, Volume 45, Issue 2, pp 311–337 | Cite as

Power laws in EU country exports

  • Ignacio del Rosal
Original Paper


International trade flows are highly concentrated in the top units of analysis. In this paper, we study the size distribution of exports at the product level, using Comext data for the 28 EU countries over the period 2002–2014. We fit power law relationships running log rank–log size regressions. The estimated Pareto exponent may be interpreted as a single measure of the inequality between the top products; it thus constitutes an alternative to other measures of export diversification. The Pareto exponent estimates are quite stable for most EU countries between 2002 and 2014. However, some countries stand out for their increase or decrease in the Pareto exponent. Some preliminary evidence suggesting negative correlation between volatility in EU country exports and export diversification at the product level is also provided.


Power law distribution Pareto exponent EU exports Comext data 

JEL Classification

F14 F15 C13 C16 



I would like to thank the editor for his help and two anonymous referees for their comments that substantially improved the paper. Financial support from the Consejería de Educación, Cultura y Deporte del Principado de Asturias, is acknowledged.


  1. Acemoglu D, Carvalho VM, Ozdaglar A, Tahbaz-Salehi A (2012) The network origins of aggregate fluctuations. Econometrica 80:1977–2016CrossRefGoogle Scholar
  2. Agosin MR, Alvarez R, Bravo-Ortega C (2012) Determinants of export diversification around the World: 1962–2000. World Econ 35:295–315CrossRefGoogle Scholar
  3. Amurgo-Pacheco A, Pierola MD (2008) Patterns of export diversification in developing countries: intensive and extensive margins. World Bank Policy Research Working Paper 4473Google Scholar
  4. Arkolakis C, Costinot A, Rodríguez-Clare A (2012) New trade models, same old gains? Am Econ Rev 102:94–130CrossRefGoogle Scholar
  5. Axtell RL (2001) Zipf distribution of US firm sizes. Science 293:1818–1820CrossRefGoogle Scholar
  6. Black D, Henderson V (2003) Urban evolution in the USA. J Econ Geogr 3:343–372CrossRefGoogle Scholar
  7. Bottazzi G, Pirino D, Tamagni F (2015) Zipf law and the firm size distribution: a critical discussion of popular estimators. J Evol Econ 25:585–610CrossRefGoogle Scholar
  8. Cadot O, Carrère C, Strauss-Kahn V (2011) Export diversification: what’s behind the hump? Rev Econ Stat 93:590–605CrossRefGoogle Scholar
  9. Cadot O, Carrère C, Strauss-Kahn V (2013) Trade diversification, income, and growth: what do we know? J Econ Surv 27:790–812CrossRefGoogle Scholar
  10. Camanho da Costa Neto N, Romeu R (2011) Did export diversification soften the impact of the global financial crisis? IMF Working Paper WP/11/99Google Scholar
  11. Canals C, Gabaix X, Vilarubia JM, Weinstein D (2007) Trade patterns, trade balances, and idiosyncratic shocks. Bank of Spain Working Papers no. 721Google Scholar
  12. Carvalho VM, Gabaix X (2013) The great diversification and its undoing. Am Econ Rev 103:1697–1727CrossRefGoogle Scholar
  13. Chaney T (2008) Distorted gravity: the intensive and extensive margins of international trade. Am Econ Rev 98:1707–1721CrossRefGoogle Scholar
  14. Cirillo P, Hüsler J (2009) On the upper tail of Italian firms’ size distribution. Phys A 388:1546–1554CrossRefGoogle Scholar
  15. De Benedictis L, Gallegati M, Tamberi M (2009) Overall trade specialization and economic development: countries diversify. Rev World Econ 145:37–55CrossRefGoogle Scholar
  16. Del Rosal I (2013) The granular hypothesis in EU country exports. Econ Lett 120:433–436CrossRefGoogle Scholar
  17. Dennis A, Shepherd B (2011) Trade facilitation and export diversification. World Econ 34:101–122CrossRefGoogle Scholar
  18. Devadoss S, Luckstead J (2016) Size distribution of U.S. lower tail cities. Phys A 444:158–162CrossRefGoogle Scholar
  19. Di Giovanni J, Levchenko AA (2012) Country size, international trade, and aggregate fluctuations in granular economies. J Polit Econ 120:1083–1132CrossRefGoogle Scholar
  20. Di Giovanni J, Levchenko AA, Ranciere R (2011) Power laws in firm size and openness to trade: measurement and implications. J Int Econ 85:42–52CrossRefGoogle Scholar
  21. Di Giovanni J, Levchenko AA, Mejean I (2014) Firms, destinations, and aggregate fluctuations. Econometrica 82:1303–1340CrossRefGoogle Scholar
  22. Easterly W, Reshef A (2016) African export successes: surprises, stylized facts, and explanations. In: Edwards S, Johnson S, Weil DN (eds) African successes, Volume III: Modernization and development. University of Chicago Press, Chicago (forthcoming) Google Scholar
  23. Easterly W, Reshef A, Schwenkenberg J (2009) The power of exports. World Bank Policy Research Working Paper 5081Google Scholar
  24. Eaton J, Kortum S, Kramarz F (2011) An anatomy of international trade: evidence from French firms. Econometrica 79:1453–1498CrossRefGoogle Scholar
  25. Eeckhout J (2004) Gibrat’s law for (all) cities. Am Econ Rev 94:1429–1451CrossRefGoogle Scholar
  26. Eurostat (2015) User guide on European statistics on international trade in goods. Publications Office of the European Union, LuxembourgGoogle Scholar
  27. Feenstra RC (1994) New product varieties and the measurement of international prices. Am Econ Rev 84:157–177Google Scholar
  28. Funke M, Ruhwedel R (2001) Export variety and export performance: empirical evidence from East Asia. J Asian Econ 12:493–505CrossRefGoogle Scholar
  29. Funke M, Ruhwedel R (2002) Export variety and export performance: empirical evidence for the OECD Countries. Rev World Econ 138:97–114Google Scholar
  30. Gabaix X (2009) Power laws in economics and finance. Annu Rev Econ 1:255–293CrossRefGoogle Scholar
  31. Gabaix X (2011) The granular origins of aggregate fluctuations. Econometrica 79:733–772CrossRefGoogle Scholar
  32. Gabaix X (2016) Power laws in economics: an introduction. J Econ Perspect 30:185–206CrossRefGoogle Scholar
  33. Gabaix X, Ibragimov R (2011) Rank-1/2: a Simple way to improve the OLS estimation of tail exponents. J Bus Econ Stat 29:24–39CrossRefGoogle Scholar
  34. Giesen K, Suedekum J (2014) City age and city size. Eur Econ Rev 71:193–208CrossRefGoogle Scholar
  35. Head K, Mayer T (2014) Gravity equations: workhorse, toolkit, and cookbook. In: Gopinath G, Helpman E, Rogoff K (eds) Handbook of international economics, vol 4. Elsevier, Amsterdam, pp 131–195Google Scholar
  36. Helpman E, Melitz MJ, Yeaple SR (2004) Export versus FDI with heterogeneous firms. Am Econ Rev 94:300–316CrossRefGoogle Scholar
  37. Hinloopen J, Van Marrewijk C (2006) Comparative advantage, the rank-size rule, and Zipf’s law. Tinbergen Institute Discussion Paper TI 2006-100/1Google Scholar
  38. Hinloopen J, Van Marrewijk C (2012) Power laws and comparative advantage. Appl Econ 44:1483–1507CrossRefGoogle Scholar
  39. Hummels D, Klenow PJ (2005) The variety and quality of a nation’s exports. Am Econ Rev 95:704–723CrossRefGoogle Scholar
  40. Imbs J, Wacziarg R (2003) Stages of diversification. Am Econ Rev 93:63–86CrossRefGoogle Scholar
  41. Klinger B, Lederman D (2004) Discovery and development: an empirical exploration of “new” products. World Bank Policy Research Working Paper 3450Google Scholar
  42. Klinger B, Lederman D (2006) Diversification, innovation, and imitation inside the Global Technological Frontier. World Bank Policy Research Working Paper 3872Google Scholar
  43. Koren M, Tenreyro S (2007) Volatility and development. Q J Econ 122:243–287CrossRefGoogle Scholar
  44. Mau K (2015) Export diversification and income differences reconsidered: the extensive product margin in theory and application. Rev World Econ 152:351–381CrossRefGoogle Scholar
  45. Melitz M (2003) The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 71:1695–1725CrossRefGoogle Scholar
  46. Melitz M, Redding S (2014) Heterogeneous firms and trade. In: Gopinath G, Helpman E, Rogoff K (eds) Handbook of international economics, vol 4. Elsevier, Amsterdam, pp 1–54Google Scholar
  47. Minondo A (2011) Does comparative advantage explain countries’ diversification level? Rev World Econ 147:507–526CrossRefGoogle Scholar
  48. Neary JP (2010) Two and a half theories of trade. World Econ 33:1–19CrossRefGoogle Scholar
  49. O’Brien D, Scally J (2012) Cost competitiveness and export performance of the Irish economy. Cent Bank Irel Q Bull 3:86–102Google Scholar
  50. Parteka A (2010) Employment and export specialisation along the development path: some robust evidence. Rev World Econ 145:615–640CrossRefGoogle Scholar
  51. Parteka A (2013) Trade diversity and stages of development-evidence on EU countries. Ekonomia 30:23–44Google Scholar
  52. Parteka A, Tamberi M (2013a) What determines export diversification in the development process? Empirical assessment. World Econ 36:807–826CrossRefGoogle Scholar
  53. Parteka A, Tamberi M (2013b) Product diversification, relative specialisation and economic development: import export analysis. J Macroecon 38:121–135CrossRefGoogle Scholar
  54. Peng G (2010) Zipf’s law for Chinese cities: rolling sample regressions. Phys A 389:3804–3813CrossRefGoogle Scholar
  55. Regolo J (2013) Export diversification: how much does the choice of the trading partner matter? J Int Econ 91:329–342CrossRefGoogle Scholar
  56. Schaffar A, Dimou M (2012) Rank-size city dynamics in China and India, 1981–2004. Reg Stud 46:707–721CrossRefGoogle Scholar
  57. Segarra A, Teruel M (2012) An appraisal of firm size distribution: does sample size matter? J Econ Behav Organ 82:314–328CrossRefGoogle Scholar
  58. Shepotylo O (2013) Export diversification across countries and products: do Eastern European (EE) and Commonwealth of Independent States (CIS) countries diversify enough? J Int Trade Econ Dev 22:605–638CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Applied EconomicsUniversity of OviedoOviedoSpain

Personalised recommendations