Validating Survey Data Using Benford's Law

• Activity Number: 21
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Kevin Foster*
• Companies: Federal Reserve Bank of Boston
• Keywords: diary ; survey ; consumer payments ; Federal Reserve ; Benford's Law ; rounding bias

Abstract

The 2012 Diary of Consumer Payment Choice (DCPC) is a survey of U.S. consumers produced by the Federal Reserve Banks of Boston, Richmond, and San Francisco. Benford's Law, sometimes known as the First Digit Law, can be applied to the dollar amounts of over 12,000 consumer payments measured in the DCPC. The analysis shows that the distribution of the first digits of the dollar amounts follow Benford's Law reasonably well. In addition, the distribution of first digits in the DCPC dollar amounts is similar to other analyses done by the US Bureau of Labor Statistics on data from the Consumer Expenditure Survey. A generalized version of Benford's Law can be used to find the expected distribution of the nth digit. Using techniques described in the generalized Law, DCPC respondents who reported rounded dollar values can be identified. The analysis will determine if those respondents who round and those who do not round report different mean dollar values for their payment activity.