Robust Likelihood Ratio Tests for Incomplete Economic Models

TL;DR

This paper introduces a robust testing framework for incomplete economic models that lack a unique likelihood function, using least favorable pairs and sharp restrictions to ensure optimality and computational tractability.

Contribution

It develops likelihood ratio tests for incomplete models based on least favorable pairs, incorporating sharp restrictions for computational efficiency and optimality.

Findings

Tests are robust to model incompleteness.

Monte Carlo experiments show strong performance.

Framework applies to models with strategic interactions.

Abstract

This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however, allows us to construct tests based on the least favorable pairs of likelihoods using the theory of Huber and Strassen (1973). We develop tests robust to model incompleteness that possess certain optimality properties. We also show that sharp identifying restrictions play a role in constructing such tests in a computationally tractable manner. A framework for analyzing the local asymptotic power of the tests is developed by embedding the least favorable pairs into a model that allows local approximations under the limits of experiments argument. Examples of the hypotheses we consider include those on the presence of strategic interaction effects in discrete games of complete information. Monte Carlo experiments demonstrate the robust performance of the proposed tests.