A note on the different interpretation of the correlation parameters in the Bivariate Probit and the Recursive Bivariate Probit - Massimo Filippini; William Greene; Nilkanth Kumar; Adan Martinez-Cruz (ETH Zurich, CER-ETH - Center of Economic Research, 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: C25; 330; Bivariate probit; Recursive Bivariate probit; Tetrachoric correlation; Monte Carlo simulation