An IV Model of Quantile Treatment Effects

Abstract

Headnote.The ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications. However, in observational studies, the variables of interest (e.g. education, prices) are often endogenous, making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes. In order to address this problem, we develop a model of quantile treatment effects (QTE) in the presence of endogeneity and obtain conditions for identification of the QTE without functional form assumptions. The principal feature of the model is the imposition of conditions which restrict the evolution of ranks across treatment states. This feature allows us to overcome the endogeneity problem and recover the true QTE through the use of instrumental variables. The proposed model can also be equivalently viewed as a structural simultaneous equation model with non-additive errors, where QTE can be interpreted as the structural quantile effects (SQE).

The Japanese Taylor rule estimated using censored quantile regressions

“…Using these CPI data, we construct 1-year-ahead ex post core inflation 6 rates and, 3 Although Chevapatrakul et al (2009) present data up to 2005 for Japan, their estimation uses a sample that ends before February 1999, to study the monetary policy when the ZLB is approached. 4 The 2SQR methodology is based on the fitted value approach, which extends Amemiya (1982), whereas the IVQR method builds on the instrumental variable approach suggested by Chernozhukov and Hansen (2005, 2008. 5 The call rate data are available from July 1985 at the Bank of Japan's web site.…”

Quantile Uncorrelation and Instrumental Regressions

“…As in the classical 2SLS, median uncorrelation leads to an estimator that is derived by taking a "sample analogue" of the median uncorrelation measure. This estimator, similar to one used by Chernozhukov and Hansen (2005) (or CH) , is consistent provided that this uncorrelation holds (along with other standard assumptions). Other applications are natural counterparts of existing least squares methods.…”

“…There are a set of papers that deal with endogeneity in linear (and nonlinear) quantile based models. See for example Amemiya (1981) for a 2 stage interpretation of the 2SLS, and Chernozhukov and Hansen (2005) for an approach to inference in quantile based models, both linear and nonlinear, in the presence of endogenous regressors.…”

“…Then, based on method of moments, Honoré and Hu (2004) provide methods that can be used to do inference on parameters defined though separable moment models (that can be nonlinear). Chernozhukov and Hansen (2005) (CH) in a series of papers shed new light on general class of monotonic models with conditional quantile restrictions. They provide sufficient point identification conditions for these models, and also an estimator that they is consistent under those conditions.…”

Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure

“…Benkard and Berry (2006) showed that this claim is incorrect, leaving uncertain the nonparametric identifiability of fully simultaneous models. Completeness conditions (Lehmann andScheffe (1950, 1955)) offer one possible approach, and in Berry and Haile (2014a) we showed how identification arguments in Newey and Powell (2003) or Chernozhukov and Hansen (2005) can be adapted to an example of the class of models considered below. 3 However, independent of general concerns one might have with the interpretability of completeness conditions, this approach may be particularly unsatisfactory in a simultaneous equations setting.…”