  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.
