IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/7463.html
   My bibliography  Save this paper

Multivariate Sarmanov Count Data Models

Author

Listed:
  • Miravete, Eugenio

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.

Suggested Citation

  • Miravete, Eugenio, 2009. "Multivariate Sarmanov Count Data Models," CEPR Discussion Papers 7463, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:7463
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP7463
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meghan R. Busse, 2000. "Multimarket Contact and Price Coordination in the Cellular Telephone Industry," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 9(3), pages 287-320, June.
    2. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    3. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
    4. Jung, Robert C & Winkelmann, Rainer, 1993. "Two Aspects of Labor Mobility: A Bivariate Poisson Regression Approach," Empirical Economics, Springer, vol. 18(3), pages 543-556.
    5. 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.
    6. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
    7. 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 108-115, February.
    8. Windmeijer, F A G & Silva, J M C Santos, 1997. "Endogeneity in Count Data Models: An Application to Demand for Health Care," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 281-294, May-June.
    9. Hausman, Jerry A. & Leonard, Gregory K. & McFadden, Daniel, 1995. "A utility-consistent, combined discrete choice and count data model Assessing recreational use losses due to natural resource damage," Journal of Public Economics, Elsevier, vol. 56(1), pages 1-30, January.
    10. , & ,, 2008. "Nonlinear pricing, market coverage, and competition," Theoretical Economics, Econometric Society, vol. 3(1), March.
    11. Gurmu, Shiferaw & Elder, John, 2000. "Generalized bivariate count data regression models," Economics Letters, Elsevier, vol. 68(1), pages 31-36, July.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    2. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eugenio Miravete, 2014. "Testing for complementarities among countable strategies," Empirical Economics, Springer, vol. 46(4), pages 1521-1544, June.
    2. A. Colin Cameron & Per Johansson, 2004. "Bivariate Count Data Regression Using Series Expansions: With Applications," Working Papers 9815, University of California, Davis, Department of Economics.
    3. Atella, Vincenzo & Deb, Partha, 2008. "Are primary care physicians, public and private sector specialists substitutes or complements? Evidence from a simultaneous equations model for count data," Journal of Health Economics, Elsevier, vol. 27(3), pages 770-785, May.
    4. Parsons, George R. & Jakus, Paul M. & Tomasi, Ted, 1999. "A Comparison of Welfare Estimates from Four Models for Linking Seasonal Recreational Trips to Multinomial Logit Models of Site Choice," Journal of Environmental Economics and Management, Elsevier, vol. 38(2), pages 143-157, September.
    5. Jeon, Doh-Shin & Menicucci, Domenico, 2009. "Bundling and Competition for Slots: On the Portfolio Effects of Bundling," IDEI Working Papers 574, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jul 2011.
    6. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    7. Eugenio J. Miravete, 2004. "The Doubtful Profitability of Foggy Pricing," Working Papers 04-07, NET Institute.
    8. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.
    9. Gihwan Yi & Min Kim & Hoe Sang Chung, 2024. "The Revenue Impact of Differential Seat Pricing and Competition in the Movie Theater Market," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 64(3), pages 361-382, May.
    10. Glenn Ellison, 2005. "A Model of Add-On Pricing," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(2), pages 585-637.
    11. Henrik Jacobsen Kleven & Claus Thustrup Kreiner & Emmanuel Saez, 2007. "The Optimal Income Taxation of Couples as a Multi-Dimensional Screening Problem," Working Papers 2007-1, Princeton University. Economics Department..
    12. Barelli, Paulo & Basov, Suren & Bugarin, Mauricio & King, Ian King, 2010. "The Inclusiveness of Exclusion," Insper Working Papers wpe_211, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    13. Massimiliano Bratti & Alfonso Miranda, 2010. "Endogenous Treatment Effects for Count Data Models with Sample Selection or Endogenous Participation," DoQSS Working Papers 10-05, Quantitative Social Science - UCL Social Research Institute, University College London, revised 10 Dec 2010.
    14. Simon Cowan, 2012. "Third-Degree Price Discrimination and Consumer Surplus," Journal of Industrial Economics, Wiley Blackwell, vol. 60(2), pages 333-345, June.
    15. Paulo Barelli & Suren Basov & Mauricio Bugarin & Ian King, 2012. "The Robustness of Exclusion in Multi-dimensional Screening," RCER Working Papers 571, University of Rochester - Center for Economic Research (RCER).
    16. Eugenio J. Miravete, 2009. "Competing with Menus of Tariff Options," Journal of the European Economic Association, MIT Press, vol. 7(1), pages 188-205, March.
    17. Calzolari, Giacomo & Denicolo, Vincenzo, 2010. "Competitive quantity discounts," CEPR Discussion Papers 8144, C.E.P.R. Discussion Papers.
    18. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    19. Danny Ben-Shahar, 2008. "Default, Credit Scoring, and Loan-to-Value: a Theoretical Analysis under Competitive and Non-Competitive Mortgage Markets," Journal of Real Estate Research, American Real Estate Society, vol. 30(2), pages 161-190.
    20. Winkelmann, Rainer, 2006. "Reforming health care: Evidence from quantile regressions for counts," Journal of Health Economics, Elsevier, vol. 25(1), pages 131-145, January.

    More about this item

    Keywords

    Sarmanov distributions; Double poisson; Gamma; Multivariate count data models; Tariff options;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:7463. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.