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On the Specification of the Gravity Model of Trade: Zeros, Excess Zeros and Zero-inflated Estimation


  • Martijn Burger
  • Frank van Oort
  • Gert-Jan Linders


Abstract Conventional studies of bilateral trade patterns specify a log-normal gravity equation for empirical estimation. However, the log-normal gravity equation suffers from three problems: the bias created by the logarithmic transformation, the failure of the homoskedasticity assumption, and the way zero values are treated. These problems normally result in biased and inefficient estimates. Recently, the Poisson specification of the trade gravity model has received attention as an alternative to the log-normality assumption (Santos Silva & Tenreyro, 2006). However, the standard Poisson model is vulnerable for problems of overdispersion and excess zero flows. To overcome these problems, this paper considers modified Poisson fixed-effects estimations (negative binomial, zero-inflated). Extending the empirical model put forward by Santos Silva & Tenreyro (2006), we show how these techniques may provide viable alternatives to both the log-normal and standard Poisson specification of the gravity model of trade. Caractéristiques du modèle de gravité du commerce: zéros, zéros en excès et estimation du zéro-inflated Résumé Des études conventionnelles sur la structure des échanges commerciaux bilatéraux définissent une équation de gravité log-normale pour estimation empirique. Cependant, l’équation de gravité log-normale souffre de trois problèmes: le biais créé par la transformation logarithmique, l’échec de l'hypothèse d'homoscédasticité, et la manière dont sont traitées les valeurs zéro. Ces problèmes conduisent en général à des estimations biaisées et inefficaces. La spécification de Poisson du modèle de gravité du commerce a récemment retenu l'attention en tant qu'alternative à l'hypothèse de log-normalité (Santos Silva et Tenreyro, 2006). Toutefois, le modèle standard de Poisson est vulnérable en ce qui concerne les problèmes d'hyperdispersion et de flux d'excès en zéro. Afin de surmonter ces problèmes, cet article considère des estimations de Poisson modifiées à effets fixes (binomiale négative, zéro-inflated). En élargissant ce modèle empirique rapporté par Santos Silva et Tenreyro (2006), nous démontrons que ces techniques peuvent apporter des méthodes alternatives viables à la spécification log-normale, ainsi qu’à la spécification Poisson standard du modèle de gravité du commerce. Sobre la especificación del modelo de gravedad del comercio: estimaciones cero, cero en exceso y cero infladas Résumén Los estudios convencionales de patrones de comercio bilateral especifican una ecuación de gravedad log-normal para la estimación empírica. No obstante, la ecuación de gravedad log-normal tiene tres problemas: el sesgo creado por la transformación logarítmica, el fracaso de la suposición de homocedasticidad, y la forma en que se tratan los valores cero. Estos problemas generalmente arrojan estimaciones sesgadas e ineficientes. Recientemente, la especificación Poisson del modelo de gravedad del comercio ha recibido atención como una alternativa a la suposición de log-normalidad (Santos Silva y Tenreyro, 2006). Sin embargo, el modelo Poisson estándar es vulnerable por problemas de sobredispersión y exceso de flujos cero. Para superar estos problemas, este estudio considera las estimaciones modificadas Poisson de efecto fijo (binomial negativa, cero-infladas). Al extender el modelo empírico propuesto por Santos Silva y Tenreyro (2006), mostramos que estas técnicas pueden proporcionar alternativas viables para especificaciones log-normal y Poisson estándar del modelo de gravedad del comercio.

Suggested Citation

  • Martijn Burger & Frank van Oort & Gert-Jan Linders, 2009. "On the Specification of the Gravity Model of Trade: Zeros, Excess Zeros and Zero-inflated Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(2), pages 167-190.
  • Handle: RePEc:taf:specan:v:4:y:2009:i:2:p:167-190
    DOI: 10.1080/17421770902834327

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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.
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    More about this item


    International trade; distance; gravity model; modified Poisson models; C13; C21; F15;

    JEL classification:

    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • F17 - International Economics - - Trade - - - Trade Forecasting and Simulation
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M13 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - New Firms; Startups
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D


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