Financial statement errors: evidence from the distributional properties of financial statement numbers

Abstract

Motivated by methods used to evaluate the quality of data, we create a novel firm-year measure to estimate the level of error in financial statements. The measure, which has several conceptual and statistical advantages over available alternatives, assesses the extent to which features of the distribution of a firm's financial statement numbers diverge from a theoretical distribution posited by Benford's Law. After providing intuition for the theory underlying the measure, we use numerical methods to demonstrate that certain error types in financial statement numbers increase the deviation from the theoretical distribution. We corroborate the numerical analysis with simulation analysis that reveals that the introduction of errors to reported revenue also increases the deviation. We then provide empirical evidence that the measure captures financial statement data quality. We first show the measure's association with commonly used measures of accruals-based earnings management and earnings manipulation. Next, we demonstrate that (1) restated financial statements more closely conform to Benford's Law than the misstated versions in the same firm-year and (2) as divergence from Benford's Law increases, earnings persistence decreases. Finally, we show that our measure predicts material misstatements as identified by SEC Accounting and Auditing Enforcement Releases and can be used as a leading indicator to identify misstatements.

Financial crime ‘hot spots’ – empirical evidence from the foreign exchange market

“…Given the highly volatile environment in the FX market, a MM is constructed to allow for random differences between the WMR benchmark and the TR rate at higher digit positions, but to account for nonrandom currency spikes at lower digit positions. Similar to Amiram, Bozanic, and Rouen (2015), who calculate the average over the absolute differences between observed and theoretical frequencies of the nine first digits, the MAD is defined for each FX rate as the median over all digit bins of d p ∈ {0, 1, 2, . .…”

“…Over the last three decades, extensive work applied the Benford method to data sets in order to detect digit patterns of potential misconduct. Yet, the set-up of a Benford test was predominantly applied to accounting and taxation data (Carslaw 1988;Thomas 1989;Nigrini and Mittermaier 1997;Herrmann and Thomas 2005;Guan, He, and Yang 2006;Amiram, Bozanic, and Rouen 2015). In regards to financial markets, Ley (1996) documents that the first digits of the time series of daily returns on stock market indices reasonably agree with the Benford distribution.…”

“…Moreover, Osler (2003) and Osler (2005) conduct digit analysis in the FX market with regard to currency orders and exchange rate dynamics. In addition, a large and growing body of digit analysis applies the Benford method (Newcomb 1881;Benford 1938) to detect accounting and taxation fraud in reported data (Carslaw 1988;Thomas 1989;Nigrini and Mittermaier 1997;Herrmann and Thomas 2005;Guan, He, and Yang 2006;Amiram, Bozanic, and Rouen 2015). El Mouaaouy and Riepe (forthcoming) apply the Benford method to segment-level data of internal capital markets in order to indicate managerial engagement in the allocation outcomes of German banks.…”

“…The Benford method refers to an empirical observation of digits in data sets, known as Benford's law (Newcomb 1881;Benford 1938). Many studies apply the Benford test to detect manipulation patterns in reported data (Carslaw 1988;Thomas 1989;Nigrini and Mittermaier 1997;Herrmann and Thomas 2005;Guan, He, and Yang 2006;Amiram, Bozanic, and Rouen 2015). However, a concern of the Benford approach is that the approximation based on Benford's expected digit frequencies might result in highly significant deviations despite no material manipulation (Mitchell 2001;Mitchell and Izan 2006).…”

The Power of Numbers: Base-Ten Threshold Effects in Reported Revenue

“…Benford's Law also emerges naturally for any data set in which the observed values are randomly drawn from different distributions, and this phenomenon has been shown to be true in accounting data (Nigrini 1996;Nigrini and Mittermaier 1997). Amiram et al (2015) use deviations from Benford's Law to calculate a measure of financial statement data quality and predict material misstatements.…”