Partial Identification by Extending Subdistributions

46 Pages Posted: 8 Jul 2015 Last revised: 17 Apr 2018

Date Written: April 4, 2018

Abstract

I show that sharp identified sets in a large class of econometric models can be characterized by solving linear systems of equations. These linear systems determine whether, for a given value of a parameter of interest, there exists an admissible joint dis- tribution of unobservables that can generate the distribution of the observed variables. The joint distribution of unobservables is not required to satisfy any parametric re- strictions, but can (if desired) be assumed to satisfy a variety of location, shape and/or conditional independence restrictions. To prove sharpness of the characterization, I generalize a classic result in copula theory concerning the extendibility of subcopulas to show that related objects—termed subdistributions—can be extended to proper dis- tribution functions. I describe this characterization argument as partial identification by extending subdistributions, or PIES. One particularly attractive feature of PIES is that it focuses directly on the sharp identified set for a parameter of interest, such as an average treatment effect, without needing to construct the identified set for the entire model. I apply PIES to univariate and bivariate bivariate response models. A notable product of the analysis is a method for characterizing the sharp identified set for the average treatment effect in Manski’s (1975; 1985; 1988) semiparametric binary response model.

Keywords: partial identification, maximum score, bivariate probit, copulas, linear programming, discrete choice, semiparametric, endogeneity

JEL Classification: C14, C20, C51

Suggested Citation

Torgovitsky, Alexander, Partial Identification by Extending Subdistributions (April 4, 2018). Available at SSRN: https://ssrn.com/abstract=2627764 or http://dx.doi.org/10.2139/ssrn.2627764

Alexander Torgovitsky (Contact Author)

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

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