Partial identification by extending subdistributions

• 成果类型: Article
• 署名作者: Torgovitsky, Alexander
• 署名单位: University of Chicago
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE634
• 发表日期: 2019
• 页码: 105-144
• 关键词: partial identification; maximum score; bivariate probit; copulas; linear programming; discrete choice; semiparametric; endogeneity

摘要

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 distribution of unobservables that can generate the distribution of the observed variables. The joint distribution of unobservables is not required to satisfy any parametric restrictions, 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 distribution 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 binary 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 (, , ) semiparametric binary response model.