A note on the different interpretation of the correlation parameters in the Bivariate Probit and the Recursive Bivariate Probit

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 corol...

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Bibliographic Details
Published in:Economics letters 2018-06, Vol.167, p.104-107
Main Authors: Filippini, Massimo, Greene, William H., Kumar, Nilkanth, Martinez-Cruz, Adan L.
Format: Article
Language:English
Subjects:
Bivariate probit
Correlation analysis
Endogenous
Monte Carlo simulation
Recursive Bivariate probit
Studies
Tetrachoric correlation
Variance analysis
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Summary: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. •The correlation in an RBP does not capture the correlation of the endogenous variables.•No extra arguments are needed if an RBP and BP deliver correlations of opposite sign.•A zero-correlation parameter in a BP may mask the presence of a recursive system.
ISSN:0165-1765
1873-7374
DOI:10.1016/j.econlet.2018.03.018