Econometrica: Jan 1996, Volume 64, Issue 1

Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable

https://doi.org/0012-9682(199601)64:1<103:SEOARM>2.0.CO;2-V
p. 103-137

Joel L. Horowitz

This paper presents a method for estimating the model $\Lambda(Y) = \beta'X + U$, where $Y$ is a scalar, $\Lambda$ is an unknown increasing function, $X$ is a vector of explanatory variables, $\beta$ is a vector of unknown parameters, and $U$ has unknown cumulative distribution function $F$. It is not assumed that $\Lambda$ 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 $\Lambda$ and/or $F$. The paper develops $n^{1/2}$-consistent, asymptotically normal estimators of $\Lambda, F$, and quantiles of the conditional distribution of $Y$. Estimators of $\beta$ 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.

Log In To View Full Content

Back