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Distributional Effects in Censored Quantile Regressions with Endogeneity and Heteroskedasticity

Xi Wang

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.

Distributional Effects in Censored Quantile Regressions with Endogeneity and Heteroskedasticity

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.
Paper Structure (12 sections, 7 theorems, 106 equations, 2 figures, 4 tables)

This paper contains 12 sections, 7 theorems, 106 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. SCFCQ Estimation
  3. Motivating examples
  4. Model and identification
  5. Estimation
  6. Asymptotic Properties
  7. Non-additive Structure
  8. Monte Carlo Experiments
  9. SCFCQ Estimation Algorithm
  10. Monte Carlo Simulations
  11. Heterogeneous Income Elasticities of Demand
  12. Conclusion

Key Result

Theorem 1

Under the model (censor1)-(endo1), suppose Assumption ID1 holds. Then for any $v,\tau \in (0,1)$, where $\nabla _{r}$ and $\nabla _{z}$ denote partial derivatives with respect to $r$ and $z$, respectively..

Figures (2)

  • Figure 1: Expenditure Elasticities
  • Figure 2: Expenditure Pattern

Theorems & Definitions (17)

  • Theorem 1
  • Example 1
  • Theorem 2
  • Remark 1
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Example 2
  • Example 3
  • ...and 7 more