Partial Identification of Distributional Parameters in Triangular Systems

Abstract: I study partial identification of distributional parameters in triangular systems. This model consists of a nonparametric outcome equation and a selection equation. This allows for general unobserved heterogeneity and selection on unobservables. The distributional parameters considered in this paper are the marginal distributions of potential outcomes, their joint distribution, and the distribution of treatment effects. I investigate how different types of plausible restrictions contribute to identifying these parameters. The restrictions I consider include stochastic dominance and quadrant dependence between unobservables and monotonicity between potential outcomes. My identification applies to the whole population without a full support condition on instrumental variables and does not rely on rank similarity. I also provide numerical examples to illustrate the identification power of each assumption.