Unconditional Quantile Partial Effects via Conditional Quantile Regression

TL;DR

This paper introduces a semi-parametric method to estimate unconditional quantile partial effects using a two-step process involving quantile regression and nonparametric regression, with proven asymptotic properties and demonstrated robustness.

Contribution

It provides a novel identification and estimation approach for unconditional quantile effects based on conditional quantile regression coefficients.

Findings

Estimator shows excellent finite sample performance.

Method is robust to bandwidth and kernel choices.

Application to Engel's curve illustrates practical utility.

Abstract

This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates, unconditional quantile effects are a weighted average of conditional ones at particular quantile levels that depend on the covariates. We propose a two-step estimator for the unconditional effects where in the first step one estimates a structural quantile regression model, and in the second step a nonparametric regression is applied to the first step coefficients. We establish the asymptotic properties of the estimator, say consistency and asymptotic normality. Monte Carlo simulations show numerical evidence that the estimator has very good finite sample performance and is robust to the selection of bandwidth and kernel. To illustrate the proposed method, we study the canonical application of the Engel's curve, i.e. food expenditures as a share of income.