Zipf's law and world income distribution

Abstract

The aim of this article is to demonstrate regularity in the world income distribution. In particular, using GDP per capita data for the period 1980 to 2004, the article shows that the world income distribution follows the well know ‘rank-size rule’.

Acknowledgement

I would like to thank Sara Borelli for the useful comments.

Notes

¹See for example, Baumol (1986), Barro (1991), Sala-i-Martin (1996).

²The rank-size rule can be considered a ‘sister’ of the Zipf's law. In fact, the Zipf's law is a necessary condition for the existence of the rank-size rule. For a more detailed discussion about this relation see Gabaix (1999).

³See respectively, Gabaix (1999) and Stanley et al. (1995).

⁴This explains the fact that empirical evidence on the rank-size rule is used to prove the existence of the Zipf's law, Alperowitch (1982).

⁵The idea that most countries are likely to have the same growth of rate has been supported by many models of endogenous growth. For a detailed discussion see Barro and Sala-i-Martin (2004).

⁶In fact, outliers in the distribution of GDP per capita tend to increase considerably the SD, while have less impact on the estimate of the slope: (cov(ln(GDP/N), ln Rank)/var(ln Rank)).

Fig. 1. Rank-size rule over time