Lack of Global Convergence and the Formation of Multiple Welfare Clubs across Countries: An Unsupervised Machine Learning Approach

Carlos Mendez

doi:10.3390/economies7030074

Abstract

The cross-country convergence hypothesis is one of the central topics of long-run macroeconomics. This paper revisits this hypothesis in a context beyond GDP. It uses a novel welfare index that incorporates measures of consumption, leisure, life expectancy, and inequality. Based on a sample of 128 countries over the 1980–2007 period, the lack of global sigma and beta convergence is first documented. Next, the paper incorporates some recent developments from the unsupervised machine learning literature to evaluate the existence of local convergence. In particular, the application of a distribution-based clustering algorithm suggests the formation of three local convergence clubs. Under this classification, beta convergence is recovered for each club. However, only the core members of the richest club appear to be reducing their welfare differences in a way that is consistent with the strong notion of sigma convergence. Overall, these results re-emphasize the finding that beta convergence is necessary, but not sufficient for sigma convergence, even within convergence clubs and in a context beyond GDP.

Highlights

In the study of long-run macroeconomics, a central topic is the empirical testing of the convergence hypothesis across countries (Johnson and Papageorgiou 2018)
Based on a sample of 128 countries over the 1980–2007 period, this paper finds that welfare differences across countries are characterized by a lack of both sigma and beta convergence
The lack of country mobility and the emergence of multiple basins of attraction in the main diagonal are typically interpreted as suggestive evidence of convergence clubs

Summary

Introduction

In the study of long-run macroeconomics, a central topic is the empirical testing of the convergence hypothesis across countries (Johnson and Papageorgiou 2018). Differences across countries are conceptually defined in terms of living standards or national welfare. From an empirical and operational standpoint, GDP per-capita has been used in most of the literature as the key proxy variable for measuring living standards. The use of GDP per-capita is sometimes useful and informative, economist are well aware that it is an incomplete measure of national welfare 2009; Fleurbaey and Blanchet 2013, Stiglitz et al 2010, 2019) In this context, a series of different alternatives has been proposed by economists and non-economists alike (Becker et al 2005; Cordoba and Verdier 2008; Fleurbaey and Gaulier 2009). Given the comprehensive coverage of this index, it can be used as an alternative proxy variable for the study of the convergence hypothesis

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