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

See all articles by Massimo Filippini

Massimo Filippini

ETH Zürich; University of Lugano - Faculty of Economics

William H. Greene

New York University Stern School of Business

Nilkanth Kumar

ETH Zürich - CER-ETH - Center of Economic Research at ETH Zurich; Centre for Energy Policy and Economics (CEPE) at ETH Zurich

Adan L. Martinez-Cruz

Department of Forest Economics, SLU; CERE; ETH Zürich - Centre for Energy Policy and Economics (CEPE)

Date Written: September 18, 2017

Abstract

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

Filippini, Massimo and Greene, William H. and Kumar, Nilkanth and Martinez-Cruz, Adan L., A Note on the Different Interpretation of the Correlation Parameters in the Bivariate Probit and the Recursive Bivariate Probit (September 18, 2017). Available at SSRN: https://ssrn.com/abstract=3038804 or http://dx.doi.org/10.2139/ssrn.3038804

Massimo Filippini (Contact Author)

ETH Zürich ( email )

ETH-Zentrum
CH-8092 Zurich
Switzerland

University of Lugano - Faculty of Economics ( email )

Via Giuseppe Buffi 13
CH-6900 Lugano, CH-6904
Switzerland

William H. Greene

New York University Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States
212-998-0876 (Phone)

HOME PAGE: http://people.stern.nyu.edu/wgreene

Nilkanth Kumar

ETH Zürich - CER-ETH - Center of Economic Research at ETH Zurich ( email )

Zürichbergstrasse 18
Zurich, 8092
Switzerland

Centre for Energy Policy and Economics (CEPE) at ETH Zurich ( email )

8092 Zurich
Switzerland

HOME PAGE: http://www.cepe.ethz.ch/

Adan L. Martinez-Cruz

Department of Forest Economics, SLU ( email )

S-901 83 Umea
Sweden

HOME PAGE: http://https://www.researchgate.net/profile/Adan_Martinez-Cruz

CERE ( email )

Almas Allé 10
Umeå, 750 07
Sweden

ETH Zürich - Centre for Energy Policy and Economics (CEPE) ( email )

8092 Zurich
Switzerland
+41 44 633 80 97 (Phone)

HOME PAGE: http://www.eepe.ethz.ch/people/madan

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