Working Paper: NBER ID: w16997
Authors: Victor Chernozhukov; Iván Fernández-Val; Amanda E. Kowalski
Abstract: In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol.
Keywords: Censored Quantile Regression; Endogeneity; Instrumental Variables; Engel Curves
JEL Codes: C14
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| CQIV estimator (C36) | addresses censoring and endogeneity (C24) |
| traditional mean and quantile regression estimators (C51) | inconsistent results (C52) |
| censoring and endogeneity (C24) | correlation between regressors and error terms (C20) |
| CQIV estimator (C36) | combines Powell's censored quantile regression with control variable approach (C24) |
| first stage estimation (C51) | estimates control variable (C51) |
| second stage estimation (C51) | estimates nonadditive censored quantile regression model (C24) |
| CQIV estimator (C36) | valid estimates for Engel curves for alcohol (C51) |
| CQIV estimator (C36) | performs comparably to Tobit IV (C24) |
| CQIV estimator (C36) | outperforms Tobit IV under heteroskedasticity (C24) |