The Millennium Peak in Club Convergence: A New Look at Distributional Changes in The Wealth of Nations

Abstract

Summary This paper proposes an easy‐to‐use nonparametric indicator for club convergence, or convergence within clusters of countries: it measures whether the modes of the gross domestic product (GDP) per capita distribution become more pronounced over time. Relying on changes in the critical bandwidth for unimodality, the indicator is a dynamic extension of concepts from often‐used multimodality tests. Its evolution suggests the new empirical result of a ‘millennium peak’ in club convergence in the worldwide GDP per capita distribution. The club convergence movements of the 1980s and 1990s, when groups of poor and rich countries converged to two separate points, was followed by a de‐clubbing movement after the turn of the millennium. Copyright © 2016 John Wiley & Sons, Ltd.

What Remains of Cross-Country Convergence?

“…Krause (2016) uses the critical bandwidth (the largest bandwidth allowing for a finding of bimodality) as measure of the coalescence of countries around the peaks in the cross-country distribution of per capita income. Analyzing data from 1970 to 2011, she finds a tendency for the countries of the world to converge to two groups which has weakened since 2000.…”

Empirical analysis of strategy selection for the technology leading and technology catch‐up in the IT industry

“…The indicator of club convergence must reflect how distinct the peaks are compared with other parts in the distribution, and it must be invariant to changes in the overall distribution's variance. This can be achieved by working with a standardized density that has the same shape as the original [7]. Proposition If is the kernel density function, and if it is standardized in the support and bandwidth with y i = ( x i – μ )/ 𝜎 , , will have the same shape as the original .…”

“…The indicator of club convergence must reflect how distinct the peaks are compared with other parts in the distribution, and it must be invariant to changes in the overall distribution's variance. This can be achieved by working with a standardized density that has the same shape as the original [7].…”

“…They found three constituent peaks in the income distribution. Krause [7], who provided the basis for our methodology, proposed the calculation of CBs of specificity and diversity to prove the existence of multiple peaks as a widely used validation. σ-convergence and β-convergence are the traditional analysis methods closely related to convergence using the distribution dynamics discussed above.…”

“…The new measurement method is based on the literature on the nonparametric multimodality test, which was proposed by Silverman [5] and implemented by Bianchi [6]. In particular, Krause [7] proposed the critical bandwidth (CB) calculation of the singularity and multiplicity for proving the existence of several peaks as a widely used test. In this study, to understand the change of convergence of Korean IT companies by applying these research studies, the technology change was decomposed, so the decomposed factors were dynamically examined and quantitatively measured.…”