How to detect what drives deviations from Benford’s law? An application to bank deposit data

Abstract

The Newcomb-Benford law states that the frequency of different leading significant digits in many datasets typically follows a specific distribution. Deviations from this law are often a sign of data manipulation. There has been no established method to test whether the non-reliability of observations depends on some potential explanatory variables. A novel method to address this issue is presented. If a leading significant digit has a higher observed frequency than implied by Benford’s distribution, such observations are particularly likely to be non-reliable. Dividing the frequency in Benford’s distribution by the observed frequency of the same leading significant digit yields an ordinal explained variable. The method is applied to bank deposit data collected in interviews. Many interviewees have provided rounded data, which may be a problem. Answers seem unreliable if the respondent belongs to the age group 51–65, has only primary education, does not live alone, and lives in a city.