Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions

Abstract

The yearly aggregated tax income data of all, more than 8000, Italian municipalities are analyzed for a period of five years, from 2007 to 2011, to search for conformity or not with Benford's law, a counter-intuitive phenomenon observed in large tabulated data where the occurrence of numbers having smaller initial digits is more favored than those with larger digits. This is done in anticipation that large deviations from Benford's law will be found in view of tax evasion supposedly being widespread across Italy. Contrary to expectations, we show that the overall tax income data for all these years is in excellent agreement with Benford's law. Furthermore, we also analyze the data of Calabria, Campania and Sicily, the three Italian regions known for strong presence of mafia, to see if there are any marked deviations from Benford's law. Again, we find that all yearly data sets for Calabria and Sicily agree with Benford's law whereas only the 2007 and 2008 yearly data show departures from the law for Campania. These results are again surprising in view of underground and illegal nature of economic activities of mafia which significantly contribute to tax evasion. Some hypothesis for the found conformity is presented.