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On Uniform Inference in Nonlinear Models with Endogeneity

Shakeeb Khan () and Denis Nekipelov ()
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Shakeeb Khan: Boston College, Postal: Dept. of Economics, Boston College, Chestnut Hill, MA 02467 USA

No 986, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: This paper explores the uniformity of inference for parameters of interest in nonlinear econometric models with endogeneity. Here the notion of uniformity arises because the behavior of estimators of parameters is shown to vary with where they lie in the parameter space. As a result, inference becomes nonstandard in a fashion that is loosely analogous to inference complications found in the unit root and weak instruments lit-erature, as well as the models recently studied in Andrews and Cheng (2012), Chen, Ponomareva, and Tamer (2014), Han and McCloskey (2019). Our main illustrative example is the standard sample selection model, where the parameter is the intercept term as in Heckman (1990), Andrews and Schafgans (1998) and Lewbel (2007). We show here there is a discontinuity in the limiting distribution for an estimator despite it being uniformly (across degrees of selection) consistent. This discontinuity prevents standard inference procedures from being uniformly valid, and motivates the development of new methods, for which we establish asymptotic properties. Finite sample properties of the procedure is explored through a simulation study and an empirical illustration using the Mroz (1987) data set as in Newey, Powell, and Walker (1990).

Keywords: Selection on observables and unobservables; uniform inference; fixed and drifting sequences of parameters (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 C15 (search for similar items in EconPapers)
Date: 2019-09-30
New Economics Papers: this item is included in nep-ore
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