Regression spline bivariate probit models: A practical approach to testing for exogeneity

ABSTRACT

Bivariate probit models can deal with a problem usually known as endogeneity. This issue is likely to arise in observational studies when confounders are unobserved. We are concerned with testing the hypothesis of exogeneity (or absence of endogeneity) when using regression spline recursive and sample selection bivariate probit models. Likelihood ratio and gradient tests are discussed in this context and their empirical properties investigated and compared with those of the Lagrange multiplier and Wald tests through a Monte Carlo study. The tests are illustrated using two datasets in which the hypothesis of exogeneity needs to be tested.

KEYWORDS:

• Bivariate probit model
• Endogeneity
• Gradient test
• Lagrange multiplier test
• Likelihood ratio test
• Non-random sample selection
• Penalized regression spline
• Wald test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62G10

Acknowledgments

We thank the Editor and reviewer for their constructive criticism which helped to improve the presentation of the article considerably.