Headnote.The ability of quantile regression models to characterize the heteroge-neous impact of variables on different points of an outcome distribution makes them appealing in many economic applications. However, in observational studies, the vari-ables of interest (e.g. education, prices) are often endogenous, making conventional quantile regression inconsistent and hence inappropriate for recovering the causal ef-fects 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). Key Words: endogeneity, quantile regression, simultaneous equations, instrumental re-gression, identification, nonlinear model, monotone likelihood ratio, bounded completeness,

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some preliminary nonparametric estimators. Our results extend existing theories like those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We apply our results to two examples: a ‘hit rate’ and a partially linear median regression with some endogenous regressors.

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.

For the analysis of consumer demand and expenditure, separability is one of the typical assumptions when constructing econometric models. This is crucial for interpretability and feasibility. While the estimation of nonparametric estimation under separability is well studied for unlimited dependent variables, it is less the case for censored or truncated dependent models. Here we study the example of the estimation of Engel curves for luxury goods but many other examples are thinkable. We introduce a method for non- and semiparametric estimation of partial linear and additively separable models for censored dependent data combining the methods of Lewbel and Linton (2002) with Kim, Linton, and Hengartner (1999) and average derivatives respectively. We extend it to the inclusion of endogenous covariates proposing a two step instrumental variable method. We provide the asymptotic behavior for our final estimates. Key Words: semiparametric censored regression, partial linear additive models, consumer expenditure, marginal integration. 1

Quantile regression techniques have been widely used in empirical economics. In this paper, we consider the estimation of a generalized quantile regression model when data are subject to fixed or random censoring. Through a discretization technique, we transform the censored regression model into a sequence of binary choice models and further propose an integrated smoothed maximum score estimator by combining individual binary choice models, following the insights of Horowitz (1992) and Manski (1985). Unlike the estimators of Horowitz (1992) and Manski (1985), our estimators converge at the usual parametric rate through an integration process. In the case of fixed censoring, our approach overcomes a major drawback of existing approaches associated with the curve-of-dimensionality problem. Our approach for the fixed censored case can be extended readily to the case with random censoring for which other existing approaches are no longer applicable. Both of our estimators are consistent and asymptotically normal. A simulation study demonstrates that our estimators perform well in finite samples.

Acknowledgement: This paper was presented at the Econometric Society Australasian

We propose an instrumental variable quantile regression (IVQR) estimator for spatial autoregressive (SAR) models. Like the GMM estimators of Lin and Lee (2006) and Kelejian and Prucha (2006), the IVQR estimator is robust against heteroscedasticity. Unlike the GMM estimators, the IVQR estimator is also robust against outliers and requires weaker moment conditions. More importantly, it allows us to characterize the heterogeneous impact of variables on different points (quantiles) of a response distribution. We derive the limiting distribution of the new estimator. Simulation results show that the new estimator performs well in finite samples at various quantile points. In the special case of median restriction, it outperforms the conventional QML estimator without taking into account of heteroscedasticity in the errors; it also outperforms the GMM estimators with or without considering the heteroscedasticity.