Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers.
Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical datanominal and ordinalin applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory.
This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data typescontinuous, nominal, and ordinalwithin one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables.
Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.
|Publisher:||Princeton University Press|
|Edition description:||New Edition|
|Product dimensions:||7.00(w) x 10.00(h) x 5.20(d)|
About the Author
Qi Li is Professor of Economics and Hugh Roy Cullen Professor in Liberal Arts at Texas A&M University. Jeffrey Scott Racine is Professor of Economics, Professor in the Graduate Program in Statistics, and Senator William McMaster Chair in Econometrics at McMaster University.
Table of Contents
PART I: Nonparametric Kernel Methods 1
Chapter 1: Density Estimation 3
1.1 Univariate Density Estimation 41.2 Univariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods 141.3 Univariate Bandwidth Selection: Cross-Validation ZMethods 151.3.1 Least Squares Cross-Validation 151.3.2 Likelihood Cross-Validation 181.3.3 An Illustration of Data-Driven Bandwidth Selection 191.4 Univariate CDF Estimation 191.5 Univariate CDF Bandwidth Selection: Cross- Validation Methods 231.6 Multivariate Density Estimation 241.7 Multivariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods 261.8 Multivariate Bandwidth Selection: Cross-Validation Methods 271.8.1 Least Squares Cross-Validation 271.8.2 Likelihood Cross-Validation 281.9 Asymptotic Normality of Density Estimators 281.10 Uniform Rates of Convergence 301.11 Higher Order Kernel Functions 331.12 Proof of Theorem 1.4 (Uniform Almost Sure Convergence) 351.13 Applications 401.13.1 Female Wage Inequality 411.13.2 Unemployment Rates and City Size 431.13.3 Adolescent Growth 441.13.4 Old Faithful Geyser Data 441.13.5 Evolution of Real Income Distribution in Italy, 1951-1998 451.14 Exercises 47
Chapter 2: Regression 57
2.1 Local Constant Kernel Estimation 602.1.1 Intuition Underlying the Local Constant Kernel Estimator 642.2 Local Constant Bandwidth Selection 662.2.1 Rule-of-Thumb and Plug-In Methods 662.2.2 Least Squares Cross-Validation 692.2.3 AICc 722.2.4 The Presence of Irrelevant Regressors 732.2.5 Some Further Results on Cross-Validation 782.3 Uniform Rates of Convergence 782.4 Local Linear Kernel Estimation 792.4.1 Local Linear Bandwidth Selection: Least Squares Cross-Validation 832.5 Local Polynomial Regression (General pth Order) 852.5.1 The Univariate Case 852.5.2 The Multivariate Case 882.5.3 Asymptotic Normality of Local Polynomial Estimators 892.6 Applications 922.6.1 Prestige Data 922.6.2 Adolescent Growth 922.6.3 Inflation Forecasting and Money Growth 932.7 Proofs 972.7.1 Derivation of (2.24) 982.7.2 Proof of Theorem 2.7 1002.7.3 Definitions of Al,p+1 and Vl Used in Theorem 2.10 1062.8 Exercises 108
Chapter 3: Frequency Estimation with Mixed Data 115
3.1 Probability Function Estimation with Discrete Data 1163.2 Regression with Discrete Regressors 1183.3 Estimation with Mixed Data: The Frequency Approach 1183.3.1 Density Estimation with Mixed Data 1183.3.2 Regression with Mixed Data 1193.4 Some Cautionary Remarks on Frequency Methods 1203.5 Proofs 1223.5.1 Proof of Theorem 3.1 1223.6 Exercises 123
Chapter 4: Kernel Estimation with Mixed Data 125
4.1 Smooth Estimation of Joint Distributions with Discrete Data 1264.2 Smooth Regression with Discrete Data 1314.3 Kernel Regression with Discrete Regressors: The Irrelevant Regressor Case 1344.4 Regression with Mixed Data: Relevant Regressors 1364.4.1 Smooth Estimation with Mixed Data 1364.4.2 The Cross-Validation Method 1384.5 Regression with Mixed Data: Irrelevant Regressors 1404.5.1 Ordered Discrete Variables 1444.6 Applications 1454.6.1 Food-Away-from-Home Expenditure 1454.6.2 Modeling Strike Volume 1474.7 Exercises 150
Chapter 5: Conditional Density Estimation 155
5.1 Conditional Density Estimation: Relevant Variables 1555.2 Conditional Density Bandwidth Selection 1575.2.1 Least Squares Cross-Validation: Relevant Variables 1575.2.2 Maximum Likelihood Cross-Validation: Relevant Variables 1605.3 Conditional Density Estimation: Irrelevant Variables 1625.4 The Multivariate Dependent Variables Case 1645.4.1 The General Categorical Data Case 1675.4.2 Proof of Theorem 5.5 1685.5 Applications 1715.5.1 A Nonparametric Analysis of Corruption 1715.5.2 Extramarital Affairs Data 1725.5.3 Married Female Labor Force Participation 1755.5.4 Labor Productivity 1775.5.5 Multivariate Y Conditional Density Example: GDP Growth and Population Growth Conditional on OECD Status 1785.6 Exercises 180
Chapter 6: Conditional CDF and Quantile Estimation 181
6.1 Estimating a Conditional CDF with Continuous Covariates without Smoothing the Dependent Variable 1826.2 Estimating a Conditional CDF with Continuous Covariates Smoothing the Dependent Variable 1846.3 Nonparametric Estimation of Conditional Quantile Functions 1896.4 The Check Function Approach 1916.5 Conditional CDF and Quantile Estimation with Mixed Discrete and Continuous Covariates 1936.6 A Small Monte Carlo Simulation Study 1966.7 Nonparametric Estimation of Hazard Functions 1986.8 Applications 2006.8.1 Boston Housing Data 2006.8.2 Adolescent Growth Charts 2026.8.3 Conditional Value at Risk 2026.8.4 Real Income in Italy, 1951-1998 2066.8.5 Multivariate Y Conditional CDF Example: GDP Growth and Population Growth Conditional on OECD Status 2066.9 Proofs 2096.9.1 Proofs of Theorems 6.1, 6.2, and 6.4 2096.9.2 Proofs of Theorems 6.5 and 6.6 (Mixed Covariates Case) 2146.10 Exercises 215
PART II: Semiparametric Methods 219
Chapter 7: Semiparametric Partially Linear Models 221
7.1 Partially Linear Models 2227.1.1 Identification of 2227.2 Robinson's Estimator 2227.2.1 Estimation of the Nonparametric Component 2287.3 Andrews's MINPIN Method 2307.4 Semiparametric Efficiency Bounds 2337.4.1 The Conditionally Homoskedastic Error Case 2337.4.2 The Conditionally Heteroskedastic Error Case 2357.5 Proofs 2387.5.1 Proof of Theorem 7.2 2387.5.2 Verifying Theorem 7.3 for a Partially Linear Model 2447.6 Exercises 246
Chapter 8: Semiparametric Single Index Models 249
8.1 Identification Conditions 2518.2 Estimation 2538.2.1 Ichimura's Method 2538.3 Direct Semiparametric Estimators for 2588.3.1 Average Derivative Estimators 2588.3.2 Estimation of g() 2628.4 Bandwidth Selection 2638.4.1 Bandwidth Selection for Ichimura's Method 2638.4.2 Bandwidth Selection with Direct Estimation Methods 2658.5 Klein and Spady's Estimator 2668.6 Lewbel's Estimator 2678.7 Manski's Maximum Score Estimator 2698.8 Horowitz's Smoothed Maximum Score Estimator 2708.9 Han's Maximum Rank Estimator 2708.10 Multinomial Discrete Choice Models 2718.11 Ai's Semiparametric Maximum Likelihood Approach 2728.12 A Sketch of the Proof of Theorem 8.1 2758.13 Applications 2778.13.1 Modeling Response to Direct Marketing Catalog Mailings 2778.14 Exercises 281
Chapter 9: Additive and Smooth (Varying) Coefficient Semiparametric Models 283
9.1 An Additive Model 2839.1.1 The Marginal Integration Method 2849.1.2 A Computationally Efficient Oracle Estimator 2869.1.3 The Ordinary Backfitting Method 2899.1.4 The Smoothed Backfitting Method 2909.1.5 Additive Models with Link Functions 2959.2 An Additive Partially Linear Model 2979.2.1 A Simple Two-Step Method 2999.3 A Semiparametric Varying (Smooth) Coefficient Model 3019.3.1 A Local Constant Estimator of the Smooth Coefficient Function 3029.3.2 A Local Linear Estimator of the Smooth Coefficient Function 3039.3.3 Testing for a Parametric Smooth Coefficient Model 3069.3.4 Partially Linear Smooth Coefficient Models 3089.3.5 Proof of Theorem 9.3 3109.4 Exercises 312
Chapter 10: Selectivity Models 315
10.1 Semiparametric Type-2 Tobit Models 31610.2 Estimation of a Semiparametric Type-2 Tobit Model 31710.2.1 Gallant and Nychka's Estimator 31810.2.2 Estimation of the Intercept in Selection Models 31910.3 Semiparametric Type-3 Tobit Models 32010.3.1 Econometric Preliminaries 32010.3.2 Alternative Estimation Methods 32310.4 Das, Newey and Vella's Nonparametric Selection Model 32810.5 Exercises 330
Chapter 11: Censored Models 331
11.1 Parametric Censored Models 33211.2 Semiparametric Censored Regression Models 33411.3 Semiparametric Censored Regression Models with Nonparametric Heteroskedasticity 33611.4 The Univariate Kaplan-Meier CDF Estimator 33811.5 The Multivariate Kaplan-Meier CDF Estimator 34111.5.1 Nonparametric Regression Models with Random Censoring 34311.6 Nonparametric Censored Regression 34511.6.1 Lewbel and Linton's Approach 34511.6.2 Chen, Dahl and Khan's Approach 34611.7 Exercises 348III Consistent Model Specification Tests 349
Chapter 12: Model Specification Tests 351
12.1 A Simple Consistent Test for Parametric Regression Functional Form 35412.1.1 A Consistent Test for Correct Parametric Functional Form 35512.1.2 Mixed Data 36012.2 Testing for Equality of PDFs 36212.3 More Tests Related to Regression Functions 36512.3.1 Härdle and Mammen's Test for a Parametric Regression Model 36512.3.2 An Adaptive and Rate Optimal Test 36712.3.3 A Test for a Parametric Single Index Model 36912.3.4 A Nonparametric Omitted Variables Test 37012.3.5 Testing the Significance of Categorical Variables 37512.4 Tests Related to PDFs 37812.4.1 Testing Independence between Two Random Variables 37812.4.2 A Test for a Parametric PDF 38012.4.3 A Kernel Test for Conditional Parametric Distributions 38212.5 Applications 38512.5.1 Growth Convergence Clubs 38512.6 Proofs 38812.6.1 Proof of Theorem 12.1 38812.6.2 Proof of Theorem 12.2 38912.6.3 Proof of Theorem 12.5 38912.6.4 Proof of Theorem 12.9 39112.7 Exercises 394
Chapter 13: Nonsmoothing Tests 397
13.1 Testing for Parametric Regression Functional Form 39813.2 Testing for Equality of PDFs 40113.3 A Nonparametric Significance Test 40113.4 Andrews's Test for Conditional CDFs 40213.5 Hong's Tests for Serial Dependence 40413.6 More on Nonsmoothing Tests 40813.7 Proofs 40913.7.1 Proof of Theorem 13.1 40913.8 Exercises 410
PART IV: Nonparametric Nearest Neighbor and Series Methods 413
Chapter 14: K-Nearest Neighbor Methods 41514.1 Density Estimation: The Univariate Case 41514.2 Regression Function Estimation 41914.3 A Local Linear k-nn Estimator 42114.4 Cross-Validation with Local Constant k-nn Estimation 42214.5 Cross-Validation with Local Linear k-nn Estimation 42514.6 Estimation of Semiparametric Models with k-nn Methods 42714.7 Model Specification Tests with k-nn Methods 42814.7.1 A Bootstrap Test 43114.8 Using Different k for Different Components of x 43214.9 Proofs 43214.9.1 Proof of Theorem 14.1 43514.9.2 Proof of Theorem 14.5 43514.9.3 Proof of Theorem 14.10 44014.10 Exercises 444
Chapter 15: Nonparametric Series Methods 445
15.1 Estimating Regression Functions 44615.1.1 Convergence Rates 44915.2 Selection of the Series Term K 45115.2.1 Asymptotic Normality 45315.3 A Partially Linear Model 45415.3.1 An Additive Partially Linear Model 45515.3.2 Selection of Nonlinear Additive Components 46115.3.3 Estimating an Additive Model with a Known Link Function 46315.4 Estimation of Partially Linear Varying Coefficient Models 46615.4.1 Testing for Correct Parametric Regression Functional Form 47115.4.2 A Consistent Test for an Additive Partially Linear Model 47415.5 Other Series-Based Tests 47915.6 Proofs 48015.6.1 Proof of Theorem 15.1 48015.6.2 Proof of Theorem 15.3 48415.6.3 Proof of Theorem 15.6 48815.6.4 Proof of Theorem 15.9 49215.6.5 Proof of Theorem 15.10 49715.7 Exercises 502
PART V: Time Series, Simultaneous Equation, and Panel Data Models 503
Chapter 16: Instrumental Variables and Efficient Estimation of Semiparametric Models 50516.1 A Partially Linear Model with Endogenous Regressors in the Parametric Part 50516.2 A Varying Coefficient Model with Endogenous Regressors in the Parametric Part 50916.3 Ai and Chen's Efficient Estimator with Conditional Moment Restrictions 51116.3.1 Estimation Procedures 51116.3.2 Asymptotic Normality for 51316.3.3 A Partially Linear Model with the Endogenous Regressors in the Nonparametric Part 51516.4 Proof of Equation (16.16) 51716.5 Exercises 520
Chapter 17: Endogeneity in Nonparametric Regression Models 521
17.1 A Nonparametric Model 52117.2 A Triangular Simultaneous Equation Model 52217.3 Newey-Powell Series-Based Estimator 52717.4 Hall and Horowitz's Kernel-Based Estimator 52917.5 Darolles, Florens and Renault's Estimator 53217.6 Exercises 533
Chapter 18: Weakly Dependent Data 535
18.1 Density Estimation with Dependent Data 53718.1.1 Uniform Almost Sure Rate of Convergence 54118.2 Regression Models with Dependent Data 54118.2.1 The Martingale Difference Error Case 54118.2.2 The Autocorrelated Error Case 54418.2.3 One-Step-Ahead Forecasting 54618.2.4 d-Step-Ahead Forecasting 54718.2.5 Estimation of Nonparametric Impulse Response Functions 54818.3 Semiparametric Models with Dependent Data 55118.3.1 A Partially Linear Model with Dependent Data 55118.3.2 Additive Regression Models 55218.3.3 Varying Coefficient Models with Dependent Data 55318.4 Testing for Serial Correlation in Semiparametric Models 55418.4.1 The Test Statistic and Its Asymptotic Distribution 55418.4.2 Testing Zero First Order Serial Correlation 55518.5 Model Specification Tests with Dependent Data 55618.5.1 A Kernel Test for Correct Parametric Regression Functional Form 55618.5.2 Nonparametric Significance Tests 55718.6 Nonsmoothing Tests for Regression Functional Form 55818.7 Testing Parametric Predictive Models 55918.7.1 In-Sample Testing of Conditional CDFs 55918.7.2 Out-of-Sample Testing of Conditional CDFs 56218.8 Applications 56418.8.1 Forecasting Short-Term Interest Rates 56418.9 Nonparametric Estimation with Nonstationary Data 56618.10 Proofs 56718.10.1 Proof of Equation (18.9) 56718.10.2 Proof of Theorem 18.2 56918.11 Exercises 572
Chapter 19: Panel Data Models 575
19.1 Nonparametric Estimation of Panel Data Models: Ignoring the Variance Structure 57619.2 Wang's Efficient Nonparametric Panel Data Estimator 57819.3 A Partially Linear Model with Random Effects 58419.4 Nonparametric Panel Data Models with Fixed Effects 58619.4.1 Error Variance Structure Is Known 58719.4.2 The Error Variance Structure Is Unknown 59019.5 A Partially Linear Model with Fixed Effects 59219.6 Semiparametric Instrumental Variable Estimators 59419.6.1 An Infeasible Estimator 59419.6.2 The Choice of Instruments 59519.6.3 A Feasible Estimator 59719.7 Testing for Serial Correlation and for Individual Effects in Semiparametric Models 59919.8 Series Estimation of Panel Data Models 60219.8.1 Additive Effects 60219.8.2 Alternative Formulation of Fixed Effects 60419.9 Nonlinear Panel Data Models 60619.9.1 Censored Panel Data Models 60719.9.2 Discrete Choice Panel Data Models 61419.10 Proofs 61819.10.1 Proof of Theorem 19.1 61819.10.2 Leading MSE Calculation of Wang's Estimator 62119.11 Exercises 624
Chapter 20: Topics in Applied Nonparametric Estimation 627
20.1 Nonparametric Methods in Continuous-Time Models 62720.1.1 Nonparametric Estimation of Continuous-Time Models 62720.1.2 Nonparametric Tests for Continuous-Time Models 63220.1.3 Ait-Sahalia's Test 63220.1.4 Hong and Li's Test 63320.1.5 Proofs 63620.2 Nonparametric Estimation of Average Treatment Effects 63920.2.1 The Model 64020.2.2 An Application: Assessing the Efficacy of Right Heart Catheterization 64220.3 Nonparametric Estimation of Auction Models 64520.3.1 Estimation of First Price Auction Models 64520.3.2 Conditionally Independent Private Information Auctions 64820.4 Copula-Based Semiparametric Estimation of Multivariate Distributions 65120.4.1 Some Background on Copula Functions 65120.4.2 Semiparametric Copula-Based Multivariate Distributions 65220.4.3 A Two-Step Estimation Procedure 65320.4.4 A One-Step Efficient Estimation Procedure 65520.4.5 Testing Parametric Functional Forms of a Copula 65720.5 A Semiparametric Transformation Model 65920.6 Exercises 662
A Background Statistical Concepts 663
1.1 Probability, Measure, and Measurable Space 6631.2 Metric, Norm, and Functional Spaces 6721.3 Limits and Modes of Convergence 6801.3.1 Limit Supremum and Limit Infimum 6801.3.2 Modes of Convergence 6811.4 Inequalities, Laws of Large Numbers, and Central Limit Theorems 6881.5 Exercises 694
Bibliography 697Author Index 737Subject Index 744
What People are Saying About This
This book represents a very significant contribution to the field of econometrics. It provides an extremely thorough coverage of our knowledge in the area of nonparametric and semiparametric methods as they apply to economic models and economic data. And it makes accessible, for the first time, a body of relatively new material relating to discrete and 'mixed' data. There is a good balance of theoretical material and applications. Apart from serving as a superb teaching text in graduate-level courses where the students have a strong econometrics/statistics preparation, I believe this book will become a must-have reference resource for many researchers.
David E. Giles, University of Victoria
Very few studies have tried to apply the nonparametric techniques to analyze real data. The lack of applications of those techniques is perhaps attributable to the lack of a good textbook that explains intuitively how and why those techniques work. This book by Li and Racine serves both applied researchers and graduate students. It is written in plain language so that it can be understood by anyone with basic econometrics but zero knowledge of nonparametric methods. And it contains enough specifics that clearly spell out steps to implement those methods.
Chunrong Ai, University of Florida
Nonparametric Econometrics by Li and Racine is a must for any serious econometrician or statistician who is working on cutting-edge problems. The theoretical treatment of nonparametric methods is remarkably complete in its coverage of mainstream and relatively arcane topics. I particularly like Li and Racine's general treatment of continuous and discrete regressors and of specification testing, topics that I have not seen handled in such a comprehensive fashion. I will certainly use this in my graduate econometrics courses and in conducting my own research.
Robin Sickles, Rice University