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The Poisson quasi-maximum likelihood estimator: a solution to the ‘adding up’ problem in gravity models


  • Jean-François Arvis
  • Ben Shepherd


This article shows that the Poisson Quasi-Maximum Likelihood (QML) estimator applied to the gravity model produces estimates in which, summing across all partners, actual and estimated total trade flows are identical. Other methods such as OLS do not have this desirable property. Indeed, Poisson is the only QML estimator that preserves total trade flows. This result is an additional reason for preferring Poisson as a workhorse gravity model estimator.

Suggested Citation

  • Jean-François Arvis & Ben Shepherd, 2013. "The Poisson quasi-maximum likelihood estimator: a solution to the ‘adding up’ problem in gravity models," Applied Economics Letters, Taylor & Francis Journals, vol. 20(6), pages 515-519, April.
  • Handle: RePEc:taf:apeclt:v:20:y:2013:i:6:p:515-519 DOI: 10.1080/13504851.2012.718052

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    References listed on IDEAS

    1. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    2. Santos Silva, J.M.C. & Tenreyro, Silvana, 2011. "Further simulation evidence on the performance of the Poisson pseudo-maximum likelihood estimator," Economics Letters, Elsevier, vol. 112(2), pages 220-222, August.
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    Cited by:

    1. Chenaf-Nicet, Dalila & Rougier, Eric, 2016. "The effect of macroeconomic instability on FDI flows: A gravity estimation of the impact of regional integration in the case of Euro-Mediterranean agreements," International Economics, Elsevier, vol. 145(C), pages 66-91.
    2. Lin, Xiaohua & Yang, Xiyan, 2017. "From human capital externality to entrepreneurial aspiration: Revisiting the migration-trade linkage," Journal of World Business, Elsevier, vol. 52(3), pages 360-371.
    3. Larch, Mario & Yotov, Yoto, 2016. "General Equilibrium Trade Policy Analysis with Structural Gravity," School of Economics Working Paper Series 2016-9, LeBow College of Business, Drexel University.
    4. Rutger Teulings, 2017. "Brexit and The Impact of Gradual Economic Integration on Export," Tinbergen Institute Discussion Papers 17-075/VI, Tinbergen Institute.
    5. Steinbach, Sandro, 2015. "Bilateral export trade and income similarity: Does the Linder hypothesis hold for agricultural and food trade?," 144th Seminar, February 9-13, 2015, Innsbruck-Igls, Austria 206217, European Association of Agricultural Economists.
    6. Fally, Thibault, 2015. "Structural gravity and fixed effects," Journal of International Economics, Elsevier, vol. 97(1), pages 76-85.
    7. Piermartini, Roberta & Yotov, Yoto, 2016. "Estimating Trade Policy Effects with Structural Gravity," School of Economics Working Paper Series 2016-10, LeBow College of Business, Drexel University.
    8. Scott L. Baier & Yoto V. Yotov & Thomas Zylkin, 2016. "On the Widely Differing Effects of Free Trade Agreements: Lessons from Twenty Years of Trade Integration," CESifo Working Paper Series 6174, CESifo Group Munich.
    9. Steinbach, Sandro, 2015. "Bilateral export trade and income similarity: Does the Linder hypothesis hold for agricultural and food trade?," 2015 International European Forum, February 17-21, 2014, Innsbruck-Igls, Austria 206217, International European Forum on Innovation and System Dynamics in Food Networks.
    10. Zhao, Yong & Tang, Kam Ki & Wang, Li-li, 2013. "Do renewable electricity policies promote renewable electricity generation? Evidence from panel data," Energy Policy, Elsevier, vol. 62(C), pages 887-897.
    11. Jean-François Arvis & Yann Duval & Ben Shepherd & Chorthip Utoktham, 2012. "Trade Costs in the Developing World:1995 – 2010," Working Papers 12112, Asia-Pacific Research and Training Network on Trade (ARTNeT), an initiative of UNESCAP and IDRC, Canada..

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • F10 - International Economics - - Trade - - - General


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