A test of non-identifying restrictions and confidence regions for partially identified parameters

TL;DR

This paper introduces a practical test for the validity of theoretical restrictions on economic variables that may not fully identify the data generating process, applicable to models with censoring and multiple equilibria.

Contribution

It develops an easily implementable testing procedure for non-identifying restrictions and constructs confidence regions for partially identified parameters.

Findings

Test effectively assesses theoretical restrictions validity.

Confidence regions can be derived for partially identified parameters.

Method accommodates models with censoring and multiple equilibria.

Abstract

We propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables, which do not necessarily identify the data generating process. The restrictions can be derived from any model of interactions, allowing censoring and multiple equilibria. When the restrictions are parameterized, the test can be inverted to yield confidence regions for partially identified parameters, thereby complementing other proposals, primarily Chernozhukov et al. [Chernozhukov, V., Hong, H., Tamer, E., 2007. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 1243-1285].