Identification in Multiple Treatment Models under Discrete Variation

TL;DR

This paper introduces a method to estimate bounds on causal effects in models with multiple treatments and discrete instruments, accommodating complex selection mechanisms and shape restrictions.

Contribution

It develops a two-step computational approach for sharp bounds in multi-treatment models with unobserved heterogeneity, relaxing previous point-identification assumptions.

Findings

Provides sharper bounds on treatment effects under weaker assumptions

Demonstrates robustness of Head Start program effects analysis

Allows for nonparametric shape restrictions in treatment response functions

Abstract

We develop a marginal treatment effect based method to learn about causal effects in multiple treatment models with discrete instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that permit multidimensional unobserved heterogeneity. An inherent complication is that the primitives characterizing the selection model are not generally point-identified. Allowing these primitives to be point-identified up to a finite-dimensional parameter, we show how a two-step computational program can be used to obtain sharp bounds for a number of treatment effect parameters when the marginal treatment response functions are allowed to satisfy only nonparametric shape restrictions or are additionally parameterized. We demonstrate the benefits of our method by revisiting Kline and Walters' (2016) empirical analysis of the Head Start program. Our approach relaxes their point-identifying assumptions on the selection model and marginal treatment response functions, allowing us to assess the robustness of their conclusions.