Informational Content of Factor Structures in Simultaneous Binary Response Models

TL;DR

This paper investigates how factor structures in binary response models enhance parameter identification, showing that weaker assumptions suffice for point identification, especially with multiple measurements of the common factor.

Contribution

It formally quantifies the informational content of factor structures in binary systems, relaxing traditional exclusion restrictions for identification.

Findings

Point identification achieved under weaker assumptions.

Exclusion restrictions can be relaxed in models with multiple measurements.

Identification extends to more general factor structures with continuous measurements.

Abstract

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross sectional and panel data models, and in this paper we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a "non-standard" exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.