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Bibliographic Details
Main Authors:	Mittelhammer, Ron C. (Author), Judge, George G. 1925- (Author), Miller, Douglas J. 1965- (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2000
Edition:	1. publ.
Subjects:	Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie Lehrbuch
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009035062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XXVIII, 756 S. graph. Darst. 1 CD-ROM (12 cm)
ISBN:	0521623944

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245	1	0	\|a Econometric foundations \|c Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller
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adam_text	Contents Preface xxv I Information Processing and Recovery 1 1 The Process of Econometric Information Recovery 3 1.1 Introduction 4 1.2 The Nature of Economic Data 4 1.3 The Probability Approach to Economics 5 1.4 The Process of Searching for Quantitative Economic Knowledge 6 1.4.1 Econometric Model Components 6 1.4.2 Econometric Analysis 8 1.5 The Inverse Problem 9 1.6 A Comment 10 1.7 Notation 10 1.8 Idea Checklist - Knowledge Guides 12 2 Probability-Econometric Models 13 2.1 Parametric, Semiparametric, and Nonparametric Models 14 2.1.1 Parametric Models 14 2.1.2 Nonparametric and Semiparametric Models 15 2.2 The Classical Linear Regression Model 17 2.2.1 Establishing a Linkage between Dependent and Explanatory Variables 17 2.2.2 The Distribution of Y around the Systematic Component 20 2.23 Inverse Problems: Estimation, Inference, and Interpretation 21 2.2.4 Some Variants of the Linear Regression Model 22 2.3 A Class of Probability Models 26 2.4 Class of Inverse Problems and Solutions 28 2.5 Concluding Comments 29 vii CONTENTS 2.6 Exercises 30 2.6.1 Idea Checklist - Knowledge Guides 30 2.6.2 Problems 30 2.7 References 31 II Regression Model - Estimation and Inference 33 3 The Multivariate Normal Linear Regression Model: ML Estimation 35 3.1 The Linear Regression Model 35 3.1.1 The Linearity Assumption and the Inverse Problem 36 3.1.2 Linearity and Beyond: Sampling Implication of Model Assumptions 37 3.1.3 The Parametric Model 39 3.2 Maximum Likelihood Estimation of β and σ2 39 3.2.1 The Normal Linear Regression Model 40 3.2.2 The Maximum Likelihood (ML) Criterion 40 3.2.3 Maximum Likelihood Estimators for β and σ2 41 3.2.4 Distribution, Moments, and Bias Properties of the ML Estimator 42 3.3 Efficiency of the Bias-Adjusted ML Estimators of β and σ2 43 3.4 Consistency, Asymptotic Normality, and Asymptotic Efficiency of ML Estimators of β and σ2 44 3.4.1 Consistency 44 3.4.2 Asymptotic Normality 46 3.4.3 Asymptotic Efficiency 47 3.5 Summary of the Finite Sample and Asymptotic Sampling Properties of the ML Estimator 48 3.6 Estimating є and cov^â) 49 3.6.1 An Estimator for є 50 3.6.2 An Estimator for covGQ) 51 3.7 Concluding Remarks 51 3.8 Exercises 53 3.8.1 Idea Checklist - Knowledge Guides 53 3.8.2 Problems 53 3.8.3 Computer Problems 54 3.9 Appendix: Admissibility of ML Estimator - Introduction to Biased Estimation 54 3.9.1 Is the ML Estimator Inadmissible? 55 3.9.2 Risk Comparisons for Restricted and Unrestricted ML Estimator 57 3.10 Appendix: Proofs 58 3.11 References 60 4 The Multivariate Normal Linear Regression Model: Inference 61 4.1 Introduction 61 4.2 Some Basic Sampling Distributions of Functions of β and S2 62 VUl CONTENTS 4.3 Hypothesis Testing 64 4.3.1 Test Statistics 65 4.3.2 Generalized Likelihood Ratio (GLR) Test 65 4.3.3 Properties of the GLR Test 66 4.3.4 Testing Hypotheses Relating to Linear Restrictions on β 67 4.3.5 Testing Linear Inequality Hypotheses 72 4.3.6 Bonferroni Joint Tests of Inequality and Equality Hypotheses about β 73 4.3.7 Testing Hypotheses about σ2 74 4.4 Confidence Interval and Region Estimation 76 4.4.1 Meaning of Confidence Interval or Region 76 4.4.2 Rationale for the Use of Confidence Regions 77 4.4.3 Confidence Intervals, Regions, and Bounds for β 77 4.4.4 Confidence Bounds on σ2 79 4.5 Pretest Estimators Based on Hypothesis Tests: Introduction 80 4.5.1 The Pretest Estimator 80 4.5.2 The Pretest Estimator Risk Function 81 4.6 Concluding Remarks 82 4.7 Exercises 84 4.7.1 Idea Checklist - Knowledge Guides 84 4.7.2 Problems 84 4.7.3 Computer Exercises 85 4.8 References 85 The Linear Semiparametric Regression Model: Least-Squares Estimation 86 5.1 The Semiparametric Linear Regression Model 86 5.2 The Problem of Estimating β 88 5.2.1 The Squared-Error Metric and the Least-Squares Principle 89 5.2.2 The Least-Squares Estimator 90 5.3 Statistical Properties of the LS Estimator 91 5.3.1 Mean, Covariance, and Unbiasedness 92 5.3.2 GAUSS Markov Theorem: β Is BLUE, Not Necessarily MVUE 93 5.3.3 β Is a Minimax Estimator of β under Quadratic Risk 94 5.3.4 Consistency 95 5.3.5 Asymptotic Normality 96 5.4 Estimating ε, σ2, and cov^â) 97 5.4.1 An Estimator for ε 98 5.4.2 An Estimator for σ2 and cov(^) 99 5.5 Critique 100 5.6 Exercises 101 5.6.1 Idea Checklist - Knowledge Guides 101 5.6.2 Problems 101 5.6.3 Computer Exercises 102 ix CONTENTS 5.7 References 103 5.8 Appendix: Proofs 103 6 The Linear Semiparametric Regression Model: Inference 105 6.1 Asymptotics: Why, What Kind, and How Useful? 107 6.1.1 Why? 107 6.1.2 What Kind? 108 6.1.3 How Useful? 108 6.2 Hypothesis Testing: Linear Equality Restrictions on β 109 6.2.1 Wald (W) Tests ПО 6.2.2 Lagrange Multiplier (LM) Tests 114 6.2.3 The W and LM Tests under Normality 118 6.2.4 W and LM Tests: Interrelationships and Extensions 120 6.3 Confidence Region Estimation 120 6.3.1 Wald-Based Confidence Regions 121 6.3.2 LM-Based Confidence Regions 122 6.4 Testing Linear Inequality Hypotheses and Generating Confidence Bounds on β 123 6.4.1 Linear Inequality Hypotheses 124 6.4.2 Confidence Bounds for c/3 125 6.5 Critique 126 6.6 Comprehensive Computer Application 127 6.7 Exercises 128 6.7.1 Idea Checklist - Knowledge Guides 128 6.7.2 Problems 128 6.73 Computer Exercises 129 6.8 References 129 III Extrémům Estimators and Nonlinear and Nonnormal Regression Models 131 7 Extrémům Estimation and Inference 133 7.1 Introduction 133 7.2 ML and LS Estimators Expressed in Extrémům Estimator Form 136 7.3 Asymptotic Properties of Extrémům Estimators 136 7.3.1 Consistency of Extrémům Estimators 136 73.2 Asymptotic Normality of Extrémům Estimators 138 7.4 Asymptotic Properties of Maximum Likelihood Estimators in an Extrémům Estimator Context 139 7.4.1 Consistency of the ML-Extremum Estimator 140 7.4.2 Asymptotic Normality of the ML-Extremum Estimator 141 7.5 Asymptotic Properties of the Least-Squares Estimator in an Extrémům Estimator Context 142 7.5.1 Consistency of the LS-Extremum Estimator 142 7.5.2 Asymptotic Normality of the LS-Extremum Estimator 143 CONTENTS 7.6 Inference Based on Extrémům Estimation 144 7.6.1 Lagrange Multiplier Tests and Confidence Regions 144 7.6.2 Wald Tests and Confidence Regions 148 7.6.3 Pseudo-Likelihood Ratio Tests and Confidence Regions 149 7.6.4 Testing Linear Inequalities and Confidence Bounds 152 7.7 Critique 153 7.8 Exercises 154 7.8.1 Idea Checklist - Knowledge Guides 154 7.8.2 Problems 154 7.8.3 Computer Problems 155 7.9 References 155 8 The Nonlinear Semiparametric Regression Model: Estimation and Inference 157 8.1 The Nonlinear Regression Model 157 8.1.1 Assumed Probability Model Characteristics: Discussion 159 8.1.2 The Inverse Problem 161 8.2 The Problem of Estimating β 162 8.2.1 The Nonlinear Least-Squares Estimator 162 8.2.2 Parameter Identification Relative to a Probability Model 163 8.2.3 Parameter Identification Relative to the Least-Squares Criterion and Given Data 165 8.3 Sampling Properties of the NLS Estimator 167 8.4 The Problem of Estimating ε, σ2, and covOâ) 169 8.4.1 An Estimator for ε 169 8.4.2 An Estimator for σ2 and covC/â) 170 8.5 Wald Statistics: Tests and Confidence Regions 171 8.5.1 Hypotheses Relating to Differentiable Functions of β 171 8.5.2 Wald (W) Tests 172 8.5.3 Wald Statistic Distribution under На 173 8.5.4 Test Application 174 8.5.5 Confidence Region Estimation 175 8.6 LM Statistics: Tests and Confidence Regions 176 8.6.1 Lagrange Multiplier Distribution 176 8.6.2 Classical Form of LM Test 178 8.6.3 Score Form of LM Test 178 8.6.4 LM Statistic Distribution under Ha 179 8.6.5 Test Application 179 8.6.6 Confidence Region Estimation 180 8.7 Pseudo-Likelihood Ratio Statistic: Tests and Confidence Regions 180 8.7.1 The Pseudo-Likelihood Ratio Statistic 180 8.7.2 Distribution of PLR under Ho 181 8.73 Test and Confidence Region Application and Properties 182 xi CONTENTS 8.8 Nonlinear Inequality Hypotheses and Confidence Bounds 183 8.8.1 Testing Nonlinear Inequalities: Z-Statistics 183 8.8.2 Confidence Bounds 185 8.9 Asymptotic Properties of the NLS-Extremum Estimator 186 8.9.1 Consistency 186 8.9.2 Asymptotic Normality 187 8.9.3 Asymptotic Linearity 190 8.9.4 Best Asymptotically Linear Consistent Estimator 191 8.10 Concluding Comments 192 8.11 Exercises 192 8.11.1 Idea Checklist - Knowledge Guides 192 8.11.2 Problems 193 8.11.3 Computer Exercises 193 8.12 References 194 8.13 Appendixes 195 8.13.1 Appendix A: Computation of NLS Estimates (with Ronald Schoenberg) 195 8.13.2 Newton-Raphson Method 195 8.13.3 Gauss-Newton Method 197 8.13.4 Quasi-Newton Methods 198 8.13.5 Computational Issues 199 8.13.6 Appendix В : Proofs 202 Nonlinear and Nonnormal Parametric Regression Models 204 9.1 The Normal Nonlinear Regression Model 204 9.1.1 Maximum Likelihood— Extrémům Estimation 205 9.1.2 Maximum Likelihood-Extremum Inference 207 9.2 Nonnormality 209 9.2.1 A Nonnormal Dependent Variable, Normal Noise Component Case: The Box -Сох Transformation 209 9.2.2 A Nonnormal Noise Component Case 212 9.3 General Considerations in Applying the ML-Extremum Criterion 215 9.3.1 Point Estimation 216 9.3.2 Testing and Confidence-Region Estimation 217 9.4 A Final Remark 220 9.5 Exercises 220 9.5.1 Idea Checklist - Knowledge Guides 220 9.5.2 Problems 220 9.5.3 Computer Exercises 221 9.6 References 221 xii CONTENTS IV Avoiding the Parametric Likelihood 223 10 Stochastic Regressors and Moment-Based Estimation 225 10.1 Introduction 225 10.2 Linear Model Assumptions, Estimation, and Inference Revisited 227 10.3 LS and ML Estimator Properties 229 10.3.1 LS Estimator Properties: Finite Samples 229 10.3.2 LS Estimator Properties: Asymptotics 230 10.3.3 ML Estimation of β and σ2 under Conditional Normality 232 10.4 Hypothesis Testing and Confidence-Region Estimation 233 10.4.1 Semiparametric Case 233 10.4.2 Parametric Case 233 10.5 Summary: Statistical Implications of Stochastic X 235 10.6 Method of Moments Concept 235 10.6.1 Asymptotic Properties 236 10.6.2 A Linear Model Formulation 238 10.6.3 Extensions to Nonlinear Models 239 10.7 Concluding Comments 241 10.8 Exercises 242 10.8.1 Idea Checklist - Knowledge Guides 242 10.8.2 Problems 242 10.8.3 Computer Exercises 242 10.9 References 243 10.10 Appendix: Proofs 244 11 Quasi-Maximum Likelihood and Estimating Equations 245 11.1 Quasi-Maximum Likelihood Estimation and Inference 247 11.2 QML-E Estimation and Inference 248 11.2.1 Consistency and Asymptotic Normality 248 11.2.2 True PDF Approximation Property and Asymptotic Normality of Inconsistent QML-E Estimators 249 11.2.3 Consistent Estimation of the Asymptotic Covariance Matrix 251 11.2.4 Necessary and Sufficient Conditions for Consistency and Asymptotic Normality 251 11.2.5 QML Inference 254 11.2.6 QML Generalizations 255 11.2.7 QML Summary Comments 256 11.3 Estimating Equations: LS, ML, QML-E, and Extrémům Estimators 256 11.3.1 Linear and Nonlinear Estimating Functions 259 113.2 Optimal Unbiased Estimating Functions: Finite Sample Optimality of ML 261 xiii CONTENTS 11.3.3 Consistency of the ЕЕ Estimator 265 11.3.4 Asymptotic Normality and Efficiency of ЕЕ Estimators 267 11.3.5 Inference in the Context of ЕЕ Estimation 268 11.4 Unifying-Linking OptEF and QML: QML-EE Estimation and Inference 270 11.4.1 The Best Linear-Unbiased QML-EE 272 11.4.2 General QML-EE Estimation and Inference 274 11.5 Final Remarks 275 11.6 Exercises 275 11.6.1 Idea Checklist - Knowledge Guides 275 11.6.2 Problems 276 11.6.3 Computer Problems 277 11.7 References 277 11.8 Appendix: Proofs 279 12 Empirical Likelihood Estimation and Inference 281 12.1 Empirical Likelihood: iid Case 282 12.1.1 The EL Concept 283 12.1.2 Nonparametric Maximum Likelihood Estimate of a Population Distribution 284 12.1.3 Empirical Likelihood Function for θ 286 12.2 Maximum Empirical Likelihood Estimation: iid Case 292 12.2.1 Maximum Empirical Likelihood Estimator 292 12.2.2 MEL Efficiency Property 293 12.2.3 MEL Estimation of a Population Mean 294 12.2.4 MEL Estimation Based on Two Moments 297 12.3 Hypothesis Tests and Confidence Regions: iid Case 298 12.3.1 Empirical Likelihood Ratio Tests and Confidence Regions for 0(0) 299 12.3.2 Wald Tests and Confidence Regions for c(0) 300 12.3.3 Lagrange Multiplier Tests and Confidence Regions for c(0) 300 12.3.4 Z-Tests of Inequality Hypotheses for the Value of c(0) 301 12.3.5 Testing the Validity of Moment Equations 301 12.3.6 MEL Testing and Confidence Intervals for Population Mean 302 12.3.7 Illustrative MEL Confidence Interval Example 303 12.4 MEL in the Linear Regression Model with Stochastic X 304 12.4.1 MEL Regression Estimation for Stochastic X 304 12.4.2 EL-Based Testing and Confidence Regions When X Is Stochastic 306 12.4.3 Extensions to the Nonlinear Regression Model for Stochastic X 307 12.5 MEL in the Linear Regression Model with Nonstochastic X: Extensions to the Non-iid Case 307 12.6 Concluding Comments 309 xiv CONTENTS 12.7 Exercises 310 12.7.1 Idea Checklist - Knowledge Guides 310 12.7.2 Problems 311 12.7.3 Computer Exercises 311 12.8 References 312 13 Information Theoretic-Entropy Approaches to Estimation and Inference 313 13.1 Solutions to Systems of Estimating Equations and Kullback-Leibler Information 313 13.1.1 Kullback-Leibler Information Criterion (KLIC) 316 13.1.2 Relationship Between the MEL Objective and KL Information 317 13.1.3 Relationship Between the Maximum Entropy (ME) Objective and KL Information 319 13.2 The General MEEL Alternative Empirical Likelihood Formulation 321 13.2.1 The MEEL Estimator and Likelihood 321 13.2.2 MEEL Asymptotics 322 13.2.3 MEEL Inference 323 13.2 .4 Contrasting the Use of Estimating Functions in ЕЕ and MEEL Contexts 326 13.3 A Cross-Entropy Formalism and Solution 326 13.4 α -Entropy: Unifying the MEL, MEEL, and CEEL Estimation Objectives 328 13.5 Application of the Maximum Entropy Principle to the Regression Model 329 13.5.1 Stochastic X in the Linear Model 329 13.5.2 Fixed χ in the Linear Model 331 13.5.3 Extensions to Nonlinear Regression Models 331 13.5.4 Inference in Regression Models 331 13.6 Concluding Remarks - Which Criterion? 332 13.7 Exercises 334 13.7.1 Idea Checklist-Knowledge Guides 334 13.7.2 Problems 334 13.7.3 Computer Problems 334 13.8 References 335 13.9 Supplemental References 335 V Generalized Regression Models 337 14 Regression Models with a Known General Noise Covariance Matrix 339 14.1 Applying LS-ML to the Linear Model and Untransformed Data: Ignoring that Ψ φ Ι 340 14.1.1 Point Estimation 341 14.1.2 Testing and Confidence-Region Estimation 342 xv CONTENTS 14.2 GLS-ML-Extremum Analysis of the Linear Model: Incorporating a Known Ψ 344 14.2.1 ML-Extremum Estimators for β and σ2 344 14.2.2 LS-Extremum Estimators for β and σ2 : Transformed Linear Model 345 14.2.3 Asymptotic Properties 347 14.2.4 Hypothesis Testing and Confidence Regions 349 14.3 GLS-ML-Extremum Analysis of the Nonlinear Model: Incorporating a Known Φ 350 14.3.1 Estimator Properties 350 14.3.2 Hypothesis Testing and Confidence Regions 351 14.3.3 Applying NLS to Untransformed Data 352 14.4 Parametric Specifications of Noise Covanance Matrices 353 14.4.1 Estimation and Inference with AR(1) Noise 354 14.4.2 Heteroscedasticity - Structural Specification Known, Parameters Unknown 355 14.4.3 General Considerations 356 14.5 Sets of Regression Equations 356 14.5.1 Sets of Linear Equations 357 14.5.2 Sets of Nonlinear Equations 359 14.6 The Estimating Equations - Quasi-Maximum Likelihood View: A Unified Approach 361 14.6.1 ЕЕ Estimation of β and σ2 in the Linear Model When Φ Is Known 361 14.6.2 ЕЕ Estimation of β and σ2 in the Nonlinear Model When Φ Is Known 363 14.6.3 ЕЕ Estimation of β and σ2 in the Linear or Nonlinear Normal Parametric Regression Model When Φ Is Known 364 14.6.4 QML-EE Estimation of β and σ2 in the Linear or Nonlinear Regression Model 365 14.6.5 ЕЕ Estimation of β and σ2 in Systems of Regression Equations 366 14.7 Some Comments 367 14.8 Exercises 368 14.8.1 Idea Checklist - Knowledge Guides 368 14.8.2 Problems 368 14.8.3 Computer Exercises 369 14.9 References 369 15 Regression Models with an Unknown General Noise Covariance Matrix 370 15.1 Linear Regression Models with Unknown Noise Covariance 371 15.1.1 Single-Equation Semiparametric Linear Regression Model 372 15.1.2 Single-Equation Parametric Linear Regression Model - The ML Approach 377 xvi CONTENTS 15.2 System of Linear Regression Equations 378 15.2.1 Estimation: Semiparametric Case 379 15.2.2 Testing and Confidence Regions: Semiparametric Case 380 15.2.3 ML Approach: Parametric Case 381 15.3 Nonlinear Regression Models with Unknown Noise Covariance 383 15.3.1 Single-Equation Semiparametric Nonlinear Regression Model 383 15.3.2 Estimation 383 15.3.3 Testing and Confidence Regions 384 15.3.4 Single-Equation Parametric Nonlinear Regression Model - ML Approach 385 15.3.5 Sets of Nonlinear Regression Equations 386 15.4 Robust Solution Methods: OLS and Robust Covariance Matrix Estimation 387 15.4.1 Heteroscedasticity 389 15.4.2 Heteroscedasticity and Autocorrelation 391 15.5 The Estimating Equations - Quasi-Maximum Likelihood View: A Unified Approach 393 15.5.1 A Unified ЕЕ Characterization of Inverse Problem Solutions 393 15.5.2 QML-EE Estimation 395 15.5.3 ЕЕ Extensions 396 15.5.4 MEL and MEEL Applications of ЕЕ 397 15.6 Some Comments 398 15.7 Exercises 400 15.7.1 Idea Checklist - Knowledge Guides 400 15.7.2 Problems 400 15.7.3 Computer Exercises 400 15.8 References 401 VI Simultaneous Equation Probability Models and General Moment-Based Estimation and Inference 403 16 Generalized Moment-Based Estimation and Inference 405 16.1 Parameter Estimation in Just-determined and Overdetermined Models with iid Observations: Back to the Future 406 16.1.1 OptEF Approach 409 16.1.2 Empirical Likelihood Approaches 410 16.1.3 Summary and Foreword 411 16.2 GMM Solutions for Unbiased Estimating Equations in the Overdetermined Case 412 16.2.1 GMM Concept 412 16.2.2 GMM Linear Model Estimation 413 16.23 GMM Estimators - General Properties 420 16.3 IV Solutions in the Just-determined Case When Ε[Χ ε] φ 0 423 16.3.1 Traditional Instrumental Variable Estimator in the Linear Model 424 xvii CONTENTS 16.3.2 GLS as an IV Estimator 426 16.3.3 Extensions: Nonlinear IV Formulations and Non-iid Sampling 427 16.3.4 Hypothesis Testing and Confidence Regions 428 16.3.5 Summary: IV Approach to Estimation and Inference 429 16.4 Solutions in the Overdetermined Case When Ε[Χ ε] φ 0 429 16.4.1 Unbiased Estimating Equations Basis for Inverse Problem Solutions When Ε[Χ ε] φ 0 430 16.4.2 GMM Approach 431 16.43 MEL and MEEL Approaches 432 16.4.4 OptEF-Quasi-ML Approach: Asymptotic Unification of Inverse Solution Methods 436 16.4.5 Asymptotic Sampling Properties and Inference 437 16.4.6 Testing Moment Equation Validity 438 16.4.7 Relationship Between Estimator Efficiency and the Number and Type of Estimating Equations 439 16.5 Concluding Comments 441 16.6 Exercises 443 16.4.1 Idea Checklist - Knowledge Guides 443 16.4.2 Problems 443 16.4.3 Computer Exercises 444 16.7 References 444 17 Simultaneous Equations Econometric Models: Estimation and Inference 446 17.1 Linear Simultaneous Equations Models 447 17.1.1 An Equivalent Vectorized System of Equations 450 17.1.2 The Reduced-Form Regression Model 451 17.1.3 Estimating the Reduced-Form Coefficients 453 17.1.4 The Identification Problem 455 17.2 Least-Squares and GMM Estimation: The Semiparametric Case 458 17.2.1 Estimators of Parameters for a Just-Identified Structural Equation 459 17.2.2 GMM Estimator of Parameters for an Overidentified Structural Equation 460 17.2.3 Estimation of a Complete System of Equations 462 17.3 Maximum Likelihood Estimation in the Linear Model: The Parametric Case 465 17.3.1 Full-Information Maximum Likelihood (FIML) 465 17.3.2 Limited Information Maximum Likelihood (LIML) 467 17.4 Nonlinear Simultaneous Equations 468 17.4.1 Single-Equation Estimation: Semiparametric Case 469 17.4.2 Complete System Estimation: Semiparametric Case 472 xviü CONTENTS 17.4.3 Nonlinear Maximum Likelihood Estimation: Parametric Case 473 17.4.4 Identification in Nonlinear Systems of Equations 474 17.5 Information Theoretic Procedures 475 17.5.1 Minimum KLIC Approach: MEEL and MEL 476 17.5.2 MEEL Estimation and Inference 479 17.5.3 MEL Estimation 484 17.5.4 The KLIC-MEEL-MEL Procedures: Critique 485 17.6 OptEF Estimation and Inference 486 17.6.1 The OptEF Estimator in Simultaneous Equations Models 486 17.6.2 OptEF Asymptotic Unification of Inverse Problem Solutions 487 17.7 Concluding Comments 488 17.8 Exercises 489 17.8.1 Idea Checklist - Knowledge Guides 489 17.8.2 Problems 489 17.8.3 Computer Problems 490 17.9 References 491 17.10 Appendix: Historical Perspective 492 VII Model Discovery 495 18 Model Discovery: The Problem of Variable Selection and Conditioning 497 18.1 Introduction 497 18.1.1 Experiments in Nonexperimental Model Building 498 18.1.2 The Chapter Format 499 18.2 Variable Selection Problem in a Loss or MSE Context 500 18.2.1 Bias-Variance Trade-Off in Incorrect Variable Selection 501 18.2.2 Statistical Implications under an MSE Matrix Measure 503 18.2.3 Statistical Implications under a Quadratic Risk Function Measure 505 18.2.4 Extensions to Nonlinear Models, General Covariance Structures, and Systems of Equations 506 18.3 Fisherian Testing and Model Choice: Critique 507 18.4 Estimated Risk Criteria and Model Choice: Mallows Cp Criterion 509 18.5 An Information Theoretic Model Selection Criterion: Akaiké Information 511 18.5.1 Basic Rationale for the AIC and Variants 511 18.5.2 A Comment 513 18.6 Shrinkage as a Basis for Dealing with Variable Uncertainty 514 18.6.1 Stein-Like Shrinkage Estimators 514 18.6.2 Multiple Shrinkage Estimator 515 18.7 The Problem of an Ill-Conditioned Explanatory Variable Matrix 517 18.7.1 Penalized Estimation 518 18.7.2 Finite Sample Performance 520 xix CONTENTS 18.8 Final Comments and Critique 521 18.9 Exercises 524 18.9.1 Idea Checklist- Knowledge Guides 524 18.9.2 Problems 524 18.9.3 Computer Problems 524 18.10 References 525 19 Model Discovery: The Problem of Noise Covariance Matrix Specification 528 19.1 Introduction 528 19.2 Specific Parametric Specifications of the Noise Covariance Matrix: Estimation and Inference 530 19.2.1 AR(1) Noise 530 19.2.2 Heteroscedastic Noise: af = (z¡ .α)2 533 19.3 Tests for Heteroscedasticity: Rationale and Application 535 19.3.1 Types of Heteroscedasticity Tests 536 19.3.2 Motivation for Tests Based on ε2 536 19.3.3 Motivation for the Test Based on 1η(ε2) 540 19.3.4 Motivation for Test Based on êt \| 541 19.3.5 More Tests 542 19.4 Tests for Autocorrelation: Rationale and Application 543 19.4.1 Autocorrelation Processes 543 19.4.2 Estimation 546 19.4.3 Autocorrelation Tests 547 19.5 Pretest Estimators Defined by Heteroscedasticity or Autocorrelation Testing 551 19.5.1 Two-Equation Linear System with Potential Heteroscedasticity 552 19.5.2 A Heteroscedasticity Pretest Estimator 553 19.5.3 An Autocorrelation Pretest Estimator 555 19.6 Concluding Comments 556 19.7 Exercises 557 19.7.1 Idea Checklist - Knowledge Guides 557 19.7.2 Problems 557 19.7.3 Computer Problems 557 19.8 References 558 VIII Special Econometric Topics 561 20 Qualitative-Censored Response Models 563 20.1 Binary-Discrete Choice Response Models 565 20.1.1 A Linear Probability Model 566 20.1.2 A Reformulated Binary Response Model 567 xx CONTENTS 20.2 Maximum Likelihood Estimation and Inference for the Discrete Choice Model 570 20.2.1 Logit Model 571 20.2.2 Probit Model 573 20.2.3 Probit or Logit? 575 20.3 Multinomial Discrete Choice 575 20.3.1 Multinomial Logit 576 20.3.2 Information Theoretic Estimation of the Multinomial Decision Model 581 20.3.3 Ordered Multinomial Choice 584 20.4 Censored Response Data 585 20.4.1 Censoring Versus Truncation 585 20.4.2 Tobit Model 587 20.4.3 Extensions of the Tobit Formulation 591 20.5 Concluding Remarks 592 20.6 Exercises 594 20.6.1 Idea Checklist - Knowledge Guides 594 20.6.2 Problems 594 20.6.3 Computer Problems 595 20.7 References 595 20.8 Appendix 597 21 Introduction to Nonparametric Density and Regression Analysis 599 21.1 Density Estimation via Kernels 601 21.1.1 Kernels 602 21.1.2 IMSE, AIMSE, and Kernel Choice 604 21.1.3 Bandwidth Choice 606 21.1.4 Other Properties and Issues 608 21.1.5 Multivariate Extensions 609 21.2 Kernel Regression Estimators 611 21.2.1 Nonparametric Regression Model Specification 612 21.2.2 Nadaraya-Watson Kernel Regression: Alias Zero-Order Local Polynomial Regression 613 21.3 Local Polynomial Regression 622 21.4 Prequel of Fundamental Concepts: Local Weighted Averages, Local Linear Regressions, and Histograms 624 21.4.1 Nonparametric Regression under Repeated Sampling: Simple Sample Means 625 21.4.2 Local Sample Means: Using Data Neighborhoods 626 21.4.3 Local Weighted Averages within Data Neighborhoods: Local Least-Squares Regressions 628 21.4.4 Local Polynomial Regressions 629 21.4.5 Histograms: Precursor to Kernel Density Estimation 630 21.5 Concluding Comments 636 xxi CONTENTS 21.6 Exercises 637 21.6.1 Idea Checklist - Knowledge Guides 637 21.6.2 Problems 637 21.6.3 Computer Problems 638 21.7 References 638 21.8 Appendix: Derivation of Equation (21.4.31) 640 IX Bayesian Estimation and Inference 643 22 Bayesian Estimation: General Principles with a Regression Focus 645 22.1 Introduction 645 22.1.1 Bayes Theorem 646 22.1.2 A Format for Bayesian Reasoning 647 22.2 Bayesian Probability Models and Posterior Distributions 649 22.2.1 Prior Distributions 650 22.2.2 Posterior Probability Distributions 651 22.3 The Bayesian Linear-Regression-Based Probability Model 652 22.3.1 Bayesian Regression Analysis under Normality and Uninformative Priors 653 22.3.2 Uninformative Priors and Proper Marginal Posteriors 654 22.3.3 Posterior Distribution under an Uninformative Prior 655 22.3.4 Marginal Posteriors 656 22.4 Bayesian Regression Analysis under Normality and Conjugate Informative Priors 658 22.4.1 The Joint Posterior Distribution under the Conjugate Prior 660 22.4.2 The Marginal Posteriors 660 22.5 Bayesian Point Estimates 661 22.5.1 Minimum Expected Risk 663 22.5.2 Admissibility 663 22.5.3 Consistency and Asymptotic Normality 663 22.5.4 Comments on Bayes Estimator Properties 664 22.6 On the Use of Conjugate Priors and Coincidence of Classical and Bayesian Estimates 665 22.7 Concluding Remarks 666 22.8 Exercises 667 22.8.1 Idea Checklist-Knowledge Guides 667 22.8.2 Problems 667 22.83 Computer Problems 668 22.9 References 669 22.10 Appendix: Bayesian Asymptotics 669 22.10.1 Bayesian Asymptotics: Specific Cases 670 22.10.2 Bayesian Asymptotics: General Considerations 672 22.103 Appendix References 674 xxii CONTENTS 23 Alternative Bayes Formulations for the Regression Model 675 23.1 g-Priors 676 23.1.1 A Family of g-priors and Associated Posteriors 676 23.1.2 Rationalizing and Specifying g-priors 678 23.2 An Empirical Bayes Estimator 679 23.3 General Bayesian Regression Analysis with Nonconjugate Informative-Uninformative Prior 682 23.3.1 Normal Noise Component 682 23.3.2 Nonnormal Noise Component 687 23.3.3 Summary Comments 688 23.4 Bayesian Method of Moments 688 23.4.1 Continuous Entropy Formulation 691 23.4.2 A Posterior Density Function 692 23.5 Concluding Remarks 693 23.6 Exercises 694 23.6.1 Idea Checklist- Knowledge Guides 694 23.6.2 Problems 694 23.6.3 Computer Problems 695 23.7 References 696 24 Bayesian Inference 698 24.1 Credible Regions 699 24.1.1 General Principles 699 24.1.2 Highest Posterior Density Credible Regions 700 24.1.3 Credible Regions in the Regression Model 701 24.2 Hypothesis Evaluation and Decision 702 24.2.1 General Principles 703 24.3 General Hypothesis Testing and Credible Sets in the Regression Model 704 24.3.1 Evaluating Composite Hypotheses about β and Bayes Factors 704 243.2 Evaluating Simple Hypotheses about β 706 24.4 A Comment 708 24.5 Exercises 708 24.5.1 Idea Checklist-Knowledge Guides 708 24.5.2 Problems 708 24.5.3 Computer Problems 709 24.6 References 709 X Epilogue 711 Appendix: Introduction to Computer Simulation and Resampling Methods 713 A.1 Pseudorandom Number Generation 713 A.1.1 Generating U(0, 1) Pseudorandom Numbers 714 xxiii CONTENTS АЛЈ2 Generating Continuous Nonuniform Pseudorandom Numbers 715 A.1.3 Generating Discrete Pseudorandom Numbers 717 A.1.4 Evaluating the Performance of Pseudorandom Number Generators 718 A.2 Monte Carlo Simulation 719 A.2.1 Background and Conceptual Motivation 720 A.2.2 Key Assumptions 721 A.2.3 Basic Properties of Monte Carlo Simulation Estimators 722 A.3 Bootstrap Resampling 724 A.3.1 Basic Properties of the Bootstrap 725 A.3.2 Bootstrap Simulation Procedures for Regression Models 728 A.4 Numerical Tools for Evaluating Posterior Distributions 730 A.4.1 The Gibbs Sampling Algorithm 731 A.4.2 The Metropolis-Hastings Algorithm 733 A.5 Concluding Remarks 734 A.6 Exercises 735 A.6.1 Idea Checklist 735 A.6.2 Problems 735 A.6.3 Computer Problems 735 A.7 References 736 Author Index 739 Subject Index 743 CD-ROM Foundations Review El Probability Theory E2 Classical Estimation and Inference Principles E3 Ill-Posed Inverse Problems ELECTRONIC MANUALS Matrix Review Manual Econometric Examples Manual GAUSS Tutorial and Technical Archive GAUSS Software XXIV
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spellingShingle	Mittelhammer, Ron C. Judge, George G. 1925- Miller, Douglas J. 1965- Econometric foundations Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie (DE-588)4132280-0 gnd
subject_GND	(DE-588)4132280-0 (DE-588)4123623-3
title	Econometric foundations
title_auth	Econometric foundations
title_exact_search	Econometric foundations
title_full	Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller
title_fullStr	Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller
title_full_unstemmed	Econometric foundations Ron C. Mittelhammer ; George G. Judge ; Douglas J. Miller
title_short	Econometric foundations
title_sort	econometric foundations
topic	Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie (DE-588)4132280-0 gnd
topic_facet	Lehrbuch - Ökonometrie Ökonometrie / Theorie Econometrics Ökonometrie Lehrbuch
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