It is possible to identify lies about birth dates in public records statistically, even if you can't tell which particular birth dates are lies. This trick was used to track honesty by region in Italy, and shifts in the honest of different regions over time.
Using census data, we study false birth-date registrations in Italy, a phenomenon well known to demographers, in a setting that allows us to separate honesty from the benefits of cheating and deterrence. By comparing migrants leaving a locality with those who remain in it, we illustrate the tendency of Italians to sort themselves across geographic areas according to their honesty levels. Over time, this tendency has modified the average honesty level in each locality, with relevant consequences for the distribution across geographic areas of outcomes like human capital, productivity, earnings growth, and the quality of local politicians and government.
Massimo Anelli, Tommaso Colussi, and Andrea Ichino, "Rule Breaking, Honesty, and Migration" 66(2) Journal of Law and Economics (2023) (Supplemental Data here). This closed access paper is analyzed in the comments at Marginal Revolution and at another blog that it links to discussing the paper.
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