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Inconsistency transmission and variance reduction in two-stage quantile regression

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.
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Submitted on : Thursday, March 5, 2020 - 12:53:32 PM
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Tae-Hwan Kim, Christophe Muller. Inconsistency transmission and variance reduction in two-stage quantile regression. Communications in Statistics - Simulation and Computation, Taylor & Francis, 2020, 49 (4), pp.1044-1077. ⟨10.1080/03610918.2018.1493505⟩. ⟨hal-02084505⟩

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