A Guide to Econometrics. 6th edition [6 ed.] 1405182571, 9781405182577
This is the perfect (and essential) supplement for all econometrics classes--from a rigorous first undergraduate course,
202 68 7MB
English Pages 598 [599] Year 2008
Table of contents :
Contents ... 6
Preface ... 11
Dedication ... 13
1 Introduction ... 14
1.1 What is Econometrics? ... 14
1.2 The Disturbance Term ... 15
1.3 Estimates and Estimators ... 17
1.4 Good and Preferred Estimators ... 18
General Notes ... 19
1.2 The Disturbance Term ... 22
1.3 Estimates and Estimators ... 22
1.4 Good and Prefe rred Estimators ... 22
2 Criteria for Estimators ... 24
2.1 Introduction ... 24
2.2 Computational Cost ... 24
2.3 Least Squares ... 25
2.4 Highest R2 ... 26
2.5 Unbiasedness ... 27
2.6 Efficiency ... 29
2.7 Mean Square Error ... 30
2.8 Asymptotic Properties ... 31
2.9 Maximum Likelihood ... 34
2.10 Monte Carlo Studies ... 35
2.11 Adding Up ... 38
General Notes ... 39
2.2 Computational Cost ... 39
2.4 Highest R2 ... 39
2.3 Least Squares ... 39
2.5 Unbiasedness ... 41
3 The Classical Liner Regression Model ... 53
3.1 Textbooks as Catalogs ... 53
3.2 The Five Assumptions ... 54
3.3 The OLS Estimator in the CLR Model ... 56
General Notes ... 57
3.1 Textbooks as Catalogs ... 57
3.3 The OLS Estimator in the CLR Model ... 57
3.2 The Five Assumptions ... 60
3.3 The OLS Estimator in the CLR Model ... 61
4 Interval Estimation and Hypothesis Testing ... 64
4.1 Introduction ... 64
4.2 Testing a Single Hypothesis: The t Test ... 64
4.3 Testing a Joint Hypothesis: the F Test ... 65
4.4 Interval Estimation for a Parameter Vector ... 67
4.5 LR,W, and LM Statistics ... 69
4.6 Bootstrapping ... 71
General Notes ... 72
4.1 Introduction ... 72
4.2 Testing a Single Hypothesis: The t Test ... 75
4.3 Testing a Joint Hypothesis: The F Test ... 75
4.4 Interval Estimation fo r a Parameter Vector ... 77
4.5 LR,W, and LM Statistics ... 77
4.6 Bootstrapping ... 78
Technical Notes ... 79
4.1 Introduction ... 80
4.3 Testing a Joint Hypothesis: The F Test ... 81
4.5 LR, W, and LM Statistics ... 81
4.6 Bootstrapping ... 82
5 Specification ... 84
5.1 Introduction ... 84
5.2 Three Methodologies ... 85
5.2.1 Average Economic Regression (AER) ... 85
5.2.2 Test,Test,Test (TTT) ... 86
5.2.3 Fragility Analysis ... 86
5.3 General Principles for Specification ... 88
5.4 Misspecification Tests/D iagnostics ... 89
5.5 R^2 Again ... 92
General Notes ... 94
5.1 Introduction ... 94
5.2 Three Methodologies ... 94
5.3 General Principles for Specification ... 98
5.4 Misspecifica tion Tests/Diagnostics ... 100
5.5 R^2 Again ... 102
Technical Notes ... 102
5.1 Introduction ... 102
5.2 Three Methodologies ... 102
5.4 Misspecification Tests/D iagnostics ... 103
6 Violating Assumption 1: Wrong Regressors, Nonliearities, Parameter Inconsistency ... 106
6.1 Introduction ... 106
6.2 Incorrect Set of Independent Variables ... 106
6.3 Nonlinearity ... 108
6.3.1 Transformations ... 108
6.3.2 Computer-Assisted Numerical Techniques ... 109
6.4 Changing Parameter Values ... 110
6.4.1 Switching Regimes ... 111
6.4.2 Parameters Determined by Other Variables ... 111
6.4.3 Random Coefficients ... 112
General Notes ... 113
6.1 Introduction ... 113
6.2 Incorrect Set of Independent Variables ... 113
6.3 Nonlinearity ... 115
6.4 Changing Parameter Values ... 118
Technical Notes ... 119
6.3 Nonlinearity ... 119
6.4 Changing Parameter Values ... 121
7 Violating Assumption Two: Nonzero Expected Disturbance ... 122
8 Violating Assumption Three: Nonspherical Disturbances ... 125
8.1 Introduction ... 125
8.2 Consequences of Violation ... 126
8.3 Heteroskedasticity ... 128
8.3.1 The Eyeball Test ... 129
8.3.2 The Goldfeld-Quandt Test ... 129
8.3.3 The Breusch-Pagan Test ... 129
8.3.4 The White Test ... 130
8.4 Autocorrelated Disturbances ... 131
8.4.1 Cochrane-Orcutt Iterative Least Squares ... 134
8.4.2 Durbin's Two-Stage Method ... 134
8.4.3 Hildreth-Lu Search Procedure ... 134
8.4.4 Maximum Likelihood ... 134
8.5 Generalized Method of Moments ... 135
General Notes ... 136
8.1 Introduction ... 136
8.2 Consequences of Violation ... 136
8.3 Heteroskedasticity ... 137
8.4 Autocorrelated Disturbances ... 139
Technical Notes ... 142
8.1 Introduction ... 142
8.2 Consequences of Violation ... 142
8.3 Heteroskedasticity ... 144
8.4 Autocorrelated Disturbances ... 145
8.5 Generalized Method of Moments ... 147
9 Violating Assumption Four: Instrumental Variable Estimation ... 150
9.1 Introduction ... 150
9.2 The IV Estimator ... 154
9.3 IV Issues ... 157
9.3.1 How can we test if errors are correlated with regressors? ... 157
9.3.2 How can we test if an instrument is uncorrelated with the error? ... 157
9.3.3 How can we test if an instrument's correlation with the troublesome variable is strong enough? ... 158
9.3.4 How should we interpret IV estimates? ... 158
General Notes ... 159
9.1 Introduction ... 159
9.2 The IV Estimator ... 160
9.3 IV Issues ... 162
Technical Notes ... 164
9.1 Introduction ... 164
9.2 IV Estimation ... 164
9.3 IV Issues ... 166
10 Violating Assumpton Four: Measurement Errors and Autoregression ... 170
10.1 Errors in Variables ... 170
10.1.1 Weighted Regression ... 171
10.1.2 Instrumental Variables ... 172
10.1.3 Linear Structural Relations ... 173
10.2 Autoregression ... 173
General Notes ... 176
10.1 Errors in Variables ... 176
10.2 Autoregression ... 179
Technical Notes ... 180
10.1 Errors in Variables ... 180
10.2 Autoregression ... 181
11 Violating Assumption Four: Simultaneous Equations ... 184
11.1 Introduction ... 184
11.2 Identification ... 186
11.3 Single-Equation Methods ... 189
11.3.1 Ordinary Least Squares ... 190
11.3.2 Indirect Least Squares ... 190
11.3.3 The Instrumental Variable (IV) Technique ... 191
11.3.4 Two-Stage Least Squares (2SLS) ... 191
11.3.5 Limited Info rmation, Maximum Likelihood (LI/ML) ... 192
11.4 Systems Methods ... 192
11.4.1Three-Stage Least Squares (3SLS) ... 193
11.4.2 Full Information,Maximum Likelihood (FUML) ... 194
General Notes ... 194
11.l Introduction ... 194
11.2 Identification ... 196
11.3 Single-Equation Methods ... 197
11.4 Systems Methods ... 198
Technical Notes ... 199
11.1 Introduction ... 199
11.2 Identification ... 200
11.3 Single-Equation Methods ... 201
11.4 Systems Methods ... 203
12 Violating Assumtion Five: Multicollinearity ... 205
12.1 Introduction ... 205
12.2 Consequences ... 206
12.3 Detecting Multicollinearity ... 207
12.4 What To Do ... 209
12.4.1 Do Nothing ... 209
12.4.2 Incorporate Additional Information ... 209
General Notes ... 211
12.2 Consequences ... 211
12.3 Detecting Multicollinearity ... 212
12.4 What to Do ... 212
Technical Notes ... 215
13 Incorporating Extraneous Information ... 216
13.1 Introduction ... 216
13.2 Exact Restrictions ... 216
13.3 Stochastic Restrictions ... 217
13.4 Pre-Test Estimators ... 217
13.5 Extraneous Information and MSE ... 219
General Notes ... 220
13.1 Introduction ... 220
13.2 Exact Restrictions ... 221
13.3 Stochastic Restrictions ... 222
13.4 Pre-test Estimators ... 223
13.5 Extraneous Information and MSE ... 223
Technical Notes ... 224
13.3 Stochastic Restrictions ... 224
13.5 Extraneous Information and MSE ... 225
14 The Bayesian Approach ... 226
14.1 Introduction ... 226
14.2 What is a Bayesian Analysis? ... 226
14.3 Advantages of the Bayesian Approach ... 229
14.4 Overcoming Practitioners' Complaints ... 230
14.4.1 Choosing a Prior ... 230
14.4.2 Finding and Using the Posterior ... 232
14.4.3 Convincing Others ... 232
General Notes ... 233
14.1 Introduction ... 233
14.2 What is a Bayesian Analysis? ... 233
14.3 Advantages of the Bayesian Approach ... 236
14.4 Overcoming Practitioners' Complaints ... 237
Technical Notes ... 239
14.1 Introduction ... 239
14.2 What is a Bayesian Analysis? ... 239
14.3 Advantages of the Bayesian Approach ... 241
14.4 Overcoming Practitioners' Complaints ... 243
15 Dummy Variables ... 245
15.1 Introduction ... 245
15.2 Interpretation ... 246
15.3 Adding Another Qualitative Variable ... 247
15.4 Interacting with Quantitative Variables ... 248
15.5 Observation-Specific Dummies ... 249
General Notes ... 250
15.1 Introduction ... 250
1 5.4 Interacting with Quantitative Variables ... 251
15.5 Observation-Specific Dummies ... 252
Technical Notes ... 253
16 Qualitative Dependent Variables ... 254
16.1 Dichotomous Dependent Variables ... 254
16.2 Polychotomous Dependent Variables ... 257
16.3 Ordered Logit/Probit ... 258
16.4 Count Data ... 259
General Notes ... 259
16.1 Dichotomous Dependent Variables ... 259
16.3 Ordered Logit/Probit ... 266
16.4 Count Data ... 266
Technical Notes ... 267
16.1 Dichotomous Dependent Variables ... 267
16.2 Polychotomous Dependent Variables ... 269
1 6.3 Ordered Logit/Probit ... 271
16.4 Count Data ... 272
17 Limited Dependent Variables ... 275
17.1 Introduction ... 275
17.2 The Tobit Model ... 276
17.3 Sample Selection ... 278
17.4 Duration Models ... 280
General Notes ... 282
17.1 Introduction ... 282
17.2 The Tobit Model ... 282
17.3 Sample Selection ... 283
17.4 Duration Models ... 286
Technical Notes ... 286
17.1 Introduction ... 286
17.2 The Tobit Model ... 287
17.3 Sample Selection ... 288
17.4 Duration Models ... 289
18 Panel Data ... 294
18.1 Introduction ... 294
18.2 Allowing for Different Intercepts ... 295
18.3 Fixed Versus Random Effects ... 297
18.4 Short Run Versus Long Run ... 299
18.5 Long, Narrow Panels ... 300
General Notes ... 301
18.1 Introduction ... 301
18.2 Allowing for Different Intercepts ... 302
18.3 Fixed Versus Random Effects ... 303
18.4 Short Run Versus Long Run ... 304
18.5 Long,Narrow Panels ... 305
Technical Notes ... 305
18.2 Allowing for Different Intercepts ... 305
18.3 Fixed versus Random Effects ... 305
18.5 Long, Narrow Panels ... 308
19 Time Series Econometrics ... 309
19.1 Introduction ... 309
19.2 ARIMA Models ... 310
19.3 VARs ... 311
19.4 Error Correction Models ... 312
19.5 Testing for Unit Roots ... 314
19.6 Cointegration ... 315
General Notes ... 317
19.1 Introduction ... 317
19.2 ARIMA Models ... 317
19.3 VARs ... 318
19.5 Testing fo r Unit Roots ... 320
19.6 Cointegration ... 322
Technical Notes ... 327
19.1 Introduction ... 327
19.2 ARIMA Models ... 327
19.3 VARs ... 333
19.4 Error Correction Models ... 335
19.5 Testing for Unit Roots ... 336
19.6 Cointegration ... 340
20 Forecasting ... 344
20.1 Introduction ... 344
20.2 Causal Forecasting/Econometric Models ... 345
20.3 Time Series Analysis ... 346
20.4 Forecasting Accuracy ... 347
General Notes ... 348
20.1 Introduction ... 348
20.2 Causal Forecasting/Econometric Models ... 350
20.3 Time Series Analysis ... 352
20.4 Forecasting Accuracy ... 353
Technical Notes ... 355
20.l Introduction ... 355
20.2 Causal Forecasting/E conometric Models ... 356
20.4 Forecasting Accuracy ... 356
21 Robust Estimation ... 358
21.1 Introduction ... 358
21.2 Outliers and Influential Observations ... 359
21.3 Guarding Against Influential Observations ... 360
21.4 Artificial Neural Networks ... 362
21.5 Nonparametric Estimation ... 363
General Notes ... 365
21.1 Introduction ... 365
21.2 Outliers and Influential Observations ... 365
21.3 Guarding against Influential Observations ... 366
21.4 Artificial Neural Networks ... 367
21.5 Nonparametric Estimation ... 368
Technical Notes ... 369
21.3 Guarding against Influential Observation ... 369
21.4 Artificial Neural Networks ... 370
21.5 Nonparametric Estimation ... 370
22 Applied Econometrics ... 374
22.1 Introduction ... 374
22.2 The Ten Commandments of Applied Econometrics ... 375
22.3 Getting the Wrong Sign ... 381
22.4 Common Mistakes ... 384
22.5 What do Practitioners Need to Know? ... 386
General Notes ... 387
22.1 Introduction ... 387
22.2 The Ten Commandments of Applied Econometrics ... 388
22.3 Getting the Wrong Sign ... 391
22.4 Common Mistakes ... 392
22.5 What do Practitioners Need to Know? ... 392
Technical Notes ... 396
22.2 The Ten Commandments of Applied Econometrics ... 396
22.5 What do Practitioners Need to Know? ... 396
23 Computational Considerations ... 398
23.1 Introduction ... 398
23.2 Optimizing via a Computer Search ... 399
23.3 Estimating Integrals via Simulation ... 401
23.4 Drawing Observations from Awkward Distributions ... 403
General Notes ... 405
23.1 Introduction ... 405
23.2 Optimizing via a Computer Search ... 405
23.3 Estimating Integrals via Simulation ... 408
23.4 Drawing Observations from Awkward Distributions ... 409
Technical Notes ... 410
23.2 Optimizing via a Computer Search ... 410
23.3 Estimating Integrals via Simulation ... 413
23.4 Drawing Observations from Awkward Distributions ... 414
Appendix A Sampling Distributions ... 416
I An Example ... 416
2 Implications for Studying Econometrics ... 417
3 Calculating Sampling Distributions ... 418
Appendix B All About Variance ... 420
1 Definition ... 420
2 Estimation ... 421
3 Well-Known Formulas ... 421
4 More-General Formulas ... 421
5 Examples of the More-General Formulas ... 421
6 Cramer-Rao Lower Bound ... 423
Appendix C A Primer on Asymptotics ... 425
1 Convergence in Probability ... 425
2 Convergence in Distribution ... 427
3 Asymptotic Distributions ... 427
Notes ... 428
Appendix D Exercises ... 430
Appendix E Answers to Even-Numbered Questions ... 492
Glossary ... 516
Bibliography ... 524
Name Index ... 576
Subject Index ... 586
Contents ... 6
Preface ... 11
Dedication ... 13
1 Introduction ... 14
1.1 What is Econometrics? ... 14
1.2 The Disturbance Term ... 15
1.3 Estimates and Estimators ... 17
1.4 Good and Preferred Estimators ... 18
General Notes ... 19
1.2 The Disturbance Term ... 22
1.3 Estimates and Estimators ... 22
1.4 Good and Prefe rred Estimators ... 22
2 Criteria for Estimators ... 24
2.1 Introduction ... 24
2.2 Computational Cost ... 24
2.3 Least Squares ... 25
2.4 Highest R2 ... 26
2.5 Unbiasedness ... 27
2.6 Efficiency ... 29
2.7 Mean Square Error ... 30
2.8 Asymptotic Properties ... 31
2.9 Maximum Likelihood ... 34
2.10 Monte Carlo Studies ... 35
2.11 Adding Up ... 38
General Notes ... 39
2.2 Computational Cost ... 39
2.4 Highest R2 ... 39
2.3 Least Squares ... 39
2.5 Unbiasedness ... 41
3 The Classical Liner Regression Model ... 53
3.1 Textbooks as Catalogs ... 53
3.2 The Five Assumptions ... 54
3.3 The OLS Estimator in the CLR Model ... 56
General Notes ... 57
3.1 Textbooks as Catalogs ... 57
3.3 The OLS Estimator in the CLR Model ... 57
3.2 The Five Assumptions ... 60
3.3 The OLS Estimator in the CLR Model ... 61
4 Interval Estimation and Hypothesis Testing ... 64
4.1 Introduction ... 64
4.2 Testing a Single Hypothesis: The t Test ... 64
4.3 Testing a Joint Hypothesis: the F Test ... 65
4.4 Interval Estimation for a Parameter Vector ... 67
4.5 LR,W, and LM Statistics ... 69
4.6 Bootstrapping ... 71
General Notes ... 72
4.1 Introduction ... 72
4.2 Testing a Single Hypothesis: The t Test ... 75
4.3 Testing a Joint Hypothesis: The F Test ... 75
4.4 Interval Estimation fo r a Parameter Vector ... 77
4.5 LR,W, and LM Statistics ... 77
4.6 Bootstrapping ... 78
Technical Notes ... 79
4.1 Introduction ... 80
4.3 Testing a Joint Hypothesis: The F Test ... 81
4.5 LR, W, and LM Statistics ... 81
4.6 Bootstrapping ... 82
5 Specification ... 84
5.1 Introduction ... 84
5.2 Three Methodologies ... 85
5.2.1 Average Economic Regression (AER) ... 85
5.2.2 Test,Test,Test (TTT) ... 86
5.2.3 Fragility Analysis ... 86
5.3 General Principles for Specification ... 88
5.4 Misspecification Tests/D iagnostics ... 89
5.5 R^2 Again ... 92
General Notes ... 94
5.1 Introduction ... 94
5.2 Three Methodologies ... 94
5.3 General Principles for Specification ... 98
5.4 Misspecifica tion Tests/Diagnostics ... 100
5.5 R^2 Again ... 102
Technical Notes ... 102
5.1 Introduction ... 102
5.2 Three Methodologies ... 102
5.4 Misspecification Tests/D iagnostics ... 103
6 Violating Assumption 1: Wrong Regressors, Nonliearities, Parameter Inconsistency ... 106
6.1 Introduction ... 106
6.2 Incorrect Set of Independent Variables ... 106
6.3 Nonlinearity ... 108
6.3.1 Transformations ... 108
6.3.2 Computer-Assisted Numerical Techniques ... 109
6.4 Changing Parameter Values ... 110
6.4.1 Switching Regimes ... 111
6.4.2 Parameters Determined by Other Variables ... 111
6.4.3 Random Coefficients ... 112
General Notes ... 113
6.1 Introduction ... 113
6.2 Incorrect Set of Independent Variables ... 113
6.3 Nonlinearity ... 115
6.4 Changing Parameter Values ... 118
Technical Notes ... 119
6.3 Nonlinearity ... 119
6.4 Changing Parameter Values ... 121
7 Violating Assumption Two: Nonzero Expected Disturbance ... 122
8 Violating Assumption Three: Nonspherical Disturbances ... 125
8.1 Introduction ... 125
8.2 Consequences of Violation ... 126
8.3 Heteroskedasticity ... 128
8.3.1 The Eyeball Test ... 129
8.3.2 The Goldfeld-Quandt Test ... 129
8.3.3 The Breusch-Pagan Test ... 129
8.3.4 The White Test ... 130
8.4 Autocorrelated Disturbances ... 131
8.4.1 Cochrane-Orcutt Iterative Least Squares ... 134
8.4.2 Durbin's Two-Stage Method ... 134
8.4.3 Hildreth-Lu Search Procedure ... 134
8.4.4 Maximum Likelihood ... 134
8.5 Generalized Method of Moments ... 135
General Notes ... 136
8.1 Introduction ... 136
8.2 Consequences of Violation ... 136
8.3 Heteroskedasticity ... 137
8.4 Autocorrelated Disturbances ... 139
Technical Notes ... 142
8.1 Introduction ... 142
8.2 Consequences of Violation ... 142
8.3 Heteroskedasticity ... 144
8.4 Autocorrelated Disturbances ... 145
8.5 Generalized Method of Moments ... 147
9 Violating Assumption Four: Instrumental Variable Estimation ... 150
9.1 Introduction ... 150
9.2 The IV Estimator ... 154
9.3 IV Issues ... 157
9.3.1 How can we test if errors are correlated with regressors? ... 157
9.3.2 How can we test if an instrument is uncorrelated with the error? ... 157
9.3.3 How can we test if an instrument's correlation with the troublesome variable is strong enough? ... 158
9.3.4 How should we interpret IV estimates? ... 158
General Notes ... 159
9.1 Introduction ... 159
9.2 The IV Estimator ... 160
9.3 IV Issues ... 162
Technical Notes ... 164
9.1 Introduction ... 164
9.2 IV Estimation ... 164
9.3 IV Issues ... 166
10 Violating Assumpton Four: Measurement Errors and Autoregression ... 170
10.1 Errors in Variables ... 170
10.1.1 Weighted Regression ... 171
10.1.2 Instrumental Variables ... 172
10.1.3 Linear Structural Relations ... 173
10.2 Autoregression ... 173
General Notes ... 176
10.1 Errors in Variables ... 176
10.2 Autoregression ... 179
Technical Notes ... 180
10.1 Errors in Variables ... 180
10.2 Autoregression ... 181
11 Violating Assumption Four: Simultaneous Equations ... 184
11.1 Introduction ... 184
11.2 Identification ... 186
11.3 Single-Equation Methods ... 189
11.3.1 Ordinary Least Squares ... 190
11.3.2 Indirect Least Squares ... 190
11.3.3 The Instrumental Variable (IV) Technique ... 191
11.3.4 Two-Stage Least Squares (2SLS) ... 191
11.3.5 Limited Info rmation, Maximum Likelihood (LI/ML) ... 192
11.4 Systems Methods ... 192
11.4.1Three-Stage Least Squares (3SLS) ... 193
11.4.2 Full Information,Maximum Likelihood (FUML) ... 194
General Notes ... 194
11.l Introduction ... 194
11.2 Identification ... 196
11.3 Single-Equation Methods ... 197
11.4 Systems Methods ... 198
Technical Notes ... 199
11.1 Introduction ... 199
11.2 Identification ... 200
11.3 Single-Equation Methods ... 201
11.4 Systems Methods ... 203
12 Violating Assumtion Five: Multicollinearity ... 205
12.1 Introduction ... 205
12.2 Consequences ... 206
12.3 Detecting Multicollinearity ... 207
12.4 What To Do ... 209
12.4.1 Do Nothing ... 209
12.4.2 Incorporate Additional Information ... 209
General Notes ... 211
12.2 Consequences ... 211
12.3 Detecting Multicollinearity ... 212
12.4 What to Do ... 212
Technical Notes ... 215
13 Incorporating Extraneous Information ... 216
13.1 Introduction ... 216
13.2 Exact Restrictions ... 216
13.3 Stochastic Restrictions ... 217
13.4 Pre-Test Estimators ... 217
13.5 Extraneous Information and MSE ... 219
General Notes ... 220
13.1 Introduction ... 220
13.2 Exact Restrictions ... 221
13.3 Stochastic Restrictions ... 222
13.4 Pre-test Estimators ... 223
13.5 Extraneous Information and MSE ... 223
Technical Notes ... 224
13.3 Stochastic Restrictions ... 224
13.5 Extraneous Information and MSE ... 225
14 The Bayesian Approach ... 226
14.1 Introduction ... 226
14.2 What is a Bayesian Analysis? ... 226
14.3 Advantages of the Bayesian Approach ... 229
14.4 Overcoming Practitioners' Complaints ... 230
14.4.1 Choosing a Prior ... 230
14.4.2 Finding and Using the Posterior ... 232
14.4.3 Convincing Others ... 232
General Notes ... 233
14.1 Introduction ... 233
14.2 What is a Bayesian Analysis? ... 233
14.3 Advantages of the Bayesian Approach ... 236
14.4 Overcoming Practitioners' Complaints ... 237
Technical Notes ... 239
14.1 Introduction ... 239
14.2 What is a Bayesian Analysis? ... 239
14.3 Advantages of the Bayesian Approach ... 241
14.4 Overcoming Practitioners' Complaints ... 243
15 Dummy Variables ... 245
15.1 Introduction ... 245
15.2 Interpretation ... 246
15.3 Adding Another Qualitative Variable ... 247
15.4 Interacting with Quantitative Variables ... 248
15.5 Observation-Specific Dummies ... 249
General Notes ... 250
15.1 Introduction ... 250
1 5.4 Interacting with Quantitative Variables ... 251
15.5 Observation-Specific Dummies ... 252
Technical Notes ... 253
16 Qualitative Dependent Variables ... 254
16.1 Dichotomous Dependent Variables ... 254
16.2 Polychotomous Dependent Variables ... 257
16.3 Ordered Logit/Probit ... 258
16.4 Count Data ... 259
General Notes ... 259
16.1 Dichotomous Dependent Variables ... 259
16.3 Ordered Logit/Probit ... 266
16.4 Count Data ... 266
Technical Notes ... 267
16.1 Dichotomous Dependent Variables ... 267
16.2 Polychotomous Dependent Variables ... 269
1 6.3 Ordered Logit/Probit ... 271
16.4 Count Data ... 272
17 Limited Dependent Variables ... 275
17.1 Introduction ... 275
17.2 The Tobit Model ... 276
17.3 Sample Selection ... 278
17.4 Duration Models ... 280
General Notes ... 282
17.1 Introduction ... 282
17.2 The Tobit Model ... 282
17.3 Sample Selection ... 283
17.4 Duration Models ... 286
Technical Notes ... 286
17.1 Introduction ... 286
17.2 The Tobit Model ... 287
17.3 Sample Selection ... 288
17.4 Duration Models ... 289
18 Panel Data ... 294
18.1 Introduction ... 294
18.2 Allowing for Different Intercepts ... 295
18.3 Fixed Versus Random Effects ... 297
18.4 Short Run Versus Long Run ... 299
18.5 Long, Narrow Panels ... 300
General Notes ... 301
18.1 Introduction ... 301
18.2 Allowing for Different Intercepts ... 302
18.3 Fixed Versus Random Effects ... 303
18.4 Short Run Versus Long Run ... 304
18.5 Long,Narrow Panels ... 305
Technical Notes ... 305
18.2 Allowing for Different Intercepts ... 305
18.3 Fixed versus Random Effects ... 305
18.5 Long, Narrow Panels ... 308
19 Time Series Econometrics ... 309
19.1 Introduction ... 309
19.2 ARIMA Models ... 310
19.3 VARs ... 311
19.4 Error Correction Models ... 312
19.5 Testing for Unit Roots ... 314
19.6 Cointegration ... 315
General Notes ... 317
19.1 Introduction ... 317
19.2 ARIMA Models ... 317
19.3 VARs ... 318
19.5 Testing fo r Unit Roots ... 320
19.6 Cointegration ... 322
Technical Notes ... 327
19.1 Introduction ... 327
19.2 ARIMA Models ... 327
19.3 VARs ... 333
19.4 Error Correction Models ... 335
19.5 Testing for Unit Roots ... 336
19.6 Cointegration ... 340
20 Forecasting ... 344
20.1 Introduction ... 344
20.2 Causal Forecasting/Econometric Models ... 345
20.3 Time Series Analysis ... 346
20.4 Forecasting Accuracy ... 347
General Notes ... 348
20.1 Introduction ... 348
20.2 Causal Forecasting/Econometric Models ... 350
20.3 Time Series Analysis ... 352
20.4 Forecasting Accuracy ... 353
Technical Notes ... 355
20.l Introduction ... 355
20.2 Causal Forecasting/E conometric Models ... 356
20.4 Forecasting Accuracy ... 356
21 Robust Estimation ... 358
21.1 Introduction ... 358
21.2 Outliers and Influential Observations ... 359
21.3 Guarding Against Influential Observations ... 360
21.4 Artificial Neural Networks ... 362
21.5 Nonparametric Estimation ... 363
General Notes ... 365
21.1 Introduction ... 365
21.2 Outliers and Influential Observations ... 365
21.3 Guarding against Influential Observations ... 366
21.4 Artificial Neural Networks ... 367
21.5 Nonparametric Estimation ... 368
Technical Notes ... 369
21.3 Guarding against Influential Observation ... 369
21.4 Artificial Neural Networks ... 370
21.5 Nonparametric Estimation ... 370
22 Applied Econometrics ... 374
22.1 Introduction ... 374
22.2 The Ten Commandments of Applied Econometrics ... 375
22.3 Getting the Wrong Sign ... 381
22.4 Common Mistakes ... 384
22.5 What do Practitioners Need to Know? ... 386
General Notes ... 387
22.1 Introduction ... 387
22.2 The Ten Commandments of Applied Econometrics ... 388
22.3 Getting the Wrong Sign ... 391
22.4 Common Mistakes ... 392
22.5 What do Practitioners Need to Know? ... 392
Technical Notes ... 396
22.2 The Ten Commandments of Applied Econometrics ... 396
22.5 What do Practitioners Need to Know? ... 396
23 Computational Considerations ... 398
23.1 Introduction ... 398
23.2 Optimizing via a Computer Search ... 399
23.3 Estimating Integrals via Simulation ... 401
23.4 Drawing Observations from Awkward Distributions ... 403
General Notes ... 405
23.1 Introduction ... 405
23.2 Optimizing via a Computer Search ... 405
23.3 Estimating Integrals via Simulation ... 408
23.4 Drawing Observations from Awkward Distributions ... 409
Technical Notes ... 410
23.2 Optimizing via a Computer Search ... 410
23.3 Estimating Integrals via Simulation ... 413
23.4 Drawing Observations from Awkward Distributions ... 414
Appendix A Sampling Distributions ... 416
I An Example ... 416
2 Implications for Studying Econometrics ... 417
3 Calculating Sampling Distributions ... 418
Appendix B All About Variance ... 420
1 Definition ... 420
2 Estimation ... 421
3 Well-Known Formulas ... 421
4 More-General Formulas ... 421
5 Examples of the More-General Formulas ... 421
6 Cramer-Rao Lower Bound ... 423
Appendix C A Primer on Asymptotics ... 425
1 Convergence in Probability ... 425
2 Convergence in Distribution ... 427
3 Asymptotic Distributions ... 427
Notes ... 428
Appendix D Exercises ... 430
Appendix E Answers to Even-Numbered Questions ... 492
Glossary ... 516
Bibliography ... 524
Name Index ... 576
Subject Index ... 586
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