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

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## 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.

## Keywords

Benford’s Law Financial statements errors Accounting quality Earnings management## JEL Classification

M41## Notes

### Acknowledgments

We would like to thank Patty Dechow (the editor), an anonymous referee, Anil Arya, Rob Bloomfield, Qiang Cheng, Ilia Dichev, Dick Dietrich, Peter Easton, Paul Fischer, Ken French, Joseph Gerakos (CFEA discussant), Jon Glover, Trevor Harris, Colleen Honigsberg, Jeff Hoopes, Gur Huberman, Amy Hutton, Bret Johnson, Steve Kachelmeier, Alon Kalay, Bin Ke, Bill Kinney, Alastair Lawrence, Melissa Lewis-Western, Scott Liao, Sarah McVay (FARS discussant), Rick Mergenthaler, Brian Miller, Brian Mittendorf, Suzanne Morsfield, Suresh Nallareddy, Jeff Ng, Craig Nichols, Mark Nigrini, Doron Nissim, Ed Owens, Bugra Ozel, Oded Rozenbaum, Gil Sadka, Richard Sansing, Richard Sloan, Steve Smith, Steve Stubben, Alireza Tahbaz-Salehi, Dan Taylor, Andy Van Buskirk, Kyle Welch, Jenny Zha (TADC discussant), Amir Ziv, conference participants at the 2014 AAA FARS Midyear Meeting, and workshop participants at Columbia University, Baruch College, Dartmouth College, Florida Atlantic University, George Washington University, Georgetown University, the London Trans-Atlantic Doctoral Conference, Nanyang Technological University, Singapore Management University, Syracuse University, UC Berkeley, UCLA, UNC, The University of Texas—Austin, and The University of Utah for their helpful comments and suggestions. We would also like to thank the PCAOB and the SEC for their insights.

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