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Many econometric models contain unknown functions as well as finite- dimensional parameters. Examples of such unknown functions are the distribution function of an unobserved random variable or a transformation of an observed variable. Econometric methods for estimating population parameters in the presence of unknown functions are called "semiparametric." During the past 15 years, much research has been carried out on semiparametric econometric models that are relevant to empirical economics. This book synthesizes the results that have been achieved for five important classes of models. The book is aimed at graduate students in econometrics and statistics as well as professionals who are not experts in semiparametic methods. The usefulness of the methods will be illustrated with applications that use real data.
1. Introduction.- 2. Single-Index Models.- 2.1 Definition of a Single-Index Model.- 2.2 Why Single-Index Models Are Useful.- 2.3 Other Approaches to Dimension Reduction.- 2.4 Identification of Single-Index Models.- 2.5 EstimatingGin a Single-Index Modei.- 2.6 Optimization Estimators ofß.- 2.7 Direct Semiparametric Estimators.- 2.8 Bandwidth Selection.- 2.9 An Empirical Example.- 3. Binary Response Models.- 3.1 Random-Coefficients Models.- 3.2 Identification.- 3.3 Estimation.- 3.4 Extensions of the Maximum Score and Smoothed Maximum Score Estimators.- 3.5 An Empirical Example.- 4. Deconvolution Problems.- 4.1 A Model of Measurement Error.- 4.2 Models for Panel Data.- 4.3 Extensions.- 4.4 An Empirical Example.- 5. Transformation Models.- 5.1 Estimation with ParametricTand NonparametricF.- 5.2 Estimation with NonparametricTand ParametricF.- 5.3 Estimation when BothTandFare Nonparametric.- 5.4 Predicting Y Conditional onX.- 5.5 An Empirical Example.- Appendix: Nonparametric Estimation.- A.1 Nonparametric Density Estimation.- A.2 Nonparametric Mean Regression.- References.