A Note on the Different Interpretation of the Correlation Parameters in the Bivariate Probit and the Recursive Bivariate Probit
11 Pages Posted: 20 Sep 2017
Date Written: September 18, 2017
This note makes the point that, if a Bivariate Probit (BP) model is estimated on data arising from a Recursive Bivariate Probit (RBP) process, the resulting BP correlation parameter is a weighted average of the RBP correlation parameter and the parameter associated to the endogenous binary variable. Two corollaries follow this proposition: i) a zero correlation parameter in a BP model, usually interpreted as evidence of independence between the binary variables under study, may actually mask the presence of a RBP process; and ii) the interpretation of the correlation parameter in the RBP is not the same as in the BP — i.e. the RBP correlation parameter does not necessarily reflect the correlation between the binary variables under study.
Keywords: Bivariate Probit; Recursive Bivariate Probit; Tetrachoric Correlation; Monte Carlo Simulation
JEL Classification: C25
Suggested Citation: Suggested Citation