Chapter 41 ESTIMATION MODELS Semiparametric modelling is, as its name suggests, a hybrid of the parametric and nonparametric approaches to construction, fitting, and validation of statistical models. To place semiparametric methods in context, it is useful to review the way these other approaches are used to address a generic microeconometric | Chapter 41 ESTIMATION OF SEMIPARAMETRIC MODELS JAMES L. POWELL Princeton University Contents Abstract 2444 1. Introduction 2444 . Overview 2444 . Definition of semiparametric 2449 . Stochastic restrictions and structural models 2452 . Objectives and techniques of asymptotic theory 2460 2. Stochastic restrictions 2465 . Conditional mean restriction 2466 . Conditional quantile restrictions 2469 . Conditional symmetry restrictions 2474 . Independence restrictions 2476 . Exclusion and index restrictions 2482 3. Structural models 2487 . Discrete response models 2487 . Transformation models 2492 . Censored and truncated regression models 2500 . Selection models 2506 . Nonlinear panel data models 2511 4. Summary and conclusions 2513 References 2514 This work was supported by NSF Grants 91-96185 and 92-10101 to Princeton University. I am grateful to Hyungtaik Ahn Moshe Buchinsky Gary Chamberlain Songnian Chen Gregory Chow Angus Deaton Bo Honoré Joel Horowitz Oliver Linton Robin Lumsdaine Chuck Manski Rosa Matzkin Dan McFadden Whitney Newey Paul Ruud and Tom Stoker for their helpful suggestions which were generally adopted except when they were mutually contradictory or required a lot of extra work. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2444 . Powell Abstract A semiparametric model for observational data combines a parametric form for some component of the data generating process usually the behavioral relation between the dependent and explanatory variables with weak nonparametric restrictions on the remainder of the model usually the distribution of the unobservable errors . This chapter surveys some of the recent literature on semiparametric methods emphasizing microeconometric applications using limited dependent variable models. An introductory section defines semiparametric models more precisely and reviews the techniques used to derive the .
