(1988) V, the ratio between the k period variance and one period variance, or the ratio between the two autocorrelations (4.8)

where ρj is the jth autocorrelation of ∆Yt. In a random walk, the variance of the k + 1 period difference is k + 1 times the variance of the one period difference, then the ratio V = 1. For any stationary series, the variance of the k + 1 period difference approaches to a value of twice the variance of one period difference. In this case, the ratio V approaches zero when k becomes larger. The limit of the ratio of the two variances is therefore the measure of persistence. In theory, . But, as one cannot effectively estimate A(1), one cannot effectively estimate Vk via A(1) either. This is one of the reasons for having a Vk version of persistence. To empirically obtain the persistence measurement, approaches include ARMA, nonparametric, and unobserved components methods. The ARMA approach is to estimate A(1) direct, where parameters are quite sensible to change with regard to estimation. The nonparametric approach produces the measures known as and âk , is widely adopted and has been written as two RATS procedures by Goerlich (1994) (4.9)

The nonparametric approximation of A(1) is (4.10)

The choice of k, the number of autocorrelations to be included, is important. Too few autorrelations may obscure trend reversion tendency in higher order autocorrelations. Inclusion of too many autocorrelations may exaggerate the trend reversion, since as k approaches the sample size T, the estimator approaches zero. Hence, though larger k might be preferred, k must be small relative to the sample size. The third approach to measuring persistence is to analyse the unobserved components. It is related to the decomposition of the time series into a non stationary trend and a stationary component discussed earlier in this section: the persistence measures are the relative sizes of variance in the two components. There are two rather different ways of imposing restrictions on the two components, i.e., those considering them as perfectly correlated, and those with a view of two independent processes. To the former, the Cochrane’s version of persistence V is equal to the ratio of the variance of the change in the random walk component to the variance of the total change in the time series. Campbell and Mankiw’s A(1) version is the standard deviation of the change in the random walk component divided by the standard deviation of the series. Here V and A(1) convey information on the relative importance or magnitudes of trend and cycle

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components in the economic time series. Regarding the later, the independence of the two components suggests the persistence measure V can be written as a weighted average of the equivalent measures for the two components. That is, V = V1+(1– V2), with V1 and V2 being the persistence measures for the two components, and In the case where the first component is a random walk and the second component a stationary cycle, V1 = 1 and V2 = 0. Then the total persistence measure is the ratio of the variance of the change in the random walk to the variance of the change in the time series. It is indeed the share of the random walk in a time series. The persistence measures of V and A(1) can be generalised to a multivariate time series, as proposed by Pesaran et al.(1993). The multivariate Vk and A(1) can then be jointly applied to a group of variables or sectors, e.g., industrial production, construction and services, to evaluate the cross section effects.The presentation is similar to (4.6) (4.11) The bar means a vector of variables or a vector of polynomials (matrix), and the scalar variance of residuals, a covariance matrix. The vector of polynomial, is (4.12) Assuming there are m variables in the system, then variable vector, residual vector and are (m×1) and the covariance matrix is of (m×m) dimension, respectively. The covariance matrix of the random walk component in this multivariate process is: (4.13) in a univariate time series. To evaluate the longwhich reduces, as before, to run effect of shocks in sector j on the level of activity in sector i, individual elements in VC will be selected and normalised. Pesaran et al.(1993) use the conditional variance of ∆Yj,t (the jth diagonal element of Σ) to normalise the jth column of VC. Van de Gucht et al. (1996) use the unconditional variance of ∆Yj,t to scale the jth column of VC, arguing that it is consistent with the univariate persistence measure proposed by Cochrane (1988). Both regard the diagonal elements in the normalised VC as representing total persistence in individual sectors, and off-diagonal elements as the cross effect between two sectors. e.g. an element in the ith row and jth column is the effect on ith sector due to a shock in the jth sector. Their normalisation uses a single variance for the normalisation of a column and, whether conditional or unconditional, ignores the fact that the process is multivariate. In fact, the normalisation is as simple as in univariate cases. Instead of being scaled down by the unconditional variance, the covariance matrix of the random walk components will be normalised by the unconditional covariance matrix. The multivariate persistence measure is therefore:

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(4.14) where Σ is the unconditional covariance matrix of the time series variable in this in a univariate multivariate system. This persistence measure reduces to process, the same expression as in Campbell and Mankiw (1987a, 1987b) and Cochrane’s (1988) original idea. By considering possible effects from, and links with, other sectors, this measurement of persistence for individual sectors are more precise, compared with its univariate counterpart. Both Van de Gucht et al. (1996) and Pesaran et al. (1993) aim to generalise the persistence measurement and have partly achieved this objective. To have an accurate and exact expression of multivariate persistence, the normalisation should be realised with matrix operations; it is not possible to achieve this with simple division arithmetic. With this approach, the effect on sector i due to shocks in sector j is represented by the (i,j) element in VCK, i.e. VCK(i,j), with VCK(i,i) measuring the sectorspecific persistence. Pesaran et al. (1993) use the square root of each diagonal element in VC(Pi =(Pii)0.5) which is not the ratio between ‘the variances’ but between ‘the standard deviations’, and is therefore not directly comparable to the univariate persistence measure Vk. e.g., Pi = 2 would translate into Vk = 4 in a univariate estimation procedure. Another problem is that the off- diagonal elements may be negative, and as a result, it may not be possible to assess some of the cross sectional effects. Nevertheless, they do not investigate the cross effects, and no obvious problems exposed with their estimation procedures. Both univariate and multivariate persistence measures can be viewed as an attempt to measure the size of the random component of the process in a trendcycle decomposition representation, such as (4.1). In fact, V(Tt|Ωt–1)=A2(1)σµ (4.15) (4.16) where is a vector of trend component if (4.1) is generalised to a multivariate representation. As such, multivariate persistence analysis nests almost all trendcycle models. Multivariate persistence analysis is more sensible in that, instead of analysing the individual variables separately as in the univariate cases, it allows shocks to transmit from one variable to another. Therefore, multivariate persistence analysis is able to examine the sources of shocks and the effects of the shock in one sector on other sectors. Compared with the VAR model, multivariate persistence is to evaluate the effect over an infinite horizon, while a VAR model has to cut off at a certain lag length. So, multivariate persistence takes all significant and insignificant lagged variables into account, but to produce a much smaller number of statistics. Moreover, it is able to detect the effect of certain kinds of shocks, e.g., a monetary shock, from that of other shocks. However, it is not possible to specify the‘other’shocks in a model. Unless relevant assumptions have been made and certain restrictions imposed, the objective of distinguishing demand shocks from supply shocks cannot be achieved. This issue will be discussed in the next

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section. But, bear in mind, the decomposition of shocks into demand and supply or monetary and real ones may involve variables which are not particularly helpful in most multi-sectoral analysis. Models of this kind are not always sound in empirical investigations, as assumptions have to be made and restrictions imposed with prior judgement of the researcher. Consequently, their economic meaning is difficult to explain, when many sectoral variables are included.

Sources of shocks – Supply v. demand, monetary v. non-monetary, and sectoral v. aggregate The analysis of sources of shocks is closely related to the persistence of the effect of a shock to the time series. Shocks to technology and production are viewed as having permanent and durable effects on output. Furthermore, the associated activities in which shocks to technology and production play a role are on the supply side. Hence shocks to supply and shocks to the long-run stochastic trend are perceived as equivalent. In other words, the supply shock is linked to the variance of the innovation in the non-stationary component of the time series, at least in appearance. Demand shocks, on the other hand, due mainly to financial and consumption sectors, have only temporary effects on output. Therefore, demand shocks correspond to the stationary and transitory component in the time series. The aggregate shocks are featured by a common trend and the comovement, distinguishable from those of the sectoral specific factors. Having associated demand shocks with transitory component and supply shocks with the permanent component of the time series, the study of sources of shocks then further imposes a priori restrictions on the response of the time series to each of the disturbances. Generally, there are two techniques for studying and identifying the responses to different shocks. One is univariate based on the assumptions on the time series in question itself. The other is multivariate, utilising, or being helped by, the information and attributes in other time series. Blanchard and Quah (1989) use a bivariate model, as do Campbell and Mankiw (1987b), focusing on two stationary variables, one in difference and one in level, and two disturbances, one with permanent effect and one with only a transitory effect. King et al. (1991)’s approach is multivariate, specifically with three variable and six variable models. In fact they can be easily generalised to any multivariate, or reduced to univariate cases, if one has an empirical study of his/her own in mind. Let Yt denote an N-variable vector, all of the elements are I(1). vt is an N×1 vector of serially uncorrelated structural disturbances. However, there are only two types of the disturbances, so the vector for disturbances is partitioned into two segments with

representing a k×1 sub vector of the disturbances in the non-

stationary component of the time series, i.e., the supply shock, and standing for an (n– k)×1 sub-vector of the disturbance to the stationary component, i.e., the demand shock. The two types of disturbances are independent. By definition, ∆Yt can be expressed as follows (4.17)

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with A(1) = [P0], in accordance with the partition of vt , P is an N×k non zero matrix with which has the long-term effect, and 0 is an N×(N–k) matrix of zero with which has only temporary but no permanent effect. The implications of the partition of the disturbances into permanent and transitory components and the partition of the long-run matrix A(1) into non zero and zero parts are , the jth lag effect of apparent. For any element in A(1), say mth disturbance on Y1,t is a1,m(j), while its effect on the level of Y1,t is the sum of a1,m(0), a1,m(1),…a1,m(j), as j approaches ∞ , the accumulated effect on the level of Yl,t is hence is the prerequisite for a1,m(1) times that disturbance. Then the corresponding disturbance to be transitory, i.e., a1,m(1) is in the sub set of the long-run structural matrix A(1), 0, and the disturbance in . As for those permanent disturbances vn – t to have an effect on the level of Y1,t, their corresponding structural parameters should fall in the non zero part of A(1), i.e., The structural parameters and disturbances in (4.17) are not readily identifiable, but can be deduced from the general unrestricted Wold representation of Yt (4.18)

The relationships between equations (4.17) and (4.18) indicate that

t

= A0vt and

The identification is to impose two sets of restrictions. One is the cointegration restriction on the matrix of the long-run multiplier A(1) which identifies the permanent components. The second is to impose an uncorrelation assumption on the two sets of the innovations in the permanent and transitory components. This amounts to identifying the dynamic response of the time series to the permanent disturbances. While the demand/supply shock analysis provides insights into the economic fluctuation mechanism, it has limitations in general economic studies as well as in real estate research. First, most studies on the effects of demand and supply shocks are in the framework of systems of equations which involve consumption, demand, production, investment and output and some identity relationships among them; second, they also traditionally assume that the two disturbances are uncorrelated, e.g. Blanchard and Quah (1989) and King et al. (1991); and third, both types of disturbances have no long-run effect on the stationary variables, e.g. the unemployment rate and the growth rate in GDP, and only the supply disturbance has a long-run effect on the levels of variables. The first point makes it unattractive in financial and real estate research. The second point seems to impose untested and possibly unnecessary restrictions, and may distort the true effects. The third point is arguably sound, but one might opt for some alternative. Nevertheless, these assumptions are either required by model identification or based on some kind of beliefs which may turn out to be untrue. The multivariate measurement of persistence is not built on structural relations. In addition, it is easy to include a specific kind of shock in persistence analysis and to evaluate its effects, in a not too complicated VAR framework. It is most appealing in studies such as real estate research, which involve some financial market attributes and

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where it is not appropriate to set up a system of structural equations for analysis. A specific kind of shock can be added to the model, as in the following: (4.19) where vt represents the specific shocks whose effects are to be analysed, which can be the demand shock, supply shock or monetary shock, depending on the way it is extracted from another fitted equation(s); and is a vector of polynomials of (m×1) dimensions. By evaluating (4.19) with and without vt, one can establish whether an individual sector is subject to the shock vt. Furthermore, in the existence of the effect of vt, the proportion of the persistence due to vt and that of other shocks can be identified. In theory, more than one set of shocks can be included; in which case, vt becomes an n dimension vector with n being the number of sets of shocks, and is (m×n). But, the estimation would be empirically unsound as greater inaccuracy would be introduced. In addition, this approach would lose appealing to those such as King et al. (1991) in a complicated system, if it is to lose its advantages of no subjective assumptions and restrictions. Nevertheless, if there are only two types of shocks, e.g., demand and supply, or monetary and real, then getting one implies getting the other. Under such circumstances, vt can only be one set of shocks, otherwise, (4.19) would be over-identified. Persistence can be decomposed into a component due to the specific shock and that due to other shocks: (4.20) (4.21) The total persistence is PT = Ps + P0 (4.22) If the specific shock is chosen as a demand or monetary disturbance, then the underlying assumption is that the demand/monetary shock may also have a longrun effect, as the persistence measure is about the effect on the levels of variables. This assumption can be empirically ruled out or ruled in which, in fact, becomes a hypothesis in this sense. Although Blanchard and Quah (1989) arguably excluded the demand shock from having a long-run effect, their empirical work suggests that the effect of a demand shock would decline to disappear in about 25 quarters or 5–6 years! In such a long period, the probability of a structural change or break would be rather high. If a structural change does happen, it would override any supply shocks and the effects of demand and supply shocks are almost mixed. Comparing Blanchard and Quah, and King et al. with Campbell and Mankiw, Cochrane, and Pesaran et al., the former is more based on economic theory and the latter on statistical characteristics. The latter is also empirically applicable and flexible. In this chapter, time series attributes of cycles, trends and persistence have been discussed in both univariate and multivariate circumstances. Approaches to decomposing

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time series into cycles and trends have been examined and developed. However, much attention has been paid to shocks, represented by the innovations or residuals in the time series data. This is because the effects of shocks can be rather different; some are transitory while others are permanent. Moreover, shocks come from either the supply side or demand side; and if the source is correctly identified, appropriate measures can then be taken. Shocks to technology and production are supply shocks and viewed as having permanent effects on output; whereas demand shocks are due mainly to financial and consumption factors, and only have transitory effects on output. In time series analysis, these two types of shocks are characterised by non-stationarity and stationarity respectively. This leads to the analysis of sources of shocks to a related concept of persistence, which is extended to the multivariate cases to study cross-sectional effects and to identify the monetary shock. Above issues of decomposition of time series data and identification of sources are important and relevant to real estate research. Observing real estate data gives us an impression that they appear to possess such time series attributes, as most other economic and financial data do. Thus, empirical inquires in to real estate time series data are required not only to describe the components, but also to examine the causes and effects. This would have operational and policy implications in the real estate market. This chapter has discussed a number of issues in individual aspects of time series data. Based on and extending the analysis in this chapter, the dynamic behaviour of economic and financial time series will be studied in Chapter 5, focusing on common factors in the economic system with a unified representation of economic fluctuations and dynamics.

5 A unified representation of economic fluctuations and dynamics The comprehensive analysis of specific features in economic fluctuations and dynamics naturally leads to the search for a unified representation accommodating all or most of these features. This chapter is devoted to such an approach, built on and derived from the discussion and deliberation on individual aspects and the review of current studies in the previous chapters. The approach adopted introduces a concept of ‘phase shifting common cycles’, in a system with and/or without non stationary components. Phase is originally a frequency domain term. It differs from a conventional time domain term ‘lag’, although it has analogous features with lags. Phases are also about leads/lags, but they are considered with regard to the time series data across all frequency components or cycles; whereas lags or lag structures are over a time horizon. The following two points may explain why studying phases is helpful: (a) two time series move pace with pace, even if they do not move exactly the same, provided the phase function between them is linear; (b) the mapping relationship between phases and leads/lags is nonlinear. These suggest that a simple linear relationship expressed in phases is nonlinear and complicated when expressed in lags. The relationship cannot be exhibited effectively in a complicated lag structure even with a large number of estimated lag parameters and, therefore, may be ignored. In this sense, the study of phases provides an effective way of investigating common factors among fluctuating time series. The study of common cycles is simply an extension of common trend analysis. Although the phase does not have a role in common trends or cointegration, it is critical in common cycles. Whereas the phase has been noticed as a factor in economic research for some time, it has played only a subordinate role, and has never been seriously studied. The approach is, however, appealing to those economic sectors with cyclical behaviour, including real estate. The study of common cycles together with common trends aims to generalise the Beveridge–Nelson trend cycle decomposition to a multivariate setting. The generalisation of common trends is due to Stock and Watson (1988), leading to the ‘common trend representation’, usually called the Beveridge–Nelson–Stock– Watson (BNSW) representation. Embedded in this are the concepts of cointegra-tion and the long-run comovements among several time series. Since then, the BNSW representation has naturally been extended to incorporate common cycles (Engle and Kozicki 1993, Vahid and Engle 1993a,b, and Engle and Issler 1995). The idea of common cycles and the so called cofeature relations bears are markable similarity to that of common trends and cointegration. Moreover, while a phase shift in one or more time series does not change cointegration relations, it does affect the way in which cycles may be cancelled out. In the simplest case, xt and yt have a common cycle factor such that a linear combination of xt and yt would be a current period white noise innovation with no prediction capability,

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but xt and yt–1 (or xt–1 and yt) would have no common cycles (cf Engle and Kozicki 1993). Instead they have phase shifting common cycles, or non-synchronous common cycles and codependence as in Vahid and Engle (1993b). The effect of a phase shifting common cycle would be that the combined series would have a shorter lag structure than the individual series. The introduction of common cycles and the cofeature concept, in effect, removes an untested restriction from the decomposition techniques of Blanchard and Quah (1989) and King et al. (1991), again very similar to cointegration which removes the untested restrictions (that none of the combinations of non stationary level variables would lead to stationarity, i.e., the number of cointegration vectors is zero). It is empirically helpful to make the use of terminology clear before proceeding, by reviewing the developments and current status of business cycle studies. Recent developments in business cycle studies include the decomposition of stochastic trends and cycles (Beveridge and Nelson 1981, Blanchard and Quan 1989, and Campbell and Mankiw 1987b) and the subsequent incorporation of common trends and structural cointegration (Stock andWatson 1988, and King et al. 1991). In these cases, the deterministic trends (if any) are always included. The common trend business cycle economists have kept any deterministic trends without bringing in deterministic cycles. The reason for this is that, in the real business cycle research literature, the so-called cycles are the stationary residual elements after removing trends, a concept and term specifically adopted in this kind of inquiry. Another description of cycles is as the serially-correlated residuals which fluctuate or have cyclical movement. Most recently, common cycles have been introduced into the literature. Non-synchronous common cycles, as a further generalisation in business cycle research, could be viewed in another way and be documented as phase-shifting common cycles. As in cybernetics or control engineering, two series are synchronous even if there are lags or leads so long as they keep the same lags or leads. Therefore, it would be helpful to introduce a phase-shifting common cycle operator matrix as a universal expression for common cycle relationships, with the specific case of zero phase shift representing the coincident common cycle factor. Instead of having cofeature vectors and codependence vectors separately, there would be the unified phaseshifting common cycle vectors which, unlike cofeature or codependence vectors, would have phase-shifting operators, or lag/lead operators in the vectors. This means cofeature and codependence vectors are unified under the concept of phase-shifting common cycle vectors, with a zero phase shifting standing for the former. The rest of the chapter is organised as follows: the first section proposes a unified common cycle factor representation. In the second section, common cycles are analysed together with common trends in the framework outlined earlier. The links between the VAR, the reduced form moving average process and the structural disturbance representation are established. Finally, a brief summary highlights the approach’s appealing applications in real estate research, and the differences with the previous studies in this area.

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Coincident and phase-shifting common cycles This chapter first proposes a unified common cycle factor representation scheme in which the cofeature relation or the coincident-phase common cycle factor is a special case. In general, common cycle models (coincident-phase and phase-shifting) are expressed in the VAR structure which is easy to implement in empirical studies. There are two ways to demonstrate the phase shifting common cycle effect: a shorter moving average residual structure and a shorter lag length in the resulting VAR models. The former clearly exposes that phase-shifting is a non-linear operation in the time domain. Later, this common cycle factor representation will be considered together with common trends to yield the unified model. First looking at a bivariate VAR model with p lags: (5.1)

or yt = A(L)yt = A1yt–1+…+Apyt–p+ t . (5.2) where L is the lag operator and

Three forms of common cycles are defined as follows: Definition 5.1 if there exists a vector

such that: (5.3)

then it is said that there are coincident common cycles in yt. It is equivalent to saying that: (5.4) Definition 5.2 if there exists a vector

so that: (5.5)

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where is the combination of A1,…Ap (linear and non- linear), then it is said that there are phase-shifting common cycles of order k in yt. This representation is derived via nonlinear operations, and cannot simply be expressed as in (5.4). It will be made clear later with the help of companion matrices. Definition 5.3 if there exists a vector so that: (5.6) then there are common cycles of order k in yt. Obviously it is less restrictive than (5.4) and is equivalent to saying: (5.7) The difference between Definition 2 and Definition 3 is that the former is a moving average representation of order k, and the latter is an autoregressive representation of order k(k < p). The latter is straightforward: the AR components of higher orders are cancelled out; where as in the former, non-linear operations are involved. In fact, the conditions in Definition 3 are a prerequisite for those in Definition 2. It is apparent that the issues of common cycles are, in statistics, an overidentification problem and amount to multi-colinearity in parameter matrices. For coincident common cycles, there is overidentification in the original VAR system. The overidentification happens in the moving average representation of phase-shifting common cycles after the matrix operation and transformation, and the multi-colinearity is in its parameters of the lagged variables, i.e., in the autoregressive part of the transformed specification. The matrix operations, which are both linear and non-linear, lead to cancellation of the autoregressive components and result in moving average residuals of lower order. The common cycles of order k(k < p) are, simply, a multi-collinear relation amongst the parameters representing the lagged variables at the order k and higher. In the following, the vectors and matrices are extended so that the system is expressed in the form of a first order vector autoregression or a one-step Markov transition. The variable vector is defined as: A is called the companion matrix or the Markov transition matrix with 2 × p columns and 2 × p rows, xt is a 2 × p dimension extended variable vector, and ωt a 2 × p dimension extended residual vector. It is consciously designed so that the coefficients for the same lag appear close together in the matrix. A1,…Ap, as 2 × 2 sub-matrices, form the first two rows in the A matrix;and they are orderly positioned from the left to the right as in the plag autoregressive representation in (5.2). If the basic elements in (5.8) are expressed in the 2 × 2 sub-matrices, then:

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(5.8)

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(5.9)

Now equation (5.1) and (5.2) can simply be written as: xt=Axt–1+ωt . (5.10) It is of great interest to express (5.10) in the higher order autoregressive forms, if coincident common cycles do not exist and other kinds of common cycles are to be investigated. Via iterations, (5.10) becomes: xt = Axt–1+ωt = A2xt–2+Aωt–1+ωt=… =Amxt–m+Am–1ωt–m+1+…+Aωt–1 . (5.11) The number of iterations corresponds to the order of phase-shifting. With the help of the Markov transition matrix or companion matrix, the following proposition is derived. Proposition: There exist common cycles if, and only if, A does not have a full rank. If matrix A has full rank, then according to one of the matrix operation properties, any Ak will be of full rank as well. Subsequently, any order of phase-shifting operations will not lead to the linear dependence in the rows, in particular, the first two rows, in Ak. This rules out any kind of common cycles with linear dependence among the parameters. Indeed, using the Laplace expansion, matrix A can be partitioned as:

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where Ap–=[A1…Ap–1] is 2×(2p–2) sub-matrix, Ap is a 2×2 sub-matrix, and I(2p–2)×(2p–2) is a full rank identity sub-matrix. Also let Ac = [Ap– Ap]. There are two situations: (a) Rank(Ac)=1, there is linear dependence in Ac, constituting the case of coincident common cycles already discussed. (b) Rank(Ac)=2 (this does not rule out Rank (Ai…Ap)=1, i≥2), but Rank (Ap)=1. In this case, there are no coincident common cycles, but possibly phaseshifting common cycles. Via phase-shifting operations, the linear row dependence may shift leftwards until Rank when a kth order phase-shift common cycle structure emerges. In addition, the following lemma holds: When the kth order phase-shifting exists in the system, To see how phase-shifting, developed in this chapter, works, simple examples are illustrated in the following for A2. When there are no coincident common cycles, the first two rows in A, i.e., [A1…Ap] are linearly independent. However, the first two rows in Ak (k2) may have linear dependence. Applying matrix multiplication to A2 yields: (5.12)

It is clear that the possibility of the linear row dependence lies only in the first two rows in A2, as it has been assumed that there is no linear dependence in the first two rows in A, now being moved to the third and fourth rows in A2. The linear dependence relations in the first two rows are exactly the relations in equation (25) in Vahid and Engle (1993b). However, to express them in the form of the Markov transition matrix (or the companion matrix) and the first order VAR, as proposed in this chapter, has at least two advantages. First, it reveals the phase-shift processes: no phase-shifts are required for coincident common cycles, whereas phase-shifting may result in common cycles in the higher order companion matrices of theVAR. Second, it is straight forward and extremely simple to arrive at the linear dependence relationship which is to be investigated, especially in the orders of higher than 1: they will always be found the first two rows of the matrix Ak. The higher order transition matrix and its phase-shifting property can be viewed in another way. Taking A2 for example, the sub-matrices consist of two parts. The first part is A2, A3,…Ap. A common factor in cycles is made possible via moving A2, A3,…Ap one phase forward and being added to The second part is

From a system’s point

of view, are the convolution of the system function At with At(t = 1, 2,…i,…) itself in the time domain, and the product of the system function and itself in

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a frequency domain. The following example shows how it works. Let a two variable system evolve as follows: y1t = 0.5y1,t–1 + 1t t2t = 0.2y1,t–2 + 2t it can be seen that: y2t – 0.4y1,t–1 = 2t – 0.4

1,t–1

i.e., y2t and y1,t–1 share a common factor. However, do y1,t and y2t have a common factor? If we only see a common factor among y1,t–1 and y2t, but not among y1,t and y2t, this common factor may well be overlooked as people do not usually compare one series with other lagged/lead series. Express this example system in the form of (5.8) or (5.9)

It is clear that there is no coincident common cycle, as the first two rows share no multi colinearity. But it is not clear whether there are any other kinds of common factors. However, one phase-shift in the system yields:

It is easy to see that there is linear dependence in the first two rows in A2, a higher (first) order phase-shifting common cycle by definition. In this way, we reveal that y2t and y1,t (not only y2t and y1,t–1) share a common factor also, i.e.: y1t = 0.25y1,t–2 + 0.5 1,t–1 + 1t y2t = 0.2y1,t–2 + 2t and a linear combination leading to moving average residuals exists: y2t – 0.8y1t = 2t – 0.8 1t – 0.4 1,t–1 This simple example displays one of the advantages in the phase-shifting approach: it views all variables in the system in the current period while there are leads/lags amongst

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these variables, revealing the common factors which would be difficult to find, or easily overlooked otherwise.

Common cycles in non-stationary systems So far, the common cycle structure and linear dependence relations have been defined and demonstrated. To combine common cycles in a non-stationary system would mean an inquiry into common cycles and common trends in the meantime. The prevailing practice is to adopt the multivariate Beveridge– Nelson (1981) representation of trendcycle decomposition as in Stock and Watson (1988), which follows the Wold representation theorem. Variables or a vector of variables are expressed as an infinite moving average process of residuals. This kind of study is represented by Engle and Issler (1995) (henceforth EI). King et al. (1991) use structural decomposition to classify shocks with permanent and transitory effects; there are common trends but no common cycles. The purpose of the studies combining common trends with common cycles is to remove an untested restriction of no common cycles. Gallo and Kempf’s (1995) research (henceforth GK) further incorporates the concept of structural decomposition proposed by King et al. back to common cycles. Their analysis of common cycles is purely in the form of moving average processes. It is beneficial to investigate cycles and trends in a structural form. Nevertheless the structural parameters and shocks are not readily identified, they have to be inferred from the unrestricted Wold representation of EI. Both the structural and unrestricted representations of common trends and common cycles are in the form of infinite moving average processes which are sensitive in estimation. The moving average parameters obtained, lack not only straightforward economic explanations, but also a dynamic view of the processes of fluctuation. Vahid and Engle (1993b, henceforth VE) link the unrestricted representation of common cycles and common trends to a finite VAR, where common cycles are, specifically coincident (or cofeature), but not generally phaseshifting (or codependent). Therefore, to be consistent with the representation of common cycles in this Chapter, processes with common cycles and common trends will also be presented in this way. The VAR process to be investigated is: yt = A1yt–1+…+Apyt–p+ t . (5.13) In recognition of common trends or cointegration, its ECM form is ∆yt = –A(1)yt–1+Π1∆yt–1+…+Πp∆yt–p+ t , (5.14) where a non zero rank A(1) implies cointegration or common trends, and Πi= – (Ai+1+…+Ak),i = 1,…k–1. Again, using a Markov transition or a companion matrix, the process can be expressed in the first order VAR with the ECM: (5.15)

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where,

As in Johansen (1988), A(1) can be written as the product of two n×r vectors α′ when there is cointegration relationship, and α is the cointegration vector. For common cycles to exist, the following conditions should be met: (5.16) In fact, they can be expressed as linear row dependence relation in matrix consisting of two blocks: (5.17) The higher order phase-shift common cycles (using an order of 1 as an example here) in non-stationary system would be: (5.18)

where is the column rotation matrix of with one rotation, i.e.the last column is moved to the first column, the first column to the second column, and so on. It is again the phase-shift operation when common trends are involved:

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(5.19)

The existence of phase-shifting common cycles requires linear row dependence in the following matrix: (5.20) i.e.: (5.21)

Equation (5.21) is further development of this study over Vahid and Engle (1993a,b). For the conditions of phase-shifting common cycles to hold in non-stationary system, not only the ECM term is required to be common, but also the phase-shifted ECM term.In empirical estimation, with the instrument variable method for example, the ECM terms at lag 1, as well as at lag 2, would enter in the system as instrument variables, as in Vahid and Engle (1993b). Trends and cycles can be easily separated with the help of the Beveridge– Nelson decomposition and its multivariate generalisation of Stock and Watson (1988). Indeed, this has become one of the major standard methodologies for business cycle studies. In the following,the links between the finite VAR and the (infinite)moving verage of the BNSW decomposition through the Wold representation theorem, and the structured disturbance model of King et al., will be investigated. First is the relationship between the unrestricted and the structural models. According to the Wold representation theorem, any time series or time series vector can be expressed as an infinite moving verage process: ∆yt = C(L) t,C(L) = I +C1L1+C2L2+… , (5.22) C(L) can be decomposed as C(1) + (1–L)C*(L), therefore: (5.23) Taking the summation to get the variables in levels: (5.24)

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Equation (5.24) is the Stock–Watson multivariate generalisation of the Beveridge– Nelson trend- cycle decomposition and is referred as the BNSW decomposition. Common trends or cointegration would imply (5.25) and common cycles require (5.26) where α and are cointegation vectors and cofeature vectors respectively. Therefore, equation (5.24) can be written as the sum of two components, i.e., trends and cycles: (5.27)

where and are N×(N–r) full column rank matrices, Ψ is N×(N–s) full column rank matrix, and (L) is (N–s)×N full row rank matrix polynomial. When r+s=N, the stack of α and would be an N×N full rank matrix,

and trends and cycles can be exclusively expressed in the cointegration and cofeature vectors and their combinations: (5.28)

Equations (5.24) to (5.28) have precisely depicted the nature of common trends and common cycles, their decomposition and generating processes. In particular, when the number of cointegration relations and the number of cofeature relations sum to N, the trend and cycle components can be solely written in the cointegration and cofeature vectors and their combinations. After reviewing common trends, common cycles and their decomposition following the Wold representation, it would be straightforward to establish the links between the infinite moving averageWold representation and theVAR representation. First refer to the common trends plus coincident common cycles model. The relations between the parameters of the two representations exist for the common trend component as such:

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A(1)= α′,C(1)A(1)=0,α′C(1)=0,C(1) =0 , (5.29) and for the common cycle part: (5.30) Regarding the common trends plus phase-shift common cycles model (using a first order phase- shift model), there exist not only phase-shifted cycles, but also phase-shifted trends. However, the parameters of two period lagged level variables are simply ΠA(1). Due to the fact that A(1)= α′ is the long-run relation held for the variables in levels, ΠA(1) will satisfy the long- run relation too. Therefore, for common trends to exist, the relationships between the VAR and the unrestricted MA representations are: A(1)= α′,C(1)A(1)=0,α′C(1)=0,C(1) =0 . (5.31) The common cycle relations would be more complicated: (5.32)

It can be seen that

is sufficient to remove the cycle component of the error

correction residuals in a coincident common cycle system, but the condition of cannot guarantee the cancellation of the cycle component of the error correction residuals in a phase-shifting common cycle system, the second relation in (5.32) has imposed another restriction on common cycles. Second is the relationship between the VAR model and the unrestricted moving average representation. The VAR model is easy to understand and analyse, in comparison with the unrestricted infinite moving average model, since the lagged dependent variables are on the right hand side. However, the VAR model cannot distinguish disturbances or shocks with permanent effects from those with a transitory nature. King et al. (1991) were among the first to decompose the disturbances into permanent and transitory components in a cointegrated system. Gallo and Kempf (1995) further extend King et al. to include common cycles, in which they have introduced structural form representation for common cycles of order 0 (coincident common cycles, or cofeature relation in EI and VE) and common cycles of higher order (phase-shift common cycles, or codependence relation as in EI and VE). The final relationship to be examined is that between the structural disturbance representation of common trends and common cycles and the VAR model. Following King et al, the unrestricted form and the structural form are set out as: ∆yt = C(L) t (5.33) and

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∆yt = Г(L) t , (5.34) respectively. The restrictions are: (5.35) Combining (5.31) and (5.35) yields the common trend relations: (5.36) These relationships, together with the common cycle relationships between the VAR and the unrestricted MA representations, constitute the structural VAR representation of common trends and common cycles. Compared with (5.31), the first relation in (5.36) is simply the same; in the third relation, the long-run parameter matrix C(1) of the of the structural unrestricted MA representation is replaced by Г(1) and representation, based on what has been obtained in (5.35). The other two relations are established in the same way. This chapter has presented a framework for modelling and analysing economic fluctuations and dynamics. By extending the previous work by Beveridge and Nelson, Blanchard and Quah, Stock and Watson, King et al., Engle and Kozicki, Engle and Issler, and Vahid and Engle on common trends and common cycles, the attributes of phaseshifting common cycles in a non-stationary system are further explored. First, we have generalised the common cycle representation in terms of phase-shifting operations, instead of having cofeature and codependence respectively. Phase-shifting has features which describe the cyclical co-movement. For the cyclical components to co-move, they must either have the same phase, or the differences in the phase are locked. Second, the use of the Markov transition matrix or the companion matrix not only makes the operation straightforward, but also reveals the way in which the phase-shifting mechanism works. It has been made plain that the common cycles in a one step Markov process are coincident, while the common cycles in a two or more step Markov transition process have the phase- shifting attribute. That the Markov transition matrix or the companion matrix is the reduced rank matrix is a prerequisite for common cycles to exist. A reduced row rank Markov matrix corresponds readily to the existence of common cycles without any phase-shifts. When the Markov transition matrix is not row rank reduced, the higher order of the Markov matrix is row rank reduced if, and only if, the Markov matrix itself is column rank reduced. Third, we present the analytical framework in a VAR system. Gallo and Kempf’s analysis of common cycles is purely in the form of moving average processes, and so is their link between the structural and the unrestricted forms, though they start the cointegration analysis with a VAR model. The VAR representation of common cycles and common trends has advantages in that it demonstrates the dynamic processes and the propagation of cycles and trends over time straight forwardly, and it is relatively easy to estimate. Fourth, the links between the VAR and the structural disturbance representations are examined. Finally, compared with Vahid and Engle (1993b) in which the higher order (higher than order of 1) phase-

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shifting (non-synchronous in VE) common cycles can be very complicated, our procedure presents the higher order phase-shifting common cycles simply with a higher power Markov matrix, showing that the phase-shifting is state-transition in terms of the Markov transition matrix. While the coincident common cycle relations are linear, the phase-shifting common cycle relations are non-linear displayed by the higher order Markov transition matrices.

Part III The dynamic behaviour of real estate This Part is devoted to empirical studies of the dynamic behaviour of real estate, built on the methods and models developed in the previous parts, to investigate real estate dynamics focusing on common trends and common cycles with reference to expectations and market efficiency in the real estate market. Prior to trend-cycle decomposition, it is crucial to construct are liable real estate index as a smoothed index will obviously give a wrong message about the relative importance of trends and cycles and persistence in real estate. Although there was a brief description of unsmoothing in Part I, that was only enough to display the problems caused by smoothing and to present a relatively objective performance comparison between real estate and other asset investments. Therefore, in Chapter 6, the issue of smoothing in real estate indices will be further analysed. The unsmoothed index will be constructed with a new method based on cointegration and the idea of error in variable models, in addition to those by applying the approaches proposed by Blundell and Ward (1987), Firstenberg et al. (1988), Ross and Zisler (1991), Geltner (1991, 1993a,b) and Shilling (1993). Chapter 7 analyses the persistence of shocks in real estate. It starts from the measurement of Vk and A(1) in the terminology of Campbell and Mankiw (1987a,b) and Cochrane (1988). Further, trend-cycle decomposition is carried out in both univariate and multivariate systems with the aim of detecting and analysing the relative importance of shocks from different sources, which cover sectoral and aggregate, monetary and nonmonetary, to real estate, and to conduct variance decomposition in the latter. The fundamental issues of real estate market efficiency are investigated in Chapter 8, focusing on the mechanism of price discovery in direct and indirect real estate investment markets. The core issues of common trends and common cycles in real estate are addressed in Chapter 9. These cover the analysis of the basic long-run relationship of real estate with other investment assets; multivariate trend-cycle decomposition in a cointegrated system, and joint analysis and tests of common cycles and common trends. As phases play an important role in cycles and common cycles in the economy in general, and in real estate in particular, analysis will involve both the special case of coincident common cycles and the universal case of phase-shifting common cycles.

6 Recapturing market information from appraisal-based real estate indices The issues arising from using the appraisal-based real estate indices in measuring real estate performance have been widely addressed in recent years, with most attention being paid to the second moment estimation, or so called smoothing in real estate returns. The phenomenon of smoothing was first raised by Working (1960). It arises from averaging a time series of thinner interval to get a new one with wider time span, a process of temporal aggregation. There might be several purposes for averaging: most of them are not the topic of this book. Nonetheless, the desire to get more accurate or reliable data has obviously played an important role. Naively, improvements in data accuracy and reliability could be achieved from gathering as many observations as possible for an estimate in one period. It can be observed that confidence in the use of a series for research or assessment is related to the amount of data is similar to the process applying to real estate indices and valuations. Working’s problem mainly involved the prices of agricultural commodities which bear a lot of resemblance to real estate. The multidimension nature of agricultural commodity prices, e.g., heterogeneity in character, distribution of geographical location, and non-negligible costs for the movement of commodities, is distinct from the behaviour of financial asset prices. Working’s prominent discovery was the 0.25 rule. This states that serial correlation will be induced by averaging a random walk time series, and the upper limit of the serial correlation is 0.25. Working’s example is clearly a moving average process though he did not refer to this term, as one should notice that formal econometric estimation procedures for a moving average process had yet to be developed at that time. Since then, many studies have appeared in this area. For example, Tiao (1972) examines the asymptotic behaviour of temporal aggregates of time series and provides the extreme values for the first order autoregression and moving average parameters; Campos et al. (1990) investigate the fixed n-period phase-averaging processes, and the relationship and structure in the variance and autocorrelation of the original and phase-averaging processes; and Abraham (1982) presents useful models for variousARIMA (autoregressive integrated moving average) processes for aggregated series, provided that the structures of the original ones are known. These studies give us insights to the actual data generating processes and their properties in many compiled financial and economic data series. However, as pointed out by Blundell andWard (1987), smoothing in real estate indices, represented by the first order auto regressive coefficient, is well above 0.25, the extreme value any purely temporal aggregation may cause. The implication is that smoothing in real estate indices and temporal aggregation, though similar, are not the

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same. This has prompted real estate researchers to address the smoothing problem in relation to the specific procedure in real estate appraisal. Various work can be found in Blundell and Ward (1987), Firstenberg et al. (1988), Ross and Zisler (1991), Quan and Quigley (1989, 1991), Geltner (1989, 1991, 1993a), and Giaccotto and Clapp (1992). The procedures developed by Blundell andWard (1987) (BW thereafter), Firstenberg et al. (1988), and Ross and Zisler (1991) (FRZ thereafter) are similar and widely adopted due to their simplicity, though there has never been a lack of criticism of the (unrealistic) underlying assumption that real estate market returns follow a random walk, which amounts to saying that the real estate market is efficient. Giaccotto and Clapp’s (1992) approach is Monte Carlo simulation and a varying degree of smoothing for a variety of appraisal rules is documented. Geltner (1989), applying the method of Dimson (1979) and Scholes and Williams (1977) to the US real estate, presents a different way of estimating real estate’s risk by regressing the real estate index return on contemporary as well as lagged returns from a market portfolio. However, though the question as to how much of the serial correlation is incurred in appraisal processes and how much is attributable to the market series itself has been noticed for many years, it remains unsolved and the focus for research on unsmoothing real estate indices. Recently, efforts have been made by Geltner (1993b), and Barkham and Geltner (1993, 1995) among others. They propose a reverse-filter approach to unsmoothing US and UK real estate indices, and have allocated the smoothing factor to the UK and US appraisal-based real estate indices respectively, which is reasonably closer to reality compared with the result if the seriesis ‘fully’ corrected. Another interesting study is carried out by Shilling (1993). He applies the error-in-variable method to correct the real estate indices’ second moment, though the results are sensitive to the selection of other variables in the regression. In this chapter, two approaches to unsmoothing the appraisal-based real estate indices are developed in the first section. The approaches are then applied to the real estate return indices of JLW (Jones Lang Wootten) and IPD (Investment Property Databank) in the second.

Approaches to unsmoothing valuation based real estate indices This section develops approaches to unsmoothing the valuation-based real estate indices. The approach is multivariate and utilises the cointegration and error-in-variable concept, and is informationally more efficient and superior to the univariate unsmoothing techniques. The variables involved are stock under construction (RESA) which is the accumulation of change in stock under construction (RESC), the real estate indices (JLW and IPD), and the return index of real estate company shares (FTAP). The error-in-variable method is originally used by Shilling (1993) in reassessing the true variance in real estate returns. The following analysis will first show how Shilling’s method can be viewed within the traditional unsmoothing concept. Then it will be extended to incorporate cointegration to produce better estimates. The basic equation of Shilling (1993) states that changes in inventories under construction is a linear function of the rate of return on real estate. One may regress changes in inventories under construction on the rate of return on real estate to get the

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coefficient, but due to the measurement error the coefficient would be biased. Applying the errors-in-variable method can correct the bias and infer the true variance. The procedure is as follows: RESCt = c+ rt+ t (6.1) where RESCt is changes in stock under construction (or It – changes in inventories under construction in Shilling’s), rt is the rate of return on real estate, and t is white noise is normally observed which is not precisely rt but contains the residuals. Instead of measurement error, i.e., the regression is: (6.2) where (6.3) (6.4) and c is a constant term. Equation (6.2) states that the construction process adjust to the rate of return on real estate if the hypothesis is true, changes in stock under construction is constant otherwise. The coefficient obtained from (6.2) is biased and equal to: (6.5)

By applying the instrumental variable method or other methods to get the true coefficient, the extent to which the variance has been smoothed can be inferred. It should be noted that the above procedures, in particular, (6.3) and (6.4), suggest that the variance of the observed index return (which is appraisal-based) is larger than that of the true return series which is rather out of line with the empirical research prompted by the obviously too low variance in the return on real estate indices. In fact, in real estate appraisal, the error term (if it is explained in this way) ξtt is not random, it is systematically related to the appraisal procedure to smooth the variation in real estate return series. This explanation will become clear in the following and fit into the universally accepted index formation process. As suggested by equation (6.6), when ξtt is systematically related to the variance of would be smaller than that of rt. Nevertheless, the critical and unsolved problem is how to decide the value of the smoothing factor α. Now consider the traditional appraisal smoothing equation: ra,t = αrt+(1–α)ra,t–1 (6.6)

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where ra,t is the rate of return on the smoothed index, and rt is the true rate of return. Equation (6.6) in fact relaxes two restrictions in (6.3): the coefficient of rt is one, i.e., (1– α)=1; and the error term is not only uncorrelated with rt , but also uncorrelated with ra,t. The assumptions in (6.6) allow an unrestricted coefficient for rt, and the error term to be uncorrelated with rt, but be possibly correlated with ra,t . Bringing (6.6) into (6.1) results: (6.7)

where (6.8) is serially correlated as ra,t usually has atleast first order auto regressive residual. Accordingly, the estimated coefficient would be biased because: (6.9)

and k does not converge to because the last term in (6.10) does not approach zero or disappear even in large sample cases, i.e., when T becomes very large. Instead, k is equal to: (6.10)

(6.11)

where ρ is the first order correlation in the rate of return of the appraised index and is observable in the appraised index. Applying the instrumental variable method or using Wald’s method of group average, an unbiased estimate of the coefficient can be obtained. An estimate of the smoothing factor can be solved by comparing the unbiased and the biased estimates of the coefficient, without presuming a random process in the true return series. The instrumental variable method or Wald’s method of group average, in conjunction with equation (6.6), would actually regress RESCt on rt/α.

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The modification of Shilling’s method brings the actual appraisal process into account. But is still requires an unbiased estimate of the coefficient to infer the extent to which the variance has been smoothed, i.e., to infer a reasonable smoothing factor α. In the following, a strategy using the concept of cointegration is applied. The approach is simpler to use and more efficient in that more information is utilised in the estimation procedure. There is implied information content in the cointegration relationship which is relevant to reveal the extent to which the appraised index has been smoothed. The cointegration approach to unsmoothing real estate indices is also multivariate. Consider the appraisal equation in levels: Pa,t = αPt + (1–α)Pa,t,–1 (6.6′) where Pt is the true return (price appreciation incorporating rent income) and Pa,t is the appraised return. Rearrangement of (6.6) yields: (6.12)

where ∆Pa,t = ra,t is the rate of return of the appraised index series. (6.12) can be written as: (6.13) The above formulations have several empirically important implications. First, although we are not able to observe the true return series, it is believed to be cointegrated with the appraised index, as both series in levels are I(1) and the right hand side of (6.13) is I(0). Second, the true return series and the appraised index are cointegrated with a cointegration vector (1, –1). Third, the variation in the true return is larger than that in the appraised index return revealed by (6.12). It is because that the true return in the current period is the previous period appraised return plus a term which is proportional to but larger than the change in the appraised return as α>0. In the case of α = 1, i.e., no smoothing in the index, then (6.12) simply reduces to display the return evolution path. Although there exists a cointegration relation between the true and appraised returns, equation (6.12) or (6.13) cannot be estimated as both Pt and α are unknown. However, according to one of the cointegration properties that if xt is cointegrated with yt, and xt is cointegrated with zt, then yt and zt are also cointegrated, it is possible to bring in another variable or a group of variables to infer the smoothing factor α. Suppose another series St is I(1) in levels representing a variable which has a fundamental economic relationship with real estate returns. Then if it is cointegrated with the real estate return index Pa,t with a cointegration vector (1, – ), it should also be cointegrated with Pa,t–1, St – Pa,t–1 – c = µt (6.14)

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where µt is I(0) and may have serial correlation, c is the intercept. The true return series should also be cointegrated with St, and in addition, be cointegrated with a cointegration vector (1, – ), St –Pt – c = vt (6.15) similarly, vt is I(0) and may have serial correlation, c is the intercept and the same as in (6.14). Combining ( 6.14) and (6.15) yields: Pt –Pa,t–1 = µt – vt (6.16) Recall (6.13), it is straightforward that: (6.17) Bringing (6.17) into (6.14): (6.18) When there is serial correlation in the residuals µt and vt, (6.18) can be estimated within an ARMA framework. In short, the cointegration approach involves two steps. First, it runs a cointegration regression between St, a variable which is fundamentally related to real estate, and the appraised real estate return index Pa,t–1, and get the residual. Second, it estimates the coefficient for the change in the appraised real estate index in equation (6.18), and that coefficient is in fact 1/α. There are two major advantages in adopting this strategy. First, it exploits more information embedded in other variables other than itself. Second, it is easy to carry out a cointegration analysis and there are quite a few variables to be used for this purpose, compared with the errors-in-variable method. The use of instrumental variable or other similar methods to correct for the biasedness in regression are sound in theory, but, in practice, are often rough estimates and sometimes involve rather large inaccuracies. This problem is minimal here, as the approach does not involve transformation and proxies of the variables. It is difficult to tell which one is empirically superior to the other of the two multivariate approaches to unsmoothing. There is neither nesting nor an encompassing relationship between them; and there is no criterion to examine their ex ante performance either, as the real return series is not observable. Although the implied cointegration method utilises the information in both levels and differences, it does not employ other economic variables as in the errors-in-variable model, except through the cointegrating variable, which is usually indirect real estate investment. Their application should be complemented by prudent judgement and deliberation. In a sense, the contribution of these models may lie mainly in that they provide a logical way of thinking and a description of the working mechanism underlying the behaviour, relationship and interaction of these real estate variables and other economic variables. When compared with the univariate models, these multivariate models have obvious advantages. The

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univariate models, no matter how they are set up and what kinds of assumptions are made, uses the information in the appraised real estate index alone. Evidence of smoothing in real estate indices and estimation The estimation results from applying the methods of Shilling (1993) (modified) (MF– Shilling thereafter) are reported in Tables 6.1 and 6.2, and those from the implied cointegration approach are reported in Tables 6.3 and 6.4 for the JLW index and the IPD index respectively. The smoothing factor α in the JLW index is estimated to be 0.6241 applying the implied cointegration approach and using the return on the Financial Times real estate company shares as the cointegration variable. The smoothing factor in the IPD index is 0.4179 using the implied cointegration approach. All of these estimates are in a reasonable range and confirmed by the results from applying the method of MF–Shilling, with being 0.5758 for the JLW and 0.4070 for the IPD index. α as in equations (6.6) and (6.6′) is the proportion of the return represented by the market return, so a smaller means more smoothing in the index. The smoothing factor is larger when compared with the estimates in Barkham and Geltner (1993, 1995). Indeed, the smoothing factor in Barkham and Geltner is quite close to that of fully unsmoothing: 0.3750 for the JLW and 0.2067 for the IPD index. The results of FRZ/BW which presumes that the true return follows a random walk, conceivably, assigns a smaller to both JLW and IPD indices which is 0.2785 for the JLW and 0.1315 for the IPD. These results indicate that there is serial correlation not only in the appraised but also in the true or market return series. Although the objective of running the implied cointegration and the MF– Shilling procedures is to infer the smoothing factor α, it is desirable to examine diagnostics from the tests carried out in this study. A cointegration relation is confirmed to exist between direct real estate investment, represented by the JLW and IPD indices, and indirect real estate investment represented by the FTAP index. A model with an unrestricted constant and unrestricted trend (model 5 in Johansen and Juselius 1990) gives a best fit with both cointegration tests between JLW and FTAP and between IPD and FTAP, and the cointegration relationship is accepted at the five per cent level based on the max test and the trace value. It is reasonable to include a constant and trend without imposing restrictions. Empirically, the short horizon of the data used and the volatile change in these periods would make any restrictions (including those on the long-run relationship and those suppress-

Table 6.1 Summary Statistics – MF–Shilling Method, JLW Index A: Total smoothness in index ra,t = c+ρra,t–1+ζt Dep variable ra,t

ra,t

Constanta

ra,t–1

Q

0.0033

‡

0.6772

15.0889

(1.2544)

(7.2004)

(0.5181)

‡

14.2179

–

0.7215

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(8.2379)

(0.5091)

ra,t

Q

B: OLS regression RESCt = c+ ra,t+ ′xt+ ′t Dep variable RESCt

Constanta ‡

–0.0278

‡

0.1008

14.8001

(4.3385)

(3.5645)

(0.4659)

C: Instrumental variable regression RESCt = Dep variable RESCt

Constanta ‡

Q

–0.0150

‡

0.1725

18.0030

(4.5967)

(2.6047)

(0.2066)

D: Implied α α = 1–(1–k*/k)/ρ = 1–(1–0.1008/0.1725)/0.7215 = 0.4242 MF–Shilling – modified Shilling (1993) method. a Insignificant intercept depressed in calculating ρ. xt – vector of other explanatory variables. Unlike the case of JLW, no other variables entering the regression equation with statistical significance – vector of coefficients for xt. RESCt being times 0.1e–4. Panel C: Instrumental variable regression uses FTAP as instrumental variable. Q – Ljung-Box statistic for serial correlation, the order is selected as 1/4 of the observations used. † significant at 5% level;‡ significant at 1% level.

ing constant or trend) less appealing. The maximum lag length is chosen to be two lags by the Malcolm procedure (a Johansen procedure) with RATS, and the Ljung-Box Q statistic indicates there is no serial correlation in the residuals. The diagnostic checking of the results from the MF–Shilling method also confirms the model fits well at each step. Table 6.5 summarises unsmoothing of the JLW index. It compares the smoothing factor (α), the ratio of the standard deviation of the rate of return on the unsmoothed index to that of the original index (σM/σA), and the coefficient of variance (CV) from employing different methods. Table 6 is the summary for the unsmoothing of the IPD index. By comparing and assessing these results, it can be judged that the ratio of the two standard deviations (σM/σA) is about half size of the ratio from the fully smoothing procedure. Although only the variance of the indices is of interest, also it is helpful to point out that the mean of the unsmoothed indices change as well, as this fact has been largely ignored by most previous unsmoothing studies. For a stochastic process, the mean rate of return is µ–σ2/2. So, if unsmoothing is applied to returns or value, instead of rates of return, an increased σ will cause µ–σ2/2 to decrease. It is because the mean of returns or value will not change in such unsmoothing processes, therefore only σ increases but µ does not change. However, if unsmoothing is applied to rates of return,

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Table 6.2 Summary Statistics – MF–Shilling Method, IPD Index A: Total smoothness in index ra,t = c+ρra,t–1+

t

Dep variable ra,t

Constanta ‡

0.8661

(0.1014) ra,t

ra,t–1

Q

1.1743

0.0004

(7.7702)

(0.9472)

‡

–

0.8685

1.1532

(8.1585)

(0.9493)

ra,t

Q

B: OLS regression RESCt = c+ ra,t+ ′xt+ ′t Dep variable RESCt

Constanta ‡

‡

–0.0082

0.2642

2.5370

(4.7457)

(5.1903)

(0.7709)

C: Instrumental variable regression RESCt = Dep Variable

Constanta

RESCt

–0.0096‡

0.4086‡

3.3217

(4.2158)

(2.6901)

(0.6505)

Q

D: Implied α α = 1–(1–k*/k)/ρ = 1–(1–0.2642/0.4086)/0.885 = 0.5930 MF–Shilling – modified Shilling (1993) method. a Insignificant intercept depressed in calculating ρ. xt – vector of other explanatory variables. They are lagged dependent variable, real growth in GDP, unemployment rate and Treasury bill yields in this case. – vector of coefficients for xt. RESCt being times 0.1e–4. Panel C: Instrumental variable regression uses FTAP as instrumental variable. Q – Ljung-Box statistic for serial correlation, the order is selected as 1/4 of the observations used. †significant at 5% level; ‡significant at 1% level.

they will not change, implying µ increases by the same amount as σ2/2 after unsmoothing. Nonetheless, the effect is minimal even in the former case, as σ2/2 is very small relative to µ. To show how much smoothness has been caused in the appraisal index, the original series, the series unsmoothed by the implied cointegration approach and the series assuming a random walk, along with the return series of FT real estate company shares, are graphed in Fig. 6.1 and Fig. 6.2. Fig. 6.1 is for the comparison between the JLW and

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FTAP quarterly indices, and Fig. 2 is for the IPD and FTAP monthly indices. It can be seen that the appropriately unsmoothed real estate indices and the return on FT real estate company shares have a very similar pattern. On the one hand, the rates of return on the original indices are too smooth to be reliable. On the other hand, the rates of return on the fully unsmoothed

Figure 6.1 Smoothing in the appraisalbased index – original and unsmoothed JLW quarterly indices against FTAP

Recapturing market information from appraisal-based real estate indices

Figure 6.2 Smoothing in the appraisalbased index–original and unsmoothed IPD monthly indices against FTAP

91

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Table 6.3 Summary statistics – implied cointegration, JLW A: Unit root in levels and in difference (ADF test) .

.

Levels

.

Difference

JLW

.

–.3634

.

–3.9660†

FTAP

.

−2.1806

.

–7.0774‡

B: Implied cointegration analysis St –Pa,t–1 = µt

max

α

trace †

†

Q of vt

α

†

0.6241

1.0134

16.60

18.22

1.6022

13.9039

(30.1660)

.

.

(2.1306)

(0.4569)

Critical values in Johansen and Juselius (1990) and Osterwald-Lenum (1992) are used as cointegration criterion; results from running Malcolm procedure with RATS. The lag length in the ADF test is decided by the AIC, subject to satisfying the Ljung-Box statistic for serial correlation. * significant at 10% level, † significant at 5% level; ‡ significant at 1% level (with regard to unit root tests, it is to reject the null of a unit root; with regard to cointegration tests, it is to reject the null of no cointegration).

indices seem to be too volatile: the standard deviation of JLW would be 0.0704 while that of FTAP is 0.1202 in the period of 1977 Quarter 2 to 1992 Quarter 4; and the standard deviation of IPD would be 0.0539 compared with the standard deviation of 0.0809 of FTAP in the period from 1987 Month 2 to 1992 Month 12. When financial leverage in real estate companies is considered, which is about 0.50 (for example, equity was £1,659.8m and debt was £2,281.1m in MEPC; and equity was £1,579.5m and debt was £1,515.3m in the British Land Plc in 1995), the standard deviation of real estate company returns may be even lower, though not substantially lower due to the reason that bond volatility was not considerably lower than that of shares during this period. Therefore, a full correction for smoothing implies higher volatility in the return in direct real estate investment than in the return in real estate companies, which seems unlikely. Theoretical reasoning and prudent judgement are in support of the unsmoothing procedures which recognise both the importance of correction for smoothing and the fact that true real estate returns do not (necessarily) follow a random walk; instead, there is serial correlation in true real estate returns. Due to transaction costs, market segmentation, lack of channels for swift information dissemination and other market inefficiencies and imperfections, the response to a shock in the real estate market ought to be slower than in other liquid financial markets and the effect would be felt for a longer period than in other liquid financial markets. This suggests that returns on real estate are smoother than returns on other kinds of investments in relatively liquid financial markets.

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This chapter has proposed two multivariate approaches to unsmoothing the valuationbased real estate indices. In contrast to the univariate methods, these unsmoothing procedures utilise information in other economic and financial variables implied by the underlying economic relationships and the cointegration re lationships. Therefore, smoothing due to valuation can be detected and corrected properly and efficiently, and serial correlation in the market returns is not unrealistically removed. Applying these procedures to the UK real estate indices of JLW and IPD, the estimates of the smoothing factor suggest a reasonable volatility in direct real estate investment which is close to the

Table 6.4 Summary statistics – implied cointegration, IPD A: Unit root in levels and in difference (ADF test) .

.

Levels

.

Difference

JLW

.

–1.0773

.

–3.7507†

FTAP

.

–1.1002

.

–6.6336‡

B: Implied cointegration analysis St –Pa,t–1 = µt

max

α

trace †

†

Q of vt

α

*

0.4179

0.9671

18.25

21.62

2.3930

12.0385

(243.2681)

.

.

(1.8999)

(0.7413)

Critical values in Johansen and Juselius (1990) and Osterwald-Lenum (1992) are used as cointegration criterion; results from running Malcolm procedure with RATS. The lag length in the ADF test is decided by the AIC, subject to satisfying the Ljung-Box statistic for serial correlation. * significant at 10% level, † significant at 5% level; ‡ significant at 1% level (with regard to unit root tests, it is to reject the null of a unit root; with regard to cointegration tests, it is to reject the null of no cointegration).

Table 6.5 Unsmoothing of the JLW index Original σM/σA (implied) α (implied) CV

FRZ/BW

BG

MF–Shilling

Implied CI

1.0000

2.4862

2.0817

1.9274

1.4848

01.0000

0.2785

0.3750

0.4242

0.6241

2.4594

6.9106

5.0816

4.5051

3.2392

FRZ/BW–Firstenberg, Ross and Zisler (1988), Ross and Zisler (1991) and Blundell and Ward (1987); MF-Shilling-modified Shilling (1993) method; BG–estimates in Barkham and Geltner(1993, 1995); Implied CI – implied cointegration. CV – coefficient of variance; the CV of FTAP is 12.3039 during this period.

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Table 6.6 Unsmoothing of the IPD index Original

FRZ/BW

BG

MF–Shilling

Implied CI

σM/σA (implied)

1.0000

3.7695

2.9455

1.5404

1.9457

α (implied)

1.0000

0.1315

0.2067

0.5930

0.4179

CV

4.9324

24.5986

15.0278

6.1170

7.7359

FRZ/BW–Firstenberg, Ross and Zisler (1988), Ross and Zisler (1991) and Blundell and Ward (1987); MF-Shilling–modified Shilling (1993) method; BG–estimates in Barkham and Geltner (1993, 1995); Implied CI – implied cointegration. CV – coefficient of variance; the real rate of return on FTAP is negative and the nominal rate of return on FTAP is too small to get a sensible CV during this period.

real world reality. Nevertheless, the estimated results should always be complemented by prudent judgement, though the method is informationally superior and efficient. It is crucial to construct are liable real estate index prior to analysing real estate’s characteristics and relationships with other economic and financial variables. For example, it might change persistence patterns; or change the relative importance of cycles at different frequencies, and therefore, distort the results of common cycle analysis. The unsmoothed JLW real estate index will be applied to each of the next three chapters – the main empirical inquiries into real estate market behaviour and dynamics in this book. The IPD index was examined and unsmoothed in this chapter merely as another example to support the proposed unsmoothing procedures. It will not be used in the following chapters as many other economic and financial data sets are much longer than the IPD index and are available at a quarterly frequency.

7 Real estate’s response to shocks This chapter is concerned with shock response patterns in the real estate market. It is motivated by the need to advance our knowledge about the response of the real estate market to shocks in the long run, and the impact of shocks in other economic and financial variables on the volatility in real estate. This knowledge would enable us to evaluate the effect on the real estate market when certain shocks occur or are forecast to occur, and to take corresponding measures accordingly. While there have been several studies on the long-run characteristics of the real estate market, they mainly used the cointegration technique to investigate the long-run co-movement of real estate and other economic and financial variables, and causal relations among them, for example, Lizieri and Satchell (1997), and Wang et al. (1997). Few, if any, have ever studied the long-run volatility and volatility patterns over a very long period, and the influence of other economic and financial variables on the volatility in real estate market. An interesting but different kind of study on persistence in real estate is Grenadier (1995), which examines the prolonged cycles in real estate markets. Traditionally, real estate returns, along with many economic and financial time series, are considered to be stationary in their first difference (rate of return) and non-stationary in their levels, and a shock would have a one-off effect on the rate of return but permanent effect on the level. However, two points make further scrutiny necessary. First is the case where a non-stationary time series is not a purely random walk: even if a time series is non-stationary in its level, its behaviour can be quite different, depending on the serial correlation structure. If there is positive serial correlation overall, the effect of shocks would be compounding, whereas shocks on a mean-inverting process would have smaller effect. Second is the case where economic and financial time series consist of both stationary and non-stationary components. This is the view expressed by Campbell and Mankiw (1987a,b), and Cochrane (1988). Their work challenged the prevailing practice of modelling economic and financial time series as a unit root process which is strictly first difference stationary which has sometimes falsely forced many researchers to either accept or reject a unit root in the process. Therefore, the appropriate question asked by them is not whether a time series is stationary or not. It is how big is the random walk component in the time series, or the relative importance of permanent and transitory components in the time series. This argument has lead to the development of an overall persistence measure. Nevertheless, the size of the persistence measure of one variable is not necessarily inversely related to the transitory component of a shock. Therefore, transitory and permanent components will be further decomposed, using the Beveridge– Nelson (1981) trend-cycle decomposition approach. As the effect of cycles gradually diminishes and that of the trend dominates with the time horizon, the decomposition would reveal the transitional path towards the long-run destination.

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Univariate persistence Since the persistence measurement in the sense of Campbell and Mankiw (1987a,b) and Cochrane (1988) is for the long run, it is particularly helpful in the study with the longrun nature, such as the real estate market. Considering smoothing in real estate indices. It would distort the observed persistence pattern of real estate. However, persistence is a long-run measurement whereas smoothing is mainly reflected in the first order (or at most upto fourth order for quarterly data) autoregression. In this regard, persistence is a more sensible measure of the way in which the real estate market responds to a shock. That is, accuracy in estimated persistence is less affected by smoothing in the variance of real estate returns. To demonstrate this feature empirically, the persistence measure of Vk and A(1), as described in the section ‘Properties of trends and cycles’ in Chapter 4, is calculated for the original appraised index series and the unsmoothed series (both with and without assuming a random walk) and shown in Fig. 7.1. To compare relative persistence of shocks in real estate and other economic and financial activities, Vk and A(1) are also calculated for a list of variables which may influence and be influenced by real estate. These variables are FTAP, FTA, CO, NO, NTW, and GLT, and the market index of real estate performance HPK. Only one of the two major real estate indices, JLW, is used. The reason is that, although the numbers of observations in JLW and IPD are in the same range, the JLW quarterly index spans a longer time period and, consequently the persistence measurement is more reliable and meaningful. It also avoids repetitions of calculation of Vk and A(1) for the above mentioned variables against two indices. Examining the Vk and A(1) measurement of the JLW index in Fig. 7.1, both original and unsmoothed indices display similar patterns, though conceivably, the magnitude of Vk and A(1) of the original index at the peak is higher than that of the unsmoothed index. When k becomes large (that is what Vk really means), the Vk of both indices approaches gradually to, but remains above, the random walk benchmark. As the patterns show, the impact of a shock reaches its peak in about 10 to 11 quarters or slightly less than three years. As long as the index is not fully unsmoothed, the patterns of Vk and A(1) are very much the same, as shown by the graph. The Vk of the fully unsmoothed JLW index displays the property of mean reversion and, understandably, converges to the random walk benchmark, which may not be true due to the over correction. This becomes clear when a comparison is made with some of the real sectors in the economy. In fact, there is no mean reversion in the Vk of GDP and construction output; there is a tendency for mean reversion in construction new orders but it never crossed and fell below the random walk benchmark (except for the first few periods). The JLW index shares some similarity with GDP in that a shock usually takes about three years to have its greatest impact. However, the shape of Vk is much flatter in GDP than in JLW, suggesting larger sensitivity and over reaction in the real estate market. Over reaction to a shock in construction output is longlasting: there is little sign of readjustment even after a very long period. Whereas construction new orders are the most close to a random walk among the variables. This is sensible, since it is easier to make adjustments to construction new orders than to output in the construction sector in particular and to the economy in general. The indices representing stock market investment are relatively close to a random walk. In fact, Vk of FTA and FTAP can be regarded as random walks and A(1) is not

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significantly different from 1, considering the wide range of standard error in Vk and A(1). Vk of GLT is always very close to the random walk benchmark. Interestingly, the pattern of Vk and A(1) of NTW (Nationwide Building Society House Price Index) are remarkably similar to those of original and unsmoothed JLW, but not to the fully unsmoothed JLW. The patterns of HPK, which is claimed to be a market index, also bears remarkable similarity (and it speak of impact is even higher than that of the unsmoothed JLW). These two points convince us to believe that certain degree of unsmoothing is necessary, the choice of the smoothing factor is not too crucial, and full unsmoothing is not desirable. Fig. 7.2 shows the persistence patterns in the first difference, i.e., the rate of return on investment or rate of change in economic activities. Vk almost approaches zero when k becomes large (at around seven years), if the wide standard error has been taken into account. This is an alternative way of observing stationarity. It is understandable that a shock, no matter whether it is from demand or supply, should normally have no permanent effect on the rate of return (while a supply shock may be able to increase or decrease the level of activity permanently). Inspecting Vk in Fig. 7.2 confirms this conclusion, at least as far as the variables used in this book are concerned. A(1)k, as it is so designed, is always larger than Vk, and the patterns suggest there is serial correlation in the rates of return or changes. Ironically, the HPK index, which is presumed to be a market index, is more persistent than the original JLW index, and its relatively larger standard error in its Vk and A(1)k implies large inaccuracy. A more insightful evaluation of relative shocks is to generalise the persistence measurement of Vk and A(1) to multivariate cases and jointly apply them to a group of variables or sectors. The multivariate persistence analysis is more accurate in that it removes the constraint preventing shocks being transmitted from one variable to another, implicitly imposed in univariate cases. Therefore, multivariate persistence analysis can examine the sources of shocks and the effects of a shock in one sector on other sectors.

Econometric analysis of the real estate market and investment

Figure 7.1 Persistence in real estate market and other economic activities – levels

98

Real estate’s response to shocks

99

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Real estate’s response to shocks

101

Econometric analysis of the real estate market and investment

Figure 7.2 Persistence in real estate market and other economic activities – first difference

102

Real estate’s response to shocks

103

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104

Real estate’s response to shocks

105

Permanent and transitory components in shocks (trends and cycles) In the previous section, the persistence of shocks to real estate has been examined with the univariate model. It is worthwhile pointing out that the amplitude of the persistence measure for one variable is not inversely linked to the proportion of its transitory components of shocks, as persistence measures are for very long periods when all the transitory effects have disappeared. For example, if variable xt has a Vk of 1.8 and yt has a Vk of 1.2, this does not suggest that the transitory component in xt would necessarily be smaller than that in yt in, say, two years time. In a sense, the decomposition of shocks into transitory and permanent parts illustrates, as the names suggest, the transitional path leading to certain points in the level and there are many ways to reach the ‘destination’. To return to the empirical analysis in this chapter, transitory and permanent components are decomposed, using Beveridge–Nelson trend-cycle decomposition approach. The algorithm is by Newbold (1990), and written as a RATS procedure by Philip Meguire of North Carolina State University (1994). Prior to trend-cycle decomposition, an ARIMA model is estimated for each variable. The order of the ARIMA model is determined according to the principle of parsimony, subject to satisfying the Ljung–Box Q statistic. The results are reported in Table 7.1 with one period (one quarter), one year and five years’ horizons. In addition to the previously-defined variables, PDN stands for the production sector, SVC for the services sector, and MNG for manufacturing. FTA and FTAP are not in the table, because they are very close to a purely random walk and, therefore, only have trend but no cycle components. The fully unsmoothed JLW series is excluded for the same reason.

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From Table 7.1 it can be observed that real estate has a rather small transitory component in shocks, relative to the real sectors in the economy. The transitory component only accounts for less than five per cent of total shocks after one quarter, and it drops to about one per cent in one year. By contrast, the transitory component in construction output shocks constitutes more than 20 per cent of the total in one quarter, diminishing to about five per cent in one year. This reflects that

Table 7.1 Transitory component in shocks (% of total shocks) One period (quarter)

One year

Five years

JLWUS

4.52

1.14

0.42

JLW

2.09

0.69

0.29

HPK

0.73

0.27

0.16

CO

20.87

4.84

2.37

NO

14.87

11.85

3.72

NTW

3.01

0.65

0.06

GDP

11.77

5.88

1.29

PDN

9.54

1.83

0.33

SVC

14.67

3.45

0.73

MNG

12.28

3.38

0.75

the construction sector adjusts intentionally and frequently to accommodate the demand and supply state and the price condition in commercial and residential real estate markets. With regard to the economy as a whole, as represented by GDP, the transitory component in shocks is about twelve per cent and six per cent of the total in one quarter and one year respectively, reflecting the aggregate contribution of the production, construction, services and other sectors. Interestingly again, the pattern of real estate’s response to shocks is most close to that of housing, represented by NTW, though the latter is slightly smaller. In a sense, real estate bears some characteristics pertinent to the real sectors in the economy and some other characteristics pertinent to financial market investments, with regard to the permanent and transitory components in shocks. Although real estate has a similar long-run persistence pattern with the real sector of the economy, its transitory, or cycle component, is profoundly smaller than that in the latter. Indeed, real estate’s transitory component is as small as being negligible beyond one year’s horizon. This means that cycles decay quickly and stochastic trends dominate. By comparison, there is more transitory component in most economic activities. The results appear to be surprising at first glance, as real estate is perceived to fluctuate more noticeably. But, indeed, there is no economic rationalisation to justify such a view. As a long-term investment and with long-term utility involving no frequent transactions, what matters is the end of (long) period values and returns, not the values and returns within the holding period. Relatively large transaction costs and illiquidity

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also prevent real estate from joining those activities whose swift reaction to innovations in the economy is essential to maximise values and returns to be realised immediately. Consequently, real estate is not changed by these short-term innovations as much as many other economic activities, and especially financial market activities. The test, analysis and discussion in this section help clarify the matter.

Sources of shocks: multivariate and joint persistence with other sectors The univariate persistence of real estate has been examined in the first section of this chapter. This Section extends persistence analysis to multivariate time series by applying the multivariate model to a group of variables to evaluate cross-sectional effects where real estate is perceived to influence and to be influenced by. Multivariate persistence analysis is more sensible in that, instead of analysing the individual variables separately as in the univariate case, it allows shocks to be transmitted from one variable to another. Therefore, multivariate persistence analysis is able to examine the sources of shocks and the effects of a shock in one sector on other sectors. Moreover, it is able to detect the effect of certain kinds of shocks, e.g., a monetary shock, from that of other types of shock. The selection of the sectors to be included in multivariate persistence analysis and shock decomposition should be linked to the nature and characteristics of the empirical work to be carried out. A standard and simplified set-up of the system consists of output, consumption and investment, as represented by King et al. (1991). The interpretation of disturbances by Blanchard and Quah (1989) is influ-enced by a traditional Keynesian view: permanent effects, which are persistent, are due to supply shocks, and transitory effects, which are not persistent, are due to demand shocks. By applying a variant of Fischer’s (1977) model, their empirical estimation simply involves just two macroeconomic variables: output and the unemployment rate. Long and Plosser (1987) and Pesaran et al. (1993) are typical studies on sectoral and aggregate levels, where sectors can be aggregated to total output. In the case of Long and Plosser, the aggregate is the manufacturing sector and the disaggregates are thirteen sections under manufacturing; and Pesaran et al. covers ten sectors which comprise GNP. The aggregation relationship between variables is: and where Ya is the aggregate of Yi(i = 1,…m). Liu and Mei (1994), combining Campbell and Mankiw’s (1987a, 1987b) univariate persistence estimation method and Campbell and Shiller’s (1987) present value model and its extensions (Campbell and Shiller 1989, Campbell 1991), restrict their analysis to financial market activities and apply it to indirect real estate investment represented by US REITs: there are no disaggregate and aggregate relations. They first estimate a present value model in a VAR with returns on stock portfolio, small stock portfolio and equity REITs portfolio, dividend yield and Treasury bills; then calculate the persistence measure which is, in fact, univariate. The last two types of analysis on the effects of shocks are the most practical and appealing in this chapter. However, one should recognise that real estate is heavily influenced by both financial market and real economic activities, and, consequently, both kinds of variables should be present. In the UK, GDP is traditionally disaggregated into

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four broad categories and nine sectors. Before 1992 these were called section 1 for ‘agriculture’ to section 9 for ‘government and other services’. These sections are classified, by the SIC (standard industrial classification) codes of 1992, as A, B (Agriculture), C (Mining and quarrying), D (Manufacturing), E (Utilities), F (Construction), G, H (Distribution), I (Transport and communication), J, K (Business services, J and part of K, exactly), and L–Q (Government and other services, part of K, L–Q). Among these sections, ‘mining and quarrying’, ‘manufacturing’, ‘utilities’ (C, D, and E) are grouped as the ‘production’ sector; ‘business services’, and ‘government and other services’ as the ‘services’ sector (G–Q); ‘construction’ and ‘agriculture’ stand on their own. Among these industries, ‘construction’ is most relevant. ‘Production’ and ‘services’ will play a different role in the economy. These sectors constitute one facet of study which is largely under-researched. There is no doubt that real estate, as an investment, has been recognised to have links with the stock market and, to a certain extent, with the non-commercial real estate market, i.e., the housing market. After these considerations, the multivariate persistence model would consists of the real estate return index, the FTSE index, the house price index, construction output, production, and services. This group of selected variables differs from those variables used in the univariate persistence analysis. On the one hand, some variables are certainly able to provide useful information when evaluated individually, but are not appropriate to be included in a simultaneous estimation system altogether. All the economic data are quarterly from the Office for National Statistics. They are all seasonally adjusted for consistency, as not all data are available in the form of nonseasonally adjusted. Table 7.2 presents the multivariate persistence estimates with the six sectors represented by JLW, FTAP, NWT, CO, PDN, and SVC. The diagonal elements in the table are sector-specific persistence measures (the diagonal elements in the VCK matrix) which are equivalent to those depicted in the first section of this chapter, but are more reliable. This is because, unlike the univariate persistence measure which ignores the effects from other sectors, the multivariate persistence measure takes into account the interactions between sectors. Furthermore, it is able to evaluate the effects on one sector due to a shock in other sectors. The sector-specific persistence measure is close to the univariate persistence measure estimated earlier, except that the persistence in construction is much lower, with VCK = 2.8815 and A(1)=2.3618. In fact, the univariate persistence estimates for construction output are too large and have no tendency to converge to a certain point like other variables. FTAP, the stock market index, is most close to a random walk with its A(1) being very close to unity. The two new variables, production and services industries, do not have as large persistence measure as real estate, housing and construction. No direct comparison with other studies is possible, because there have been virtually no studies of persistence of shocks in the UK economy and sectors. Nevertheless, this is not a serious concern as this book is not centred on these sectors themselves but on their relationship with real estate. Several US studies have reported that the services sector has a large persistence measure estimate while the production sector has a relatively low value for persistence measurement. It is also documented that utilities exhibit considerable persistence while manufacturing has a rather small value, for persistence measurement. For example, Pesaran et al. (1993) have estimated that, with the US data, VCK = 1.76 in utilities, VCK = 1.0 in durables manufacturing and VCK = 0.64 in non-durables manufacturing, and VCK = 3.75 in

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business services. In Table 7.2 the production sector’s VCK of 1.3348 would be an aggregate estimate combining a higher value of persistence for utilities and lower value of persistence for manufacturing. As the intention of this multivariate persistence analysis is to investigate the cross-sectional effects between real estate and the broadly classified sectors, no further disaggregation is necessary or appropriate here. The off-diagonal elements in Table 7.2 provide information that is not found in univariate persistence analysis. It has been revealed that shocks from the housing market have the largest effect on the persistence in real estate, followed by the services sector which is also quite substantial, the production sector, and construction. Shocks in the stock market have effects on the persistence in real estate, but they are not as large as those in the selected sectors in the economy. Regarding the effects of the real estate market on other sectors, again, the largest impacts seem to be felt in the housing market: so the commercial and non-commercial real estate markets have very close links in this perspective. The effects of shocks on the services sector are larger than those on the production sectors, as expected. A negative figure for the effects on construction suggests, in statistical terms, the one period covariance and the n(n→∞) period covariance have the different signs. This is only possible in covariance but not in variance. The empirical meaning of a negative crosssectional persistence measure would be: a positive shock in real estate market which also results in an increase in construction (i.e., a positive one period covariance is assumed) would eventually lead to the decrease in construction output, or contraction in construction industry, in the long run. This would have profound economic implications if the particular construction figures had not been taken into account. When one looks at the graph of construction output during this period, its universal application seems to be less appealing, as construction output has consistently been declining, while almost all other variables had upward trends. The multivariate persistence measures are also estimated with the original JLW index and with the fully-unsmoothed JLW index, and reported in Tables 7.3 and 7.4. It can be seen that, with the original index, the persistence measure is too large for real estate as in the univariate case. This large persistence in real estate also has consequence on the estimates of persistence measure in other sectors. That is, not only the cross-sectional, but also the sector-specific, persistence measures become larger; and the change is rather out of line of the results for those sectors if the real estate index were not included. When the fully-unsmoothed index is used in the model, persistence measures tend to be lower, but the amount of deduction is very trivial, except in that of real estate itself and those where real estate is directly involved. In fact, the persistence measures for the fully unsmoothed JLW index is close to that of the stock market index. Through analysing these three sets of results, it can be seen that the use of original JLW index in the model would distort persistence measures across sectors and, therefore, should not be adopted. A fullyunsmooothed JLW index would leave the persistence measures of other sectors largely intact, compared with the appropriately unsmoothed JLW index; but the persistence measure for real estate itself would become, unreasonably, close to that for a random walk. In this sense, the use of an unsmoothed index appears to be, no matter what the underlying assumption, better than the original smoothed index. However, only the use of appropriately unsmoothed index in the model gives sound estimates for real estate and

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across sectors, and renders insightful implications on the persistence patterns and interactions between sectors in response to multi-sectoral shocks. The reported multivariate persistence measurement estimates are derived with an unrestricted VAR model of order 2, which effectively provides along-lag ARMA structure (see Pesaran et al. 1993 and Van de Gucht et al. 1996). The restricted model, which drops the regressors whose t-statistic of coefficient is less than one, was also tested. The two sets of results are similar, so the unrestricted model is adopted for reasons that it is easy to implement in the future and in slightly different situations. This is in consistence with Cochrane’s (1988) recommendation of including all autocorrelation terms even if they are insignificant. Both models were estimated with SUR (seemingly unrelated regression), though there are no efficiency gains from using an OLS procedure to applying SUR in the unrestricted model.

Table 7.2 Multivariate persistence VK (with unsmoothed JLW index) Sources of shocks Effect on

JLW

FTAP

NTW

CON

PDN

SVC

JLW

2.6243

0.8744

2.7542

1.0119

1.0782

1.5273

FTAP

0.7962

0.8284

1.2710

0.6919

0.1238

1.0530

NTW

3.0412

1.5032

4.4957

1.3024

1.3020

2.3466

–0.3611

–0.0746

–0.9907

2.8815

0.7135

0.8976

PDN

0.4385

–0.1939

0.0468

1.5431

1.3348

0.5788

SVC

0.8457

0.6488

0.9700

1.9384

0.7768

1.5798

CO

Table 7.3 Multivariate persistence VK (with original JLW index) Sources of shocks Effect on

JLW

FTAP

NTW

CON

PDN

SVC

JLW

6.2270

2.0697

5.0143

1.8930

1.6725

3.2187

FTAP

1.5452

1.1821

1.8337

0.9622

0.2591

1.5018

NTW

4.7747

2.2073

5.4450

1.9377

1.4215

3.2803

–0.1658

0.2065

–0.4443

3.0320

0.9240

1.2556

PDN

0.7190

0.1420

0.4433

1.8663

1.3368

1.0110

SVC

0.7174

1.1903

1.8178

2.3612

0.9585

2.2668

CO

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111

Sources of shocks: persistence and monetary shocks It would be of further interest to decompose shocks into monetary and non-monetary shocks. The above tests have analysed the ‘sources’ of shocks, and the sources are sectors. In the following, the sources are divided into monetary and non-monetary ones. The reasons for adopting this line for analysis have been given in the section on ‘Sources of shocks’ in Chapter 4. Monetary shocks can be derived from estimating a money supply growth model and getting its residuals. The money supply growth model is specified as follows: ∆Mt = α+ ∆Mt–1+ ∆SVCt–1+ UERt–1+vt (7.1) where Mt is money supply, SVCt is services sector output including the business sector and the government, UERt is the unemployment rate. M0, the narrowly defined money, is chosen as the money supply variable in this model. The reasons for using M0 instead of M4, the broad money supply, are empirical. There is a big break in the M4 series in the fourth quarter of 1981 caused by the switch between the old banking sector and the new monetary sector. In July 1989, Abbey National’s conversion to a public limited company caused minor breaks to the M0 series and major breaks in the M4 series. Although the first breaks in the fourth quarter of 1981 were removed from the changes in M4, the removal of the breaks in the changes in M4 resulted in as much distortion as the retaining of the breaks in M4 levels. Besides these breaks, the M0 and M4 series have a similar pattern. Beyond the concern in breaks, M0 is more liquid and more public sensitive in representing demand factors, separated from supply factors or real factors. Table 7.5. gives the summary statistics for fitting this model. The multivariate shock persistence model has been re-estimated with the monetary shocks, the residuals from the money supply growth model being included. All the

Table 7.4 Multivariate persistence VK (with fullyunsmoothed JLW index) Sources of shocks Effect on

JLW

FTAP

NTW

CON

PDN

SVC

JLW

0.7908

0.4364

1.4113

0.4351

0.5238

0.7001

FTAP

0.4334

0.7028

1.1013

0.5038

0.1091

0.8581

NTW

1.5724

1.2683

4.1899

0.8956

1.2844

1.9447

–0.0567

–0.1355

–0.9377

2.6298

0.7534

0.7752

PDN

0.2964

–0.2477

0.1098

1.3447

1.4548

0.4784

SVC

0.5081

0.4973

0.8540

1.6176

0.8244

1.3300

CO

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Table 7.5 Summary statistics for the money growth model α M0

Q ‡

‡

0.0155

0.4551

(3.2723)

(4.1013)

0.3616

‡

†

–0.0011

19.9744

(2.4180)

(0.2753)

(2.6350)

Q – Ljung–Box statistic for serial correlation, the order is selected as 1/4 of the observations used. p-value in brackets. † significant at 5% level; ‡ significant at 1% level.

estimates are reported in Table 7.6, and a summary with sector-specific estimates and the percentage of monetary and non-monetary effects is provided in Table 7.7. The first line for each variable in Table 7.6. is the total persistence, the second line the effects of non-monetary shocks as represented by the second term on the right hand side of equation (4.19), and the third line the effects of monetary shocks represented by the first term on the right hand side of equation (4.19). As above, the diagonal elements are sector-specific persistence measurement, and off-diagonal elements the cross persistence measurement. Overall, the persistence estimates are smaller than those in Table 7.2, except for the construction sector. This is because of the inclusion of the monetary shocks, which are expected to have smaller effects in the long run, in the model. In previous estimation without an explicit monetary shock variable (or a monetary variable), the persistence effects due to monetary shocks, are mixed with other shocks. Further, scrutiny has found that the decrease in the persistence measure happens in those sectors which are subject to monetary shocks to a substantial degree. e.g., housing with monetary shocks account for 28 per cent in total persistence, services, 16 per cent, and stock market 20 per cent. Monetary shocks only account for 4 per cent of total persistence in construction, and an even smaller figure of less than one per cent in the production sector, so their total persistence estimates are largely unaffected. In summary, a broadly defined production sector including construction, or the real economy, or the supply side of economy, is not subject to monetary shocks

Table 7.6 Multivariate persistence VK, monetary shocks decomposed Sources of shocks Effect on JLW

FTAP

JLW

FTAP

NTW

CON

PDN

SVC

2.2304

0.4559

2.0688

0.6253

0.6802

0.8212

2.0389

0.3347

1.5680

0.7949

0.7011

0.7515

0.1915

0.1212

0.5008

–0.1695

–0.0208

0.0697

0.3265

0.5301

0.5480

0.4431

–0.1140

0.6191

0.3253

0.4216

0.3856

0.4922

–0.0267

0.5090

0.0012

0.1084

0.1624

–0.0492

–0.0874

0.1101

Real estate’s response to shocks

NTW

CO

113

2.2713

0.7616

3.3395

0.5288

0.7238

1.1391

1.9208

0.5440

2.4043

0.8496

0.7536

1.0188

0.3505

0.2176

0.9352

–0.3209

–0.0298

0.1204

–0.4758

–0.0522

–1.2515

3.0167

0.7594

0.9497

–0.3522

–0.0362

–1.0157

2.9111

0.7699

0.9403

–0.1236

–0.0160

0.0849

0.1057

–0.0105

0.0094

0.1860

–0.2489

–0.2548

1.4501

1.2941

0.4737

0.1776

–0.2774

–0.3397

1.4776

1.2826

0.4481

0.0083

0.0285

0.0849

–0.0275

0.0115

0.0256

0.1568

0.3699

–0.0256

1.6847

0.4481

1.2115

0.2742

0.2303

–0.0559

1.7202

0.6274

1.0124

PDN

SVC

−0.1174

0.1396

−0.0354

0.0303

−0.1794

0.1991

Table 7.7 Multivariate persistence VK, summary of monetary and non-monetary shocks Monetary shocks VK

Non-monetary shocks

%

VK

.

%

Total

JLW

0.1915

8.59

2.0389

91.41

2.2304

FTAP

0.1084

20.45

0.4216

79.55

0.5301

NTW

0.9352

28.00

2.4043

72.00

3.3395

CO

0.1057

3.50

2.9111

96.50

3.0167

PDN

0.0115

0.89

1.2826

99.11

1.2941

SVC

0.1991

16.43

1.0124

83.57

1.2115

in the long run. However, the services sector, broadly defined to include housing and the stock market, or the demand side of economy, or the consumption, is very much influenced by monetary shocks. Commercial real estate, due to its fundamental links to the real economy and financial markets, reasonably stands in the between with the effects of monetary shocks being responsible for 9 per cent of total persistence measurement, and a large part of persistence comes from non-monetary shocks caused in the real sector in the economy. This chapter first investigated the persistence patterns in the real estate market with the original and unsmoothed real estate indices, and examined the impact of shocks in other economic and financial variables on the real estate market. The shock persistence in the real estate market was jointly evaluated with financial market investment and the real world economic activities. In addition, the effects of monetary and non-monetary shocks on the real estate market was also studied.

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In the long-run, what matters more is the persistence pattern than the autoregression at a few lags. The latter is sometimes equivalent to smoothing, a combined effect of appraisal procedure and market return process; and much effort has been devoted to it. Although different unsmoothing methods have produced different estimates of smoothing factor, and the discrepancy is sometimes large, the persistence patterns and the long-run relationship with other economic and financial variables are not significantly changed from applying one smoothing factor to another. This is because the smoothing factor has the largest influence on the first few correlation coefficients alone and in the long run its effect is minimal. Examining the univariate cases, as long as the index is not fully unsmoothed which has been accepted by most real estate researchers, the patterns in the JLW index are virtually the same and the persistence measurements reach their peak in about two and a half to three years before declining. This means that the effect of positive (negative) shocks is reinforced by other positive (negative) shocks in the first 11–12 quarters in an economics sense, and there is positive serial correlation (when more than the first order autoregression is considered, the total effect would be of positive serial correlation) in statistical measurements. The persistence pattern of the JLW index is very similar to that of GDP, but the latter is flatter, suggesting larger sensitivity and overreaction in the real estate market, relative to the national economy as a whole. The patterns in financial market investments are even flatter and any effect of shocks would be exhausted in relatively short period and the adjustment takes place relatively quickly. Compared with some real world economic activities which have close relationships with real estate, e.g., construction, real estate investment is less persistent. It is reasonable as real estate bears attributes of both construction and development and financial market investments. As such, real estate investment should always be analysed, in relation not only to financial markets, but also to the real economy. Transitory and permanent components were decomposed next. Real estate was found to have a rather small transitory component in shocks, relative to the real sectors in the economy. The transitory component only accounts for less than five per cent of total shocks after one quarter, and it drops to about one per cent in one year. By contrast, the transitory component is much larger in the real sectors of the economy. In particular, the construction sector has the largest transitory component in shocks, reflecting that the construction sector adjusts intentionally and frequently to accommodate the demand and supply state and the price condition in commercial and residential real estate markets. It was also observed that commercial and residential real estate markets share much similarity with regard to the permanent and transitory components in shocks. In the study of sources of shocks and multivariate persistence, the sectorspecific persistence measure is close to that of the univariate persistence, except that the persistence in construction is much more sensible, verifying the superior of the multivariate procedure. Moreover, the multivariate persistence analysis demonstrates the cross-effects of shocks between real estate and other economic and financial variables. It has been revealed that shocks from the housing market have the largest effect on the persistence in real estate, followed by the services sector, production sector, andc onstruction. Where as shocks in real estate company shares, i.e. the stock market investment of real estate, have relatively small effects on the persistence in real estate. This is one of the reasons that why real estate should be studied with the real world economic activities, although the stock market investment of real estate has been

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perceived as having close relationship with real estate, and has been used as a proxy to the latter in case of lack of information or a reliable indicator for the latter. The largest effects of shocks in the real estate market are felt on housing market, so the commercial and residential real estate markets have very close links. The effects of shocks on service sector are also substantial, followed by the production sector. However, the most interesting finding is with the construction sectorwithanegativecrosspersistencemeasure. Thatis,theoneperiodcovariance and the n(n→∞) period covariance have different signs. This suggests that a positive shock in the real estate market which increases construction output would eventually lead to the decease in construction output, or contraction in construction industry in the long-run. To a certain extent, the similar phenomenon is attributed to demand uncertainty and construction lags by Grenadier (1995). The effects of monetary shocks were examined in the final section. Monetary shocks appear to have most influential in housing market, stock market and the services sector, which can be grouped into a wide sense services sector in the economy. They have the least impact on production and construction sectors, or the supply side of the economy. Real estate, due to its fundamental links to financial markets and the real sectors in the economy, stands in between. Although real estate, the stock market investment of real estate, housing and the construction sector are linked in many ways, their response to monetary shocks are rather different, depending largely on whether they are on the demand or supply side of the economy.

8 Price discovery and study of real estate market efficiency This chapter investigates the price discovery mechanism in real estate investment markets. That is, price discovery in direct real estate investment and indirect real estate investment in the stock market. The analysis takes into account both the long-run and short-term relationships between these two investments and, therfefore adopts the cointegration approach. In real estate research, there are several other reasons to use the cointegration techniques The difficulties in compiling a reliable transaction driven real estate index have prompted many real estate researchers to use some sort of proxies to a real estate index. In the US, real estate investment trusts (REITs) are widely used for this purpose. In the UK, there is no exact REIT counterpart, and the share price/ total return index of real estate companies seems to be the only source with this merit. The US REITs and the UK real estate company shares are indirect investment in real estate as the investment is channelled to real estate via REITs or real estate company shares. Obviously the investment in real estate companies is different to the direct investment in real estate. A typical real estate company is usually geared, it has diversified activities, and its performance may diverge from the performance of the properties it manages and controls in the short term. Although indirect real estate investment is associated with direct real estate investment, real estate company share prices may outperform or underperform direct real estate investment. The ways in which the two investments are linked are subject to empirical investigations.

The price discovery mechanism From the market point of view, there is a price discovery mechanism between two related markets, and price discovery takes place in the more efficient market. Regarding real estate investment markets, the indirect real estate investment market of REITs or real estate company shares is obviously much more efficient compared with the direct real estate investment market. As it is fairly difficult to gather proper information in the direct real estate investment market, the use of information in the indirect real estate investment market via the price discovery mechanism looks necessary and prudent. Traditionally in real estate investment research the correlation structure (contemporary and lagged) between the returns on direct real estate and other financial and economic variables is examined. The correlation is usually weak and the real estate return is typically lagged for several periods, so not much information seemed utilisable from other sources, including the indirect real estate investment market. A long-run view differs from the correlation analysis on returns which results in information loss. Hence it would be possible to find a stronger price discovery mechanism in the long run between the two

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real estate investment markets, to help analyse and predict the direct real estate investment market. This chapter follows the cointegration framework, and further carries out tests on causality and price discovery in both the short and long run. Therefore the focus of investigation is the relationship between direct real estate investment and indirect real estate investment with specific reference to the price discovery between these two investment markets in the sense of Granger causality. However, it should be borne in mind that the Granger-type causality test is based on the concept of ‘predictability’ and not on the concept of ‘cause and effect’ in an acceptable philosophical sense and thus is more a technical treatment than a fundamental relationship. The outcome of tests should thus be interpreted with careful empirical judgements. While this chapter examines direct real estate investment in relation to indirect real estate investment with FTAP being a proxy, it should be borne in mind that, the aggregate of stock market investment represented by FTA has a cointegration relationship with real estate return indices as well, and the relationship appears to be stronger, as suggested by the statistics in Chapter 2. Nevertheless, it is of greater interest to make inquiry into the links between these two real estate investments, so the focus of this chapter is the two real estate investment markets instead of the real estate market and the general stock market. Prior to proceeding, it needs to be made clear what cointegration implies, since many have used cointegration to address the market efficiency hypothesis, as well as the longrun equilibrium of two or more economic time series. For example, Granger (1986) suggests that the prices of assets determined in an efficient market cannot be cointegrated. However, this view has been challenged by a few of researchers, e.g., Dwyer and Wallace (1992) state that market efficiency does not preclude cointegration, ‘With market efficiency defined as the lack of arbitrage opportunities, there is no general equivalence between market inefficiency and cointegration.’ They show cointegration can be consistent with market efficiency in various contexts in which the converse has been suggested. Although Dwyer and Wallace’s claim needs stricter scrutiny within the general financial analysis framework by at least clearly refereeing to the risk, it does, however, point out the danger of simply relating cointegration to market inefficiency which so prevails in much of the recent applied literature. Sephton and Larsen (1991) have also raised the concern in using the cointegration relationship as a criterion for market efficiency. Here, real estate’s attributes are explored within a cointegration framework for investigating Granger causality, price discovery and weak exogeneity only, without referring specifically to market efficiency issues. Therefore, the cointegration analysis is able to unveil more fundamental relationships among economic time series and concentrate on more essential issues. Conventionally, quite a few financial assets have positively correlated returns. However, their innovations or noise components or some shocks, which could originate from and/or be influenced by some common factors, will not necessarily be moving in the same direction. This may be one of the intuitive implications behind cointegration. As far as direct real estate investment and indirect real estate investment are concerned, it is reasonable to term direct investment in real estate as the underlying asset and the indirect investment in real estate (real estate company shares) as the derivative asset. Information is usually compounded in the derivative market, serving for its own

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purposes and partly for expectations in the underlying market; which in this case means price discovery comes from the indirect real estate investment market. In addition, it is expected that price discovery comes from more liquid and efficient markets which again supports the argument that the indirect real estate investment market, with less market frictions, has price discovery over the direct real estate investment. However, fundamentally, the returns on the derivative asset would not be independent of its underlying asset, suggesting that the returns on the two series representing underlying and derivative assets would not always diverge, at least in the long run (after considering the risk premia), even if, in the short term, there might exist no clear relationships. This is the rationale for assuming a cointegration framework in the investigation of real estate investment in the two markets. The relationships between those markets under concern will be further investigated in terms of causality. The underlying series, may or may not induce short-term dynamic changes in other series, however in the long run there would be disequilibrium information feedback to the underlying series. This hypothesis will be tested.

Empirical evidence in the real estate market A routine unit root test is carried out and the test statistics are reported in Table 8.1. There is a regime shift around the end of 1989 and the beginning of 1990 with JLW and FTAP all had a negative return in the second subperiod. Hence the statistics in Table 8.1 are reported for the whole period as well as for the two subperiods. Also the procedure for checking the stationarity in the data series should consider the structural change in the period. For this reason, Perron’s (1989, 1993) methodology is applied to the unit root test. The break date is chosen (a) as known (observed from the data series), and (b) inferred by the model. The lag length is determined by the Akaike information criterion (AIC). The models are outlined as follows. (8.1)

(8.2) where DUt = 1, if t > TB and 0 otherwise. D(TB)t = 1 if t = TB+1 and 0 otherwise. These two models are documented as Model (1) and Model (2) in Perron (1993) respectively. Variable DUt represents a change in the intercept, variable represents a change in the deterministic trend, and D(TB)t is the one time shock. The unit root test is carried out for JLW and FTAP in level and in difference respectively. In each of the data series, we present two sets of the testing results, one (the first line) for the break date TB being treated as known, and the other (the second line) for TB being decided by the model by maximising the t-statistic (absolute value) on the change in slope or intercept and with k being decided according to the AIC. When we say the break date is

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Table 8.1 Unit root test, Perron’s (1993) models TB JLW unsmoothed

89Q3 1

89Q3 1

JLW original

89Q4 1

89Q3 1

FTAP

89Q2 2

89Q2 2 ∆JLW unsmoothed

89Q3 6

89Q3 6 ∆JLW original

89Q4 1

89Q3 1 ∆FTAP

α

k

89Q2 1

89Q3 1

t (aic)

t(aic)

0.0010

–0.0998‡

0.0028

0.0240

.

(1.2043)

(–3.5453)

(0.9644)

0.0010

–0.0998‡

0.0028

0.0240

–0.4069

(1.2043)

(–3.5453)

(0.9644)

0.0010†

–0.0712‡

0.0019

0.9881

.

(2.253)

(–3.669)

(0.953)

0.0010†

–0.0712‡

0.0019

0.9881

–0.3676

(2.2787)

(–3.712)

(0.9636)

0.0086‡

–0.0259

–0.0299†

0.7413

.

(2.484)

(–0.296)

(–2.376)

0.0086‡

–0.0259

–0.0029†

0.7413

–2.181

(2.484)

(–0.296)

(–2.376)

0.0027‡

–0.0304‡

.

0.8224

(4.3729)

(1.9975)

0.0027‡

−0.0304‡

.

0.8224 –4.5205‡

(4.3729)

(1.9975)

0.0007‡

–0.0495‡

.

0.2569

(2.521)

(3.292)

0.0007‡

–0.0495‡

.

0.2569 –4.1236†

(2.621)

(−3.423)

0.0014

–0.1686‡

(0.893)

(2.801)

0.0014

–0.1686‡

(0.889)

(−2.820)

. –0.4492

–0.4069

–0.3634

–2.181

. –4.5205‡

. –3.9660†

. –7.0774‡

. –0.4492 –7.1257‡

t-statistics in brackets except for t(aic) and t (aic) which are separately listed. † significant at 5% level, ‡ significant at 1% level. t(aic) is the value of the t-statistic for testing α = 1 when TB is treated as known and k is chosen according to the AIC. t (aic) is the value of the t-statistic when TB is chosen to maximize the tstatistic on the change in slope or intercept and k is decided according to the AIC; critical values are based on Perron (1989, 1993). JLW and FTAP are reported as quarterly data starting in the second quarter in 1977 and ending in the second quarter of 1993. IPD is monthly data from January 1987

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120

to December 1992. The reason for not reporting monthly FTAP has been explained in the text.

known, we mean the time series reached a turning point (the peak in this chapter). It is quite interesting that, for the original JLW index, the model judges the break date was earlier than that viewed in the graph, implying the emphasis of the model on the slowing down of activity. Another point to mention is that, for indirect real estate investment, although the peak of the index was the second quarter 1989, the model again chooses the third quarter 1989 as the break date for the data in difference, the same data series are confirmed to be I(1) series. i.e., the hypothesis of a unit root is break date as for direct real estate investment. In general, as expected, all of the rejected in the difference but not in the level, by examining the value of t(aic) and t (aic). There is a deterministic trend in the JLW data series in difference, implying an increasing (real term) return on the JLW index during that period. However, the regime shift is only reflected in the change in intercept (a significant and negative ), not in the change in slope ( ). Regarding the FTAP index, a deterministic trend only appears in levels but not in the differenced series. This means there is no increasing return (real term) on the FTAP index during the period. This is reasonable as the shares of real estate companies are traded on a much more efficient stock market than in the direct real estate investment market, and consistent return patterns should not exist. The regime shift is also exhibited in FTAP from the third quarter of 1989. It seems helpful to have conducted Perron’s unit root tests, in that not only has the stationarity of the data in level and in difference been checked, but also the performance of the relevant indices and structural change in those indices has been analysed. In summary, the data series of JLW and FTAP are all confirmed to be I(1) series, i.e. they are non stationary in level and stationary in first difference. There is a big difference between the data series representing direct real estate investment and those for indirect real estate investment as the former are appraisal based and smoothed. The Johansen maximum likelihood procedure is used as it is more powerful than Engle–Granger two-step method in estimation and, inparticular, various long-run and short-term restrictions can be easily imposed and tested dynamically. Johansen’s model H3 (Johansen and Juselius 1990) is used which imposes no restrictions on intercept and assumes no trends in the model but allows for linear trends in DGP (data generating process). This is evident in the JLW and FTAP series. The test statistics are reported in Table 8.2 for the unsmoothed JLW with FTAP, and in Table 8.3 for the original JLW index with FTAP. In each table, a is for the test on the cointegration rank; b is for the test on the restrictions on α, a test for weak exogeneity of JLW and FTAP, or the exclusion of the long-run variables in one or both equations; and c is for the tests for the exclusion of short-term variables and all variables in these equations. The statistics in a and b are from running Malcolm, the dynamic Johansen approach. For simpler tests, c is based on Engle– Granger two-step static method. There is no much difference between Table 8.2 and Table 8.3, so, only the results for the unsmoothed JLW index and FTAP are explained and discussed. Both the max test and trace test confirm there is only one cointegrating vector between direct real estate investment and indirect real estate investment. The existence of cointegration reveals that the relationships between direct and indirect real estate investments are stronger than previously perceived. There at least exists a long-run price discovery mechanism to link

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the two real estate investment markets. This confirms the findings of Barkham and Geltner (1995) using a simple Granger causality framework. However, there is asymmetry regarding the causal relations in these two markets in the long-run, and the price

Table 8.2 Cointegration, long-run and short-term relationship, unsmoothed JLW and FTAP a. ,

max

and Trace test

Number of cointegration vectors i

–T.ln(1– )

–TΣln(1– )

max

trace(.95)

1

.24

16.46

14.07

19.14

15.41

2

.04

2.68

3.76

2.68

3.76

Critical values from Table 1 in Osterwald–Lenum (1992). Malcolm procedure reports two decimal digital points for max test and Trace test.

b. Long-run parameters and restrictions α

αi = 0 χ2

Sig level

JLW

1.0000

–0.1652

12.4978

0.0004

FTAP

–0.6272

0.1199

0.4144

0.5198

i = 1 for JLW and i = 2 for FTAP.

c. Long-run and short-term lagged ∆JLWt

ECMt–1 F-stat

Sig level

F-stat

Sig level

lagged ∆FTAPt F-stat

Sig level

All F-stat

Sig level

JLW

16.6316

0.0002

4.3861

0.0043

2.7185

0.0407

4.2976

0.0004

FTAP

2.3181

0.1344

1.9656

0.1149

1.6464

0.1780

1.2183

0.3063

discovery is from the indirect real estate market to the direct real estate market. The restriction on the long-run parameter α2 is valid with the test statistic being not significant at all in Table 8.2 b, implying the long-run error correction term does not enter the FTAP equation and does not help explain and predict the changes in the FTAP series. On the other hand, the restriction on α1, the long-run parameter in the JLW equation, is invalid and the test statistic is highly significant. This suggests the FTAP series causes the JLW series in the long run. The asymmetric feature in the long-run parameters also implies the information on the price disequilibrium between real estate and real estate company shares has been fully utilised by stock market participants and no abnormal returns can be made by developing a trading rule based on this information, while the cointegration indicates the fundamental association between these two kinds of investments. Due to the price discovery in the indirect real estate investment market which is disseminated to the

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direct real estate investment market, there seems to be some prediction ability of the model regarding direct real estate investment. However, whether the direct real estate investment market would be more efficient by utilising the long-run disequilibrium information is a complicated empirical matter, depending on the tradeoff between the transactions cost, the length of time taken to complete transactions, and the gain from acting on such kind of information. Table 8.2 c covers both the tests on the long-run and short-term parameters, with more lagged variables in difference included (up to lag 4, which are largely individually insignificant). Again, Granger causality from the FTAP series to JLW is evident, but that from JLW to FTAP is rejected, in the long-run parameters alone,

Table 8.3 Cointegration, long-run and short-term relationship, original JLW and FTAP a. ,

max

and Trace test

Number of cointegration vectors i

–T·ln(1– )

–TΣln(1– )

max

trace(.95)

1

.22

14.76

14.07

17.54

15.41

2

.05

2.79

3.76

2.79

3.76

Critical values from Table 1 in Osterwald–Lenum (1992). Malcolm procedure reports two decimal digital points for max test and Trace test.

b. Long-run parameters and restrictions α

αi = 0 χ

2

Sig level

JLW

1.0000

–0.1037

10.3524

0.0013

FTAP

–0.5762

0.1331

0.4034

0.5254

i = 1 for JLW and i = 2 for FTAP.

c. Long-run and short-term ECMt–1

lagged ∆JLWt

F-stat

Sig level

F-stat

JLW

16.8786

0.0002

8.4220

FTAP

2.2952

0.1362

1.6038

Sig level 0.0000 0.1883

lagged ∆FTAPt F-stat 2.5489 1.5817

Sig level

All F-stat

Sig level

0.0512

8.8473

0.0000

0.1940

1.1656

0.3375

the short-term parameters alone, and both. These indicate that the real estate stock market is not predictable through the differenced terms of direct and indirect real estate investments, while the changes in direct real estate investment are correlated either with the lagged variables in difference. Associated with long-run analysis, this implies that the real estate stock market is more efficient, as this market is more liquid than the direct real estate investment market. When this sub-market for real estate investment (consisting of

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123

direct and indirect real estate investments only) is considered in isolation, the results accept the efficient market hypothesis (EMH) in the indirect real estate investment market in both the weak and semi-strong forms, as no trading rules could be developed to achieve abnormal returns based on its own past history of returns or public available information (returns on real estate and the price disequilibrium between real estate and real estate companies shares). However, in the direct real estate investment market, the EMH is conclusively rejected. It has now been made clear that real estate company shares dominate direct real estate investment in the process of price formation, as we have expected given that information usually flows from more liquid assets. The weak exogeneity of the indirect real estate investment variables indicates the information flow is asymmetric between the direct and indirect real estate investment markets in the long run, as the equation for indirect real estate investment does not contain information on the long-run parameters while that for direct real estate investment does. The fact that direct real estate investment is Granger caused by indirect real estate investment in both the short term and long run while indirect real estate investment is not Granger caused by direct real estate investment does not necessarily mean that indirect real estate investment is more a ‘cause’than direct real estate investment. Rather, the weak exogenous nature of indirect real estate investment suggests it is not a fundamental underlying direct real estate investment. The information flow asymmetry, however, does suggest that indirect real estate investment precedes direct real estate investment. In this chapter, the price discovery mechanism in real estate investment markets was investigated. To put it more precisely, it was price discovery in direct real estate investment and indirect real estate investment in the stock market. The analysis takes into account both long run and short-term relationships between these two investments and, therefore adopts the cointegration approach. It has been confirmed that there exists at least one cointegration or long-run relationship between direct and indirect real estate investments. Prediction can therefore be improved, according to Engle and Granger (1987). Moreover, it has been further demonstrated that there exists asymmetry, i.e., the Granger causality is a oneway effect from indirect real estate investment to direct real estate investment, so that real estate company shares dominate direct real estate investment in the process of price formation, and indirect real estate investment is the main price discovery vehicle in real estate investment markets. These results suggest that the rate of return on direct real estate investment can be explained not only by the past rates of return on real estate company shares and on direct real estate investment itself, but also by the past disequilibrium term between these two investments. As both long-run and short-term parameters are not statistically significant for the variable representing indirect real estate investment, i.e., real estate company shares, the indirect real estate investment market appears informationally efficient – improvements in prediction can only be achieved in the direct real estate investment market. Yet, the predictability of real estate prices cannot simply be interpreted as evidence against market efficiency. The two investment markets have to be considered together, and no market is absolutely efficient or inefficient without taking into account of other related markets and operations. The fact that real estate company share prices largely follow a random walk without a predictable pattern means that nobody can persistently earn excess returns from investing in real estate company shares. If there were clear

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patterns in real estate company share prices then one could exploit the patterns with some strategies, such as selling high and buying low, in the stock market where transaction costs are relatively low and the market is relatively liquid. The forecasted price changes in real estate indices, and therefore, individual properties owned by one real estate company or institution, and their impact on earning power and profit, would have been already anticipated and incorporated in the share prices. It is also true that any trading profit or loss from a real estate transaction is fully reflected in the swift changes in the share prices of the company. Like in the circumstances for any other market which is doomed to be inefficient due to the built-in characteristics, efficiency can and has to be achieved with the help of another related market; and most players would be participating in both markets, or at least, few would isolate themselves in the former – the relatively inefficient market alone. The practice of UK fund managers appears to contradict this reasoning at first glance, as they rarely have large holdings in real estate companies. However, if we recall the discussions in Chapter 2 that real estate returns are not only cointegrated with real estate company returns represented by FTAP, but also with returns on all shares represented by FTA. Then the statistics suggest that the cointegration relationship appears to be stronger between real estate return indices and the latter than that between real estate return indices and the former. Therefore, fund managers can always invest in the stock market in which the real estate company sector is a small part, to achieve efficiency. In fact, as our results imply, this might be a superior way to achieve efficiency.

9 Cyclical fluctuations in the real estate market This chapter examines common cycles, with both coincident and phase-shifting attributes, in the economy involving real estate. Common cycle analysis is, in a sense, an extension of common trend analysis which has been popular in more than a decade and proved useful in investigating the long-run relationship between economic variables. Common cycles differ from common trends in that the phase matters in the former; whereas there is no role for it in the latter. With common trends and cointegration analysis, one of the properties can be stated as: if xt is cointegrated with yt, then xt is also cointegrated with yt–1. However, this does not hold in common cycle analysis. It is possible that xt and yt have no common cycle but xt and yt–1 share a common cycle. This nature is important because usually economic fluctuations and movement are not in the same phase. Without phase-shifting operators, any common fluctuations and common cyclical movement, other than those coincident, would be left undetected, and a possible economic relation would be overlooked. Real estate is one of the variables which have noticeable cyclical characteristic but may not be in the same phase as the aggregate economic fluctuations. Therefore, analysis on phase-shifting common cycles, in addition to coincident common cycles, would have profound implications in real estate research. In addition, as the usual time domain methods for phase-shifting relations are empirically difficult to implement, frequency domain analysis is also employed in the chapter. In fact, spectral analysis is particularly useful and easy to understand regarding cycles and their phase.

Identifying coincident and phase-shifting common cycles Tests on cycles Prior to common feature tests, the existence of cycles should be checked. It is comparable to the cointegration test in that one should verify the existence of a unit root in the time series before carrying on the cointegration test. If a time series has a unit root, or similarly has a cycle, then the time series can be described as having a feature, as in Engle and Kozicki (1993). In addition to unit roots and cycles, other features could be outliers, breaks, and so on. If two or more time series share a feature, then that feature may disappear in the combined time series, and the two time series are said to have a common feature, which is cointegration or the common trend when the feature is a unit root and a common cycle when the feature is a cycle or serial correlation in the time series. If one series has a feature and the other has not, then a testing procedure would put all the weight to the series which has no feature and zero weight to the series with the

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feature. Therefore, the time series without a feature, which is cycles or fluctuations here, should be ruled out from analysis. Table 9.1 reports the statistics on the individual time series. The Ljung–Box Q statistic for serial correlation includes lags up to 4, 8 and 16, with the last one being a quarter of the total observations. The purpose for using several lags is partly to see whether there is any possibility for stock market indices to have serial correlation, so they can be involved in common cycle analysis. The answer is a clear no. For the FTA series which represents the stock market investment in general, the significance level is 0.5131 for lag 4, 0.4349 for lag 8 and 0.4977 for lag 16. The respective numbers are 0.4977, 0.7506 and 0.5541 for the FTAP series, the index of real estate company shares, or indirect real estate investment. Gilts is also very much a white noise, the significance level is 0.9391, 0.8617 and 0.5005 for these lags. Therefore, no information in stock market indices can be used for common cycle analysis. This is one of the reasons that why one should rely on the real sectors in the economy for real estate research. In a sense, the stock market is simply too efficient to be useful for this kind of inquiry. In general, most sectors have serial correlation. Those having highly significant serial correlation is construction, housing, the money supply, the services sector, the coincident leading indicator and lagging indicator of the ONS (Office for National Statistics). Aggregation seems to reduce serial correlation (which can be regarded as to have common cycles in their component variables). e.g., manufacturing has significant serial correlation using Q(4) and Q(8), but total production only has marginally significant serial correlation with Q(4), the appropriate measure Q(16) is not significant at all. The serial correlation displayed in GDP is also rather weak. Three sets of Q statistic are provided for the JLW index, with each for the unsmoothed, original, and fully unsmoothed series. The unsmoothed JLW index displays a reasonable degree of serial correlation. The fully unsmoothed JLW index, although based on the random walk assumption, still has serial correlation or cycle, but the serial correlation is very little. In addition, its serial correlation structure is distorted. Therefore, the fully unsmoothed JLW index is excluded from common cycle analysis. The stock market indices simply do not have any serial correlation or cycles and cannot be used for common cycle analysis either. After those time series without significant serial correlation, or fluctuation, being ruled out (also just one leading indicator is used, as the difference between leading indicators is mainly in their phase), features and common features will be tested. Same as on the test of cointegration and common trends where one would have difficulty to confer some economic meanings to more than one cointegration vector, one would also possibly encounter difficulty in explaining more than one common cycle. Therefore, the feature test and common feature test are carried out in pairs between real estate and the other variables. Table 9.2. is to check whether the feature, which is serial correlation with the lagged variables in the pair which generates fluctuations, exists in real estate represented by the unsmoothed JLW index, and Table 9.3. is for the feature in other variables. The test results with the original JLW index are also provided as in Tables 9.4 and 9.5. There is no need to have a test using the fully unsmoothed index as the index itself has not got a feature. The test statistics used as criteria are F-statistic and χ2 statistic, and the lag length is chosen as two. The contribution of any further lags in most series is found trivial, in

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common with other studies, e.g., Engle and Kozicki (1993) and Engle and Issler (1995). It can be observed that the JLW series has a feature with all these series.

Table 9.1 Serial correlation in individual series Series

Q(4)

JLW-unsmoothed

20.4372

0.0004

22.8767

0.0035

38.3555

0.0008

JLW-original

70.4336

0.0000

74.3681

0.0000

107.9479

0.0000

JLW-fully unsmoothed

5.9759

0.2010

10.2941

0.2450

15.8439

0.3925

PDN

7.5302

0.1104

9.0012

0.3422

12.1354

0.7346

CO

34.3577

0.0000

44.1157

0.0000

50.7638

0.0000

SVC

17.7542

0.0013

24.1725

0.0021

33.8870

0.0056

NWT

59.9269

0.0000

61.2236

0.0000

81.3520

0.0000

GDP

1.8768

0.7584

12.0061

0.1509

25.5425

0.0608

114.3367

0.0000

158.0207

0.0000

165.7199

0.0000

M0

60.3252

0.0000

71.9651

0.0000

87.4877

0.0000

MNG

15.1925

0.0043

16.6892

0.0335

20.5253

0.1975

FTAP

1.9614

0.7429

5.0648

0.7506

14.5999

0.5541

FTA

3.2738

0.5131

7.9852

0.4349

15.3707

0.4977

GLT

0.7954

0.9391

3.9486

0.8617

15.3311

0.5005

UER

211.6895

0.0000

290.6080

0.0000

318.3295

0.0000

CC

130.8385

0.0000

145.6726

0.0000

249.0968

0.0000

LL

96.1702

0.0000

127.4169

0.0000

233.2890

0.0000

SL

102.7752

0.0000

119.2907

0.0000

232.8703

0.0000

LG

127.2216

0.0000

144.7604

0.0000

230.8134

0.0000

RESA

sig level

Q(8)

sig level

Q(16)

sig level

Table 9.2 Feature (cycles) tests – JLW has a feature involving other variables (with unsmoothed JLW index) Series

F-test

sig level

χ2 test

sig level

PDN

3.6726

0.0062

11.0799

0.0009

CO

3.1009

0.01578

9.0472

0.0026

SVC

4.1795

0.0028

12.6927

0.0004

NTW

4.5202

0.0017

13.7359

0.0002

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GDP

3.4765

0.0086

10.3800

0.0013

RESA

3.0061

0.0184

8.6990

0.0032

M0

2.8771

0.0227

8.2175

0.0041

MNG

2.6376

0.0334

7.2987

0.0069

UER

3.9667

0.0068

10.0212

0.0015

CC

2.4600

0.0562

5.3972

0.0202

Table 9.3 Feature (cycles) tests – other variables have a feature involving JLW (with unsmoothed JLW index) Series

F-test

sig level

χ2 test

sig level

PDN

3.6726

0.0062

11.0799

0.0009

CO

3.7880

0.0052

11.4326

0.0007

SVC

4.5192

0.0016

13.7834

0.0002

NTW

13.7728

0.0000

30.9195

0.0000

GDP

0.1868

0.9663

1.0217

0.3121

RESA

55.6031

0.0000

48.6621

0.0000

M0

9.8676

0.0000

25.7435

0.0000

MNG

6.2643

0.0001

18.5098

0.0000

UER

490.8699

0.0000

58.2426

0.0000

CC

254.0238

0.0000

56.6950

0.0000

Table 9.4 Feature (cycles) tests – JLW has a feature involving other variables (with the original JLW index) Series

F-test

sig level

χ2 test

sig level

PDN

11.3667

0.0000

28.0602

0.0000

CO

12.2946

0.0000

29.3434

0.0000

SVC

15.7999

0.0000

33.3834

0.0000

NTW

12.4889

0.0000

29.5992

0.0000

GDP

12.7949

0.0000

29.9935

0.0000

RESA

11.6308

0.0000

28.4363

0.0000

M0

12.9567

0.0000

30.1979

0.0000

MNG

11.2039

0.0000

27.8239

0.0000

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UER

14.2936

0.0000

28.4420

0.0000

CC

13.0109

0.0000

26.9294

0.0000

When the feature in other variables is considered, all but GDP has a clear feature. GDP is still included for analysis, because it has small serial correlation up to very long lags. When the original JLW index is applied in the analysis, the feature test statistics for the other variables become slightly smaller but are largely unaffected, so the influence of the original JLW series on the other is slightly smaller than that of the unsmoothed JLW series. The feature test statistics in JLW have increased considerably due to the much larger amount of serial correlation in the original JLW series, which reduces the relative importance of the role of the other variables in the feature for JLW. The comparison between the two sets of the results is interesting that large serial correlation in the JLW series can only influence the feature in JLW itself but not in the other variables. That the unsmoothing is sound can be viewed

Table 9.5 Feature (cycles) tests–other variables have a feature involving JLW (with original JLW index) Series

F-test

sig level

χ2 test

sig level

PDN

3.4064

0.0094

10.1894

0.0014

CO

3.6614

0.0063

11.0420

0.0009

SVC

4.3976

0.0019

13.4601

0.0002

NTW

12.4577

0.0000

29.5584

0.0000

GDP

0.2493

0.9384

1.3536

0.2447

RESA

55.0949

0.0000

49.2556

0.0000

M0

11.4016

0.0000

28.3238

0.0000

5.4155

0.0004

16.4079

0.0001

UER

565.4358

0.0000

59.4209

0.0000

CC

254.5229

0.0000

57.5925

0.0000

MNG

from another point: there is increased influence of JLW on the other variables, and increased influence of the other variables on JLW. Unit roots and cointegration Routine unit root test is carried out as well. The existence of a unit root in the variables in levels can be confirmed and a unit root in the variables in the first difference can be ruled out generally. The cointegration relation between real estate and other variables is verified by Malcolm, a Johansen testing procedure with RATS. The results are briefly reported in Table 9.6. Leading indicators and the unemployment rate are stationary, so

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they are excluded from the table. All the other variables are confirmed to have the cointegration relationship with real estate and there is only one cointegration vector in each pair between real estate and other variables. The selection of the cointegration models is mainly based on visual inspection of the graphs, as Johansen and Juselius (1992) did. In the following common cycle analysis, the error correction term is included when there is a cointegration relation in the pair, and no error correction term otherwise. In fact, only the analysis of real estate’s relations with the unemployment rate and the leading indicator does not have an error correction term, as these two variables are stationary themselves and there exists no error correction mechanism between them and real estate. Only the unsmoothed JLW index is used in the cointegration analysis. Once a cointegration relation is confirmed by the unsmoothed real estate index, that relation should also exist for the original index, and vice versa. The confirmation of a cointegration relation with these variables means that real estate shares a common trend with them, and it is rather unusual if real estate does not move together with most economic and financial activities in the long-run. In the following, it will be revealed that the situation is different for cycles and common cycles.

Table 9.6 Cointegration and common cycles One cointegration vector max a

PDN b

CO

SVC

c a

NTW

GDPd RESA

a

M0c d

MNG

Two cointegration vectors

trace

max

trace

15.83

23.32*

7.49

7.49

19.83†

26.54‡

6.71

6.71

16.78†

16.97†

0.19

0.19

15.70*

21.66†

e

5.96

5.96e

23.45†

32.00‡

8.55

8.55

18.42†

19.40†

0.98

0.98

15.70†

16.87†

1.17

1.17

18.03*

27.12‡

9.09

9.09

* significant at 10% level, † significant at 5% level, ‡ significant at 1% level. a. model H5: with unrestricted constant and trend; b. model H2: with restricted constant and no trend; c. model H3: with unrestricted constant and no trend; d. model H4: unrestricted constant and restricted trend. e. the statistic is significant with this model; other models reject the hypothesis of two cointegration vectors, but marginally accept the hypothesis of one cointegration vector.

Common cycles The results from common feature or common cycle tests are reported in Table 9.7, using the unsmoothed JLW series to represent real estate investment. Both the existence of coincident common cycles and one phase-shift common cycles are tested. The instrumental variable (IV) method is used to estimate the coefficient in a relation that (∆y1t – ∆y2t) has no cycles. This means (∆y1t – ∆y2t) is the white noise residual and has

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131

no serial correlation with lagged ∆y1t and ∆y2t, and the cointegration residual at t–1 if y1t and y2t are cointegrated. The coefficient from direct regression of ∆y1t on ∆y2t would be biased, as ∆y2t is correlated with the current period innovation. The instruments used are the first and second lags of the JLW series and the other variable in the pair, plus the first lag of the cointegration vector if there is a cointegration relation. In the case of phaseshifting common cycles, the instruments are the second and third lags of the relevant variables, plus the second lag of the cointegration vector when the two variables in levels are cointegrated. 2SLS (2 Stage Least Squares) is a similar method. There are four statistics reported. , the coefficient of the other variable (∆y2t) in the regression (the coefficient of JLW is set to one); a significant suggests a relation or correlation, though may not necessarily a common cycle relation, exists between real estate and ∆y2t, Both F-test and χ2 statistics are used to check the existence of common cycles, or the cancelation of cyclical components, which is suggested by the insignificant test statistics. The combined series is also examined against the serial correlation with the Ljung–Box Q statistic – no correlation with the lagged variables is equivalent to no serial correlation in the combined series itself. First looking at the coincident common cycles. JLW’s common cycle feature is clearly found to be with the house price represented by the NTW index, the services sector (SVC) and the manufacturing sector (MNG), with very low insignificant levels for F, χ2 and Q, and a very significant . Real estate seems to be more cyclical, i.e., the magnitude of its cycles are larger, than the service sector with of 2.5033. Put it another way, the magnitude of cycles in real estate is about two and a half times that of the cycles in the services sector. But the cyclical fluctuations in real estate are less that those in the housing market, suggested by the coefficient of 0.7103. The magnitude is about the same for real estate and the manufacturing sector. The existence of common cycles between real estate and the money supply (M0) and between real estate and total production (PDN) is marginally confirmed. In the case of total production, the Ljung– Box Q statistic is the criterion, but recall that the PDN series is much closer to being a white noise than the MNG series, partly due to the aggregation, this result should be viewed with caution. With the money supply, only the F statistic marginally accepts the existence of common cycles, and real estate is relatively less cyclical than the money supply variable. There is no common cycle feature found between real estate and the GDP series. This is not to rule out the cyclical co-movement of real estate with GDP because, the aggregation in GDP has reduced or phased out the fluctuations in the GDP index in general, and the GDP series is rather white in this given short period in particular. In a sense, investigations at the sectoral level is helpful, not only in the sectoral analysis itself, but also in inferring implications for some economic aggregates. Quite beyond imagination, if not surprisingly, real estate shares no common cycles with the construction sector, though the existence of common trends or long-run co-movement between them is so evident. Common cycle feature remains non-existent even if stock under construction, a derived variable which has profound long-run relationship with real estate, is used in the test. The series of coincident leading indicator, GDP and total production, though lack a common cycle feature with real estate, have a very clear correlation with real estate. One should notice that, theoretically and empirically, the conditions for common cycles are rather less possible to meet than those for common trends or cointegration, as the former requires that the components in two series are

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132

proportional at every frequency of their cycles, whereas in the latter, merely the zero frequency component plus some elements very close to zero frequency (in fact it is these elements which would decide a cointegration relation, otherwise two I(1) series would always be cointegrated). Therefore, while many economic time series variables have common trends and are cointegrated, not so many have common cycles. Put it another way, there are many different paths to reach a certain level of activity. Any path different from a pure random walk path is cycles or fluctuations. So, there could be many different cycle patterns even two time series are bound to move together in their levels. For those sectors with which real estate has no coincident common cycles, inquiry is made on whether there are phase-shifting common cycles. The existence of coincident common cycles does not preclude phase-shifting common cycles, as phase-shifting common cycles (of order one) cancel (a majority of) cyclical

Table 9.7 Common feature tests – coincident common cycles using IV method Series PDN

CO

SVC

F-test 1.0038

18.5485

(0.0465)

(0.0795) (0.0339)

(0.2928)

–0.0814

3.6716 9.5803

42.8476

(0.6448)

(0.0062) (0.0020)

(0.0003)

0.7650 2.2982

15.6771

(0.5791) (0.1295)

(0.4757)

1.0086 3.0500

19.7933

(0.4217) (0.0807)

(0.1800)

2.8848 8.8887

23.8026

(0.0222) (0.0029)

(0.0939)

3.1168 4.0808

36.6884

(0.0152) (0.0434)

(0.0014)

1.9423 5.1160

29.4691

(0.1024) 0.0237)

(0.0210)

1.5394 0.2551

19.7070

(0.1931) (0.6135)

(0.2337)

3.3809 9.0456

41.9067

(0.0152) (0.0026)

(0.0004)

2.9531 4.1912

34.3338

(0.0278) (0.0406)

(0.0049)

2.5033

0.7103 (0.0001)

GDP

2.4395 (0.0087)

RESA

0.0501 (0.3460)

M0

0.7684 (0.0095)

MNG

0.9347 (0.0151)

UER

0.0010 (0.0306)

CC

Q

2.0996 4.5010

(0.0000) NTW

χ2 test

0.0009 (0.2604)

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133

components but leaves an MA(1) in its residuals. While a test on the existence of phaseshifting common cycles is just a little bit more difficult than that on coincident common cycles, the test on phase lead or lag is empirically ambiguous or infeasible, as there still exists an MA(1) in the residual, and viewing a graph with the two time series involved may be a better alternative. However, one may resort to frequency domain analysis to deal with this problem. In fact, spectral analysis is particularly useful and easy to understand regarding cycles and their phase. The usual time domain results are reported in Table 9.8. It seems that there is no clear pattern emerged. Only GDP appears to have possible common cycle components after one phase shift suggested by the F-test and the Ljung–Box Q statistic. This possible phase difference between real estate and GDP should also come from some of the GDP sectors. Construction is one which still has no common cycles with real estate but coherence has increased after one phase shift, viewed by the increased, but still significant, test statistics. The production and services sectors may also have some phase differences with real estate. As mentioned before, it is not easy to tell leads from lags in these pairs, and it is possible one series has leads over the other at, say, lower frequencies but lags at higher frequencies. With phase shift common cycles of order one, the residual is MA(1), so longer lags in variables are also used and tested (with two lags, the components to be excluded are lags 2 and 3, and the remaining ingredient

Table 9.8 Common feature tests. Phase-shifting common cycles using IV method (two lags) Series PDN

CO

SVC

NTW

GDP

RESA

M0

MNG

F-test

χ2 test

Q

1.0717

2.2909

5.2909

16.9678

(0.0730)

(0.0586)

(0.0214)

(0.3877)

0.0069

3.3400

7.4187

40.4072

(0.9715)

(0.0107)

(0.0065)

(0.0007)

2.5538

1.0101

3.3091

15.3678

(0.0000)

(0.4210)

(0.0689)

(0.4979)

0.7768

0.7530

2.0872

19.0690

(0.0003)

(0.5876)

(0.1485)

(0.2106)

2.8607

1.7042

3.6462

21.7875

(0.0055)

(0.1497)

(0.0562)

(0.1502)

0.0492

3.1666

4.6833

35.7926

(0.3649)

(0.0142)

(0.0305)

(0.0019)

0.7827

2.5916

7.7120

29.0958

(0.0139)

(0.0360)

(0.0055)

(0.0233)

0.7922

2.0476

2.3817

21.7709

(0.0424)

(0.0868)

(0.1228)

(0.1507)

Econometric analysis of the real estate market and investment

UER

CC

134

0.0010

2.8542

7.4330

40.7596

(0.0325)

(0.0322)

(0.0064)

(0.0006)

0.0013

3.0516

4.7109

32.2767

(0.1427)

(0.0244)

(0.0300)

(0.0085)

includes innovations in current period and at lag one). According to Table 9.9, real estate and the unemployment rate seem to have some common cycle elements with one phaseshift – the F-test statistic is not significant at five per cent level. The unemployment rate, though regarded and should be a stationary variable, is in fact very persistent and has some kind of upward trends, so further test, e.g., with even longer lags to accommodate its serial correlation at higher orders, is of no much help. With regard to leading indicators, they all have substantial higher frequency components to (more than) reflect economic fluctuations. These higher frequency components would not be cancelled out in most of their combinations with economic and financial time series. In this sense, common cycle analysis in the frequency domain would be helpful and supplementary to the analysis in the time domain.

Frequency domain analysis and presentation The frequency domain results are better viewed with the coherence and the phase graphs. The only research on real estate using a frequency domain method is Barras and Ferguson (1985), which examines the spectra of real estate regarding its different cycle components, or relative magnitude of cycles at different frequencies. This chapter further investigates the cross-spectra of real estate with other economic

Table 9.9 Common feature tests. Phase-shifting common cycles using IV method (four lags) Series PDN

CO

SVC

NTW

GDP

F-test

χ2 test

Q

0.9939

1.5126

3.9789

16.1872

(0.0753)

(0.1714)

(0.0461)

(0.4400)

0.2151

2.6923

7.1684

36.1416

(0.1783)

(0.0130)

(0.0074)

(0.0028)

2.5616

1.8927

6.0528

15.2049

(0.0000)

(0.0764)

(0.0139)

(0.5097)

0.8059

1.5290

3.0898

15.0102

(0.0005)

(0.1657)

(0.0788)

(0.4507)

2.4859

1.6058

5.5996

22.4413

(0.0002)

(0.1412)

(0.0180)

(0.1295)

Cyclical fluctuations in the real estate market

RESA

M0

MNG

UER

CC

135

0.0740

2.1578

3.9322

31.6439

(0.1657)

(0.0427)

(0.0474)

(0.0072)

0.7210

2.5962

12.1518

28.6301

(0.0335)

(0.0161)

(0.0004)

(0.0266)

0.9406

1.1166

7.5964

16.6337

(0.0135)

(0.3701)

(0.0058)

(0.4097)

0.0009

1.8123

6.6421

39.0673

(0.0396)

(0.0979)

(0.0100)

(0.0011)

0.0011

2.0460

5.3291

32.5282

(0.2201)

(0.0605)

(0.0210)

(0.0085)

activities, emphasising common cycles and their phases. The magnitude of crossspectrum is coherence and the imaginary part is phase. Coherence is about how much in common of two time series, and phase is about the lead/lag relations. The advantages of using these two frequency domain statistics are obvious: they reveal and show the proportions of common components in two time series at each frequency or each cycle, and the phase lead/lag in the same way. In Fig. 9.1 four examples are depicted to show typical leads ranging from one phase lead to four phaselead, using one time series (GDP indifference) against its own lags. The lefthand side axis is for coherence and the right-hand side axis for phase. Coherence is symmetric about the vertical axis and phase is symmetric about the origin point, therefore only the right half of the graph is displayed. The horizontal axis ranges from zero to πf (the other half from–πf to zero) with 2πf being one cycle (one quarter in this case). At the half point of the horizontal axis the frequency is lower at f /2 and a complete cycle is in two quarters, at the frequency of f /4 the cycle is annual, and so on. A value of one for coherence at a particular point means the two series are altogether in common at that frequency or cycle, and if coherence is one over the whole spectrum then the two series are common at all frequencies or cycles. If there is no phase lead/lag, the line for phase would be zero over the whole range in horizontal axis. If there is a strict one phase (period) lead at every frequency, then it would be a linear line as depicted in Fig. 9.1 a. A value of

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Figure 9.1 Coherence and phase – an example (GDP with lagged GDP) one means 180°(π) degree lead in half cycle (as the other half is not displayed). A time series has perfect coherence with itself so the value of coherence is one over the whole spectrum. The phase statistic is one (180°) lead for the quarterly frequency in half quarter, equivalent to 360° in one quarter; at the half point on the horizontal axis, the phase is 0.5 (90°) lead for the semi-annual frequency that is also one quarter (1/4×2 quarters ×2). So, as long as the line for phase statistic is linear, every frequency component will have the same lead; if the line is not linear, then some frequency components would have longer or shorter leads than others, and would not be a purely, say, one phase lead. Fig. 9.1 b is for two phase lead, its coherence is the same, the phase is twice as big as in Fig. 9.1 a, as–1isthe same as +1 (360° +(–180° = 180°)), and the negative part of the phase line can be continued upwards at the point (0.5f , 1). In Fig. 9.1 c, the phase is three times as big as that in Fig. 9.1 a, and in Fig. 9.1 d, four times as big. As can be seen, the coherence becomes more distorted, as the series is not ideal (from –∞ to +∞ in time). With these basic ideas, real estate is analysed in the frequency domain with other economic variables regarding their common cycles and phase leads/lags. First looking at the graph of JLW with GDP in Fig. 9.2. There is about 80 per cent coherence in most of the cyclical components from quarterly to semi-annual cycles, but the cycles around the annual frequency have little in common in these two series. Real estate and GDP are in the same phase over nearly the whole spectrum except real estate lags in the annual cycle. As the phase statistic is not on a straight line as in Fig. 9.1a, they are not purely coincident nor phase-shift with a single order, so time domain techniques are not effective (there would be many statistics for different leads, few of them would be

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statistically significant individually, while a possible joint significant statistic dose not tell anything about which leads and the how big is the lead at each cycle). It has been seen that the time domain analysis on common cycles between real estate and GDP suggested that there probably exist such characteristics. The coherence of real estate with construction is about 0.5, with no regular phase patterns, as shown in Fig. 9.2b. The higher coherence happens with the quarterly cycle which seems to be in the same phase, and the annual cycle with rather large leads (about three quarters to one year at this frequency). Overall, no single order phase shift (and even two or three combinations) can describe their phase relations, resulting a straightforward rejection of any common features in cycles in the time domain. In fact, real estate and construction do share some common cyclical movements or fluctuations. Real estate and housing have higher coherence at the lower frequencies, close to 0.8 at around the bi-annual cycle, and the value is about 0.5 at the higher frequencies around the quarterly cycle. They lack coherence at about the annual frequency, and large phase difference also occurs at this frequency. With the services sector, real estate has large coherence of about 0.8 at both the higher and lower ends of frequencies and the two series are in the same phase at these frequencies. There is a three-quarter lead or an annual lead (if one compares with Fig. 9.1b–9.1d) in the three-quarterly and annual cycles, but the value of their corresponding coherence is relatively small. The patterns for JLW with the production and manufacturing sectors are similar, and again, real estate and these sectors are in the same phase at the lower and higher ends of the spectrum, and some three-quarter leads at the annual and bi-annual frequencies. As the services and production sectors constitute a large part of GDP, real estate’s coherence and phase relations with these sectors should be reflected in the relations with GDP as well. In fact, a one-quarter lead in an annual cycle is equivalent to a three-quarter lag. If housing is further considered, real estate’s phase relations with GDP are reasonably consistent with the mixture of these sectors, and so does the coherence. One interesting and common feature found is that real estate seems to have large discrepancy with almost all the other sectors in the cycles with the annual frequency, with less coherence and larger phase leads/lags. Real estate’s coherence with the unemployment rate is found largely at quarterly or semi-annual frequencies, beyond that, there is little in common. Real estate seems to lag behind unemployment for about a third of a complete phase, amounting to a month with the quarterly data; this is by no means quite accurate when the quarterly data have to be used. A large phase difference at the semiannual cycle does not count much as the coherence at that point is so small. With the coincident leading indicator, real estate appears to be in the same phase, except in the very low frequency cycles (annual and lower). But the phase lag closing to the vertical axis just accounts for a very small portion, when the spectrum is considered to be continuous, not discrete. Since these two series are (regarded) stationary in their original form, a big difference with all other series emerges at the zero frequency: the coherence is about zero. In Fig. 9.2a–9.2f, the coherence

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Figure 9.2 Coherence and phase – real estate with other variables

138

Cyclical fluctuations in the real estate market

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at the zero frequency (the unit root circle) is about their cointegration vector (1, ), with being close to the coherence at the zero frequency. If coherence and phase are analysed with the variables in levels, e.g., JLW with NTW, then the coherence is about 0.9 (the value at the zero frequency in Fig. 9.2d) and the phase is zero over the whole horizontal axis. This also holds when the pair is JLW and the lagged NTW, and simply means that if one series is cointegrated with another series, then it is also cointegrated with the lagged series. Therefore, phase does not play a role in cointegration but it matters in common cycle analysis. This comparison may not be appropriate but does point out that cointegration, or the verifying of a cointegration relationship, is not always necessary and rarely reveals something, at least in many studies carried out in the last decade. In this chapter, both coincident and phase-shifting common cycles were examined in the economy involving real estate. Common cycle analysis on its own is an extension of common trend analysis. But common cycles differ from common trends in that the phase matters in the former, therefore analysis is more complicated, and sometimes, rather difficult. When these attributes and trend-cycle behaviour are investigated together in a dynamic system, as proposed in Chapter 5, the study of this chapter is a further advancement of the previous two chapters, especially Chapter 7. The investigation has been reinforced by the frequency domain analysis method, which is more effective in presentation when phases are concerned. It has been found that, first, real estate fits into the business cycle well and has the long-run comovement with most parts of the economy. It is because real estate is not a purely financial market investment. It is mainly an investment in production, trading, work and storage spaces and capacity from the point of view of most companies or industries. Due to the reason that amounts of available real estate cannot be increased or reduced quickly and easily, the magnitude in real estate cycles is larger than that in the business cycle for the economy as a whole and for some sectors. Second, it is once again observed that commercial real estate and residential real estate have close links with regard to common cycles. Third, real estate also has common cycles with the services sector and manufacturing sector, but their magnitudes of cycles are of more interest. Cycles in the real estate market are larger than those in GDP and the services sector, but are of the same size as those in the manufacturing sector. This suggests that adjustments in the real estate market are sluggish than those in the economy in general, and in the services sector, the most liquid part of the economy, in particular. Fourth, the size of cycles in real estate is smaller than that in the house price, which could be attributed to the existence of an indirect investment market for commercial real estate which reduces the cycles in the direct real estate investment market. These results and findings are also confirmed by frequency domain analysis.

10 Summary This book has examined UK real estate investment markets in an economic and econometric analytical framework. The book starts from a descriptive analysis of UK real estate investment markets and their performance over the last two decades. The changing patterns of real estate was studied and the role played by the institutions and real estate companies in the course analysed. Attention has also been paid to the relationships between real estate and other economic and financial sectors. Preliminary but broad statistical figures provided in Part I reveal that the fluctuations in real estate is linked to its economic environment in a variety of ways. This suggests that, on the one hand, the research should not restrain itself to the real estate sector only; and on the other hand, the unique characteristics of real estate should be addressed and investigated more effectively. It has been made clear that further scrutiny is required to gain insights into the crucial relationships and underlying mechanism in the real estate market. This would be achieved by utilising and developing more constructive economic and econometric models and analytical techniques pertinent to the research. These analyses, together with the review on the recent developments in the real estate research literature, outline the issues and set the framework for advanced studies in the following parts of this book. Part II studied the issues on economic fluctuations and real estate research. Econometric models and analytical approaches are presented, extended and developed. The underlying message is to address real estate in an integrated economic system implied by the multivariate time series modelling strategy. Fluctuations and the dynamic behaviour in real estate investment markets are prominently reflected in cycles, trends, and their response to shocks; and the common factors which real estate shares with other economic and financial sectors in both the short term and the long run. To investigate such issues, time series attributes, characteristics and modelling were explored in the fields of persistence in statistical measures and with economic sense and explanations, trend-cycle decomposition and their relative contributions in responding to shocks, and common factors among trends and cycles. This part has, in many ways, extended the current literature in the study of economic dynamics and developed the econometric modelling framework and strategies which will be utilised to make empirical inquiry into UK real estate markets in the later chapters. Part III was an empirical study on the dynamic behaviour of real estate. This part extended real estate research to such areas outlined in part I which are either new or remain important and unsolved, and applied both the existing econometric approaches and the approaches developed in the previous chapters to the inquiries. The critical issue of smoothing in the appraisal-based real estate return indices was dealt with, and the actual smoothedness in UK real estate return indices of JLW and IPD was decided, in Chapter 6. This issue has the highest priority, though it may not be the most important, as any study employing these indices would be thought of as unreliable as the indices themselves if some kind of remedy has not been taken. This chapter, unlike

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most previous studies, exploits the information embedded in other variables which have a fundamental economic and financial relationship with real estate. Two multivariate approaches are developed which are informationally more efficient and, therefore, superior to the univariate unsmoothing techniques. Applying these unsmoothing procedures to UK real estate return indices, appropriate smoothing factor has been found for the JLW and IPD indices, which is about 0.58 for the former and 0.41 for the latter judged by the implied cointegration approach. These smoothing factors are then used to correct for smoothing in the JLW and IPD indices, and the unsmoothed indices are constructed and used in the studies in the later chapters, leading to a number of empirical findings in the following. Direct and indirect real estate investments share little similarity in their response to shocks and their long-run persistence patterns. Trend-cycle behaviour of real estate cannot be fully understood by examining its relationships with real estate company shares alone. These findings are the results from examining real estate’s univariate attributes and characteristics in the first two sections in Chapter 7, which are concerned with the permanent and transitory components in shocks in real estate return series and the patterns in their response to shocks, and their relative contributions to the total deviation from the mean return. These attributes and characteristics are compared with those of other economic and financial activities to reveal the difference, similarity and link between them. It has been confirmed that, although indirect real estate investment, which is investment in real estate company shares in the UK and REITs (Real Estate Investment Trusts) in the US, is perceived as a proxy to direct real estate investment, they share little similarity in their response to shocks and their long-run persistence patterns. Real estate investment, as represented by the JLW index, has a long-run persistence pattern similar to that in many sectors in the economy. Whereas indirect real estate investment, as represented by the return series of FT’s real estate company sector, understandably, has all attributes close to those for a white noise. Therefore, to examine real estate’s relationships with real estate company shares alone is not able to show the whole picture about real estate’s trend-cycle behaviour. Real estate’s response to shocks is found to have a compounding attribute with the effect being felt most momentously in about three years time, then reduces to that of a random walk. Smoothing in the JLW index does not change the persistence pattern, but it does change the magnitude of the persistence measure at its peak, though in a not sensitive way. This suggests that smoothing is not a too big issue in the long run. Taking the long-run attributes of real estate investment into account, smoothing may not be a big issue overall which may in turn partly explain why the profession copes with these indices well. Evidence in the residential real estate market also seems to support these findings. Real estate bears some characteristics pertinent to the real sectors in the economy and some other characteristics pertinent to financial market investments, with regard to the permanent and transitory components in shocks. Although real estate has a similar longrun persistence pattern with the real sector of the economy, its transitory, or cycle component, is profoundly smaller than that in the latter. Instead, real estate’s transitory component is as small as being negligible beyond one year’s horizon. This means that cycles decay quickly and stochastic trends dominate. However, this is by no means to suggest that real estate does not fluctuate significantly. With less transitory component, or

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stationary element in statistical terms, real estate investment carries high uncertainty. By comparison, there is more transitory component in most economic activities. Regarding real estate related sectors, residential real estate and commercial real estate again share similarity in their trend-cycle decompositions. By contrast, construction output has substantial cycle component, reflecting that the construction sector adjusts intentionally and frequently to accommodate the demand and supply state and the price condition in commercial and residential real estate markets, though not always in the right way and right direction. Persistence in real estate is not influenced most by shocks in the indirect real estate investment market, as has been revealed by multivariate persistence analysis in the last section of Chapter 7. The largest effect on the persistence in real estate is caused by shocks from the housing market, followed by those in the services sector, production sector and construction sector. In a word, shocks in real economic activities contribute more to the long-run persistence in real estate than those in financial markets, even if it is the financial market for indirect real estate investment. Reciprocally, shocks in real estate have largest effect on the housing market, once again confirming that a close link exists between commercial and residential real estate markets. The impact on the services, production and construction sectors is also substantial. Real estate has a mixed attribute in responding to monetary shocks in the longrun. While the demand side of the economy is influenced by monetary shocks to a great degree and the supply side of the economy is not subject to monetary shocks in the longrun, real estate is on neither side due to its fundamental links to both the real economy and financial markets. Real estate company shares dominate direct real estate investment in the process of price formation and indirect real estate investment is the main price discovery vehicle in real estate investment markets. Although direct real estate investment and indirect real estate investment differ in many ways in their response to shocks in the long run, their composition of trend and cycle components and their evolution paths over investment horizon, these two investments are fundamentally linked. Moreover, their fundamental relationship displays prominent asymmetry. The findings in Chapter 8 have revealed that the rate of return on direct real estate investment can be explained not only by the past rates of return on real estate company shares and on direct real estate investment itself, but also by the past disequilibrium term between these two investments. The results of analysis also re-affirm that the return on indirect real estate investment generally follows a random walk, an attribute found in the previous chapter which fails to deal with some aspects of real estate’s dynamic behaviour studied in that chapter. These results suggest that the indirect real estate investment market is informationally efficient, whereas prediction can be improved for returns on direct real estate investment. However, the predictability of real estate prices can not simply be viewed as evidence against market efficiency. The fact that real estate company share prices largely follow a random walk without a predictable pattern means that nobody can persistently earn excess returns from investing in real estate company shares. The forecasted price changes in real estate indices, and therefore, individual properties owned by one real estate company or institution, and their impact on earning power and profit, would have been already anticipated and incorporated in the share prices. It is also true that any trading profit or loss from a real estate transaction is fully reflected in the swift changes in the

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share prices of the company. Due to low liquidity and long-time period to complete a transaction, the efficiency has to be achieved with the help of an indirect real estate investment market. Ultimately, it is shareholders, not companies, who have made gain or loss. Real estate fits into the business cycle well and has a long-run comovement with most parts of the economy, as has been confirmed by the research in Chapter 9. Real estate is not a purely financial market investment. It is mainly an investment in production, trading, work and storage spaces and capacity from the point of view of most companies or industries. With this nature, real estate has found its place in the economy. Due to the reason that amounts of available real estate cannot be increased or reduced quickly and easily, the magnitude in real estate price changes or real estate cycles is larger than that in the business cycle for the economy as a whole and for some sectors. Real estate, represented by the JLW index, has clearly shown to have common cycles with the housing market. That is, price changes in real estate and housing are proportional at every lag and at every cycle frequency, once again confirming close links between commercial and residential real estate markets. Real estate also have common cycles with the services sector and manufacturing sector. The magnitudes of cycles in the real estate market are larger than those in GDP and the services sector, but are of the same size as those in the manufacturing sector. This suggests that adjustments in the real estate market are sluggish than those in the economy in general, and in the services sector, the most liquid part of the economy, in particular. However, the size of cycles in real estate is smaller than that in the house price, which could be attributed to the existence of an indirect investment market for commercial real estate which reduces the cycles in the direct real estate investment market. Frequency domain analysis, which emphasises similarity in each cycle instead of each lag and deals with phase differences, also confirms the above findings. Studies in this book have made a number of contributions not only to real estate research, but also to the econometric analytical methods. While each of these elements has its own merits and makes contributions to their individual area, the research has high integrity and a central theme. Real estate has been portrayed as an integrated part of the economy on which all investigations have focused. With this theme this study has been guided to reveal the mechanism governing the interactions between real estate and the other sectors in the economy, real and financial, and to examine the ways in which real estate influences and is influenced by the economy. To achieve the research objectives, the econometric analytical methods of multivariate persistence, multivariate unsmoothing procedures, and phase-shifting common cycles have been developed, and applied to the empirical inquiry in this book. Nevertheless, research in the book has a few limitations. By addressing these limitations it is hoped that new directions and focuses of further research will emerge as logical developments of this study and improvements in modelling real estate market behaviour and fluctuations can be achieved more effectively. From the very beginning of the book it has been stated clearly that the objectives were to investigate real estate market behaviour and to investigate it in a framework of macro dynamics involving business cycles, market efficiency and rational expectations. These suggest that the study should have a macro analysis focus. While these objectives have been duly achieved, they are limited to the macro aspects of the real estate market. In

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other words, this book has been entirely based on macroeconomic analysis of real estate performance and dynamics. While it has been acknowledged that the analysis of market microstructure and institutional behaviour helps lay down foundations for macroeconomic analysis, a purely macro study may lose some intuition and consequently the results may not have much practical appeal. Nevertheless, most micro and institutional aspects of real estate performance have been considered, though not thoroughly examined, in this book, so as not to distract attention from the macro dynamic focus of the book. Future research may have a focus on market microstructure and other micro aspects of real estate performance but will benefit from the results and discussions in this book. Analysis of the responses of real estate to various shocks in the book, although has revealed important patterns and offered sensible explanations and insights which challenge many of the previous misperceptions, has been built on appraisalbased real estate indices. While the extent to which the indices have been unsmoothed does not matter much in the long run, it may distort short-term results. Consequently, methods of unsmoothing are crucial to the successful identification of short-term patterns in real estate performance. Bearing this in mind, caution has been taken in developing two new procedures of unsmoothing and comparing the results of this book with those of previous studies. This may mitigate the problem of smoothing, but the problem may never be fully solved as long as the indices are appraisal based. Thus the results and findings may not be totally unassailable. Taking regional and sectoral segmentations in real estate investment and performance into account, investigation of real estate market efficiency at the aggregate level, as adopted in this book, may only have offered partially blurred results. Large transaction costs and illiquidity in the real estate market imply that there could be large discrepancies in real estate performance across regions, while no arbitrage profits could be made in the meantime. At the sectoral level, real estate performance is much influenced by the user market in its own sector. Therefore, sectoral segmentations would also prevent investors from making arbitrage profits even if real estate returns vary in different sectors. In addition, different liquidity preferences make real estate performance and other financial market performance not readily comparable. As mentioned above, research in this book is based on appraisal-based real estate indices, so the degree of market inefficiency may be affected by the unsmoothing procedure, though the qualitative rejection of market efficiency remains the same. Future research will benefit greatly from using transactionbased real estate indices or a reliable substitute. It is perceived that much effort should be made in this area, because almost all empirical investigations have to be built on a reliable real estate performance data set. Rationality in real estate markets and investment, as an important element in dynamic analysis, is not directly tested but instead inferred in the book. This is constrained by the concentration and focus of the book. Until now, it has only been partly studied by Tegene and Kuchler (1993) who investigated the existence of speculative bubbles in farmland prices, and Liu and Mei (1994) who analysed real estate risk using the present value model. The former uses a very small sample of data and the latter tests in direct real estate investment only, and both have investigated just one aspect of rationality. Future research may give attention to this important issue in general and incorporate liquidity preferences and segmentations into the analysis in particular. Combined with real estate

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market efficiency and real estate cycles, studies of rationality in the real estate market would doubtless provide a fuller picture of real estate market behaviour and further advance people’s knowledge in this important area of research.

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Index of names Abel, A.B. 149 Abraham, B. 85, 149 Alesina, A. 149 Alogoskoufis, G 149 Ariel, R.A. 38, 149 Armitage, S. 38, 149 Ashenfelter, O. 149 Attanasio, O.P. 149 Balchin, P.N. 149 Ball, R. 38, 149 Banerjee, A. 27, 149 Banz, R.W. 38, 149 Barkham, R. 6, 86, 91, 97, 124, 149 Barras, R. 137, 150 Barro, R.J. 40, 41, 42, 45, 48, 150 Bernard, V.L. 38, 150 Beveridge, S. 53, 67, 68, 75, 77, 78, 80, 100, 110, 150 Biddle, G.C. 38, 150 Black, F. 37, 38, 150 Blanchard, O.J. 45, 53, 55, 63 64, 65, 66, 68, 80, 111, 150, 151 Blundell, G.F. 6, 83, 86, 97, 151 Bollerslev, T. 36, 151 Breeden, D.T. 37, 151 Broadhurst, R. 151 Brown, G.R. 151 Brown, P. 38, 149 Bull, G.H. 149 Callender, M. 7, 151 Campbell, J.Y. 6, 36, 48, 49, 53, 55, 59, 60, 62, 63, 66, 68, 83, 99, 100, 112, 151 Campeau, F. 6, 151 Campos, J. 85, 151 Canova, F. 151 Case, K.E. 5, 151 Chan, K.C. 5, 152 Chen, N.F. 38, 152 Chowdhury, A.R. 45, 152 Clapp, J. 86, 155 Clark, P.K. 53, 55, 56, 152 Clark, T.E. 152 Cochrane, J.H. 53, 55, 60, 61, 62, 66, 83, 99, 100, 114, 152 Cole, R. 159

Index of names

160

Cutler, D.M. 152 Das, S. 153 Davidson, R. 42, 152 Dekimpe, M.G. 162 Denton, F.T. 152 Devaney, M. 160 Dickey, D.A. 25, 42, 52, 152 Dickson, D.G. 159 Diebold, F.X. 152 Dimson, E. 38, 86, 153 DiPasquale, D. 153 Dobson, S.M. 153 Dolado, J. 149, 153 Downs, A. 153 Dwyer, G.P. Jr 121, 153. Eberly, J. 149 Eichenbaum, M.S. 42, 153 Elton, E. 53, 153 Engle, E.M.R.A. 25 Engle, R.F. 25, 27, 29, 52, 53, 68, 73, 75, 77, 80, 81, 124, 127, 129, 131, 153, 162 Ericsson, N.R. 151 Evans, G. 53, 153 Evans, R. 160 Fama, E.F. 34, 35, 36 ,37, 38, 153 Ferguson, D. 137, 150 Filardo, A.J. 154 Finnerty, J.E. 38, 154 Firstenberg, P.M. 83, 86, 97, 154 Fischer, I. 42, 154 Fischer, S. 40, 41, 112, 154 Fisher, J.D. 4, 154 Fisher, L. 154 Fomby, T.B. 152 Forni, M. 154 Fraser, W.D. 154 French, K.R. 36, 38, 153 Friedman, M. 40, 42, 154 Frisch, R. 42, 154 Froot, K.A. 154 Fuller, W.A. 25, 42, 52, 152, 154 Galbraith, J.W. 149 Gallo, G.M. 75, 79, 80, 154 Garratt, A. 154 Gau, G.W. 5, 154 Geltner, D. 6, 83, 86, 91, 97, 124, 149, 154 Genesove, D. 149

Index of names

161

Geroski, P.A. 155 Giaccotto, C. 86, 155 Giliberto, S.M. 155 Goddard, J.A. 153 Goerlich, P. 60, 155 Gordon, S. 151, 154 Granger, C.W.J. 6, 11, 25, 29, 45, 52, 121 124, 125, 127, 153, 155 Greig, W. 158 Grenadier, S.R 99, 119, 155. Grissom, T.V. 158 Grossman, S.J. 35, 39, 155 Gruber, M. 153 Guilkey, D. 4, 159, 162 Guntermann, K.L. 5, 155 Gyourko, J. 5, 155 Haberler, G. 40, 41, 155 Hall, S.G. 154, 155 Hansen, A.H. 40, 41, 155 Hansen, B.E. 52, 155 Hansen, G.D. 156 Hansen, L.P. 37, 156 Hartzell, D. 156, 157, 158 Harvey, A. 53, 55, 56, 156 Hekman, J.S. 156 Hendershott, P.H. 152 Henderson, G.V. Jr. 159 Hendry, D.F. 149, 151, 156 Hlavka, M. 153 Hodrick, R.J. 17, 21, 22, 29, 55, 156 Hoesli, M. 157 Huffman, G.W. 156 Hulbert, M. 38, 156 Hurn, S. 159 Ibbotson, R.G 38, 156. Ingram, B.F. 156 Ippolito, R.A. 39, 156 Isaac, D. 11, 156 Issler, J.V. 68, 75, 80, 131, 153 Jaffe, J.F. xii, 38, 156 Jenkinson, T. 153 Jensen, M.C. 35, 39, 151, 156 Johansen, S. 25, 26, 27, 76, 91, 92, 96, 97, 124, 133, 156 Juselius, K. 25, 91, 96, 97, 124, 133, 156 Kaplan, R.S. 38, 156 Karras, G. 157 Keim D.B. 5, 155

Index of names

162

Kempf, H. 75, 79, 80, 154 Keogh, G. 157 Key, T. 7, 46, 151, 157 Khoo, T. 157 Kieve, J.L. 149 Kim, T. xii, 157 King, R.G. 40, 42, 55, 63, 64, 65, 66, 68, 75, 77, 79, 80, 111, 157 Kleim, D.B. 38, 157 Kocherlakota, N.R. 156 Kozicki, S. 68, 80, 129, 131, 152 Kuchler, F.R. 6, 148, 162 Kwok, C.C. 162 Kydland, F.E. 40, 41, 42, 48, 157 Lakonishok, J. 38, 157 Larsen, H.K. 121, 161 Lawrence, C. 48, 157 Lee, K.C. 160 Lee, T.H. 155, 157 Leitch, G. 157 Lewbel, A. 157 Lindahl, F.W. 158 Linneman, P. 5, 157 Lippi, M. 56, 57, 158 Liu, C.H. 5, 38, 112, 148, 158 Liu, P. 158 Lizieri, C. 6, 99, 158 Long, J.B. 40, 41, 42, 54, 112, 158 Loughran, T. 38, 158 Lütkepohl, H. 54, 158 Lucas, R.E. Jr. 37, 40, 41, 48, 158 MacGregor, B.D. 6, 157, 158 MacKinnon, J.G. 42, 152 Mankiw, N.W. 53, 55, 59, 60, 62, 63, 66, 68, 83, 99, 100, 112, 150, 151 Marrinan, J. 1512 Marsh, P.R. 38, 153 Matysiak, G. 6, 159, 162 McCallum, B.T. 42, 159 McFarland, J.W. 160 McGibany, J.M. 152 McGough, T. 159 McGrattan, E.R. 159 McIntosh, W. 5, 159 McMahon, P.C. 160 Meguire, P. 110, 159 Mei, J. 112, 148, 158 Miles, M. 4, 5, 156, 159, 162 Mullineux, A.W. 159 Muscatelli, V.A. 159 Muth, J.F. 47, 48, 159

Index of names

163

Nanthakumaran, N. 6, 157, 158 Nelson, C.R. 42, 44, 52, 53, 55, 56, 67, 68, 75, 77, 80, 110, 150, 159 Nerlove, M. 152 Newbold, P. 53, 110, 159 Norrbin, S.C. 5, 155 Nourzad, F. 152 Obstfeld, M. 154 Osborn, D.R. 159 Osterwald-Lenum, M. 96, 97, 125, 126, 160 Perron, P. 42, 122, 123, 124, 160 Pesaran, M.H., 55, 61, 62, 66, 112, 113, 114, 160 Phillips, P.C.B. 52, 155, 160 Pierse, R.G. 160 Plosser, C.I. 40, 41, 42, 43, 44, 52, 54, 55, 56, 112, 157, 158, 159 Poterba, J.M. 152 Prescott, E.C. 17, 21, 29, 40, 41, 42, 48, 156, 157, 158, 160 Priestley, M.B. 160 Quah, D. 53, 55, 63, 64, 65, 66, 68, 80, 111, 150, 160 Quan, D.C. 68, 86, 160 Quigley, J.M. 86, 160 Rao, B.B. 160 Rapping, L.A. 48, 158 Rayburn, W. 5, 160 Rebelo, S.T. 157 Reichlin, L. 53, 56, 57, 153, 154, 158 Reimers, H. 54, 158 Reinganum, M.R. 38, 160 Rhodes, G.F. Jr. 152, 155 Ritter, J.R. 38, 158, 160 Roll, R. 38, 152, 154, 156 Ross, S.A. xii, 37, 83, 86, 97, 152, 154, 160 Roubini, N. 149 Rouwenhorst, K.G. 161 Royal Institution of Chartered Surveyors 46, 161 Rubinstein, M. 37, 161 Sackley, W.H. 163 Sanders, A.B. 152 Sargent, T.J. 40, 41, 48, 161 Satchell, S. 6, 99, 158 Savin, N.E. 156 Sephton, P.S. 121, 161 Seyhun, H.N. 38, 161 Shapiro, M.D. 45, 161 Shiller, R.J. 5, 6, 36, 48, 49, 112, 151, 161

Index of names

164

Shilling, J.D. 83, 86, 89, 91, 92, 93, 97, 161 Scholes, M. 86, 161 Sims, C.A. 42, 45, 161 Singleton, K.J. 37, 42, 45, 153, 156, 161 Smidt, S. 38, 157 Smith, R. 149 Smith, R.L. 5, 155 Smith, R. T. 161 Smith, S.D. 158 Society of Property Researchers 161 Solow, R.M. 42, 161 Sosvilla-Rivero, S. 153 Stiglitz, J.E. 35, 39, 155 Stock, J.H. 45, 53, 55, 67, 68, 75, 77, 78, 80, 157, 162 Strum, B.J. 162 Summers, L.H. 152 Syed, A.A. 158 Tanner, J.E. 157 Tegene, A. 6, 148, 162 Thomas, J.K. 3, 150 Timmermann, A. 162 Tsolacos, S. 28, 159 Vahid, F. 53, 68, 73, 75, 77, 80, 162 Van de Gucht, L.M. 61, 162 Venmore-Rowland, P. 6, 158 Wallace, M.S. 92, 121, 153 Wallace, N. 40, 41, 48, 161 Wallis, K.F. 156 Wang, P. 5, 6, 99, 159, 162 Ward, C.W.R. 6, 83, 86, 97, 151 Watson, M.M. 53, 162 Watson, M.W. 45, 53, 55, 67, 68, 75, 77, 80, 150, 157, 161, 162 Webb, R.B. 4, 154 West, K.D. 163 Wheaton, W. 153 Wheaton, W.C. 163 Wickens, M. 163 Williams, J.T. 86, 161 Wilson, T. 163 Working, H. 85, 163 Zarkesh, F. 157 Zeria, J. 163 Zisler, R.C. 83, 86, 97, 154, 160 Zorn, T.S. 163

Subject index Akaike information criterion (AIC) 25, 122–123 American Stock Exchange (AMSE) 5 arbitrage pricing theory (APT) 4, 37 asymmetry 57, 124–127 augmented Dickey–Fuller (ADF) 25–28 autoregressive integrated moving average (ARIMA) 55, 85, 110 autoregressive moving average (ARMA) 53, 56–58, 90, 114 Beveridge–Nelson decomposition 53, 67, 77–78, 110 Beveridge–Nelson–Stock–Watson representation 67–68, 77–78 Box–Jenkins 52 British Association of Insurers 8 British Land 10 Business cycle theory 3, 33, 39–47; disequilibrium see disequilibrium business cycle theory; equilibrium see equilibrium business cycle theory; Keynesian see Keynesian business cycle theory; monetary see monetary business cycle theory (MBC); new classical see new classical business cycle theory (NC); real see real business cycle theory (RBC) capital asset pricing model (CAPM) 4–5 Central Statistical Office (CSO) see Office for National Statistics (ONS) change in stock under construction (RESC) 16, 20–24, 86–89, 131–138 coefficient of variance (CV) 12–14, 92, 97 coherence 138–142 coincident indicator (CC) 16, 20–24, 131–132, 136–137, cointegration 25–28, 49, 89–91, 93, 96–96, 125–126, 133–134 common cycle 3, 54, 67–81, 129–130, 134–137; coincident 69, 129, 134–135; phase shifting 70, 72–77, 129, 134–135 common factor 54 common feature 129–131, 134 common trend 3, 54; representation see Beveridge–Nelson–Stock–Watson representation construction new order (NO) 16, 20–28, 100, 104, 108, 110 construction output on new work (CO) 16, 20–28, 100, 104, 108, 110, 113, 115–117, 131–138 cumulative abnormal return (CAR) 37–38 cycle, common see common cycle

Subject index

166

decomposition, trend-cycle see Beveridge–Nelson decomposition Dickey–Fuller (DF) 25 difference stationary (DS) 17, 44, 52, 55–57 disequilibrium business cycle theory 40–42 DYMIMIC 5 efficient market hypothesis (EMH) 3, 33–39, 47, 126 equilibrium business cycle theory 40–42 error correction mechanism (ECM) 52, 75–77 errors-in-variable 87 feature, common see common feature Financial Times Actuary (FTA) all share index 12–14, 20–28, 100–101, 103, 107, 121, 128, 130– 131 property sector (FTAP) 12–14, 20–28, 86, 91, 97, 100–101, 103, 107, 113, 115–117, 121–126, 128, 130–13 Frank Russell Company 5 frequency domain analysis 137–142 generalised autoregressive conditional heteroscedasticity (GARCH) 36 generalised method of moment (GMM) 37 gilts (GLT) 14, 20–28, 100–101, 105, 109 gross domestic product (GDP) 111, 118, 131–138 Halifax Building Society house price index (HFX) 16, 20–28, 100–101, 105, 109–110 Hillier Parker property market return index (HPK) 13–14, 100–101, 105, 109–110 Hodrick–Prescott (HP) filter 17–18, 29 House price index Halifax Building Society see Halifax Building Society house price index (HFX) Nationwide Building Society see Nationwide Building Society house price index (NTW) indicator of fixed investment in dwellings (DWG) 16, 20–28 industrial production (PDN) 110, 115–117 instrumental variable 134 insurance company 7–11 Investment Property Databank (IPD) 9, 13, 86, 91–98, 100, 144 Johansen procedure 25, 92, 124 Jones Lang Wootten 86 Jones Lang Wootten property return index (JLW) 12–14, 19–22, 25–27, 91–98, 100–102, 106, 110, 113–118, 130–135, 144, 146 Kalman filter 53 Keynesian business cycle theory 40–42, 46 lagging indicator (LG) 16, 20–24, 131, Land Securities 10 leading indicator: long see long leading indicator (LL); short see short leading indicator (SL)

Subject index

167

Ljung–Box Q* 25, 110, 134 longer leading indicator (LL) 16, 20–24, 131, M0, 115–116, 131–138 M4, 115 manufacturing sector (MNG) 110, 131–138 market efficiency 15, 33–39 Markov transition 70–73; matrix 71–73 Markowitz efficient portfolio 4 mean squared errors (MSEs) 39 MEPC 10 monetary business cycle theory (MBC) 40–42 monetary shock 63–66, 115–117, National Council of Real Estate Investment Fiduciaries (NCREIF) 5 Nationwide Building Society house price index (NTW) 16, 100–101, 104, 108, 110–111, 113, 115– 117, 131–138 new classical business cycle theory (NC) 40–42 New York Stock Exchange (NYSE) 5 number of property transactions (NPT) 16, 20–21, 23–24 Office for National Statistics (ONS) 19, 130 pension funds 7–12 persistence 3; multivariate 61–63, 111–117; joint 111; univariate 59–61, 100–109 present value model 49 price discovery 120, 124–127 production sector (PDN) 110, 113, 115–117 property market return index, Hillier Parker see Hillier Parker property market return index (HPK) property return index, Jones Lang Wootten see Jones Lang Wootten property return index (JLW) random walk 35 rational expectations hypothesis (REH) 3, 33, 47–50, real business cycle theory (RBC) 40–42, 46 real estate investment trusts (REITs) 5, 120, 144 real shock 63–66 root mean square errors (RMSE) 39 Schwartz’s criterion (SC) 25 seemingly unrelated regression (SUR) 114 services sector (SVC) 110, 113, 115–117, 131–138 shock: monetary see monetary shock; real see real shock shorter leading indicator (SL) 16, 20–24, 131, smoothing 85–86

Subject index spectrum 137–139 stationary: difference see difference stationary (DS); trend see trend stationary (TS) stock under construction (RESA) 16, 26–28, 86 trend, common see common trend trend stationary (TS) 17, 44, 55–57 unemployment rate (UER) 115, 131–138 unit root 123, 133 unsmoothing 86–98 V 60 VC 61–62 VCk 62, 113 Vector autoregression (VAR) 45, 54, 62, 75–81 Vk 100–101 60 26–28, 125–126, 134 26–28, 125–126, 134

168