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On the Existence of the Maximum Likelihood Estimates for Poisson Regression


  • J. M. C. Santos Silva
  • Silvana Tenreyro


We note that the existence of the maximum likelihood estimates for Poisson regression depends on the data configuration. Because standard software does not check for this problem, the practitioner may be surprised to find that in some applications estimation of the Poisson regression is unusually difficult or even impossible. More seriously, the estimation algorithm may lead to spurious maximum likelihood estimates. We identify the signs of the non-existence of the maximum likelihood estimates and propose a simple empirical strategy to single out the regressors causing this type of identification failure.

Suggested Citation

  • J. M. C. Santos Silva & Silvana Tenreyro, 2009. "On the Existence of the Maximum Likelihood Estimates for Poisson Regression," CEP Discussion Papers dp0932, Centre for Economic Performance, LSE.
  • Handle: RePEc:cep:cepdps:dp0932

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    References listed on IDEAS

    1. Dr Alex Bryson, 2009. "Employee Voice and Private Sector Workplace Outcomes in Britain, 1980-2004," National Institute of Economic and Social Research (NIESR) Discussion Papers 329, National Institute of Economic and Social Research.
    2. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    4. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
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    Cited by:

    1. Michel BEINE & Frédéric DOCQUIER & Caglar,OZDEN, 2015. "Dissecting Network Externalities in International Migration," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 81(4), pages 379-408, December.
    2. Pels, 2010. "International Asset Holdings and the Euro," The Institute for International Integration Studies Discussion Paper Series iiisdp331, IIIS.
    3. Egger, Peter & Larch, Mario, 2011. "An assessment of the Europe agreements' effects on bilateral trade, GDP, and welfare," European Economic Review, Elsevier, vol. 55(2), pages 263-279, February.

    More about this item


    Poisson estimation; gravity equation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • F10 - International Economics - - Trade - - - General

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