Using digital frequencies to detect anomalies in receivables and payables: an analysis of the Italian universities

Motivation: The research aims at evaluating the anomalies and unusual patterns of accounting numbers reported by Italian universities. Prior literature and evidence on local authorities suggest that failing institutions may engage in fraudulent financial reporting to conceal their distress and avoid regulatory intervention. They manipulate accounting values within the scope of the generally accepted accounting principles, using estimates and adjustments for achieving a desired result. Often, they overestimate the receivables and underestimate the payables in order to present a higher level of surplus or a minor deficit. Therefore, the research examines the receivables and payables values contained in the financial reports of Italian universities during the years 2004-2012, hypothesizing that a gradual reduction of the ordinary funding from the Ministry, and the difficulty of attracting private resources, caused financial stress and led management to accounting manipulations. Object and methodology: We apply a mathematical law, known as Benford’s Law, to the receivables and payables reported values, obtained from the Statistical Office of the Ministry of Higher Education, for identifying the existence of manipulated numbers. Benford’s Law implies that, in a naturally occurring set of numbers, the leading digits of the numbers are discrete exponentially distributed rather than uniformly distributed, meaning that the numbers 1 through 9 do not have equal probability of occurring. In particular, the number 1 occurs as the leading digit about 30% of the time, while the number 9 occurs as the first digit less than 5% of the time. As Benford’s Law shows that there is some predictability in the distribution of the first digit in a series of data, it can be used to indicate the presence of fictitious or artificially manipulated numbers. Results: Surprisingly, the statistical tests show a large degree of compliance between the observed and the expected distributions. The conformity is clear and persistent over all the 9 years.