Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford's Law

The Consumer Expenditure Survey (CE) is a nationwide household survey conducted by the U.S. Bureau of Labor Statistics (BLS) to find out how Americans spend their money. As with any survey, the accuracy of CE’s published expenditure estimates depends on the accuracy of the collected data. The CE survey has several procedures already in place to ensure the accuracy of its published expenditure estimates. They include reinterviews of some respondents, computerized checks for the logical consistency of responses given by respondents, an outlier review of individual survey responses, and another outlier review of the summarized expenditure estimates before they are published (BLS Handbook of Methods). In this paper we describe another method of identifying inaccurate survey data. The method is little-known, but it has been rapidly gaining popularity over the past decade. The method involves examining the distribution of the leading (or left-most) digits of all the numbers reported on a survey form. These leading digits have been observed to follow a certain distribution regardless of the nature of the survey. This phenomenon is called Benford’s Law. By knowing the distribution of the leading digits, one can identify unusual data which may be fraudulent or generated by an error-prone process by identifying the interviews in which the distribution of leading digits does not follow the expected distribution. In this paper we will describe the Consumer Expenditure Survey and the current methods used in that survey to identify inaccurate data. Then we will describe Benford’s Law, describe some applications of it in other settings, and then we will give an example showing how Benford’s Law can be used to identify unusual data in a survey setting using CE data as an example.