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On Uniform Inference in Nonlinear Models with Endogeneity

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  • Shakeeb Khan
  • Denis Nekipelov

Abstract

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.

Suggested Citation

  • Shakeeb Khan & Denis Nekipelov, 2013. "On Uniform Inference in Nonlinear Models with Endogeneity," Working Papers 13-16, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:13-16
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    Cited by:

    1. Rothe, Christoph, 2015. "Robust Confidence Intervals for Average Treatment Effects under Limited Overlap," IZA Discussion Papers 8758, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Selection on observables and unobservables; uniform inference; fixed and drifting sequences of parameters;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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