Informational Content of Factor Structures in Simultaneous Discrete Response Models

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a a variety of settings in cross sectional and panel data models, and in this paper we formal quantify their informational content in a bivariate system often employed in the treatment e↵ects literature. Our main findings are that under the factor structures often imposed in the literature, we show point identification of parameters of interest, such as both the (discrete) treatment e↵ect and the factor load, is attainable under weaker assumptions than usually required in these systems. A fundamental improvement we show is that an exclusion restriction, requiring an explanatory variable in the outcome equation not present in the treatment equation is no longer necessary for identification. Furthermore, we show support conditions of included instruments in the outcome equation can be substantially weakened, resulting in settings where the identification results become regular. Under such settings we propose an estimator for the treatment e↵ect parameter, the factor load, and the average structural function that we show to be root-n consistent and asymptotically normal. The estimator’s finite sample properties are demonstrated through a simulation study and an empirical illustration.