On Uniform Inference in Nonlinear Models with Endogeneity
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This paper explores the uniformity of inference for parameters of interest in nonlinear models with endogeneity. The notion of uniformity is fundamental in these models because due to potential endogeneity, the behavior of standard estimators of these parameters is shown to vary with where they lie in the parameter space. Consequently, uniform inference becomes nonstandard in a fashion that is loosely analogous to inference complications found in the unit root and weak instruments literature, as well as the models recently studied in Andrews and Cheng (2012a), Andrews and Cheng (2012b) and Chen, Ponomareva, and Tamer (2011). We illustrate this point with two models widely used in empirical work. The first is the standard sample selection model, where the parameter is the intercept term (Heckman (1990), Andrews and Schafgans (1998) and Lewbel (1997a)). We show that with selection on unobservables, asymptotic theory for this parameter is not standard in terms of there being nonparametric rates and non-gaussian limiting distributions. In contrast if the selection is on observables only, rates and asymptotic distribution are standard, and consequently an inference method that is uniform to both selection on observables and unobservables is required. As a second example, we consider the well studied treatment effect model in program evaluation (Rosenbaum and Rubin (1983) and Hirano, Imbens, and Ridder (2003)), where a parameter of interest is the ATE. Asymptotic behavior for existing estimators varies between standard and nonstandard across differing levels of treatment heterogeneity, thus also requiring new inference methods.
Professor Khan is on leave at Boston College for the 2016-17 academic year.
Professor Khan specializes in the fields of mathematical economics, statistics, and applied econometrics. His studies have explored a variety of subjects from covariate dependent censoring and non-stationary panel data, to causal effects of education on wage inequality and the variables affecting infant mortality rates in Brazil. He was awarded funding by National Science Foundation grants for his projects entitled, “Estimation of Binary Choice and Nonparametric Censored Regression Models” and “Estimation of Cross-Sectional and Panel Data Duration Models with General Forms of Censoring.” He has published numerous papers in leading academic journals, including such writings as, “Heteroskedastic Transformation Models with Covariate Dependent Censoring” with E. Tamer and Y. Shin; “The Identification Power of Equilibrium in Simple Games;” “Partial Rank Estimation of Duration Models with General Forms of Censoring” with E. Tamer; and more. He is currently collaborating with D. Nekipelov and J.L. Powell on the project, “Optimal Point and Set Inference in Competing Risk Models;” with A. Lewbel on, “Identification and Estimation of Stochastic Frontier Models;” and with E. Tamer on, “Conditional Moment Inequalities in Roy Models with Cross-Section and Panel Data.”
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