Pension systems similarity assessment: An application of Kendall's W to statistical multivariate analysis

The study aims at empirical verification of the quality of pension system clustering based on two dimensions: the extent of involvement of the state in the pension system and the level of voluntariness. To answer the question of whether these two dimensions actually determine the division into homogeneous groups that constitute pension regimes, Kendall's W concordance coefficient is employed. It is typically used in Delphi studies as an indicator of expert consensus, but it has been shown that the concept of concordance can also be applied to statistical multivariate analysis to measure intra-group similarity. This empirical research comprises 30 OECD countries grouped into three pension regimes. It employs the classical chi-square test as well as the permutation test of the coefficient of concordance previously applied to empirical problems in biology. Additionally, this study proposes a new permutation procedure that allows for verifying the quality of clustering from a different perspective.