# Partial Identification of Distributional Parameters in Triangular Systems 

Ju Hyun Kim ∗ 

July 3, 2018 

## Abstract 

I study partial identification of distributional parameters in triangular systems. The model consists of a nonparametric outcome equation and a selection equation. This allows for general unobserved heterogeneity in potential outcomes and selection on unobservables. The distribu- tional parameters considered in this paper are the marginal distributions of potential outcomes, their joint distribution, and the distribution of treatment effects. I explore different types of plausible restrictions to tighten existing bounds on these parameters. The restrictions include stochastic dominance, 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 numer- ical examples to illustrate identifying power of the restrictions. 

Keywords: Partial Identification, Triangular Systems, Stochastic Monotonicity, Monotone Treatment Response, Quadrant Dependence 

JEL Classifications: C14, C21, C61, C81. 

