Econometric Modeling

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