Revisiting Pareto: A re-analysis of the specific requirements of Pareto's law

Over one century ago Pareto found seemingly unrelated heterogeneous agents act in concert to produce large-scale patterns in macroeconomic systems such that, as the size of the system grows larger, the relative distribution of income groups within that system remain constant---a perspective now shared with modern complexity theorists. Three of the five components of Pareto's original theory have been extensively reconfirmed and extended to similar observations about economic distributions in the growth of firms, financial markets, and countries. Although there has been nearly continuous interest in Pareto's theory, his observation about a persistent power law relationship in economic relationships is now investigated primarily within the interdisciplinary framework of complexity sciences. From that perspective, the Pareto law is a macroeconomic example of an emergent property of the underlying macroeconomic activity. Recent research from an econophysics perspective confirms the generality of Pareto law behavior, but little attention is given to the specifics indicated by Pareto. Recent research also creates uncertainty about two components of Pareto's original theory. Using the five components of Pareto's original observation as a framework for analysis, I investigate the relationship proposed by Pareto as an enduring expression of the distribution of firms in a given country. I also investigate the component of Pareto's observation about the certain level of income where the Pareto law applies in a country's income distribution. These specific requirements of Pareto are analyzed using annual revenue data from firms in the G7 countries. Mixed support is found for hypotheses that test the two components of Pareto's original observation. Conducting that analysis emphasizes the need for structure in conducting and definition in reporting Pareto law research.