Fraud Power Laws

• Published date: 01 June 2024
• Author: EDWIGE CHEYNEL,DAVIDE CIANCIARUSO,FRANK S. ZHOU
• Date: 01 June 2024
• DOI: http://doi.org/10.1111/1475-679X.12520

DOI: 10.1111/1475-679X.12520

Journal of Accounting Research

Vol. 62 No. 3 June 2024

Printed in U.S.A.

Fraud Power Laws

EDWIGE CHEYNEL ,∗DAVIDE CIANCIARUSO,†

AND FRANK S. ZHOU ‡

Received 1 December 2022; accepted 21 November 2023

ABSTRACT

Using misstatement data, we find that the distribution of detected fraud

features a heavy tail. We propose a theoretical mechanism that explains such

a relatively high frequency of extreme frauds. In our dynamic model, a man-

ager manipulates earnings for personal gain. A monitor of uncertain quality

can detect fraud and punish the manager.As the monitor fails to detect fraud,

the manager’s posterior belief about the monitor’s effectiveness decreases.

Over time, the manager’s learning leads to a slippery slope, in which the size

of frauds grows steeply, and to a power law for detected fraud. Empirical anal-

yses corroborate the slippery slope and the learning channel. As a policy im-

plication, we establish that a higher detection intensity can increase fraud

by enabling the manager to identify an ineffective monitor more quickly.

∗Olin Business School, Washington University; †New Economic School; ‡The Wharton

School of the University of Pennsylvania

Accepted by Philip Berger. We acknowledge helpful comments from an anonymous re-

viewer, John Barrios, Matt Bloomfield, Jennifer Blouin, Sofya Budanova, Daniel Fabisch,

Paul Fischer, Rich Frankel, Pingyang Gao, Jonathan Glover (discussant), Robert Göx, Mirko

Heinle, Xu Jiang, Rick Lambert, Jing Li, Irina Luneva, Xiumin Martin, Suresh Nallareddy, Al-

lison Nicoletti, Aneesh Raghunandan (discussant), Katherine Schipper, Cathy Schrand, Carol

Seregni, Phil Stocken, Alfred Wagenhofer, Hao Xue, Sarah Zechman, Christina Zhu, and

workshop participants at Duke University, the EIASM 2022 in Rotterdam, the ARW 2023 in

Zurich, the Asian AES workshop, the Olin brownbag, Georgia State University, DAR&DART

Accounting Theory Seminar, and the Wharton School of the University of Pennsylvania. We

gratefully acknowledge the financial support from our respective institutions and the Jacobs

Levy Equity Management Center for Quantitative Financial Research at the Wharton School,

University of Pennsylvania. All errors are our own. An online appendix to this paper can be

downloaded at https://www.chicagobooth.edu/jar-online-supplements.

echeynel@wustl.edu

833

© 2023 The Chookaszian Accounting Research Center at the University of Chicago Booth School of

Business.

834 e. cheynel, d. cianciaruso, and f. s. zhou

Further, nondetection of frauds below a materiality threshold, paired with

a sufficiently steep punishment scheme, can prevent large frauds.

JEL codes: D01, M4, M41, M42, M48

Keywords: corporate fraud; earnings manipulation; heavy tails; learning;

misstatements; slippery slope; punishment; zero tolerance

1. Introduction

Despite various regulatory reforms and institutions aimed at preventing

fraud, corporate scandals keep recurring, with high-profile examples such

as Health South, Enron, WorldCom, and Toshiba (Hennes, Leone, and

Miller [2008], Karpoff, Lee, and Martin [2008], Amiram, Huang, and Raj-

gopal [2020]). Studies estimate that between 10% and 22% of firms misre-

port annually (Zakolyukina [2018]), and such misreporting caused equity

value losses estimated to range from $0.83 trillion to $1.14 trillion in 2021

alone (Dyck, Morse, and Zingales [2023]). Our study is driven by the wor-

rying observation that the distribution of detected income-increasing mis-

statements exhibits a substantial heavy tail. For example, the largest 20%

misstatements account for 92.0% of the total misstated amount.

Figure 1 shows that the empirical distribution of restatement amounts

(dashed line) can be approximated by a power law distribution (solid line).

A power distribution describes a quantity for which the probability of events

of large size decreases as a power of the size itself. The lower the power, also

called shape parameter or tail index, the lower the rate of decay and the

heavier the tail will be. Following the procedure recommended by Clauset,

Shalizi, and Newman [2009], we estimate the shape parameter (ζ) as 0.65,

which indicates an even heavier tail than the typical power law with unit

shape parameter (e.g., the net worth of Americans or population in cities

or magnitude of earthquakes).

The frequent occurrence of large misstatements in the data, despite the

high costs incurred if detected, raises crucial questions about the factors

that contribute to fraud and the effectiveness of monitoring. We seek to un-

derstand a mechanism that explains this large frequency of extreme frauds

and validate it empirically, along with recommendations for how to miti-

gate the risk of their occurrence. We develop a dynamic fraud model that

accounts for the strategic behavior of managers who commit fraud when

they are uncertain about the monitor’s effectiveness. An effective monitor

can detect fraud and sanction managers by imposing a penalty that is in-

creasing and convex in the fraud size (e.g., loss of reputation and job and

legal liabilities), whereas an ineffective monitor cannot catch any fraudu-

lent behavior.

The lack of detection when the manager commits fraud is indicative

of monitor ineffectiveness because the ineffective monitor is less likely

to detect fraudulent behavior than the effective monitor. Thus, for the

manager, fraud is not only a means to obtain private benefits, but also an

fraud power laws 835

Fig. 1.—Empirical PDF and fitted power law PDF. This figure plots the estimated power law

PDF for restatement amounts (solid line) against the empirical PDF (dashed line) based on

1,173 unique restatement events from Audit Analytics Restatement between 2005 and 2021.

The restatement amount is the cumulative amount of misstatement of earnings for a restate-

ment event. A quantity ˜xis distributed according to a power law if the frequency with which

˜xexceedsa certain threshold xis, for sufficiently large x(i.e., x≥ω), approximately equal to

C·x−ζ,whereC>0 is a normalizing constant and ζ>0 is a shape parameter or tail index.

The sample consists of restatement events that likely correct intentional manipulations. These

events are identified using (i) ex post measures, namely, fraud or external or internal inves-

tigations (i.e., Securities Exchange Commission [SEC] or board of director investigations)

(Hennes, Leone, and Miller [2008]) and (ii) ex ante measures, namely, core account classi-

fications (Palmrose, Richardson, and Scholz [2004], Zakolyukina [2018]). We further keep

annual misstatements that increase net income and restatements for which the beginning to-

tal assets exceed $1 million. All restatement amounts are scaled by the total assets before the

restatement beginning date. Statistical tests, detailed in appendix C, cannot reject the null that

the restatement distribution follows a power law.Section S.1.1 in the online appendix provides

additional evidence for this phenomenon.

experimentation device that allows the manager to learn the monitor’s

type. Initially, the manager commits small frauds and, if they go unde-

tected, she revises downward her belief about the monitor’s effectiveness.

Over time the manager gains confidence that she will not get caught

and finds it optimal to increase fraud size. This slippery slope creates a