Testing Identifying Assumptions in Parametric Separable Models: A Conditional Moment Inequality Approach

TL;DR

This paper introduces a straightforward testing method for key assumptions in parametric separable models, utilizing intersection bounds and existing inference tools, with empirical validation and applications to instrumental variable models.

Contribution

It develops a simple, implementable test for identifying assumptions in parametric models using intersection bounds and demonstrates its effectiveness through simulations and real data applications.

Findings

Test controls size and is consistent in simulations.

Rejection of some instrumental variable models in empirical tests.

The IV model is untestable without functional form assumptions.

Abstract

In this paper, we propose a simple method for testing identifying assumptions in parametric separable models, namely treatment exogeneity, instrument validity, and/or homoskedasticity. We show that the testable implications can be written in the intersection bounds framework, which is easy to implement using the inference method proposed in Chernozhukov, Lee, and Rosen (2013), and the Stata package of Chernozhukov et al. (2015). Monte Carlo simulations confirm that our test is consistent and controls size. We use our proposed method to test the validity of some commonly used instrumental variables, such as the average price in other markets in Nevo and Rosen (2012), the Bartik instrument in Card (2009), and the test rejects both instrumental variable models. When the identifying assumptions are rejected, we discuss solutions that allow researchers to identify some causal parameters of interest after relaxing functional form assumptions. We show that the IV model is nontestable if no functional form assumption is made on the outcome equation, when there exists a one-to-one mapping between the continuous treatment variable, the instrument, and the first-stage unobserved heterogeneity.