Inconsistency transmission and variance reduction in two-stage quantile regression

Tae Hwan Kim, Christophe Muller

Research output: Contribution to journalArticle

Abstract

In this paper, we propose a new variance reduction method for quantile regressions with endogeneity problems, for alpha-mixing or m-dependent covariates and error terms. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions. Second, we exhibit an inconsistency transmission property derived from the asymptotic representation of our estimator. Third, using a reformulation of the dependent variable, we improve the efficiency of the two-stage quantile estimators by exploiting a tradeoff between an inconsistency confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the fine performance of our approach. In particular, by combining quantile regressions with first-stage trimmed least-squares estimators, we obtain more accurate slope estimates than 2SLS, 2SLAD and other estimators for a broad set of distributions. Finally, we apply our method to food demand equations in Egypt.

Original languageEnglish
JournalCommunications in Statistics: Simulation and Computation
DOIs
Publication statusAccepted/In press - 2019 Jan 1

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Quantile Regression
Variance Reduction
Inconsistency
Estimator
Quantile
Slope
α-mixing
Endogeneity
Asymptotic Representation
Dependent
Least Squares Estimator
Intercept
Error term
Reduction Method
Reformulation
Asymptotic distribution
Covariates
Monte Carlo Simulation
Trade-offs
Estimate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation

Cite this

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