Zipf rank approach and cross-country convergence of incomes

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 ${\cal G}_{i,t} $. 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 ${\cal G}_{i,t} $ of richer countries declined more rapidly than the ${\cal G}_{i,t} $ of poorer countries, in contrast to EU where the ${\cal G}_{i,t} $ of developing EU countries declined faster than the ${\cal G}_{i,t} $ 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.