Econometric theory

목차 (Table of Contents)

• CONTENTS
• Figures = xv
• Symbols and Abbreviations = xvi
• Preface = xx
• Ⅰ Basic Regression Theory = 1
• 1 The Linear Regression Model = 3
• 1.1 The Model = 3
• 1.2 The Least Squares Estimator = 4
• 1.2.1 Derivation of the Estimator = 4
• 1.2.2 Goodness of Fit = 6
• 1.2.3 The Projection Matrices = 6
• 1.2.4 Linear Transformations = 7
• 1.2.5 The Partitioned Linear Model = 8
• 1.3 The Statistical Model = 9
• 1.4 Model Specification = 12
• 1.4.1 Linearity = 12
• 1.4.2 Included Variables = 13
• 1.4.3 Relevant Variables = 15
• 2 Statistical Analysis of the Regression Model = 17
• 2.1 Statistical Assumptions = 17
• 2.2 The Properties of OLS = 18
• 2.2.1 Mean and Variance = 18
• 2.2.2 The Residuals = 20
• 2.2.3 The Gauss-Markov Theorem = 20
• 2.3 Generalized Least Squares = 23
• 2.3.1 Failure of the Assumptions = 23
• 2.3.2 Aitken's Theorem = 24
• 2.3.3 Interpreting Residual Autocorrelation = 25
• 2.4 The Gaussian Linear Model = 26
• 2.4.1 Interval Estimation = 26
• 2.4.2 Testing Hypotheses = 28
• 2.4.3 The F Test of Linear Restrictions = 28
• 2.4.4 The Constrained Estimation Approach = 29
• 2.4.5 Significance Tests = 30
• 2.5 Stability Analysis = 32
• 2.5.1 Structural Breaks = 32
• 2.5.2 Prediction = 33
• 3 Asymptotic Analysis of the Regression Model = 37
• 3.1 Stochastic Convergence = 37
• 3.1.1 Modes of Convergence = 37
• 3.1.2 Related Results = 39
• 3.2 The Law of Large Numbers = 40
• 3.2.1 Independent Sequences = 40
• 3.2.2 Chebyshev's Theorem = 42
• 3.3 The Central Limit Theorem = 43
• 3.3.1 The i.i.d. Case = 43
• 3.3.2 Heterogeneous Data = 43
• 3.3.3 Vector Sequences = 44
• 3.4 Asymptotic Estimation Theory = 46
• 3.5 Asymptotics of the Stochastic Regressor Model = 48
• 3.5.1 Assumptions = 48
• 3.5.2 Consistency = 49
• 3.5.3 Asymptotic Normality = 49
• 3.5.4 A Common Pitfall = 50
• 3.5.5 Asymptotic Test Criteria = 51
• 3.6 Linear CAN Estimators and Asymptotic Efficiency = 52
• 3.6.1 The Linear CAN Class = 52
• 3.6.2 The Instrumental Variables Class = 53
• Ⅱ Dynamic Regression Theory = 57
• 4 Modelling Economic Time Series = 59
• 4.1 Data Generation Processes = 59
• 4.1.1 DGPs and Models = 60
• 4.1.2 Nonstochastic Time Variation = 61
• 4.1.3 General Distributions = 61
• 4.2 The VAR(1) Process = 62
• 4.2.1 The Gaussian DGP = 63
• 4.2.2 The Structural Form = 63
• 4.2.3 Example : A Simple Keynesian Model = 64
• 4.3 Distribution of the VAR Process = 65
• 4.3.1 Stability Conditions = 66
• 4.3.2 The Mean and Variance = 66
• 4.3.3 The Sample Density = 67
• 4.3.4 Higher Order Dynamics = 68
• 4.4 Sequence Properties = 69
• 4.4.1 Stationarity = 69
• 4.4.2 Mixing = 70
• 4.4.3 Ergodicity = 71
• 4.5 Marginalizing, Conditioning and Exogeneity = 71
• 4.5.1 conditioning Variables = 71
• 4.5.2 Factorization of the Density = 72
• 4.5.3 Parameters of Interest and Weak Exogeneity = 74
• 4.5.4 Granger Causality and Strong Exogeneity = 75
• 4.5.5 A Bivariate Example = 75
• 4.5.6 Exogeneity and Regression = 77
• 4.5.7 Other Notions of Exogeneity = 78
• 4.6 The General Conditional Model = 79
• 4.7 Structural Change = 80
• 4.7.1 Observational Equivalence = 80
• 4.7.2 Super-exogeneity = 81
• 5 Principles of Dynamic Modelling = 84
• 5.1 The Lag Operator = 84
• 5.1.1 Definition = 84
• 5.1.2 Inverting Lag Polynomials = 85
• 5.1.3 The General Case = 86
• 5.2 Autoregressive and Moving Average Dynamic Structures = 87
• 5.2.1 Innovation Processes = 87
• 5.2.2 Thr ARMA Process = 89
• 5.2.3 The Wold Decomposition = 90
• 5.2.4 Linear Processes = 91
• 5.2.5 Autocovariance Analysis = 92
• 5.2.6 Representing the MA(q) Process = 93
• 5.2.7 Integrated Processes = 94
• 5.2.8 Vector Autoregressions = 96
• 5.2.9 The Simple Keynesian Model Again = 98
• 5.3 Dynamic Regression Models = 99
• 5.3.1 The General ARMADL Model = 99
• 5.3.2 The Autoregressive Distributed Lag Model = 100
• 5.3.3 Common Factors = 100
• 5.3.4 Rational Lags = 101
• 5.3.5 Polynomial Distributed lags = 101
• 5.3.6 The Error Correction Model = 102
• 5.4 Models of Dynamic Behaviour = 103
• 5.4.1 The Partial Adjustment Model = 103
• 5.4.2 Adaptive Expectations = 105
• 5.4.3 Stock Adjustment = 106
• 5.5 Rational Expectations Models = 107
• 5.5.1 The ARMA(1,1) Process = 108
• 5.5.2 A System with Lagged Expectations = 109
• 5.5.3 Systems with Current Expectations = 109
• 5.5.4 Dynamic Optimization = 110
• 5.6 Conditional Heteroscedasticity = 113
• 5.7 Appendix : Proof of Theorem 5.2.1 = 116
• 6 Asymptotics for Dynamic Models = 119
• 6.1 The Simple Autoregressive Model = 119
• 6.2 Martingale Difference Processes = 121
• 6.2.1 Definitions = 121
• 6.2.2 Properties = 122
• 6.2.3 Limit Results = 123
• 6.3 Properties of the Autoregression = 124
• 6.3.1 Consistency = 124
• 6.3.2 Finite Sample Bias = 127
• 6.3.3 Asymptotic Distribution = 128
• 6.4 Mixing and Near-Epoch Dependence = 129
• 6.4.1 Basic Concepts = 129
• 6.4.2 Application to the AR(1) = 131
• 6.4.3 Properties and Limit Results = 132
• 6.5 Application : the Misspecified AR(1) = 134
• 6.5.1 Consistency = 135
• 6.5.2 Asymptotic Normality = 136
• 6.6 Appendix : Additional Proofs = 137
• 7 Estimation and Testing = 140
• 7.1 The Dynamic Regression Model = 140
• 7.1.1 The Setup = 140
• 7.1.2 Consistency = 142
• 7.1.3 Asymptotic Normality = 143
• 7.1.4 A VAR Application = 144
• 7.1.5 Asymptotic Efficiency = 146
• 7.2 Extensions of the Basic Model = 147
• 7.2.1 Dummy Regressors = 147
• 7.2.2 Global Nonstationarity = 148
• 7.3 Consequences of Misspecification = 151
• 7.3.1 Misspecification in Mean = 151
• 7.3.2 Misspecification in Variance = 152
• 7.4 The Model Selection Problem = 153
• 7.4.1 Spurious Regression = 153
• 7.4.2 Data Coherency and Theory Consistency = 154
• 7.5 Model-Building Methodology = 155
• 7.5.1 Variable Addition／Deletion Tests = 156
• 7.5.2 Significance Tests and Diagnostic Tests = 157
• 7.5.3 Encompassing and Non-Nested Testing = 158
• 7.6 Diagnostic Tests = 160
• 7.6.1 Residual Autocorrelation = 160
• 7.6.2 The Durbin-Watson Test = 161
• 7.6.3 The Q Test = 162
• 7.6.4 Unrestricted Dynamics = 162
• 7.6.5 Parameter Stability = 162
• 7.6.6 Nonlinear Functional Form = 163
• 7.6.7 Conditional Heteroscedasticity = 163
• 7.6.8 ARCH Effects = 164
• 7.6.9 Non-normality = 164
• 7.7 Modelling Strategies = 165
• 7.7.1 Testing Up vs Testing Down = 165
• 7.7.2 Significance Levels in Multiple Tests = 166
• 7.7.3 Data Mining = 167
• 7.8 Appendix : Pitfalls With Autocorrelation Testing = 169
• 8 Simultaneous Equations = 172
• 8.1 The Consumption Model Revisited = 172
• 8.1.1 Statistical Assumptions = 172
• 8.1.2 Estimation with Instrumental Variables = 173
• 8.1.3 Testing Exogeneity = 174
• 8.2 Estimating Simultaneous Equations = 176
• 8.2.1 Structural and Reduced Forms = 176
• 8.2.2 Setup and Notation = 177
• 8.2.3 Two-stage Least Squares = 178
• 8.2.4 Asymptotoic Properties of 2SLS = 180
• 8.2.5 Asymptotoic Efficiency of 2SLS = 183
• 8.3 The Rank Condition for Identification = 185
• 8.4 Testing the Ⅳ Specification = 188
• 8.4.1 More on Testing Exogeneity = 188
• 8.4.2 Testing Overidientifying Restrictions = 190
• 8.5 Nonlinear Simultaneous Equations = 191
• 8.5.1 Fisher's Identification Analysis = 191
• 8.5.2 Example = 193
• 8.5.3 Kelejian's Approach = 194
• Ⅲ Advanced Estimation Theory = 197
• 9 Optimization Estimators Ⅰ : Theory = 199
• 9.1 Preliminaries = 199
• 9.2 Numerical Optimization = 202
• 9.2.1 Line Search = 203
• 9.2.2 Gradient Methods for Multivariate Optimization = 205
• 9.2.3 Quasi-Newton Methods = 208
• 9.2.4 Direct Search Methods = 210
• 9.2.5 Practical Implementation = 212
• 9.3 Asymptotic Propertis = 213
• 9.3.1 Existence of OEs = 213
• 9.3.2 Consistency = 215
• 9.3.3 Identification = 217
• 9.3.4 Asymptotic Normality = 219
• 9.4 Other Issues = 221
• 9.4.1 Model Selection = 221
• 9.4.2 Two-step Estimation = 221
• 9.4.3 Estimation of Covariance Matrices = 226
• 9.5 Appedix : Additional Proofs = 229
• 10 Optimization Estimators Ⅱ : Examples = 234
• 10.1 Linear Least Squares = 234
• 10.2 Nonlinear Least Squares = 235
• 10.2.1 Computation = 236
• 10.2.2 Asymptotic Properties = 236
• 10.2.3 The AR(1) Error Model : Computation = 238
• 10.2.4 The AR(1) Error Model : Asymptotics = 240
• 10.2.5 the MA(1) Error Model = 243
• 10.2.6 The Adaptive Expectations／Stock Adjustment Model = 243
• 10.2.7 The Error Correction Model = 244
• 10.3 Generalized Method of Moments = 245
• 10.3.1 Asymptotic Theory = 245
• 10.3.2 A Nonlinear Example = 247
• 10.3.3 Application to Rational Expectations = 247
• 10.3.4 Nonlinear 2SLS = 248
• 10.4 Modelling Second Moments = 249
• 10.4.1 Residual Variance Estimation = 249
• 10.4.2 Conditional Heteroscedasticity and ARCH Models = 252
• 10.5 Misspecified Regression Models = 256
• 10.6 Appendix : Proof of Theorem 10.5.3 = 260
• 11 The Method of Maximum Likelihood = 262
• 11.1 Introduction = 262
• 11.2 Examples = 262
• 11.2.1 The Calassical Gaussian Regression Model = 264
• 11.2.2 The Stationary Gaussian AR Model = 265
• 11.2.3 The Daynamic Regression Model = 267
• 11.2.4 Conditional Heteroscedasticity = 267
• 11.2.5 Discrete and Censored Data Models = 268
• 11.3 Properties of the MLE = 271
• 11.3.1 Preliminaries = 271
• 11.3.2 Consistency and Identification = 272
• 11.3.3 Asymptotic Normality = 274
• 11.3.4 Model Seclection = 276
• 11.3.5 Computational Issues = 277
• 11.3.6 Asymptotic Efficiency = 278
• 11.4 General Distributions = 280
• 12 Testing Hypotheses = 283
• 12.1 Basic Ideas = 283
• 12.1.1 Concepts and Definitions = 283
• 12.1.2 Test Priciples = 285
• 12.2 The Wald Test = 287
• 12.3 Tests Based on Constrained Estimation = 289
• 12.3.1 Distribution of the Constrained OE = 289
• 12.3.2 The Likelihood Ratio Test = 290
• 12.3.3 The Lagrange Multiplier Test = 292
• 12.3.4 Testing for Autocorrelation = 294
• 12.3.5 Testing for Heteroscedasticity = 296
• 12.4 Power Calculations = 297
• 12.4.1 Pitman Drift = 297
• 12.4.2 Asymptotic Distributions under $$H_A$$ = 299
• 12.5 M Tests = 301
• 12.5.1 Theory = 301
• 12.5.2 M Tests for Heteroscedasticity = 304
• 12.5.3 Tests of Functional Form = 304
• 12.5.4 The Information Matrix Test = 306
• 13 System Estimation = 308
• 13.1 Three-stage Least Squares = 308
• 13.1.1 Construction of 3SLS = 308
• 13.1.2 Distribution of 3SLS = 311
• 13.1.3 Special Cases = 312
• 13.2 Full Information Maximum Likelihood = 314
• 13.2.1 Set-up and Computation = 314
• 13.2.2 Properties = 315
• 13.2.3 Least Generalized Variance = 317
• 13.3 Least Generalized Variance Ratio = 317
• 13.3.1 Subsystem Estimation = 317
• 13.3.2 LIML = 318
• 13.3.3 Asymptotic Equivalence of LIML and 2SLS = 319
• 13.4 Nonlinear FIML = 321
• 13.4.1 Preliminaries = 321
• 13.4.2 Computation = 322
• 13.4.3 Consistency of the MLE = 323
• 13.4.4 Quasi-FIML = 325
• 13.5 System GMM = 327
• 13.5.1 The One-stage Estimator = 327
• 13.5.2 The Efficient Case = 328
• 13.5.3 The Two-stage Estimator = 330
• 13.5.4 Nonlinear SUR = 332
• Ⅳ Cointegration Theory = 335
• 14 Unit Roots = 337
• 14.1 The Random Walk Model = 337
• 14.2 The Probability Background = 338
• 14.2.1 Function Spaces = 338
• 14.2.2 Brownian Motion = 340
• 14.2.3 The Functional CLT = 342
• 14.3 The Unit Root Autoregression = 345
• 14.3.1 Basic Convergence Results = 345
• 14.3.2 Tests of the Ⅰ(1) Hypothesis = 346
• 14.3.3 Serial Correlation = 349
• 14.3.4 Including an Intercept = 351
• 14.4 Allowing Deterministic Trends = 352
• 14.4.1 Distribution of the AR Coefficient = 352
• 14.4.2 Test of Ⅰ(1) = 354
• 14.5 Testing the Null of Ⅰ(0) = 355
• 14.6 Appendix : Proof of Theorem 14.3.1 = 358
• 15 Cointegrating Regression = 360
• 15.1 Cointegrated Time Series = 360
• 15.1.1 Basic Concepts = 360
• 15.1.2 Cointegrated Equation Systems = 361
• 15.1.3 The VECM Representation = 362
• 15.2 Limit Theory for Cointegrating Regressions = 364
• 15.2.1 Limit Theory Preliminaries = 364
• 15.2.2 Static Least Squares = 366
• 15.2.3 When Static Least Squares is Optimal = 369
• 15.2.4 Including Ⅰ(0) Regressors = 371
• 15.2.5 The Error Correction Model Approach = 375
• 15.2.6 Fully Modified Least Squares = 376
• 15.3 Testing for Cointegration = 378
• 15.3.1 Regression Without Cointegration = 378
• 15.3.2 Residual-based Tests = 379
• 15.3.3 Correcting for Autocorrelation = 381
• 15.3.4 Drawbacks with Residual-based Tests = 382
• 15.4 Trended Variales = 382
• 15.4.1 Simple Regression = 382
• 15.4.2 Detrending the Data = 384
• 15.4.3 Testing for Cointegration = 385
• 15.5 A Postscript on OE Analysis = 386
• 16 Cointegrated Systems = 388
• 16.1 The VECM Framework = 388
• 16.1.1 Modeling Issues = 388
• 16.1.2 Least Squares Analysis = 390
• 16.2 Johansen's Analysis = 391
• 16.2.1 The General Dynamic Model = 391
• 16.2.2 Reduced Rank Regression = 393
• 16.3 Inference in the Cointegrating VAR = 395
• 16.3.1 Tests for Cointegrating Rank = 395
• 16.3.2 Likelihood Ratio Tests = 398
• 16.3.3 Inference on β = 399
• 16.3.4 The Other Parameters = 402
• 16.4 Allowing Deterministic Trends = 403
• 16.4.1 Modifications to the Analysis = 403
• 16.4.2 The Cointegrating Vectors = 405
• 16.4.3 Restricting and Testing Tends = 407
• 16.4.4 Trends in the Cointegraion Space = 409
• 16.5 Partial Models and Exogeneity = 410
• 16.5.1 The Conditional Model = 410
• 16.5.2 Testing Cointegrating Rank = 412
• 16.5.3 Estimating β = 413
• 16.6 Structural Cointegrating Relations = 415
• 16.6.1 Identification = 415
• 16.6.2 Single Equation Analysis = 419
• 16.6.3 System Analysis = 421
• 16.7 Appendix : Additional Proofs = 424
• Ⅴ Technical Appendices = 427
• A Matrix Algebra Basics = 429
• A.1 Vectors and Matrices = 429
• A.2 Matrix Inversion = 431
• A.3 Linear Dependence and Rank = 433
• A.4 Equation Systems = 433
• A.5 Eigenvalues and Eigenvectors = 434
• A.6 Diagonalization of Symmetric Matrices = 435
• A.7 Definite Matrices = 435
• A.8 Generalized Inverses = 437
• A.9 Matrix Calculus = 438
• A.10 Vecs and Kronecker Products = 439
• B Probability and Distribution Theory = 441
• B.1 Set Theory Basics = 441
• B.2 Probability = 442
• B.3 Random Variable = 443
• B.4 Expectations = 446
• B.5 Joint Distributions = 450
• B.6 Conditional Expectations = 453
• B.7 Independence = 455
• B.8 Random Vectors = 456
• B.9 Change of Variable = 457
• B.10 Conditioning on a Sigma-field = 458
• C The Gaussian Distribution and its Relatives = 461
• C.1 The Univariate and Multivariate Cases = 461
• C.2 The Conditional and Marginal Distributions = 464
• C.3 The Chi-squared, F and t Distributions = 465
• C.4 Quadratic Forms in Normal Variables = 466
• References = 469
• Author Index = 485
• Subject Index = 489