Wealth distribution and Pareto's law in the Hungarian medieval society

Abstract

The distribution of wealth in the medieval Hungarian aristocratic society is studied and reported. Assuming the wealth of a noble family to be directly related to the size and agricultural potential of the owned land, we take the number of owned serf families as a measure of the respective wealth. Our data analysis reveals the power-law nature of this wealth distribution, confirming the validity of the Pareto law for this society. Since, in the feudal society, land was not commonly traded, our targeted system can be considered as an experimental realization of the no-trade limit of wealth-distribution models. The obtained Pareto exponent ($\alpha =0.92$–0.95) close to 1, is in agreement with the prediction of such models.

Introduction

At the end of the XIX century the economist Vilfredo Pareto [1] discovered a universal law regarding the wealth/income distribution in societies. His measurement results on several European countries, kingdoms and cities for the XV–XIX centuries revealed that the cumulative distribution of income (the probability that the income of an individual is greater than a given value) exhibits a universal functional form. Pareto found that in the region containing the richest part of the population, generally less than $5\%$ of the individuals, this distribution is well described by a power-law (see for example Ref. [2] for a review). The exponent of this power-law is denoted by $\alpha$ and named Pareto index. In the limit of low and medium wealth, the shape of the cumulative distribution is fitted by either an exponential or a log-normal function.

The power-law revealed by Pareto has been confirmed by many recent studies on the economy of several corners of the world. The presently available data is coming from so apart as Australia [3], Japan [4], [5], the US [6], continental Europe [7], [8], India [9] or the UK [10], [11]. The data is also spanning so long in time as ancient Egypt [12], Renaissance Europe [13] or the XX century Japan [14]. Since it is difficult to measure wealth, most of the available data comes from tax declarations of individual income. Empirical results are also available, which are based on a direct estimate of the wealth of individuals or institutions. The area of the houses in ancient Egypt [12], the inheritance taxation or the capital transfer taxes [15], [11], the size/wealth of firms [7] or wealth rankings provided by some popular magazines [9], [16] are examples of such studies. While wealth and income are related, one has to note that this relation is not a simple proportionality. The distribution of wealth is usually broader than the distribution of income, or equivalently, the Pareto index for wealth distribution is smaller than the corresponding one for income (see Ref. [9] as an example). In the present paper, we present and discuss empirical studies of wealth distribution in a medieval society—the Hungarian aristocratic society around the year 1550. In those times, the wealth of a nobleman was directly related to the size and agriculture potential of the lands he owned. To quantify this wealth, we take the number of owned serf (villein) families—a measure generally used by historians and for which well documented data exist. In a feudal society, land was not commonly traded. Moreover, in the Hungarian society, the family land was not divided among the children nor given as dowry—almost everything was inherited by the eldest son. The case under study offers thus a somehow idealized example of a system without a relevant wealth-exchange mechanism and may be taken as an experimental realization of the no-trade limit of current wealth-distribution models. Our results also give further evidence for the universal nature of Pareto's law.