scholarly journals Decentralization estimators for instrumental variable quantile regression models

2021 ◽  
Vol 12 (2) ◽  
pp. 443-475 ◽  
Author(s):  
Hiroaki Kaido ◽  
Kaspar Wüthrich
Keyword(s):  
Quantile Regression ◽  
Objective Function ◽  
Instrumental Variable ◽  
Regression Models ◽  
Black Box ◽  
Estimation Problem ◽  
Endogenous Covariates ◽  
Instrumental Variable Quantile Regression ◽  
High Level

The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen (2005)) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the nonsmoothness and nonconvexity of the IVQR GMM objective function. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression subproblems which are convex and can be solved efficiently. This reformulation leads to new identification results and to fast, easy to implement, and tuning‐free estimators that do not require the availability of high‐level “black box” optimization routines.

scholarly journals INSTRUMENTAL VARIABLE QUANTILE REGRESSION WITH MISCLASSIFICATION

2020 ◽  
pp. 1-36
Author(s):  
Takuya Ura
Keyword(s):  
Quantile Regression ◽  
Instrumental Variable ◽  
Reduced Form ◽  
Outcome Variable ◽  
Annual Review ◽  
Monotonicity Condition ◽  
Treatment Variable ◽  
Treatment Status ◽  
Instrumental Variable Quantile Regression ◽  
Quantile Treatment Effect

This article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

Factor instrumental variable quantile regression

2015 ◽  
Vol 19 (1) ◽  
Author(s):  
Jau-er Chen
Keyword(s):  
Quantile Regression ◽  
Factor Structure ◽  
Instrumental Variable ◽  
Asymptotic Properties ◽  
Principal Component ◽  
Firm Level ◽  
Data Set ◽  
Monte Carlo Studies ◽  
Instrumental Variable Quantile Regression ◽  
Unobservable Factors

AbstractThis paper proposes a factor instrumental variable quantile regression (FIVQR) estimator and studies its asymptotic properties. The proposed estimators share with quantile regression the advantage of exploring the shape of the conditional distribution of the dependent variable. When there are a factor structure and co-movement for economic variables, the underlying unobservable factors (or common components) are more efficient instruments. The proposed estimators achieve the optimality in the following sense: The method of principal component consistently estimates the space spanned by the ideal instruments which are utilized to control the endogeneity in the quantile regression analysis. Analyzing the asymptotic properties of the estimator, we assume that a panel of observable instruments follows a factor structure and the endogenous variables also share the same unobservable factors. Using the estimated factors as instruments, we show that the FIVQR estimator is consistent and asymptotically normal. Furthermore, when compared in the GMM framework, the proposed estimator is more efficient than the GMM estimator using many observable instruments directly. Monte Carlo studies demonstrate that the proposed estimators perform well. For an empirical application, we use a firm-level panel data set consisting of trading volumes and returns on DJIA to explore the asymmetric return–volume relation, controlling the endogeneity problem with the estimated factor instruments.

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