Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions

TL;DR

This paper introduces a flexible Gaussian modeling framework for estimating conditional distribution functions, offering a unified, efficient, and monotonic approach with practical benefits demonstrated through an application to the gender wage gap.

Contribution

It develops a novel Gaussian representation for conditional distributions with a concave likelihood, enabling unified, efficient estimation of various distributional functions.

Findings

Provides a unified framework for density, distribution, and quantile estimation.

Achieves parametric rate of convergence in estimation.

Demonstrates finite sample improvements over existing methods.

Abstract

We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative distribution functions, including in finite samples and under general misspecification. We use these representations to provide a unified framework for the flexible Maximum Likelihood estimation of conditional density, cumulative distribution, and quantile functions at parametric rate. Our formulation yields substantial simplifications and finite sample improvements over related methods. An empirical application to the gender wage gap in the United States illustrates our framework.