Media Briefings

THE ‘IRON LAW OF CONVERGENCE’: New evidence on how fast poor countries can catch up with the advanced economies

  • Published Date: June 2015

Analysis of two long-run cross-country data sets on economic growth lends support to the idea that there is a robust empirical regularity in the rate at which poor economies can close the income gap with rich economies.

The study by Professor Robert Barro, published in the June 2015 Economic Journal, also finds evidence for the ‘modernisation hypothesis’: that there is two-way causation between a country’s economic development and its maintenance of institutional quality, including a well-functioning representative democracy and the rule of law.

Professor Barro, who first proposed the existence of an ‘iron law of convergence’, notes that a rate of 2% per year implies that it takes 30 years for a poor country to converge half the way to its long-run or steady-state level of per capita GDP.

This ‘beta convergence’ – the tendency for a poor economy to grow faster than a rich one – is conditional in the sense that a country’s long-run position depends on its fixed or slowly varying characteristics, such as the quality of institutions and human capital. Hence, a poor country may not tend to catch up with a rich one if the poor country has lower quality institutions and human capital or if it pursues harmful public policies.

The 2% conditional convergence rate is confirmed in the new research in an 80-country panel since the 1960s and a 34-country panel with data starting between 1870 and 1896.

Data from the two panels also support the modernisation hypothesis in the sense of positive effects of per capita GDP and schooling on the quality of institutions, gauged by indicators of democracy and the rule of law.

A measure of proportionate dispersion of living standards – the standard deviation of the log of per capita GDP – is reasonably stable for 25 countries with data since 1870. This lack of ‘sigma convergence’ – which refers to a tendency for dispersion or inequality to fall across a group of economies – is consistent with the presence of beta convergence.

For 34 countries – including China and India – with data since 1896, the proportionate dispersion of per capita GDP declines from the late 1970s, especially when the countries are weighted by population. This decline in inequality reflects particularly the incorporation of China and India into the world market economy. Research by others has shown that the economic improvements in Asia have been key contributors to the dramatic drop in world poverty rates since the 1970s.


Notes for editors: ‘Convergence and Modernisation’ by Robert Barro is published in the June 2015 issue of the Economic Journal.

Robert Barro is
Paul M Warburg Professor of Economics
at Harvard University.

For further information: contact Romesh Vaitilingam on +44-7768-661095 (email:; Twitter: @econromesh); Robert Barro via email: