Econometric Modeling
A Likelihood Approach
1st Edition
Published on 16. November 2022
384 pages
978-1-4008-4565-1 (ISBN)
Description
Econometric Modeling provides a new and stimulating introduction to econometrics, focusing on modeling. The key issue confronting empirical economics is to establish sustainable relationships that are both supported by data and interpretable from economic theory. The unified likelihood-based approach of this book gives students the required statistical foundations of estimation and inference, and leads to a thorough understanding of econometric techniques.
David Hendry and Bent Nielsen introduce modeling for a range of situations, including binary data sets, multiple regression, and cointegrated systems. In each setting, a statistical model is constructed to explain the observed variation in the data, with estimation and inference based on the likelihood function. Substantive issues are always addressed, showing how both statistical and economic assumptions can be tested and empirical results interpreted. Important empirical problems such as structural breaks, forecasting, and model selection are covered, and Monte Carlo simulation is explained and applied.
Econometric Modeling is a self-contained introduction for advanced undergraduate or graduate students. Throughout, data illustrate and motivate the approach, and are available for computer-based teaching. Technical issues from probability theory and statistical theory are introduced only as needed. Nevertheless, the approach is rigorous, emphasizing the coherent formulation, estimation, and evaluation of econometric models relevant for empirical research.
David Hendry and Bent Nielsen introduce modeling for a range of situations, including binary data sets, multiple regression, and cointegrated systems. In each setting, a statistical model is constructed to explain the observed variation in the data, with estimation and inference based on the likelihood function. Substantive issues are always addressed, showing how both statistical and economic assumptions can be tested and empirical results interpreted. Important empirical problems such as structural breaks, forecasting, and model selection are covered, and Monte Carlo simulation is explained and applied.
Econometric Modeling is a self-contained introduction for advanced undergraduate or graduate students. Throughout, data illustrate and motivate the approach, and are available for computer-based teaching. Technical issues from probability theory and statistical theory are introduced only as needed. Nevertheless, the approach is rigorous, emphasizing the coherent formulation, estimation, and evaluation of econometric models relevant for empirical research.
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Book
04/2007
Princeton University Press
€108.94
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Persons
David F. Hendry is Professor of Economics at the University of Oxford and a Fellow of Nuffield College. Bent Nielsen is Reader in Econometrics at the University of Oxford and a Fellow of Nuffield College
Content
Preface ix
Data and software xi
Chapter 1: The Bernoulli model 1
1.1 Sample and population distributions 1
1.2 Distribution functions and densities 4
1.3 The Bernoulli model 6
1.4 Summary and exercises 12
Chapter 2: Inference in the Bernoulli model 14
2.1 Expectation and variance 14
2.2 Asymptotic theory 19
2.3 Inference 23
2.4 Summary and exercises 26
Chapter 3: A first regression model 28
3.1 The US census data 28
3.2 Continuous distributions 29
3.3 Regression model with an intercept 32
3.4 Inference 38
3.5 Summary and exercises 42
Chapter 4: The logit model 47
4.1 Conditional distributions 47
4.2 The logit model 52
4.3 Inference 58
4.4 Mis-specification analysis 61
4.5 Summary and exercises 63
Chapter 5: The two-variable regression model 66
5.1 Econometric model 66
5.2 Estimation 69
5.3 Structural interpretation 76
5.4 Correlations 78
5.5 Inference 81
5.6 Summary and exercises 85
Chapter 6: The matrix algebra of two-variable regression 88
6.1 Introductory example 88
6.2 Matrix algebra 90
6.3 Matrix algebra in regression analysis 94
6.4 Summary and exercises 96
Chapter 7: The multiple regression model 98
7.1 The three-variable regression model 98
7.2 Estimation 99
7.3 Partial correlations 104
7.4 Multiple correlations 107
7.5 Properties of estimators 109
7.6 Inference 110
7.7 Summary and exercises 118
Chapter 8: The matrix algebra of multiple regression 121
8.1 More on inversion of matrices 121
8.2 Matrix algebra of multiple regression analysis 122
8.3 Numerical computation of regression estimators 124
8.4 Summary and exercises 126
Chapter 9: Mis-specification analysis in cross sections 127
9.1 The cross-sectional regression model 127
9.2 Test for normality 128
9.3 Test for identical distribution 131
9.4 Test for functional form 134
9.5 Simultaneous application of mis-specification tests 135
9.6 Techniques for improving regression models 136
9.7 Summary and exercises 138
Chapter 10: Strong exogeneity 140
10.1 Strong exogeneity 140
10.2 The bivariate normal distribution 142
10.3 The bivariate normal model 145
10.4 Inference with exogenous variables 150
10.5 Summary and exercises 151
Chapter 11: Empirical models and modeling 154
11.1 Aspects of econometric modeling 154
11.2 Empirical models 157
11.3 Interpreting regression models 161
11.4 Congruence 166
11.5 Encompassing 169
11.6 Summary and exercises 173
Chapter 12: Autoregressions and stationarity 175
12.1 Time-series data 175
12.2 Describing temporal dependence 176
12.3 The first-order autoregressive model 178
12.4 The autoregressive likelihood 179
12.5 Estimation 180
12.6 Interpretation of stationary autoregressions 181
12.7 Inference for stationary autoregressions 187
12.8 Summary and exercises 188
Chapter 13: Mis-specification analysis in time series 190
13.1 The first-order autoregressive model 190
13.2 Tests for both cross sections and time series 190
13.3 Test for independence 192
13.4 Recursive graphics 195
13.5 Example: finding a model for quantities of fish 197
13.6 Mis-specification encompassing 200
13.7 Summary and exercises 201
Chapter 14: The vector autoregressive model 203
14.1 The vector autoregressive model 203
14.2 A vector autoregressive model for the fish market 205
14.3 Autoregressive distributed-lag models 213
14.4 Static solutions and equilibrium-correction forms 214
14.5 Summary and exercises 215
Chapter 15: Identification of structural models 217
15.1 Under-identified structural equations 217
15.2 Exactly-identified structural equations 222
15.3 Over-identified structural equations 227
15.4 Identification from a conditional model 231
15.5 Instrumental variables estimation 234
15.6 Summary and exercises 237
Chapter 16: Non-stationary time series 240
16.1 Macroeconomic time-series data 240
16.2 First-order autoregressive model and its analysis 242
16.3 Empirical modeling of UK expenditure 243
16.4 Properties of unit-root processes 245
16.5 Inference about unit roots 248
16.6 Summary and exercises 252
Chapter 17: Cointegration 254
17.1 Stylized example of cointegration 254
17.2 Cointegration analysis of vector autoregressions 255
17.3 A bivariate model for money demand 258
17.4 Single-equation analysis of cointegration 267
17.5 Summary and exercises 268
Chapter 18: Monte Carlo simulation experiments 270
18.1 Monte Carlo simulation 270
18.2 Testing in cross-sectional regressions 273
18.3 Autoregressions 277
18.4 Testing for cointegration 281
18.5 Summary and exercises 285
Chapter 19: Automatic model selection 286
19.1 The model 286
19.2 Model formulation and mis-specification testing 287
19.3 Removing irrelevant variables 288
19.4 Keeping variables that matter 290
19.5 A general-to-specific algorithm 292
19.6 Selection bias 293
19.7 Illustration using UK money data 298
19.8 Summary and exercises 300
Chapter 20: Structural breaks 302
20.1 Congruence in time series 302
20.2 Structural breaks and co-breaking 304
20.3 Location shifts revisited 307
20.4 Rational expectations and the Lucas critique 308
20.5 Empirical tests of the Lucas critique 311
20.6 Rational expectations and Euler equations 315
20.7 Summary and exercises 319
Chapter 21: Forecasting 323
21.1 Background 323
21.2 Forecasting in changing environments 326
21.3 Forecasting from an autoregression 327
21.4 A forecast-error taxonomy 332
21.5 Illustration using UK money data 337
21.6 Summary and exercises 340
Chapter 22: The way ahead 342
References 345
Author index 357
Subject index 359
Data and software xi
Chapter 1: The Bernoulli model 1
1.1 Sample and population distributions 1
1.2 Distribution functions and densities 4
1.3 The Bernoulli model 6
1.4 Summary and exercises 12
Chapter 2: Inference in the Bernoulli model 14
2.1 Expectation and variance 14
2.2 Asymptotic theory 19
2.3 Inference 23
2.4 Summary and exercises 26
Chapter 3: A first regression model 28
3.1 The US census data 28
3.2 Continuous distributions 29
3.3 Regression model with an intercept 32
3.4 Inference 38
3.5 Summary and exercises 42
Chapter 4: The logit model 47
4.1 Conditional distributions 47
4.2 The logit model 52
4.3 Inference 58
4.4 Mis-specification analysis 61
4.5 Summary and exercises 63
Chapter 5: The two-variable regression model 66
5.1 Econometric model 66
5.2 Estimation 69
5.3 Structural interpretation 76
5.4 Correlations 78
5.5 Inference 81
5.6 Summary and exercises 85
Chapter 6: The matrix algebra of two-variable regression 88
6.1 Introductory example 88
6.2 Matrix algebra 90
6.3 Matrix algebra in regression analysis 94
6.4 Summary and exercises 96
Chapter 7: The multiple regression model 98
7.1 The three-variable regression model 98
7.2 Estimation 99
7.3 Partial correlations 104
7.4 Multiple correlations 107
7.5 Properties of estimators 109
7.6 Inference 110
7.7 Summary and exercises 118
Chapter 8: The matrix algebra of multiple regression 121
8.1 More on inversion of matrices 121
8.2 Matrix algebra of multiple regression analysis 122
8.3 Numerical computation of regression estimators 124
8.4 Summary and exercises 126
Chapter 9: Mis-specification analysis in cross sections 127
9.1 The cross-sectional regression model 127
9.2 Test for normality 128
9.3 Test for identical distribution 131
9.4 Test for functional form 134
9.5 Simultaneous application of mis-specification tests 135
9.6 Techniques for improving regression models 136
9.7 Summary and exercises 138
Chapter 10: Strong exogeneity 140
10.1 Strong exogeneity 140
10.2 The bivariate normal distribution 142
10.3 The bivariate normal model 145
10.4 Inference with exogenous variables 150
10.5 Summary and exercises 151
Chapter 11: Empirical models and modeling 154
11.1 Aspects of econometric modeling 154
11.2 Empirical models 157
11.3 Interpreting regression models 161
11.4 Congruence 166
11.5 Encompassing 169
11.6 Summary and exercises 173
Chapter 12: Autoregressions and stationarity 175
12.1 Time-series data 175
12.2 Describing temporal dependence 176
12.3 The first-order autoregressive model 178
12.4 The autoregressive likelihood 179
12.5 Estimation 180
12.6 Interpretation of stationary autoregressions 181
12.7 Inference for stationary autoregressions 187
12.8 Summary and exercises 188
Chapter 13: Mis-specification analysis in time series 190
13.1 The first-order autoregressive model 190
13.2 Tests for both cross sections and time series 190
13.3 Test for independence 192
13.4 Recursive graphics 195
13.5 Example: finding a model for quantities of fish 197
13.6 Mis-specification encompassing 200
13.7 Summary and exercises 201
Chapter 14: The vector autoregressive model 203
14.1 The vector autoregressive model 203
14.2 A vector autoregressive model for the fish market 205
14.3 Autoregressive distributed-lag models 213
14.4 Static solutions and equilibrium-correction forms 214
14.5 Summary and exercises 215
Chapter 15: Identification of structural models 217
15.1 Under-identified structural equations 217
15.2 Exactly-identified structural equations 222
15.3 Over-identified structural equations 227
15.4 Identification from a conditional model 231
15.5 Instrumental variables estimation 234
15.6 Summary and exercises 237
Chapter 16: Non-stationary time series 240
16.1 Macroeconomic time-series data 240
16.2 First-order autoregressive model and its analysis 242
16.3 Empirical modeling of UK expenditure 243
16.4 Properties of unit-root processes 245
16.5 Inference about unit roots 248
16.6 Summary and exercises 252
Chapter 17: Cointegration 254
17.1 Stylized example of cointegration 254
17.2 Cointegration analysis of vector autoregressions 255
17.3 A bivariate model for money demand 258
17.4 Single-equation analysis of cointegration 267
17.5 Summary and exercises 268
Chapter 18: Monte Carlo simulation experiments 270
18.1 Monte Carlo simulation 270
18.2 Testing in cross-sectional regressions 273
18.3 Autoregressions 277
18.4 Testing for cointegration 281
18.5 Summary and exercises 285
Chapter 19: Automatic model selection 286
19.1 The model 286
19.2 Model formulation and mis-specification testing 287
19.3 Removing irrelevant variables 288
19.4 Keeping variables that matter 290
19.5 A general-to-specific algorithm 292
19.6 Selection bias 293
19.7 Illustration using UK money data 298
19.8 Summary and exercises 300
Chapter 20: Structural breaks 302
20.1 Congruence in time series 302
20.2 Structural breaks and co-breaking 304
20.3 Location shifts revisited 307
20.4 Rational expectations and the Lucas critique 308
20.5 Empirical tests of the Lucas critique 311
20.6 Rational expectations and Euler equations 315
20.7 Summary and exercises 319
Chapter 21: Forecasting 323
21.1 Background 323
21.2 Forecasting in changing environments 326
21.3 Forecasting from an autoregression 327
21.4 A forecast-error taxonomy 332
21.5 Illustration using UK money data 337
21.6 Summary and exercises 340
Chapter 22: The way ahead 342
References 345
Author index 357
Subject index 359
