Testing Exogeneity in the Bivariate Probit Model: A Monte Carlo Study*

Abstract

We conduct an extensive Monte Carlo experiment to examine the finite sample properties of maximum-likelihood-based inference in the bivariate probit model with an endogenous dummy. We analyse the relative performance of alternative exogeneity tests, the impact of distributional misspecification and the role of exclusion restrictions to achieve parameter identification in practice. The results allow us to infer important guidelines for applied econometric practice. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2007.

Testing the hypothesis of absence of unobserved confounding in semiparametric bivariate probit models

“…4.8). However, because ρ is not penalized, it is still possible to use the classic result that L M has a χ 2 1 limiting distribution (Monfardini and Radice 2008). This can be seen by observing that gδ…”

“…Here, the statistic is given by twice the difference of the model log-likelihoods under H 1 and H 0 , and has a χ 2 1 limiting distribution for parametric models (Monfardini and Radice 2008). In the current context, we are however faced with a difficulty which inhibits the use of this approach for testing H 0 .…”

“…Note that the study design detailed in Sects. 4.1.1 and 4.2.1 extends the simulation study of Monfardini and Radice (2008) to recognize the specific challenges that arise when there are nonlinear response-covariate relationships. …”

“…DGP1 and DGP2 relate to models (11) and (12). α and n denote the critical value and sample size considered Monfardini and Radice (2008) found the same for parametric recursive bivariate probit models. This has also been confirmed in other contexts by Maldonado and Greenland (1994) and Louis (1982).…”

Innovative work practices and sickness absence: what does a nationally representative employee survey tell?

“…No exclusion restrictions are needed for the identification of the parameters, because the model is non-linear (Wilde, 2000). However, using the exclusion restrictions improves the validity of tests of exogeneity of the endogenous dummy explanatory variable (essentially, a test of whether the correlation of the error terms of the probit models is zero) (Monfardini and Radice, 2008). Thus, we assume that the variables X 1 and X 2 are not exactly the same.…”