Semiparametric Regression for the Applied Econometrician

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Cambridge University Press, Jun 2, 2003 - Business & Economics - 213 pages
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This book provides an accessible collection of techniques for analyzing nonparametric and semiparametric regression models. Worked examples include estimation of Engel curves and equivalence scales, scale economies, semiparametric Cobb-Douglas, translog and CES cost functions, household gasoline consumption, hedonic housing prices, option prices and state price density estimation. The book should be of interest to a broad range of economists including those working in industrial organization, labor, development, urban, energy and financial economics. A variety of testing procedures are covered including simple goodness of fit tests and residual regression tests. These procedures can be used to test hypotheses such as parametric and semiparametric specifications, significance, monotonicity and additive separability. Other topics include endogeneity of parametric and nonparametric effects, as well as heteroskedasticity and autocorrelation in the residuals. Bootstrap procedures are provided.
 

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Contents

Introduction to Differencing
1
12 Estimation of the Residual Variance
2
14 Specification Test
4
Scale Economies in Electricity Distribution
7
17 Why Differencing?
8
18 Empirical Applications
11
19 Notational Conventions
12
Background and Overview
15
Household Gasoline Demand and Price Endogeneity
88
410 Alternative Differencing Coefficients
89
411 The Relationship of Differencing to Smoothing
90
412 Combining Differencing and Smoothing
92
4123 Combining Differencing and Smoothing
93
4124 Reprise
94
Nonparametric Functions of Several Variables
99
513 Loess
101

22 The Curse of Dimensionality and the Need for Large Data Sets
17
23 Local Averaging Versus Optimization
19
233 Naive Optimization
22
24 A BirdsEye View of Important Theoretical Results
23
244 BiasVariance TradeOff
25
245 Asymptotic Distributions of Estimators
26
Introduction to Smoothing
27
312 A Basic Approximation
28
313 Consistency and Rate of Convergence
29
515 Smoothing Matrix
30
32 Kernel Smoothers
32
322 Asymptotic Normality
34
323 Comparison to Moving Average Smoother
35
325 Uniform Confidence Bands
36
Engel Curve Estimation
37
332 Properties
39
333 Spline Smoothers
40
342 Properties
41
Engel Curve Estimation
42
35 Selection of Smoothing Parameter
43
352 Nonparametric Least Squares
44
353 Implementation
46
36 Partial Linear Model
47
362 Nonparametric Least Squares
48
364 Heteroskedasticity
50
365 Heteroskedasticity and Autocorrelation
51
37 Derivative Estimation
52
372 Average Derivative Estimation
53
38 Exercises
54
HigherOrder Differencing Procedures
57
412 Basic Properties of Differencing and Related Matrices
58
422 Properties
59
423 Optimal Differencing Coefficients
60
424 Moving Average Differencing Coefficients
61
425 Asymptotic Normality
62
43 Specification Test
63
432 Heteroskedasticity
64
LogLinearity of Engel Curves
65
44 Test of Equality of Regression Functions
66
442 The Differencing Estimator Applied to the Pooled Data
67
443 Properties
68
Testing Equality of Engel Curves
69
45 Partial Linear Model
71
452 Heteroskedasticity
72
46 Empirical Applications
73
462 Scale Economies in Electricity Distribution
76
463 Weather and Electricity Demand
81
47 Partial Parametric Model
83
CES Cost Function
84
48 Endogenous Parametric Variables in the Partial Linear Model
85
482 Hausman Test
86
49 Endogenous Nonparametric Variable
87
52 Additive Separability
102
522 Additively Separable Nonparametric Least Squares
103
53 Differencing
104
532 Higher Dimensions and the Curse of Dimensionality
105
54 Empirical Applications
107
55 Exercises
110
Constrained Estimation and Hypothesis Testing
111
62 GoodnessofFit Tests
113
622 Rapid Convergence under the Null
114
63 Residual Regression Tests
115
632 Ustatistic Test Scalar xs Moving Average Smoother
116
633 Ustatistic Test Vector xs Kernel Smoother
117
64 Specification Tests
119
642 Hardle and Mammen 1993
120
643 Hong and White 1995
121
644 Li 1994 and Zheng 1996
122
65 Significance Tests
124
66 Monotonicity Concavity and Other Restrictions
125
662 Why Monotonicity Does Not Enhance the Rate of Convergence
126
663 KernelBased Algorithms for Estimating Monotone Regression Functions
127
665 Residual Regression and GoodnessofFit Tests of Restrictions
128
Estimation of Option Prices
129
67 Conclusions
134
68 Exercises
136
Index Models and Other Semiparametric Specifications
138
713 Properties
139
714 Identification
140
Engels Method for Multiple Family Types
142
72 Partial Linear Index Models
144
722 Estimation
146
723 Covariance Matrix
147
724 BaseIndependent Equivalence Scales
148
725 Testing BaseIndependence and Other Hypotheses
149
73 Exercises
151
Bootstrap Procedures
154
812 Location Scale Models
155
813 Regression Models
156
814 Validity of the Bootstrap
157
816 Limitations of the Bootstrap
159
818 Further Reading
160
83 Bootstrap GoodnessofFit and Residual Regression Tests
163
832 Residual Regression Tests
164
84 Bootstrap Inference in Partial Linear and Index Models
166
85 Exercises
171
Mathematical Preliminaries
173
Proofs
175
Optimal Differencing Weights
183
Nonparametric Least Squares
187
Variable Definitions
194
References
197
Index
209
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