Measures of Exports of the United States 9780231886345

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STUDIES IN HISTORY, ECONOMICS AND PUBLIC LAW Edited by the FACULTY OF POLITICAL SCIENCE OF COLUMBIA UNIVERSITY

NUMBER 356

MEASURES OF EXPORTS OF THE UNITED STATES BY DUDLEY J . COWDEN

ACKNOWLEDGMENT THE writer wishes to acknowledge his indebtedness to those who have generously aided him in this study. Before undertaking this project he conferred with Dr. E. Dana Durand, of the Department of Commerce, who explained in detail the methods followed in constructing the index of that Department, furnished a list of the commodities included in their sample, and gave warning concerning the pitfalls which would be encountered. Professors Wesley C. Mitchell, Frederick C. Mills and James W. Angell read the manuscript while in preliminary form, and offered helpful advice. The encouragement and help in many ways of his friend Professor Frederick E. Croxton was responsible in no small measure for the completion of this study. The writer feels especially grateful to Professor Robert E. Chaddock for assistance in preparing the manuscript for publication. The tremendous amount of computing which this work involves might have proved an unsurmountable obstacle had it not been for assistance by Charles E. Bideker, Charles H. Wittman, Archie Sabin, and the writer's wife, Mercedes S. Cowden. The American Telephone and Telegraph Company also cooperated in computations connected with constructing the monthly indexes of foodstuffs and raw materials. DUDLEY J . COWDEN.

5

CONTENTS rtsi CHAPTER I D E F I N I T I O N OF O B J E C T

13

CHAPTER II T H E DATA FROM WHICH THESE M E A S U R E S ARE COMPUTED

I. II. III. IV.

Publications from which Obtained Meaning of Terms Method of Collection Evaluation of the Data 1. Accuracy 2. Reliability on a Monthly Basis 3. Comparability Between Periods (1) Changes in Classification (2) Homogeneity (3) Changes in Quality

15 16 18 18 18 21 22 22 22 23

CHAPTER III SELECTION OP THE S A M P L E

I. Representativeness 1. Proportionate Value Representation 2. Proportionate Value Changes II. Adequacy III. Limitations on the Choice of Commodities

26 36 29 33 36

CHAPTER IV METHODS OF CONSTRUCTION

I. Methods Available 1. Averages (1) Simple Averages, Arithmetic and Harmonic (2) Weighted Averages, Arithmetic and Harmonic .. (3) Aggregates 7

40 40 40 42 43

8

CONTENTS FACE

2. Chain Indexes 3. Tests of Index Numbers II. The Purpose of Index Numbers I I I . Considerations in Determining Methods of Construction 1. Object for which Intended 2. Peculiarities of the Data (1) Relationship Between Price and Quantity Movements of Commodities in the Sample (2) Lack of Comparability (3) Completeness of the Data (4) Dominating Importance of a Few Commodities.. 3. Ease of Construction I V . Solution of the Problem 1. Annual Indexes 2. Monthly Indexes CHAPTER

43 49 51 58 58 59 59 60 61 62 63 64 66 69

V

RESULTS

I. Statistical Result« 1. Observed Differences Between Preceding Period and Given Period W e i g h t i n g 2. The Circular Test 3. Relationship Between Price, Volume and Value Changes 4. Comparison with Department of Commerce Indexes II. Economic Results

73 73 75 76 76 78

APPENDICES A . Procedure Followed in Constructing Index Numbers

91

B . Commodities Included in Sample and Unit of Measure in 1930, and Official Class Numbers of Commodities in Sample in 1923 and 1930, by Economic Classes

92

C. Indexes 99 1. Price Indexes of Domestic Exports, by Economic Classes 99 2. Indexes of Volume and Seasonal Volume Variation of Domestic Exports, by Economic Classes 102 D . Other Published Indexes of United States Foreign Trade 1. Kreps Index 2. Berridge Export Index 3. Department of Commerce Agricultural Export Index 4. Department of Commerce Indexes of Changes in Quantity, Price and Value of Imports and Domestic Exports

105 105 107 109 110

CONTENTS

9 PACK

5. 6. 7. 8. INDEX

Rogers Volume Estimate Federal Reserve Board International Price Index Federal Reserve Board Foreign Trade Index The American Tariff League Import Volume Index

115 116 118 119 121

LIST OF CHARTS PACK

I. Percentage Distribution of Domestic Exports of the Different Economic Classes by Commodity Groups in 1928 CHART II. Comparison of Annual Value Changes of All Domestic Exports with those of Sample, by Class Groups. Classes A , B and C CHART III. Comparison of Annual Value Change* of all Domestic Exports with those of Sample, by Class Groups. Classes D and E CHART IV. Comparison of Annual Value Changes of All Domestic Exports with those of Sample, by Economic Classes CHART V . Value of the Forty Leading Commodities Exported in 1928, and Coefficients of their Price Variation.. CHART V I . Percentage Deviations of Monthly Volume Indexes from Annual, and Corrections for Weight Correlation Bias CHART V I I . Comparison of Monthly Value Changes of All Domestic Exports with Product of Price and Volume Indexes C H A R T VIII. United States Department of Commerce Volume and Price Indexes of Domestic Exports Compared with those Constructed by D. J. Cowden CHART IX. Annual Price, Volume and Value Indexes of Domestic Exports, by Economic Classes CHART X . Monthly Price Indexes of Domestic Exports, by Economic Classes CHART XI. Seasonal Variation of Volume of Domestic Exports, by Economic Classes C H A R T XII. Monthly Volume Indexes of Domestic Exports, by Economic Classes. Classes A , B and C C H A R T XIII. Monthly Volume Indexes of Domestic Exports, by Economic Classes. Classes D, E and Total 11 CHART

38 30 31 32 38 71 77 79 81 83 85 86 87

CHAPTER

I

DEFINITION OF OBJECT

ONE of the most important problems which have engaged the attention of economists and statisticians in the United States has been that of trying to unravel the tangle of factors which bring about or are affected by the more or less regularly alternating periods of " prosperity " and " depression ". Among those factors which affect or are affected by the departure of business phenomena from an even trend are those which manifest themselves through the export trade of the United States. These causes or results may show themselves through price, volume or value changes; and they may show themselves through the sum total of our exports, through groups or classes of commodities, or only through certain specific commodities. However that may be, the importance of these factors cannot be measured nor the manner in which they act discovered until we have satisfactory data with which to work. We have at the present time in the United States official value figures, monthly as well as annual, for the different commodities exported, for total domestic exports, and for the five economic classes and eleven commodity groups into which our foreign trade is divided by the Department of Commerce. Value figures are given on an annual basis only for group subdivisions of classes. For a large proportion of the individual commodities, quantities exported are also shown. What has been said concerning domestic exports is also true concerning general imports. The Department of Commerce publishes annual indexes of price and volume 13

I4

MEASURES

OF EXPORTS

OF THE UNITED

STATES

changes of our exports as a whole and our imports as a whole. Furthermore, the American Tariff League maintains a monthly volume index of imports by economic classes, beginning January, 1920. 1 But we have no corresponding measure of exports. A number of other indexes of United States foreign trade have been published from time to time and for various purposes. A survey of some of these and of the two previously mentioned has aided in selecting methods of solving the present problem. These indexes are described in Appendix D. The object, then, of the present study is to provide material in the shape of monthly and annual price and volume indexes of United States domestic exports by economic classes. It is primarily intended that this material will be of some use in the study of business cycles, but it is also hoped that it will be found useful for other purposes. 1 Constructed by W. R. Peabody and published in the Statistical Bulletin of the American Tariff League.

CHAPTER

II

T H E D A T A FROM W H I C H THESE M E A S U R E S ARE C O M P U T E D I. PUBLICATIONS FROM W H I C H OBTAINED

THE data from which these measures are computed are published in convenient form by the Department of Commerce. In addition to convenience it might be added that the easy access to these publications of any one who wishes to use the indexes adds to their usefulness. In large part the data are drawn from the Monthly Summary of Foreign Commerce of the United States. In this publication are shown, month by month and year by year, values and quantities of United States exports and imports, by commodities.1 Quantities are not given for all commodities, but they are for most. The data are broken up into eleven commodity groups: Group Group Group Group

oo. o. i. 2.

Group Group Group Group

3. 4. 5. 6.

Group 7.

Animals and animal products, edible. Animals and animal products, inedible. Vegetable food products and beverages. Vegetable products, inedible, except fibers and wood. Textiles. Wood and paper. Nonmetallic minerals. Metals and manufactures, except machinery and vehicles. Machinery and vehicles.

Figures published in current numbers are preliminary figures. Revised figures appear one year later. In this study revised figures are used for every year except 1930. 15 1

J6

MEASURES

OF EXPORTS

OF THE UNITED

STATES

Group 8. Chemicals and related products. Group 9. Miscellaneous. This publication also total value of exports economic classes, the facture and economic Class A. Class B. Class C. Class D. Class E.

shows for each month and year the and imports of each of the following bases of which are degree of manuuse:

Raw Materials. Raw Foodstuffs. Manufactured foodstuffs. Semimanufactures. Finished manufactures.

. It is thought that indexes based on this latter classification will prove more significant in the study of business cycles than those based on the commodity classification, or than a single general index of export prices or quantities.' It is advisable, however, to make use of the commodity classification; and in order to ascertain the value of each class group (commodity group within an economic class) of exports for each year, as well as to discover within what class a given commodity belongs one must turn to Foreign Commerce and Navigation of the United States, an annual publication of the Department of Commerce. II.

M E A N I N G OF T E R M S

In order to know exactly what our various indexes mean, we should define such terms as " United States ", " foreign countries ", " domestic exports ", and " export value The definitions here offered are found in the Monthly Summary.2 1 The American Tariff League uses the classification based on degree of manufacture and economic use. The Department of Commerce in its annual summary, Foreign Trade of the United States, each year analyzes our foreign trade by economic classes; and for some time has intended to construct index numbers using this classification.

U . S. Department of Commerce, Bureau of Foreign and Domestic Commerce, Monthly Summary of Foreign Commerce of the United States, Part I, January, 1930, p. 2. l

DATA

FROM

WHICH

MEASURES

ARE

COMPUTED

j7

The statistics of the foreign commerce of the United States include the trade of the customs districts of Alaska, Hawaii, and Porto Rico with foreign countries, but not the trade of these Territories with the United States, which is shown separately in the section of " Commerce with noncontiguous Territories." In the statistics of the foreign commerce of the United States the Philippine Islands are treated as a foreign country, while the collectors of customs in the islands are under the jurisdiction of the W a r Department. . . . 1 The statement of domestic exports exhibits the exports of domestic products or manufactures, also exports of commodities of foreign origin which have been changed from the form in which they were imported or enhanced in value by further manufacture in the United States, such as sugar refined in this country from imported raw sugar, flour ground from imported wheat, and articles, utensils, etc., made from imported materials. The value of exports of domestic merchandise is the actual cost or the value at the time of exportation in the ports of the United States whence they are exported, as declared by the shippers on the export declarations. 2 T o these statements it might be added that exports by rail as well as by sea are included, and that " parcel-post exports of merchandise are supposed to be included in the statistics f o r each shipment valued at $ 2 5 or more made by a 1 1

The Virgin Islands also are treated as a foreign country.

" The values stated should be the actual cost or selling price, if the goods are sold, including the cost of cases and other containers and actual or estimated inland freight charges from the interior place of shipment to the seaport or border point of exportation. . . . " Freight and other charges from the port of departure in the United States to the place of destination in the foreign country or noncontiguous territory to which shipped must not be included in the export value." See Schedule B, Statistical Classification of Domestic Commodities Exported from the United States, and regulations governing statistical returns of exports of domestic commodities, effective January 1, 1930, U. S. Department of Commerce, Bureau of Foreign and Domestic Commerce, pp. 1-2.

jg

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

wholesale dealer. There is no law requiring an export declaration to be filed when a parcel-post shipment is made and there is reason to believe that many shipments are not reported III.

METHOD OF COLLECTION

L. F. Schmeckebier, in describing the collection of export statistics, states that each shipper or his agent must file an export declaration containing statements under oath regarding the character of the merchandise, the quantity, the value, whether the product of the United States or of a foreign country, and the destination. The export declaration is checked against the manifest, which must be filed by the master of a vessel before it is granted clearance. After the entries and the shippers' declarations are checked they are classified according to the commodity and geographic classification used in the statistical reports. The data are then transferred to punched cards, which are run through sorting and tabulating machines in order to obtain the totals desired.2 IV.

EVALUATION OF T H E DATA

The character of the data directly determines the reliability of the index numbers; but as will be shown in Chapters III and I V , it affects also the choice of commodities for the sample, and the methods employed in their combination. I.

Accuracy

Export statistics have long had a reputation for inaccuracy. Writing in 1918, John Cummings states that " except for exports by rail, it is probably true that our returns of exports have become progressively less accurate and complete, nearly in proportion as the volume of exports has 1 Schmeckebier, L . F., The Statistical ment, Baltimore, 1925, p. 340. 2

Ibid., pp. 326-327.

Work

of the National

Govern-

DATA

FROM WHICH MEASURES

increased " - 1

A s late o f

ARE COMPUTED

ig

1 9 2 2 the B u r e a u o f F o r e i g n a n d

D o m e s t i c C o m m e r c e m a d e the f o l l o w i n g s t a t e m e n t : T h e thoughtless practice o f some exporters in assigning office boys or inexperienced clerks to prepare shippers' export declarations is seriously jeopardizing the accuracy of official foreign trade figures, and the Department of Commerce requests that more care be exercised in preparing these vitally important documents. Accurate, timely trade statistics will be impossible unless shippers extend more personal cooperation in seeing that necessary papers are properly prepared. T h e work should not be assigned to boys or some secondary agency having no special interest in the matter. T h e new e x p o r t classification recently adopted at the request of exporters to a f f o r d A m e r i c a n business really useful statistical service has brought out the fact that serious errors have existed in the official figures f o r years, particularly in classes showing values only. M o s t of these errors are due to inaccurate description in the export declarations presented to customs officials by the shipper or his agent. Investigation has developed, f o r example, that ship and tank plates, punched and shaped, are reported as low as 1 cent per p o u n d ; alloyed steel bars at 1.6 cents per p o u n d ; copper w i r e at 4 cents per pound; wood and denatured alcohol at 1 l/i cents per gallon; white lead at less than 2 cents per p o u n d ; 370 stationary electric motors of less than 200 horsepower at an average price of $ 1 1 ; 183 road plows, scrapers, and rollers at $ 1 1 each; 1 centering lathe chuck at $3,800; grinding and sharpening machines at $5 and $5,000; and hoes and rakes at $132. T h e department realizes that the preparation of the necessary 1 Cummings, John, Statistician, United States Bureau of the Census, " Statistical Work of the Federal Government of the United States ", in The History of Statistics: Their Development and Progress in Many Countries (seventy-fifth anniversary volume of The American Statistical Association). Collected and edited by John Koren, New York, 1918, p. 595-

2o

MEASURES

OF EXPORTS

OF

THE

UNITED

STATES

papers at times represents something of a burden and it does not wish to appear unreasonable. It expresses the hope, however, that export shippers generally will appreciate the fact that the figures in point are being compiled primarily for the benefit of the exporters who are now asked to cooperate. The illustrations given should convince any reasonable exporter as to the utter ridiculousness of some of the returns now received. Just a little more care to the column " Class No. of Schedule B." on the export declaration, to make certain that an accurate entry is made of the number of statistical export classification of 1922, under which the goods should be properly classified, will be a great help. It will avoid the time and expense involved in returning erroneous declarations to the original custom house, in some cases the West Coast, and will help the Department of Commerce to clear itself of the possible stigma of inefficiency when the burden of responsibility rests squarely upon the shoulders of the offending exporters. 1 The Section of Customs Statistics of the Bureau of Foreign and Domestic Commerce believes that they have had considerable success in their appeal to the exporters. In fact, they go so far as to say that for individual commodities, statistics of exports are more accurate than are those of imports, in spite of the fact that importers' returns are scrutinized by customs officials to prevent evasion of the payment of import duties. This is because import procedure is handled largely by brokers who have no interest in trade statistics, but are interested only in doing the minimum amount of work which will satisfy customs officials. 2 E x ports, on the other hand, are classified and collected solely ' Commerce Reports, June 12, 1922, p. 683. bier in The

Statistical

Work

of

Quoted by L . F . Schtnecke-

the National

Government,

Baltimore,

1925. PP- 338-339J T h i s information w a s obtained f r o m M r . L . J. Mahoney, Chief of the Section of Customs Statistics, in an interview on November 22, 1929.

DATA

FROM

WHICH

MEASURES

ARE

COMPUTED

2I

for statistical purposes, and it is urged by the Department of Commerce that the declarations be prepared by the actual exporter, who has personal knowledge of the goods shipped. Forwarding or shipping agents acting for the exporter in preparing the declarations should be furnished with complete information, as the data on bills of lading or railroad waybills are not in sufficient detail.1 2. Reliability on a Monthly

Basis

It is unfortunate that monthly data are not reliable for more than a few years back. Owing to pressure of work it has sometimes been necessary to carry figures from one month over to the next; so that to some extent at least, and during certain periods, the data represents, not goods which have been exported in a given month, but data which the Section of Customs Statistics had time to compile during the month. Officially, however, it is stated that both export and import statistics have been up to date since the middle of 1923.2 In view of this circumstance it hardly seems advisable to extend a monthly index back of 1923. In addition to the above difficulty it happens that every month a few export declarations come in which should have been made out by exporters the previous month, but this does not occasion any great error, and being approximately a constant error, results in no bias. 1

Schedule B., op. cit., p. 2.

This statement was obtained from Mr. L. J. Mahoney, Chief of the Section of Customs Statistics, in an interview on November 22, 1929. The transfer in January, 1923, of the Bureau of Customs statistics, with entire control of the compilation of foreign trade statistics from the Treasury Department to the Department of Commerce, may be partly responsible for the improvement of export statistics. 2

22

MEASURES

OF EXPORTS

OF THE UNITED

STATES

3. Comparability Between Periods ( 1 ) Changes in Classification One factor which occasions a certain amount of inconvenience and somewhat affects the comparability of the data between periods is the fact that occasionally there is a change in the way in which groups of similar commodities are broken up into separate items. For instance, cotton cloth, colored, was classified as piece-dyed, printed and yarn or stock-dyed until January 1928. Since then the classification has been : Voiles. Percales and prints, 32 inches and narrower. Percales and prints, over 32 inches wide. Flannels and flannelettes. Khaki and fustians. Denims. Suitings (drills, etc.). Ginghams. Chambrays. All other printed fabrics. 73/2 yards per pound and lighter (beginning January Heavier than 7J/2 yards per pound (beginning January All other piece-dyed fabrics. 5 yards per pound and lighter (beginning January Heavier than 5 yards per pound (beginning January All other yarn-dyed fabrics. Cotton and rayon mixtures (cotton chief value).

1929) 1929) 1929) 1929)

Changes in value groupings of passenger automobiles occasion a similar difficulty. (2) Homogeneity Commodities itemized in the official returns are not subject to rigid specifications. Wheat, for instance, is not classified according to grade. It is within the realm of possi-

DATA FROM WHICH MEASURES

ARE COMPUTED

23

bility for this defect in the material to result in grave error in any attempt to measure price change. Assume two grades of a commodity to be exported as follows: 1923

1924

Grade A Grade B

5 units @ $ 1 2 = $60 5 units @ 4 = 20

1 unit @ $15 = $ 1 5 9 units @ 5 = 45

Average

10 units @ $ 8 = $80

10 units @ $ 6 = $60

In spite of an increase in the price of each grade of 25 per cent during the period, the average, or export price shows a 25 per cent decrease. Had the quantities (not values) exported remained the same, or changed proportionately, the change in the average price would be an accurate index of price change regardless of whether the prices of the two grades showed the same percentage changes or even the same direction, since it would be the equivalent of the familiar aggregative index with base-year weights. ( 3 ) Changes in Quality Just as different proportions of different varieties of the same commodity may be exported in different periods, so we may find the general quality of the commodity changing. This is especially true with manufactured goods. Sometimes this change is sudden, as when there is a radical change in the model of an important make of automobile; sometimes it is a gradual change, usually a gradual improvement. Hence we can never be sure that when the unit value of a commodity changes the change is a real change in price. It may be due to a change in the proportion of different grades exported, to a change in model of an important variety, or to a gradual improvement in quality. Likewise a decrease in the number of commodities exported may not be significant in the manner indicated by the figures. For instance, if four machines which will turn out ten units of work each

24 MEASURES OF EXPORTS OF THE UNITED

STATES

in a given period of time are exported in one year at $ 1 0 0 each, and if the next year only three machines are exported at $ 1 5 0 each, but each one will do twice as much work as the previous year's models, should we say that the price has increased 50 per cent and the quantity decreased 2 5 per cent ? Or should we say that we have exported 50 per cent more units of " work power " at a decrease in price of 2 5 per cent per unit ? T h e latter view seems more nearly correct. These defects in the data which result in lack of comparability cannot be completely eliminated. Strictly speaking, it may be said that no two commodities are ever exactly alike. Even within a given grade of wheat there is enough room f o r variation to induce millers to buy their wheat by sample. But one can pick and choose between commodities so as to obtain ones which are fairly homogeneous, or at least ones f o r which the lack of homogeneity is likely to create the least error. On a monthly basis comparisons are of course less reliable than on an annual. There is less opportunity f o r differences to average out, and there may in some cases be seasonal quality changes. B y selecting a large sample it is hoped that these errors will in part cancel each other. T h e tendency of the Department of Commerce to break its commodities up into more and more detail is improving the comparability of the items listed. About the only s a f e generalizations concerning the accuracy of the data are that it is not all that could be hoped f o r ; that the more inclusive the grouping the more accurate (and less significant) do the data become; and that manufactured articles are on the whole the least satisfactory. One consoling factor is that absolute accuracy is not important; the important thing is whether the error is constant in magnitude and direction so that the data are comparable. E v e n if there were a bias in the data so that prices of certain commodities were always quoted too high or too low, this

DATA FROM WHICH MEASURES

ARE COMPUTED

2$

would not affect the accuracy of a price index, provided the bias were always of the same magnitude. But there is no reason to suspect any bias in the data. Errors there doubtless are, but they probably are of the compensating variety. Consequently the data used in these indexes are the official figures obtained largely from the Monthly Summary.

C H A P T E R SELECTION I.

OF

III SAMPLE

REPRESENTATIVENESS

i. Proportionate

Value

Representation

Regardless o f the method of combining the data, the sample selected should be representative. One w a y of obtaining representativeness is that of random sampling, so that each type of item has an equal chance of inclusion. When one chooses only the most important commodities he violates somewhat the principle of randomness, yet this seems to be necessary if one is to be at all economical of his labor, or is to secure a sample which is adequate. B u t it is possible to improve upon random sampling. W e may break up our data into what we believe to be homogeneous groups, and either choose the proper number o f commodities in each group or so weight the groups that the proportions of each group will be the same in the sample as in the totality, thus assuring ourselves that each type of item will be represented. In attempting to secure representativeness one assumption is made: that prices and quantities in particular class groups have characteristic movements. Therefore domestic exports have been broken up into the five economic classes mentioned in Chapter II. In combining the separate indexes into a general index the five classes have been weighted by the exact value of all the domestic exports of each class during the periods in question. T h e classes themselves have been broken up into the class groups, again following the official classification. A s a starting point in the 26

SELECTION

OF

SAMPLE

27

selection of the sample the commodities used by the Department of Commerce in their more general index has been taken. Then commodities have been added, or in a few cases, omitted, until the percentage distribution of the value of the different groups within each class has approximated the same proportions as in the totality of commodities from which the sample is drawn. 1 In a few cases it seemed best to vary this procedure somewhat. In class C, group oo was found to be overweighted; hence the weight of this group has been reduced by multiplying it by .9. Group 6 in class D has been multiplied by .8 for the same reason. In class E , group 5 has been multiplied by .4. Sub-group 7' (machinery and vehicles, except automobiles, parts, and accessories) has been multiplied by 3 until 1927, 2.5 in 1928, and 1 . 5 in 1929 and 1 9 3 0 ; whereas sub-group 7" (automobiles, parts, and accessories) has been divided by 3. The justification for reducing the weight of sub-group 7' in 1928, and again in 1929, is that in this group in particular, and in those years especially, new commodities of importance have been added to the sample. These adjustments give approximately correct weights to these class groups for each year. The results achieved are shown in Chart I. The period selected is the year 1928. This was the last year for which class group values were available when the sample was selected. Average values for the period 1923-28 inclusive show just as good results. * ' It is not necessarily a criticism of the sample which the Department of Commerce uses that some of their class groups are inadequately represented, since they do not publish indexes for the separate classes. Deficiencies in a class group within a class are frequently compensated by an excess of the same class group within a different class. 2

Data for charts i, ii, iii and iv were obtained from Foreign Commerce end Navigation of the United States. In 1926 the classification of com-

28

MEASURES

OF EXPORTS

OF THE UNITED

STATES

SELECTION

OF

SAMPLE

29

2. Proportionate Value Changes A second method of obtaining a representative sample is that of so making up the sample that the value changes for each class, and for each group within a class, will correspond as closely as possible with all the commodities in that class, or class group.

Although there has been some change in the

composition of the sample, it has been possible to make a substantially accurate comparison by first comparing identical samples in successive periods, and then chaining back. Charts II, I I I , and I V indicate the success with which this test is met.

T h e class groups in Charts I I and I I I are ar-

ranged on the page in order of importance in 1 9 2 3 - 2 5 , and this average value indicated.

It will be noticed that while

the two lines representing class groups usually run along almost parallel on most of the charts, a f e w cases are not very good.

But if one will glance back at Chart I, or notice the

export values indicated in this series of charts, these class groups will usually be found to be of very slight importance. Usually it is impractical to include very many commodities in such class groups. In arriving at values for group 7 the total value of automobiles, parts, and accessories (adjusted as indicated above) has been added to the sample (also adjusted) of machinery and vehicles other than automobiles, parts, and accessories. T h a t is to say, the total value of sub-group 7 " has been used rather than just the sample, which includes automobiles only. T h e reason for this is that while previously to 1 9 2 9 automobile exports tended to increase relative to those of automobiles, parts, and accessories, in 1 9 2 9 the reverse was true. In that year automobiles, parts, and accessories showed a modifies was changed, without warning, in this publication. Hence it was necessary to revise the 1923 and 1924 figures obtained from this publication, as there are no revised tables published, except f o r the year 1925. T h e Department of Commerce has verified my corrections.

30

MEASURES

OF EXPORTS

OF

CHART COMPARISON

OF A N N U A L

VALUE

THE

UNITED

STATES

II

CHANGES

or

THOSE OF S A M P L E , BY C L A S S GROUPS.

ALL D O M E S T I C CLASSES A , B

EXPORTS

WITH

AND C .

( C l a s s groups are r e f e r r e d to by numbers oo to 9 inclusive.

Figures in

parentheses indicate the total value of exports of the different class groups in the base period.

1923-25=100.)

SELECTION

OF

SAMPLE

SCALE.- ONE. SPACE = 2 0 PER CENT C H A R T COMPARISON

OF A N N U A L

VALUE

III

CHANGES

OF ALL

THOSE OF S A M P L E , BY C L A S S GROUPS.

DOMESTIC

CLASSES D

EXPORTS

AND

WITH

E.

(Class groups are referred to by numbers o to 9 inclusive. Figures in parentheses indicate the total value of exports of the different class groups in the base period. 1923-25=100.)

32

MEASURES

OF EXPORTS

CLASS

PERCENT 1201

OF THE UNITED TOTAL

C

STATES

EXPORTS \

\

100

\\ V

80 60 1923

24

'25

'26

'27

CLASS

1923 '24

25

'26

'25

'29

'30 '23

'24

'25

B

'27

CLASS

1923 2 4

28

'27

CLASS

'28

'29

'30 '23

'24

'25

A

CHART

'24 2 5 SAMPLE

'26

'26

'29

1930

27

'28

'29

1930

'28

'29

1930

D

'27

IV

V A L U E CHANCES

OF ALL DOMESTIC

W I T H THOSE OF S A M P L E , BY ECONOMIC CLASSES. (1923-25 =

'20

E

CLASS

'26 '27 28 '29 '30 '23 ALL COMMODITIES

COMPARISON OF A N N U A L

26

100)

EXPORTS

SELECTION

OF

SAMPLE

big increase, while automobiles (excluding parts and accessories) showed an actual falling o f f ; indicating an increased tendency to ship parts abroad for assembly there in combination with foreign parts, rather than to export automobiles as such. A s will be explained in more detail in chapter V , a price index has been constructed from the sample (automobiles) and used to deflate the value of automobiles, parts and accessories in arriving at indexes of price and volume for Class E. 1 It is in meeting this test of representativeness that the sample used by the Department of Commerce is most defective. In a relatively short time a sample, selected on the basis of the importance of the exports during a specified period, apparently becomes out of date. Some commodities become of dwindling importance, and unless these are replaced or supplemented by commodities of growing importance, the value of the sample deviates downward from the value of the totality from which it was drawn. This difficulty was observable in nearly every class group of the Department of Commerce Sample. T o get around this difficulty the department, in effect, constructed its volume index by using a price index with which to deflate. 2 Unfortunately this tendency of the sample to deviate downward has shown itself in the brief period which has elapsed since the sample for the present indexes was drawn. II. ADEQUACY

If a large number of commodities are included in the sample the reliability of each index number is increased. Since the probable error of the arithmetic mean varies inversely with the square root of the number of commodities, and also the proportion of the total included, it is important 1

Cf. infra, p. 66.

2

Cf. infra, Appendix D, pp. in-114.

MEASURES

OF EXPORTS

OF THE UNITED

STATES

to have a sample which is large, not only absolutely, but relatively. 1 The number of commodities which are included in the sample in different years is as follows : Class

1923

1928

1930

A B C

23 IS 41

23 IS 42

23 IS 42

D

S3

59

59

E

80

91

116

212

230

255

Total

Since there were over 1300 different kinds of items exported in 1928 according to the official classification, only about 17.5 per cent of these commodities are covered by the sample. Quantities are given for about 1 1 5 0 of the 1300 items, so about 20 per cent of the commodities which it would have been possible to have used were actually selected. Of course, quantities for a large proportion of the 1 1 5 0 commodities are quite meaningless. The number of items in the sample seems to be unavoidably growing. The reason for this is that each year the government is constantly breaking up commodities into smaller and smaller subdivisions. Although this involves more labor on the part of the computer of index numbers, at the same time it improves the quality of the index, as it makes the commodities in the sample more homogeneous. 1 The formula for the standard error of the arithmetic mean, when n is the number of items in the sample, and N the number of items in the universe, may be written

g sample Vn

j ^

1

n N

See Bowley, A . L., " Measurement of the Precision Attained in Samp-

ling ", Bulletin, de L'Institut International de Statistique, 1926, Tome xxii, 1ère livraison, troisième partie, p. [9].

SELECTION

OF

SAMPLE

35

On the other hand the percentage of the total value which the sample comprises is much higher than the percentage of the total number. Although the latter was only 17.5 per cent in 1928, the table below indicates that the former varied in that year from 50.2 per cent in the case of finished manufactures to 95.6 per cent in the case of raw materials. A word of explanation is necessary concerning this table. The columns labeled " actual" refer to a summation of the values of the commodities selected. The " effective " columns, however, refer to a summation of the adjusted class groups. For instance, in Class E , Class Group 5 has been multiplied by .4. The commodities included in the sample vary from year to year; but the values used in computing this table refer to commodities used in linking a given year with the preceding, rather than the following, year. Actual 1928

Effective 1923 1928

Class

1923

A B C D E

95-5 95-8 85.2 72.2 45-7

95-6 95-0 82.0 74.6 50.2

95 5 95-8 79.8 65.9 35.9

95-6 95-0 77.9 67.9 36.1

72.8

70.9

67.7

63.2

All Classes

It is unfortunate that Class E , the class of greatest absolute and most rapidly growing importance, is least adequately represented in point of value. Total domestic exports of each class in 1923 and 1928 expressed as a percentage of total domestic exports of all classes is as follows: Class

1923

1928

A B C D E

29.5 6.3 14-3 13.8 36.1

25.7 5-8 9-3 14.3 44-9

Total

100.0

100.0

36

MEASURES

OF EXPORTS

OF THE UNITED

STATES

Although it is unfortunate that Class E is under-represented relatively to the other classes, this is unavoidable, as the following section shows. III. L I M I T A T I O N S ON T H E CHOICE OF COMMODITIES

There are several limitations in the selection of a sample, imposed by the nature of the data. The first is lack of quantity figures. This is especially serious in the case of finished manufactures, and particularly in the case of machinery and vehicles. A second limitation is lack of homogeneity. It has been remarked that none of the commodities from which we must choose are strictly homogeneous, and many of them are quite otherwise. It has also been pointed out that this fact is of no significance provided the composition of the shipments does not vary. But many commodities show quantities which are immediately seen to be quite meaningless. Again finished manufactures, and especially machinery and vehicles, are bad offenders. Such a designation as pounds of " other industrial machinery and parts, n. e. s." is sufficient to warn the most unwary not to include the commodity as part of a sample to be used in constructing an index number.1 Other commodities give such strong internal evidence of unreliability that it seems best to exclude the worst of them. Shipments of commodities which are non-homogeneous we would expect to vary in price to different countries. Therefore it was decided to exclude commodities which show a wide geographical dispersion of prices. It is not meant to imply that non-homogeneity is the only cause of price dispersion. Differences in packing, which is closely akin to lack of homogeneity, differences in distance from production center to seaboard point of export, differences in the time of 1

" n. e. s." is an abbreviation of " not elsewhere specified"

SELECTION

OF SAMPLE

37

year in which shipments are made to different countries, price discrimination in favor of certain areas, and no doubt other factors, would all result in price dispersion. Also, considerable non-homogeneity could exist without displaying any symptom of price dispersion. Nevertheless, in choosing between different commodities, it is believed to be advantageous to select those commodities which show the least differences in price, and to exclude those which exhibit the most. Some leniency has been shown, however, if the same geographical price structure persisted in successive years. Weighted average deviations have therefore been computed for each commodity included or " tried out " for the index. More specifically, coefficients of price variation were computed as follows: Export prices were computed (by dividing values by quantities) for the five most important countries to which we export each commodity. The weighted arithmetic mean of these export prices was computed, and the weighted average deviation of these export prices from the weighted arithmetic mean. The result (average deviation) was then divided by the weighted arithmetic mean and became a coefficient of variation. The weights used were not exact weights, but for the sake of speed in calculation were whole numbers whose sum is 10. Prices to unimportant countries were overweighted, rather than the opposite. Whenever a commodity has been added to the sample selected by the Department of Commerce, coefficients of variation have been computed for more than one year. An additional check in some cases has been to compare export price changes of the selected commodity with domestic prices of standard grades of the same commodity. Chart V exhibits coefficients of price variation (narrow bars) of the forty leading exports in 1928 which were included in the sample. No significance is to be attached to the length of a wide bar (indicating value of exports) rela-

38 MEASURES OF EXPORTS OF THE UNITED STATES

CLASS

GROUP C O M M O D I T Y A 3 A A A A A

B B B B B B

S H O R T STAPLE

MILLIONS OF DOLLARS 0

50 25

PERCENTO

100 50

150 75

200 100

COTTON

2 BRIGHT FLUE CURED T O B A C C O 3 LONG STAPLE COTTON 5 BITUMINOUS C O A L 5 ANTHRACITE COAL 5 CRUDE PETROLEUM

I I I I

WHEAT BARLEY CORN A P P L E S IN B O X E S I R Y E I ORANGES

COOLARD C I W H E A T F L O U R C O O HAMS A N D S H O U L D E R S . C U R E D COO B A C O N L C I P R U N E S D D D D D D D D

6 5 6 4 2 4 6 5

R E F I N E D C O P P E R G A S AND FUEL OIL T I N P L A T E ETC. BOARDS ETC,SOUTHERN PINE, ROUGH G U M ROSIN BOARDS ETC.,DOUGLAS FIR.ROUSH IRON OR STEEL SHEETS,GALVANIZED J SULPHUR OR B R I M S T O N E ¡P

E E E E E E E E E E E E E E E

S 7 7 5 5 7 5 S 7 7 5 2 7 2 7

GASOLINE,ETC., IN B U L K PASSENGER CARS.UPT0 $ 1 0 0 0 PASSENGER C A R S , $ K > 0 0 - $ 2 0 0 0 KEROSENE,IN B U L K LUBRICATIN6 OIL, RED A N D PALE MOTOR T R U C K S . U P T O I T O N GASOLINE, ETC, IN C O N T A I N E R S K E R O S E N E , IN CONTAINERS WHEEL TRACTORS, 15-32 B E L T R P MOTOR T R U C K S . 1 - 2 / » T O N S LUBRICATING OIL.CYLINDER AUTOMOBILE CASINGS PASSENGER C A R S , OVER $2000 C I G A R E T T E S STANDARD T Y P E W R I T E R S . N E W

1 1

1

1

1

1

1

1

1 1

1 1 1 1

!

CHART V V A L U E OF T H E F O R T Y L E A D I N G C O M M O D I T I E S E X P O R T E D I N A N D C O E F F I C I E N T S OF T H E I R P R I C E V A R I A T I O N .

1928,

SELECTION

OF

SAMPLE

39

tive to a corresponding narrow bar (indicating coefficient of variation). However, some importance should be attached to any correlation between the importance and the price variation of these commodities If it should appear that important commodities tend to be least reliable (as judged by this test), less confidence could be placed in the final indexes than if the contrary should be the case. With the exception of such heterogeneous items as other industrial machinery and parts, n. e. s. ; automobile parts for assembly; automobile parts for replacements; and household and personal effects, the commodities shown in this chart are also the forty leading domestic exports. The percentage of the sample in number and in value which these forty items included in 1928 is as follows:

Class

Percentage of number of commodities

Percentage of value of commodities

A B C D E

26 40 12 14 16

94 86 60 56 74

17

78

All Classes

A final limitation on the selection of commodities is a concession to practicability. A compromise must be struck between accuracy and labor. It hardly seems worth while to retain commodities which do not amount during any year to $1,000,000. Several items used by the Department of Commerce have been dropped for this reason. If, however, inclusion of small items seems to make the sample appreciably more representative, they have been included.

CHAPTER IV M E T H O D S OF

CONSTRUCTION

I . METHODS AVAILABLE

i.

Averages

THERE would be no advantage in reviewing all the types of average and all the formulas which can be discovered. In particular we will not consider the median, the mode, or the geometric mean. The median and the mode are not reliable if the number of items is small (as is the case with raw materials and raw foodstuffs), and are not suitable for combining separate indexes into a general one. While the geometric mean is admirably suited to averaging relatives, it does not convey the precise shade of meaning desired, since it fails to show to what extent changes in income are due to price change or to quantity change. The use of the geometric mean involves also a large amount of labor. But it seems worth while to follow a line of thought which has a direct bearing on the methods finally chosen. ( i ) Simple Averages, Arithmetic and Harmonic The so-called unweighted arithmetic average of relatives is among the easiest of index numbers to compute. Let us take a simple illustration: Commodity

40

1923

1924

¡925

A

Price . . . Quantity

1

2

3

B

Price . . . Quantity

2

C

Price . . . Quantity

5

3

4 4

3

METHODS

OF CONSTRUCTION

4I

Price index numbers are as follows: 1924/1923: 3 / ' + 3 / 3 + 4/5 1925/1923:

3 / 1 + 4// + 3 / 5

=

=

= ¿

I43.33

p^

cent

= 186.67 per cent

Really the indexes just considered are not unweighted at all; but merely weighted on the assumption that the same value of each commodity was traded in during the base period. T a k e the following expansion of the previous illustration: Commodity

1923

Price Quantity

1 100

Value

100

„

Price Quantity

P

Price Quantity

a

2 50

1924

1925

2

3

3

4

4

3

100

Value

5 20 100

Value

Using P0 Qo weights we get the same results as above. Jg24/I923.

2/1 (100) + 3 / 2 Q O O ) + 4 / 5 (100)

ioas/1021y

3/1

(I00) + 4 / 2

(IOO) + 3 / S

300

(I00>

=

=

g?

=

143.33 per cent

=186.67 per cent 300

560

Neither the unweighted harmonic average nor the harmonic average weighted by P 0 Q 0 weights give the same results. But if the same quantities are traded in each year, the harmonic average, weighted by given year value weights, gives identical results:

42

MEASURES OF EXPORTS OF THE UNITED Commodity Price Quantity

¡9*3

W4

W5

I 100

2 ioo

3 100

200

300

3 5«

4 So

150

200

4 20

3 20

80

60

Value „

Price Quantity

2 50

Value Price Quantity

C

STATES

5 20

Value

1024/102-1 , 4 3 / ° — r ~ l — / / 0 x = 300 — = 1 4 3 - 3 3 per cent liWJ • ,-/r2- ?(20,,)r -+i — 2 / 3 (,50) + 5/4 (80) 1925/1923:

=

1/3 (30°) + 2/4^200) + 5/3 (60) = S

18667

^

^

( 2 ) Weighted Averages, Arithmetic and Harmonic This relationship is not due to the particular combination of figures. Let us substitute different weights. Commodity

B

c

1923

1924

Quantity Price

5 1

5 2

5 3

Value

5

10

15

Price Quantity

2 4

3 4

4 4

Value

8

12

16

Price

5

4

3

Quantity

6

6

6

30

24

18

Value

1925

Arithmetic Average, P 0 Q 0 weights: 1924/23:

2/1

( 5 ) + 3 / 2 ( 8 ) + 4 / 5 (30) 43

1925/33: 3 / 1 . ( 5 1 + 4 / 2 . ( 8 ) + 3 / 5 j 3 g ) 43

=

=

I 6 — ,06.98 per cent 43 49 = 43

per

cent

METHODS OF CONSTRUCTION

4 3

Harmonic Average, Pi Qi weights: 1924/23:

1/2 (10) + 2 / 3 * 2 ) + 5 / 4 ( 2 4 ) = £ =

10698

cent

1925/231

1/3 (15) + ^ 6 ) +5/3 (-8) = 4 1 ^

1 1 3 95 PCr CCnt

The difference between the arithmetic and harmonic averages can thus be resolved into a matter of weighting. (3) Aggregates It is a well-known fact that an arithmetic average of relatives with base period value weights is the equivalent of an aggregative index with base period quantity weights. Likewise a harmonic average with given year value weights is the equivalent of an aggregative index with given year quantity weights.1 In the following illustrations, therefore, since an aggregative index is easier to construct than an average of relatives, the former will be used. 2. Chain Indexes Suppose now that we compute a chain index from the same data: 1924/23: 1925/241

46

= 46 = 106.98 per cent

15+16+18 49 , 1 0 + 1 2 + 24 = 4 6 = 4 9 = 1 0 6 . 5 2 per cent

46 49 49 1925/23: y 3 X - 6 = ~ 3 =

113.95 per cent

There appears to be no bias in a chain index, using either the aggregative method or the arithmetic or the harmonic average of relatives, provided the quantity elements in the weights do not change. The value weights used in the average of relatives of course must change. To carry our illustration a step further let us assume that our quantity weights do not remain constant. Let us assume 1

See p. 68 for an application of this fact.

44

MEASURES

OF EXPORTS

OF THE UNITED

STATES

that there is positive (though not necessarily perfect) correlation between the price and quantity movements of one or more of our commodities.

5

1924 2 5

1925 3 5

....

5

10

15

... ....

2 4

3 5

4 6

Value

....

8

15

24

Price Quantity

....

5 6

4 6

3 6

Value

. . . . 30

24

18

Total Value

. . . . 43

48

57

Commodity

¡9*3

A

Price Quantity

D

Price Quantity

I

... . . . .

Value

...

Fixed base indexes, constant weights: 1924/1923: 1925/1923:

1 0 + 1 2 + 24 = 46 = 8 + 30 43 15+16+18 g +

30

106-98 per

cent

49 = -3 = 113.95 per cent

Fixed base indexes, given year weights: 1924/1923 : 1925/1923:

1 0 + 1 5 + 24

49 = 4"s = 108.89 per cent

15 + 2 4 + 1 8 s-_^I2 + 3 0 =

57 = 121.28 per cent

47

Chain indexes, preceding year weights: 46 1924/1923: ^ = 106.98 per cent . 15 + 2 0 + 1 8 53 1925/1924: , 0 + I S + 2 4 = - = 108.16 per cent , 46 53 1925/1923: T ^ X " = 1 1 5 7 1 per cent

METHODS OF

CONSTRUCTION

45

Chain indexes, given year weights: 1924/1923:

49

= 108.89 per cent

15 + 2 4 + 1 8 _ 57 1925/1924: - „ , + 18 + 24 " 5 2 =

.

49 . . 57

l

°9- 6 a I* 1 "

cent

,

1925/1923: - J X J 2 = 1 1 9 36 per cent

Recapitulating, we have price indexes f o r 1 9 2 5 relative to 1 9 2 3 , arranged f r o m lowest to highest, as f o l l o w s : Per cent Fixed Chain Chain Fixed

base index, constant weights index, preceding year weights index, given year weights base, given year weights

113.95 115.71 119.36 121.28

This is as we should expect. Commodity B was weighted least heavily in the fixed base, constant weight illustration. The chain indexes gradually increased the weight of this commodity, given year weights increasing it more than preceding year weights. T h e fixed base index with given year weights found its weight suddenly jumped to full strength. A s indicated in a previous illustration, had the maximum quantity weight been attained in 1924, the last two indexes in the table would have been exactly the same. It should be noted that the reason why the fixed base index with given year weights is the highest is not because there was positive correlation between prices and quantities, but merely because an item which showed a strong upward trend was heavily weighted in the last year. The illustration could just as well have been drawn in such a way that the quantity of commodity B returned to the 1 9 2 3 level; or that the positive correlation was between prices and quantities whose trend was downward. The purpose of these illustrations has been to point out that the divergence of chain-index numbers f r o m fixed base

46 MEASURES OF EXPORTS OF THE UNITED STATES index numbers is not due to the use of the arithmetic (or harmonic) average; nor to the use of given year or preceding year weights (provided the system of weighting used is appropriate to the average selected) ; but to the particular relationship which exists between the price and quantity movements of the series of which the index is composed. No sweeping statement can be made concerning how a chain index will act until the underlying economic and natural factors have been explored. Even then it is difficult to predict. It is worth while to state our conclusions in more exact language. If commodities whose prices rise more (or fall less) than the average are also commodities whose quantities rise more (or fall less) than the average; and/or if commodities whose prices fall more (or rise less) than the average are also commodities whose quantities fall more (or rise less) than the average; an index number with given year weights will tend to deviate upward from an index number with base year weights. If this situation persists for several periods, a chain index with either system of weighting may deviate upward from a fixed base index with base year weights. If the opposite relationship holds true, the effects will be the opposite of that described above. The mere positive or negative correlation between price or quantity movements is not sufficient to produce the results mentioned. For instance, if a price which has increased relatively but decreased absolutely is associated with a quantity which has increased both relatively and absolutely, we have negative correlation of prices and quantities; yet the given year weighted index number is larger than the base year weighted index number. (In our illustration an absolute increase was also a relative increase.) The statement which has just been made holds true also of volume indexes. Results obtained for volume indexes constructed from the same data are as follows:

METHODS

OF

CONSTRUCTION

47

Percent Fixed base index, constant weights ., Chain index, preceding year weights , Chain index, given year weights Fixed base index, given year weights

109.30 . 111.06 114-56 116.33

In order to give effect to both given year and preceding year weighting in chain indexes, recourse is sometimes had to averaging (geometrically) the t w o types.

T h i s results in

the so-called " i d e a l " index number of I r v i n g Fisher.

Since

under certain conditions a chain index using either the given or the preceding year w e i g h t s will diverge in a specified direction f r o m a fixed base index, it is not surprising that a geometric average of the t w o will likewise diverge in that direction.

W a r r e n M . Persons, w h o has made extensive

studies along this line finds further that if important commodities rise in price more than the average (relative to a fixed base) and remain high in price in the succeeding period (relative to the average for that period), regardless of higher production, and if important commodities fall in price more than the average (relative to a fixed base) and remain low in price regardless of smaller production (i. e., if in general it is difficult to adjust production to prices and if more than one year is required for adjustment and in the meantime production is increased due to stimulus of high prices but not enough to cause a significant decline in price, and production of other commodities is curtailed on account of lower prices but not enough to cause a significant rise in prices) then . . . the fixed base will tend upward faster than the chain index or, in other words, the chain index will diverge downward. 1 And again: Between any pair of consecutive periods the chain index will increase less rapidly (or decrease more rapidly) than the fixed 1

Persons, Warren M., The Construction of Index Numbers, Boston,

1928, pp. 70-71.

48

MEASURES

OF EXPORTS

OF THE UNITED

STATES

base index computed by the same formula if a certain kind of relationship or correlation exists between the movements of prices and movements of weights for those periods. Likewise, the chain index will increase more rapidly (or decrease less rapidly) than the fixed base index if the converse of the relationship or correlation (indicated in the preceding statement) exists. Specifically, if we use formula v, the " ideal," the " certain kind of relationship or correlation between the movements of prices and movements of weights " that will cause the chain index to increase less rapidly in any interval than the fixed base index is one in which the [high?] price relatives of period (n) continue high in period (n -f- i ) , but quantities increase and / or low price relatives of period (n) continue low in period ( n - f i ) , but quantities decrease . . . The situation described in the preceding paragraph is apt to occur if the adjustment of the quantities to the stimulus of high prices or the depressing effect of low prices are not in fact accomplished in the interval between the two periods in question. If the adjustments of quantities to prices take several periods the chain index would tend to diverge more and more widely downward from the fixed base index. This is more apt to be the situation for agricultural products than for the products of manufacturing and mining. 1 W e have been considering how chain index numbers behave in one respect; we have been considering " weight correlation bias " . T h i s term was coined by Warren M . Persons to indicate that chain indexes diverge from fixed base indexes due to some relationship between changes in price relatives and the weights with which they are associated. 2 It may be worth while to consider briefly how the types of index numbers we have been considering behave in 1

Persons, op. cit., pp. 82-83.

Ibid., the book is devoted almost entirely to an exposition of this matter. 2

METHODS

OF

CONSTRUCTION

49

certain other respects. How do they behave with respect to certain much disputed tests of index numbers. 3. Tests of Index

Numbers

If we wish to shift the base from 1923 to 1924, it is of course legitimate to do so in the case of the chain index, for its base-shifting character is its essence. It is also legitimate to do this in the case of the fixed base, constant weight, aggregative index; for since the price index compares the changing value of a fixed aggregate of goods at changing prices, it makes no difference whether that aggregate be the amount traded in during the base period, or some other period. Likewise, since the volume index measures the changing value of a varying aggregate at fixed prices, it makes no logical difference whether or not the prices are base period prices. Nevertheless it must not be supposed that aggregative indexes, chain or fixed base, using only one system of weights, meet the " time reversal " test. The " time reversal " test requires that if the time subscripts in a formula " be interchanged, the new formula resulting will become the reciprocal of the old." 1 This technical requirement can be met, however, by using the " ideal " formula, which, as has been explained, is an average of two index numbers. The " circular " test is usually considered as an extension of the "time reversal" test. If " P 12 X P 23 X P 31 = 1 " the condition is satisfied.2 The reason for wishing to meet this test is that one may wish to make compari1 Fisher, Irving, The Making of Index Numbers (Publications of the Pollack Foundation for Economic Research, No. i ) , Third Edition, Revised, Boston, 1927, p. 71.

- Ibid., p. 413. The symbol " P 12 " refers to the price index number of period 2 relative to period 1, and similarly for the other symbols. Any number of periods may be included in the circle.

50 MEASURES

OF EXPORTS

OF THE UNITED

STATES

sons between adjacent periods and also between periods f a r separated in time. Or to put it another way, one may wish his index to reflect both long-time and short-term changes. Needless to say, any index number which is subject to " weight correlation bias " will not s a t i s f y the " circular test". It is sometimes considered desirable also if one can mul tiply a price index number by a volume index number and get a resulting figure which accurately represents change in relative value. Whenever one uses a price index to deflate values, the resulting measure of volume, if it is to have any definite meaning as an index number, must be capable of being expressed in some direct formula. If one multiplies the price indexes of 1 9 2 5 / 1 9 2 3 in the above illustrations by volume indexes of the same type, he obtains value indexes as follows: Per cent Fixed Chain Chain Fixed

base indexes, constant weights indexes, preceding year weights indexes, given year weights base indexes, given year weights

124.5 128 5 136.7 140.8

The relative value change, however, is 1 3 2 . 6 per cent. I f , however, we multiply together two fixed base indexes with opposite systems of weighting, or two chain indexes with opposite systems of weighting, we get the desired result. Algebraically the reason for this is clear. Thus z P. Q o v £ P, Q, n r 2 p i Qi v - po Q> _ 2 p i Q. n r v > 2 P. Qo 2 P. Q, J P, Q, * * P. Q. ~ * P. Qo VP In the case of the fixed base indexes we must use one very flexible index and one very inflexible. In the case of the chain indexes both are flexible, although in different degree; the one with given year weights being most responsive to changing economic conditions.

METHODS

OF

CONSTRUCTION

51

A g a i n , however, these pairs of index numbers do not meet the " factor reversal " test. T h i s test requires that the product of a price index and a volume index, which results f r o m interchanging the P and Q factors in the price index, be an accurate measure of value change. 1 A g a i n also, a geometric average of the two price (or quantity) indexes, one with given year weights and the other with preceding year weights, meets a strict interpretation of the test. II. T H E P U R P O S E OF I N D E X

NUMBERS

It has been said that these tests are much disputed. The dispute concerns the very nature of index numbers. Before summing up our own position on the matter we shall present some of the leading opinions on the points at issue. " Let us assume ", says Irving Fisher, " that we have accurate and complete data both as to prices and quantities and, therefore, values. . . . W h a t formula for the index number of, say, prices is the most accurate? " 2 There is a reasonable question to ask in his opinion, for, " a good formula for one purpose is a good formula for all known purposes ", 3 Therefore he applies tests to different formulae to discover which is best. The " time r e v e r s a l " test and the " factor r e v e r s a l " test are " constituted the two legs on which index number can be made to walk ".* Although Mr. Fisher thinks that " a good formula for one purpose is a good formula for all known purposes " , in reasoning which leads him to reject the circular test, he discriminates, perhaps inconsistently, between different uses of index numbers. His illustration is very interesting, and we shall quote it at length. 1

Fisher, op. cit., p. 79.

2

Ibid., p. 213.

3

Ibid., pp. 229-230.

* Ibid., preface, p. xiii.

52

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

Let us take three places which, to fix our ideas, we shall call Georgia, Norway, and Egypt. Take a list of 15 commodities of which 5, led by lumber, are important in both Georgia and Norw a y ; 5, led by cotton, are important in both Georgia and E g y p t ; and 5, led by paper, are important in both Egypt and Norway. L e t us further suppose that the lumber group, important in both Georgia and Norway, have about the same prices in Georgia and Norway, and that they so dominate the price comparison between these two countries that the index number is about the same in both countries, the other two groups of commodities in these two countries not greatly interfering with this equality, because one is unimportant in Georgia and the other is unimportant in Norway. Likewise, in comparing Georgia and Egypt, the cotton group so dominates the Georgia-Egypt index number as to make Georgia and Egypt about the same price level. W e might conclude, since " two things equal to the same thing are equal to each other," that, therefore, the price levels of Egypt and Norway must be equal, and this would be the case if we thus compare Egypt and Norway via Georgia. But evidently, if we are intent on getting the very best comparison between Norway and Egypt, we shall not go to Georgia for our weights. In the direct comparison between Norway and Egypt the weighting is, so to speak, none of Georgia's business. It is the concern only of Egypt and Norway. In such a direct comparison between Norway and Egypt, the paper group, which played little part in the other two comparisons now tends to dominate the situation; and if these 5 commodities are higher in price in Norway than in Egypt, that fact may suffice to make the whole Norwegian price level somewhat higher than the Egyptian. T h e paradox of finding the price levels of Norway and Egypt different, although by separate comparisons the price level of each is the same as that of Georgia, is no more strange than that we may find two people each resembling in their features a third person without resembling each other. Since an index number is a composite dependent on heterogeneous elements, a variation in the composition will change the comparison quali-

METHODS

OF

CONSTRUCTION

S3

tatively. There is really, therefore, no contradition or absurdity in the apparent inconsistencies; for the three comparisons are all different

in

kind}

Warren M. Persons seems to fall into the same school of thought to which Irving Fisher belongs. He explains at length in his book on The Construction of Index Numbers what he calls " weight correlation bias " ; which is the kind of " bias " which prevents satisfaction of the "circular test". This test is one on which he places a great deal of reliance. Exact satisfaction of the factor reversal test is not of great practical importance in the construction of index numbers, and exact satisfaction of the base reversal test is not a necessary condition for the securing of a good index number if weights and averages are selected in such a way as to avoid weight correlation basis.2 The only way in which the fixed base indexes and the chain index can be made to give results which are not inconsistent with each other for an intercomparison of three or more periods is to use fixed or constant weights in constructing indexes of average prices for the periods to be compared. In other words, satisfaction of the " circular test" is indicated.3 Mr. Persons believes that " the best index number of prices or quantities for a binary comparison is given by the ' ideal' formula ", 4 " The best index number of prices or quantities for an intercomparison of three or more periods he thinks however, " is the aggregative average with fixed weights based upon arithmetic mean quantities of prices, respectively, for all the periods covered." 5 1

Fisher, op. cit., pp. 271-273.

2

Persons, Warren M., The 1928, p. 81. 3

Ibid., p. 84.

* Ibid., p. 85. 6

Ibid., p. 86.

Construction

of Index

Numbers,

Boston,

54

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

Opposed to this way of thinking is Wesley C. Mitchell, who says: The first step, framing a clear idea of the ultimate use of the results, is most important, since it affords the clue to guide the compiler through the labyrinth of subsequent choices. It is, however, the step most frequently omitted.1 A more extreme statement of this position is given by Willford I. King. " The commonly accepted ' tests' for index numbers " , he says, " are entirely useless." 4 " The mission of the index number is to make the sample tell the same story as the totality." ' But the story to be told depends on the question asked. " A n y one of . . . five answers might be given in reply to the question: ' What was the ratio of stock prices at the last date to stock prices at the first date?' " since " the question in this form is too vague to permit of a definite answer." r These five answers would be replies to the following specific questions: /. How did the average price of all shares dealt in on the last day compare with the average prices on the first day? 2. How would the total value of stocks on the last day have compared with the total value on the first day if the same number of shares of each kind of stock had been sold on the last day as on the first? j. Considering each stock as of equal importance, what was the average ratio of the price on the last day to the price on the first day? 4. What per cent would an investor have gained or lost 1

Mitchell, Wesley C., Index Numbers of Wholesale Prices in the United States and Foreign Countries, Bulletin No. 284 of the United States Bureau of Labor Statistics, part i, p. 23. 1

King, Willford I., Index Numbers Elucidated, New York, 1930, p. 57.

'Ibid.,

p. 54.

* Ibid., p. 52.

METHODS OF CONSTRUCTION

55

through changes in stock values had be bought one share of each stock dealt in on the first day of the period and sold out on the last day of the period? 5. When all the stockholders on the first day under consideration are taken as a unit, what per cent of gain or loss in the value of their securities is shown by the prices on the last day? 1 It is, however, not necessarily to be " assumed that the formula required to answer a given question from complete data is the best one to use with sample data ". 2 Professor King's insistence that there can be no " b e s t " formula for an index number, since different formulae answer different questions, seems quite reasonable. It does not follow, however, that to serve any particular purpose best the question which is appropriate to ask is one which can be simply worded. In the case of exports, for instance, no comparison of the varying value of a given aggregate of commodities exported at changing prices would be a completely satisfactory price index, for the composition of the aggregate itself varys considerably under actual conditions. Perhaps a chain index with varying weights would answer a more appropriate question. We can think of a chain index of price as representing the varying fortune of a trader who buys goods at one period and sells them at the next, reinvesting the proceeds. His profits of course depend on price changes, and also on whether he makes a judicious selection of commodities in each period. A chain index of volume (with preceding period weights) on the other hand, represents the varying fortune of an underwriter who participates in offering a fat sum for the " exportable surplus " and hedges against price change by placing a contract (perhaps with the other trader) to sell the entire aggregate of goods at specified unit prices. This underwriter likewise always 1

King, op. cit., p. 51.

2 Ibid., p 185.

56

MEASURES

OF EXPORTS

OF THE UNITED

STATES

risks his entire fortune. It is not even necessary in order to be specific, that a question be capable of being formulated in words. The most appropriate question to ask might be a very complicated one; but if it can be expressed in a mathematical formula it is quite definite. A s a practical matter it is usually impossible to formulate a simple question and answer it with index numbers. Any substitution or addition of commodities as they become available invalidates the index number as an answer to such a question. But according to Professor K i n g the formula which would best answer the question when applied to the whole population is not necessarily the best one to apply to the sample. It would seem therefore quite conceivable that some very complex formula, such as the " ideal", which Professor King condemns, might be the most appropriate to apply to the sample. In order to discover which formula, when applied to the sample, best answers the question we wish to ask of the totality, we have two courses open. First, we can experiment. This is not practical, f o r : ( i ) complete data is rarely available, and ( 2 ) if one constructed an index number with complete data there would be little point in constructing another with sample data. The second course is nearly as doubtful. W e may accept as being of general applicability the results of Professor King's experiments with a limited variety of data. Even these experiments were not in each case with data which were actually complete; they were merely assumed to be complete for the purpose at hand. 1 We may conclude therefore: ( 1 ) that a simple question is not always an appropriate one to ask, regardless of the completeness of the data; ( 2 ) that even with complete data the necessity of adding items which become available from time to time makes difficult the formulation of a simple 1

See King, op. cit., chapter vii, especially pp. 168 el seq.

METHODS

OF

CONSTRUCTION

57

question to be answered; and ( 3 ) that in some cases we must use fairly complicated methods to make the sample behave like the totality. Since we are of the opinion that the purpose of the index determines the methods to be used, there can be no object in seeking to satisfy certain tests, unless the satisfaction of those particular tests makes the index more suitable for the particular purpose at hand. Furthermore it is difficult to see under what circumstances it would be desirable to meet the " time reversal" and " factor reversal" tests as defined by Irving Fisher. There may be situations in which it is desirable to have the product of one's price and quantity indexes indicate accurately a change in value; as in the present instance it is desired to compare price, volume and value changes. But just why it is necessary that the volume formula be the price formula with P and Q factors interchanged is not clear. Likewise it may be desirable to shift the base of one's index number in order to compare it with another; but this hardly seems a reason for requiring that a reversal of the time subscripts in a formula result in a new formula which is a reciprocal of the other. It is our opinion that the formula to be used depends on the purpose of the index; but that the question to be asked need not be a simple one, or even one capable of verbal formulation. Since it is impossible to find a formula which satisfies perfectly all purposes, it is necessary either to construct separate indexes for each purpose, or else to decide what method will most nearly satisfy the objects for which it is intended, but satisfy best the objects of primary importance. A compromise of this sort seems necessary if an index number is to be of any but very limited use.

58

MEASURES

OF EXPORTS

OF THE

UNITED

III. C O N S I D E R A T I O N S I N D E T E R M I N I N G

STATES

METHODS

OF C O N S T R U C T I O N

I. Object for which

Intended

I f these indexes are to be useful in connection with the study of cyclical movements of business, then they should be ones which reflects short-term changes in price and volume, rather than the long-time trend, if one index number cannot do both. A n aggregative price index with constant weights shows the varying value of a fixed aggregate of goods as prices change over a period of time. But is it not more important to know the change in price of goods exported during successive periods? Nor would it help matters to retain the fixed base idea, but use changing weights. Such comparisons would be between various periods and a remote common base, but not between successive periods. Y e t it seems more logical to suppose that business conditions in 1927 are more nearly related to price changes relative to the preceding year of goods exported in 1927 than to the price changes between, say, 1923 and 1927. A chain index, on the other hand, compares adjacent periods, and always has up-to-date weights. A v e r a g e prices and quantities change in accordance with their current (or immediately preceding period) importance. Such index numbers sensitively reflect changes in the current economic situation. Although a sensitive index is of prime importance in studying cyclical fluctuations, the trend may have a direct bearing on these fluctuations. Furthermore, it may throw additional light on the subject to study cycles without removing trends, as well as to study these two types of change separately. Since the same index cannot measure both types of change with absolute accuracy it may be justifiable to sacrifice sensitivity slightly in order to secure a reasonably accurate trend. This means either that the idea of a chain

METHODS

OF

CONSTRUCTION

59

index must be abandoned, or some way found to rid it, at least partly of " weight correlation bias " , so that the " circular " test will be approximately met. A n added reason f o r so doing lies in the possibility that index numbers such as those here shown may prove of some use other than the one primarily intended. Since an object of these indexes is to break up value changes into their component parts, price changes and volume changes, it seems desirable to select formulae which are not on their face inconsistent. It would be strange, for instance, if the price index stood at 105, and the volume index at 105, and yet the actual relative value was 95. Such a thing could conceivably happen if both the price and volume indexes were of the aggregative fixed base and fixed weight variety. I f the product of the price and volume indexes were 95, it would not prove the accuracy of either; but it would be more convincing, and very convenient. Types of index numbers which satisfy this condition have been discussed. 1 2. Peculiarities

of the Data

( 1 ) Relationship Between Price and Quantity Movements of Commodities in the Sample It is apparent that there may be economic causes which tend to bring about systematic relationships between price and quantity changes of individual commodities in our sample. F o r instance, a rise in price may stimulate an immediate response in shipments, or a large crop of wheat may lead to large shipments and depress price. These relationships may be immediate or they may be postponed so that quantities may lag behind prices or prices may lag 1

Cf. supra, pp. 50-51-

60

MEASURES OF EXPORTS OF THE UNITED

STATES

behind quantities with an inverse correlation. Or finally there may be no systematic relationship between price and quantity movements. Also the type of relationship which exists in one class o f commodities may be entirely different from that which exists in another. The presence or absence of such systematic relationships has a bearing on the method of weighting we adopt and determines the amount of difference which is found between chain indexes and fixed base indexes computed by the same formula, or between chain indexes with different methods o f weighting. More specifically, if we wish to preserve a reasonable trend in our indexes, it may be necessary to use constant weights, or find some way o f correcting for this " weight correlation bias " . I f the relationship in any class tends to be a persisting one it will not be difficult to apply a correction. T o the extent that the data are inaccurate or non-homogeneous, there may be an inaccurate relationship between apparent prices and quantities. This would not necessarily be a random relationship. F o r instance, if the shipments o f a commodity during any month happen to be shipments consisting of small individual units, the price per unit would probably be a high one. This might result in a negative relationship between prices and quantities. ( 2 ) Lack of Comparability Ordinarily the maker of index numbers chooses only commodities which conform to definite specifications. Our data do not conform to rigid specifications. The bearing of this point on the matter under consideration is that just as the object of our index numbers dictates the use of a method which compares adjacent rather than distant periods, so the defects of our data compel the same thing. It may be true that we cannot compare price or quantity changes accurately even for adjacent periods; it certainly is true

METHODS

OF

CONSTRUCTION

6l

that we cannot compare periods far separated in time, for with the lapse of time the incomparability of the data increases. We are compelled from time to time to add commodities, to subdivide some, occasionally to drop one, and to compare totals rather than individual items when the classification is changed. The comparison of totals instead of separate items is of course a makeshift, and it lessens the accuracy of the index number. In the case of a fixed base index it results in an inaccurate comparison of every subsequent period with the base; in the case of a chain index one link only is weakened. Technically also, whenever any of these changes are introduced into a fixed base index, by any process of splicing, its clear meaning is destroyed. (3) Completeness of the Data Value and quantity figures are available for most commodities. From these prices can be derived. Therefore we are not limited by our data as to the type of formula we adopt. Since we are trying to break up known value changes into price changes and quantity changes, it is desirable that our index numbers meet the factor-reversal test; or at least that we use price and quantity index formulae which, when multiplied together, show value changes. W e are not, however, so much interested in obtaining indexes which, when multiplied together will give a true figure for value changes of our sample as we are in obtaining indexes which will be consistent with the true value of all the commodities, including the sample. This does not mean that if our index numbers are not inconsistent with total value changes they are correct, but that their correctness is to be doubted if they are not so consistent. Again the nature of our data permits us to apply this test, for we have total value figures, not only for

62

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

all domestic exports, but for individual classes and groups; and these are available both monthly and annually. ( 4 ) Dominating Importance of a F e w Commodities Such important commodities as wheat and cotton tend to dominate their respective classes. ( S e e Chart V . ) If the price and quantity movements of these commodities conform to the general movement of commodities in their respective classes this is no occasion for alarm. But when their movements do not so conform the question arises, how did the prices and the quantities of commodities not in the sample move—the same as did wheat, or more like the other commodities, or unlike either? W h e n one stops to think of it and inquires why the crop and exports of wheat are low in a particular year and the price high, he realizes that those factors have at least no more in common with the price and quantity movements of exports such as cattle, poultry, grapes, etc. (which commodities are not included in my sample) than do the other fourteen commodities in Class B Exports. This suggests some method of toning down the influence of commodities important in value, but independent in their movements. T h e Department of Commerce solves this problem by using in some years a weighted price index of all commodities except wheat (or cotton) to deflate the value of all the commodities not covered by the sample. 1 Their reasoning and experience is that not only are commodities like cotton and wheat apt to be unrepresentative as to price and quantity movements, but that even the other commodities are representative only as to price. T h e Federal Reserve Bank of N e w Y o r k , which constructs a rough import price index for deflating purposes, uses a simple arithmetic average of all commodities to deflate commodities not covered by the sample. 2 T h e American T a r i f f League import volume 1

Cf. infra, Appendix D, pp. 112-114.

* This index is not published and is not described in Appendix D.

METHODS

OF

CONSTRUCTION

63

index uses price weights but arbitrarily reduces the price of certain important commodities.1 James Harvey Rogers begs the question by not trying to eliminate price changes from all commodities.2 Likewise the present index of agricultural exports excludes cotton and tobacco, considering them separately. Mr. King has found by experiment that with small samples a simple average more nearly approximates the results of a weighted arithmetic average of relatives with complete data than does a weighted average of the relatives contained in the sample.3 The reason for this is that occasionally an erratic price movement occurs in an important commodity. As the sample gets larger, however (the point being somewhere between 125 and 200 times), the weighted average of relatives gives better results. Furthermore, it was found that results could be improved, using either the unweighted or the weighted average, if items deviating from the median more than six times the interquartile range were eliminated. 3. Ease of Construction Other things being equal, the easiest method of doing a thing should always be chosen. This is a point against the geometric mean, chain indexes in general, and the " ideal " index in particular. The only difficulty is that one cannot always determine whether indexes computed by two methods, an easy one and a laborious one, are approximately equivalent until both methods are tried. A number of methods were tried out in the earlier stages of this study, and the experience of the Department of Commerce has been utilized. 1

Cf. infra, Appendix D, p. 119.

2

Cf. infra, Appendix D, p. 115.

• King, Willford I., Index Numbers Elucidated, New York, 1930, pp. 168-187.

64

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

IV. SOLUTION OF T H E PROBLEM

A consideration of the purpose of these index numbers and the peculiarities of the data, in connection with various methods which are available, seems to indicate the use of a chain index. Consequently a chain index of the aggregative type has been chosen. Being a chain index, the choice of a base period is not particularly important. T h e 1923-25 average was chosen, however, largely to facilitate comparison with the general index of the Department of Commerce. One of the perplexing problems faced by some of the index number constructors referred to in Appendix D w a s what to do when the value changes of the sample did not conform to the value changes of the totality. Dr. Berridge and Dr. Durand each constructed their index numbers on the assumption that the quantity changes of their sample were not representative, but that the price changes were. 1 O f the two solutions, the one adopted seems the more logical. T h e volume of exports of a particular commodity are frequently determined in large part by the weather, or by conditions in that particular industry; but there is considerable interdependence in the prices of somewhat similar commodities. It is to be noted, however, that if the price index is satisfactory, and when used as a deflator gives the same result as an independently constructed volume index, there can be no question concerning the representativeness of the volume changes of the sample. In the present instance price and quantity formulae were chosen so that the product of the price and quantity indexes reflects accurately the value change of the sample. Furthermore although perfection can never be attained, the value changes of the sample conform rather closely to the value changes of the totality. (See Chart I V . Value changes of the sample were obtained by multiplying 1

Cf. infra, Appendix D, pp. 108, 112.

METHODS

OF

CONSTRUCTION

65

the price index by the volume index.) It is also believed that since the sample contains such a large percentage of the total value, it is not only the product of the two indexes which is satisfactory, but also each index taken separately. 1 On account of the adequacy of the sample and the excellence with which changes in its value conform with changes in the value of all commodities it is thought best (with the exceptions given in the next paragraph) to apply to the sample the same methods which would have been used had complete data been available. With complete data no special consideration need be given to the movements of important but erratic commodities. The Department of Commerce, using sample data, sees fit, to tone down the effect of commodities like cotton and wheat.2 But when the data are broken down into classes the problem becomes easier to solve. The samples of raw materials (which includes cotton) and raw foodstuffs (which includes wheat) each contain 95 per cent of the total value of all commodities in their respective classes. It is difficult to imagine, therefore, how indexes for these classes could be distorted by overweighting cotton or wheat. The separate class indexes are combined by an average which gives to each its exact (i. e., except for all exports, not sample alone) weight each period, thus automatically reducing cotton and weight to approximately their correct weights relative to total exports. In other classes too certain commodities tend to stand out in importance. (See Chart V . ) But it will be noticed that in every case they occur in class groups the weight of which has been somewhat arbitrarily reduced. 1

The sample of finished manufactures is less adequate than that of the other classes. Cf. supra, pp. 35-38. a For the procedure followed cf. infra, Appendix D, pp. 112-114.

66

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

i. Annual Indexes Price and volume indexes for each economic class have been constructed by means of the so-called " ideal " formula; and a general index by combining the separate indexes. The only variation from the usual procedure has been that the pairs of index numbers have been chained back before being crossed. An illustration showing the construction of the 1927 price index number of raw materials will make the procedure clear. The subscripts 0 and 1 refer to the years 1926 and 1927 respectively.

Symbol 1927 1927 quantities at 1926 prices 1926 quantities at 1927 prices 1926

» Pj q, I P0 Q / «p,g0b » p0 q„

Value of Sample (thousands of dollars) 1,132,721 1,160,545 1,175,821 MIO,583

* In the case of sub-group 7" (automobiles, parts, and accessories) > p0 q t was obtained by deflating given year actual values of this subgroup by a price index of automobile exports using given year quantity weights. Thus:

A similar procedure was followed with monthly index numbers. b t Pj q 0 of group 7" was obtained by "inflating" preceding year actual values of this sub-group by a price index of automobile exports using preceding year quantity weights. Thus:

Price index, 1927/1926:

V

' P i Qi 'Poii

' Pi * PoQo

4

1,132,721 1,175.821 = V .9760 X .9713 •Tr X "1,160,545 1,210,583

Chain index numbers of price: 1926/1923-25, given year weights 1926/1923-25, preceding year weights

73.02 72-55

METHODS

OF

CONSTRUCTION

67

1927/1923-25: V (.73M x .9760) X (.7255 x .9713) = 1/ 7127 X .7047 = 70.87 per cent The illustration continues, showing how price indexes for this class and the others are combined into a general price index of all domestic exports. Actual Value of all Commodities (thousands of dollars)

Class

Price Index of Sample (per cent)

'Pi qi * P» Qi 97.60 10045 92.52 93 40 92.83

' P. Q,

A • • 1,192,775 421,107 B . C .... • • 463,299 D ... -. 699,728 E ... .. 1,981,954 Total

4,758.863 =

P, Q.)

'P.Q. .. 1,261,325 A B ... • • 335.063 C ... • - 503.005 D ... • • 655,547 E .... .. 1,956,781 Total

' Pi

100 130

ARITHMETIC

SCALE

120

110

100 90 130

120

no 100 98

CHART

V I — P E R C E N T A G E D E V I A T I O N , OF M O N T H L Y V O L U M E INDEXES FROM A N N U A L , AND CORRECTIONS FOR W E I G H T CORRELATION B I A S Solid lines c o n n e c t p o i n t s r e p r e s e n t i n g v a l u e s o b t a i n e d bT d i v i d i n g a n n u a l a v e r a g e s of m o n t h l y i n d e x n u m b e r s b y c o r r e s p o n d i n g annual i n d e x n u m b e r s . T h e d o t t e d l i n e s , r e p r e s e n t i n g c o r r e c t i o n f a c t o r s , a r e t r e n d s fitted by i n s p e c t i o n . ( P a g e 71)

72

MEASURES

OF EXPORTS OF THE UNITED

STATES

tained. The deviation of Class B is 1/4 of one per cent per month; of Class E , 5 / 1 2 of one per cent per month; and of total exports, 1 / 3 of one per cent per month, the first correction being applied to November, 1924. The proper correction factors for these classes can be obtained from tables showing the amount of 1 at compound interest. Those of other classes are easily computed, since they increase month by month in arithmetic progression. The approximate correction factor for each month for any class can be read from the chart. Monthly price indexes are corrected by multiplying the index number by the proper correction factor; volume indexes by multiplying by the reciprocal of the price correction factor. Whether, and how far into the future it would be justifiable to extend these trends, of course cannot be known in advance. The correction factor for Class B was determined before 1929 and 1930 data became available. Furthermore, the regularity of the increase in the deviations suggests that they are due to persisting economic factors.

CHAPTER

V

RESULTS

It is the purpose of this study to provide a means of comparing price and volume movements of domestic exports with cyclical fluctuations in American business. Results will therefore be presented very briefly, largely in graphical form. These results will be shown under two headings, statistical and economic. I. STATISTICAL RESULTS

i. Observed Differences Between Preceding and Given Period Weighting

Period

Some idea of the difference between given year and base year weighting in these indexes is obtained by comparing the two 1930 price indexes of each class, one with preceding year weights and the other with given year weights. These are not differences resulting from a comparison involving one pair of successive years, but are the net difference between the two systems after chaining back to 1923-25 for the eight years in question: Class A B

C

D E A l l Classes

Preceding year weights

(1) 61.27

Given year weights

Difference

(2) 60.66

(3)

79-29 83-94

.61

86.49

85.92

90.00

86.81

3-99 8-53 •57 3-19

82.53

77-74

479

83.28 92.47

73

7 4 MEASURES

OF EXPORTS

OF THE UNITED

STATES

In spite of the fact that the net effect by classes and f o r the total of using preceding year quantity weights in an aggregative chain index of price (arithmetic average of relatives with preceding year value weights) is to make these index numbers ( f r o m these data) higher in every case than similar indexes using given year quantity weights (harmonic average of relatives with given year value weights) ; in more than one-third of the individual yearly comparisons of the unchained index numbers the given year weights give larger figures. Results of such comparisons are summarized in the following frequency distribution: Preceding year weight numbers minus given year weight numbers (Per cent) —1.50 —1.25 —1.00 — .75 — .50 — .25 .25 .50 .75 1.00 1.25 1.50 1.75 2.00

but under but under but under but under but under but under but under but under but under but under but under but under but under and over Total

—1.25 —1.00 — .75 — .50 — .25 >25 .50 .75 1.00 1.25 1.50 1.75 2.00

Frequency 2 3 o 2 4 12 7 6 1 3 o 2 o 6 48

A r r a n g i n g the results by classes and by years shows that this upward tendency of base year weighted index numbers is much more prevalent in some classes than in others. It also reveals that, generally speaking, boom years in American business are years when the divergence of preceding year weighting is upward; but in years of depression this system of weighting deflects the index downward. These

RESULTS

75

results are shown by the following table: D I F F E R E N C E B E T W E E N R E S U L T S O B T A I N E D BY PRECEDING Y E A R AND GIVEN

YEAR

WEIGHTING

IN

YEAR

TO Y E A R

OF D O M E S T I C E X P O R T S BY E C O N O M I C

WEIGHTING

COMPARISONS

CLASSES

(Bold face type denotes that given year -weighting give the largest results) A

1923 1924 1925 192 6 1927 1928 192 9 1930

B

C

D

E

21

.66

.08

26

1.3«

1 13

4-38

1.40 47

.08 1.11 1.04

1.60 1.09 5 S8 .89

.08 .12 -25 .21

.21

.54 .08 .63 -81

1.68 12 39

1-23 3-59

.65 .58 -25

.08 -39

.43

1.11 .36 .38 3-44

Total

.53

.04 2.63 .08

.60 .56 .41 2.26

Chart V I likewise reveals that preceding period weighting tends to cause an upward divergence of monthly index numbers constructed from these data. There seems, however, to be little relationship between the magnitudes of the divergences of the annual numbers and the monthly numbers. The results obtained by using different types of index numbers do not indicate that a general proposition can be laid down that any type of average approximately weighted has an upward bias or a downward bias. They merely indicate that in the case of United States domestic exports the relationship between price and quantity changes of individual commodities is such that an arithmetic average using preceding period weights diverges upward over a period of time from a harmonic average using given period weights. Needless to say, the results do not indicate that either system of weighting is to be preferred to the other. 2. The Circular Test In constructing these indexes 1923-25 prices and quantities have actually been taken as a starting point. The annual indexes have completed the circle by using 1928 as

76

MEASURES

OF EXPORTS

OF THE UNITED

STATES

base year and 1923-25 as given period. T o meet the test perfectly each index should end as it began, at exactly 100. Actually the results are as follows for the price indexes: Class Class Class Class Class Total

A B C D E

99.83 99 30 100.55 101.66 99.80 100.04

There is some question as to how seriously this test should be taken, not only because the test is of doubtful validity, but because we did not end with the same sample with which we began. Consequently in making the final price comparison, only commodities common to both periods were used. The volume indexes can hardly be expected to meet this test, since one reason for adding commodities to the sample was to counteract the downward tendency of the sample. 3. Relationship Between Price, Volume and Value Changes Formulas have been so chosen that the product of price and volume indexes indicates the value changes of the sample. The extent to which it indicates value changes of all commodities is shown on an annual basis by Chart I V . The same is shown on a monthly basis by Chart V I I . 4. Comparison with Department of Commerce Indexes It is interesting to compare the results obtained in this study with those of the Department of Commerce, since the experience of that department has been relied on so heavily. This comparison is shown by Chart V I I I . The differences can probably be largely accounted for in two ways. First, the Department of Commerce index is perhaps

RESULTS

77

78

MEASURES

OF EXPORTS

OF THE UNITED

STATES

inadequately weighted with finished manufactures. Therefore, since these commodities have not fallen in price as rapidly as have those of other classes, one would expect that index to decline more rapidly than one more heavily weighted with those commodities. Since their volume index is obtained by a deflating process, low price index numbers result in high volume index numbers. Secondly, a difference of slightly more than two per cent between the two volume indexes in 1929 can be accounted for by the decline in the value of my sample relative to the value of all commodities. (See Chart I V . ) II. ECONOMIC RESULTS

Regardless of the relationship between business conditions in the United States and other countries we should expect positive correlation between domestic and export prices, since exports of most products constitute only a small proportion of their production. Lack of coincidence in timing of cyclical fluctuations among the various countries would accentuate the correlation between export prices and domestic prices, and between export prices and American business activity. Because values exported are in part a reflection of price changes, any apparent correlation between the value of United States exports and domestic business conditions may be due to this price factor. If there is little agreement between the timing of cyclical fluctuations in various countries, then we might expect the low prices prevailing in times of depression in the United States to stimulate the volume of exports in such periods; and high prices to discourage exports during periods of prosperity. Furthermore, if in times of business activity there is a tendency to fill American orders first, and if in in times of inactive American demand there is a tendency

RESULTS

79

VOLUME

PER CENT 140 1 3 0 D E

?'T

120

/

\

O F

C O M M E R C E

/

/ /

110

/ /

\

\

/

\ W D E N

y /

\

/

\

\

V \ \

y

\

\

\

100 90 1923

1924

1925

1926

PER CENT HO

100 O F

1927

1928

1929

1930

PRICE

\ s D E P " 1 % C O M M E R C E ^

90

X O N A / C > E N N

s

80 70 1923

1924

1925

1926 CHART

»927

1928

V V

\

1929

N

(930

VIII

UNITED STATES DEPARTMENT OF COMMERCE V O L U M E AND PRICE INDEXES OF DOMESTIC EXPORTS COMPARED WITH THOSE CONSTRUCTED BY D . J . COWDEN.

8 o MEASURES OF EXPORTS OF THE UNITED

STATES

to cut prices to foreign buyers while maintaining prices at home, we might find considerable negative correlation between the volume of exports and production in the United States. Even with good agreement in timing between American business activity and that of other countries, the offsetting factors mentioned might easily result in no appreciable positive correlation between American business conditions and the volume of Ameriacn exports. A complete analysis of the volume of American exports would of course call for a consideration of the relationship between exports and imports, and between exports and investments abroad; both of which factors react by affecting foreign business conditions. Still another factor is the relationship between American and foreign crops. All that will be done in this study, however, is to call attention to certain obvious relationships between American exports and American business. Chart I X shows how our exports have behaved from 1923 to date on an annual basis. In the case of total exports clearly and certain classes less clearly the principal source of change in the value index is the change in the quantity index. Where this is not the case, value changes are due in approximately equal degree to price changes and volume changes. The price, volume and value movements of raw materials and raw foodstuffs are dominated to a large extent by cotton and wheat respectively, and reflect in large measure crop conditions, here and abroad, of these products. In all classes except those mentioned cyclical price fluctuations are much as we should expect, although the 1924 price decline of finished products is negligible. No startling similarity between the value changes of American exports and the changes of the commonly accepted measures of American business activity is suggested by these charts. The results of removing the effect of price change is inter-

RESULTS PERCENT 1201

MANUFACTURED FOODSTUFFS I I

1923

'25 '26 '27 28 29 CRUDE F O O D S T U F F S

NL 1923 >OI

24

I 24

I I 1 I '25 '26 '27 '28 CRUDE M A T E R I A L S R~~

I 27

I '28

:E

TOTAL

1930

1923

PERCENT MO

I I I I I I 2D '25 26 27 28 29 FINISHED MANUFACTURES

I '29

I 1930 1923 24

'25 26 '27 28 SEMIMANUFACTURES

29 1

I '29

M 1930

1923 24

VOLUME

PRICE, V O L U M E

EXPORTS 1

%J80

1930

1180

C H A R T ANNUAL

8L

AND V A L U E

BY E C O N O M I C (1923-25 =

25

26

27

'28

29

180 1930 1140

160 1930

VALUE

IX INDEXES o r CLASSES. 100)

DOMESTIC

EXPORTS,

82

MEASURES

OF EXPORTS

OF THE UNITED

STATES

esting, however. The comparatively steady value of semimanufactures is converted into peaks in the depression periods of 1924 and 1927-28. Chart I V reveals that the sample of this class is the least satisfactory of any of the classes. However, if we derive a volume index by a deflating process, we still have these humps, although they are less peaked. The volume index of finished manufactures removes almost completely the 1 9 2 7 value depression; and as a result the physical volume of exports of finished manufactures appears to have had a very steady and continuous growth until 1930. In general, the results observable in finished manufacture are also true of total domestic exports. Very slight humps are observable in 1924 and 1927, but the curve is a remarkably regular one, showing a growth (until 1 9 3 0 ) at a decreasing rate. Several general observations may also be made. Without exception, and in contradiction to other depression years, value, volume and price changes were abruptly downward in 1930. A decline in prices of each class has set in since 1 9 2 5 ; and in each case 1930 prices are the lowest of the period. 1930 export values are likewise the lowest of the period for total exports, and every class but finished manufactures. Only the two foodstuff classes show the smallest physical volume in this year, however. Chart X displays the price changes of each class and of total domestic exports. Cyclical fluctuations are plainly observable, being the most accentuated in the case of semimanufactures. There is considerable similarity between the price movements of the two foodstuff classes. Manufactured products, both food and other, are less variable than the same commodities in a raw or semi-manufactured state. In order to observe whatever cyclical changes there are in the physical volume of exports it is necessary to remove the effect of seasonal variations. T o this end indexes of

RESULTS PER C E N T

TOTAL

120!

1923

EXPORTS

1924

1925 1926 1927 1928 FINISHED MANUFACTURES

1924

1925

1926

1927

1928

SEMIMANUFACTURES

1925

1926

1927

1928

MANUFACTURED F O O D S T U F F S

1923

1924 1925 1926 1927 ¡928 RAW^ MATERI ALS AND RAW FOODSTUFFS I •

RAW

1929

¡930

FOODSTUFFS

RAW MATERIALS

CHART

X

M O N T H L Y PRICE INDEXES OF DOMESTIC EXPORTS, BY ECONOMIC CLASSES. (1923-25 =

100)

84

MEASURES

OF EXPORTS

OF THE UNITED

STATES

seasonal variations have been computed. This has been done by the link relative method, averaging the six middle items in arrays. Chart X I shows the results of this procedure. Since corrections were not made for the number of working days in a month before constructing and applying the seasonal indexes, a chart showing these partly adjusted volume indexes would be of a rather jagged nature. Therefore the lines have been smoothed slightly by means of a three-month moving average in which the middle item has been double-weighted. It is believed that this almost entirely removes the effect of the varying number of Sundays in a month. The final results are shown in Charts X I I and X I I I . There seems to be little of what we are accustomed to think of as cyclical in the volume changes of foodstuffs or raw materials. Yet towards the end of 1923 and beginning of 1924, and again towards the end of 1927 or beginning of 1928, there is a falling-off in the volume of exports of raw materials and raw foodstuffs. Also in the early part of 1929 exports of manufactured foodstuffs were a little higher than usual. The 1924 and 1927-28 humps are still observable, however, in the volume of exports of semi-manufactures. A slight degree of cyclical fluctuation corresponding to American business conditions is observable in finished manufactures. The net result for all domestic exports seems to be somewhat more cyclical in nature than we should expect. Depressions in 1924 and 1927-28 are observable, and peaks in 1926-27 and 1929.

RESULTS

85

C H A R T XI S E A S O N A L V A R I A T I O N OF V O L U M E OF DOMESTIC EXPORTS, BY ECONOMIC

(Average for year =

100)

CLASSES.

86

MEASURES

OF EXPORTS

PER CENT

A

•

OF THE UNITED

STATES

MANUFACTURED FOODSTUFFS

PER CENT

A*

1 1 1 1

V

\J

«1

%

Vs \»

V

V

V

A

V

A r\ /

V N

\

1923

1924

1925

1926

1927

1928

1929

1930

CHART XII MONTHLY

VOLUME

INDEXES OF DOMESTIC EXPORTS, BY ECONOMIC

CLASSES.

Classes A, B and C. Seasonal Eliminated, Three Month Weighted Moving Average. (1923-25 = 100)

RESULTS PERCENT

PER CENT

140

87

TOTAL E X P O R T S

PERCENT

SEMIMANUFACTURES

PER CENT

120 100

80 1923

1924

1925

1926

1927

1928

1929

1930

CHART XIII MONTHLY

VOLUME INDEXES OF DOMESTIC EXPORTS BY ECONOMIC

CLASSES.

Classes D, E and Total. Seasonal Eliminated, Three Month Weighted Moving Average. (1923-25=100)

88

MEASURES

OF EXPORTS

OF THE

UNITED

STATES

A by-product of this study has been the results obtained in the construction o f these index numbers by the use of different systems of weighting. Aggregative price-index numbers of the type we have been using measure value changes due to price alone, of commodities exported in either the period in question or the preceding period. N o w if all commodities increased or decreased equally in price, or equally in quantity, it would make no difference which system of weighting we used. But if commodities whose price increase happen to be those which increase greatly in quantity, it is quite evident that if we use given period weighting we are measuring the value change due to price of a list of commodities weighted most heavily with those whose price increase is especially high. This fact tends to pull the price index upward. B y virtue of the fact that the remainder of the commodities which do not increase so rapidly in price receive relatively slight weight in our list of commodities, since their importance quantitatively has declined, we have another force (or perhaps the same force) tending to prevent this index from declining. This reasoning applies regardless of whether the price trend is upward or downward, and regardless of the general quantity trend. The important thing is the relative increase or decrease (relative to the average) of individual prices and quantities. If the opposite relationship between price and quantity changes exists, our conclusions likewise are reversed. That is, if commodities whose prices rise more (or fall less) than the average are commodities whose quantities rise less (or fall more) than the average; and/or commodities whose prices fall more (or rise less) than the average are commodities whose quantities fall less (or rise more) than the average; then index numbers with preceding period weighting tend to diverge upward from those with given period weighting. 1 1

Cf. supra, p. 46.

RESULTS All

the reasoning

89

in the preceding

paragraph

applies

equally to the measurement of quantity changes in an aggregate of commodities whose price has been held constant. A n d of course these are general statements, applying to index numbers in general, as well as to exports in particular. It has been noticed however, that these index numbers of United States exports which use preceding period weighting tend to diverge upward weighting.

from

those with

given

period

Hence w e may tentatively conclude that in the

case o f United States exports factors affecting demand are of a fairly general character; and the effect of changes in the supply of a particular commodity on changes in its value exported is thereby limited.

Thus an unusual increase in

the supply o f a particular commodity is offset by a decline in its price greater than that o f exports in general ( o r its price fails to rise proportionately to that of other commodities).

But if the supply suffers an unusual curtailment, the

price enjoys an unusual ( r e l a t i v e ) enhancement.

T h e net

result, in short, is to limit the extent to which value changes of individual commodities exported may diverge f r o m those of exports in general.

O f course the demand f o r individual

commodities changes also; but the quantitative effect of such changes on United States exports does not seem to be as great

as that

commodities.

of

changes

in the

supply

of

individual

APPENDIX

A

PROCEDURE FOLLOWED I N CONSTRUCTIVE I N D E X

NUMBERS

T o secure the maximum accuracy with the minimum labor was the aim of the following procedure: In copying data from Monthly Summaries figures have been carried to the nearest thousand dollars or quantity units. When the resulting number is of less than four digits, three digits have been copied under any circumstance, and four if the number began with i , 2 or 3. The work of copying was proved by balancing the twelve monthly totals for any class group with the annual total for the same class group. Prices were obtained by dividing values by quantities. Prices show four digits. Values obtained by multiplying prices by quantities are carried to the nearest thousand dollars. All prices and all p0 q j or pj q0 values were computed twice. Other work likewise was proved by being repeated unless an internal proof could be devised, such as proving final index numbers by balancing the product of price and value index numbers with relative value change. Index numbers unadjusted for seasonal variation were carried to the nearest one-hundredth of one per cent; data used in computing seasonal indexes, seasonal indexes, and volume indexes corrected for seasonal variation to the nearest one-tenth of one per cent; volume indexes smoothed by three-month moving averages to the nearest per cent. 91

APPENDIX

B

COMMODITIES INCLUDED IN SAMPLE AND U N I T OF MEASURE I N 1930, AND OFFICIAL CLASS NUMBERS OF COMMODITIES IN SAMPLE IN 1 9 2 3 AND 1930,

BY ECONOMIC CLASSES

(According to SCHEDULE B., Statistical Commodities

exported

of Foreign

and Domestic

Department Class Number JÇ23 1930

Classification

from the United of

States,

Commerce,

of

Domestic

Bureau

U. S.

Commerce.) Unit of Measure

Commodity RAW

MATERIALS

501

0501

Cattle hides

505

0505

Calfskins

Lb. Lb.

717

0717

Undressed furs, Muskrat

No.

732

0722

Undressed furs, Skunk and civet cat

No.

723

0723

Undressed furs, Opossum

No.

2325

3205

Ginseng

Lb.

2406

2406

Timothy seed

Lb.

2601

2601

Leaf tobacco, Bright

2603

2603

Leaf tobacco, Dark-fired Kentucky and Tennessee..

2604

2604

Leaf tobacco, Dark Virginia

Lb.

2931

2931

Broom corn

Ton

2951

2951

Hops

Lb.

flue-cured

Lb. Lb.

Raw cotton, except linters: 3002

3002

3003

3003

4013

4013

inches and over, other than Pima Upland cotton, under 1 % inches Logs and hewn timber, Cedar

Lb. Lb. M . ft.

4699

4699

Rags and other paper stock

Lb.

5001

5001

Coal, Anthracite

Ton Ton

5002

5002

Coal, Bituminous

50x1

5011

Petroleum, crude

Bbl.

6001

6001

Iron ore

Ton

6301

6301

Bauxite and other aluminum ores and concentrates..

Ton

8513

8513

Phosphate rock, high-grade hard rock

Ton

8514

8514

Phosphate rock, land pebble and other

Ton

92

APPENDIX RAW

39 194

0029 0450

B

FOODSTUFFS

Hogs Eggs, in the shell

No. Dot.

1011

1011

Barley

Bu.

1031 1041

1031 1041

Corn Oats

Bn. Bu.

1053 1061 1071 1 jo 1 1211 1302 1303

1053 1061 1071 1201 1211 1302 1303

Rice Rye Wheat Beans, dried Potatoes, white Grapefruit Lemons

Lb. Bn. Bu. Bu. Bu. Box Box

1305 1311 1312

1305 1311 1312

Oranges Apples in boxes Apples in barrels

Box Box Bbl.

MANUFACTURED

FOODSTUFFS

109

0109

Beef and veal, pickled or cured

Lb.

121 125 126

0121 0125 0126

Pork, carcasses, fresh or frozen Hams and shoulders, cured Bacon

Lb. Lb. Lb.

129 141 162

0129 0131 0142

Pickled pork Mutton and lamb Canned meats, Pork

Lb. Lb. Lb.

401 431 432 441 202

0160 0166 0167 0171 0202

Oleo oil Lard Neutral lard Oleo stearin Milk and cream, condensed

Lb. Lb. Lb. Lb. Lb.

203 204

0203 0204

Milk and cream, evaporated Milk and cream, dried

Lb. Lb.

215 351

0215 0351

Cheese Fish, canned, Salmon

Lb. Lb.

352 10:3 1073 1115 1116 1121 1241 1242 1245

0352 1013 1072 1115 1116 1121 1241 1242 1245

Canned fish, Sardines Malt Wheat flour Oil cake. Cottonseed cake Oil cake, Linseed cake Oil-cake meal. Cottonseed meal Vegetables, canned, Asparagus Canned vegetables, Baked Beans and Pork and Beans Canned vegetables, Soups

Lb. Bu. Bbl. Ton Ton Ton Lb. Lb. Lb.

APPENDIX

94

1246

B

1324

1246 Canned vegetables, Tomatoes 1251 Ketchup and other tomato saaces 1324 Dried and evaporated fruits, Raisins

Lb. Lb. Lb.

>3*5 1326 1328 1340 '343 '344 I34S 1424 15x2 1619 1629 1639 1642 1643

'325 1326 1328 1340 '343 >344 I34S 1424 1512 1619 1629 1639 1642 1643

Lb Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Gal. Lb. Lb. Lb.

Dried and evaporated fruits, Apples Dried and evaporated fruits, Apricots Dried and evaporated fruits, Prunes Canned fruits, Apricots Canned fruits, Peaches Canned fruits, Pears Canned fruits, Pineapples Cottonseed oil, crude Coffee, roasted Sugar, refined Molasses Chewing-gum Honey Glucose SEMI-MANUFACTURES

603

0604 0605 060 0607 0608 611 0611 612 613 0613 614 619 624 0624 447 0847 2 1 1 1 2110 2111 2114 2114 1423 2230 1433 3008 3011

4031 4032

2233 3008 3011 3012 3712 4060 4063

Upper leather (except patent) : Calf and kip, black Calf and kip, other Goat and kid, black Goat and kid, other Patent upper leather, patent side upper leather

Sq. Sq. Sq. Sa. Sq.

Patent upper leather, Goat and kid

Sq. f t .

Sole leather, bends, backs, and sides Oleic acid, or red oil Naval stores, Gam rosin Naval stores, Wood rosin Naval stores, Gum spirits of turpentine Cocoanut oil

Lb. Lb. Bbl. Bbl. Gal. Lb.

Soy-bean oil Cotton rags, except paper stock Cotton yarn, carded, not combed Cotton yarn, combed yarn, mercerized Tram, organize, hard twists, and spun silk Sawed timber, Southern pine Sawed timber, Dougles fir Boards, planks, and scantling:

Lb. Lb. Lb. Lb. Lb. M. f t . M. f t .

ft. ft. ft. ft. ft.

APPENDIX 4101 4102 4103 4104 4112 4122 4124 4125 4211 4602 9910 5029 5046

B

4101 4102 4103 4104 4112 4121 4124 4125 4211 4212 4602 479S 5029 $046

Douglas fir, rough Douglas fir, dressed Southern pine, rough Southern pine, dressed Hemlock Gum, red and sap Oak Poplar Box shooks, Southern pine . . . . Box shooks, Hemlock Sulphite wood pulp Vulcanized fiber sheets, strips, rods, and tubes Gas a n d fuel oil Paraffin wax, refined

M. f t . M. f t . M. f t M. f t . M. f t . M. f t . M. f t M. f t . Board f t . Board f t . Ton Lb. Bbl. Lb.

5047 5161 57'4 6007 6033 6034 6035 6040 6303 6412 6413 6424 6440 6505 6506 6582

Ton Bbl. Ton Ton Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Gal. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Ton Lb.

6035 6040 6303 6412 6413 6424 6452 6505 6506 6844 6845 8002 8245 8287 8289

8002 8230 8347 8353

Petroleum asphalt Cement, hydraulic S u l p h u r or brimstone, crude, in lumps P i g iron, not containing alloys I r o n sheets, galvanized Steel sheets, galvanized Steel sheets, black T i n plate, terneplate, a n d teggers tin Aluminum plates, sheets, bars, strips, and rods . . . . Refined copper in ingots, bars, or other f o r m s Old and scrap copper Copper rods Brass and bronze, scrap a n d old Lead in pigs, bars, etc Lead in pigs, bars, etc Zinc, cast in slabs, blocks, or pigs Zinc, cast in slabs, blocks, or pjgs Benzol Baking powder Copper sulphate Dextrine o r British gum

8344 8351 8362 8411 8423 8505 8741

8362 8365 8373 8411 8423 8505 9820

Sodium borate Soda ash Sodium hydroxide Zinc oxide Carbon black Sulphate of ammonia Pyroxylin products in sheets, rods, or tubes

5161 5714 6007 6034

95

96

APPENDIX FINISHED

B

MANUFACTURES

66i

0661

Boots and shoes, men's and boys'

Pair

697

0697

Leather belting, new

Lb.

>039

2034

C a n v a s shoes with rubber soles

Pair

2061

2060

Automobile casings, truck a n d bus c a s i n g s

No.

3063

2062

Automobile casings, other automobile c a s i n g s

No.

2063

Automobile inner tubes

No.

2268

2268

Peppermint oil

Lb.

2622

2622

Cigarettes

M.

2811 3021

2811

Corn starch and corn

3020

T i r e f a b r i c , cord

flour

Sq. y d .

3025

Cotton duck, unbleached, ounce

Sq. yd.

3026

Cotton duck, unbleaohed, numbered

Sq. yd.

3032

Cotton cloth, unbleached, sheetings 40 inches w i d e and under

Lb.

Sq. y d .

Cotton cloth, c o l o r e d : 3051

3043

Voiles

Sq. y d .

3061

3051

Percales and prints, 32 inches and n a r r o w e r . . .

Sq. y d . Sq. y d .

3071

3092

3052

Percales and prints, over 32 inches wide

3055

Flannels and

3056

K h a k i and f u s t i a n s

Sq. y d .

3057

Denims

Sq. y d .

3058

Suitings

Sq. y d .

3059

Ginghams

Sq. y d .

3060

Chambrays

Sq. y d .

3063

Other printed f a b r i c s , 7Yi and more yds. per lb.

Sq. y d .

3064

Other printed f a b r i c s , less than 1 l / i yds. per lb.

Sq. y d .

3065

Other piece-dyed f a b r i c s , 5 and more yds. per lb.

Sq. y d .

3066

Other piece-dyed f a b r i c s , less than 5 yds. per lb.

Sq. y d .

3071

A l l other yarn-dyed f a b r i c s

Sq. y d .

3072

Cotton and rayon mixtures (chief value cotton)

Sq. y d .

flannelettes

Sq. y d .

3093

Cotton hosiery, women's

3094

Cotton hosiery, children's

D o z . prs. Doz. prs.

3°95

Cotton hosiery, men's socks

Doz. prs.

3117

3117

Cotton shirts

Doz.

3721

3723

Broad silks, other than satins and other f o r shoes. .

Yd.

3758

3755

W o m e n ' s full-fashioned silk hose

Doz. prs.

3455

3854

R a y o n hosiery, women's

D o z . prs.

3856

R a y o n hosiery, men's socks

Doz. prs.

3911

3911

Oilcloth

Sq. y d .

4711

4711

N e w s p r i n t paper

Lb.

4714

4714

Book paper, not coated

Lb.

4723

4723

W r a p p i n g paper

Lb.

APPENDIX

B

97

4726 4731

Tissue and crepe paper Box board

4738

4738

Wall ¡board o f paper or pulp

Sq. ft.

479 1

479 1

Lb.

5021

5021 5022 5025 5026 5033 5035 6045 6051

Boxes and cartons Gasoline, naphtha, and other finished light products: in bulk in containers Illuminating oil, in bulk Illuminating oil, in containers Lubricating oil, red and pale Lubricating oil, cylinder Structural iron and steel shapes, not f a b r i c a t e d . . . . Rails, 50 pounds and over per yard

Bbl. Bbl. Bbl. Bbl. Bbl. Bbl. Ton Ton

6082 6083 6087

6058 6061 6062 6070 6071 6072 6073 6082 6083 6087

Railroad spikes Boiler tubes Casing and oil-line pipe Welded steel black pipe Welded wrought iron black pipe Welded steel galvanized pipe Welded wrought iron galvanized pipe Galvanized wire Barbed wire Wire rope

Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb.

6113 6151 6155 6192

6113 6150 6158 6192

Safety-razor Mades Axes Files and rasps Chains, other than sprocket and other power transmission

Doz. Doz. Doz.

6422 6425 6453 6454 7118

6422 6425 6453 6454 7013 7014 7°S7

Copper pipes and tubes Copper wire Brass and bronze, pipes and tubes Brass and 'bronze, pipe fittings and valves Six-volt storage batteries Other storage batteries Electric household refrigerators

Lb. Lb. Lb. Lb. No. No.cells No.

7164

7063 7064 7066 7068 7077 7311

Electric incandescent light bul'bs: For automobiles, flash-lights, and Christmas trees Other metal-filament bulbs Flash-light cases Electric household washing machines Radio receiving sets Rock drills

No. No. No. No. No. No.

7551

Sewing machines for domestic use

No.

7753

Typewriter-bookkeeping-billing machines

No.

4726

5025 5033 5035 6045 6051 6058 6061 6062 6063 6064

7166

7311 7S51

Lb. Lb.

Lb.

APPENDIX

98 7716

7847

7886 7891 7910 7912 7914 7920 7921 7922 792S 795 2 7046 8751 8433 8601 8604 8713 8733 9113 91 IS 9116 9211 9241 9342 9302 9312 9322

:

B

7770 7772

Standard typewriters, new Portable typewriters, new

No. n0.

7774 7847 7849 7882 7885 7891

Used and rebuilt typewriters Grain harvesters and binders Combines Wheel tractors, 15 to 32 belt horsepower TrackJaying tractors Windmills Motor trucks, busses, and chassis, except electric: Up ito 1 ton Over I to 2}4 tons Over 2}4 tons Passenger cars, and chassis, except electric: Group A—low price range, up to $1,000

No. No. jj0i No. No. No!

7902 7903 7904 7905 7907

No. No. No. No,

Group B—medium price range, over $1000 to

$2000 No. 7909 Group C—high price range, over $2000 No. 795 2 Motor cycles No. 7957 Detachable motors (outboard) No. 8291 Shoe polishes Lb. 8431 Enamel paints Gal. 8438 Other ready-mixed paints Gal. 8601 Smokeless powder Lb. 8604 Dynamite Lb. 8713 Laundry soap Lb. 8734 Dental creams Lb. 9 1 1 3 Motion-picture films, sensitized, not exposed Lin. ft. 9*22 Motion-picture films, positive films, silent Lin. ft. 9123 Motion-picture films, positive films, sound Lin. ft. 9125 Other sensitive films, not exposed No. rolls or packs 9211 Player pianos No. 9241 Phonographs No. 9242 Phonograph records No. 9302 Pencils, other than refillable Doz. 9312 Fountain pens Doz. 9322 Printer's and lithographic ink Lb. 9491 Metallic cartridges Lb.

APPENDIX C INDEXES

The indexes shown in the tables below are corrected for " weight correlation b i a s b u t not for seasonal variation; although indexes of seasonal volume variation are shown in Table 2 in the column at the extreme right. Each row labeled " average " contains numbers which are averages of the separate monthly index numbers of each year. In the case of volume indexes this is a simple average ( 1 / 1 2 of the sum of the monthly index numbers) ; but in obtaining the average of the price index numbers of any year one must first multiply each price index number by its corresponding volume index number, and then divide the sum of these products by the sum of the volume weights. Just below these averages are shown the annual index numbers computed as described in Chapter IV. The purpose of this comparison is to show how nearly the applicaion of our correction factors to our monthly indexes have brought the latter into agreement with our annual indexes. 1 . PRICE I N D E X E S OF DOMESTIC EXPORTS, BY ECONOMIC CLASSES TOTAL DOMESTIC EXPORTS

'923 January February March April May June July August September October November December Average Annual index ..

99 IOI

102 102 100 100 100

1924

/ 92$

1926

IOO

97 97 97

105 103 100 100

102 102 102

IOO

IOI

98

99 99 98

99 IOI

96

102 102 102 103

98

IOI

99 99

98 97

99 99

IOI IOI

103 105 IOI IOI

96 96 96 96 97

96 92 89

88 94 93

/927

/928

1929

1930

88 88

88 88 88

88 88 88 89 89

88 86

87

86 85

86 88 87

90 90 90 90 87 88

87

89 89 90 89 89 88 89 89 89 «9

8S

87

84 82 80

90

79 79 78

88 89 89 88 88 88 88 99

75 74

7o 80 80

APPENDIX

IOO

RAW

January February March April May June July

MATERIALS

IQ23

IQ24

IQ25

1926

1927

1928

1Q29

103 109 113 109

93 93 94 95

82 82 80 78

63 63 63 63

80 78 77 78

80 76 78 75

92

77

65

79

74

65

100 101

123 120 108 no no 106 107

93 94

76 78

66 68

82 82

72 74

62 61

101

August

C

I930

72 69 65 64

98

102

93

78

73

78

74

60

....

104 108 115 122

94 93 93 92

96 93 87 84

77 69 65 62

86 85 84 83

78 78 79 80

76 76 74 73

60 58 56 52

Average Annual index . .

109 109

102 101

92 93

73 73

72 71

79 78

75 76

61 61

1923

¡924

1928

1929

89 91 90 92

79 81 81 83

89 89 91 89 84

87

84 89 100 96 96 93 93

83 79 80 77 71 69 67 80 81

September October November December

RAW

January February March April May June July August September October November December

....

Average Annual index . .

FOODSTUFFS

192s

1927

107 108 105 105

IOO 97 100 100

89

83

123

101

103

88 86 Si 83 84 83 80

87 93 100 102 114 117 120

123 119 122 113 105 108 107

99 101 99 98 96 99 99

108 106 101 99 96 96 97

95 99 104 104 ill 109 104 92 88 87 87 87

86 86

103 101

121 117

100 99

100 99

93 94

91 90

1928

1929

99 95 96 95

96 95 95 97

MANUFACTURED

January February March April May June

1926

127 142 136 124

1923

1924

93 92 92 96

96 91 91 90

95

88

95

87

192$

IIO 112 114 115 no 113

1930

94 91 91 94

FOODSTUFFS 1926

109 109 107 107

1927

102 103 102 101

1930

95 95 93 92

108

100

97

99

90

113

101

99

94

90

APPENDIX

C

101

July

94

89

115

lit

102

100

96

87

August

93

95

116

no

101

100

99

85

September

95

99

115

108

101

99

99

85

October

97

104

115

107

100

99

100

84

November

99

107

112

105

99

98

97

82

December

97

108

no

104

98

94

96

81

Average

95

96

113

108

101

97

97

88

A n n u a l index . .

95

95

113

108

100

97

97

88

1923

1924

192;

1926

1927

192S

1929

1930

January

98

99

101

102

99

92

96

96

February

100

98

101

103

98

93

98

97

SEMI-MANUFACTURES

March

104

100

104

102

97

94

99

96

April

108

100

102

101

97

92

101

95

May

106

95

101

99

95

93

98

88

June

103

96

too

99

95

93

98

8$

July

103

95

101

101

93

93

98

83

August

102

93

102

101

92

94

97

83

Sep:ember

....

October

101

96

102

104

92

93

98

79

100

96

104

IOJ

92

94

99

76

November

99

97

104

100

92

95

98

74

December

100

99

101

100

93

95

98

70

Average

102

97

102

101

95

93

98

85

A n n u a l index . .

101

97

102

101

95

94

99

86

FINISHED MANUFACTURES

¡923

1924

192$

1926

1927

1928

1929

1930

January

100

99

95

IOO

98

93

93

95

February

100

99

96

100

99

94

92

92

March

100

99

97

101

96

93

92

92

April

99

99

98

101

95

92

94

91

101

102

98

102

91

95

96

90

June

103

102

99

101

91

93

94

88

Julv

105

100

98

100

93

95

93

88

May

August

102

98

98

102

95

95

93

87

100

99

99

100

93

98

94

86

100

97

99

100

94

94

93

83

99

97

98

98

95

95

93

83

....

99

96

98

98

95

95

94

85

Average

101

99

98

101

95

94

93

89

A n n u a l index . .

100

100

100

101

93

92

91

88

September

....

October November December

APPENDIX

IO 2

C

2. INDEXES OF V O L U M E AND SEASONAL VOLUME VARIATION OF DOMESTIC EXPORTS, BY ECONOMIC CLASSES TOTAL DOMESTIC EXPORTS

January February . . . . March April May June July August September . . . October November . . . December . . . Average Annual index. •

>9*3

'9*4

IÇ2S

IQ2Ô

1927

1928

1929

89 81 88 84 84 84

102

120 99 116 104

I08 96 102 107

122 no 124 m

97 83 85 95 ios

99 91 98 103 122

126 m 120 126 119 no

148

95 89 91 88 80 72 88 118 142

103 116

HI

132 121

127 116 125

131 141 140

>23 143 136 119

127 167 165 144

102 102

106 106

HI

121 121

78 83 100 104 102 108 91 90

"3

127 117 116

135 148 128 114 121 103 116 129

'93° I2S 112 "S 102 97 96 88 100

157 131 130

105 113 103 101

128 126

132 129

T05 101

Seasonal Variation 105 95 102 97 93 87 84 92 104 119 "3 109 100

R A W MATERIALS

January February March April May June

....

1923

IÇ24

IÇ2S

IQ2Ó

1927

1928

1929

1930

89 64

99 87 70 66 62

I66

126

I26

98 93 92

125 108 10;

«34 108

II6

175 147 «S3 120 102

59 141 209 228

98 83 67 69 60 61

'3° 87 95 70 54 53 Si 80

135 213 181

145 166 150

173

159

134

124

114

125

113

101 101

63 59 47 60

52

79 63 50 54 70 "7 213 185 167

79 74 83 87 144 224 238 236

118 116

131 131

July August September . . . October November . . . December . . .

130 138

47 55 126 162 196 168

Average . . . . Annual index.

84 84

99 100

52 60 118 129

85 71 66 108 175 159 128 124 126

85 103 82 66

Seasonal variation »7 93 90 76 64 58 53 59 "5 167 «63 144 100

APPENDIX RAW

'9*3

1924

105 116

January February . . . . March April May June July August September . . . October November . . . December

FOODSTUFFS

1925

1926

'927

1928

'9*9

66

74 60

81

68

84

74

9i 75 79 «5

72 5« 54 49

89

59 44 59

64

51 39 5' 49 9» 75

126

63

88

46

68

124

110

»7 Ml 344

84

I I I

« 5

93

Average . . . . Annual index.

112

68

86

61 84

190

76 173

57 47 116

104

108

179

366

181

113

83

62

138

»47

236

88

138

9i 74

no 103

112

61

192

62

140

182

69

127

68

102

88

94 94

119

79

102

122

82

I°3

133 134

1923

1924

1925

.

113

129

102

.... •

" 3

119

86

.

132

" 3

.

IO9

98

.

107

88

.

90

83

7o 78 79

78 95

88 100

97 95 86 99

• ... .

102

106

.

112

119

... . 109 ... • " 9

Average . Annual index. .

105 104

106

104

105

105

1930

73 S5 37 36 51 57 75

MANUFACTUKCD

January February March April May June July August September October November December

C

1926

« 3

99 98

103

93 67 94

130

7*

73 7i 88

72 77 163 145 120

74

101

91 93

67 66

100

1929

1930

FOODSTUFFS

'9*7

1928

83

90

102

79 78 74 65

86

86

9»

63

75 72 78 75 74

80

65

64

63

86

84

72

91 79 74 73 77 78 87 98 93

88 88

88

83

92

102

73

Seasonal variation

68

67 63 73 77

96

82

94

97

87

92

93

89

96 98

81

79

82

81

80

82

H I

89

85 85

Seasonal variation 105 87 7o 95 100 74 61

87

69

86

62

84

57 70

83 97

69

108

79

122

72

114

66

118

70

100

70

APPENDIX

C

SEMI-MANUFACTURES

1923 January

1924

1925

1926

>927

1928

1929

1930

Seasonal variation

•

8S

HI

122

136

13a

98

IOS

71

101

117 92

98

,. •

89

10S

116

86

March

•

84

98

122

97

115

" S 128

125

93

91 100

April

•

8S

99

118

» 3

118

117

121

93

100

May

.

88

112

116

" S

140

104

•

91

106

109

132

132

113 120

105

June

99 109

n o

106

July

•

94

IOI

116

102

129

93

102

•

8s

102

98

103

128

125 114

116

August

HI

98

... •

84

107

96

106

IIS

106

110

97 90

•

90

" 3

94

100

115

120

125

95

... • ... .

95 102

107

91 105

124

118

118

97

83

125

124

» 3

105

93

97 102 100

February

September

.

October November December Average Annual

110

.

88

106

106

105

120

122

116

95

index. .

89

105

106

105

121

122

116

95

1928

1929

1930

95 100

F I N I S H E D MANUFACTURES

>9*3 January February

....

March April

•

May

1924

>925

1926

1927

82

98

105

119

123

126

171

146

82

97

96

" 7

114

121

154

98

102

99

130

131

130

ISO

173 209

155

» 3

145 161

180

143

155

» 5 109

157 160

174

131 129

182

114

160

160

116

114

133

141

150

102

til

125

128

143

99

June

•

96

98

109

m

133

July

•

90

84

107

August

• .•

91 86

99 92

T23

» 7 107

132 144

99

119

86

102

108

105

" 3 116

" 5 118

117

September October November

101 99 101

121

141

100

88

157

105

154 144

125

96

93 90

136

99

93 100

84

89

105

86

96

129

90

98

114

118

128

146

164

124

index.,

91

97

112

119

130

149

166

124

Average Annual

121

100

151

.

December

Seasonal variation

APPENDIX

D

O T H E R PUBLISHED INDEXES OF U N I T E D STATES FOREIGN TRADE I . KREPS INDEX

O n an annual basis from 1879 to 1916 inclusive there are price and quantity indexes of total exports and total imports, constructed by T . J. Kreps for the purpose of studying the gross and net barter terms of trade. 1 Among the difficulties encountered by Mr. Kreps in his export indexes was the nonhomogeneity of the commodities officially listed, and their lack of comparability over a period of years. Many commodities, notably machinery, changed radically in design and quality. The difficulty was met in part by using wholesale prices of specified standard commodities, rather than export prices, which are average prices, frequently of non-homogeneous groups of commodities, and obtainable from the Monthly Summaries. Price series were obtained from the Aldrich report up to 1890, while for later years they were obtained from wholesale price bulletins of the United States Bureau of Labor Statistics and from the Monthly Summaries. 2 Secondly, he has considerably overweighted his list with raw materials. Another difficulty was found in the gradually changing composition of our export trade, finished goods becoming relatively more important, and agricultural commodities less. Moreover, some important commodities, as wheat, fluctuated widely in value 1 Kreps, T . J., " Import and Export Prices in the United States and the Terms of International Trade, 1880-1914," The Quarterly Journal of Economics, August, 1926, vol. xl, pp. 708-720. 2 A s has been explained on p. 24 the more detailed classification of the Department of Commerce in recent years has minimized somewhat the lack of comparability of data.

105

io6

APPENDIX

D

exported f r o m year to year. In solving this problem M r . Kreps selected twenty-eight commodities, each of which formed over one half of one per cent of our toal exports for the years 1883, 1903 and 1923. These commodities aggregated f r o m forty to forty-five per cent in value of our exports. T h e base selected was the eleven-year period 1903-1913. N o t only was a broad base chosen, but the changing character of our trade was reflected in the price index by changing weights for each year's comparison with the base period. T h e formula adopted was the Marshall-Edgeworth f o r m u l a : 2 Pi

(Qo + Qi) 2po 24.8

A 1084

B 1756

+

62.0

3818 1510

4907 1136

+ —

28.2 24.8

a 2318

63771

+

6î-7

790

2843

+

259.9

[790]

1324

+

67.6

1689

[2843]

+

68.3

574 1084 700

432 1756 1324

— + +

24.8 62.0 67.6

2448

3512

+

43-5

1510 2318 1689

1136 3771 2843

— + +

24.8 62.7 68.3

5517

775°

-f

40.5

APPENDIX

114

Final Quantity Index : 1

Final Price I n d e x :

D

0 0 X \2448

=

142.0

100+ — Z X ^ = \2448 3512

223-0

5517

Final V a l u e Index : 1.42 X 2.23 - 317 per c e n t = A c t u a l r a t i o of value of all exports, 1919 to 1913. LINK RELATIVES OBTAINED FOR USE IN COMPUTING FOREIGN TRADB INDEXES OF QUANTITY (These cover only articles directly entering into the calculation, without the final result for articles not so entering) Domestic Exports weighted by prices of Ratio of 1919 1920 1921 1922 1923 1924 1925

to to to to to to to

1913 1919 1920 1921 1922 1923 1924

Earlier

Year

132.0 94.6 94.2 96.0 98.9 114.0 106.0

Later

Year

127.9 97.2 86.5 95.1 95.0 113.9 102.8

Careful consideration was given to the question whether more satisfacory results would be obtained by dividing the commodities into great groups and calculating price movements for each separately. It would seem at first thought that when articles are so divided a fairly close parallelism in price might be expected between the articles af a given group directly entering into the index and those not so covered. Examination of specific individual items, however, indicates that this is by no means necessarily the case. If one groups articles according to the character of the materials used, he would have, for example, a group of textiles. It is by no means the case that the prices of exported or imported textile fabrics, clothing and other articles made from textile fabrics move in close parallel with the prices of raw textile materials. In the case of our own textile exports, the price of cotton would completely dominate the entire group including manufactured products made f r o m all textile fibers. If, on the other hand, the attempt should be made to make calculations for economic classes—foodstuffs, raw materials, semimanufactures and manufactures—the difficulties are quite

APPENDIX

D

as great. The crude material group would be completely dominated by cotton, and there is no certainty that the crude articles not included in the index have a price movement at all similar to that of cotton. In the group of finished manufactures there are so few articles for which comparable average prices can be calculated that it would be rash to assume that the many other articles have moved in parallel with these. It is probable that later on, for the sake of getting some impression as to the relative quantitative and price changes in the foreign trade in large commodity groups and large economic classes, separate calculations for them will be made, but it is not believed that the general indexes for all articles taken together would be any better by combining these separate indexes than by a direct calculation. 5- ROGERS VOLUME ESTIMATE

In connection with his chapter on " Foreign Markets and Foreign Credits " in Recent Economic Changes, Mr. Rogers had occasion to measure the physical volume of United States exports for the years 1922 to 1927 inclusive. 1 Thirteen items were selected, each of which aggregated $50,000,000 in at least one year. ( T h e source of the material was the Monthly Summaries.) The total value of each of these commodities was divided by its corresponding quantity each year in order to obtain its unit price. The resulting prices were averaged so as to obtain the average 1922-27 price for each commodity. These prices were then multiplied by the quantities exported each year in order to find out what the value of these commodities would have been each year if they had been exported at average prices of the period covered. Then these values (with price changes eliminated) were substituted for actual values in arriving at the total value of exports. His measure is therefore that of the value changes of United States exports with the price of certain important commodities held constant. 1 Rogers, J. H . , " Foreign Markets and Foreign Credits", ch. xi of Recent Economic Changes in the United States (Report of the Committee on Recent Economic Changes, of the President's Conference on Unemployment, Herbert Hoover, Chairman. No. 13 of the National Bureau of Economic Research Series.) First edition, New Y o r k , volume ii, 1929. T h e method used is explained on page 710.

APPENDIX

116

D

Mr. Rogers uses this method to measure volume changes in exports to different countries and regions as well as changes in the volume exported of different groups of commodities. According to Mr. Rogers, " this method of measuring quantities has an advantage over the usual one in that it facilitates comparisons with corresponding values at the same time that the relative importance of the export is kept automatically in the mind of the reader." 1 It should be noted, however, that the advantage does not lie in failing to remove price changes from all commodities, but in the fact that the index is not reduced to index numbers relative to a base period. In fact the plan was considered as little more than a makeshift. The calculation of average prices of such extremely broad groups of commodities as " Meats " and " Boards and Timber " would seem to give especially rough results. Yet Mr. Rogers considers that the results agree fairly well with the more refined measure of the Department of Commerce. 6 . FEDERAL RESERVE BOARD I N T E R N A T I O N A L PRICE

INDEX

The story of this index and the " Foreign Trade Index " may be read from beginning to end in various issues of the Federal Reserve Bulletin. W e read in the May 1920 issue that it will publish a group of index numbers for different countries, all constructed in the same fashion, using the same base year, the same type of quotations, and approximately the same number of commodities. " Many staple commodities will be included in all the indexes; in addition the index of each country will include a certain number of commodities of special importance in its economic life." 2 Several overlapping indexes were made; of raw materials, producers' goods, consumers' goods; goods produced, goods imported, goods consumed, goods exported. The export index started with thirty-eight different items, a few others being added later. 1 1

Rogers, op. cit., p. 716. Federal Reserve Bulletin,

M a y , 1920, vol. vi, no. 5, p. 499.

APPENDIX

D

II7

T h e quotations are all taken at wholesale on a weekly or monthly basis, a contract price being used if actual transactions in the commodity are usually made on this basis. E x p o r t goods are . . . quoted in American markets. Quotations have been obtained f o r the most part f r o m trade journals, although a considerable number have been furnished b y private firms. In general, the sources are the same as those used by the Price Section of the W a r Industries B o a r d in its study of prices during the war. In this study a special effort was made to obtain the most representative quotations for each of the commodity lines. In many cases the quotations are the same as those used by the Bureau o f L a b o r Statisics and are being furnished us by that bureau. 1 T h e index, w h i c h was of the aggregative type, used approximate quantities exported in 1 9 1 3 as weights. But: In applying the weights to the prices, the commodity quoted has been allowed to represent other commodities in the same general class. In other words, the weight applied to petroleum in the production index is total production of petroleum in the United States, not merely the production in the California and mid-continent fields (the grades f o r which quotations are carried). 2 In a subsequent issue we r e a d : T h e index number of the Federal Reserve Board has been constructed primarily with a view to international comparisons of wholesale prices. Due t o difficulties connected with the collection of foreign prices, the foreign index numbers are still incomplete, but in spite of this it has seemed advisable to publish the American number, since it contains certain classifications of commodities not otherwise available, namely, the prices of important goods imported into this country, and of goods largely exported, and compares them with the general price level in the United States. 3 T h e index, which is on an annual and a monthly basis, covers 1

Federal

Reserve

Bulletin,

op. cit., p. 499.

^ I bid., p. 500. 3

Ibid.. June, 1921, vol. 7, no. 6, p. 702n.

APPENDIX

II8

D

1913, 1919, and subsequent years, until January, 1926. N o international price index other than that for United States w a s published until 1922, when the English number appeared. Other countries appeared at later dates. In the March, 1926 issue we find this statement: W i t h this issue of the Federal Reserve Bulletin the Board discontinues the publication of its indexes of wholesale prices in England, Canada, and Japan, and of the index for the United States, compiled for the purpose of comparison with the price levels in these countries. T h e compilation and publication of these indexes for the purpose of facilitating international comparisons were undertaken by the board in 1920, when widespread monetary disorganization prevailed. Since that time price fluctuations caused by the instability of the exchanges have become less important, and, with the reestablishment in 1925 of the gold standard in England and other countries, the board has decided to depend for its information on price movements in England, Canada, and Japan, on the indexes compiled in these countries and regularly included in the table on wholesale prices in principal countries. 1 7.

FEDERAL RESERVE BOARD FOREIGN TRADE INDEX

In July, 1920, there appeared a companion index to the United States International Price Index designed to reflect movements in foreign trade in the United States with fluctuations due to price changes eliminated. T h e commodities chosen for these indexes are those for which prices are compiled by the Federal Reserve Board in the preparation of its international price index. T h e list includes 14 of the most important imports the value of which in 1913 formed 40.6 per cent of the total import values, and 29 of the most important exports the value of which in 1913 formed 56.3 per cent of the total export values. 2 T h e method is similar to that used in constructing the international price indexes. Prices of goods exported in 1913 are the weights for aggregative indexes. There were four such 1

Federal Reserve Bulletin, op. cit., March. 1926, vol. 12, no. 3, p. 196.

2

¡bid., July, 1920, vol. 6, no. 7, p. 694.

APPENDIX

D

119

export indexes; raw materials, producers' goods, consumers' goods, and grand total. The May, 1925, issue of the Federal Reserve Bulletin was the last appearance of the Foreign Trade index. No reason for or notice of its suspension was given. 8 . T H E AMERICAN TARIFF LEAGUE IMPORT VOLUME INDEX

This index, constructed by W . R. Peabody, is on a monthly basis and by economic classes.1 The reason for breaking up the index is to enable one to follow the trend of any one group independently. T o facilitate comparison with value totals the Department of Commerce classification has been retained. Material is obtained entirely from Monthly Summaries, revised data being used whenever possible. His sample contains more than 200 items, comprising over 75 per cent of the total value of imports in the years 1923-25, the base period. The indexes are of the aggregative type. Base period prices, obtained by dividing values by quantities, are the weights. The price weights of coffee and sugar have been reduced arbitrarily. Each of these commodities represent a major proportion of the economic group in which it is classified and by virtue of this fact changes in the imports of this commodity exert great influence on the group index. This influence would be increased in the sample because of the omission of many of the lesser items. We have assumed that the movement of the remainder of our sample for the group is more typical of the movement of the unenumerated commodities than is the movement of coffee or sugar and have accordingly reduced the weights of these two commodities so that they hold a place in the sample equal to the proportion they represent in their economic group. 2 The separate indexes are combined into a general index by an arithmetic average in which the weights are the percent each class formed of the value imported in the base period. ' The method he follows is described in the Statistical Bulletin of the American Tariff League, October, 1929, no. 12, under the heading: " Résumé of Method Followed in Constructing Volume Index of Imports." 2

Ibid., p. 2.

INDEX Accuracy, mathematical, 91 Aggregative index numbers, relation to arithmetic averages, 43; relation to harmonic averages, 43; best for certain purposes, S3 Agricultural exports, index of, 109110 Alaska, 17 Aldrich report, 105 American Tariff League, import index, 14, 16, 62-63, 119 Animal products, see commodity groups Animals, see commodity groups Annual indexes, method o j construction, 66-68 Arithmetic averages, relationship between simple and weighed, 4 1 ; relationship to harmonic, 41-42; relative accuracy of simple and weighted, 63; simple, 40-41; weighted, 41, 42, 68 Automobiles, parts and accessories, exports o f , 29, 3 3 ; method of estimating values of, 66 Base period chosen, 64 Base reversal test, 53 Berridge, William S., 64, 107-109 Beverages, see commodity groups Bias, of chain indexes, 43, 46; of data, 24-25; see also weight correlation bias Bowley, A. L., 34n Business cycles and export trade, 13-14, 78-87 Chain index numbers, bias o f , 43, 46; effect of changing weights, 43-48; effect of correlation of price and quantity changes, 43-48, 59-60; sensitivity of, 58; weighting o f , 43 Circular test, 49, 51-53. 68, 69, 7576 Class groups, adjustments of to secure representative sample, 27,

29; definition of, 16; percentage distribution within classes, 28 Commodities, erratic, 63, 65, 105, 112, 1 1 9 ; forty leading, 37-39; included in sample, 92-98 Commodity groups, 15-16, 1 1 4 - 1 1 5 Comparability of data, effect of non-comparability on index numbers, 61 Correlation, American and foreign crops, 80; American and foreign business cycles, 78; exports and foreign investments, 80; exports and imports, 80; export prices and domestic prices, 78; export prices and business activity, 78, 8 0 8 3 ; export values and business activity, 78, 8 1 ; export values and export volume, 80; export volume and business activity, 78, 80-82, 84, 86, 87 Cotton, adjustment for, 62, 112114; effect on index, 65 Cummings, John, 18 Deflation, of automobiles, parts and accessories, 6 6 ; of class totals, 68, 108, 109; of excluded items, 62, 1 1 2 - 1 1 3 Deflators, price indexes as, 62, 66, 68, 112-113; quantity indexes as, 58, 108, 109 Demand, effect on exports, 89 Department of Commerce, index compared with Cowden index, 76-79; indexes of, 13-14, 109-110, 110-115; method used in adjusting wheat and cotton, 62, 112113; sample used by, 27, 33, 110 Divergency, of monthly indexes f r o m annual, 69-72, 70n; of total exports f r o m class indexes, 70n Domestic exports, definition of, 17 Durand, E . Dana, 64, n o Economic classes, 16, 114-115; percentage distribution o f , 35 121

122

INDEX

Edgeworth. Marshall-, formula, 106 Export data, accuracy of, 18-21, 24; bias of, 21, 24-35; changes in classification of, 22; changes in quality, 23-24; commodities showing quantities exported, 34, 36; comparability of, 22-24; h o m o g e n e i t y of, 22-23, 24; finished manufactures unsatisfactory, 35-36; method of collection, 18; reliability on monthly basis, 21; sources of, 13, 15-16, 25 Export declarations, 18, 19 Export indexes, comparison with Department of Commerce index, 76-79; shown graphically, 81, 83, 85-87; tabulated, 99-104 Exports, behavior during 1930, 82; varying composition of, 105, 111 Export value, definition of, 17, i7n

Hoover, Herbert, 115

Factor reversal test, 50-51, 53, 57, 59, 68 Federal Reserve Bank of New York, 62 Federal Reserve Board, indexes of, 116-119 Finished manufactures, commodities, 96-98; price indexes, 81, 83, 101; seasonal volume indexes, 84-85, 104; value indexes, 31-32, 81; volume indexes, 81, 87, 104; see also economic classes Fisher, Irving, 47, 49, 51-53 Food products, see commodity groups Foreign and Domestic Commerce, Bureau of, 16, 17, 19 Foreign Commerce and Navigation, 16, 27 Foreign countries, definition of, 17 Foreign trade index, 118-119 Forwarding agents, 21

Machinery, see commodity groups. Mahoney, L. J., 20, 21 Manufactured foodstuffs, commodities, 93-94; price indexes, 81, 83, 100-101; seasonal volume indexes, 84-85, 103; value indexes, 30, 32, 81; volume indexes, 81. 86, 103; see also economic classes Manufactures, see finished manuf a c t u r e s , semi-manufactures, manufactured foodstuffs Marshall-Edgeworth formula, 106 Median, 40, 106 Metals, see commodity groups Methods, factors affecting, comparability of data, 60-61; completeness of data, 61-62; ease of construction, 63; object of study, 58-59; relationship between price and quantity changes, 59-60; relative importance of commodities, 62-63 Minerals, see commodity groups Mitchell, Wesley C., 54 Mode, 40 Monthly indexes, method of construction, 69-72 Monthly summary, 15-16 Moving average, weighted, 84

Geometric mean, 40, 63, 68 Harmonic average, relation to arithmetic, 41-42; weighted, 4142, 43, 68 Hawaii, 17 Homogeneity, effect of non-homogeneity on index numbers, 2223, 60; non-homogeneity and price variation, 36-37

Ideal index, 47, 49, 51, 53, 56, 63, 66, 68,

in

Import data, 13 Import indexes, 105, 107, 110-115, 116, 118, 119 Inflation, of automobiles, parts and accessories, 66; of class totals, 68; of items excluded from sample, 113 Inflators, price indexes as, 66, 68, 113 ; quantity indexes as, 68 International price index, 116-118; of England, 118 King, Willford I., 54-55, 56, 63 Koren, John, 19 Kreps, T . J., 105-107 Labor Statistics, Bureau of, 105, 117

Xonmetallic minerals, modity groups

see

com-

123 Paper, see commodity groups Parcel-post exports, 17-18 Peabody, W . R., 14, 119 Persons, Warren M., 47-49, S3 Phillipine Islands, 17 Porto Rico, 17 Prices, how obtained, 91 Price variation, coefficients o f , 3739 Probable error of mean, 33 Procedure in constructing index numbers, 91 Purpose of index numbers, 51-57, 58-59 Random sampling, 26 R a w foodstuffs, commodities, 93; price indexes, 81, 83, 100; seasonal volume indexes, 84-85, 103; value indexes, 30, 32, 81; volume indexes, 81, 86, 103; see also economic classes Raw materials, commodities, 92; price indexes, 81, 83, 100; seasonal volume indexes, 84-85, 102; value indexes, 30, 32, 81; volume indexes, 81, 86, 102; see also economic classes Rogers, James Harvey, 63, 115 Sample, adequacy, 34-35; limitations on choice of commodities, 36-39; minimum value of items, 39; number of commodities, 34; representativeness, 28, 30-32; value of sample, 35 Sampling, adequacy, 33-34. 63; proportionate representation, 26-28; proportionate value changes, 2933; randomness, 26 Schedule B., i7n, 21, 92 Schmeckebier, L. F., 18, 20 Seasonal variations, and varying length of months, 84; methods of eliminating, 84, 109; indexes of, 85, 102-104 Semimanufactures, commodities,

94-95; price indexes, 81, 83, 101; seasonal volume indexes, 84-85, 104; value indexes, 31-32, 8 1 ; volume indexes, 81, 87, 104; see also economic classes Shipping agents, 21 Shipper's manifest, 18 Section of customs statistics, 20, 21 Smoothing of volume indexes, 84 Standard error of mean, 34n Strong, H. M., 109-110 Supply, effect on exports, 89 Texts of index numbers, 49-58 Textiles, see commodity groups Time reversal test, 49, 57 United States, definition of, 17 Value indexes, 29-33, 76-77 Vegetable food products, see commodity groups Vegetable products, see commodity groups Vehicles, see commodity groups Virgin Islands, i7n War Industries Board, 117 Weight correlation bias, 48, 50, 53, 69, 99; correction for, 59, 60; measurement of, 69-72 Weighting, and bias of chain indexes, 43-49; importance of accuracy, 107; double weighting of averages, 108; of aggregative index numbers, 43; of arithmetic averages, 41; of harmonic averages, 4 1 ; relative accuracy of simple and weighted average, 63; results obtained by different systems, 73-75; simple averages really weighted, 4 1 ; up-to-date weights in chain index, 58; used in moving average, 84 Wheat, ddjustment for, 62, 112114; effect on index, 65 Wood, see commodity groups