Testing parameter significance in instrumental variables probit estimators: some simulation

Abstract

Binary choice models that contain endogenous regressors can now be estimated routinely using modern software. Each of the two packages, Stata 11 [Stata Statistical Software: Release 11, StataCorp LP, College Station, TX, 2009] and Limdep 9 [Econometric Software Inc., Plainview, NY, 2008], contains two estimators that can be used to estimate such a model. This paper compares the performance of maximum likelihood, Newey's Amemiya's generalized least-squares (AGLS) estimator, an instrumental variables plug-in estimator and others in samples of sizes 200 and 1000 using simulation. Specifically, this paper focuses on tests of parameter significance under various degrees of instrument strength and severity of endogeneity. Although the maximum-likelihood estimator performs well in large samples, there is some evidence that the more computationally robust AGLS estimator may perform better in smaller samples when instruments are weak. It also appears that instruments in endogenous probit estimation need to be even stronger than when used in linear instrumental variables (IV) estimation.

Keywords:

• probit
• GMM
• instrumental variables
• Monte Carlo
• significance tests
• dichotomous choice
• endogenous regressors
• generalized linear model
• binary response

Acknowledgements

I thank Randy Campbell and an anonymous referee for their careful reading of the article. All remaining errors are mine.

Notes

This is not intended as a criticism of Rivers and Vuong 2 since the behaviour of instrumental variable estimators when instruments are weak had yet to be systematically considered when their paper was written.

This is verified using the ivregress gmm command in Stata 11. See Section 1 for example code.

and γ=0 and