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

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 n^1/2-consistent, asymptotically normal estimators of A, F, and quantiles of the conditional distribution of Y. Estimators of β that are n^1/2-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.