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Multivariate Sarmanov Count Data Models

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  • Miravete, Eugenio J

Abstract

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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7463.

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Date of creation: Sep 2009
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Handle: RePEc:cpr:ceprdp:7463

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

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  1. Frank Windmeijer & Joao Santos Silva, 1996. "Endogeneity in count data models; an application to demand for health care," IFS Working Papers W96/15, Institute for Fiscal Studies.
  2. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
  3. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
  4. Andreas Million & Regina T. Riphahn & Achim Wambach, 2003. "Incentive effects in the demand for health care: a bivariate panel count data estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 387-405.
  5. Gurmu, Shiferaw & Elder, John, 2008. "A bivariate zero-inflated count data regression model with unrestricted correlation," Economics Letters, Elsevier, vol. 100(2), pages 245-248, August.
  6. Terza, Joseph V & Wilson, Paul W, 1990. "Analyzing Frequencies of Several Types of Events: A Mixed Multinomial-Poisson Approach," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 108-15, February.
  7. Yang, Huanxing & Ye, Lixin, 2008. "Nonlinear pricing, market coverage, and competition," Theoretical Economics, Econometric Society, vol. 3(1), March.
  8. Gurmu, Shiferaw & Elder, John, 2000. "Generalized bivariate count data regression models," Economics Letters, Elsevier, vol. 68(1), pages 31-36, July.
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