Distributional Effects in Censored Quantile Regressions with Endogeneity and Heteroskedasticity

2026-02-22

AI Summary

Existing quantile estimation methods struggle to ensure consistency when censoring, endogenous regressors, and conditional heteroskedasticity coexist, thereby limiting accurate identification of heterogeneous economic effects. This study proposes a two-step sequential control function censored quantile (SCFCQ) estimator, which for the first time integrates the control function approach with sequential quantile regression to effectively address identification of distributional effects in the presence of unbounded endogeneity and heteroskedasticity. The method enjoys strong theoretical properties and computational tractability. Applied to the UK Family Expenditure Survey data, it successfully uncovers the heterogeneous distribution of income elasticities across household preference dimensions, demonstrating both robustness and empirical relevance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Distributed Search

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Distributional effects, characterized by quantile frameworks, are well-known to capture 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 develops a Sequential Control Function Censored Quantile (SCFCQ) estimator for distributional effects in censored quantile models with unbounded endogenous regressors. Our method combines the sequential analysis with the control function approach, particularly adapting for conditional heteroskedasticity in the endogenous regressor. The estimation algorithm is a two-step procedure composed of series quantile regressions, thereby providing applied researchers with a computationally tractable and practically feasible tool. We apply the SCFCQ method to estimate heterogeneous income elasticities over household preferences using data from the UK Family Expenditure Survey.

Problem

• Censored Quantile Regression
• Endogeneity
• Heteroskedasticity
• Distributional Effects
• Quantile Framework

Innovation

• Censored Quantile Regression
• Endogeneity
• Control Function
• Heteroskedasticity
• Distributional Effects