Inequality in the Past: How Much Can We Really Trust the Numbers?
Artificial intelligence, technological transition, and profound changes in the labor market are altering the distribution of wealth, prompting economists and policymakers to wonder how inequalities might evolve in the coming decades.
To find some answers, some scholars are looking to the past. Prehistoric and historical societies, in fact, constitute an immense natural laboratory: they allow us to observe how institutions, technological innovations, and different forms of economic organization influenced the distribution of wealth long before the modern economy. Comparing a Neolithic farming community, a Mesopotamian city, or the Roman Empire means vastly expanding the range of experiences from which to learn.
However, there is an obstacle that inevitably accompanies this type of research: the data are often incomplete and imprecise. Archaeologists uncover only a fraction of settlements, many artifacts have been lost, and historical sources rarely describe the entire population. Consequently, any measure of inequality carries with it a degree of uncertainty that often remains hidden.
It is from this awareness that the new study published in Proceedings of the National Academy of Sciences (PNAS) by Mattia Fochesato (Department of Social and Political Sciences, Dondena Center, GREEN – Center for Research on Geography, Resources, Environment, Energy & Networks, and the Bocconi Institute for Data Science and Analytics at Bocconi University), together with Samuel Bowles of the Santa Fe Institute, emerged. Rather than proposing a new indicator of inequality, the authors change the way we interpret historical and archaeological data, showing how it is possible to measure not only the wealth of the past but also the degree of confidence we can place in the estimates.
The problem is not a lack of data, but the illusion of precision
In recent years, scholars have reconstructed the distribution of wealth in ancient societies using traces left by the past: the size of dwellings, grave goods, crop storage areas, cultivated land, and other material indicators.
The limitation is obvious. These data represent only part of the reality. Some settlements have never been excavated, many objects have disappeared, and the poorest people often leave no trace. Furthermore, different indicators describe different aspects of wealth and cannot be directly compared. According to the authors, the risk is that these inevitable gaps are overlooked when moving from the analysis of artifacts to quantitative results.
They summarize this with a particularly effective statement:
“Ignoring these uncertainties is to claim ‘specious accuracy’.”
The expression “specious accuracy,” borrowed from the economist Oskar Morgenstern, refers to accuracy that is only apparent. The problem is not making mistakes (which are inevitable when studying societies that existed thousands of years ago) but presenting the results as if they were much more precise than the sources actually allow. For Fochesato and Bowles, a good analysis should not eliminate uncertainty: it should make it explicit and measure it.
BRIDGE: a method that also measures what we do not know
To address this problem, Fochesato and Bowles developed BRIDGE (Bayesian-Resampling and Informed Priors with Data-driven Gini Estimation), a statistical methodology that combines the Bayesian approach with resampling techniques and error-propagation models.
The idea is simple in principle, though sophisticated in its implementation. Instead of assigning a single Gini coefficient to each society, BRIDGE constructs a probability distribution of plausible inequality values. In this way, the final result is not only “how unequal” a given society was, but also “how confident we are” in that estimate.
To carry out this work, the authors analyzed data from 431 sites and historical periods spanning approximately 12,000 years, correcting for five main sources of bias: samples that were too small, differences between individual and household data, the exclusion of people without assets, the use of different indicators of wealth, and variations in the size of the observed populations.
One of the most surprising findings concerns sample size itself. We tend to assume that limited data automatically leads to unreliable estimates. The study shows, however, that small samples can be surprisingly accurate when they are truly representative of the population. The problem arises mainly when the sample is systematically skewed—for example, because excavations focus on the most monumental dwellings or the richest tombs.
When the method changes, so does history
The introduction of these corrections often significantly alters the results. The case of Akkadian Mesopotamia is emblematic. The Gini coefficient derived directly from the data is 0.802 (values closer to 1 indicate greater inequality in the distribution of wealth). After correcting for the main distortions present in the sources, the average estimate becomes 0.7. But the most important finding is another: BRIDGE shows that it makes no sense to consider this number as an “exact” value. On the contrary, there is a range of plausible values much wider than that estimated using traditional methods. The problem, therefore, is not determining whether the correct value is 0.70 or 0.75, but recognizing that the available data do not allow us to distinguish between them with certainty.
A comparison with bootstrapping—one of the most widely used statistical techniques for estimating uncertainty—leads to an equally significant conclusion. The authors write:
“We find that widely used methods (e.g., relying solely on conventional bootstrapping) provide misleading and, for the most part, substantially underestimated measures of uncertainty.”
The criticism is not directed at bootstrapping itself, but at the exclusive use of this technique. Resampling the same data does, in fact, allow for the estimation of sampling uncertainty, but it does not account for the many other sources of error that characterize archaeological data: what has not been excavated, people who do not appear in the sources, differences in indicators of wealth, or the varying sizes of the populations being compared. When all these components are considered together, the uncertainty is, on average, about 1.4 times greater than that estimated using bootstrapping alone.
A lesson that applies beyond archaeology
In their conclusions, the authors revisit an insight formulated over a century ago by the British statistician Arthur Bowley, one of the pioneers of economic measurement.
“...to tabulate our knowledge or ignorance ... as definitely as possible.”
With these words, Bowley argued that good statistics should not merely provide an estimate, but should state just as clearly how reliable that estimate is. In other words, it is not enough to indicate the most likely value of inequality; one must also show how wide the margin of uncertainty surrounding it is. This is precisely the principle guiding BRIDGE, which replaces the traditional “single number” with a distribution of possible values.
The study’s contribution therefore extends far beyond economic history. The authors themselves note that a similar approach could be applied to many other fields, from reconstructing historical wages to other economic time series based on incomplete sources. Whenever data are fragmentary, the quality of the research depends not only on the ability to produce an estimate, but also on the transparency with which its limitations are communicated.
