A Reconsideration of Kuznets Curve Across Countries: Evidence from the Co-Summability Approach

The Kuznets curve initiated many economists to examine the deeper and further relationship between growth and inequality over the past sixty-five years. However, the results yet converge into one generalized growth-inequality relationship. As consequences, these disparities have derived into a complex debate for the relationship and have challenged researchers and policymakers as the broadening income inequality gap is the utmost difficulties the world economy is facing. This study re-examines the existence of an inverted U-shaped relationship between economic growth and income inequality. Our paper employs the idea of the order of summability formalized by Berenguer-Rico and Gonzalo (2013 and 2014) to deal with nonlinear transformations of heterogeneous and persistent processes on a sample of 55 countries from 1980 to 2010. The co-integration technique can be generalized by defining balancedness and co-summability. Balancedness is achieved when the order of summability of a dependent variable in a postulated hypothesis equals the persistent and heterogeneous explanatory variables, possibly nonlinear. A co-summable relationship describes a long-run equilibrium that can be nonlinear when the errors have a lower order of summability (Nasr et al. 2019). The analysis of our study is focused on whether there exists nonlinearity in the long-run growth-inequality nexus. Suppose there is no evidence supporting nonlinear long-run relations between economic growth and income inequality. In that case, standard empirical specifications, which apply polynomial or threshold functions, can be seen as misspecified (Eberhardt 2019). The mean- and median-based subsampling summability results reject the null hypothesis of summability of order zero. Based on the summability results, we tested for balancedness, which is confirmed only for specifications with a constant term. For specifications where the balancedness is achieved, we tested co-summability and the results show that co-summability is rejected for all considered specifications. Our finding presents no evidence supporting the Kuznets inverted U-shape and challenges some of the previous results, which implies that conventional empirical specifications in the existing literature adopting polynomial or threshold functions are misspecified. Consequently, such policy implications based on misspecification should be taken with cautiousness.