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E-MailThe following post comes to us from Dan Amiram and Ethan Rouen, both of the Accounting Division at Columbia University, and Zahn Bozanic of the Department of Accounting and MIS at Ohio State University.
Irregularities in financial statements lead to inefficiencies in capital allocation and can become costly to investors, regulators, and potentially taxpayers if left unchecked. Finding an effective way to detect accounting irregularities has been challenging for academics and regulators. Responding to this challenge, we rely on a peculiar mathematical property known as Benford’s Law to create a summary red-flag measure to capture the likelihood that a company may be manipulating its financial statement numbers.
Benford’s Law states that the distribution of the first digits of numbers from datasets of varying magnitude should follow a downward-sloping distribution, where the number 1 appears as the first digit roughly 30% of the time while the number 9 appears only 4.5% of the time. In our paper, Financial Statement Irregularities: Evidence from the Distributional Properties of Financial Statement Numbers, we examine the first digits of the numbers that appear on the balance sheet, income statement and statement of cash flows for publicly traded U.S. firms from 2001-2011. We construct the Financial Statement Divergence (FSD) Score, which measures the extent to which the entire distribution of the first digits in a firm’s financial statements diverges from the theoretical distribution specified by Benford’s Law.
We show that in aggregate all industries and all years follow Benford’s Law and that 84% of the firm-year financial statements in our sample follow the law. Critically, we show that firms that restated their financial statements more closely conform to Benford’s Law (i.e., have a lower FSD Score) in the restated numbers compared to the misstated numbers. Since this test compares a firm’s misstated numbers in a specific year to its corrected numbers, it allows us to keep constant factors that change over time and across firms. We continue by showing that increased FSD Scores are related to greater information asymmetry and weaker earnings persistence, which may potentially reflect accounting quality concerns.
Focusing on firms that received SEC Accounting and Auditing Enforcement Releases (AAER’s), we further show that such firms have significantly higher FSD Scores than non-AAER firms in the two years leading up to the AAER’s—a trend which exhibits a dramatic decrease in the year contemporaneous with the AAER. This pattern is consistent with the argument that the SEC only pursues firms that engage in the most egregious misstatements and only once those firms run out of room to manipulate their accounting numbers.
The results of the paper collectively suggest that some firms engage in activities that allow their financial statement irregularities to remain undetected by the SEC, yet such activities leave a trace of the irregularities in features of the distributional properties of financial statement numbers. The creation of this score is particularly timely given that the SEC has been working on implementing its Accounting Quality Model (AQM) to flag suspicious firms for review.
The full paper is available for download here.
