Zipf rank approach and cross-country convergence of incomes

¹ Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
² Institute of Solid State Physics, Bulgarian Academy of Sciences - Sofia, Bulgaria, EU
³ Harvard Medical School and Division of Sleep Medicine, Brigham and Women's Hospital Boston, MA 02115, USA
⁴ Faculty of Economics, University of Belgrade - 11000 Belgrade, Serbia
⁵ National Bank of Serbia
⁶ Faculty of Civil Engineering, University of Rijeka - Rijeka, Croatia
⁷ Zagreb School of Economics and Management - 10000 Zagreb, Croatia
⁸ Faculty of Economics, University of Ljubljana - Slovenia, EU

^a plamen@buphy.bu.edu
^b hes@buphy.bu.edu
^c bp@phy.hr

Received: 10 December 2010
Accepted: 28 March 2011

Abstract

We employ a concept popular in physics —the Zipf rank approach— in order to estimate the number of years that EU members would need in order to achieve “convergence” of their per capita incomes. Assuming that trends in the past twenty years continue to hold in the future, we find that after t≈30 years both developing and developed EU countries indexed by i will have comparable values of their per capita gross domestic product . Besides the traditional Zipf rank approach we also propose a weighted Zipf rank method. In contrast to the EU block, on the world level the Zipf rank approach shows that, between 1960 and 2009, cross-country income differences increased over time. For a brief period during the 2007–2008 global economic crisis, at world level the of richer countries declined more rapidly than the of poorer countries, in contrast to EU where the of developing EU countries declined faster than the of developed EU countries, indicating that the recession interrupted the convergence between EU members. We propose a simple model of GDP evolution that accounts for the scaling we observe in the data.