A mathematical and statistical model of income growth and distribution

In this paper, we propose a mathematical and statistical model of the dynamic evolution of incomes and of their distributional patterns among the three traditional income classes: aristocracy, populace, and the bourgeoisie. After highlighting their major features and historical evolution from the Neolithic Era to date, the Maddison income data sets, as well as Gini coefficients and other distributional variables spanning the years 1-2017 C.E., are introduced for 11 West European countries, selected among the most representative of the vestiges of the Roman Empire resting within the "limen" (perceived threshold). Most of the series pertaining to the data sets originally come in low-resolution terms prior to the year 1850. Their corresponding high-resolution annual observations are computed by means of backcasting from Bayesian calibration, and further appropriately denoised.

The data processing applied in the present context is novel, and the results of the computations involved are interesting. In fact, the end results of the computations point to three major important findings regarding the evolution of personal income levels, growth rates, and distribution over the last 20 centuries in Western Europe: (i) incomes and living conditions enjoyed during the Roman Era remain unprecedented only after the inception of the Industrial Revolution; (ii) the Kuznets curves behaved in accordance with accepted theory by significantly exhibiting an overtime inverted-U pattern; (iii) the engine of economic growth is in the vast majority of cases, perhaps unexpectedly, represented by the bourgeoisie.

Conclusively, the results obtained fare well far from accepted hypotheses and ideologies, providing a robust rationale of the combined process of growth and income distribution.