Distributional Effects in Censored Quantile Regressions with Endogeneity and Heteroskedasticity

TL;DR

This paper introduces a two-nested-step estimation method for censored quantile models that accounts for endogeneity and heteroskedasticity, enabling more accurate analysis of distributional effects in empirical data.

Contribution

It develops a novel two-step estimator combining sequential analysis and control functions, suitable for heterogeneous distributional effects in complex censored data.

Findings

Estimator performs well in finite sample Monte Carlo simulations.

Method applied to UK data reveals heterogeneous income elasticities across expenditure ranks.

Provides a computationally feasible tool for empirical researchers dealing with censored, endogenous, and heteroskedastic data.

Abstract

Distributional effects, captured by quantile frameworks, are well-received for characterizing heterogeneous impacts of economic factors across the unobserved relative ranks. Censored outcome, endogenous regressor and heteroskedastic error are prevalent in empirical work, yet challenge the consistency of existing quantile estimation methods. This paper proposes a two-nested-step(TNS) estimation method for distributional effects in censored quantile models with endogeneity and heteroskedasticity. It combines the sequential analysis with the control function approach, adapting for heterogeneous distributional effects. The estimation algorithm is a two-step procedure nested with a sequence of series quantile regressions, thereby providing applied researchers with a computationally tractable and practically feasible tool. Monte Carlo simulation results demonstrate the good performance of our estimator in a finite sample. We apply the proposed method to estimate heterogeneous income elasticities of households across relative ranks of commodity expenditure using data from the UK Family Expenditure Survey.