Transformation Models in High-Dimensions

TL;DR

This paper extends transformation models to high-dimensional data, proposing an estimator for the transformation parameter that is asymptotically normal, with validation through simulations and an application to US wage data.

Contribution

It introduces a new estimator for transformation parameters in high-dimensional settings, accounting for nuisance functions that depend on the target parameter.

Findings

Estimator performs well in small samples

Transformation validity tested on US wage data

Asymptotic normality established for the estimator

Abstract

Transformation models are a very important tool for applied statisticians and econometricians. In many applications, the dependent variable is transformed so that homogeneity or normal distribution of the error holds. In this paper, we analyze transformation models in a high-dimensional setting, where the set of potential covariates is large. We propose an estimator for the transformation parameter and we show that it is asymptotically normally distributed using an orthogonalized moment condition where the nuisance functions depend on the target parameter. In a simulation study, we show that the proposed estimator works well in small samples. A common practice in labor economics is to transform wage with the log-function. In this study, we test if this transformation holds in CPS data from the United States.