Nonparametric econometrics : theory and practice

A comprehensive, up-to-date textbook on nonparametric methods for students and researchers

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 data--nominal and ordinal--in 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 types--continuous, nominal, and ordinal--within 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.

Author Notes

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.

Preface	p. xvii
Part I Nonparametric Kernel Methods	p. 1
Chapter 1 Density Estimation	p. 3
1.1 Univariate Density Estimation	p. 4
1.2 Univariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods	p. 14
1.3 Univariate Bandwidth Selection: Cross-Validation ZMethods	p. 15
1.3.1 Least Squares Cross-Validation	p. 15
1.3.2 Likelihood Cross-Validation	p. 18
1.3.3 An Illustration of Data-Driven Bandwidth Selection	p. 19
1.4 Univariate CDF Estimation	p. 19
1.5 Univariate CDF Bandwidth Selection: Cross- Validation Methods	p. 23
1.6 Multivariate Density Estimation	p. 24
1.7 Multivariate Bandwidth Selection: Rule-of-Thumb and Plug-In Methods	p. 26
1.8 Multivariate Bandwidth Selection: Cross-Validation Methods	p. 27
1.8.1 Least Squares Cross-Validation	p. 27
1.8.2 Likelihood Cross-Validation	p. 28
1.9 Asymptotic Normality of Density Estimators	p. 28
1.10 Uniform Rates of Convergence	p. 30
1.11 Higher Order Kernel Functions	p. 33
1.12 Proof of Theorem 1.4 (Uniform Almost Sure Convergence)	p. 35
1.13 Applications	p. 40
1.13.1 Female Wage Inequality	p. 41
1.13.2 Unemployment Rates and City Size	p. 43
1.13.3 Adolescent Growth	p. 44
1.13.4 Old Faithful Geyser Data	p. 44
1.13.5 Evolution of Real Income Distribution in Italy, 1951-1998	p. 45
1.14 Exercises	p. 47
Chapter 2 Regression	p. 57
2.1 Local Constant Kernel Estimation	p. 60
2.1.1 Intuition Underlying the Local Constant Kernel Estimator	p. 64
2.2 Local Constant Bandwidth Selection	p. 66
2.2.1 Rule-of-Thumb and Plug-In Methods	p. 66
2.2.2 Least Squares Cross-Validation	p. 69
2.2.3 AICc	p. 72
2.2.4 The Presence of Irrelevant Regressors	p. 73
2.2.5 Some Further Results on Cross-Validation	p. 78
2.3 Uniform Rates of Convergence	p. 78
2.4 Local Linear Kernel Estimation	p. 79
2.4.1 Local Linear Bandwidth Selection: Least Squares Cross-Validation	p. 83
2.5 Local Polynomial Regression (General pth Order)	p. 85
2.5.1 The Univariate Case	p. 85
2.5.2 The Multivariate Case	p. 88
2.5.3 Asymptotic Normality of Local Polynomial Estimators	p. 89
2.6 Applications	p. 92
2.6.1 Prestige Data	p. 92
2.6.2 Adolescent Growth	p. 92
2.6.3 Inflation Forecasting and Money Growth	p. 93
2.7 Proofs	p. 97
2.7.1 Derivation of (2.24)	p. 98
2.7.2 Proof of Theorem 2.7	p. 100
2.7.3 Definitions of Al,p+1 and Vl Used in Theorem 2.10	p. 106
2.8 Exercises	p. 108
Chapter 3 Frequency Estimation with Mixed Data	p. 115
3.1 Probability Function Estimation with Discrete Data	p. 116
3.2 Regression with Discrete Regressors	p. 118
3.3 Estimation with Mixed Data: The Frequency Approach	p. 118
3.3.1 Density Estimation with Mixed Data	p. 118
3.3.2 Regression with Mixed Data	p. 119
3.4 Some Cautionary Remarks on Frequency Methods	p. 120
3.5 Proofs	p. 122
3.5.1 Proof of Theorem 3.1	p. 122
3.6 Exercises	p. 123
Chapter 4 Kernel Estimation with Mixed Data	p. 125
4.1 Smooth Estimation of Joint Distributions with Discrete Data	p. 126
4.2 Smooth Regression with Discrete Data	p. 131
4.3 Kernel Regression with Discrete Regressors: The Irrelevant Regressor Case	p. 134
4.4 Regression with Mixed Data: Relevant Regressors	p. 136
4.4.1 Smooth Estimation with Mixed Data	p. 136
4.4.2 The Cross-Validation Method	p. 138
4.5 Regression with Mixed Data: Irrelevant Regressors	p. 140
4.5.1 Ordered Discrete Variables	p. 144
4.6 Applications	p. 145
4.6.1 Food-Away-from-Home Expenditure	p. 145
4.6.2 Modeling Strike Volume	p. 147
4.7 Exercises	p. 150
Chapter 5 Conditional Density Estimation	p. 155
5.1 Conditional Density Estimation: Relevant Variables	p. 155
5.2 Conditional Density Bandwidth Selection	p. 157
5.2.1 Least Squares Cross-Validation: Relevant Variables	p. 157
5.2.2 Maximum Likelihood Cross-Validation: Relevant Variables	p. 160
5.3 Conditional Density Estimation: Irrelevant Variables	p. 162
5.4 The Multivariate Dependent Variables Case	p. 164
5.4.1 The General Categorical Data Case	p. 167
5.4.2 Proof of Theorem 5.5	p. 168
5.5 Applications	p. 171
5.5.1 A Nonparametric Analys

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