Multivariate Sarmanov Count Data Models

34 Pages Posted: 7 Oct 2009

See all articles by Eugenio J. Miravete

Eugenio J. Miravete

University of Texas at Austin; Centre for Economic Policy Research (CEPR)

Date Written: September 2009


I present two flexible models of multivariate, count data regression that make use of the Sarmanov family of distributions. This approach overcomes several existing difficulties to extend Poisson regressions to the multivariate case, namely: i) it is able to account for both over and underdispersion, ii) it allows for correlations of any sign among the counts, iii) correlation and dispersion depend on different parameters, and iv) constrained maximum likelihood estimation is computationally feasible. Models can be extended beyond the bivariate case. I estimate the bivariate versions of two of these models to address whether the pricing strategies of competing duopolists in the early U.S. cellular telephone industry can be considered strategic complements or substitutes. I show that a Sarmanov model with double Poisson marginals outperforms the alternative count data model based on a multivariate renewal process with gamma distributed arrival times because the latter imposes very restrictive constraints on the valid range of the correlation coefficients.

Keywords: Double Poisson, Gamma, Multivariate Count Data Models, Sarmanov Distributions, Tariff Options

JEL Classification: C16, C35, L11

Suggested Citation

Miravete, Eugenio J., Multivariate Sarmanov Count Data Models (September 2009). CEPR Discussion Paper No. DP7463, Available at SSRN:

Eugenio J. Miravete (Contact Author)

University of Texas at Austin ( email )

Department of Economics
1 University Station C3100
Austin, TX 78712-0301
United States
512-232-1718 (Phone)
512-471-3510 (Fax)


Centre for Economic Policy Research (CEPR)

United Kingdom

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