Empirical Economics

, Volume 52, Issue 2, pp 447–461 | Cite as

Marginal effects in multivariate probit models



Estimation of marginal or partial effects of covariates x on various conditional parameters or functionals is often a main target of applied microeconometric analysis. In the specific context of probit models, estimation of partial effects involving outcome probabilities will often be of interest. Such estimation is straightforward in univariate models, and results covering the case of quadrant probability marginal effects in bivariate probit models for jointly distributed outcomes y have previously been described in the literature. This paper’s goals are to extend Greene’s results to encompass the general \(M\ge 2\) multivariate probit context for arbitrary orthant probabilities and to extended these results to models that condition on subvectors of y and to multivariate ordered probit data structures. It is suggested that such partial effects are broadly useful in situations, wherein multivariate outcomes are of concern.


Multivariate probit Marginal effects 

JEL Classification

C30 C35 



Thanks are owed to Kevin Denny, Bill Greene, Jeff Hoch, Alberto Holly, Stephen Jenkins, Mari Palta, Ron Thisted, participants in seminars at University College Dublin, Minnesota, AHRQ, and Wisconsin, and an anonymous referee for their helpful comments, and to Katherine Mullahy for valuable editorial assistance. This work has been supported in part by the Health & Society Scholars Program, by NICHD grant P2C HD047873 to the Center for Demography and Ecology, and by the Robert Wood Johnson Foundation Evidence for Action Program (Grant 73336), all at the University of Wisconsin-Madison. An earlier, longer draft was circulated as NBER W.P. 17588.


  1. Cappellari L, Jenkins SP (2003) Multivariate probit regression using simulated maximum likelihood. Stata J 3(3):278–294Google Scholar
  2. Christofides LN, Stengos T, Swidinsky R (1997) On the calculation of marginal effects in the bivariate probit model. Econ Lett 54(3):203–208CrossRefGoogle Scholar
  3. Christofides LN, Stengos T, Swidinsky R (2000) Corrigendum. Econ Lett 68(3):339CrossRefGoogle Scholar
  4. Frees EW, Valdez EA (1998) Understanding relationships using copulas. N Am Actuar J 2(1):1–25CrossRefGoogle Scholar
  5. Greene WH (1996) Marginal effects in the bivariate probit model. NYU Stern School of Business working paper EC-96-11Google Scholar
  6. Greene WH (1998) Gender economics courses in liberal arts colleges: further results. J Econo Educ 29(4):291–300CrossRefGoogle Scholar
  7. Greene WH (2004) Convenient estimators for the panel probit model: further results. Empir Econ 29(1):21–47CrossRefGoogle Scholar
  8. Greene WH, Hensher DA (2010) Modeling ordered choices: a primer. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. Hajivassiliou V, McFadden D, Ruud P (1996) Simulation of multivariate normal rectangle probabilities and their derivatives: theoretical and computational results. J Econom 72(1–2):85–134CrossRefGoogle Scholar
  10. Huguenin J, Pelgrin F, Holly A (2009) Estimation of multivariate probit models by exact maximum likelihood. University of Lausanne, IEMS working paper 09-02Google Scholar
  11. Mullahy J (2016) Estimation of multivariate probit models via bivariate probit. Stata J 16(1):37–51Google Scholar
  12. Rao CR (1973) Linear statistical inference and its applications, 2nd edn. Wiley, New YorkCrossRefGoogle Scholar
  13. Trivedi PK, Zimmer DM (2005) Copula modeling: an introduction for practitioners. Found Trends Econom 1(1):1–111CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of Wisconsin-MadisonMadisonUSA
  2. 2.NUI GalwayGalwayIreland
  3. 3.NBERCambridgeUSA

Personalised recommendations