Partial identification by extending subdistributions

Artikel

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 (1975, 1985, 1988) semiparametric binary response model.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Quantitative Economics ; ISSN: 1759-7331 ; Volume: 10 ; Year: 2019 ; Issue: 1 ; Pages: 105-144 ; New Haven, CT: The Econometric Society

Classification and Topics

• Classification: Wirtschaft ; Semiparametric and Nonparametric Methods: General ; Single Equation Models; Single Variables: General ; Model Construction and Estimation
• Subject: Partial identification ; maximum score ; bivariate probit ; copulas ; linear programming ; discrete choice ; semiparametric ; endogeneity

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Torgovitsky, Alexander
• Event: Veröffentlichung
• (who): The Econometric Society
• (where): New Haven, CT
• (when): 2019

Further information

• DOI: doi:10.3982/QE634
• Handle: http://hdl.handle.net/10419/217138
• Last update: 10.03.2025, 11:43 AM CET