Econometric analysis:
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| Format: | Book |
| Language: | English |
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Upper Saddle River, NJ
Pearson/Prentice Hall
2008
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| Edition: | 6. ed., internat. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 1099 - 1146 |
| Physical Description: | XXXVII, 1178 S. graph. Darst. |
| ISBN: | 9780135137406 0135137403 |
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| 245 | 1 | 0 | |a Econometric analysis |c William H. Greene |
| 250 | |a 6. ed., internat. ed. | ||
| 264 | 1 | |a Upper Saddle River, NJ |b Pearson/Prentice Hall |c 2008 | |
| 300 | |a XXXVII, 1178 S. |b graph. Darst. | ||
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| _version_ | 1804137397175189504 |
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| adam_text | CONTENTS EXAMPLES AND APPLICATIONS XXVI PREFACE XXXIII PART I THE LINEAR
REGRESSION MODEL CHAPTER 1 INTRODUCTION 1 1.1 ECONOMETRICS 1 1.2
ECONOMETRIC MODELING 2 1.3 METHODOLOGY 5 1.4 THE PRACTICE OF
ECONOMETRICS 6 1.5 PLAN OF THE BOOK 7 CHAPTER 2 THE CLASSICAL MULTIPLE
LINEAR REGRESSION MODEL 8 2.1 INTRODUCTION 8 2.2 THE LINEAR REGRESSION
MODEL 8 2.3 ASSUMPTIONS OF THE CLASSICAL LINEAR REGRESSION MODEL 11
2.3.1 LINEARITY OF THE REGRESSION MODEL 12 23.2 FULL RANK 14 2.3.3
REGRESSION 15 2.3.4 SPHERICAL DISTURBANCES 16 2.3.5 DATA GENERATING
PROCESS FOR THE REGRESSORS 17 2.3.6 NORMALITY 18 2.4 SUMMARY AND
CONCLUSIONS 19 CHAPTER 3 LEAST SQUARES 20 3.1 INTRODUCTION 20 3.2 LEAST
SQUARES REGRESSION 20 3.2.1 THE LEAST SQUARES COEFFICIENT VECTOR 21
3.2.2 APPLICATION: AN INVESTMENT EQUATION 22 3.2.3 ALGEBRAIC ASPECTS OF
THE LEAST SQUARES SOLUTION 25 3.2.4 PROJECTION 25 3.3 PARTITIONED
REGRESSION AND PARTIAL REGRESSION 27 3.4 PARTIAL REGRESSION AND PARTIAL
CORRELATION COEFFICIENTS 29 VII VIII CONTENTS 3.5 GOODNESS OF FIT AND
THE ANALYSIS OF VARIANCE 32 3.5.1 THE ADJUSTED R-SQUARED AND A MEASURE
OF FIT 35 3.5.2 R-SQUARED AND THE CONSTANT TERM IN THE MODEL 37 3.5.3
COMPARING MODELS 38 3.6 SUMMARY AND CONCLUSIONS 39 CHAPTER 4 STATISTICAL
PROPERTIES OF THE LEAST SQUARES ESTIMATOR 43 4.1 INTRODUCTION 43 4.2
MOTIVATING LEAST SQUARES 44 4.2.1 THE POPULATION ORTHOGONALITY
CONDITIONS 44 4.2.2 MINIMUM MEAN SQUARED ERROR PREDICTOR 45 4.2.3
MINIMUM VARIANCE LINEAR UNBIASED ESTIMATION 46 4.3 UNBIASED ESTIMATION
46 4.4 THE VARIANCE OF THE LEAST SQUARES ESTIMATOR AND THE GAUSS-MARKOV
THEOREM 48 4.5 THE IMPLICATIONS OF STOCHASTIC REGRESSORS 49 4.6
ESTIMATING THE VARIANCE OF THE LEAST SQUARES ESTIMATOR 51 4.7 THE
NORMALITY ASSUMPTION AND BASIC STATISTICAL INFERENCE 52 4.7.7 TESTING A
HYPOTHESIS ABOUT A COEFFICIENT 52 4.7.2 CONFIDENCE INTERVALS FOR
PARAMETERS 54 4.7.3 CONFIDENCE INTERVAL FOR A LINEAR COMBINATION OF
COEFFICIENTS: THE OAXACA DECOMPOSITION 55 4.7.4 TESTING THE SIGNIFICANCE
OF THE REGRESSION 56 4.7.5 MARGINAL DISTRIBUTIONS OF THE TEST STATISTICS
57 4.8 FINITE-SAMPLE PROPERTIES OF THE LEAST SQUARES ESTIMATOR 58 4.8.1
MULTICOLLINEARITY 59 4.8.2 MISSING OBSERVATIONS 61 4.9 LARGE SAMPLE
PROPERTIES OF THE LEAST SQUARES ESTIMATOR 63 4.9.1 CONSISTENCY OF THE
LEAST SQUARES ESTIMATOR OF J3 64 4.9.2 ASYMPTOTIC NORMALITY OF THE LEAST
SQUARES ESTIMATOR 65 4.9.3 CONSISTENCY OFS 2 AND THE ESTIMATOR OFASY.
VARFB] 67 4.9.4 ASYMPTOTIC DISTRIBUTION OF A FUNCTION OFB; THE DELTA
METHOD AND THE METHOD OFKRINSKY AND ROBB 68 4.9.5 ASYMPTOTIC EFFICIENCY
71 4.9.6 MORE GENERAL DATA GENERATING PROCESSES 72 4.10 SUMMARY AND
CONCLUSIONS 75 CHAPTER 5 INFERENCE AND PREDICTION 81 5.1 INTRODUCTION 81
5.2 RESTRICTIONS AND NESTED MODELS 81 5.3 TWO APPROACHES TO TESTING
HYPOTHESES 83 5.3.1 THE F STATISTIC AND THE LEAST SQUARES DISCREPANCY 83
5.3.2 THE RESTRICTED LEAST SQUARES ESTIMATOR 87 5.3.3 THE LOSS OF FIT
FROM RESTRICTED LEAST SQUARES 89 CONTENTS SX 5.4 NONNORMAL DISTURBANCES
AND LARGE SAMPLE TESTS 92 5.5 TESTING NONLINEAR RESTRICTIONS 96 5.6
PREDICTION 99 5.7 SUMMARY AND CONCLUSIONS 102 CHAPTER 6 FUNCTIONAL FORM
AND STRUCTURAL CHANGE 106 6.1 INTRODUCTION 106 6.2 USING BINARY
VARIABLES 1.06 6.2.1 BINARY VARIABLES IN REGRESSION 106 6.2.2 SEVERAL
CATEGORIES 107 6.2.3 SEVERAL GROUPINGS 108 6.2.4 THRESHOLD EFFECTS AND
CATEGORICAL VARIABLES 110 6.2.5 SPLINE REGRESSION 111 6.3 NONLINEARITY
IN THE VARIABLES 112 6.3.1 FUNCTIONAL FORMS 112 6.3.2 IDENTIFYING
NONLINEARITY 114 6.3.3 INTRINSIC LINEARITY AND IDENTIFICATION 117 6.4
MODELING AND TESTING FOR A STRUCTURAL BREAK 120 6.4.1 DIFFERENT
PARAMETER VECTORS 121 6.4.2 INSUFFICIENT OBSERVATIONS 121 6.4.3 CHANGE
IN A SUBSET OF COEFFICIENTS 122 6.4.4 TESTS OF STRUCTURAL BREAK WITH
UNEQUAL VARIANCES 123 6.4.5 PREDICTIVE TEST 127 6.5 SUMMARY AND
CONCLUSIONS 128 CHAPTER 7 SPECIFICATION ANALYSIS AND MODEL SELECTION 133
7.1 INTRODUCTION 133 7.2 SPECIFICATION ANALYSIS AND MODEL BUILDING 133
7.2.1 BIAS CAUSED BY OMISSION OF RELEVANT VARIABLES 133 7.2.2 PRETEST
ESTIMATION 134 7.2.3 INCLUSION OF IRRELEVANT VARIABLES 136 7.2.4 MODEL
BUILDING*A GENERAL TO SIMPLE STRATEGY 136 13 CHOOSING BETWEEN NONNESTED
MODELS 137 7.3.1 TESTING NONNESTED HYPOTHESES 138 7.3.2 AN ENCOMPASSING
MODEL 138 7.3.3 COMPREHENSIVE APPROACH * THE J TEST 139 7.3.4 VUONG S
TEST AND THE KULLBACK-LEIBLER INFORMATION CRITERION 140 7.4 MODEL
SELECTION CRITERIA 142 7.5 MODEL SELECTION 143 7.5.1 CLASSICAL MODEL
SELECTION 144 7.5.2 BAYESIAN MODEL AVERAGING 144 7.6 SUMMARY AND
CONCLUSIONS 146 X CONTENTS PART II THE GENERALIZED REGRESSION MODEL
CHAPTER 8 THE GENERALIZED REGRESSION MODEL AND HETEROSCEDASTICITY 148
8.1 INTRODUCTION 148 8.2 LEAST SQUARES ESTIMATION 149 8.2.1
FINITE-SAMPLE PROPERTIES OF ORDINARY LEAST SQUARES 150 8.2.2 ASYMPTOTIC
PROPERTIES OF LEAST SQUARES 151 8.2.3 ROBUST ESTIMATION OF ASYMPTOTIC
COVARIANCE MATRICES 153 8.3 EFFICIENT ESTIMATION BY GENERALIZED LEAST
SQUARES 154 8.3.1 GENERALIZED LEAST SQUARES (GLS) 154 8.3.2 FEASIBLE
GENERALIZED LEAST SQUARES (FGLS) 156 8.4 HETEROSCEDASTICITY 158 8.4.1
ORDINARY LEAST SQUARES ESTIMATION 159 8.4.2 INEFFICIENCY OF LEAST
SQUARES 160 8.4.3 THE ESTIMATED COVARIANCE MATRIX OF B 160 8.4.4
ESTIMATING THE APPROPRIATE COVARIANCE MATRIX FOR ORDINARY LEAST SQUARES
162 8.5 TESTING FOR HETEROSCEDASTICITY 165 8.5.1 WHITE S GENERAL TEST
165 8.5.2 THE BREUSCH-PAGAN/GODFREY LM TEST 166 8.6 WEIGHTED LEAST
SQUARES WHEN 2 IS KNOWN 167 8.7 ESTIMATION WHEN Q CONTAINS UNKNOWN
PARAMETERS 169 8.8 APPLICATIONS 170 8.8.1 MULTIPLICATIVE
HETEROSCEDASTICITY 170 8.8.2 GROUPWISE HETEROSCEDASTICITY 172 8.9
SUMMARY AND CONCLUSIONS 175 CHAPTER 9 MODELS FOR PANEL DATA 180 9.1
INTRODUCTION 180 9.2 PANEL DATA MODELS 180 9.2.1 GENERAL MODELING
FRAMEWORK FOR ANALYZING PANEL DATA 182 9.2.2 MODEL STRUCTURES 183 9.2.3
EXTENSIONS 184 9.2.4 BALANCED AND UNBALANCED PANELS 184 9.3 THE POOLED
REGRESSION MODEL 185 9.3.1 LEAST SQUARES ESTIMATION OF THE POOLED MODEL
185 9.3.2 ROBUST COVARIANCE MATRIX ESTIMATION 185 9.3.3 CLUSTERING AND
STRATIFICATION 188 9.3.4 ROBUST ESTIMATION USING GROUP MEANS 188 9.3.5
ESTIMATION WITH FIRST DIFFERENCES 190 9.3.6 THE WITHIN- AND
BETWEEN-GROUPS ESTIMATORS 191 9.4 THE FIXED EFFECTS MODEL 193 9.4.1
LEAST SQUARES ESTIMATION 194 9.4.2 SMALL TASYMPTOTICS 196 CONTENTS XI
9.4.3 TESTING THE SIGNIFICANCE OF THE GROUP EFFECTS 197 9.4.4 FIXED TIME
AND GROUP EFFECTS 197 9.5 RANDOM EFFECTS 200 9.5.1 GENERALIZED LEAST
SQUARES 202 9.5.2 FEASIBLE GENERALIZED LEAST SQUARES WHEN IS UNKNOWN
203 9.5.3 TESTING FOR RANDOM EFFECTS 205 9.5.4 HAUSMAN S SPECIFICATION
TEST FOR THE RANDOM EFFECTS MODEL 208 9.5.5 EXTENDING THE UNOBSERVED
EFFECTS MODEL: MUNDLAK S APPROACH 209 9.6 NONSPHERICAL DISTURBANCES AND
ROBUST COVARIANCE ESTIMATION 210 9.6.1 ROBUST ESTIMATION OF THE FIXED
EFFECTS MODEL 211 9.6.2 HETEROSCEDASTICITY IN THE RANDOM EFFECTS MODEL
212 9.6.3 AUTOCORRELATION IN PANEL DATA MODELS 213 9.7 EXTENSIONS OF THE
RANDOM EFFECTS MODEL 213 9 J.I NESTED RANDOM EFFECTS 214 9J.2 SPATIAL
AUTOCORRELATION 218 9.8 PARAMETER HETEROGENEITY 222 9.8.1 THE RANDOM
COEFFICIENTS MODEL 223 9.8.2 RANDOM PARAMETERS AND SIMULATION-BASED
ESTIMATION 226 9.8.3 TWO-STEP ESTIMATION OF PANEL DATA MODELS 229 9.8.4
HIERARCHICAL LINEAR MODELS 233 9.8.5 PARAMETER HETEROGENEITY AND DYNAMIC
PANEL DATA MODELS 238 9.8.6 NONSTATIONARY DATA AND PANEL DATA MODELS 243
9.9 CONSISTENT ESTIMATION OF DYNAMIC PANEL DATA MODELS 244 9.10 SUMMARY
AND CONCLUSIONS 246 CHAPTER 10 SYSTEMS OF REGRESSION EQUATIONS 252 10.1
INTRODUCTION 252 10.2 THE SEEMINGLY UNRELATED REGRESSIONS MODEL 254
10.2.1 GENERALIZED LEAST SQUARES 256 10.2.2 SEEMINGLY UNRELATED
REGRESSIONS WITH IDENTICAL REGRESSORS 257 10.2.3 FEASIBLE GENERALIZED
LEAST SQUARES 258 10.2.4 TESTING HYPOTHESES 259 10.2.5
HETEROSCEDASTICITY 263 10.2.6 AUTOCORRELATION 263 10.2.7 A SPECIFICATION
TEST FOR THE SW MODEL 264 10.2.8 THE POOLED MODEL 266 10.3 PANEL DATA
APPLICATIONS 267 10.3J RANDOM EFFECTS SUR MODELS 267 10.3.2 THE RANDOM
AND FIXED EFFECTS MODELS 268 XII CONTENTS 10.4 SYSTEMS OF DEMAND
EQUATIONS: SINGULAR SYSTEMS 272 10.4.1 COBB-DOUGLAS COST FUNCTION
(EXAMPLE 6.3 CONTINUED) 273 10.4.2 FLEXIBLE FUNCTIONAL FORMS: THE
TRANSLOG COST FUNCTION 275 10.5 SUMMARY AND CONCLUSIONS 280 CHAPTER 11
NONLINEAR REGRESSIONS AND NONLINEAR LEAST SQUARES 285 11.1 INTRODUCTION
285 11.2 NONLINEAR REGRESSION MODELS 285 11.2.1 ASSUMPTIONS OF THE
NONLINEAR REGRESSION MODEL 286 11.2.2 THE ORTHOGONALITY CONDITION AND
THE SUM OF SQUARES 287 11.2.3 THE LINEARIZED REGRESSION 288 11.2.4 LARGE
SAMPLE PROPERTIES OF THE NONLINEAR LEAST SQUARES ESTIMATOR 290 112.5
COMPUTING THE NONLINEAR LEAST SQUARES ESTIMATOR 292 11.3 APPLICATIONS
294 11.3.1 A NONLINEAR CONSUMPTION FUNCTION 294 11.3.2 THE BOX-COX
TRANSFORMATION 296 11.4 HYPOTHESIS TESTING AND PARAMETRIC RESTRICTIONS
298 11.4.1 SIGNIFICANCE TESTS FOR RESTRICTIONS: F AND WALD STATISTICS
298 11.4.2 TESTS BASED ON THE LM STATISTIC 299 11.5 NONLINEAR SYSTEMS OF
EQUATIONS 300 11.6 TWO-STEP NONLINEAR LEAST SQUARES ESTIMATION 302 11.7
PANEL DATA APPLICATIONS 307 11.7.1 A ROBUST COVARIANCE MATRIX FOR
NONLINEAR LEAST SQUARES 307 11.7.2 FIXED EFFECTS 308 11.7.3 RANDOM
EFFECTS 310 11.8 SUMMARY AND CONCLUSIONS 311 PART III INSTRUMENTAL
VARIABLES AND SIMULTANEOUS EQUATIONS MODELS CHAPTER 12 INSTRUMENTAL
VARIABLES ESTIMATION 314 12.1 INTRODUCTION 314 12.2 ASSUMPTIONS OF THE
MODEL 315 12.3 ESTIMATION 316 12.3.1 ORDINARY LEAST SQUARES 316 12.3.2
THE INSTRUMENTAL VARIABLES ESTIMATOR 316 12.3.3 TWO-STAGE LEAST SQUARES
318 12.4 THE HAUSMAN AND WU SPECIFICATION TESTS AND AN APPLICATION TO
INSTRUMENTAL VARIABLE ESTIMATION 321 12.5 MEASUREMENT ERROR 325 12.5.1
LEAST SQUARES ATTENUATION 325 12.5.2 INSTRUMENTAL VARIABLES ESTIMATION
327 12.5.3 PROXY VARIABLES 328 12.6 ESTIMATION OF THE GENERALIZED
REGRESSION MODEL 332 CONTENTS XIII 12.7 NONLINEAR INSTRUMENTAL VARIABLES
ESTIMATION 333 12.8 PANEL DATA APPLICATIONS 336 12.8.1 INSTRUMENTAL
VARIABLES ESTIMATION OF THE RANDOM EFFECTS MODEL* THE HAUSMAN AND TAYLOR
ESTIMATOR 336 12.82 DYNAMIC PANEL DATA MODELS*THE ANDERSON/HSIAO AND
ARELLANO/BOND ESTIMATORS 340 12.9 WEAK INSTRUMENTS 350 12.10 SUMMARY AND
CONCLUSIONS 352 CHAPTER 13 SIMULTANEOUS EQUATIONS MODELS 354 13.1
INTRODUCTION 354 13.2 FUNDAMENTAL ISSUES IN SIMULTANEOUS EQUATIONS
MODELS 354 13.2.1 ILLUSTRATIVE SYSTEMS OF EQUATIONS 354 1,322
ENDOGENEITY AND CAUSALITY 357 13.2.3 A GENERAL NOTATION FOR LINEAR
SIMULTANEOUS EQUATIONS MODELS 358 13.3 THE PROBLEM OF IDENTIFICATION 361
13.3.1 THE RANK AND ORDER CONDITIONS FOR IDENTIFICATION 365 13.3.2
IDENTIFICATION THROUGH OTHER NONSAMPLE INFORMATION 370 13.4 METHODS OF
ESTIMATION 370 13.5 SINGLE EQUATION: LIMITED INFORMATION ESTIMATION
METHODS 371 13.5.1 ORDINARY LEAST SQUARES 371 13.52 ESTIMATION BY
INSTRUMENTAL VARIABLES 372 13.5.3 TWO-STAGE LEAST SQUARES 373 13.5.4
LIMITED INFORMATION MAXIMUM LIKELIHOOD AND THE K CLASS OF ESTIMATORS 375
13.5.5 TESTING IN THE PRESENCE OF WEAK INSTRUMENTS 377 13.5.6 TWO-STAGE
LEAST SQUARES IN MODELS THAT ARE NONLINEAR IN VARIABLES 380 13.6 SYSTEM
METHODS OF ESTIMATION 380 13.6.1 THREE-STAGE LEAST SQUARES 381 13.6.2
FULL INFORMATION MAXIMUM LIKELIHOOD 383 13.7 COMPARISON OF
METHODS*KLEIN S MODEL I 385 13.8 SPECIFICATION TESTS 387 13.9 PROPERTIES
OF DYNAMIC MODELS 389 13.9.1 DYNAMIC MODELS AND THEIR MULTIPLIERS 389
13.9.2 STABILITY 390 13.9.3 ADJUSTMENT TO EQUILIBRIUM 391 13.10 SUMMARY
AND CONCLUSIONS 394 PART IY ESTIMATION METHODOLOGY CHAPTER 14 ESTIMATION
FRAMEWORKS IN ECONOMETRICS 398 14.1 INTRODUCTION 398 XIV CONTENTS 14.2
PARAMETRIC ESTIMATION AND INFERENCE 400 14.2.1 CLASSICAL
LIKELIHOOD-BASED ESTIMATION 400 14.2.2 MODELING JOINT DISTRIBUTIONS WITH
COPULA FUNCTIONS 402 14.3 SEMIPARAMETRIC ESTIMATION 405 14.3.1 GMM
ESTIMATION IN ECONOMETRICS 406 14.3.2 LEAST ABSOLUTE DEVIATIONS
ESTIMATION 406 143.3 PARTIALLY LINEAR REGRESSION 409 14.3.4 KERNEL
DENSITY METHODS 411 14.3.5 COMPARING PARAMETRIC AND SEMIPARAMETRIC
ANALYSES 412 14.4 NONPARAMETRIC ESTIMATION 413 14.4.1 KERNEL DENSITY
ESTIMATION 414 14.4.2 NONPARAMETRIC REGRESSION 416 14.5 PROPERTIES OF
ESTIMATORS 420 14.5.1 STATISTICAL PROPERTIES OF ESTIMATORS 420 14.5.2
EXTREMUM ESTIMATORS 421 14.5.3 ASSUMPTIONS FOR ASYMPTOTIC PROPERTIES OF
EXTREMUM ESTIMATORS 421 14.5.4 ASYMPTOTIC PROPERTIES OF ESTIMATORS 424
14.5.5 TESTING HYPOTHESES 425 14.6 SUMMARY AND CONCLUSIONS 426 CHAPTER
15 MINIMUM DISTANCE ESTIMATION AND THE GENERALIZED METHOD OF MOMENTS 428
15.1 INTRODUCTION 428 15.2 CONSISTENT ESTIMATION: THE METHOD OF MOMENTS
429 15.2.1 RANDOM SAMPLING AND ESTIMATING THE PARAMETERS OF
DISTRIBUTIONS 430 15.2.2 ASYMP TOTIC PROPERTIES OF THE METHOD OF MOMENTS
ESTIMATOR 434 15.2.3 SUMMARY*THE METHOD OF MOMENTS 436 15.3 MINIMUM
DISTANCE ESTIMATION 436 15.4 THE GENERALIZED METHOD OF MOMENTS (GMM)
ESTIMATOR 441 15.4.1 ESTIMATION BASED ON ORTHOGONALITY CONDITIONS 442
15.4.2 GENERALIZING THE METHOD OF MOMENTS 443 15.4.3 PROPERTIES OF THE
GMM ESTIMATOR 447 15.5 TESTING HYPOTHESES IN THE GMM FRAMEWORK 451
15.5.1 TESTING THE VALIDITY OF THE MOMENT RESTRICTIONS 452 15.5.2 GMM
COUNTERPARTS TO THE WALD, LM, AND LR TESTS 453 15.6 GMM ESTIMATION OF
ECONOMETRIC MODELS 455 15.6.1 SINGLE-EQUATION LINEAR MODELS 455 15.6.2
SINGLE-EQUATION NONLINEAR MODELS 461 15.6.3 SEEMINGLY UNRELATED
REGRESSION MODELS 464 15.6.4 SIMULTANEOUS EQUATIONS MODELS WITH
HETEROSCEDASTICITY 466 15.6.5 GMM ESTIMATION OF DYNAMIC PANEL DATA
MODELS 469 15.7 SUMMARY AND CONCLUSIONS 480 CONTENTS XV CHAPTER 16
MAXIMUM LIKELIHOOD ESTIMATION 482 16.1 INTRODUCTION 482 16.2 THE
LIKELIHOOD FUNCTION AND IDENTIFICATION OF THE PARAMETERS 482 16.3
EFFICIENT ESTIMATION: THE PRINCIPLE OF MAXIMUM LIKELIHOOD 484 16.4
PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS 486 16.4.1 REGULARITY
CONDITIONS 487 16.4.2 PROPERTIES OF REGULAR DENSITIES 488 16.4.3 THE
LIKELIHOOD EQUATION 490 16.4.4 THE INFORMATION MATRIX EQUALITY 490
16.4.5 ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR 490
16,4.5.A CONSISTENCY 491 16,4.5.B ASYMPTOTIC NORMALITY 492 16.4.5.C
ASYMPTOTIC EFFICIENCY 493 16.4.5.D INVARIANCE 494 16.4.5.E CONCLUSION
494 16.4.6 ESTIMATING THE ASYMPTOTIC VARIANCE OF THE MAXIMUM LIKELIHOOD
ESTIMATOR 494 16.5 CONDITIONAL LIKELIHOODS, ECONOMETRIC MODELS, AND THE
GMM ESTIMATOR 496 16.6 HYPOTHESIS AND SPECIFICATION TESTS AND FIT
MEASURES 498 16.6.1 THE LIKELIHOOD RATIO TEST 498 16.6.2 THE WALD TEST
500 16.6.3 THE LAGRANGE MULTIPLIER TEST 502 16.6.4 AN APPLICATION OF THE
LIKELIHOOD-BASED TEST PROCEDURES 504 16.6.5 COMPARING MODELS AND
COMPUTING MODEL FIT 506 16.7 TWO-STEP MAXIMUM LIKELIHOOD ESTIMATION 507
16.8 PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION AND ROBUST ASYMPTOTIC
COVARIANCE MATRICES 511 16.8.1 MAXIMUM LIKELIHOOD AND GMM ESTIMATION 512
16.8.2 MAXIMUM LIKELIHOOD AND M ESTIMATION 512 16.8.3 SANDWICH
ESTIMATORS 514 16.8A CLUSTER ESTIMATORS 515 16.9 APPLICATIONS OF MAXIMUM
LIKELIHOOD ESTIMATION 517 16.9.1 THE NORMAL LINEAR REGRESSION MODEL 518
16.9.2 THE GENERALIZED REGRESSION MODEL 522 16.9.2,A MULTIPLICATIVE
HETEROSCEDASTICITY 523 16.9.2.B AUTOCORRELATION 527 16.9.3 SEEMINGLY
UNRELATED REGRESSION MODELS 529 16.9.3.A THE POOLED MODEL 530 16.9.3.B
THE SUR MODEL 531 16.9.3.C EXCLUSION RESTRICTIONS 532 XVI CONTENTS
16.9.4 SIMULTANEOUS EQUATIONS MODELS 536 16.9.5 MAXIMUM LIKELIHOOD
ESTIMATION OF NONLINEAR REGRESSION MODELS 537 16.9.5.A NONNORMAL
DISTURBANCES* THE STOCHASTIC FRONTIER MODEL 538 16.9.5. B ML ESTIMATION
OF A GEOMETRIC REGRESSION MODEL FOR COUNT DATA 542 16.9.6 PANEL DATA
APPLICATIONS 547 16.9.6.A ML ESTIMATION OF THE LINEAR RANDOM EFFECTS
MODEL 547 16.9.6. B RANDOM EFFECTS IN NONLINEAR MODELS: MLE USING
QUADRATURE 550 16.9.6.C FIXED EFFECTS IN NONLINEAR MODELS: FULL MLE 554
16.9.7 LATENT CLASS AND FINITE MIXTURE MODELS 558 16.9.7.A A FINITE
MIXTURE MODEL 559 16.9.7.B MEASURED AND UNMEASURED HETEROGENEITY 560
16.9.7. C PREDICTING CLASS MEMBERSHIP 561 16.9. 7. D A CONDITIONAL
LATENT CLASS MODEL 561 16.9.7. E DETERMINING THE NUMBER OF CLASSES 564
16.9.7.F A PANEL DATA APPLICATION 564 16.10 SUMMARY AND CONCLUSIONS 567
CHAPTER 17 SIMULATION-BASED ESTIMATION AND INFERENCE 573 17.1
INTRODUCTION 573 17.2 RANDOM NUMBER GENERATION 573 17.2.1 GENERATING
PSEUDO-RANDOM NUMBERS 574 17.2.2 SAMPLING FROM A STANDARD UNIFORM
POPULATION 575 17.2.3 SAMPLING FROM CONTINUOUS DISTRIBUTIONS 575 17.2.4
SAMPLING FROM A MULTIVARIATE NORMAL POPULATION 576 17.2.5 SAMPLING FROM
A DISCRETE POPULATION 576 17.3 MONTE CARLO INTEGRATION 576 17.3.1 HALTON
SEQUENCES AND RANDOM DRAWS FOR SIMULATION-BASED INTEGRATION 577 17.3.2
IMPORTANCE SAMPLING 580 173.3 COMPUTING MULTIVARIATE NORMAL
PROBABILITIES USING THE GHK SIMULATOR 582 17.4 MONTE CARLO STUDIES 584
17.4.1 A MONTE CARLO STUDY: BEHAVIOR OF A TEST STATISTIC 585 17.4.2 A
MONTE CARLO STUDY: THE INCIDENTAL PARAMETERS PROBLEM 586 17.5
SIMULATION-BASED ESTIMATION 589 17.5.1 MAXIMUM SIMULATED LIKELIHOOD
ESTIMATION OF RANDOM PARAMETERS MODELS 590 17.5.2 THE METHOD OF
SIMULATED MOMENTS 595 17.6 BOOTSTRAPPING 596 17.7 SUMMARY AND
CONCLUSIONS 598 CONTENTS XVII CHAPTER 18 BAYESIAN ESTIMATION AND
INFERENCE 600 18.1 INTRODUCTION 600 18.2 BAYES THEOREM AND THE POSTERIOR
DENSITY 601 18.3 BAYESIAN ANALYSIS OF THE CLASSICAL REGRESSION MODEL 603
18.3.1 ANALYSIS WITH A NONINFORMATIVE PRIOR 604 18.3.2 ESTIMATION WITH
AN INFORMATIVE PRIOR DENSITY 606 18.4 BAYESIAN INFERENCE 609 18.4.1
POINT ESTIMATION 609 18.4.2 INTERVAL ESTIMATION 610 18.4.3 HYPOTHESIS
TESTING 611 18.4.4 LARGE SAMPLE RESULTS 613 18.5 POSTERIOR DISTRIBUTIONS
AND THE GIBBS SAMPLER 613 18.6 APPLICATION: BINOMIAL PROBIT MODEL 616
18.7 PANEL DATA APPLICATION: INDIVIDUAL EFFECTS MODELS 619 18.8
HIERARCHICAL BAYES ESTIMATION OF A RANDOM PARAMETERS MODEL 621 18.9
SUMMARY AND CONCLUSIONS 623 PART V TIME SERIES AND MACROECONOMETRICS
CHAPTER 19 SERIAL CORRELATION 626 19.1 INTRODUCTION 626 19.2 THE
ANALYSIS OF TIME-SERIES DATA 629 19.3 DISTURBANCE PROCESSES 632 19.3.1
CHARACTERISTICS OF DISTURBANCE PROCESSES 632 19.3.2 AR(1) DISTURBANCES
633 19.4 SOME ASYMPTOTIC RESULTS FOR ANALYZING TIME-SERIES DATA 635
19.4.1 CONVERGENCE OF MOMENTS*THE ERGODIC THEOREM 636 19.4.2 CONVERGENCE
TO NORMALITY*A CENTRAL LIMIT THEOREM 638 19.5 LEAST SQUARES ESTIMATION
640 79.5.1 ASYMPTOTIC PROPERTIES OF LEAST SQUARES 640 19.5.2 ESTIMATING
THE VARIANCE OF THE LEAST SQUARES ESTIMATOR 642 19.6 GMM ESTIMATION 643
19.7 TESTING FOR AUTOCORRELATION 644 19.7.1 LAGRANGE MULTIPLIER TEST 644
19.7.2 BOX AND PIERCE S TEST AND LJUNG S REFINEMENT 645 19.7.3 THE
DURBIN-WATSON TEST 645 19.7.4 TESTING IN THE PRESENCE OF A LAGGED
DEPENDENT VARIABLE 646 19.7.5 SUMMARY OF TESTING PROCEDURES 646 19.8
EFFICIENT ESTIMATION WHEN 9, IS KNOWN 647 19.9 ESTIMATION WHEN FT IS
UNKNOWN 648 19.9.1 AR(1) DISTURBANCES 648 19.9.2 APPLICATION: ESTIMATION
OF A MODEL WITH AUTOCORRELATION 649 19.9.3 ESTIMATION WITH A LAGGED
DEPENDENT VARIABLE 651 19.10 AUTOCORRELATION IN PANEL DATA 652 XVIII
CONTENTS 19.11 COMMON FACTORS 655 1912 FORECASTING IN THE PRESENCE OF
AUTOCORRELATION 656 19.13 AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY
658 19.13.1 THE ARCH(L) MODEL 659 19.13.2 ARCH (Q), ARCH-IN-MEAN, AND
GENERALIZED ARCH MODELS 660 19.13.3 MAXIMUM LIKELIHOOD ESTIMATION OF THE
GARCH MODEL 662 19.13.4 TESTING FOR GARCH EFFECTS 664 19.13.5
PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION 666 19.14 SUMMARY AND CONCLUSIONS
667 CHAPTER 20 MODELS WITH LAGGED VARIABLES 670 20.1 INTRODUCTION 670
20.2 DYNAMIC REGRESSION MODELS 671 20.2.1 LAGGED EFFECTS IN A DYNAMIC
MODEL 672 20.2.2 THE LAG AND DIFFERENCE OPERATORS 674 20.2.3
SPECIFICATION SEARCH FOR THE LAG LENGTH 676 20.3 SIMPLE DISTRIBUTED LAG
MODELS 677 20.4 AUTOREGRESSIVE DISTRIBUTED LAG MODELS 681 20.4.1
ESTIMATION OF THE ARDL MODEL 682 20.4.2 COMPUTATION OF THE LAG WEIGHTS
IN THE ARDL MODEL 683 20.4.3 STABILITY OF A DYNAMIC EQUATION 684 20.4.4
FORECASTING 686 20.5 METHODOLOGICAL ISSUES IN THE ANALYSIS OF DYNAMIC
MODELS 689 20.5.1 AN ERROR CORRECTION MODEL 689 20.5.2 AUTOCORRELATION
691 20.5.3 SPECIFICATION ANALYSIS 692 20.6 VECTOR AUTOREGRESSIONS 693
20.6.1 MODEL FORMS 695 20.6.2 ESTIMATION 696 20.6.3 TESTING PROCEDURES
696 20.6.4 EXOGENEITY 698 20.6.5 TESTING FOR GRANGER CAUSALITY 699
20.6.6 IMPULSE RESPONSE FUNCTIONS 701 20.6.7 STRUCTURAL VARS 702 20.6.8
APPLICATION: POLICY ANALYSIS WITH A VAR 703 20.6.8. A A VAR MODEL FOR
THE MACROECONOMIC VARIABLES 703 20.6.8.B THE SACRIFICE RATIO 704
20.6.8.C IDENTIFICATION AND ESTIMATION OF A STRUCTURAL VAR MODEL 704
20,6.8.D INFERENCE 707 20.6.8.E EMPIRICAL RESULTS 707 20.6.9 VARS IN
MICROECONOMICS 711 20.7 SUMMARY AND CONCLUSIONS 712 CONTENTS XIX CHAPTER
21 TIME-SERIES MODELS 715 21.1 INTRODUCTION 715 21.2 STATIONARY
STOCHASTIC PROCESSES 716 21.2.1 AUTO REGRESSIVE MOVING-AVERAGE PROCESSES
716 21.2.2 STATIONARITY AND INVERTIBILITY 718 21.23 AUTOCORRELATIONS OF
A STATIONARY STOCHASTIC PROCESS 721 21.2.4 PARTIAL AUTOCORRELATIONS OF A
STATIONARY STOCHASTIC PROCESS 723 21.2.5 MODELING UNIVARIATE TIME SERIES
726 21.2.6 ESTIMATION OF THE PARAMETERS OF A UNIVARIATE TIME SERIES 728
21.3 THE FREQUENCY DOMAIN 731 21.3.1 THEORETICAL RESULTS 732 21.3.2
EMPIRICAL COUNTERPARTS 734 21.4 SUMMARY AND CONCLUSIONS 738 CHAPTER 22
NONSTATIONARY DATA 739 22.1 INTRODUCTION 739 22.2 NONSTATIONARY
PROCESSES AND UNIT ROOTS 739 22.2.1 INTEGRATED PROCESSES AND
DIFFERENCING 739 22.2.2 RANDOM WALKS, TRENDS, AND SPURIOUS REGRESSIONS
741 22.2.3 TESTS FOR UNIT ROOTS IN ECONOMIC DATA 744 22.2.4 THE
DICKEY-FULLER TESTS 745 22.2.5 THE KPSS TEST OF STATIONARITY 755 22.3
COINTEGRATION 756 22.3.1 COMMON TRENDS 759 22.3.2 ERROR CORRECTION AND
VAR REPRESENTATIONS 760 22.3.3 TESTING FOR COINTEGRATION 761 22.3.4
ESTIMATING COINTEGRATION RELATIONSHIPS 764 22.3.5 APPLICATION: GERMAN
MONEY DEMAND 764 22,3.5,A COINTEGRATION ANALYSIS AND A LONG-RUN
THEORETICAL MODEL 765 22.3.5, B TESTING FOR MODEL INSTABILITY 766 22.4
NONSTATIONARY PANEL DATA 767 22.5 SUMMARY AND CONCLUSIONS 768 PART VI
CROSS SECTIONS, PANEL DATA, AND MICROECONOMETRICS CHAPTER 23 MODELS TOT
DISCRETE CHOICE 770 23.1 INTRODUCTION 770 23.2 DISCRETE CHOICE MODELS
770 23.3 MODELS FOR BINARY CHOICE 772 23.3.1 THE REGRESSION APPROACH 772
23.3.2 LATENT REGRESSION*INDEX FUNCTION MODELS 775 23.3.3 RANDOM UTILITY
MODELS 777 XX CONTENTS 23.4 ESTIMATION AND INFERENCE IN BINARY CHOICE
MODELS 777 23.4.1 ROBUST COVARIANCE MATRIX ESTIMATION 780 23.4.2
MARGINAL EFFECTS AND AVERAGE PARTIAL EFFECTS 780 23.4.3 HYPOTHESIS TESTS
785 23.4.4 SPECIFICATION TESTS FOR BINARY CHOICE MODELS 787 23.4.4.A
OMITTED VARIABLES 788 23.4.4.B HETEROSCEDASTICITY 788 23.4.5 MEASURING
GOODNESS OF FIT 790 23.4.6 CHOICE-BASED SAMPLING 793 23.4.7 DYNAMIC
BINARY CHOICE MODELS 794 23.5 BINARY CHOICE MODELS FOR PANEL DATA 796
23.5.1 RANDOM EFFECTS MODELS 797 23.5.2 FIXED EFFECTS MODELS 800 23.5.3
MODELING HETEROGENEITY 806 23.5.4 PARAMETER HETEROGENEITY 807 23.6
SEMIPARAMETRIC ANALYSIS 809 23.6.1 SEMIPARAMETRIC ESTIMATION 810 23.6.2
A KERNEL ESTIMATOR FOR A NONPARAMETRIC REGRESSION FUNCTION 812 23.7
ENDOGENOUS RIGHT-HAND-SIDE VARIABLES IN BINARY CHOICE MODELS 813 23.8
BIVARIATE PROBIT MODELS 817 23.8.1 MAXIMUM LIKELIHOOD ESTIMATION 817
23.8.2 TESTING FOR ZERO CORRELATION 820 23.8.3 MARGINAL EFFECTS 821
23.8.4 RECURSIVE BIVARIATE PROBIT MODELS 823 23.9 A MULTIVARIATE PROBIT
MODEL 826 23.10 ANALYSIS OF ORDERED CHOICES 831 23.10.1 THE ORDERED
PROBIT MODEL 831 23.10.2 BIVARIATE ORDERED PROBIT MODELS 835 23.10.3
PANEL DATA APPLICATIONS 837 23,10.3.A ORDERED PROBIT MODELS WITH FIXED
EFFECTS 837 23.10.3. B ORDERED PROBIT MODELS WITH RANDOM EFFECTS 838
23.11 MODELS FOR UNORDERED MULTIPLE CHOICES 841 23.11.1 THE MULTINOMIAL
LOGIT MODEL 843 23.11.2 THE CONDITIONAL LOGIT MODEL 846 23.11.3 THE
INDEPENDENCE FROM IRRELEVANT ALTERNATIVES ASSUMPTION 847 23.11.4 NESTED
LOGIT MODELS 847 23.11.5 THE MULTINOMIAL PROBIT MODEL 850 23.11.6 THE
MIXED LOGIT MODEL 851 23.11.7 APPLICATION: CONDITIONAL LOGIT MODEL FOR
TRAVEL MODE CHOICE 852 23.11.8 PANEL DATA AND STATED CHOICE EXPERIMENTS
858 23.12 SUMMARY AND CONCLUSIONS 859 CONTENTS XXL CHAPTER 24
TRUNCATION, CENSORING, AND SAMPLE SELECTION 863 24.1 INTRODUCTION 863
24.2 TRUNCATION 863 24.2.1 TRUNCATED DISTRIBUTIONS 863 24.2.2 MOMENTS OF
TRUNCATED DISTRIBUTIONS 864 24.2.3 THE TRUNCATED REGRESSION MODEL 867
24.3 CENSORED DATA 869 24.3.1 THE CENSORED NORMAL DISTRIBUTION 869 2432
THE CENSORED REGRESSION (TOBIT) MODEL 871 24.3.3 ESTIMATION 874 24.3.4
SOME ISSUES IN SPECIFICATION 875 24.3.4. A HETEROSCEDASTICITY 875 24.3
AB MISSPECIFICATIONOFPROH[Y* 0] 877 24.3.4.C CORNER SOLUTIONS 878
24.3A.D NONNORMALIIY 880 24.4 PANEL DATA APPLICATIONS 881 24.5 SAMPLE
SELECTION 882 24.5.1 INCIDENTAL TRUNCATION IN A BIVARIATE DISTRIBUTION
883 24.5.2 REGRESSION IN A MODEL OF SELECTION 884 24,53 ESTIMATION 886
24.5.4 REGRESSION ANALYSIS OF TREATMENT EFFECTS 889 24.5.5 THE NORMALITY
ASSUMPTION 891 24.5.6 ESTIMATING THE EFFECT OF TREATMENT ON THE TREATED
891 24.5.7 SAMPLE SELECTION IN NONLINEAR MODELS 895 24.5.8 PANEL DATA
APPLICATIONS OF SAMPLE SELECTION MODELS 898 24,5.8.A COMMON EFFECTS IN
SAMPLE SELECTION MODELS 899 24.5 AB ATTRITION 901 24.6 SUMMARY AND
CONCLUSIONS 903 CHAPTER 25 MODELS FOR EVENT COUNTS AND DURATION 906 25.1
INTRODUCTION 906 25.2 MODELS FOR COUNTS OF EVENTS 907 25.2.1 MEASURING
GOODNESS OF FIT 908 25.2.2 TESTING FOR OVERDISPERSION 909 25.2.3
HETEROGENEITY AND THE NEGATIVE BINOMIAL REGRESSION MODEL 911 25.2A
FUNCTIONAL FORMS FOR COUNT DATA MODELS 912 25.3 PANEL DATA MODELS 915
253.1 ROBUST COVARIANCE MATRICES 915 25.3.2 FIXED EFFECTS 916 253.3
RANDOM EFFECTS 918 25.4 HURDLE AND ZERO-ALTERED POISSON MODELS 922 XXII
CONTENTS 25.5 CENSORING AND TRUNCATION IN MODELS FOR COUNTS 924 25.5.1
CENSORING AND TRUNCATION IN THE POISSON MODEL 925 25.5.2 APPLICATION:
CENSORING IN THE TOBIT AND POISSON REGRESSION MODELS 925 25.6 MODELS FOR
DURATION DATA 931 25.6.1 DURATION DATA 932 25.6.2 A REGRESSION-LIKE
APPROACH: PARAMETRIC MODELS OF DURATION 933 25.6,2.A THEORETICAL
BACKGROUND 933 25.62. H MODELS OF THE HAZARD FUNCTION 934 25.6.2.C
MAXIMUM LIKELIHOOD ESTIMATION 936 25.6.2J EXOGENOUS VARIABLES 937
25.6.2.E HETEROGENEITY 938 25.6.3 NONPARAMETRIC AND SEMIPARAMETRIC
APPROACHES 939 25.7 SUMMARY AND CONCLUSIONS 942 PART VII APPENDICES
APPENDIX A MATRIX ALGEBRA 945 A.I TERMINOLOGY 945 A.2 ALGEBRAIC
MANIPULATION OF MATRICES 945 A.2.1 EQUALITY OF MATRICES 945 A.2.2
TRANSPOSITION 946 A2.3 MATRIX ADDITION 946 A.2.4 VECTOR MULTIPLICATION
947 A2.5 A NOTATION FOR ROWS AND COLUMNS OF A MATRIX 947 A2.6 MATRIX
MULTIPLICATION AND SCALAR MULTIPLICATION 947 A.2.7 SUMS OF VALUES 949
A2.8 A USEFUL IDEMPOTENT MATRIX 950 A.3 GEOMETRY OF MATRICES 951 A.3.1
VECTOR SPACES 951 A.3.2 LINEAR COMBINATIONS OF VECTORS ARID BASIS
VECTORS 953 A.3.3 LINEAR DEPENDENCE 954 A.3.4 SUBSPACES 955 A3.5 RANK OF
A MATRIX 956 A.3.6 DETERMINANT OF A MATRIX 958 A3.7 A LEAST SQUARES
PROBLEM 959 A.4 SOLUTION OF A SYSTEM OF LINEAR EQUATIONS 961 AA.L
SYSTEMS OF LINEAR EQUATIONS 961 A.4.2 INVERSE MATRICES 962 AA.3
NONHOMOGENEOUS SYSTEMS OF EQUATIONS 964 AA.4 SOLVING THE LEAST SQUARES
PROBLEM 964 A.5 PARTITIONED MATRICES 964 A.5.1 ADDITION AND
MULTIPLICATION OF PARTITIONED MATRICES 965 A.52 DETERMINANTS OF
PARTITIONED MATRICES 965 CONTENTS XXIII A.5.3 INVERSES OF PARTITIONED
MATRICES 965 A.5.4 DEVIATIONS FROM MEANS 966 A.5.5 KRONECKER PRODUCTS
966 A.6 CHARACTERISTIC ROOTS AND VECTORS 967 A.6.1 THE CHARACTERISTIC
EQUATION 967 A.6.2 CHARACTERISTIC VECTORS 968 A.6.3 GENERAL RESULTS FOR
CHARACTERISTIC ROOTS AND VECTORS 968 A.6,4 DIAGONALIZATION AND SPECTRAL
DECOMPOSITION OF A MATRIX 969 A.6.5 RANK OF A MATRIX 969 A.6.6 CONDITION
NUMBER OF A MATRIX 971 A, 6.7 TRACE OF A MATRIX 9 71 A.6.8 DETERMINANT
OF A MATRIX 972 A.6.9 POWERS OF A MATRIX 972 A.6.10 IDEMPOTENT MATRICES
974 A.6,11 FACTORING A MATRIX 974 A.6,12 THE GENERALIZED INVERSE OF A
MATRIX 975 A.I QUADRATIC FORMS AND DEFINITE MATRICES 976 A J.I
NONNEGATIVE DEFINITE MATRICES 977 A.7.2 IDEMPOTENT QUADRATIC FORMS 978
A.7.3 COMPARING MATRICES 978 A.8 CALCULUS AND MATRIX ALGEBRA 979 A.8.1
DIFFERENTIATION AND THE TAYLOR SERIES 979 A.8.2 OPTIMIZATION 982 A.8.3
CONSTRAINED OPTIMIZATION 984 A.8A TRANSFORMATIONS 986 APPENDIX B
PROBABILITY AND DISTRIBUTION THEORY 987 B.I INTRODUCTION 987 B.2 RANDOM
VARIABLES 987 B.2.1 PROBABILITY DISTRIBUTIONS 987 B.2.2 CUMULATIVE
DISTRIBUTION FUNCTION 988 B.3 EXPECTATIONS OF A RANDOM VARIABLE 989 B.4
SOME SPECIFIC PROBABILITY DISTRIBUTIONS 991 B.4,1 THE NORMAL
DISTRIBUTION 991 B.4.2 THE CHI-SQUARED, T, AND FDISTRIBUTIONS 993 B.4.3
DISTRIBUTIONS WITH LARGE DEGREES OF FREEDOM 995 BAA SIZE DISTRIBUTIONS:
THE LOGNORMAL DISTRIBUTION 996 B.4.5 THE GAMMA AND EXPONENTIAL
DISTRIBUTIONS 996 BA.6 THE BETA DISTRIBUTION 997 BA.7 THE LOGISTIC
DISTRIBUTION 997 BA,8 THE WISHART DISTRIBUTION 997 BA.9 DISCRETE RANDOM
VARIABLES 998 B.5 THE DISTRIBUTION OF A FUNCTION OF A RANDOM VARIABLE
998 XXIV CONTENTS B,6 REPRESENTATIONS OF A PROBABILITY DISTRIBUTION 1000
B.7 JOINT DISTRIBUTIONS 1002 B. 7,1 MARGINAL D ISTRIB UTIONS 1002 B.7.2
EXPECTATIONS IN A JOINT DISTRIBUTION 1003 B.7.3 COVARIANCE AND
CORRELATION 1003 B.7 A DISTRIBUTION OF A FUNCTION OF BIVARIATE RANDOM
VARIABLES 1004 B.8 CONDITIONING IN A BIVARIATE DISTRIBUTION 1006 B.8.1
REGRESSION: THE CONDITIONAL MEAN 1006 B.8.2 CONDITIONAL VARIANCE 1007
B.8.3 RELATIONSHIPS AMONG MARGINAL AND CONDITIONAL MOMENTS 1007 B.8.4
THE ANALYSIS OF VARIANCE 1009 B.9 THE BIVARIATE NORMAL DISTRIBUTION 1009
B.10 MULTIVARIATE DISTRIBUTIONS 1010 B.10.1 MOMENTS 1010 B.10.2 SETS OF
LINEAR FUNCTIONS 1011 B.10.3 NONLINEAR FUNCTIONS 1012 B.LL THE
MULTIVARIATE NORMAL DISTRIBUTION 1013 B.LL.L MARGINAL AND CONDITIONAL
NORMAL DISTRIBUTIONS 1013 B.LL.2 THE CLASSICAL NORMAL LINEAR REGRESSION
MODEL 1014 B.LL.3 LINEAR FUNCTIONS OF A NORMAL VECTOR 1015 B.LL A
QUADRATIC FORMS IN A STANDARD NORMAL VECTOR 1015 B.H.5 THE F
DISTRIBUTION 1017 B.I 1.6 A FULL RANK QUADRATIC FORM 1017 B.I 1.7
INDEPENDENCE OF A LINEAR AND A QUADRATIC FORM 1018 APPENDIX C ESTIMATION
AND INFERENCE 1019 C.1 INTRODUCTION 1019 C.2 SAMPLES AND RANDOM SAMPLING
1020 C.3 DESCRIPTIVE STATISTICS 1020 C.4 STATISTICS AS
ESTIMATORS*SAMPLING DISTRIBUTIONS 1023 C.5 POINT ESTIMATION OF
PARAMETERS 1027 C.5.1 ESTIMATION IN A FINITE SAMPLE 1027 C.5.2 EFFICIENT
UNBIASED ESTIMATION 1030 C.6 INTERVAL ESTIMATION 1032 C.7 HYPOTHESIS
TESTING 1034 C.7.1 CLASSICAL TESTING PROCEDURES 1034 C.7.2 TESTS BASED
ON CONFIDENCE INTERVALS 1037 C7.3 SPECIFICATION TESTS 1038 APPENDIX D
LARGE-SAMPLE DISTRIBUTION THEORY 1038 D.I INTRODUCTION 1038 CONTENTS XXV
D.2 LARGE-SAMPLE DISTRIBUTION THEORY 1039 D.2.1 CONVERGENCE IN
PROBABILITY 1039 D. 22 OTHER FORMS OF CONVERGENCE AND LAWS OF LARGE
NUMBERS 1042 D.2.3 CONVERGENCE OF FUNCTIONS 1045 D.2 A CONVERGENCE TO A
RANDOM VARIABLE 1046 D.2.5 CONVERGENCE IN DISTRIBUTION: LIMITING
DISTRIBUTIONS 1048 D.2,6 CENTRAL. LIMIT THEOREMS 1050 D.2.7 THE DELTA
METHOD 1055 D.3 ASYMPTOTIC DISTRIBUTIONS 1056 D.3.1 ASYMPTOTIC
DISTRIBUTION OF A NONLINEAR FUNCTION 1058 D.3.2 ASYMPTOTIC EXPECTATIONS
1059 D.4 SEQUENCES AND THE ORDER OF A SEQUENCE 1060 APPENDIX E
COMPUTATION AND OPTIMIZATION 1061 E.I INTRODUCTION 1061 E.2 COMPUTATION
IN ECONOMETRICS 1062 E.2.1 COMPUTING INTEGRALS 1062 E22 THE STANDARD
NORMAL CUMULATIVE DISTRIBUTION FUNCTION 1062 E2.3 THE GAMMA AND RELATED
FUNCTIONS 1063 E.2.4 APPROXIMATING INTEGRALS BY QUADRATURE 1064 E.3
OPTIMIZATION 1065 E.3.1 ALGORITHMS 1067 E.3.2 COMPUTING DERIVATIVES 1068
E.3.3 GRADIENT METHODS 1069 E3A ASPECTS OF MAXIMUM LIKELIHOOD ESTIMATION
1072 E.3.5 OPTIMIZATION WITH CONSTRAINTS 1073 E.3.6 SOME PRACTICAL
CONSIDERATIONS 1074 E.3,7 THE EM ALGORITHM 1076 E.4 EXAMPLES 1078 E.4.1
FUNCTION OF ONE PARAMETER 1078 E.42 FUNCTION OF TWO PARAMETERS: THE
GAMMA DISTRIBUTION 1079 EA.3 A CONCENTRATED LOG-LIKELIHOOD FUNCTION 1080
APPENDIX F DATA SETS USED IN APPLICATIONS 1081 APPENDIX G STATISTICAL
TABLES 1093 REFERENCES 1099 AUTHOR INDEX 1147 SUBJECT INDEX 1154 PPN:
277426944 TITEL: ECONOMETRIC ANALYSIS / WILLIAM H. GREENE. - . - UPPER
SADDLE RIVER, N.J : PRENTICE HALL, 2008 ISBN: 978-0-13-513740-6;
0-13-513740-3 BIBLIOGRAPHISCHER DATENSATZ IM SWB-VERBUND
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CONTENTS EXAMPLES AND APPLICATIONS XXVI PREFACE XXXIII PART I THE LINEAR
REGRESSION MODEL CHAPTER 1 INTRODUCTION 1 1.1 ECONOMETRICS 1 1.2
ECONOMETRIC MODELING 2 1.3 METHODOLOGY 5 1.4 THE PRACTICE OF
ECONOMETRICS 6 1.5 PLAN OF THE BOOK 7 CHAPTER 2 THE CLASSICAL MULTIPLE
LINEAR REGRESSION MODEL 8 2.1 INTRODUCTION 8 2.2 THE LINEAR REGRESSION
MODEL 8 2.3 ASSUMPTIONS OF THE CLASSICAL LINEAR REGRESSION MODEL 11
2.3.1 LINEARITY OF THE REGRESSION MODEL 12 23.2 FULL RANK 14 2.3.3
REGRESSION 15 2.3.4 SPHERICAL DISTURBANCES 16 2.3.5 DATA GENERATING
PROCESS FOR THE REGRESSORS 17 2.3.6 NORMALITY 18 2.4 SUMMARY AND
CONCLUSIONS 19 CHAPTER 3 LEAST SQUARES 20 3.1 INTRODUCTION 20 3.2 LEAST
SQUARES REGRESSION 20 3.2.1 THE LEAST SQUARES COEFFICIENT VECTOR 21
3.2.2 APPLICATION: AN INVESTMENT EQUATION 22 3.2.3 ALGEBRAIC ASPECTS OF
THE LEAST SQUARES SOLUTION 25 3.2.4 PROJECTION 25 3.3 PARTITIONED
REGRESSION AND PARTIAL REGRESSION 27 3.4 PARTIAL REGRESSION AND PARTIAL
CORRELATION COEFFICIENTS 29 VII VIII CONTENTS 3.5 GOODNESS OF FIT AND
THE ANALYSIS OF VARIANCE 32 3.5.1 THE ADJUSTED R-SQUARED AND A MEASURE
OF FIT 35 3.5.2 R-SQUARED AND THE CONSTANT TERM IN THE MODEL 37 3.5.3
COMPARING MODELS 38 3.6 SUMMARY AND CONCLUSIONS 39 CHAPTER 4 STATISTICAL
PROPERTIES OF THE LEAST SQUARES ESTIMATOR 43 4.1 INTRODUCTION 43 4.2
MOTIVATING LEAST SQUARES 44 4.2.1 THE POPULATION ORTHOGONALITY
CONDITIONS 44 4.2.2 MINIMUM MEAN SQUARED ERROR PREDICTOR 45 4.2.3
MINIMUM VARIANCE LINEAR UNBIASED ESTIMATION 46 4.3 UNBIASED ESTIMATION
46 4.4 THE VARIANCE OF THE LEAST SQUARES ESTIMATOR AND THE GAUSS-MARKOV
THEOREM 48 4.5 THE IMPLICATIONS OF STOCHASTIC REGRESSORS 49 4.6
ESTIMATING THE VARIANCE OF THE LEAST SQUARES ESTIMATOR 51 4.7 THE
NORMALITY ASSUMPTION AND BASIC STATISTICAL INFERENCE 52 4.7.7 TESTING A
HYPOTHESIS ABOUT A COEFFICIENT 52 4.7.2 CONFIDENCE INTERVALS FOR
PARAMETERS 54 4.7.3 CONFIDENCE INTERVAL FOR A LINEAR COMBINATION OF
COEFFICIENTS: THE OAXACA DECOMPOSITION 55 4.7.4 TESTING THE SIGNIFICANCE
OF THE REGRESSION 56 4.7.5 MARGINAL DISTRIBUTIONS OF THE TEST STATISTICS
57 4.8 FINITE-SAMPLE PROPERTIES OF THE LEAST SQUARES ESTIMATOR 58 4.8.1
MULTICOLLINEARITY 59 4.8.2 MISSING OBSERVATIONS 61 4.9 LARGE SAMPLE
PROPERTIES OF THE LEAST SQUARES ESTIMATOR 63 4.9.1 CONSISTENCY OF THE
LEAST SQUARES ESTIMATOR OF J3 64 4.9.2 ASYMPTOTIC NORMALITY OF THE LEAST
SQUARES ESTIMATOR 65 4.9.3 CONSISTENCY OFS 2 AND THE ESTIMATOR OFASY.
VARFB] 67 4.9.4 ASYMPTOTIC DISTRIBUTION OF A FUNCTION OFB; THE DELTA
METHOD AND THE METHOD OFKRINSKY AND ROBB 68 4.9.5 ASYMPTOTIC EFFICIENCY
71 4.9.6 MORE GENERAL DATA GENERATING PROCESSES 72 4.10 SUMMARY AND
CONCLUSIONS 75 CHAPTER 5 INFERENCE AND PREDICTION 81 5.1 INTRODUCTION 81
5.2 RESTRICTIONS AND NESTED MODELS 81 5.3 TWO APPROACHES TO TESTING
HYPOTHESES 83 5.3.1 THE F STATISTIC AND THE LEAST SQUARES DISCREPANCY 83
5.3.2 THE RESTRICTED LEAST SQUARES ESTIMATOR 87 5.3.3 THE LOSS OF FIT
FROM RESTRICTED LEAST SQUARES 89 CONTENTS SX 5.4 NONNORMAL DISTURBANCES
AND LARGE SAMPLE TESTS 92 5.5 TESTING NONLINEAR RESTRICTIONS 96 5.6
PREDICTION 99 5.7 SUMMARY AND CONCLUSIONS 102 CHAPTER 6 FUNCTIONAL FORM
AND STRUCTURAL CHANGE 106 6.1 INTRODUCTION 106 6.2 USING BINARY
VARIABLES 1.06 6.2.1 BINARY VARIABLES IN REGRESSION 106 6.2.2 SEVERAL
CATEGORIES 107 6.2.3 SEVERAL GROUPINGS 108 6.2.4 THRESHOLD EFFECTS AND
CATEGORICAL VARIABLES 110 6.2.5 SPLINE REGRESSION 111 6.3 NONLINEARITY
IN THE VARIABLES 112 6.3.1 FUNCTIONAL FORMS 112 6.3.2 IDENTIFYING
NONLINEARITY 114 6.3.3 INTRINSIC LINEARITY AND IDENTIFICATION 117 6.4
MODELING AND TESTING FOR A STRUCTURAL BREAK 120 6.4.1 DIFFERENT
PARAMETER VECTORS 121 6.4.2 INSUFFICIENT OBSERVATIONS 121 6.4.3 CHANGE
IN A SUBSET OF COEFFICIENTS 122 6.4.4 TESTS OF STRUCTURAL BREAK WITH
UNEQUAL VARIANCES 123 6.4.5 PREDICTIVE TEST 127 6.5 SUMMARY AND
CONCLUSIONS 128 CHAPTER 7 SPECIFICATION ANALYSIS AND MODEL SELECTION 133
7.1 INTRODUCTION 133 7.2 SPECIFICATION ANALYSIS AND MODEL BUILDING 133
7.2.1 BIAS CAUSED BY OMISSION OF RELEVANT VARIABLES 133 7.2.2 PRETEST
ESTIMATION 134 7.2.3 INCLUSION OF IRRELEVANT VARIABLES 136 7.2.4 MODEL
BUILDING*A GENERAL TO SIMPLE STRATEGY 136 13 CHOOSING BETWEEN NONNESTED
MODELS 137 7.3.1 TESTING NONNESTED HYPOTHESES 138 7.3.2 AN ENCOMPASSING
MODEL 138 7.3.3 COMPREHENSIVE APPROACH * THE J TEST 139 7.3.4 VUONG'S
TEST AND THE KULLBACK-LEIBLER INFORMATION CRITERION 140 7.4 MODEL
SELECTION CRITERIA 142 7.5 MODEL SELECTION 143 7.5.1 CLASSICAL MODEL
SELECTION 144 7.5.2 BAYESIAN MODEL AVERAGING 144 7.6 SUMMARY AND
CONCLUSIONS 146 X CONTENTS PART II THE GENERALIZED REGRESSION MODEL
CHAPTER 8 THE GENERALIZED REGRESSION MODEL AND HETEROSCEDASTICITY 148
8.1 INTRODUCTION 148 8.2 LEAST SQUARES ESTIMATION 149 8.2.1
FINITE-SAMPLE PROPERTIES OF ORDINARY LEAST SQUARES 150 8.2.2 ASYMPTOTIC
PROPERTIES OF LEAST SQUARES 151 8.2.3 ROBUST ESTIMATION OF ASYMPTOTIC
COVARIANCE MATRICES 153 8.3 EFFICIENT ESTIMATION BY GENERALIZED LEAST
SQUARES 154 8.3.1 GENERALIZED LEAST SQUARES (GLS) 154 8.3.2 FEASIBLE
GENERALIZED LEAST SQUARES (FGLS) 156 8.4 HETEROSCEDASTICITY 158 8.4.1
ORDINARY LEAST SQUARES ESTIMATION 159 8.4.2 INEFFICIENCY OF LEAST
SQUARES 160 8.4.3 THE ESTIMATED COVARIANCE MATRIX OF B 160 8.4.4
ESTIMATING THE APPROPRIATE COVARIANCE MATRIX FOR ORDINARY LEAST SQUARES
162 8.5 TESTING FOR HETEROSCEDASTICITY 165 8.5.1 WHITE'S GENERAL TEST
165 8.5.2 THE BREUSCH-PAGAN/GODFREY LM TEST 166 8.6 WEIGHTED LEAST
SQUARES WHEN 2 IS KNOWN 167 8.7 ESTIMATION WHEN Q CONTAINS UNKNOWN
PARAMETERS 169 8.8 APPLICATIONS 170 8.8.1 MULTIPLICATIVE
HETEROSCEDASTICITY 170 8.8.2 GROUPWISE HETEROSCEDASTICITY 172 8.9
SUMMARY AND CONCLUSIONS 175 CHAPTER 9 MODELS FOR PANEL DATA 180 9.1
INTRODUCTION 180 9.2 PANEL DATA MODELS 180 9.2.1 GENERAL MODELING
FRAMEWORK FOR ANALYZING PANEL DATA 182 9.2.2 MODEL STRUCTURES 183 9.2.3
EXTENSIONS 184 9.2.4 BALANCED AND UNBALANCED PANELS 184 9.3 THE POOLED
REGRESSION MODEL 185 9.3.1 LEAST SQUARES ESTIMATION OF THE POOLED MODEL
185 9.3.2 ROBUST COVARIANCE MATRIX ESTIMATION 185 9.3.3 CLUSTERING AND
STRATIFICATION 188 9.3.4 ROBUST ESTIMATION USING GROUP MEANS 188 9.3.5
ESTIMATION WITH FIRST DIFFERENCES 190 9.3.6 THE WITHIN- AND
BETWEEN-GROUPS ESTIMATORS 191 9.4 THE FIXED EFFECTS MODEL 193 9.4.1
LEAST SQUARES ESTIMATION 194 9.4.2 SMALL TASYMPTOTICS 196 CONTENTS XI
9.4.3 TESTING THE SIGNIFICANCE OF THE GROUP EFFECTS 197 9.4.4 FIXED TIME
AND GROUP EFFECTS 197 9.5 RANDOM EFFECTS 200 9.5.1 GENERALIZED LEAST
SQUARES 202 9.5.2 FEASIBLE GENERALIZED LEAST SQUARES WHEN IS UNKNOWN
203 9.5.3 TESTING FOR RANDOM EFFECTS 205 9.5.4 HAUSMAN'S SPECIFICATION
TEST FOR THE RANDOM EFFECTS MODEL 208 9.5.5 EXTENDING THE UNOBSERVED
EFFECTS MODEL: MUNDLAK'S APPROACH 209 9.6 NONSPHERICAL DISTURBANCES AND
ROBUST COVARIANCE ESTIMATION 210 9.6.1 ROBUST ESTIMATION OF THE FIXED
EFFECTS MODEL 211 9.6.2 HETEROSCEDASTICITY IN THE RANDOM EFFECTS MODEL
212 9.6.3 AUTOCORRELATION IN PANEL DATA MODELS 213 9.7 EXTENSIONS OF THE
RANDOM EFFECTS MODEL 213 9 J.I NESTED RANDOM EFFECTS 214 9J.2 SPATIAL
AUTOCORRELATION 218 9.8 PARAMETER HETEROGENEITY 222 9.8.1 THE RANDOM
COEFFICIENTS MODEL 223 9.8.2 RANDOM PARAMETERS AND SIMULATION-BASED
ESTIMATION 226 9.8.3 TWO-STEP ESTIMATION OF PANEL DATA MODELS 229 9.8.4
HIERARCHICAL LINEAR MODELS 233 9.8.5 PARAMETER HETEROGENEITY AND DYNAMIC
PANEL DATA MODELS 238 9.8.6 NONSTATIONARY DATA AND PANEL DATA MODELS 243
9.9 CONSISTENT ESTIMATION OF DYNAMIC PANEL DATA MODELS 244 9.10 SUMMARY
AND CONCLUSIONS 246 CHAPTER 10 SYSTEMS OF REGRESSION EQUATIONS 252 10.1
INTRODUCTION 252 10.2 THE SEEMINGLY UNRELATED REGRESSIONS MODEL 254
10.2.1 GENERALIZED LEAST SQUARES 256 10.2.2 SEEMINGLY UNRELATED
REGRESSIONS WITH IDENTICAL REGRESSORS 257 10.2.3 FEASIBLE GENERALIZED
LEAST SQUARES 258 10.2.4 TESTING HYPOTHESES 259 10.2.5
HETEROSCEDASTICITY 263 10.2.6 AUTOCORRELATION 263 10.2.7 A SPECIFICATION
TEST FOR THE SW MODEL 264 10.2.8 THE POOLED MODEL 266 10.3 PANEL DATA
APPLICATIONS 267 10.3J RANDOM EFFECTS SUR MODELS 267 10.3.2 THE RANDOM
AND FIXED EFFECTS MODELS 268 XII CONTENTS 10.4 SYSTEMS OF DEMAND
EQUATIONS: SINGULAR SYSTEMS 272 10.4.1 COBB-DOUGLAS COST FUNCTION
(EXAMPLE 6.3 CONTINUED) 273 10.4.2 FLEXIBLE FUNCTIONAL FORMS: THE
TRANSLOG COST FUNCTION 275 10.5 SUMMARY AND CONCLUSIONS 280 CHAPTER 11
NONLINEAR REGRESSIONS AND NONLINEAR LEAST SQUARES 285 11.1 INTRODUCTION
285 11.2 NONLINEAR REGRESSION MODELS 285 11.2.1 ASSUMPTIONS OF THE
NONLINEAR REGRESSION MODEL 286 11.2.2 THE ORTHOGONALITY CONDITION AND
THE SUM OF SQUARES 287 11.2.3 THE LINEARIZED REGRESSION 288 11.2.4 LARGE
SAMPLE PROPERTIES OF THE NONLINEAR LEAST SQUARES ESTIMATOR 290 112.5
COMPUTING THE NONLINEAR LEAST SQUARES ESTIMATOR 292 11.3 APPLICATIONS
294 11.3.1 A NONLINEAR CONSUMPTION FUNCTION 294 11.3.2 THE BOX-COX
TRANSFORMATION 296 11.4 HYPOTHESIS TESTING AND PARAMETRIC RESTRICTIONS
298 11.4.1 SIGNIFICANCE TESTS FOR RESTRICTIONS: F AND WALD STATISTICS
298 11.4.2 TESTS BASED ON THE LM STATISTIC 299 11.5 NONLINEAR SYSTEMS OF
EQUATIONS 300 11.6 TWO-STEP NONLINEAR LEAST SQUARES ESTIMATION 302 11.7
PANEL DATA APPLICATIONS 307 11.7.1 A ROBUST COVARIANCE MATRIX FOR
NONLINEAR LEAST SQUARES 307 11.7.2 FIXED EFFECTS 308 11.7.3 RANDOM
EFFECTS 310 11.8 SUMMARY AND CONCLUSIONS 311 PART III INSTRUMENTAL
VARIABLES AND SIMULTANEOUS EQUATIONS MODELS CHAPTER 12 INSTRUMENTAL
VARIABLES ESTIMATION 314 12.1 INTRODUCTION 314 12.2 ASSUMPTIONS OF THE
MODEL 315 12.3 ESTIMATION 316 12.3.1 ORDINARY LEAST SQUARES 316 12.3.2
THE INSTRUMENTAL VARIABLES ESTIMATOR 316 12.3.3 TWO-STAGE LEAST SQUARES
318 12.4 THE HAUSMAN AND WU SPECIFICATION TESTS AND AN APPLICATION TO
INSTRUMENTAL VARIABLE ESTIMATION 321 12.5 MEASUREMENT ERROR 325 12.5.1
LEAST SQUARES ATTENUATION 325 12.5.2 INSTRUMENTAL VARIABLES ESTIMATION
327 12.5.3 PROXY VARIABLES 328 12.6 ESTIMATION OF THE GENERALIZED
REGRESSION MODEL 332 CONTENTS XIII 12.7 NONLINEAR INSTRUMENTAL VARIABLES
ESTIMATION 333 12.8 PANEL DATA APPLICATIONS 336 12.8.1 INSTRUMENTAL
VARIABLES ESTIMATION OF THE RANDOM EFFECTS MODEL* THE HAUSMAN AND TAYLOR
ESTIMATOR 336 12.82 DYNAMIC PANEL DATA MODELS*THE ANDERSON/HSIAO AND
ARELLANO/BOND ESTIMATORS 340 12.9 WEAK INSTRUMENTS 350 12.10 SUMMARY AND
CONCLUSIONS 352 CHAPTER 13 SIMULTANEOUS EQUATIONS MODELS 354 13.1
INTRODUCTION 354 13.2 FUNDAMENTAL ISSUES IN SIMULTANEOUS EQUATIONS
MODELS 354 13.2.1 ILLUSTRATIVE SYSTEMS OF EQUATIONS 354 1,322
ENDOGENEITY AND CAUSALITY 357 13.2.3 A GENERAL NOTATION FOR LINEAR
SIMULTANEOUS EQUATIONS MODELS 358 13.3 THE PROBLEM OF IDENTIFICATION 361
13.3.1 THE RANK AND ORDER CONDITIONS FOR IDENTIFICATION 365 13.3.2
IDENTIFICATION THROUGH OTHER NONSAMPLE INFORMATION 370 13.4 METHODS OF
ESTIMATION 370 13.5 SINGLE EQUATION: LIMITED INFORMATION ESTIMATION
METHODS 371 13.5.1 ORDINARY LEAST SQUARES 371 13.52 ESTIMATION BY
INSTRUMENTAL VARIABLES 372 13.5.3 TWO-STAGE LEAST SQUARES 373 13.5.4
LIMITED INFORMATION MAXIMUM LIKELIHOOD AND THE K CLASS OF ESTIMATORS 375
13.5.5 TESTING IN THE PRESENCE OF WEAK INSTRUMENTS 377 13.5.6 TWO-STAGE
LEAST SQUARES IN MODELS THAT ARE NONLINEAR IN VARIABLES 380 13.6 SYSTEM
METHODS OF ESTIMATION 380 13.6.1 THREE-STAGE LEAST SQUARES 381 13.6.2
FULL INFORMATION MAXIMUM LIKELIHOOD 383 13.7 COMPARISON OF
METHODS*KLEIN'S MODEL I 385 13.8 SPECIFICATION TESTS 387 13.9 PROPERTIES
OF DYNAMIC MODELS 389 13.9.1 DYNAMIC MODELS AND THEIR MULTIPLIERS 389
13.9.2 STABILITY 390 13.9.3 ADJUSTMENT TO EQUILIBRIUM 391 13.10 SUMMARY
AND CONCLUSIONS 394 PART IY ESTIMATION METHODOLOGY CHAPTER 14 ESTIMATION
FRAMEWORKS IN ECONOMETRICS 398 14.1 INTRODUCTION 398 XIV CONTENTS 14.2
PARAMETRIC ESTIMATION AND INFERENCE 400 14.2.1 CLASSICAL
LIKELIHOOD-BASED ESTIMATION 400 14.2.2 MODELING JOINT DISTRIBUTIONS WITH
COPULA FUNCTIONS 402 14.3 SEMIPARAMETRIC ESTIMATION 405 14.3.1 GMM
ESTIMATION IN ECONOMETRICS 406 14.3.2 LEAST ABSOLUTE DEVIATIONS
ESTIMATION 406 143.3 PARTIALLY LINEAR REGRESSION 409 14.3.4 KERNEL
DENSITY METHODS 411 14.3.5 COMPARING PARAMETRIC AND SEMIPARAMETRIC
ANALYSES 412 14.4 NONPARAMETRIC ESTIMATION 413 14.4.1 KERNEL DENSITY
ESTIMATION 414 14.4.2 NONPARAMETRIC REGRESSION 416 14.5 PROPERTIES OF
ESTIMATORS 420 14.5.1 STATISTICAL PROPERTIES OF ESTIMATORS 420 14.5.2
EXTREMUM ESTIMATORS 421 14.5.3 ASSUMPTIONS FOR ASYMPTOTIC PROPERTIES OF
EXTREMUM ESTIMATORS 421 14.5.4 ASYMPTOTIC PROPERTIES OF ESTIMATORS 424
14.5.5 TESTING HYPOTHESES 425 14.6 SUMMARY AND CONCLUSIONS 426 CHAPTER
15 MINIMUM DISTANCE ESTIMATION AND THE GENERALIZED METHOD OF MOMENTS 428
15.1 INTRODUCTION 428 15.2 CONSISTENT ESTIMATION: THE METHOD OF MOMENTS
429 15.2.1 RANDOM SAMPLING AND ESTIMATING THE PARAMETERS OF
DISTRIBUTIONS 430 15.2.2 ASYMP TOTIC PROPERTIES OF THE METHOD OF MOMENTS
ESTIMATOR 434 15.2.3 SUMMARY*THE METHOD OF MOMENTS 436 15.3 MINIMUM
DISTANCE ESTIMATION 436 15.4 THE GENERALIZED METHOD OF MOMENTS (GMM)
ESTIMATOR 441 15.4.1 ESTIMATION BASED ON ORTHOGONALITY CONDITIONS 442
15.4.2 GENERALIZING THE METHOD OF MOMENTS 443 15.4.3 PROPERTIES OF THE
GMM ESTIMATOR 447 15.5 TESTING HYPOTHESES IN THE GMM FRAMEWORK 451
15.5.1 TESTING THE VALIDITY OF THE MOMENT RESTRICTIONS 452 15.5.2 GMM
COUNTERPARTS TO THE WALD, LM, AND LR TESTS 453 15.6 GMM ESTIMATION OF
ECONOMETRIC MODELS 455 15.6.1 SINGLE-EQUATION LINEAR MODELS 455 15.6.2
SINGLE-EQUATION NONLINEAR MODELS 461 15.6.3 SEEMINGLY UNRELATED
REGRESSION MODELS 464 15.6.4 SIMULTANEOUS EQUATIONS MODELS WITH
HETEROSCEDASTICITY 466 15.6.5 GMM ESTIMATION OF DYNAMIC PANEL DATA
MODELS 469 15.7 SUMMARY AND CONCLUSIONS 480 CONTENTS XV CHAPTER 16
MAXIMUM LIKELIHOOD ESTIMATION 482 16.1 INTRODUCTION 482 16.2 THE
LIKELIHOOD FUNCTION AND IDENTIFICATION OF THE PARAMETERS 482 16.3
EFFICIENT ESTIMATION: THE PRINCIPLE OF MAXIMUM LIKELIHOOD 484 16.4
PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS 486 16.4.1 REGULARITY
CONDITIONS 487 16.4.2 PROPERTIES OF REGULAR DENSITIES 488 16.4.3 THE
LIKELIHOOD EQUATION 490 16.4.4 THE INFORMATION MATRIX EQUALITY 490
16.4.5 ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR 490
16,4.5.A CONSISTENCY 491 16,4.5.B ASYMPTOTIC NORMALITY 492 16.4.5.C
ASYMPTOTIC EFFICIENCY 493 16.4.5.D INVARIANCE 494 16.4.5.E CONCLUSION
494 16.4.6 ESTIMATING THE ASYMPTOTIC VARIANCE OF THE MAXIMUM LIKELIHOOD
ESTIMATOR 494 16.5 CONDITIONAL LIKELIHOODS, ECONOMETRIC MODELS, AND THE
GMM ESTIMATOR 496 16.6 HYPOTHESIS AND SPECIFICATION TESTS AND FIT
MEASURES 498 16.6.1 THE LIKELIHOOD RATIO TEST 498 16.6.2 THE WALD TEST
500 16.6.3 THE LAGRANGE MULTIPLIER TEST 502 16.6.4 AN APPLICATION OF THE
LIKELIHOOD-BASED TEST PROCEDURES 504 16.6.5 COMPARING MODELS AND
COMPUTING MODEL FIT 506 16.7 TWO-STEP MAXIMUM LIKELIHOOD ESTIMATION 507
16.8 PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION AND ROBUST ASYMPTOTIC
COVARIANCE MATRICES 511 16.8.1 MAXIMUM LIKELIHOOD AND GMM ESTIMATION 512
16.8.2 MAXIMUM LIKELIHOOD AND M ESTIMATION 512 16.8.3 SANDWICH
ESTIMATORS 514 16.8A CLUSTER ESTIMATORS 515 16.9 APPLICATIONS OF MAXIMUM
LIKELIHOOD ESTIMATION 517 16.9.1 THE NORMAL LINEAR REGRESSION MODEL 518
16.9.2 THE GENERALIZED REGRESSION MODEL 522 16.9.2,A MULTIPLICATIVE
HETEROSCEDASTICITY 523 16.9.2.B AUTOCORRELATION 527 16.9.3 SEEMINGLY
UNRELATED REGRESSION MODELS 529 16.9.3.A THE POOLED MODEL 530 16.9.3.B
THE SUR MODEL 531 16.9.3.C EXCLUSION RESTRICTIONS 532 XVI CONTENTS
16.9.4 SIMULTANEOUS EQUATIONS MODELS 536 16.9.5 MAXIMUM LIKELIHOOD
ESTIMATION OF NONLINEAR REGRESSION MODELS 537 16.9.5.A NONNORMAL
DISTURBANCES* THE STOCHASTIC FRONTIER MODEL 538 16.9.5. B ML ESTIMATION
OF A GEOMETRIC REGRESSION MODEL FOR COUNT DATA 542 16.9.6 PANEL DATA
APPLICATIONS 547 16.9.6.A ML ESTIMATION OF THE LINEAR RANDOM EFFECTS
MODEL 547 16.9.6. B RANDOM EFFECTS IN NONLINEAR MODELS: MLE USING
QUADRATURE 550 16.9.6.C FIXED EFFECTS IN NONLINEAR MODELS: FULL MLE 554
16.9.7 LATENT CLASS AND FINITE MIXTURE MODELS 558 16.9.7.A A FINITE
MIXTURE MODEL 559 16.9.7.B MEASURED AND UNMEASURED HETEROGENEITY 560
16.9.7. C PREDICTING CLASS MEMBERSHIP 561 16.9. 7. D A CONDITIONAL
LATENT CLASS MODEL 561 16.9.7. E DETERMINING THE NUMBER OF CLASSES 564
16.9.7.F A PANEL DATA APPLICATION 564 16.10 SUMMARY AND CONCLUSIONS 567
CHAPTER 17 SIMULATION-BASED ESTIMATION AND INFERENCE 573 17.1
INTRODUCTION 573 17.2 RANDOM NUMBER GENERATION 573 17.2.1 GENERATING
PSEUDO-RANDOM NUMBERS 574 17.2.2 SAMPLING FROM A STANDARD UNIFORM
POPULATION 575 17.2.3 SAMPLING FROM CONTINUOUS DISTRIBUTIONS 575 17.2.4
SAMPLING FROM A MULTIVARIATE NORMAL POPULATION 576 17.2.5 SAMPLING FROM
A DISCRETE POPULATION 576 17.3 MONTE CARLO INTEGRATION 576 17.3.1 HALTON
SEQUENCES AND RANDOM DRAWS FOR SIMULATION-BASED INTEGRATION 577 17.3.2
IMPORTANCE SAMPLING 580 173.3 COMPUTING MULTIVARIATE NORMAL
PROBABILITIES USING THE GHK SIMULATOR 582 17.4 MONTE CARLO STUDIES 584
17.4.1 A MONTE CARLO STUDY: BEHAVIOR OF A TEST STATISTIC 585 17.4.2 A
MONTE CARLO STUDY: THE INCIDENTAL PARAMETERS PROBLEM 586 17.5
SIMULATION-BASED ESTIMATION 589 17.5.1 MAXIMUM SIMULATED LIKELIHOOD
ESTIMATION OF RANDOM PARAMETERS MODELS 590 17.5.2 THE METHOD OF
SIMULATED MOMENTS 595 17.6 BOOTSTRAPPING 596 17.7 SUMMARY AND
CONCLUSIONS 598 CONTENTS XVII CHAPTER 18 BAYESIAN ESTIMATION AND
INFERENCE 600 18.1 INTRODUCTION 600 18.2 BAYES THEOREM AND THE POSTERIOR
DENSITY 601 18.3 BAYESIAN ANALYSIS OF THE CLASSICAL REGRESSION MODEL 603
18.3.1 ANALYSIS WITH A NONINFORMATIVE PRIOR 604 18.3.2 ESTIMATION WITH
AN INFORMATIVE PRIOR DENSITY 606 18.4 BAYESIAN INFERENCE 609 18.4.1
POINT ESTIMATION 609 18.4.2 INTERVAL ESTIMATION 610 18.4.3 HYPOTHESIS
TESTING 611 18.4.4 LARGE SAMPLE RESULTS 613 18.5 POSTERIOR DISTRIBUTIONS
AND THE GIBBS SAMPLER 613 18.6 APPLICATION: BINOMIAL PROBIT MODEL 616
18.7 PANEL DATA APPLICATION: INDIVIDUAL EFFECTS MODELS 619 18.8
HIERARCHICAL BAYES ESTIMATION OF A RANDOM PARAMETERS MODEL 621 18.9
SUMMARY AND CONCLUSIONS 623 PART V TIME SERIES AND MACROECONOMETRICS
CHAPTER 19 SERIAL CORRELATION 626 19.1 INTRODUCTION 626 19.2 THE
ANALYSIS OF TIME-SERIES DATA 629 19.3 DISTURBANCE PROCESSES 632 19.3.1
CHARACTERISTICS OF DISTURBANCE PROCESSES 632 19.3.2 AR(1) DISTURBANCES
633 19.4 SOME ASYMPTOTIC RESULTS FOR ANALYZING TIME-SERIES DATA 635
19.4.1 CONVERGENCE OF MOMENTS*THE ERGODIC THEOREM 636 19.4.2 CONVERGENCE
TO NORMALITY*A CENTRAL LIMIT THEOREM 638 19.5 LEAST SQUARES ESTIMATION
640 79.5.1 ASYMPTOTIC PROPERTIES OF LEAST SQUARES 640 19.5.2 ESTIMATING
THE VARIANCE OF THE LEAST SQUARES ESTIMATOR 642 19.6 GMM ESTIMATION 643
19.7 TESTING FOR AUTOCORRELATION 644 19.7.1 LAGRANGE MULTIPLIER TEST 644
19.7.2 BOX AND PIERCE'S TEST AND LJUNG'S REFINEMENT 645 19.7.3 THE
DURBIN-WATSON TEST 645 19.7.4 TESTING IN THE PRESENCE OF A LAGGED
DEPENDENT VARIABLE 646 19.7.5 SUMMARY OF TESTING PROCEDURES 646 19.8
EFFICIENT ESTIMATION WHEN 9, IS KNOWN 647 19.9 ESTIMATION WHEN FT IS
UNKNOWN 648 19.9.1 AR(1) DISTURBANCES 648 19.9.2 APPLICATION: ESTIMATION
OF A MODEL WITH AUTOCORRELATION 649 19.9.3 ESTIMATION WITH A LAGGED
DEPENDENT VARIABLE 651 19.10 AUTOCORRELATION IN PANEL DATA 652 XVIII
CONTENTS 19.11 COMMON FACTORS 655 1912 FORECASTING IN THE PRESENCE OF
AUTOCORRELATION 656 19.13 AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY
658 19.13.1 THE ARCH(L) MODEL 659 19.13.2 ARCH (Q), ARCH-IN-MEAN, AND
GENERALIZED ARCH MODELS 660 19.13.3 MAXIMUM LIKELIHOOD ESTIMATION OF THE
GARCH MODEL 662 19.13.4 TESTING FOR GARCH EFFECTS 664 19.13.5
PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION 666 19.14 SUMMARY AND CONCLUSIONS
667 CHAPTER 20 MODELS WITH LAGGED VARIABLES 670 20.1 INTRODUCTION 670
20.2 DYNAMIC REGRESSION MODELS 671 20.2.1 LAGGED EFFECTS IN A DYNAMIC
MODEL 672 20.2.2 THE LAG AND DIFFERENCE OPERATORS 674 20.2.3
SPECIFICATION SEARCH FOR THE LAG LENGTH 676 20.3 SIMPLE DISTRIBUTED LAG
MODELS 677 20.4 AUTOREGRESSIVE DISTRIBUTED LAG MODELS 681 20.4.1
ESTIMATION OF THE ARDL MODEL 682 20.4.2 COMPUTATION OF THE LAG WEIGHTS
IN THE ARDL MODEL 683 20.4.3 STABILITY OF A DYNAMIC EQUATION 684 20.4.4
FORECASTING 686 20.5 METHODOLOGICAL ISSUES IN THE ANALYSIS OF DYNAMIC
MODELS 689 20.5.1 AN ERROR CORRECTION MODEL 689 20.5.2 AUTOCORRELATION
691 20.5.3 SPECIFICATION ANALYSIS 692 20.6 VECTOR AUTOREGRESSIONS 693
20.6.1 MODEL FORMS 695 20.6.2 ESTIMATION 696 20.6.3 TESTING PROCEDURES
696 20.6.4 EXOGENEITY 698 20.6.5 TESTING FOR GRANGER CAUSALITY 699
20.6.6 IMPULSE RESPONSE FUNCTIONS 701 20.6.7 STRUCTURAL VARS 702 20.6.8
APPLICATION: POLICY ANALYSIS WITH A VAR 703 20.6.8. A A VAR MODEL FOR
THE MACROECONOMIC VARIABLES 703 20.6.8.B THE SACRIFICE RATIO 704
20.6.8.C IDENTIFICATION AND ESTIMATION OF A STRUCTURAL VAR MODEL 704
20,6.8.D INFERENCE 707 20.6.8.E EMPIRICAL RESULTS 707 20.6.9 VARS IN
MICROECONOMICS 711 20.7 SUMMARY AND CONCLUSIONS 712 CONTENTS XIX CHAPTER
21 TIME-SERIES MODELS 715 21.1 INTRODUCTION 715 21.2 STATIONARY
STOCHASTIC PROCESSES 716 21.2.1 AUTO REGRESSIVE MOVING-AVERAGE PROCESSES
716 21.2.2 STATIONARITY AND INVERTIBILITY 718 21.23 AUTOCORRELATIONS OF
A STATIONARY STOCHASTIC PROCESS 721 21.2.4 PARTIAL AUTOCORRELATIONS OF A
STATIONARY STOCHASTIC PROCESS 723 21.2.5 MODELING UNIVARIATE TIME SERIES
726 21.2.6 ESTIMATION OF THE PARAMETERS OF A UNIVARIATE TIME SERIES 728
21.3 THE FREQUENCY DOMAIN 731 21.3.1 THEORETICAL RESULTS 732 21.3.2
EMPIRICAL COUNTERPARTS 734 21.4 SUMMARY AND CONCLUSIONS 738 CHAPTER 22
NONSTATIONARY DATA 739 22.1 INTRODUCTION 739 22.2 NONSTATIONARY
PROCESSES AND UNIT ROOTS 739 22.2.1 INTEGRATED PROCESSES AND
DIFFERENCING 739 22.2.2 RANDOM WALKS, TRENDS, AND SPURIOUS REGRESSIONS
741 22.2.3 TESTS FOR UNIT ROOTS IN ECONOMIC DATA 744 22.2.4 THE
DICKEY-FULLER TESTS 745 22.2.5 THE KPSS TEST OF STATIONARITY 755 22.3
COINTEGRATION 756 22.3.1 COMMON TRENDS 759 22.3.2 ERROR CORRECTION AND
VAR REPRESENTATIONS 760 22.3.3 TESTING FOR COINTEGRATION 761 22.3.4
ESTIMATING COINTEGRATION RELATIONSHIPS 764 22.3.5 APPLICATION: GERMAN
MONEY DEMAND 764 22,3.5,A COINTEGRATION ANALYSIS AND A LONG-RUN
THEORETICAL MODEL 765 22.3.5, B TESTING FOR MODEL INSTABILITY 766 22.4
NONSTATIONARY PANEL DATA 767 22.5 SUMMARY AND CONCLUSIONS 768 PART VI
CROSS SECTIONS, PANEL DATA, AND MICROECONOMETRICS CHAPTER 23 MODELS TOT
DISCRETE CHOICE 770 23.1 INTRODUCTION 770 23.2 DISCRETE CHOICE MODELS
770 23.3 MODELS FOR BINARY CHOICE 772 23.3.1 THE REGRESSION APPROACH 772
23.3.2 LATENT REGRESSION*INDEX FUNCTION MODELS 775 23.3.3 RANDOM UTILITY
MODELS 777 XX CONTENTS 23.4 ESTIMATION AND INFERENCE IN BINARY CHOICE
MODELS 777 23.4.1 ROBUST COVARIANCE MATRIX ESTIMATION 780 23.4.2
MARGINAL EFFECTS AND AVERAGE PARTIAL EFFECTS 780 23.4.3 HYPOTHESIS TESTS
785 23.4.4 SPECIFICATION TESTS FOR BINARY CHOICE MODELS 787 23.4.4.A
OMITTED VARIABLES 788 23.4.4.B HETEROSCEDASTICITY 788 23.4.5 MEASURING
GOODNESS OF FIT 790 23.4.6 CHOICE-BASED SAMPLING 793 23.4.7 DYNAMIC
BINARY CHOICE MODELS 794 23.5 BINARY CHOICE MODELS FOR PANEL DATA 796
23.5.1 RANDOM EFFECTS MODELS 797 23.5.2 FIXED EFFECTS MODELS 800 23.5.3
MODELING HETEROGENEITY 806 23.5.4 PARAMETER HETEROGENEITY 807 23.6
SEMIPARAMETRIC ANALYSIS 809 23.6.1 SEMIPARAMETRIC ESTIMATION 810 23.6.2
A KERNEL ESTIMATOR FOR A NONPARAMETRIC REGRESSION FUNCTION 812 23.7
ENDOGENOUS RIGHT-HAND-SIDE VARIABLES IN BINARY CHOICE MODELS 813 23.8
BIVARIATE PROBIT MODELS 817 23.8.1 MAXIMUM LIKELIHOOD ESTIMATION 817
23.8.2 TESTING FOR ZERO CORRELATION 820 23.8.3 MARGINAL EFFECTS 821
23.8.4 RECURSIVE BIVARIATE PROBIT MODELS 823 23.9 A MULTIVARIATE PROBIT
MODEL 826 23.10 ANALYSIS OF ORDERED CHOICES 831 23.10.1 THE ORDERED
PROBIT MODEL 831 23.10.2 BIVARIATE ORDERED PROBIT MODELS 835 23.10.3
PANEL DATA APPLICATIONS 837 23,10.3.A ORDERED PROBIT MODELS WITH FIXED
EFFECTS 837 23.10.3. B ORDERED PROBIT MODELS WITH RANDOM EFFECTS 838
23.11 MODELS FOR UNORDERED MULTIPLE CHOICES 841 23.11.1 THE MULTINOMIAL
LOGIT MODEL 843 23.11.2 THE CONDITIONAL LOGIT MODEL 846 23.11.3 THE
INDEPENDENCE FROM IRRELEVANT ALTERNATIVES ASSUMPTION 847 23.11.4 NESTED
LOGIT MODELS 847 23.11.5 THE MULTINOMIAL PROBIT MODEL 850 23.11.6 THE
MIXED LOGIT MODEL 851 23.11.7 APPLICATION: CONDITIONAL LOGIT MODEL FOR
TRAVEL MODE CHOICE 852 23.11.8 PANEL DATA AND STATED CHOICE EXPERIMENTS
858 23.12 SUMMARY AND CONCLUSIONS 859 CONTENTS XXL CHAPTER 24
TRUNCATION, CENSORING, AND SAMPLE SELECTION 863 24.1 INTRODUCTION 863
24.2 TRUNCATION 863 24.2.1 TRUNCATED DISTRIBUTIONS 863 24.2.2 MOMENTS OF
TRUNCATED DISTRIBUTIONS 864 24.2.3 THE TRUNCATED REGRESSION MODEL 867
24.3 CENSORED DATA 869 24.3.1 THE CENSORED NORMAL DISTRIBUTION 869 2432
THE CENSORED REGRESSION (TOBIT) MODEL 871 24.3.3 ESTIMATION 874 24.3.4
SOME ISSUES IN SPECIFICATION 875 24.3.4. A HETEROSCEDASTICITY 875 24.3
AB MISSPECIFICATIONOFPROH[Y* 0] 877 24.3.4.C CORNER SOLUTIONS 878
24.3A.D NONNORMALIIY 880 24.4 PANEL DATA APPLICATIONS 881 24.5 SAMPLE
SELECTION 882 24.5.1 INCIDENTAL TRUNCATION IN A BIVARIATE DISTRIBUTION
883 24.5.2 REGRESSION IN A MODEL OF SELECTION 884 24,53 ESTIMATION 886
24.5.4 REGRESSION ANALYSIS OF TREATMENT EFFECTS 889 24.5.5 THE NORMALITY
ASSUMPTION 891 24.5.6 ESTIMATING THE EFFECT OF TREATMENT ON THE TREATED
891 24.5.7 SAMPLE SELECTION IN NONLINEAR MODELS 895 24.5.8 PANEL DATA
APPLICATIONS OF SAMPLE SELECTION MODELS 898 24,5.8.A COMMON EFFECTS IN
SAMPLE SELECTION MODELS 899 24.5 AB ATTRITION 901 24.6 SUMMARY AND
CONCLUSIONS 903 CHAPTER 25 MODELS FOR EVENT COUNTS AND DURATION 906 25.1
INTRODUCTION 906 25.2 MODELS FOR COUNTS OF EVENTS 907 25.2.1 MEASURING
GOODNESS OF FIT 908 25.2.2 TESTING FOR OVERDISPERSION 909 25.2.3
HETEROGENEITY AND THE NEGATIVE BINOMIAL REGRESSION MODEL 911 25.2A
FUNCTIONAL FORMS FOR COUNT DATA MODELS 912 25.3 PANEL DATA MODELS 915
253.1 ROBUST COVARIANCE MATRICES 915 25.3.2 FIXED EFFECTS 916 253.3
RANDOM EFFECTS 918 25.4 HURDLE AND ZERO-ALTERED POISSON MODELS 922 XXII
CONTENTS 25.5 CENSORING AND TRUNCATION IN MODELS FOR COUNTS 924 25.5.1
CENSORING AND TRUNCATION IN THE POISSON MODEL 925 25.5.2 APPLICATION:
CENSORING IN THE TOBIT AND POISSON REGRESSION MODELS 925 25.6 MODELS FOR
DURATION DATA 931 25.6.1 DURATION DATA 932 25.6.2 A REGRESSION-LIKE
APPROACH: PARAMETRIC MODELS OF DURATION 933 25.6,2.A THEORETICAL
BACKGROUND 933 25.62. H MODELS OF THE HAZARD FUNCTION 934 25.6.2.C
MAXIMUM LIKELIHOOD ESTIMATION 936 25.6.2J EXOGENOUS VARIABLES 937
25.6.2.E HETEROGENEITY 938 25.6.3 NONPARAMETRIC AND SEMIPARAMETRIC
APPROACHES 939 25.7 SUMMARY AND CONCLUSIONS 942 PART VII APPENDICES
APPENDIX A MATRIX ALGEBRA 945 A.I TERMINOLOGY 945 A.2 ALGEBRAIC
MANIPULATION OF MATRICES 945 A.2.1 EQUALITY OF MATRICES 945 A.2.2
TRANSPOSITION 946 A2.3 MATRIX ADDITION 946 A.2.4 VECTOR MULTIPLICATION
947 A2.5 A NOTATION FOR ROWS AND COLUMNS OF A MATRIX 947 A2.6 MATRIX
MULTIPLICATION AND SCALAR MULTIPLICATION 947 A.2.7 SUMS OF VALUES 949
A2.8 A USEFUL IDEMPOTENT MATRIX 950 A.3 GEOMETRY OF MATRICES 951 A.3.1
VECTOR SPACES 951 A.3.2 LINEAR COMBINATIONS OF VECTORS ARID BASIS
VECTORS 953 A.3.3 LINEAR DEPENDENCE 954 A.3.4 SUBSPACES 955 A3.5 RANK OF
A MATRIX 956 A.3.6 DETERMINANT OF A MATRIX 958 A3.7 A LEAST SQUARES
PROBLEM 959 A.4 SOLUTION OF A SYSTEM OF LINEAR EQUATIONS 961 AA.L
SYSTEMS OF LINEAR EQUATIONS 961 A.4.2 INVERSE MATRICES 962 AA.3
NONHOMOGENEOUS SYSTEMS OF EQUATIONS 964 AA.4 SOLVING THE LEAST SQUARES
PROBLEM 964 A.5 PARTITIONED MATRICES 964 A.5.1 ADDITION AND
MULTIPLICATION OF PARTITIONED MATRICES 965 A.52 DETERMINANTS OF
PARTITIONED MATRICES 965 CONTENTS XXIII A.5.3 INVERSES OF PARTITIONED
MATRICES 965 A.5.4 DEVIATIONS FROM MEANS 966 A.5.5 KRONECKER PRODUCTS
966 A.6 CHARACTERISTIC ROOTS AND VECTORS 967 A.6.1 THE CHARACTERISTIC
EQUATION 967 A.6.2 CHARACTERISTIC VECTORS 968 A.6.3 GENERAL RESULTS FOR
CHARACTERISTIC ROOTS AND VECTORS 968 A.6,4 DIAGONALIZATION AND SPECTRAL
DECOMPOSITION OF A MATRIX 969 A.6.5 RANK OF A MATRIX 969 A.6.6 CONDITION
NUMBER OF A MATRIX 971 A, 6.7 TRACE OF A MATRIX 9 71 A.6.8 DETERMINANT
OF A MATRIX 972 A.6.9 POWERS OF A MATRIX 972 A.6.10 IDEMPOTENT MATRICES
974 A.6,11 FACTORING A MATRIX 974 A.6,12 THE GENERALIZED INVERSE OF A
MATRIX 975 A.I QUADRATIC FORMS AND DEFINITE MATRICES 976 A J.I
NONNEGATIVE DEFINITE MATRICES 977 A.7.2 IDEMPOTENT QUADRATIC FORMS 978
A.7.3 COMPARING MATRICES 978 A.8 CALCULUS AND MATRIX ALGEBRA 979 A.8.1
DIFFERENTIATION AND THE TAYLOR SERIES 979 A.8.2 OPTIMIZATION 982 A.8.3
CONSTRAINED OPTIMIZATION 984 A.8A TRANSFORMATIONS 986 APPENDIX B
PROBABILITY AND DISTRIBUTION THEORY 987 B.I INTRODUCTION 987 B.2 RANDOM
VARIABLES 987 B.2.1 PROBABILITY DISTRIBUTIONS 987 B.2.2 CUMULATIVE
DISTRIBUTION FUNCTION 988 B.3 EXPECTATIONS OF A RANDOM VARIABLE 989 B.4
SOME SPECIFIC PROBABILITY DISTRIBUTIONS 991 B.4,1 THE NORMAL
DISTRIBUTION 991 B.4.2 THE CHI-SQUARED, T, AND FDISTRIBUTIONS 993 B.4.3
DISTRIBUTIONS WITH LARGE DEGREES OF FREEDOM 995 BAA SIZE DISTRIBUTIONS:
THE LOGNORMAL DISTRIBUTION 996 B.4.5 THE GAMMA AND EXPONENTIAL
DISTRIBUTIONS 996 BA.6 THE BETA DISTRIBUTION 997 BA.7 THE LOGISTIC
DISTRIBUTION 997 BA,8 THE WISHART DISTRIBUTION 997 BA.9 DISCRETE RANDOM
VARIABLES 998 B.5 THE DISTRIBUTION OF A FUNCTION OF A RANDOM VARIABLE
998 XXIV CONTENTS B,6 REPRESENTATIONS OF A PROBABILITY DISTRIBUTION 1000
B.7 JOINT DISTRIBUTIONS 1002 B. 7,1 MARGINAL D ISTRIB UTIONS 1002 B.7.2
EXPECTATIONS IN A JOINT DISTRIBUTION 1003 B.7.3 COVARIANCE AND
CORRELATION 1003 B.7 A DISTRIBUTION OF A FUNCTION OF BIVARIATE RANDOM
VARIABLES 1004 B.8 CONDITIONING IN A BIVARIATE DISTRIBUTION 1006 B.8.1
REGRESSION: THE CONDITIONAL MEAN 1006 B.8.2 CONDITIONAL VARIANCE 1007
B.8.3 RELATIONSHIPS AMONG MARGINAL AND CONDITIONAL MOMENTS 1007 B.8.4
THE ANALYSIS OF VARIANCE 1009 B.9 THE BIVARIATE NORMAL DISTRIBUTION 1009
B.10 MULTIVARIATE DISTRIBUTIONS 1010 B.10.1 MOMENTS 1010 B.10.2 SETS OF
LINEAR FUNCTIONS 1011 B.10.3 NONLINEAR FUNCTIONS 1012 B.LL THE
MULTIVARIATE NORMAL DISTRIBUTION 1013 B.LL.L MARGINAL AND CONDITIONAL
NORMAL DISTRIBUTIONS 1013 B.LL.2 THE CLASSICAL NORMAL LINEAR REGRESSION
MODEL 1014 B.LL.3 LINEAR FUNCTIONS OF A NORMAL VECTOR 1015 B.LL A
QUADRATIC FORMS IN A STANDARD NORMAL VECTOR 1015 B.H.5 THE F
DISTRIBUTION 1017 B.I 1.6 A FULL RANK QUADRATIC FORM 1017 B.I 1.7
INDEPENDENCE OF A LINEAR AND A QUADRATIC FORM 1018 APPENDIX C ESTIMATION
AND INFERENCE 1019 C.1 INTRODUCTION 1019 C.2 SAMPLES AND RANDOM SAMPLING
1020 C.3 DESCRIPTIVE STATISTICS 1020 C.4 STATISTICS AS
ESTIMATORS*SAMPLING DISTRIBUTIONS 1023 C.5 POINT ESTIMATION OF
PARAMETERS 1027 C.5.1 ESTIMATION IN A FINITE SAMPLE 1027 C.5.2 EFFICIENT
UNBIASED ESTIMATION 1030 C.6 INTERVAL ESTIMATION 1032 C.7 HYPOTHESIS
TESTING 1034 C.7.1 CLASSICAL TESTING PROCEDURES 1034 C.7.2 TESTS BASED
ON CONFIDENCE INTERVALS 1037 C7.3 SPECIFICATION TESTS 1038 APPENDIX D
LARGE-SAMPLE DISTRIBUTION THEORY 1038 D.I INTRODUCTION 1038 CONTENTS XXV
D.2 LARGE-SAMPLE DISTRIBUTION THEORY 1039 D.2.1 CONVERGENCE IN
PROBABILITY 1039 D. 22 OTHER FORMS OF CONVERGENCE AND LAWS OF LARGE
NUMBERS 1042 D.2.3 CONVERGENCE OF FUNCTIONS 1045 D.2 A CONVERGENCE TO A
RANDOM VARIABLE 1046 D.2.5 CONVERGENCE IN DISTRIBUTION: LIMITING
DISTRIBUTIONS 1048 D.2,6 CENTRAL. LIMIT THEOREMS 1050 D.2.7 THE DELTA
METHOD 1055 D.3 ASYMPTOTIC DISTRIBUTIONS 1056 D.3.1 ASYMPTOTIC
DISTRIBUTION OF A NONLINEAR FUNCTION 1058 D.3.2 ASYMPTOTIC EXPECTATIONS
1059 D.4 SEQUENCES AND THE ORDER OF A SEQUENCE 1060 APPENDIX E
COMPUTATION AND OPTIMIZATION 1061 E.I INTRODUCTION 1061 E.2 COMPUTATION
IN ECONOMETRICS 1062 E.2.1 COMPUTING INTEGRALS 1062 E22 THE STANDARD
NORMAL CUMULATIVE DISTRIBUTION FUNCTION 1062 E2.3 THE GAMMA AND RELATED
FUNCTIONS 1063 E.2.4 APPROXIMATING INTEGRALS BY QUADRATURE 1064 E.3
OPTIMIZATION 1065 E.3.1 ALGORITHMS 1067 E.3.2 COMPUTING DERIVATIVES 1068
E.3.3 GRADIENT METHODS 1069 E3A ASPECTS OF MAXIMUM LIKELIHOOD ESTIMATION
1072 E.3.5 OPTIMIZATION WITH CONSTRAINTS 1073 E.3.6 SOME PRACTICAL
CONSIDERATIONS 1074 E.3,7 THE EM ALGORITHM 1076 E.4 EXAMPLES 1078 E.4.1
FUNCTION OF ONE PARAMETER 1078 E.42 FUNCTION OF TWO PARAMETERS: THE
GAMMA DISTRIBUTION 1079 EA.3 A CONCENTRATED LOG-LIKELIHOOD FUNCTION 1080
APPENDIX F DATA SETS USED IN APPLICATIONS 1081 APPENDIX G STATISTICAL
TABLES 1093 REFERENCES 1099 AUTHOR INDEX 1147 SUBJECT INDEX 1154 PPN:
277426944 TITEL: ECONOMETRIC ANALYSIS / WILLIAM H. GREENE. - . - UPPER
SADDLE RIVER, N.J : PRENTICE HALL, 2008 ISBN: 978-0-13-513740-6;
0-13-513740-3 BIBLIOGRAPHISCHER DATENSATZ IM SWB-VERBUND |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 6. ed., internat. ed. |
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| isbn | 9780135137406 0135137403 |
| language | English |
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| spelling | Greene, William 1951- Verfasser (DE-588)124700551 aut Econometric analysis William H. Greene 6. ed., internat. ed. Upper Saddle River, NJ Pearson/Prentice Hall 2008 XXXVII, 1178 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 1099 - 1146 Econometrie gtt Econometrics Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Ökonometrie (DE-588)4132280-0 s DE-604 Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016328298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Greene, William 1951- Econometric analysis Econometrie gtt Econometrics Mathematische Methode (DE-588)4155620-3 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4132280-0 (DE-588)4123623-3 |
| title | Econometric analysis |
| title_auth | Econometric analysis |
| title_exact_search | Econometric analysis |
| title_exact_search_txtP | Econometric analysis |
| title_full | Econometric analysis William H. Greene |
| title_fullStr | Econometric analysis William H. Greene |
| title_full_unstemmed | Econometric analysis William H. Greene |
| title_short | Econometric analysis |
| title_sort | econometric analysis |
| topic | Econometrie gtt Econometrics Mathematische Methode (DE-588)4155620-3 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Econometrie Econometrics Mathematische Methode Ökonometrie Lehrbuch |
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