Semiparametric estimation of a regression model with an unknown transformation of the dependent variable

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Abstract

This paper presents a method for estimating the model A(Y) = β′X + U, where Y is a scalar, A is an unknown increasing function X is a vector of explanatory variables, β is a vector of unknown parameters, and U has unknown cumulative distribution function F. It is not assumed that A and F belong to known parametric families; they are estimated nonparametrically. This model generalizes a large number of widely used models that make stronger a priori assumptions about A and/or F. The paper develops n1/2-consistent, asymptotically normal estimators of A, F, and quantiles of the conditional distribution of Y. Estimators of β that are n1/2-consistent and asymptotically normal already exist. The results of Monte Carlo experiments indicate that the new estimators work reasonably well in samples of size 100.

Original languageEnglish (US)
Pages (from-to)103-137
Number of pages35
JournalEconometrica
Volume64
Issue number1
DOIs
StatePublished - Jan 1 1996

Keywords

  • Empirical process
  • Semiparametric estimation
  • Transformation model
  • Unobserved heterogeneity

ASJC Scopus subject areas

  • Economics and Econometrics

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