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Marginal Effects in Multivariate Probit and Kindred Discrete and Count Outcome Models, with Applications in Health Economics

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  • John Mullahy

Abstract

Estimation of marginal or partial effects of covariates x on various conditional parameters or functionals is often the main target of applied microeconometric analysis. In the specific context of probit models such estimation is straightforward in univariate models, and Greene, 1996, 1998, has extended these results to cover the case of quadrant probability marginal effects in bivariate probit models. The purpose of this paper is to extend these results to the general multivariate probit context for arbitrary orthant probabilities and to demonstrate the applicability of such extensions in contexts of interest in health economics applications. The baseline results are extended to models that condition on subvectors of y, to count data structures that derive from the probability structure of y, to multivariate ordered probit data structures, and to multinomial probit models whose marginal effects turn out to be a special case of those of the multivariate probit model. Simulations reveal that analytical formulae versus fully numerical derivatives result in a reduction in computational time as well as an increase in accuracy.

Suggested Citation

  • John Mullahy, 2011. "Marginal Effects in Multivariate Probit and Kindred Discrete and Count Outcome Models, with Applications in Health Economics," NBER Working Papers 17588, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:17588
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    1. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
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    6. Christofides, Louis N. & Stengos, Thanasis & Swidinsky, Robert, 1997. "On the calculation of marginal effects in the bivariate probit model," Economics Letters, Elsevier, vol. 54(3), pages 203-208, July.
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    8. Ian M. McCarthy, 2015. "Putting the Patient in Patient Reported Outcomes: A Robust Methodology for Health Outcomes Assessment," Health Economics, John Wiley & Sons, Ltd., vol. 24(12), pages 1588-1603, December.
    9. Us, Anna & Florkowski, Wojciech J. & Klepacka, Anna M., 2015. "From Water To Biofuels: Knowledge And Attitudes Towards Renewable Energy Sources Among Rural Residents In Eastern Poland," Roczniki (Annals), Polish Association of Agricultural Economists and Agribusiness - Stowarzyszenie Ekonomistow Rolnictwa e Agrobiznesu (SERiA), vol. 2015(5), October.
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    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • I1 - Health, Education, and Welfare - - Health

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