Handbook of Computational Econometrics

Handbook of Computational Econometrics......Page 5
Contents......Page 9
List of Contributors......Page 17
Preface......Page 19
1.1 Introduction......Page 21
1.2 The nature of econometric software......Page 25
1.2.1 The characteristics of early econometric software......Page 29
1.2.2 The expansive development of econometric software......Page 31
1.2.3 Econometric computing and the microcomputer......Page 37
1.3 The existing characteristics of econometric software......Page 39
1.3.1 Software characteristics: broadening and deepening......Page 41
1.3.2 Software characteristics: interface development......Page 45
1.3.3 Directives versus constructive commands......Page 49
1.3.4 Econometric software design implications......Page 55
1.4 Conclusion......Page 59
References......Page 61
2.1 Introduction......Page 75
2.2 Inaccurate econometric results......Page 76
2.2.1 Inaccurate simulation results......Page 77
2.2.2 Inaccurate GARCH results......Page 78
2.2.3 Inaccurate VAR results......Page 82
2.3 Entry-level tests......Page 85
2.4 Intermediate-level tests......Page 86
2.4.1 NIST Statistical Reference Datasets......Page 87
2.4.2 Statistical distributions......Page 91
2.4.3 Random numbers......Page 92
2.5 Conclusions......Page 95
References......Page 96
3.1.1 Optimization in econometrics......Page 101
3.1.2 Optimization heuristics......Page 103
3.1.3 An incomplete collection of applications of optimization heuristics in econometrics......Page 105
3.1.4 Structure and instructions for use of the chapter......Page 106
3.2.1 Basic concepts......Page 107
3.2.2 Trajectory methods......Page 108
3.2.3 Population-based methods......Page 110
3.2.4 Hybrid metaheuristics......Page 113
3.3.1 Optimization as stochastic mapping......Page 117
3.3.2 Convergence of heuristics......Page 119
3.3.3 Convergence of optimization-based estimators......Page 121
3.4 General guidelines for the use of optimization heuristics......Page 122
3.4.1 Implementation......Page 123
3.4.2 Presentation of results......Page 128
3.5.1 Model selection in VAR models......Page 129
3.5.2 High breakdown point estimation......Page 131
3.6 Conclusions......Page 134
References......Page 135
4.1 Introduction......Page 141
4.2 An interior point algorithm......Page 142
4.2.1 Subgradient of Φ(x) and basic iteration......Page 145
4.2.2 Primal–dual step size selection......Page 150
4.2.3 Choice of c and μ......Page 151
4.3 Global optimization of polynomial minimax problems......Page 157
4.3.1 The algorithm......Page 158
4.4 Expected value optimization......Page 163
4.4.1 An algorithm for expected value optimization......Page 165
4.5 Evaluation framework for minimax robust policies and expected value optimization......Page 167
References......Page 168
5.1 Introduction......Page 173
5.1.1 Comments on software......Page 175
5.2 Density estimation......Page 176
5.2.1 Some illustrations......Page 178
5.3 Nonparametric regression......Page 180
5.3.1 An illustration......Page 184
5.3.2 Multiple predictors......Page 186
5.3.4 Estimating conditional associations......Page 189
5.3.5 An illustration......Page 190
5.4.1 Some motivating examples......Page 191
5.4.2 A bootstrap-t method......Page 192
5.4.3 The percentile bootstrap method......Page 193
5.4.4 Simple ordinary least squares regression......Page 194
5.4.5 Regression with multiple predictors......Page 195
References......Page 197
6.1 Introduction......Page 203
6.2 Bootstrap and Monte Carlo tests......Page 204
6.3 Finite-sample properties of bootstrap tests......Page 207
6.4 Double bootstrap and fast double bootstrap tests......Page 209
6.5.1 Resampling and the pairs bootstrap......Page 213
6.5.2 The residual bootstrap......Page 215
6.5.3 The wild bootstrap......Page 216
6.5.4 Bootstrap DGPs for multivariate regression models......Page 217
6.5.5 Bootstrap DGPs for dependent data......Page 218
6.6 Multiple test statistics......Page 220
6.6.1 Tests for structural change......Page 221
6.6.2 Point-optimal tests......Page 222
6.6.3 Non-nested hypothesis tests......Page 223
6.7 Finite-sample properties of bootstrap supF tests......Page 224
References......Page 230
7.1 Introduction......Page 235
7.2.1 Motivation for Bayesian inference......Page 237
7.2.2 Bayes’ theorem as a learning device......Page 238
7.2.3 Model evaluation and model selection......Page 245
7.2.4 Comparison of Bayesian inference and frequentist approach......Page 252
7.3.1 Motivation for using simulation techniques......Page 253
7.3.2 Direct sampling methods......Page 254
7.3.3 Indirect sampling methods yielding independent draws......Page 256
7.3.4 Markov chain Monte Carlo: indirect sampling methods yielding dependent draws......Page 269
7.4 Some recently developed simulation methods......Page 281
7.4.1 Adaptive radial-based direction sampling......Page 282
7.4.2 Adaptive mixtures of t distributions......Page 292
7.5 Concluding remarks......Page 296
References......Page 297
8.1 Introduction......Page 301
8.1.1 Integrated variables......Page 302
8.1.2 Structure of the chapter......Page 303
8.1.3 Terminology and notation......Page 304
8.2.1 The levels VAR representation......Page 305
8.2.2 The VECM representation......Page 306
8.2.3 Structural forms......Page 308
8.3.1 Estimation of unrestricted VARs......Page 309
8.3.2 Estimation of VECMs......Page 311
8.3.3 Estimation with linear restrictions......Page 313
8.3.4 Bayesian estimation of VARs......Page 314
8.4.1 Choosing the lag order......Page 315
8.4.2 Choosing the cointegrating rank of a VECM......Page 317
8.5.1 Tests for residual autocorrelation......Page 318
8.5.2 Tests for non-normality......Page 320
8.5.4 Stability analysis......Page 321
8.6.1 Known processes......Page 323
8.6.2 Estimated processes......Page 324
8.7.1 Intuition and theory......Page 325
8.8.1 Levels VARs......Page 326
8.8.2 Structural VECMs......Page 328
8.8.3 Estimating impulse responses......Page 329
8.8.4 Forecast error variance decompositions......Page 330
Acknowledgments......Page 331
References......Page 332
9.1 Introduction: the semantics of filtering......Page 341
9.2 Linear and circular convolutions......Page 342
9.2.1 Kernel smoothing......Page 344
9.3 Local polynomial regression......Page 346
9.4 The concepts of the frequency domain......Page 352
9.4.1 The periodogram......Page 354
9.4.2 Filtering and the frequency domain......Page 355
9.4.3 Aliasing and the Shannon–Nyquist sampling theorem......Page 357
9.4.4 The processes underlying the data......Page 359
9.5 The classical Wiener–Kolmogorov theory......Page 361
9.6 Matrix formulations......Page 365
9.6.1 Toeplitz matrices......Page 366
9.6.2 Circulant matrices......Page 368
9.7 Wiener–Kolmogorov filtering of short stationary sequences......Page 370
9.8 Filtering nonstationary sequences......Page 374
9.9 Filtering in the frequency domain......Page 379
9.10 Structural time-series models......Page 380
9.11 The Kalman filter and the smoothing algorithm......Page 388
9.11.1 The smoothing algorithms......Page 391
9.11.2 Equivalent and alternative procedures......Page 392
References......Page 393
10.1 Introduction......Page 397
10.2.1 Linear and nonlinear processes......Page 402
10.2.2 Linear representation of nonlinear processes......Page 404
10.3 Testing linearity......Page 405
10.3.1 Weak white noise and strong white noise testing......Page 406
10.3.2 Testing linearity against a specific nonlinear model......Page 409
10.3.3 Testing linearity when the model is not identified under the null......Page 412
10.4.1 A strict stationarity condition......Page 415
10.4.2 Second-order stationarity and existence of moments......Page 417
10.4.3 Mixing coefficients......Page 418
10.4.4 Geometric ergodicity and mixing properties......Page 419
10.5 Identification, estimation and model adequacy checking......Page 421
10.5.1 Consistency of the QMLE......Page 422
10.5.2 Asymptotic distribution of the QMLE......Page 424
10.5.3 Identification and model adequacy......Page 426
10.6.1 Forecast generation......Page 429
10.6.2 Interval and density forecasts......Page 432
10.6.3 Volatility forecasting......Page 434
10.6.4 Forecast combination......Page 435
10.7.1 MCMC methods......Page 436
10.7.2 Optimization algorithms for models with several latent processes......Page 438
References......Page 442
11.1 Introduction......Page 449
11.2 Variational inequalities......Page 452
11.2.1 Systems of equations......Page 453
11.2.2 Optimization problems......Page 454
11.2.3 Complementarity problems......Page 456
11.2.4 Fixed point problems......Page 458
11.3 Transportation networks: user optimization versus system optimization......Page 463
11.3.1 Transportation network equilibrium with travel disutility functions......Page 464
11.3.2 Elastic demand transportation network problems with known travel demand functions......Page 467
11.3.3 Fixed demand transportation network problems......Page 469
11.3.4 The system-optimized problem......Page 470
11.4 Spatial price equilibria......Page 474
11.4.1 The quantity model......Page 475
11.4.2 The price model......Page 477
11.5 General economic equilibrium......Page 478
11.6 Oligopolistic market equilibria......Page 479
11.6.1 The classical oligopoly problem......Page 480
11.6.2 A spatial oligopoly model......Page 481
11.7.1 Background......Page 483
11.7.2 The projected dynamical system......Page 485
11.8.1 The path choice adjustment process......Page 490
11.8.2 Stability analysis......Page 492
11.8.3 Discrete-time algorithms......Page 493
11.8.4 A dynamic spatial price model......Page 495
11.9 Supernetworks: applications to telecommuting decision making and teleshopping decision making......Page 496
11.10 Supply chain networks and other applications......Page 498
References......Page 500
Index......Page 507