Applying 'Benford's Law' to the Crosswise Model: Findings from an Online Survey on Tax Evasion

Abstract

Many surveys on sensitive topics such as tax evasion suffer from the reluctance of respondents to provide truthful answers which can cause downward-biased estimates. This paper addresses this problem by making use of a recent survey method (Crosswise Model) designed to provide positive incentives for respondents to answer sensitive questions more truthful. We extend the Crosswise Model by applying the so-called “Benford Illusion” which allows us to increase the precision of the Crosswise Model that is less statistically efficient than other methods. To test the effectiveness of the model in providing privacy protection, we carried out an online survey in which the respondents were randomly allocated into two splits differing only by the questioning technique applied. Our results suggest that the Crosswise Model can help to increase privacy protection compared to a simple direct questioning approach. As a consequence, survey estimates of tax evasion using the Crosswise Model are likely to become more valid. At the same time, we show that were able to obtain an efficient estimator without substantially decreasing privacy protection, even for a relatively small sample size.