Testing for a Threshold in Models with Endogenous Regressors

TL;DR

This paper evaluates the size distortions of existing threshold tests in models with endogenous regressors through simulations and introduces three new tests that improve accuracy, validated by bootstrap methods, with an empirical application on government spending multipliers.

Contribution

The paper proposes three novel tests that correct size distortions in threshold models with endogenous regressors, enhancing reliability over previous methods.

Findings

Existing tests show severe size distortions in small and moderate samples.

The new tests based on GMM and unconventional 2SLS estimators effectively rectify these distortions.

Empirical application finds no strong evidence that government spending multipliers are larger in recessions.

Abstract

We show by simulation that the test for an unknown threshold in models with endogenous regressors - proposed in Caner and Hansen (2004) - can exhibit severe size distortions both in small and in moderately large samples, pertinent to empirical applications. We propose three new tests that rectify these size distortions. The first test is based on GMM estimators. The other two are based on unconventional 2SLS estimators, that use additional information about the linearity (or lack of linearity) of the first stage. Just like the test in Caner and Hansen (2004), our tests are non-pivotal, and we prove their bootstrap validity. The empirical application revisits the question in Ramey and Zubairy (2018) whether government spending multipliers are larger in recessions, but using tests for an unknown threshold. Consistent with Ramey and Zubairy (2018), we do not find strong evidence that these multipliers are larger in recessions.