Semiparametric regression for the applied econometrician

Cover......Page 1
Half-title......Page 3
Series-title......Page 5
Title......Page 7
Copyright......Page 8
Dedication......Page 9
Contents......Page 11
List of Figures and Tables......Page 17
Preface......Page 19
1.1 A Simple Idea......Page 23
1.3 The Partial Linear Model......Page 24
1.5 Test of Equality of Regression Functions......Page 26
1.6 Empirical Application: Scale Economies in Electricity Distribution......Page 29
1.7 Why Differencing?......Page 30
1.8 Empirical Applications......Page 33
1.10 Exercises......Page 34
2.1 Categorization of Models......Page 37
2.2.2 Restrictions That Mitigate the Curse......Page 39
2.3.2 Bias-Variance Trade-Off......Page 41
2.3.3 Naive Optimization......Page 44
2.4.3 Rate of Convergence......Page 45
2.4.4 Bias-Variance Trade-Off......Page 47
2.4.7 Testing Procedures......Page 48
3.1.1 The Moving Average Smoother......Page 49
3.1.2 A Basic Approximation......Page 50
3.1.4 Asymptotic Normality and Confidence Intervals......Page 51
3.1.6 Empirical Application: Engel Curve Estimation......Page 52
3.2.1 Estimator......Page 54
3.2.2 Asymptotic Normality......Page 56
3.2.4 Confidence Intervals......Page 57
3.2.5 Uniform Confidence Bands......Page 58
3.3.1 Estimation......Page 59
3.3.2 Properties......Page 61
3.4.1 Local Linear Regression......Page 62
3.4.2 Properties......Page 63
3.4.3 Empirical Application: Engel Curve Estimation......Page 64
3.5.1 Kernel Estimation......Page 65
3.5.2 Nonparametric Least Squares......Page 66
3.5.3 Implementation......Page 68
3.6.1 Kernel Estimation......Page 69
3.6.3 The General Case......Page 70
3.6.4 Heteroskedasticity......Page 72
3.6.5 Heteroskedasticity and Autocorrelation......Page 73
3.7.1 Point Estimates......Page 74
3.7.2 Average Derivative Estimation......Page 75
3.8 Exercises......Page 76
4.1.1 Definitions......Page 79
4.2.1 The mth-Order Differencing Estimator......Page 80
4.2.2 Properties......Page 81
4.2.3 Optimal Differencing Coefficients......Page 82
4.2.4 Moving Average Differencing Coefficients......Page 83
4.2.5 Asymptotic Normality......Page 84
4.3.1 A Simple Statistic......Page 85
4.3.2 Heteroskedasticity......Page 86
4.3.3 Empirical Application: Log-Linearity of Engel Curves......Page 87
4.4.1 A Simplified Test Procedure......Page 88
4.4.2 The Differencing Estimator Applied to the Pooled Data......Page 89
4.4.3 Properties......Page 90
4.4.4 Empirical Application: Testing Equality of Engel Curves......Page 91
4.5.1 Estimator......Page 93
4.5.2 Heteroskedasticity......Page 94
4.6.1 Household Gasoline Demand in Canada......Page 95
4.6.2 Scale Economies in Electricity Distribution......Page 98
4.6.3 Weather and Electricity Demand......Page 103
4.7.1 Estimator......Page 105
4.7.2 Empirical Application: CES Cost Function......Page 106
4.8.1 Instrumental Variables......Page 107
4.8.2 Hausman Test......Page 108
4.9.1 Estimation......Page 109
4.9.2 Empirical Application: Household Gasoline Demand and Price Endogeneity......Page 110
4.10 Alternative Differencing Coefficients......Page 111
4.11 The Relationship of Differencing to Smoothing......Page 112
4.12.2 Combining Differencing Procedures in Sequence......Page 114
4.12.3 Combining Differencing and Smoothing......Page 115
4.13 Exercises......Page 116
5.1.2 Kernel Estimation of Functions of Several Variables......Page 121
5.1.4 Nonparametric Least Squares......Page 123
5.2.1 Backfitting......Page 124
5.2.2 Additively Separable Nonparametric Least Squares......Page 125
5.3.1 Two Dimensions......Page 126
5.3.2 Higher Dimensions and the Curse of Dimensionality......Page 127
5.4.2 Household Gasoline Demand in Canada......Page 129
5.5 Exercises......Page 132
6.1 The Framework......Page 133
6.2.1 Parametric Goodness-of-Fit Tests......Page 135
6.2.2 Rapid Convergence under the Null......Page 136
6.3.1 Overview......Page 137
6.3.2 U-statistic Test – Scalar x’s, Moving Average Smoother......Page 138
6.3.3 U-statistic Test – Vector x’s, Kernel Smoother......Page 139
6.4.1 Bierens (1990)......Page 141
6.4.2 Härdle and Mammen (1993)......Page 142
6.4.3 Hong and White (1995)......Page 143
6.4.4 Li (1994) and Zheng (1996)......Page 144
6.5 Significance Tests......Page 146
6.6.1 Isotonic Regression......Page 147
6.6.2 Why Monotonicity Does Not Enhance the Rate of Convergence......Page 148
6.6.4 Nonparametric Least Squares Subject to Monotonicity Constraints......Page 149
6.6.5 Residual Regression and Goodness-of-Fit Tests of Restrictions......Page 150
6.6.6 Empirical Application: Estimation of Option Prices......Page 151
6.7 Conclusions......Page 156
6.8 Exercises......Page 158
7.1.2 Estimation......Page 160
7.1.3 Properties......Page 161
7.1.5 Empirical Application: Engel’s Method for Estimation of Equivalence Scales......Page 162
7.1.6 Empirical Application: Engel’s Method for Multiple Family Types......Page 164
7.2.1 Introduction......Page 166
7.2.2 Estimation......Page 168
7.2.3 Covariance Matrix......Page 169
7.2.4 Base-Independent Equivalence Scales......Page 170
7.2.5 Testing Base-Independence and Other Hypotheses......Page 171
7.3 Exercises......Page 173
8.1.1 Introduction......Page 176
8.1.2 Location Scale Models......Page 177
8.1.3 Regression Models......Page 178
8.1.5 Benefits of the Bootstrap......Page 179
8.1.7 Summary of Bootstrap Choices......Page 181
8.2 Bootstrap Confidence Intervals for Kernel Smoothers......Page 182
8.3.1 Goodness-of-Fit Tests......Page 185
8.3.2 Residual Regression Tests......Page 186
8.4.2 Index Models......Page 188
8.5 Exercises......Page 193
Appendix A – Mathematical Preliminaries......Page 195
Appendix B – Proofs......Page 197
Appendix C – Optimal Differencing Weights......Page 205
1. Sobolev Space Results......Page 209
Computation of Estimator......Page 210
Additive Separability......Page 211
3. Calculation of Representors......Page 212
Appendix E – Variable Definitions......Page 216
References......Page 219
Index......Page 231