A note on the different interpretation of the correlation parameters in the Bivariate Probit and the Recursive Bivariate Probit
指出，如果对来自递归双变量Probit过程的数据估计双变量Probit模型，得到的相关系数是递归模型相关系数与内生二元变量参数的加权平均，因此两个模型中的相关系数含义不同，零相关系数可能掩盖递归过程的存在。
This note shows 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) 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; and ii) 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 an RBP process.