Nonparametric econometrics: theory and practice
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Princeton University Press
2023
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| Beschreibung: | xxi, 746 Seiten Illustrationen |
| ISBN: | 9780691248080 9780691121611 |
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| 245 | 1 | 0 | |a Nonparametric econometrics |b theory and practice |c Qi Li and Jeffrey S. Racine |
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Contents Preface I 1 xvii Nonparanietric Kernel Methods 1 Density Estimation 3 1.1 Univariate Density Estimation 1.2 Univariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods 1.3 Univariate Bandwidth Selection: Cross-Validation Methods 1.3.1 Least Squares Cross-Validation 1.3.2 Likelihood Cross-Validation 1.3.3 An Illustration of Data-Driven Bandwidth Selection 1.4 Univariate CDF Estimation 1.5 Univariate CDF Bandwidth Selection: CrossValidation Methods 1.6 Multivariate Density Estimation 1.7 Multivariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods 1.8 Multivariate Bandwidth Selection: Cross-Validation Methods 1.8.1 Least Squares Cross-Validation 1.8.2 Likelihood Cross-Validation 1.9 Asymptotic Normality of Density Estimators 1.10 Uniform Rates of Convergence 1.11 Higher Order Kernel Functions 1.12 Proof of Theorem 1.4 (Uniform Almost Sure Convergence) 1.13 Applications 4 14 15 15 18 19 19 23 24 26 27 27 28 28 30 33 35 40
CONTENTS Female Wage Inequality Unemployment Rates and City Size Adolescent Growth Old Faithful Geyser Data Evolution of Real Income Distribution in Italy, 1951-1998 1.14 Exercises 41 43 44 44 Regression 2.1 Local Constant Kernel Estimation 2.1.1 Intuition Underlying the Local Constant Kernel Estimator 2.2 Local Constant Bandwidth Selection 2.2.1 Rule-of֊Thumb and Plug-In Methods 2.2.2 Least Squares Cross-Validation 2.2.3 AICc 2.2.4 The Presence of Irrelevant Regressors 2.2.5 Some Further Results on Cross-Validation 2.3 Uniform Rates of Convergence 2.4 Local Linear Kernel Estimation 2.4.1 Local Linear Bandwidth Selection: Least Squares Cross-Validation 2.5 Local Polynomial Regression (General pth Order) 2.5.1 The Univariate Case 2.5.2 The Multivariate Case 2.5.3 Asymptotic Normality of Local Polynomial Estimators 2.6 Applications 2.6.1 Prestige Data 2.6.2 Adolescent Growth 2.6.3 Inflation Forecasting and Money Growth 2.7 Proofs 2.7.1 Derivation of (2.24) 2.7.2 Proof of Theorem 2.7 2.7.3 Definitions of Ацр+і and Vt Used in Theorem 2.10 2.8 Exercises 57 60 1.13.1 1.13.2 1.13.3 1.13.4 1.13.5 2 3 Frequency Estimation with Mixed Data 3 1 probability Function Estimation with Discrete Data 45 47 64 66 66 69 72 73 78 78 79 83 85 85 88 89 92 92 92 93 9? 98 100 106 108 115 116
CONTEXTS 3.2 Regression with Discrete Regressors 3.3 Estimation with Mixed Data: The FrequencyApproach 3.3.1 Density Estimation with Mixed Data 3.3.2 Regression with Mixed Data 3.4 Some Cautionary Remarks on Frequency Methods 3.5 Proofs 3.5.1 Proof of Theorem 3.1 3.6 Exercises 118 118 118 119 120 122 122 123 4 Kernel Estimation with Mixed Data 4.1 Smooth Estimation of Joint Distributions with Discrete Data 4.2 Smooth Regression with Discrete Data 4.3 Kernel Regression with Discrete՝ Regressors: The Irrelevant Regressor Case 4.4 Regression with Mixed Data: Relevant Regressors 4.4.1 Smooth Estimation with Mixeel Data 4.4.2 The Cross-Validation Method 4.5 Regression with Mixed Data: Irrelevant Regressors 4.5.1 Ordered Discrete Variables 4.6 Applications 4.6.1 Food-Away-from-Home Expenditure 4.6.2 Modeling Strike Volume 4.7 Exercises 125 5 Conditional Density Estimation 5.1 Conditional Density Estimation: Relevant Variables 5.2 Conditional Density Bandwidth Selection 5.2.1 Least Squares Cross-Validation: Relevant Variables 5.2.2 Maximum Likelihood Cross-Validation: Relevant Variables 5.3 Conditional Density Estimation: Irrelevant Variables 5.4 The Multivariate Dependent Variables Case 5.4.1 The General Categorical Data Case 5.4,2 Proof of Theorem 5.5 5.5 Applications 5.5.1 A Nonparametric Analysis of Corruption 5.5.2 Extramarital Affairs Data 5.5.3 Married Female Labor Force Participation 155 155 157 126 131 134 136 136 138 140 144 145 145 147 150 157 160 162 164 167 168 171 171 172 175
viii CONTENTS Labor Productivity Multivariate Y Conditional Density Example: GDP Growth and Population Growth Conditional on OECD Status Exercises 5.5.4 5.5.5 5.6 6 Conditional CDF and Quantile Estimation 6.1 Estimating a Conditional CDF with Continuous Covariates without Smoothing the Dependent Variable 6.2 Estimating a Conditional CDF with Continuous Covariates Smoothing the Dependent Variable 6.3 Nonparametric Estimation of Conditional Quantile Functions 6.4 The Check Function Approach 6.5 Conditional CDF and Quantile Estimation with Mixed Discrete and Continuous Covariates 6.6 A Small Monte Carlo Simulation Study 6.7 Nonparametric Estimation of Hazard Functions 6.8 Applications 6.8.1 Boston Housing Data 6.8.2 Adolescent Growth Charts 6.8.3 Conditional Value at Risk 6.8.4 Real Income in Italy, 1951-1998 6.8.5 Multivariate Y Conditional CDF Example: GDP Growth and Population Growth Conditional on OECD Status 6.9 Proofs 6.9.1 Proofs of Theorems 6.1, 6.2, and 6.4 6.9.2 Proofs of Theorems 6.5 and 6.6 (Mixed Covariates Case) 214 6.10 Exercises II Semiparametric Methods 7 Semiparametric Partially Linear Models 7.1 Partially Linear Models 7.1.1 Identification of ß 7.2 Robinson’s Estimator 7.2.1 Estimation of the Nonparametric Component 177 178 ISO 181 182 184 189 191 193 196 198 200 200 202 202 206 206 209 209 215 219 221 222 222 222 228
CONTEXTS Andrews’s MINPIN Method Semiparametric Efficiency Bounds 7.4.1 The Condiționali}7 Homoskedastic Error Case 7.4.2 The Conditionally Heteroskedastic Error Case 7.5 Proofs 7.5.1 Proof of Theorem 7.2 7.5.2 Verifying Theorem 7.3 for a Partially Linear Model 7.6 Exercises 7.3 7.4 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 Identification Conditions Estimation 8.2.1 Ichimura’s Method Direct Semiparametric Estimators for /3 8.3.1 Average Derivative Estimators 8.3.2 Estimation of g{·) Bandwidth Selection 8.4.1 Bandwidth Selection for Ichimura’sMethod 8.4.2 Bandwidth Selection with DirectEstimation Methods Klein and Spady’s Estimator Lcwbcl’s Estimator Manski’s Maximum Score Estimator Horowitz’s Smoothed Maximum Score* Estimator Han’s Maximum Rank Estimator Multinomial Discrete Choice Models Ai’s Semiparametric Maximum Likelihood Approach A Sketch of the Proof of Theorem 8.1 Applications 8.13.1 Modeling Response to Direct Marketing Catalog Mailings Exercises 9 Additive and Smooth Semiparametric Models (Varying) 244 246 249 8 Semiparametric Single Index Models 8.1 8.2 230 233 233 235 238 238 251 253 253 258 258 262 263 263 265 266 267 269 270 270 271 272 275 277 277 281 Coefficient 9.1 An Additive Model 9.1.1 The Marginal Integration Method 9.1.2 A Computationally Efficient Oracle Estimator 9.1.3 The Ordinary Backfitting Method 283 283 284 286 289
x CONTENTS 9.1.4 The Smoothed Backfitting Method 9.1.5 Additive Models with Link Functions 9.2 An Additive Partially Linear Model 9.2.1 A Simple Two-Step Method 9.3 A Semiparametric Varying (Smooth) Coefficient Model 9.3.1 A Local Constant Estimator of the Smooth Coefficient Function 9.3.2 A Local Linear Estimator of the Smooth Coefficient Function 9.3.3 Testing for a Parametric Smooth Coefficient Model 9.3.4 Partially Linear Smooth Coefficient Models 9.3.5 Proof of Theorem 9.3 9.4 Exercises 290 295 297 299 301 302 303 306 308 310 312 10 Selectivity Models 315 10.1 Semiparametric Type-2 Tobit Models 316 10.2 Estimation of a Semiparametric Type-2 Tobit Model 317 10.2.1 Gallant and Nychka’s Estimator 318 10.2.2 Estimation of the Intercept in Selection Models 319 10.3 Semiparametric Type-3 Tobit Models 320 10.3.1 Econometric Preliminaries 320 10.3.2 Alternative EstimationMethods 323 10.4 Das, Newey and Vella’s Nonparametric Selection Model 328 10.5 Exercises 330 11 Censored Models 11.1 Parametric Censored Models 11.2 Semiparametric Censored Regression Models 11.3 Semiparametric Censored Regression Models with Nonparametric Heteroskedasticity 11.4 The Univariate Kaplan-Meier CDF Estimator 11.5 The Multivariate Kaplan-Meier CDF Estimator 11.5.1 Nonparametric Regression Models with Random Censoring 11.6 Nonparametric Censored Regression 11.6.1 Lewbel and Linton’s Approach 11.6.2 Chen, Dahl and Khan’s Approach 331 332 334 336 338 341 343 345 345 346
CONTEXTS 11.7 Exercises III Consistent Model Specification Tests 348 349 12 Model Specification Tests 351 12.1 A Simple Consistent Test for Parametric Regression Functional Form 354 12.1.1 A Consistent Test for Correct Parametric Functional Form 355 12.1.2 Mixed Data 360 12.2 Testing for Equality of PDFs 362 12.3 More Tests Related to Regression Functions 365 12.3.1 Hardie and Mammen’s Test for a Parametric Regression Model 365 12.3.2 An Adaptive and Rate Optimal Test 367 12.3.3 A Test for a Parametric Single Index Model 369 12.3.4 A Nonparametric Omitted Variables Test 370 12.3.5 Testing the Significance of Categorical Variables 375 12.4 Tests Related to PDFs 378 12.4.1 Testing Independence between Two Random Variables 378 12.4.2 A Test for a Parametric PDF 380 12.4.3 A Kernel Test for Conditional Parametric Distributions 382 12.5 Applications 385 12.5.1 Growth Convergence Clubs 385 12.6 Proofs 388 12.6.1 Proof of Theorem 12.1 388 12.6.2 Proof of Theorem 12.2 389 12.6.3 Proof of Theorem 12.5 389 12.6.4 Proof of Theorem 12.9 391 12.7 Exercises 394 13 Nonsmoothing Tests 13.1 Testing for Parametric Regression Functional Form 13.2 Testing for Equality of PDFs 13.3 A Nonparametric Significance Test 13.4 Andrews’s Test for Conditional CDFs 13.5 Hong’s Tests for Serial Dependence 397 398 401 401 402 401
CONTENTS 13.6 More on Nonsmoothing Tests 13.7 Proofs 13.7.1 Proof of Theorem 13.1 13.8 Exercises IV Nonparametric Nearest Neighbor and Series Methods 408 409 409 410 413 14 K-Nearest Neighbor Methods 415 14.1 Density Estimation·. The Univariate Case 415 14.2 Regression Function Estimation 419 14.3 A Local Linear /с-nn Estimator 421 14.4 Cross-Validation with Local Constant fc-nn Estimation 422 14.5 Cross-Validation with Local LinearUnn Estimation 425 14.6 Estimation of Semiparametric Models with k-nn Methods 427 14.7 Model Specification Tests with fc-nn Methods 428 14.7.1 A Bootstrap Test 431 14.8 Using Different к for Different Components of x 432 14.9 Proofs 432 14.9.1 Proof of Theorem 14.1 435 14.9.2 Proof of Theorem 14.5 435 14.9.3 Proof of Theorem 14.10 440 14.10 Exercises 444 15 Nonparametric Series Methods 15.1 Estimating Regression Functions 15.1.1 Convergence Rates 15.2 Selection of the Series Term К 15.2.1 Asymptotic Normality 15.3 A Partially Linear Model 15.3.1 An Additive Partially Linear Model 15.3.2 Selection of Nonlinear AdditiveComponents 15.3.3 Estimating an Additive Model with a Known Link Function 15 4 Estimation of Partially Linear Varying Coefficient Models 15.4.1 Testing for Correct Parametric Regression Functional Form 445 446 449 451 453 454 455 461 463 466 471
xiii CONTEXTS 15.4.2 A Consistent Test for an Additive Partially Linear Model 15.5 Other Series-Based Tests 15.6 Proofs 15.6.1 Proof of Theorem 15.1 15.6.2 Proof of Theorem 15.3 15.6.3 Proof of Theorem 15.6 15.6.4 Proofof Theorem 15.9 15.6.5 Proof of Theorem 15.10 15.7 Exercises V Time Series, Simultaneous Panel Data Models Equation, 474 479 480 480 484 488 492 497 502 and 503 16 Instrumental Variables and Efficient Estimation of Scmiparametric Models 505 16.1 A Partially Linear Model with Endogenous Regressors in the Parametric Part 505 16.2 A Varying Coefficient Model with Endogenous Regressors in the Parametric Part 509 16.3 Ai and Chen’s Efficient Estimator with Conditional Moment Restrictions 511 16.3.1 Estimation Procedures 511 16.3.2 Asymptotic Normality for Θ 513 16.3.3 A Partially Linear Model with the Endogenous Regressors in the Nonparametric Part 515 16.4 Proof of Equation (16.16} 517 16.5 Exercises 520 17 Endogeneity in Nonparametric RegressionModels 17.1 A Nonparametric Model 17.2 A Triangular Simultaneous Equation Model 17.3 Newey-Powell Series-Based Estimator 17.4 Hall and Horowitz’s Kernel-Based Estimator 17.5 Darolles, Florens and Renault’s Estimator 17.6 Exercises 18 Weakly Dependent Data 18.1 Density Estimation with Dependent Data 521 521 522 527 529 532 533 535 537
XLV CONTENTS 18.1.1 Uniform Almost Sure Rate of Convergence 18.2 Regression Models with Dependent Data 18.2.1 The Martingale Difference Error Case 18.2.2 The Autocorrelated Error Case 18.2.3 One-Step-Ahead Forecasting 18.2.4 ¿-Step-Ahead Forecasting 18.2.5 Estimation of Nonparametric Impulse Response Functions 18.3 Semiparametric Models with Dependent Data 18.3.1 A Partially Linear Model with Dependent Data 18.3.2 Additive Regression Models 18.3.3 Varying Coefficient Models with Dependent Data 18.4 Testing for Serial Correlation in Semiparametric Models 18.4.1 The Test Statistic and Its Asymptotic Distribution 18.4.2 Testing Zero First Order Serial Correlation 18.5 Model Specification Tests with Dependent Data 18.5.1 A Kernel Test for Correct Parametric Regression Functional Form 18.5.2 Nonparametric Significance Tests 18.6 Nonsmoothing Tests for Regression Functional Form 18.7 Testing Parametric Predictive Models 18.7.1 In-Sample Testing of Conditional CDFs 18.7.2 Out-of-Sample Testing of Conditional CDFs 18.8 Applications 18.8.1 Forecasting Short-Term Interest Rates 18.9 Nonparametric Estimationwith Nonstationary Data 18.10 Proofs 18.10.1 Proof of Equation (18.9) 18.10.2 Proof of Theorem 18.2 18.11 Exercises 541 541 541 544 545 547 548 551 551 552 553 554 554 555 556 556 557 558 559 559 ՝ 562 564 564 566 567 567 569 572 19 Panel Data Models 575 19.1 Nonparametric Estimation of Panel Data Models: Ignoring the Variance Structure 576 19.2 Wang’s Efficient Nonparametric Panel Data Estimator 578 19.3 A Partially Linear Model with Random Effects 584 19.4 Nonparametric Panel
Data Models with Fixed Effects 586
CONTENTS 19.4.1 Error Variance Structure Is Known 587 19.4.2 The Error Variance Structure Is Unknown 590 19.5 Λ Partially Linear Model with Fixed Effects 592 19.6 Semiparametrie Instrumental Variable Estimators 594 19.6.1 An Infeasible Estimator 594 19.6.2 The Choice of Instruments 595 19.G.3 Λ Feasible Estimator 597 19.7 Testing for Serial Correlation and for Individual Effects in Semiparametrie Models 599 19.8 Series Estimation of Panel Data Models 602 19.8.1 Additive Effects 602 19.8.2 Alternative Formulation of Fixed Effects 604 19.9 Nonlinear Panel Data Models G06 19.9.1 Censored Panel Data Models 607 19.9.2 Discrete Choice Panel Data Models 614 19.10 Proofs 618 19.10.1 Proof of Theorem 19.1 618 19.10.2 Leading AISE Calculation of Wang’s Estimator G21 19.11 Exercises 624 20 Topics in Applied Nonparamctric Estimation 627 20.1 Nonparamotric Methods İn Continuous-Time Models G27 20.1.1 Nonparamctric Estimation of ContinuousTime Models 627 20.1.2 Nonparamctric Tests for Continuous-Time Models 632 20.1.3 Ait-Sahalia’s Test 632 20.1.4 Hong and Li's Test G33 20.1.5 Proofs 636 20.2 Nonparamctric Estimation of Average Treatment Effects 639 20.2.1 The Model 640 20.2.2 An Application: Assessing the Efficacy of Right Heart Catheterization 642 20.3 Nonparamctric Estimation of Auction Models 645 20.3.1 Estimation of First Price Auction Models 645 20.3.2 Conditionally Independent Private Information Auctions 648 20.4 Copula-Based Semiparametrie Estimation of Multivariate Distributions 651
CONTENTS 20.4.1 Some Background on Copula Functions 651 20.4.2 Semiparametric Copula-Based Multivariate Distributions 652 20.4.3 A Two-Step Estimation Procedure 653 20.4.4 A One-Step Efficient Estimation Procedure 655 20.4.5 Testing Parametric Functional Forms of a Copula 657 20.5 A Semiparametric Transformation Model 659 20.6 Exercises 662 A Background Statistical Concepts Probability, Measure, and Measurable Space Metric, Norm, and Functional Spaces Limits and Modes of Convergence 1.3.1 Limit Supremum and Limit Infimum 1.3.2 Modes of Convergence 1.4 Inequalities, Laws of Large Numbers, and Central Limit Theorems $88 1.5 Exercises 1.1 1.2 1.3 663 663 672 680 680 681 Bibliography θθ^ Author Index 737 Subject Index 744 |
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Contents Preface I 1 xvii Nonparanietric Kernel Methods 1 Density Estimation 3 1.1 Univariate Density Estimation 1.2 Univariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods 1.3 Univariate Bandwidth Selection: Cross-Validation Methods 1.3.1 Least Squares Cross-Validation 1.3.2 Likelihood Cross-Validation 1.3.3 An Illustration of Data-Driven Bandwidth Selection 1.4 Univariate CDF Estimation 1.5 Univariate CDF Bandwidth Selection: CrossValidation Methods 1.6 Multivariate Density Estimation 1.7 Multivariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods 1.8 Multivariate Bandwidth Selection: Cross-Validation Methods 1.8.1 Least Squares Cross-Validation 1.8.2 Likelihood Cross-Validation 1.9 Asymptotic Normality of Density Estimators 1.10 Uniform Rates of Convergence 1.11 Higher Order Kernel Functions 1.12 Proof of Theorem 1.4 (Uniform Almost Sure Convergence) 1.13 Applications 4 14 15 15 18 19 19 23 24 26 27 27 28 28 30 33 35 40
CONTENTS Female Wage Inequality Unemployment Rates and City Size Adolescent Growth Old Faithful Geyser Data Evolution of Real Income Distribution in Italy, 1951-1998 1.14 Exercises 41 43 44 44 Regression 2.1 Local Constant Kernel Estimation 2.1.1 Intuition Underlying the Local Constant Kernel Estimator 2.2 Local Constant Bandwidth Selection 2.2.1 Rule-of֊Thumb and Plug-In Methods 2.2.2 Least Squares Cross-Validation 2.2.3 AICc 2.2.4 The Presence of Irrelevant Regressors 2.2.5 Some Further Results on Cross-Validation 2.3 Uniform Rates of Convergence 2.4 Local Linear Kernel Estimation 2.4.1 Local Linear Bandwidth Selection: Least Squares Cross-Validation 2.5 Local Polynomial Regression (General pth Order) 2.5.1 The Univariate Case 2.5.2 The Multivariate Case 2.5.3 Asymptotic Normality of Local Polynomial Estimators 2.6 Applications 2.6.1 Prestige Data 2.6.2 Adolescent Growth 2.6.3 Inflation Forecasting and Money Growth 2.7 Proofs 2.7.1 Derivation of (2.24) 2.7.2 Proof of Theorem 2.7 2.7.3 Definitions of Ацр+і and Vt Used in Theorem 2.10 2.8 Exercises 57 60 1.13.1 1.13.2 1.13.3 1.13.4 1.13.5 2 3 Frequency Estimation with Mixed Data 3 1 probability Function Estimation with Discrete Data 45 47 64 66 66 69 72 73 78 78 79 83 85 85 88 89 92 92 92 93 9? 98 100 106 108 115 116
CONTEXTS 3.2 Regression with Discrete Regressors 3.3 Estimation with Mixed Data: The FrequencyApproach 3.3.1 Density Estimation with Mixed Data 3.3.2 Regression with Mixed Data 3.4 Some Cautionary Remarks on Frequency Methods 3.5 Proofs 3.5.1 Proof of Theorem 3.1 3.6 Exercises 118 118 118 119 120 122 122 123 4 Kernel Estimation with Mixed Data 4.1 Smooth Estimation of Joint Distributions with Discrete Data 4.2 Smooth Regression with Discrete Data 4.3 Kernel Regression with Discrete՝ Regressors: The Irrelevant Regressor Case 4.4 Regression with Mixed Data: Relevant Regressors 4.4.1 Smooth Estimation with Mixeel Data 4.4.2 The Cross-Validation Method 4.5 Regression with Mixed Data: Irrelevant Regressors 4.5.1 Ordered Discrete Variables 4.6 Applications 4.6.1 Food-Away-from-Home Expenditure 4.6.2 Modeling Strike Volume 4.7 Exercises 125 5 Conditional Density Estimation 5.1 Conditional Density Estimation: Relevant Variables 5.2 Conditional Density Bandwidth Selection 5.2.1 Least Squares Cross-Validation: Relevant Variables 5.2.2 Maximum Likelihood Cross-Validation: Relevant Variables 5.3 Conditional Density Estimation: Irrelevant Variables 5.4 The Multivariate Dependent Variables Case 5.4.1 The General Categorical Data Case 5.4,2 Proof of Theorem 5.5 5.5 Applications 5.5.1 A Nonparametric Analysis of Corruption 5.5.2 Extramarital Affairs Data 5.5.3 Married Female Labor Force Participation 155 155 157 126 131 134 136 136 138 140 144 145 145 147 150 157 160 162 164 167 168 171 171 172 175
viii CONTENTS Labor Productivity Multivariate Y Conditional Density Example: GDP Growth and Population Growth Conditional on OECD Status Exercises 5.5.4 5.5.5 5.6 6 Conditional CDF and Quantile Estimation 6.1 Estimating a Conditional CDF with Continuous Covariates without Smoothing the Dependent Variable 6.2 Estimating a Conditional CDF with Continuous Covariates Smoothing the Dependent Variable 6.3 Nonparametric Estimation of Conditional Quantile Functions 6.4 The Check Function Approach 6.5 Conditional CDF and Quantile Estimation with Mixed Discrete and Continuous Covariates 6.6 A Small Monte Carlo Simulation Study 6.7 Nonparametric Estimation of Hazard Functions 6.8 Applications 6.8.1 Boston Housing Data 6.8.2 Adolescent Growth Charts 6.8.3 Conditional Value at Risk 6.8.4 Real Income in Italy, 1951-1998 6.8.5 Multivariate Y Conditional CDF Example: GDP Growth and Population Growth Conditional on OECD Status 6.9 Proofs 6.9.1 Proofs of Theorems 6.1, 6.2, and 6.4 6.9.2 Proofs of Theorems 6.5 and 6.6 (Mixed Covariates Case) 214 6.10 Exercises II Semiparametric Methods 7 Semiparametric Partially Linear Models 7.1 Partially Linear Models 7.1.1 Identification of ß 7.2 Robinson’s Estimator 7.2.1 Estimation of the Nonparametric Component 177 178 ISO 181 182 184 189 191 193 196 198 200 200 202 202 206 206 209 209 215 219 221 222 222 222 228
CONTEXTS Andrews’s MINPIN Method Semiparametric Efficiency Bounds 7.4.1 The Condiționali}7 Homoskedastic Error Case 7.4.2 The Conditionally Heteroskedastic Error Case 7.5 Proofs 7.5.1 Proof of Theorem 7.2 7.5.2 Verifying Theorem 7.3 for a Partially Linear Model 7.6 Exercises 7.3 7.4 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 Identification Conditions Estimation 8.2.1 Ichimura’s Method Direct Semiparametric Estimators for /3 8.3.1 Average Derivative Estimators 8.3.2 Estimation of g{·) Bandwidth Selection 8.4.1 Bandwidth Selection for Ichimura’sMethod 8.4.2 Bandwidth Selection with DirectEstimation Methods Klein and Spady’s Estimator Lcwbcl’s Estimator Manski’s Maximum Score Estimator Horowitz’s Smoothed Maximum Score* Estimator Han’s Maximum Rank Estimator Multinomial Discrete Choice Models Ai’s Semiparametric Maximum Likelihood Approach A Sketch of the Proof of Theorem 8.1 Applications 8.13.1 Modeling Response to Direct Marketing Catalog Mailings Exercises 9 Additive and Smooth Semiparametric Models (Varying) 244 246 249 8 Semiparametric Single Index Models 8.1 8.2 230 233 233 235 238 238 251 253 253 258 258 262 263 263 265 266 267 269 270 270 271 272 275 277 277 281 Coefficient 9.1 An Additive Model 9.1.1 The Marginal Integration Method 9.1.2 A Computationally Efficient Oracle Estimator 9.1.3 The Ordinary Backfitting Method 283 283 284 286 289
x CONTENTS 9.1.4 The Smoothed Backfitting Method 9.1.5 Additive Models with Link Functions 9.2 An Additive Partially Linear Model 9.2.1 A Simple Two-Step Method 9.3 A Semiparametric Varying (Smooth) Coefficient Model 9.3.1 A Local Constant Estimator of the Smooth Coefficient Function 9.3.2 A Local Linear Estimator of the Smooth Coefficient Function 9.3.3 Testing for a Parametric Smooth Coefficient Model 9.3.4 Partially Linear Smooth Coefficient Models 9.3.5 Proof of Theorem 9.3 9.4 Exercises 290 295 297 299 301 302 303 306 308 310 312 10 Selectivity Models 315 10.1 Semiparametric Type-2 Tobit Models 316 10.2 Estimation of a Semiparametric Type-2 Tobit Model 317 10.2.1 Gallant and Nychka’s Estimator 318 10.2.2 Estimation of the Intercept in Selection Models 319 10.3 Semiparametric Type-3 Tobit Models 320 10.3.1 Econometric Preliminaries 320 10.3.2 Alternative EstimationMethods 323 10.4 Das, Newey and Vella’s Nonparametric Selection Model 328 10.5 Exercises 330 11 Censored Models 11.1 Parametric Censored Models 11.2 Semiparametric Censored Regression Models 11.3 Semiparametric Censored Regression Models with Nonparametric Heteroskedasticity 11.4 The Univariate Kaplan-Meier CDF Estimator 11.5 The Multivariate Kaplan-Meier CDF Estimator 11.5.1 Nonparametric Regression Models with Random Censoring 11.6 Nonparametric Censored Regression 11.6.1 Lewbel and Linton’s Approach 11.6.2 Chen, Dahl and Khan’s Approach 331 332 334 336 338 341 343 345 345 346
CONTEXTS 11.7 Exercises III Consistent Model Specification Tests 348 349 12 Model Specification Tests 351 12.1 A Simple Consistent Test for Parametric Regression Functional Form 354 12.1.1 A Consistent Test for Correct Parametric Functional Form 355 12.1.2 Mixed Data 360 12.2 Testing for Equality of PDFs 362 12.3 More Tests Related to Regression Functions 365 12.3.1 Hardie and Mammen’s Test for a Parametric Regression Model 365 12.3.2 An Adaptive and Rate Optimal Test 367 12.3.3 A Test for a Parametric Single Index Model 369 12.3.4 A Nonparametric Omitted Variables Test 370 12.3.5 Testing the Significance of Categorical Variables 375 12.4 Tests Related to PDFs 378 12.4.1 Testing Independence between Two Random Variables 378 12.4.2 A Test for a Parametric PDF 380 12.4.3 A Kernel Test for Conditional Parametric Distributions 382 12.5 Applications 385 12.5.1 Growth Convergence Clubs 385 12.6 Proofs 388 12.6.1 Proof of Theorem 12.1 388 12.6.2 Proof of Theorem 12.2 389 12.6.3 Proof of Theorem 12.5 389 12.6.4 Proof of Theorem 12.9 391 12.7 Exercises 394 13 Nonsmoothing Tests 13.1 Testing for Parametric Regression Functional Form 13.2 Testing for Equality of PDFs 13.3 A Nonparametric Significance Test 13.4 Andrews’s Test for Conditional CDFs 13.5 Hong’s Tests for Serial Dependence 397 398 401 401 402 401
CONTENTS 13.6 More on Nonsmoothing Tests 13.7 Proofs 13.7.1 Proof of Theorem 13.1 13.8 Exercises IV Nonparametric Nearest Neighbor and Series Methods 408 409 409 410 413 14 K-Nearest Neighbor Methods 415 14.1 Density Estimation·. The Univariate Case 415 14.2 Regression Function Estimation 419 14.3 A Local Linear /с-nn Estimator 421 14.4 Cross-Validation with Local Constant fc-nn Estimation 422 14.5 Cross-Validation with Local LinearUnn Estimation 425 14.6 Estimation of Semiparametric Models with k-nn Methods 427 14.7 Model Specification Tests with fc-nn Methods 428 14.7.1 A Bootstrap Test 431 14.8 Using Different к for Different Components of x 432 14.9 Proofs 432 14.9.1 Proof of Theorem 14.1 435 14.9.2 Proof of Theorem 14.5 435 14.9.3 Proof of Theorem 14.10 440 14.10 Exercises 444 15 Nonparametric Series Methods 15.1 Estimating Regression Functions 15.1.1 Convergence Rates 15.2 Selection of the Series Term К 15.2.1 Asymptotic Normality 15.3 A Partially Linear Model 15.3.1 An Additive Partially Linear Model 15.3.2 Selection of Nonlinear AdditiveComponents 15.3.3 Estimating an Additive Model with a Known Link Function 15 4 Estimation of Partially Linear Varying Coefficient Models 15.4.1 Testing for Correct Parametric Regression Functional Form 445 446 449 451 453 454 455 461 463 466 471
xiii CONTEXTS 15.4.2 A Consistent Test for an Additive Partially Linear Model 15.5 Other Series-Based Tests 15.6 Proofs 15.6.1 Proof of Theorem 15.1 15.6.2 Proof of Theorem 15.3 15.6.3 Proof of Theorem 15.6 15.6.4 Proofof Theorem 15.9 15.6.5 Proof of Theorem 15.10 15.7 Exercises V Time Series, Simultaneous Panel Data Models Equation, 474 479 480 480 484 488 492 497 502 and 503 16 Instrumental Variables and Efficient Estimation of Scmiparametric Models 505 16.1 A Partially Linear Model with Endogenous Regressors in the Parametric Part 505 16.2 A Varying Coefficient Model with Endogenous Regressors in the Parametric Part 509 16.3 Ai and Chen’s Efficient Estimator with Conditional Moment Restrictions 511 16.3.1 Estimation Procedures 511 16.3.2 Asymptotic Normality for Θ 513 16.3.3 A Partially Linear Model with the Endogenous Regressors in the Nonparametric Part 515 16.4 Proof of Equation (16.16} 517 16.5 Exercises 520 17 Endogeneity in Nonparametric RegressionModels 17.1 A Nonparametric Model 17.2 A Triangular Simultaneous Equation Model 17.3 Newey-Powell Series-Based Estimator 17.4 Hall and Horowitz’s Kernel-Based Estimator 17.5 Darolles, Florens and Renault’s Estimator 17.6 Exercises 18 Weakly Dependent Data 18.1 Density Estimation with Dependent Data 521 521 522 527 529 532 533 535 537
XLV CONTENTS 18.1.1 Uniform Almost Sure Rate of Convergence 18.2 Regression Models with Dependent Data 18.2.1 The Martingale Difference Error Case 18.2.2 The Autocorrelated Error Case 18.2.3 One-Step-Ahead Forecasting 18.2.4 ¿-Step-Ahead Forecasting 18.2.5 Estimation of Nonparametric Impulse Response Functions 18.3 Semiparametric Models with Dependent Data 18.3.1 A Partially Linear Model with Dependent Data 18.3.2 Additive Regression Models 18.3.3 Varying Coefficient Models with Dependent Data 18.4 Testing for Serial Correlation in Semiparametric Models 18.4.1 The Test Statistic and Its Asymptotic Distribution 18.4.2 Testing Zero First Order Serial Correlation 18.5 Model Specification Tests with Dependent Data 18.5.1 A Kernel Test for Correct Parametric Regression Functional Form 18.5.2 Nonparametric Significance Tests 18.6 Nonsmoothing Tests for Regression Functional Form 18.7 Testing Parametric Predictive Models 18.7.1 In-Sample Testing of Conditional CDFs 18.7.2 Out-of-Sample Testing of Conditional CDFs 18.8 Applications 18.8.1 Forecasting Short-Term Interest Rates 18.9 Nonparametric Estimationwith Nonstationary Data 18.10 Proofs 18.10.1 Proof of Equation (18.9) 18.10.2 Proof of Theorem 18.2 18.11 Exercises 541 541 541 544 545 547 548 551 551 552 553 554 554 555 556 556 557 558 559 559 ՝ 562 564 564 566 567 567 569 572 19 Panel Data Models 575 19.1 Nonparametric Estimation of Panel Data Models: Ignoring the Variance Structure 576 19.2 Wang’s Efficient Nonparametric Panel Data Estimator 578 19.3 A Partially Linear Model with Random Effects 584 19.4 Nonparametric Panel
Data Models with Fixed Effects 586
CONTENTS 19.4.1 Error Variance Structure Is Known 587 19.4.2 The Error Variance Structure Is Unknown 590 19.5 Λ Partially Linear Model with Fixed Effects 592 19.6 Semiparametrie Instrumental Variable Estimators 594 19.6.1 An Infeasible Estimator 594 19.6.2 The Choice of Instruments 595 19.G.3 Λ Feasible Estimator 597 19.7 Testing for Serial Correlation and for Individual Effects in Semiparametrie Models 599 19.8 Series Estimation of Panel Data Models 602 19.8.1 Additive Effects 602 19.8.2 Alternative Formulation of Fixed Effects 604 19.9 Nonlinear Panel Data Models G06 19.9.1 Censored Panel Data Models 607 19.9.2 Discrete Choice Panel Data Models 614 19.10 Proofs 618 19.10.1 Proof of Theorem 19.1 618 19.10.2 Leading AISE Calculation of Wang’s Estimator G21 19.11 Exercises 624 20 Topics in Applied Nonparamctric Estimation 627 20.1 Nonparamotric Methods İn Continuous-Time Models G27 20.1.1 Nonparamctric Estimation of ContinuousTime Models 627 20.1.2 Nonparamctric Tests for Continuous-Time Models 632 20.1.3 Ait-Sahalia’s Test 632 20.1.4 Hong and Li's Test G33 20.1.5 Proofs 636 20.2 Nonparamctric Estimation of Average Treatment Effects 639 20.2.1 The Model 640 20.2.2 An Application: Assessing the Efficacy of Right Heart Catheterization 642 20.3 Nonparamctric Estimation of Auction Models 645 20.3.1 Estimation of First Price Auction Models 645 20.3.2 Conditionally Independent Private Information Auctions 648 20.4 Copula-Based Semiparametrie Estimation of Multivariate Distributions 651
CONTENTS 20.4.1 Some Background on Copula Functions 651 20.4.2 Semiparametric Copula-Based Multivariate Distributions 652 20.4.3 A Two-Step Estimation Procedure 653 20.4.4 A One-Step Efficient Estimation Procedure 655 20.4.5 Testing Parametric Functional Forms of a Copula 657 20.5 A Semiparametric Transformation Model 659 20.6 Exercises 662 A Background Statistical Concepts Probability, Measure, and Measurable Space Metric, Norm, and Functional Spaces Limits and Modes of Convergence 1.3.1 Limit Supremum and Limit Infimum 1.3.2 Modes of Convergence 1.4 Inequalities, Laws of Large Numbers, and Central Limit Theorems $88 1.5 Exercises 1.1 1.2 1.3 663 663 672 680 680 681 Bibliography θθ^ Author Index 737 Subject Index 744 |
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| spelling | Li, Qi Verfasser (DE-588)170846504 aut Nonparametric econometrics theory and practice Qi Li and Jeffrey S. Racine Princeton Princeton University Press 2023 xxi, 746 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Ökonometrie (DE-588)4132280-0 s Nichtparametrische Statistik (DE-588)4226777-8 s b DE-604 Racine, Jeffrey 1962- Verfasser (DE-588)133144720 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034346818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Qi Racine, Jeffrey 1962- Nonparametric econometrics theory and practice Nichtparametrische Statistik (DE-588)4226777-8 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4226777-8 (DE-588)4132280-0 (DE-588)4123623-3 |
| title | Nonparametric econometrics theory and practice |
| title_auth | Nonparametric econometrics theory and practice |
| title_exact_search | Nonparametric econometrics theory and practice |
| title_exact_search_txtP | Nonparametric econometrics theory and practice |
| title_full | Nonparametric econometrics theory and practice Qi Li and Jeffrey S. Racine |
| title_fullStr | Nonparametric econometrics theory and practice Qi Li and Jeffrey S. Racine |
| title_full_unstemmed | Nonparametric econometrics theory and practice Qi Li and Jeffrey S. Racine |
| title_short | Nonparametric econometrics |
| title_sort | nonparametric econometrics theory and practice |
| title_sub | theory and practice |
| topic | Nichtparametrische Statistik (DE-588)4226777-8 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Nichtparametrische Statistik Ökonometrie Lehrbuch |
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