Growing inequality in systems showing Zipf’s law

Abstract A central problem in economics and statistics is the assessment of income or wealth inequality starting from empirical data. Here we focus on behavior Gini index, one most used measures, presence Zipf’s law, a situation which occurs many complex financial economical systems. First, show that application asymptotic formulas to finite size systems always leads an overestimation inequality. We thus compute corrections depending exponent two distinct regimes can be observed: low inequality, where index less than maximal asymptotically tends its value one. In both cases, expanding system slowly increases just as effect growth, with scaling never faster inverse size. test our computations real systems, US cities cryptocurrency market, observing cases increase completely explained by law expanding. This shows growing effects must considered order properly assess if increasing due natural growth processes it produced change structure Finally discuss how such carefully when analyzing survey