The aim of this book is to present the main statistical tools of econometrics. It covers almost all modern econometric methodology and unifies the approach by using a small number of estimation techniques, many from generalized method of moments (GMM) estimation. The work is in four parts: Part I sets forth statistical methods, Part II covers regression models, Part III investigates dynamic models, and Part IV synthesizes a set of problems that are specific models in structural econometrics, namely identification and overidentification, simultaneity, and unobservability. Many theoretical examples illustrate the discussion and can be treated as application exercises.
Author(s): Jean-Pierre Florens, Velayoudom Marimoutou, Anne Peguin-Feissolle
Publisher: Cambridge University Press
Year: 2007
Language: English
Pages: 520
Cover......Page 1
Half-title......Page 3
Series-title......Page 5
Title......Page 7
Copyright......Page 8
Dedication......Page 9
Contents......Page 11
Foreword......Page 19
Preface......Page 21
Part I: Statistical Methods......Page 25
1.2 Sample, Parameters, and Sampling Probability Distributions......Page 27
1.3 Independent and Identically Distributed Models......Page 30
1.4 Dominated Models, Likelihood Function......Page 32
1.5 Marginal and Conditional Models......Page 34
Notes......Page 40
2.2 Sequential Stochastic Models and Asymptotics......Page 41
2.3 Convergence in Probability and Almost Sure Convergence – Law of Large Numbers......Page 45
2.4 Convergence in Distribution and Central Limit Theorem......Page 49
2.5 Noncausality and Exogeneity in Dynamic Models......Page 51
2.5.1 Wiener-Granger Causality......Page 52
2.5.2 Exogeneity......Page 54
Notes......Page 56
3.2 Estimation......Page 57
3.3 Moment Conditions and Maximization......Page 63
3.4 Estimation by the Method of Moments and Generalized Moments......Page 68
3.5 Asymptotic Properties of Estimators......Page 72
4.1 Introduction......Page 85
4.2 Tests and Asymptotic Tests......Page 86
4.3 Wald Tests......Page 89
4.4 Rao Test......Page 93
4.5 Tests Based on the Comparison of Minima......Page 97
4.6 Test Based on Maximum Likelihood Estimation......Page 100
4.7 Hausman Tests......Page 102
4.8 Encompassing Test......Page 106
Notes......Page 110
5.2 Empirical Distribution and Empirical Distribution Function......Page 111
5.3.1 Construction of the Kernel Estimator of the Density......Page 115
5.3.2 Small Sample Properties of the Kernel Estimator and Choices of Window and Kernel......Page 117
5.3.3 Asymptotic Properties......Page 120
5.4 Semiparametric Methods......Page 122
Notes......Page 126
6.2 Random Number Generators......Page 127
6.2.1 Inversion of the Distribution Function......Page 128
6.2.2 Rejection Method......Page 129
6.2.3 Random Vector Generators......Page 130
6.3.1 Monte Carlo Integration......Page 131
6.3.2 Simulation-Based Method of Moments......Page 133
6.4 Simulations and Small Sample Properties of Estimators and Tests......Page 140
6.5 Bootstrap and Distribution of the Moment Estimators and of the Density......Page 144
Part II: Regression Models......Page 151
7.2 Conditional Expectation......Page 153
7.3 Linear Conditional Expectation......Page 158
Notes......Page 164
8.1 Introduction......Page 165
8.2.1 The Assumptions of the Linear Regression Model......Page 166
8.2.2 Estimation by Ordinary Least Squares......Page 168
8.2.3 Small Sample Properties......Page 172
8.2.4 Finite Sample Distribution Under the Normality Assumption......Page 175
8.2.5 Analysis of Variance......Page 180
8.2.6 Prediction......Page 183
8.2.7 Asymptotic Properties......Page 184
8.3 Nonlinear Parametric Regression......Page 189
8.4 Misspecified Regression......Page 193
8.4.1 Properties of the Least Squares Estimators......Page 194
8.4.2 Comparing the True Regression with Its Approximation......Page 196
8.4.3 Specification Tests......Page 198
Notes......Page 201
9.1 Introduction......Page 203
9.2 Allowing for Nuisance Parameters in Moment Estimation......Page 205
9.3 Heteroskedasticity......Page 208
9.3.1 Estimation......Page 209
9.3.2 Tests for Homoskedasticity......Page 220
9.4 Multivariate Regression......Page 223
Notes......Page 236
10.1 Introduction......Page 237
10.2 Estimation of the Regression Function by Kernel......Page 238
10.2.1 Calculation of the Asymptotic Mean Integrated Squared Error......Page 240
10.2.2 Convergence of AMISE and Asymptotic Normality......Page 245
10.3 Estimating a Transformation of the Regression Function......Page 247
10.4.1 Index Models......Page 252
10.4.2 Additive Models......Page 255
Notes......Page 257
11.1 Introduction......Page 258
11.2.1 Dichotomous Models......Page 259
11.2.2 Multiple Choice Models......Page 261
11.2.3 Censored Models......Page 263
11.2.4 Disequilibrium Models......Page 267
11.2.5 Sample Selection Models......Page 268
11.3.1 Nonparametric Estimation......Page 272
11.3.2 Semiparametric Estimation by Maximum Likelihood......Page 274
11.3.3 Maximum Likelihood Estimation......Page 275
Notes......Page 281
Part III: Dynamic Models......Page 283
12.1 Introduction......Page 285
12.2 Second Order Processes......Page 286
12.3 Gaussian Processes......Page 288
12.4 Spectral Representation and Autocovariance Generating Function......Page 289
12.5.1 Filters......Page 291
12.5.2 Linear Forecasting – General Remarks......Page 294
12.5.3 Wold Decomposition......Page 296
12.6.1 Introduction......Page 297
12.6.2 Invertible ARMA Processes......Page 298
12.6.3 Computing the Covariance Function of an ARMA(p, q) Process......Page 301
12.6.4 The Autocovariance Generating Function......Page 302
12.6.5 The Partial Autocorrelation Function......Page 304
12.7 Spectral Representation of an ARMA (p,q) Process......Page 306
12.8.1 Estimation by the Yule-Walker Method......Page 307
12.8.2 Box-Jenkins Method......Page 310
12.9.1 Some Definitions and General Observations......Page 313
12.9.2 Underlying Univariate Representation of a Multivariate Process......Page 316
12.10.1 Propagation of a Shock on a Component......Page 318
12.10.2 Variance Decomposition of the Forecast Error......Page 319
12.11 Estimation of VAR(p) Models......Page 320
12.11.1 Maximum Likelihood Estimation of…......Page 322
12.11.2 Maximum Likelihood Estimation of Tones......Page 324
12.11.3 Asymptotic Distribution of…......Page 325
Notes......Page 327
13.1 Introduction......Page 328
13.2 Asymptotic Properties of Least Squares Estimators of I(1) Processes......Page 330
13.3 Analysis of Cointegration and Error Correction Mechanism......Page 349
13.3.1 Cointegration and MA Representation......Page 350
13.3.2 Cointegration in a VAR Model in Levels......Page 351
13.3.3 Triangular Representation......Page 353
13.3.4 Estimation of a Cointegrating Vector......Page 354
13.3.5 Maximum Likelihood Estimation of an Error Correction Model Admitting a Cointegrating Relation......Page 359
13.3.6 Cointegration Test Based on the Canonical Correlations: Johansen’s Test......Page 362
Notes......Page 364
14.2 Various Types of ARCH Models......Page 365
14.3 Estimation Method......Page 370
14.4 Tests for Conditional Homoskedasticity......Page 381
14.5.1 Stationarity......Page 385
14.5.2 Leptokurticity......Page 386
14.5.3 Various Conditional Distributions......Page 387
Notes......Page 389
15.1 Introduction......Page 390
15.2.1 Definitions......Page 391
15.2.2 Conditional Moments and Marginal Moments in the Homoskedastic Case: Optimal Instruments......Page 392
15.2.3 Heteroskedasticity......Page 396
15.2.4 Modifying of the Set of Conditioning Variables: Kernel Estimation of the Asymptotic Variance......Page 397
15.3 Case Where the Conditional Expectation Is Not Continuously Differentiable: Regime-Switching Models......Page 400
15.3.1 Presentation of a Few Examples......Page 401
15.3.2 Problem of Estimation......Page 403
15.4.1 All Parameters Are Identified Under H0......Page 407
15.4.2 The Problem of the Nonidentification of Some Parameters Under H0......Page 411
Notes......Page 415
Part IV: Structural Modeling......Page 417
16.1 Introduction......Page 419
16.2 Structural Model and Reduced Form......Page 420
16.3.1 General Definitions......Page 422
16.3.2 Linear i.i.d. Simultaneous Equations Models......Page 425
16.3.3 Linear Dynamic Simultaneous Equations Models......Page 431
16.4 Models from Game Theory......Page 434
16.5 Overidentification......Page 438
16.5.1 Overidentification in Simultaneous Equations Models......Page 441
16.5.2 Overidentification and Moment Conditions......Page 442
Notes......Page 443
17.1 Introduction......Page 445
17.2 Simultaneity and Simultaneous Equations......Page 446
17.3 Endogeneity, Exogeneity, and Dynamic Models......Page 449
17.4 Simultaneity and Selection Bias......Page 452
17.5.1 Introduction......Page 455
17.5.2 Estimation......Page 457
17.5.3 Optimal Instruments......Page 461
17.5.4 Nonparametric Approach and Endogenous Variables......Page 463
17.5.5 Test of Exogeneity......Page 466
Notes......Page 468
18.1 Introduction......Page 470
18.2.1 Random-Effects Models and Random-Coefficient Models......Page 472
18.2.2 Duration Models with Unobserved Heterogeneity......Page 474
18.2.3 Errors-in-Variables Models......Page 477
18.2.4 Partially Observed Markov Models and State Space Models......Page 478
18.3 Comparison Between Structural Model and Reduced Form......Page 480
18.3.1 Duration Models with Heterogeneity and Spurious Dependence on the Duration......Page 481
18.3.2 Errors-in-Variables Model and Transformation of the Coefficients of the Linear Regression......Page 483
18.3.3 Markov Models with Unobservable Variables and Spurious Dynamics of the Model......Page 484
18.4 Identification Problems......Page 485
18.5.1 Estimation Using a Statistic Independent of the Unobservables......Page 486
18.5.2 Maximum Likelihood Estimation: EM Algorithm and Kalman......Page 488
18.5.3 Estimation by Integrated Moments......Page 493
18.6 Counterfactuals and Treatment Effects......Page 494
Notes......Page 499
Bibliography......Page 501
Index......Page 517
