Partial Identification of Distributional Parameters in Triangular Systems

TL;DR

This paper explores how various plausible restrictions in triangular models enable partial identification of key distributional parameters without requiring full support conditions or rank similarity, supported by numerical examples.

Contribution

It introduces a framework for partial identification of distributional parameters in triangular systems using minimal assumptions and provides numerical illustrations of these identification strategies.

Findings

Identification of marginal distributions without full support conditions

Use of stochastic dominance and quadrant dependence assumptions

Numerical examples demonstrating identification power

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.