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Many people today believe that U.S. executives are paid too much while others believe that the size of their compensation packages are justified. For this assignment, choose a peer-reviewed article to review. Use the databases in the CSU Online Library, and find an article about executive compensation that is of interest to you. The article must be at least three pages long, and no more than 3 years old. Write a two-page review of the article that includes the following information:Briefly introduce and summarize the article. Identify the author’s main points. Who is the author’s intended audience? What types of executive compensation were addressed in the article? How does the article apply to this course? Does it support the information in your textbook? How could the author expand on the main points? After reviewing the article and the information in your textbook, state whether you think executive compensation is justified or is out of hand. Give at least three points to justify your argument.Please utilize at least two sources, one of which must be the article. The Business Source Ultimate database in the CSU Online Library is a great place to begin searching for sources. Adhere to APA Style when constructing this assignment, including in-text citations and references for all sources that are used. Please note that no abstract is needed.
Many people today believe that U.S. executives are paid too much while others believe that the size of their compensation packages are justified. For this assignment, choose a peer-reviewed article to
JOURNAL OF MANAGEMENT ACCOUNTING RESEARCHAmerican Accounting Association Vol. 32, No. 1DOI: 10.2308/jmar-52477 Spring 2020 pp. 177–201 Heaping of Executive Compensation Bjorn N. Jorgensen The London School of Economics and Political Science Paige H. Patrick University of Illinois at Chicago Naomi S. Soderstrom The University of Melbourne ABSTRACT:We investigate whether compensation grants are subject to‘‘heaping,’’the tendency of less informed individuals to provide round values when reporting estimates of discrete data. We document that an unexpectedly large number of CEOs receive round compensation (i.e., evenly divisible by 100,000 and/or 10,000). We investigate whether, consistent with heaping, the frequency of round compensation varies with proxies for boards of directors’ effort in setting compensation. We find that round compensation is more common when boards have characteristics suggesting they provide weak oversight of compensation and thus face more uncertainty in estimating compensation. We also find less frequent round compensation when boards face stronger pressure from external stakeholders, encouraging boards to expend additional cognitive effort in setting compensation. Further, consistent with weak oversight of compensation, round compensation tends to be higher than non-round compensation. However, we do not find a consistent association between this higher, round compensation and future firm performance. JEL Classifications:G30; G41; M40; M46. Data Availability:Data are available from the public sources cited in the text. Keywords:executive compensation; heaping; rounding; say on pay. I. INTRODUCTION E mpirical research on executive compensation typically appeals to models based on agency theory to help explain how boards of directors incentivize executives. These models assume numerous functional forms for compensation. However, to our knowledge, none of these models predict that the distribution of compensation will include discontinuities. Some models do predict that individual CEO compensation may re ect discontinuous earnings distributions (e.g.,Healy 1985;Melumad 1989;Fedyk 2007); however, these models do not suggest that the distribution of CEO compensation across many heterogeneous rms and years will include discontinuities. While analytical models based on the agency theory framework do not predict discontinuities in the distribution of executive compensation, research that re ects behavioral phenomena does predict that discontinuities will occur. We investigate whether the heuristic response to uncertainty known as‘‘heaping’’partially explains the observed distribution of We thank two anonymous referees, Shane S. Dikolli (editor), Brian Cadman, Frank Moers, Steve Rock, Hongtao Shen (discussant, 2014 JMAR/CJAS conference in Wuhan, China), and seminar participants at the University of Aachen, the Universities of British Columbia, Oregon, and Washington Conference, the University of Colorado Boulder, The University of Edinburgh, the University of Hohenheim, IE Business School, INSEAD, LaTrobe University, The London School of Economics and Political Science, Maastricht University, Macquarie University, Monash University, Peking University, and The University of Queensland for helpful comments. Bjorn N. Jorgensen, The London School of Economics and Political Science, London, England, U.K.; Paige H. Patrick, University of Illinois at Chicago, Department of Accounting, Chicago, IL, U.S.A.; Naomi S. Soderstrom, The University of Melbourne, Department of Accounting, Melbourne, Victoria, Australia. Editor’s note: Accepted by Shane S. Dikolli, under the Senior Editorship of Karen L. Sedatole. Submitted: August 2017 Accepted: April 2019 Published Online: July 2019 177 executive compensation. 1Heaping is the tendency to provide estimates ending in digits that are the largest divisors of the base number system. Heaping arises when people make point estimates of measures about which they lack precise information (Turner 1958). That is, when individuals have imprecise information, they provide estimates that follow a predictable pattern: the estimates tend to be multiples of the base of the number system, i.e., round numbers. The existence of heaping is widely acknowledged in disciplines such as demography, where researchers frequently rely on self-reported information by imperfectly informed individuals. Studies in diverse elds nd evidence of heaping when individuals are uncertain about the actual values of measures, such as income (Turner 1958), birthweight (Barreca, Guldi, Lindo, and Waddell 2011), blood pressure, and age (Roberts and Brewer 2001). For example, individuals are less likely to provide round estimates when they provide their own ages but are more likely to provide round estimates when they provide estimates of others’ ages. In accounting, empirical researchers document discontinuities in distributions of analyst and management forecasts, both of which are reported estimates (e.g.,Herrmann and Thomas 2005;Bamber, Hui, and Yeung 2010;Zhou 2010;Dechow and You 2012; Athanasakou and Simpson 2016). Consistent with heaping, these studies nd that both analysts and management tend to report round values of forecasted earnings when they are less certain of the estimates they are providing. Prior literature on executive compensation in accounting and nance largely explores whether compensation is structured in a fashion consistent with agency theory models that represent competitive market forces, or with managerial power over compensation (seeFrydman and Jenter 2010for a review). We build upon the existing understanding of how boards set compensation by investigating the role of heaping in determining compensation. We explore whether the distribution of compensation is consistent with heaping behavior. If executive compensation re ects heaping, the distribution of executive compensation will exhibit abnormally high levels of round compensation (i.e., compensation that is a multiple of the base ten numerical system) and these round values of compensation will vary predictably with proxies for the level of directors’ uncertainty about executive performance and optimal compensation design. To address whether distributions of compensation exhibit abnormally high levels of round compensation, we present evidence of the frequency of round CEO compensation values. We document that an unusually high number of executives earn round compensation. 2Figure 1 illustrates this phenomenon for different components of CEO compensation. In our sample, 36.1 percent of CEO salaries, 40.9 percent of bonuses, and 23.8 percent of option grants are evenly divisible by either 100,000 or 10,000. 3This phenomenon does not appear to be based upon a mechanical relation between compensation and the underlying performance metrics upon which it is based, since two commonly used performance measures, earnings per share and stock price, end in zero only 9.3 percent and 11.3 percent of the time, respectively. Thus, we provide evidence that executive compensation exhibits abnormally high frequencies of round compensation. We perform three sets of analyses to assess whether round values of compensation vary predictably with proxies for the level of directors’ uncertainty about executive performance and the design of optimal compensation, which would suggest that the distribution of CEO compensation is consistent with heaping. First, we consider whether round compensation is more common when boards have characteristics that indicate weak oversight of compensation. In these rms, we expect that directors will be less likely to have acquired and processed the information necessary to make precise estimates about executive performance. This may arise for a number of reasons: (1) weak boards are unlikely to challenge powerful executives who take measures to obfuscate relevant information about performance; (2) directors on such boards are less likely to be responsive to pressure from outside parties; or (3) such directors are not motivated by reputation concerns. Thus, if round compensation results from heaping, it will be positively associated with proxies for weak board oversight. A substantial stream of literature demonstrates that certain board characteristics are consistent with weaker oversight of compensation (e.g.,Core, Holthausen, and Larcker 1999;Coles, Daniel, and Naveen 2014). Our evidence is consistent with this prediction. We show that round compensation is more common when the board has a greater proportion of insiders and a greater proportion of directors appointed by the CEO. Second, we investigate whether stakeholder pressure is associated with round compensation. Prior research suggests that boards increase attention and effort in setting compensation in the presence of more active stakeholders (e.g.,Johnson, Porter, and Shackell 1997;Thomas and Martin, 1999;Core, Guay, and Larcker 2008;Ertimur, Ferri, and Muslu 2011;Abernethy, Kuang, and Qin 2015;Ertimur, Ferri, and Oesch 2018). If boards increase the cognitive effort they expend on setting compensation when they face greater stakeholder pressure, they will be more informed, reducing uncertainty about executive performance and about how to set optimal compensation. As such, if round compensation is consistent with heaping, greater 1While heaping is a behavior that arises in the face of uncertainty, we do not argue that heaping is necessarily economically irrational. As we discuss below, heaping may be consistent with boards expending ef cient levels of effort on costly information acquisition and processing. 2We limit our measure of rounding to compensation components that are rounded to 100,000s or 10,000s of dollars or shares granted to capture meaningful levels of rounding. 3We exclude observations of $0 or 0 shares from our analyses. Thus, these values represent the frequencies with which non-zero compensation is rounded. 178Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 stakeholder pressure will be associated with a lower incidence of round compensation. We examine the change in the frequency of round compensation following passage of the Say on Pay provision of the Dodd-Frank Act, 4which requires an advisory shareholder vote on executive compensation packages. This passage of compensation-related regulation is a reasonable proxy for changes in stakeholder pressure because it is at least partially exogenous to individual rms’ governance environments. Additionally, this identi cation strategy exploits within- rm variation in stakeholder scrutiny surrounding regulatory changes, allowing us to make stronger inferences about the effect of stakeholder scrutiny on the frequency of rounding. We nd evidence consistent with our expectations. Boards are less likely to grant round values of compensation components after passage of Say on Pay, particularly for performance-based pay, which was the focus of that regulation. In sensitivity tests, we nd a similar reduction in rounding of option grants following passage ofStatement of Financial Accounting Standards No. 123R(SFAS 123R)—Share-Based Payment(FASB 2004). 5 Third, we investigate whether, controlling for rm performance, round CEO compensation tends to be higher than non- round CEO compensation.Bebchuk and Fried (2003)suggest that self-interested managers take advantage of opportunities to extract rents from rms in the form of excess compensation. Round compensation as a result of heaping suggests that boards granting round compensation face more uncertainty when setting compensation than do boards granting non-round compensation. Self-interested CEOs may take advantage of this uncertainty to gain excess compensation. This suggests that round compensation will be greater than non-round compensation for a given level of performance. We nd evidence FIGURE 1 Distributions of Compensation Panel A: CEO Salary Compensation Salary is as reported by ExecuComp in $1,000s. The width of bins in the histogram is $20,000. The sample size for this histogram is 10,299 CEO-years from 2007 to 2014. For legibility, we exclude 122 observations in which CEOs were granted more than $2,000,000 in salary compensation, resulting in a sample size of 10,177 observations. (continued on next page) 4Dodd-Frank Wall Street Reform and Consumer Protection Act (U.S. Congress 2010).5Statement of Financial Accounting Standards No. 123: Accounting for Stock-Based Compensation(FASB 1995) allowed rms to account for option compensation using the intrinsic value method on the option grant date (usually zero) and required disclosure of the grant date fair value of option compensation expense. SFAS 123R required rms to recognize option expense at grant date fair value rather than intrinsic value. Heaping of Executive Compensation179 Journal of Management Accounting Research Volume 32, Number 1, 2020 consistent with this prediction. After controlling for rm-level determinants of compensation, we show that total compensation is higher when it is round. These analyses provide consistent evidence that heaping frequently occurs when boards set executive compensation. Our nal analysis investigates whether heaping is detrimental to rm performance. On the one hand, heaping may be associated with poorer future rm performance if heaping occurs when boards do not provide strong oversight of compensation, allowing self-interested managers to extract material rents via compensation. On the other hand, heaping of compensation may result from an ef cient allocation of board attention. Boards have many tasks in addition to setting CEO compensation, but a limited amount of attention to allocate across these competing tasks. If these competing tasks are economically important, a lack of attention to the details of compensation can be desirable. We nd mixed evidence of an association between round compensation and future rm performance. As such, we are unable to conclude whether, on average, heaping of executive compensation is detrimental to rm performance, or represents ef cient allocation of limited board attention across multiple tasks. In sum, we provide evidence that, in addition to being driven by agency cost concerns and managerial power as shown in prior literature, executive compensation also re ects behavioral tendencies. Speci cally, we demonstrate that executive compensation exhibits characteristics consistent with heaping, which is the tendency of uninformed individuals to provide round numbers when they estimate discrete, quantitative data. We show that round compensation is common and that the attributes of this round compensation are consistent with less-informed boards. These ndings contribute to our understanding of how boards determine compensation. We also contribute to the literature on discontinuities in executive compensation distributions. Prior research documents that an unusually high number of executives earn salaries of $1 million (Rose and Wolfram 2000,2002) or of $0/$1 (Hamm, Jung, and Wang 2015;Loureiro, Makhija, and Zhang 2015). In addition to these focal points, we document an unusually high number of executives earning round compensation, that is, compensation components that are rounded to 100,000s or 10,000s of dollars or shares granted.FIGURE 1 (continued) Panel B: CEO Bonus Compensation Bonus is as reported by ExecuComp in $1,000s. The width of bins in the histogram is $20,000. The initial sample size for this analysis is 1,998 non-zero bonus grants. For legibility, we exclude 67 observations in which CEOs were granted more than $5,000,000 in bonus compensation, resulting in a nal sample size of 1,931 observations. (continued on next page) 180Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 We also extend the literature on heaping to a new setting—compensation. Heaping has been widely acknowledged in other disciplines, and has received some attention in the nancial accounting literature, as well. Prior studies in accounting nd evidence of heaping in analyst and management forecasts (e.g.,Herrmann and Thomas 2005;Bamber et al. 2010;Zhou 2010; Dechow and You 2012;Athanasakou and Simpson 2016). We expand upon these prior studies by demonstrating that heaping affects additional rm stakeholders, boards of directors and rm executives. II. LITERATURE REVIEW Psychology literature explores how individuals retrieve uncertain values from memory, and explains individuals’ reliance on arithmetic prototypes (i.e., round numbers) when reporting these uncertain values (e.g.,Huttenlocher, Hedges, and Bradburn 1990). Social sciences research also observes this behavior when individuals make estimates of uncertain information, even when individuals are not retrieving this information from memory. 6The social science literature coins the term‘‘heaping’’to describe the tendency to provide estimates ending in digits that are the largest divisors of the base number system. In this literature, heaping is considered a heuristic response to uncertainty that arises when people make point estimates of measures about which they lack precise information.Simon (1990)andShah and Oppenheimer (2008)link heuristics to reduced effort associated with decision processes.FIGURE 1 (continued) Panel C: CEO Non-Equity Incentive Compensation Non-equity incentive compensation is as reported by ExecuComp, in $1,000s. The width of bins in the histogram is $20,000. The initial sample size for this analysis is 7,889 non-zero non-equity incentive grants. For legibility, we exclude 312 observations in which CEOs were granted more than $5,000,000 in non-equity incentive compensation, resulting in a nal sample size of 7,577 observations. (continued on next page) 6For example, individuals tend to report round numbers for estimates of income (Turner 1958), age (e.g.,Shryock, Siegel, and Larmon 1980;Roberts and Brewer 2001;A’Hearn, Baten, and Crayen 2009), weight and height (Rowland 1990), and blood pressure (Wen, Kramer, Hoey, Hanley, and Usher 1993). Heaping of Executive Compensation181 Journal of Management Accounting Research Volume 32, Number 1, 2020 In accounting, a handful of studies investigate whether heaping is present in distributions of earnings estimates.Herrmann and Thomas (2005 ),Zhou (2010), andDechow and You (2012) nd that analysts’ forecasts of EPS exhibit more clustering around multiples of ve cents than do actual EPS. Consistent with heaping, these studies nd that analysts who round EPS forecasts appear to be less informed, exert less effort, and have fewer resources.Bamber et al. (2010)investigate whether heaping is present in management’s earnings forecasts. In addition to re ecting uncertainty, they nd that round management forecasts are opportunistically biased. Research in nance and accounting documents in other settings rounding that does not necessarily result from heaping. In the nance literature, prior research documents clustering of share prices or returns on round values, which may represent either dealer collusion (Christie, Harris, and Schultz 1994;Christie and Schultz 1994) or naturally occurring discontinuities in distributions (Osborne 1962;Grossman, Miller, Cone, Fischel, and Ross 1997;E. Johnson, N. Johnson, and Shanthikumar 2011;Bhattacharya, Holden, and Jacobsen 2012).Amiram, Kalay, and Ozel (2013)show that bond coupon rates are set in increments of eighths. In the nancial accounting literature, researchers nd patterns consistent with rounding of unscaled reported earnings and of reported earnings per share (EPS). 7These researchers ascribe the frequency of rounding to earnings management to meet or beat earnings benchmarks.Zhou (2010)andCheong and Thomas (2011)document unusual patterns in forecasts of EPS.Amiram, Bozanic, and Rouen (2015) nd that deviations of nancial statement information from predicted distributions indicate nancial reporting irregularities.FIGURE 1 (continued) Panel D: CEO Option Grants Options are the number of options granted as reported by ExecuComp, in 1,000 shares. The width of bins in the histogram is 20,000. The initial sample size for this analysis is 5,540 non-zero option grants. For legibility, we exclude 36 observations in which CEOs were granted more than 2,000,000 options, resulting in a nal sample size of 5,504 observations. (continued on next page) 7See, among others,Carslaw (1988),Thomas (1989),Hayn (1995),Burgstahler and Dichev (1997 ),Degeorge, Patel, and Zeckhauser (1999),Das and Zhang (2003),Bamber et al. (2010),Jorgensen, Lee, and Rock (2014 ),Malenko and Grundfest (2014 ), andBurgstahler and Chuk (2015,2017). 182Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 Prior research also explores discontinuities in the distribution of executive compensation that are not related to heaping: salaries of $0/$1 and of $1 million.Hamm et al. (2015)andLoureiro et al. (2015)investigate the prevalence of and reasons for salary grants of $0 or $1. More closely related to our research,Rose and Wolfram (2000,2002)andPerry and Zenner (2001)identify increased clustering in executive salaries at $1 million subsequent to introduction of Internal Revenue Code Section 162(m), which limits the tax deductibility of top executives’ non-performance-based compensation to $1 million per year. III. HYPOTHESIS DEVELOPMENT Is the Distribution of Executive Compensation Consistent with Heaping? Determining executive compensation schemes and values is a substantial task for boards of directors and the information acquisition and processing required for this task are costly activities for directors. However, pressure from other board members, shareholders, other stakeholders, or reputation concerns can provide directors incentives to engage in information acquisition and processing, i.e., to gather and understand more, or more precise, information (e.g.,Bertrand and Mullainathan 2001;Bebchuk and Fried 2003). Directors who undertake less information acquisition or spend less time processing information related to executive performance and compensation practices will be, on average, less informed than those who expend more effort, resulting in greater uncertainty about CEO performance and how to reward it. This leads to our rst research question: Is the distribution of executive compensation consistent with heaping? We generate three hypotheses from this research question.FIGURE 1 (continued) Panel E: CEO Equity Incentive Grants Equity incentive shares are the number of incentive shares granted as reported by ExecuComp in 1,000 shares. The width of bins in the histogram is 10,000. The initial sample size for this analysis is 4,991 non-zero equity incentive grants. For legibility, we exclude 209 observations in which CEOs were granted more than 500,000 shares, resulting in a nal sample size of 4,782 observations. (continued on next page) Heaping of Executive Compensation183 Journal of Management Accounting Research Volume 32, Number 1, 2020 If heaping occurs when boards set executive compensation, we expect to observe a disproportionate number of round values of compensation grants. We also expect the frequency of round compensation to vary predictably, as we discuss in this section. Numerous studies demonstrate that certain characteristics of boards of directors are consistent with weak oversight of managers and, speci cally, of executive compensation (e.g.,Core et al. 1999;Coles et al. 2014). In such rms, we expect that directors will be less likely to have acquired and processed the information necessary to make precise, certain estimates about executive performance. This may arise because boards do not challenge powerful executives who take measures to obfuscate relevant information about performance, resulting in less precise information for decision-making. This may also arise if the directors of such boards are less responsive to pressure from outside parties or are not as motivated by reputation concerns. We thus expect boards with characteristics consistent with weak oversight of compensation to have less, or less precise, information about executive performance. In turn, if heaping is re ected in compensation, these less-informed boards will be more likely to provide round values of compensation. This leads to our rst hypothesis: H1:Rounding of compensation is negatively associated with board strength. Pressure from shareholders and other outsiders may in uence boards of directors to improve oversight of compensation. Bertrand and Mullainathan (2001)andBebchuk and Fried (2003)refer to pressure from stakeholders as‘‘outrage.’’According to this point of view, when faced with pressure from stakeholders, boards are less likely to adopt forms of compensation that embarrass directors or executives, or that might reduce shareholders’ willingness to re-elect board members. Empirical evidence suggests that boards adjust compensation practices due to stakeholder pressure.Johnson et al. (1997 ) nd that boards respond to negative publicity by granting smaller increases in compensation and by increasing the sensitivity of cash pay to performance.Core et al. (2008)obtain similar results but demonstrate that these effects may be short-lived.Thomas and Martin FIGURE 1 (continued) Panel F: CEO Other Equity Grants Other equity shares are the number of other equity shares granted as reported by ExecuComp in 1,000 shares. The width of bins in the histogram is 10,000. The initial sample size for this analysis is 5,709 non-zero other equity grants. For legibility, we exclude 172 observations in which CEOs were granted more than 300,000 shares, resulting in a nal sample size of 5,537 observations. 184Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 (1999)document that, following shareholder compensation proposals, boards reduce CEO compensation. Consistent with these results,Ertimur et al. (2011) nd that shareholder activism targeting executive compensation results in reduced excess CEO compensation.Ertimur et al. (2018)observe a $1.2 million reduction in CEO compensation following proxy advisors’ recommendations that shareholders withhold votes from directors due to concerns about pay-for-performance sensitivity. Abernethy et al. (2015) nd that, while rms in the United Kingdom adopted performance-vested stock option plans to quell public outrage, powerful executives in uence the choice of performance measures in those plans. Evidence on the effect of stakeholder pressure suggests that boards will increase their oversight efforts and that this increase in effort extends to compensation. Thus, when stakeholders increase their focus on compensation, we expect boards to expend more effort gathering information about executive performance and in determining compensation design and payments. As a result, boards will have more precise information about executive performance, and less uncertainty, resulting in less round compensation. Thus, if round compensation results from heaping, we expect a negative association between the frequency of rounding and stakeholder pressure. This leads to our second hypothesis: H2:Rounding of compensation is negatively associated with stakeholder pressure. We next investigate the association between the level of compensation and whether compensation is round.Bebchuk and Fried (2003)suggest that self-interested managers take advantage of opportunities to extract rents from rms in the form of excess compensation. Consistent withBebchuk and Fried (2003), many studies nd evidence of CEO opportunism when boards exhibit characteristics of weak oversight (e.g.,Core et al. 1999;Coles et al. 2014;Abernethy et al. 2015). If round compensation is consistent with heaping, then round compensation values can be indicative of boards that face more uncertainty when setting compensation. In these cases, self-interested CEOs may take advantage of these boards’ uncertainty to gain excess compensation. Thus, if round compensation results from heaping, then, for a given level of rm performance, compensation will be higher when it is round. This leads to our third hypothesis: H3:Ceteris paribus,round compensation is higher than non-round compensation. Is Heaping Associated with Firm Performance? In our rst three hypotheses we investigate whether round compensation arises from a heuristic response to uncertainty, heaping. We posit that uncertainty about optimal executive compensation arises because information acquisition and processing are costly, but that pressures from other board members and stakeholders will lead some boards to invest more in information acquisition and processing about compensation. In this section, we investigate whether heaping is associated with rm performance. On the one hand, if heaping results when boards do not provide strong oversight of compensation and allow self- interested managers to extract material rents via compensation, heaping may be associated with poorer rm performance. On the other hand, heaping of compensation may result from an ef cient allocation of board attention. That is, directors have numerous responsibilities, all of which require costly information acquisition and processing. As such, some boards may rationally choose to invest less in information acquisition and processing when setting compensation, as their limited attention has greater impact when focused on other decisions or activities. Because of the con icting nature of these predictions, we state our fourth hypothesis in the null form: H4:Rounding of compensation is not associated with future performance. IV. SAMPLE AND PRELIMINARY EVIDENCE ON ROUND COMPENSATION FREQUENCY Sample Design Our initial sample includes CEOs from rms covered by ExecuComp for the period 2007 through 2014. We begin our sample in 2007 because the SEC increased compensation disclosure requirements for top executives’ equity holdings and cash bonus payments beginning in December 2006. We focus our analyses on CEOs because their compensation is likely to be the most visible. Our sample is reduced due to use of data from RiskMetrics, Compustat, and CRSP for our analyses. The resulting sample includes 10,897 CEO-years. We further exclude 598 CEOs in their rst year of employment to alleviate concerns that our results are driven by any tendency to round compensation in the rst year of employment. Our main sample thus includes 10,299 CEO-years, although we place additional restrictions on our data for several of our tests. We discuss these exclusions in the research design for each test and include the sample size associated with each test in the tables. Table 1 presents distributions of regression variables. Variable de nitions are presented in the table and are described in the text below. Heaping of Executive Compensation185 Journal of Management Accounting Research Volume 32, Number 1, 2020 Preliminary Evidence on the Frequency of Round Compensation The rst step in our analysis is to explore the prevalence of round values for all forms of compensation. We consider six types of compensation grants, salary (ExecuComp variable SALARY ), discretionary bonus (ExecuComp variable BONUS), non-equity incentive cash compensation (ExecuComp variable NONEQ_INCENT), grants of options (ExecuComp variable OPTION_AWARDS_NUM), and equity compensation (ExecuComp variables EQ_TARG and SHARES_GRT). 8 Figure 1, Panel A, presents a histogram of salary compensation for our initial sample of 10,299 CEOs. We truncate this histogram at $2 million for presentation purposes. Consistent withRose and Wolfram (2000,2002), Figure 1, Panel A, suggests that a disproportionately large number of CEOs earn exactly $1 million. Of the observations in the bin containing $1,000,000 through $1,020,000, 495 represent observations in which CEOs earned exactly $1 million in salary. In addition to the high frequency of salaries equal to $1 million, Figure 1, Panel A, shows unusually high frequencies of salary compensation at other values. One large irregularity in the distribution occurs in the rst bin, where salary is $0–$20,000. The distribution of salaries within the bin is not uniform; the bin is dominated by a signi cant number of CEOs (81) whose cash compensation is no more than $1. The frequency of these observations is consistent withHamm et al. (2015)andLoureiro et al. (2015 ). However, we TABLE 1 Distributions of Selected Regression Variables Variable Mean Min. Median Max. Obs. PercentRoundAll0.247 0.000 0.250 1.000 10,299 PercentRoundPerformance0.180 0.000 0.000 1.000 9,785 PercentRoundDiscretionary0.361 0.000 0.000 1.000 10,279 Dual0.540 0.000 1.000 1.000 10,299 Insiders0.208 0.000 0.182 0.857 10,299 AppointedbyCEO0.395 0.000 0.375 1.000 10,299 PostSOP0.508 0.000 1.000 1.000 10,299 TotalCompensation6,002.913 0.001 4,147.181 156,077.912 10,299 PerformanceCompensation4,664.123 0.000 3,010.320 151,141.922 10,299 DiscretionaryCompensation1,077.851 0.000 855.000 77,926.000 10,299 ROA tþ1 0.091 1.223 0.081 1.126 10,299 Compensation components, taken from ExecuComp, are round if they are evenly divisible by 100,000 or 10,000 dollars or shares. The sample size for this table is 10,299. Not all CEOs were granted either performance-based compensation or discretionary compensation. Following prior literature, we use the natural logs of compensation variables in our empirical analyses. Variable De nitions: PercentRoundAll¼the number of round components in a compensation package divided by the number of compensation components granted; PercentRoundPerformance¼the number of round performance-based components in a compensation package divided by the number of performance- based components granted. Performance-based components include non-equity incentive compensation (the variable NONEQ_INCENT), the number of plan-based stock awards (EQ_TARG), the number of other shares granted (SHARES_GRT), and the number of options awarded (OPTION_AWARDS_NUM); PercentRoundDiscretionary¼the number of round discretionary components in a compensation package divided by the number of discretionary components granted. Discretionary components include salary (SALARY ) and bonuses awarded but not classi ed as part of a performance-based plan (BONUS); Dual¼an indicator variable set to 1 if the CEO is also the chairman of the board and 0 otherwise; Insiders¼the percentage of board members who are insiders; AppointedByCEO¼the percentage of outside board members appointed by the CEO; PostSOP¼an indicator variable set to 1 if the observation is from 2011 or later; TotalCompensation¼compensation as reported in ExecuComp, in thousands of dollars (TDC1); PerformanceCompensation¼the sum of compensation from the four performance-based compensation components, as reported in ExecuComp (NONEQ_INCENT, OPTION_AWARDS_FV, and STOCK_AWARDS_FV ), in thousands of dollars. Note that STOCK_AWARDS_FV summarizes the dollar value of EQ_TARG and SHARES_GRT, which are reported in shares; DiscretionaryCompensation¼the sum of salary and discretionary bonus compensation from ExecuComp, in thousands of dollars; and ROA tþ1 ¼return on assets measured as EBIT/average total assets measured in yeartþ1. 8We assume that boards grant equity compensation in numbers of shares rather than in estimated dollar values. We thus study the number of options or stock shares granted. This assumption biases us against nding signi cant results if rms grant estimated dollar values of equity instead of numbersof options or shares. 186Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 note unusually high frequencies of salary compensation throughout the distribution, primarily at values evenly divisible by $100,000 and, in particular, around $500,000, $1.5 million, and $2 million. We note similar irregularities around values divisible by $500,000 in the histograms of bonus compensation (Panel B) and non-equity incentive compensation (Panel C ). The pattern is less obvious when we investigate the distributions of equity granted in Panels D through F, although we observe irregularities at values evenly divisible by 100,000 shares. Overall, the histograms of the distributions of cash and equity compensation provide preliminary evidence that compensation tends to be disproportionately divisible by 100,000. Since our histograms present compensation levels in $20,000 bins, we cannot conclude that the spikes we observe are due to rounded compensation (i.e., compensation that is evenly divisibly by 100,000 or 10,000 units). In further examination of the spikes in the histograms, we investigate the prevalence of observations that end in zero. 9We restrict this analysis to non-zero values of each type of compensation grant. In Table 2, we present the frequency of the last digit being zero based on whether the amount is evenly divisible by $1,000,000 (or 1,000,000 shares), $100,000 (or 100,000 shares), or $10,000 (or 10,000 shares). While rounding to values evenly divisibly by 1,000, 100, or 10 is common in our sample, we treat these observations as non-round in subsequent analyses because they are unlikely to be economically signi cant to either rms or executives. 10 For ease of exposition, we refer to values evenly divisible by 10,000 units as round. Table 2 demonstrates that discretionary bonuses are the most likely form of compensation to be round (40.9 percent of non-zero observations are evenly divisible by $10,000), followed by salary (36.1 percent of observations are evenly divisible by $10,000). We note that forms of compensation that are more likely to be qualitative assessments of CEO performance (i.e., salary and discretionary bonuses) are those forms of compensation that are most likely to be round. This is consistent with heaping, because these forms of compensation more naturally lend themselves to estimation, presenting opportunity for heuristic responses to come into play. Performance-based compensation is a quantitative assessment of CEO performance and will therefore re ect less uncertainty. If the frequency of round compensation does not result from heaping, we would not expect the frequency of round compensation to vary systematically with whether the compensation tends to be quantitative or is more likely to be based on qualitative considerations. Table 2 also provides evidence that equity incentive shares and other equity are the least likely to be round (10.1 percent and 11.1 percent of observations are evenly divisible by 10,000 shares, respectively). Non-equity incentive and option grants are very likely to be round; 18.4 percent of non-equity incentive grants and 23.8 percent of option grants are evenly divisible by 10,000 units. In comparison, two commonly used performance measures, earnings per share and stock price, end in zero only 9.3 percent and 11.3 percent of the time, respectively (not tabulated). TABLE 2 Frequency of Round Compensation Values for CEO-Year Observations with Compensation Greater Than or Equal to $100,000 Discretionary Performance-Based Salary BonusNon-Equity Incentive OptionsEquity Incentive SharesOther Equity Shares Divisible by 1,000,000 ($ or shares) 5.3% 4.9% 2.4% 0.8% 0.2% 0.1% Divisible by 100,000 ($ or shares) 14.4% 17.6% 7.4% 7.8% 2.6% 1.8% Divisible by 10,000 ($ or shares) 16.4% 18.4% 8.6% 15.2% 7.3% 9.2% Percent of observations evenly divisible by 10,000 36.1% 40.9% 18.4% 23.8% 10.1% 11.1% Number of non-zero observations 10,218 1,998 7,889 5,540 4,991 5,709 This table presents the frequency with which non-zero observations of compensation components are evenly divisible by 10,000. All data are from ExecuComp. The base sample for this table comprises 10,299 CEO-years from 2007 to 2014. 9Benford’s Law shows that initial digits appear with differing frequencies in many datasets. As discussed inBeer (2009)and shown byDiaconis (1977 ), this effect dissipates in digits farther from the left-most digit, so that, in large data sets with large values, the expected frequency of most digits converges to 10 percent in places at least two digits from the left. Since we are interested in the right-most digit, we cannot draw inferences regarding the expected frequencies of values ending in zero from either Benford’s Law orDiaconis (1977 ). 10 We con rm that our results are qualitatively similar when we de ne round as any value ending in zero, other than zero itself. Heaping of Executive Compensation187 Journal of Management Accounting Research Volume 32, Number 1, 2020 Overall, our descriptive analyses lead us to conclude that rounding is extremely common and that rounding occurs not just around the last digit, but also at much larger magnitudes. In subsequent analyses, we investigate the determinants of rounding and the associations of rounding with compensation levels and rm performance. V. TESTS OF HYPOTHESES Discretionary and Performance-Based Compensation Our primary analyses focus on components of compensation that tend to be explicitly based on rm performance, rather than on components that are discretionary in nature. By de nition, performance-based compensation is based on CEO (or rm) performance; therefore, these grants are the result of a quantitative assessment. If directors expend more effort to acquire or process information about a CEO’s performance, they should be able to provide more precise values of compensation. Discretionary compensation, however, is based on a qualitative assessment. Thus, even if directors expend additional cognitive effort in setting discretionary compensation, substantial uncertainty in the estimate will remain, because the inputs are not quantitative. That is, additional cognitive effort may not be useful in resolving the uncertainty around discretionary compensation grants due to their qualitative nature. If round compensation results from heaping, we expect discretionary compensation to be round more frequently than performance-based compensation regardless of whether the board expends additional effort to acquire and process information. The descriptive results reported above are consistent with this conjecture. In addition, because we do not expect discretionary compensation components to vary with proxies for board effort, by including these analyses, we can provide additional evidence that our results are not spurious. Round Compensation, Board Oversight, and Stakeholder Pressure Primary Analyses Our rst two hypotheses relate to when rms are more likely to grant round compensation. H1 predicts that compensation is more likely to be round in rms with weaker boards of directors, and H2 predicts that round compensation is negatively associated with stakeholder pressure. To test these hypotheses, we estimate the following equation: PercentRound t¼aþb 1Dual tþb 2Insiders tþb 3AppointedByCEO tþb 4PostSOP tþb 5SDROA tþb 6SDReturns t þb 7Digits tþb 8NumComponents tþYearFEþIndustryFEþe t ð1Þ For total compensation, we create a composite measure that captures how much of the CEO’s compensation is round, PercentRoundAll. PercentRoundAllis the number of round compensation components granted divided by the total number of compensation components granted. 11 We next aggregate compensation components by whether the compensation granted is discretionary or performance-based because, as discussed above, our hypotheses should hold only for performance-based compensation grants. We label salary and discretionary bonus compensation as‘‘discretionary,’’and all other components (i.e., non-equity incentive plan compensation, option grants, equity incentive shares, and other equity grants) as‘‘performance- based.’’PercentRoundPerformance(PercentRoundDiscretionary) is the number of round, non-zero, performance-based (discretionary) compensation components divided by the total number of non-zero, performance-based (discretionary) compensation components granted. We present distributions of these variables in Table 1. Overall, approximately 25 percent of granted compensation components are round. Consistent with Table 2, discretionary compensation is more likely to be round than is performance-based compensation. On average, 18 percent of performance-based compensation is round, whereas 36 percent of discretionary compensation is round. Sample sizes are smaller when we split compensation into performance-based and discretionary components because some CEOs do not receive any performance-based compensation, and other CEOs do not receive any discretionary compensation. To test the association between board oversight and the frequency of round compensation, we examine measures of board oversight used in prior research. If the CEO has greater power over the board of directors, the CEO will be more likely to be able to withhold or obfuscate information about performance without repercussions from board members. In turn, the board will have less precise information upon which to base estimates of CEO effort. Additionally, board members of rms with powerful CEOs may be less responsive to outside pressure, or reputation concerns, than they are to pressure from CEOs. Our 11 For example, suppose a CEO were granted three compensation components: round salary, round non-equity incentive compensation, and a non-round number of options.PercentRoundAllwould take a value of 0.667 (two round components divided by three components granted). Further, PercentRoundDiscretionarywould take a value of 1, because the only discretionary component granted (salary) is round. Finally, PercentRoundPerformancewould take a value of 0.5, because one of the two performance-based components is round; non-equity incentive compensation is round while the option grant is not round. 188Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 rst measure of CEO power over the board isDual,an indicator variable set to one if the CEO is also the chairman of the board and 0 otherwise. Prior literature posits that these CEOs exert more control over the board of directors (e.g.,Core et al. 1999). Core et al. (1999)also suggest that boards with more insiders (Insiders) are less independent of management, allowing CEOs more power over decision-making.Insidersis the percentage of board members who are current or former employees or family members of current employees. We also include a measure of co-opted boards, measured by the number of outside directors appointed by the CEO as a percentage of board size (AppointedByCEO). These directors may be more sympathetic to the CEO, and more likely in uenced by the CEO (Core et al. 1999;Coles et al. 2014). Data on director characteristics are from RiskMetrics, and data used to determine the CEO hire date are from ExecuComp. To test the association between round compensation and stakeholder pressure, we include an indicator variable,PostSOP,which equals 1 if the observation is from 2011 or later, and 0 otherwise. We use the passage of compensation-related regulation on executive pay to proxy for stakeholder pressure (Sheehan 2012). The Say on Pay provision of the Dodd-Frank Act was passed in response to increased public concern regarding the nature and reporting of executive compensation. While passage of compensation-related regulations is the result of public concern, passage is not the result of an individual rm’s governance environment or pay practices. As a result, prior literature considers these regulation changes as primarily exogenous shocks to governance. These regulatory changes provide more robust evidence that any association between stakeholder pressure and changes in the frequency of rounding does not result from endogeneity than do other measures of stakeholder pressure, such as shareholder proposals or media attention. The Say on Pay provision requires rms to allow shareholders to vote on executive compensation packages. Although results of the vote required by Say on Pay are only advisory,Ertimur, Ferri, and Oesch (2013)document that more than half of rms with adverse Say on Pay vote outcomes change their compensation plans.Lo, Yang, and Zhang (2014 ) nd that boards respond to shareholder disapproval by amending compensation policies. Taken together, these studies suggest that Say on Pay increased boards’ accountability to shareholders for executive compensation, and therefore likely increased their effort in determining executive compensation. In our main analyses we investigate changes in the frequency of round compensation around passage of the Say on Pay provision of the Dodd-Frank Act. 12 Balsam, Boone, Liu, and Yin (2016 ) nd that in anticipation of Say on Pay, rms made CEO compensation more performance-based.Abernethy et al. (2015)also nd evidence that outrage leads to a greater emphasis on performance-based pay. This is consistent with our focus on performance-based compensation components. If round compensation results from heaping and is consistent with weak board oversight (H1), we expect positive coef cients ofDual(b 1),Insiders(b 2), andAppointedByCEO(b 3) in Equation (1). If rounding is negatively associated with shareholder pressure (H2), we expect a negative coef cient ofPostSOP(b 4) in Equation (1). In addition to our variables of interest, Equation (1) includes controls for the level of rounding in compensation that are unrelated to board effort. The standard deviation of return on assets (SDROA) controls for the noise in performance measures, because noisy performance measures provide less precise estimates of performance and may result in more heaping by the board of directors.SDROAis measured as the standard deviation ofROA tfor the three years ending in yeart,whereROA tis earnings before interest and taxes scaled by average total assets. We also control for volatility in the operating environment, which may impair the board’s ability to precisely measure CEO performance. We include the standard deviation of returns (SDReturns), which is the standard deviation of monthly returns for the 36 months ending in yeart. Two control variables capture potential mechanical reasons that round compensation might result. First, we control for the number of digits in compensation granted (Digits), because larger values are more likely to be round. Second, we control for the number of components granted (NumComponents), though we do not have a prediction for the direction of the expected association. We include industry and year xed effects in all speci cations. Because our dependent variables are bounded between zero and one, we followPapke and Wooldridge (1996 )and estimate Equation (1) using a probit fractional response model. 13 We include year and industry xed effects to control for unobservable economic factors that are correlated with both the frequency of rounding and the determinants of interest. Table 3, Panel A presents the main results of estimating Equation (1). 14 We present the results of testing H1 in Columns 1 through 3. In this speci cation we do not include the variablePostSOP. Focusing on the rst column, in which the dependent variable re ects the level of rounding across performance-based compensation components (PercentRoundPerformance), we nd evidence consistent with our predictions. We nd a positive and signi cant association ( p,0.10, one-tailed) between two of our proxies for CEO control over the board of directors,InsidersandDual,which is consistent with our rst hypothesis (H1) that boards round compensation more when CEOs have more control over boards. However, we nd no evidence that appointment by the CEO is associated with rounding of performance-based compensation;b 3is not signi cantly different from 0. In Columns 4 through 6 we add the indicator variable for the passage of Say on Pay. Consistent with H2, we nd that the percentage of round compensation 12 In sensitivity tests, we investigate changes in the frequency of round option grants following implementation of SFAS 123R, which focused on accounting for option grants. 13 Our inferences are unchanged if we use an ordered logit or ordered probit model instead of a fractional response model. 14 Our results are consistent when we include each variable of interest separately, then stack all variables together. For parsimony, we only report results when we include all variables in the same regression. Heaping of Executive Compensation189 Journal of Management Accounting Research Volume 32, Number 1, 2020 TABLE 3 Predictions of Round Compensation Components Panel A: Main Effects of Board Strength and Say on Pay PercentRound t¼aþb 1Dual tþb 2Insiders tþb 3AppointedByCEO tþb 4PostSOP tþb 5SDROA tþb 6SDReturns tþb 7Digits tþb 8NumComponents t þYearFEþIndustryFEþe t ð1Þ Pred. SignPercentRoundRefers to: PercentRoundPerformance (1)PercentRoundDiscretionary (2)PercentRoundAll (3)PercentRoundPerformance (4 )PercentRoundDiscretionary (5)PercentRoundAll (6 ) Dualþ0.052* 0.046 0.009 0.021 0.045 0.008 (1.43) ( 1.15) (0.33) (0.58) ( 1.10) ( 0.28) Insidersþ0.336** 0.263* 0.434*** 0.284* 0.266* 0.401*** (1.94 ) (1.37 ) (3.28) (1.61) (1.38) (3.00) AppointedByCEOþ0.063 0.011 0.061 0.084 0.012 0.072* (0.89) ( 0.15) (1.14 ) (1.18) ( 0.15) (1.34 ) PostSOP 0.344*** 0.016 0.193*** ( 8.85) (0.39) ( 6.86 ) SDROAþ1.351*** 0.691* 0.944** 1.350*** 0.691* 0.944** (2.64 ) (1.34 ) (2.30) (2.61) (1.34 ) (2.29) SDReturnsþ0.048 0.012 0.035 0.050 0.012 0.034 (0.92) ( 0.17 ) (0.84 ) (0.96 ) ( 0.17 ) (0.82) Digitsþ0.073*** 0.451*** 0.238*** 0.081*** 0.450*** 0.245*** (2.60) (10.60) (8.96 ) (2.86 ) (10.56 ) (9.19) NumComponents? 0.211*** 0.050 0.192*** 0.207*** 0.049 0.190*** ( 9.94 ) ( 1.13) ( 13.33) ( 9.68) ( 1.11) ( 13.15) Constant 0.946*** 3.277*** 1.837*** 0.791*** 3.285*** 1.762*** ( 4.71) ( 12.43) ( 9.52) ( 3.87 ) ( 12.44 ) ( 9.10) Observations 9,785 10,277 10,299 9,785 10,277 10,299 R 2 0.056 0.053 0.079 0.063 0.053 0.082 (continued on next page) 190Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 TABLE 3 (continued) Panel B: Predictions of Round Compensation Components Including Interaction Terms withPostSOP Pred. Sign (1) (2) (3) Dualþ 0.005 0.034 0.004 ( 0.10) ( 0.68) ( 0.11) Post Dual? 0.052 0.019 0.009 (0.93) ( 0.32) ( 0.23) Insidersþ 0.037 0.408** 0.282** ( 0.18) (1.85) (1.81) Post Insiders? 0.732*** 0.294 0.263* (2.92) ( 1.14 ) (1.46 ) AppointedbyCEOþ0.127* 0.002 0.103* (1.43) ( 0.02) (1.46 ) Post AppointedbyCEO? 0.092 0.019 0.059 ( 0.85) ( 0.16 ) ( 0.73) PostSOP 0.490*** 0.095 0.220*** ( 5.76 ) (1.07 ) ( 3.61) SDROAþ1.370*** 0.689* 0.949** (2.62) (1.34 ) (2.29) SDReturnsþ0.048 0.011 0.033 (0.91) ( 0.16 ) (0.79) Digitsþ0.082*** 0.450*** 0.245*** (2.91) (10.56 ) (9.20) NumComponents? 0.206*** 0.049 0.190*** ( 9.64 ) ( 1.10) ( 13.15) Constant 0.728*** 3.329*** 1.752*** ( 3.52) ( 12.46 ) ( 8.92) Observations 9,785 10,277 10,299 R 2 0.064 0.054 0.082 ***, **, * Indicate statistical signi cance at the 1 percent, 5 percent, and 10 percent levels (one-tailed), respectively. In Panel A the dependent variablePercentRoundrefers toPercentRoundPerformance(Columns 1 and 4 ),PercentRoundDiscretionary(Columns 2 and 5), orPercentRoundAll(Columns 3 and 6 ), as de ned in the notes to Table 1. In Panel B the dependent variablePercentRoundrefers toPercentRoundPerformance(Column 1),PercentRoundDiscretionary(Column 2), orPercentRoundAll(Column 3), as de ned in the notes to Table 1. The sample size for this table is 10,299 CEO-years from 2007 to 2014; we exclude observations in which the CEO was not granted discretionary ( performance-based) compensation from Column 1 (Column 2). We estimate Equation (1) using a probit fractional response model. Standard errors are clustered by rm. This analysis includes industry and year xed effects. Variable De nitions: Dual¼an indicator variable set to 1 if the CEO is also the chairman of the board and 0 otherwise; Insiders¼the percentage of board members who are insiders; AppointedByCEO¼the percentage of outside board members appointed by the CEO; PostSOP¼an indicator variable set to 1 if the observation is from 2011 or later; SDROA¼the three-year standard deviation ofROA tmeasured as EBIT/average total assets measured in yeart; SDReturns¼the standard deviation of the prior 36 months of returns, ending in the year for which compensation is granted; Digits¼the number of digits in values ofPerformanceCompensation, DiscretionaryCompensation,orTotalCompensation,respectively; and NumComponents¼the number of performance-based compensation components (Column 1), the number of discretionary compensation components (Column 2), or number of compensation components in a compensation package (Column 3). Heaping of Executive Compensation191 Journal of Management Accounting Research Volume 32, Number 1, 2020 components is negatively associated with the passage of Say on Pay ( p,0.01, one-tailed), suggesting that boards round compensation less when stakeholders pay more attention. These associations are consistent with the explanation that round compensation results from heaping: the frequency of round compensation in performance-based compensation is positively associated with characteristics of boards that provide weak oversight of compensation, and negatively associated with shareholder pressure. The evidence in Columns 2 and 3, and 5 and 6 is also consistent with our expectations. For example, in Column 6, where the outcome variable isPercentRoundAll,we detect positive associations between both the fraction of the board appointed by the CEO, and the fraction of the board who are insiders. We also nd that the associations between round compensation and proxies for weak board oversight and stakeholder pressure tend to be driven by performance-based compensation, rather than by discretionary compensation. That is, with one exception, the associations between our variables of interest and the outcome variable are signi cant in Columns 3 and 6, where the outcome variable isPercentRoundAll,but are not signi cant in Columns 2 and 5, where the outcome variable isPercentRoundDiscretionary. The exception is that round discretionary compensation is more common when the board has a higher proportion of insiders. We also nd that the association between the noise in performance measures (SDROA) and the percentage of round compensation components is positive and signi cant (b 5.0) in all speci cations, again driven by performance-based compensation, which is consistent with boards of directors heaping when performance measures are noisier, resulting in more uncertainty about CEO performance. We detect no association between the standard deviation of returns (SDReturns) and the frequency of rounding. 15 In additional analyses, presented in Table 3, Panel B, we consider whether the change in the level of rounding following passage of Say on Pay was the result of changes in associations between board characteristics and rounding frequency. To do so, we estimate a version of Equation (1) in which we interact all variables with the post-Say on Pay indicator,PostSOP. Speci cally, the increase in stakeholder pressure may have affected rms with weaker oversight more strongly than rms with stronger oversight. If this is the case, the interaction terms ofPostSOPand our measures of oversight (Dual, Insiders,and AppointedbyCEO) will be negative, and the main effect of thePostSOPindicator will be zero. We nd some evidence that the positive association betweenInsidersand the level of round performance-based compensation is driven by observations from the post-Say on Pay period, and some evidence that board members appointed during the CEO’s tenure were more likely to grant round performance-based compensation prior to Say on Pay. However, no interaction term betweenPostSOPand any of our measures of oversight is negative. We continue to detect a signi cantly negative association betweenPostSOPand the frequency of round compensation. These results suggest that, on average, boards were affected by the increased pressure from stakeholders associated with Say on Pay regardless of the strength of their compensation oversight. Additional Tests of Hypothesis 2 We perform two additional tests of the effect of changes in the frequency of rounding following the passage of compensation-related regulation. In these additional tests, we examine changes in the frequency of rounding around Say on Pay and around SFAS 123R, an earlier regulatory change that took effect in December 2005, affecting the treatment of option compensation expense. As an identi cation strategy, we use within- rm analysis to isolate the effect of shareholder pressure on rounding. In this changes analysis, we hold the rm constant, which controls for rm-level effects and facilitates identi cation of the impact of compensation-related regulations on boards’ effort in setting compensation. FollowingJagolinzer (2009), our comparisons within rms do not require assumptions about the functional form of how rm, board, corporate governance, and executive characteristics map into outcomes. Holding the rm constant between the pre- and post- periods also controls for the compensation size. Compensation size may impact the likelihood of rounding, since higher magnitudes of compensation are more likely to be round. Our rst test of the effect of compensation-related regulation on rounding focuses on whether, on average, boards reduced heaping following passage of Say on Pay. Our sample for this test includes two years before and two years after the adoption of Say on Pay, resulting in an initial sample size of 6,986 CEO-years; we again exclude rst-year CEOs. We next partition this sample into pre-Say on Pay (2009–2010) and post-Say on Pay (2011–2012). For tests of the change in the frequency of round compensation for each type of compensation, we exclude grants of $0, $1, or zero shares from our 15 In unreported analyses, we estimate Equation (1), excludingDigits,by compensation decile. Results fail to provide evidence that our results are driven by the size of compensation granted. We estimate Equation (1) by compensation decile rather than number of digits, because we nd evidence that some rms manage compensation up or down around round values. When we estimate Equation (1) by compensation decile, our results are consistent with the analyses we present in Table 3. We note that the associations between our variables of interest and rounding of discretionary compensation components are stronger, however. 192Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 analyses. We further restrict the sample to include only rms that granted each component of compensation in every year from 2009 through 2012. Table 4, Panel A reports the results of tests of the association between passage of Say on Pay and round compensation frequency. For each type of compensation (i.e., performance-based, discretionary, and total), we compare the mean of the frequency of round compensation values in the pre- and post-Say on Pay periods. Consistent with our expectations, we nd that boards were less likely to grant round compensation amounts after Say on Pay. Our measure of rounding for performance-based compensation components is signi cantly lower following passage of Say on Pay; it decreased from 21.3 percent in the pre-Say on Pay period to 16.6 percent in the post-Say on Pay period ( p,0.01). While we nd no statistically signi cant effect for discretionary compensation components, our composite measure of rounding is signi cantly lower following passage of Say on Pay; it decreased from 26.9 percent in the pre-Say on Pay period to 24.2 percent in the post-Say on Pay period ( p,0.01). In Table 4, Panel B we investigate the change in the frequency of round option grants (a performance-based compensation component) from before and after SFAS 123R. We limit this test to option grants because SFAS 123R speci cally addressed option compensation, unlike Say on Pay, which had implications for all forms of compensation. For this test, we include the years 2004 through 2007 and partition the sample into pre-SFAS 123R (2004–2005) and post-SFAS 123R (2006–2007 ) periods. We exclude observations of zero options from our analysis, resulting in a sample size of 4,169 CEO-years with non- zero option grants. We again restrict our sample to include rms that granted options in each year of the sample period. 16 We nd that boards are less likely to grant round option compensation following passage of SFAS 123R; the frequency of rounding to amounts evenly divisible by 100,000 or 10,000 decreased from 43.3 percent to 37.6 percent. We nd that this change is signi cantly different from zero ( p,0.01, one-tailed). Taken together, the evidence in Table 4 indicates that regulation that highlights the treatment of compensation is associated with lower frequencies of round compensation. This, in turn, is TABLE 4 Changes in Frequency of Round Compensation Values around Passage of Compensation-Related Regulation Panel A: Change in the Frequency of Round Compensation Values Pre- and Post-Say on Pay Percent of Round Performance-Based Components PercentRound PerformancePercent of Round Discretionary Components PercentRound DiscretionaryPercent of Round Components PercentRound All Pre-Say on Pay % Rounded 21.3% 35.2% 26.9% Observations 2,354 2,736 2,746 Post-Say on Pay % Rounded 16.6% 36.6% 24.2% Observations 2,354 2,736 2,746 Pre- versus Post- t-statistics 5.376*** 1.131 3.518*** Panel B: Change in the Frequency of Round Number of Options Granted Pre- and Post-SFAS 123R Pre-SFAS 123R % Rounded 43.3% Observations 866 Post-SFAS 123R % Rounded 37.6% Observations 866 Pre- versus Post- t-statistics 2.401*** *** Indicate statistical signi cance at the 1 percent level (one-tailed). The frequencies reported in Panel A refer toPercentRoundPerformance(Column 1),PercentRoundDiscretionary(Column 2), orPercentRoundAll (Column 3), as de ned in the notes to Table 1. The frequencies reported in Panel B are the percentage of non-zero option grants that are evenly divisibleby 100,000 or 10,000 shares. The pre-SOP period is 2009–2010, and the post-SOP period is 2011–2012. The pre-SFAS 123R period is 2004–2005, and the post-SFAS 123R period is 2006–2007. The sample size for Panel A is 6,986 CEO-years; only non-zero values of compensation are included in this analysis, and we exclude rst-year CEOs. We further restrict the sample for Panel A to include only rms that granted each component of compensation in 2009, 2010, 2011, and 2012. The sample size for Panel B is 6,676 CEO-years from 2004 to 2007, of which 4,169 are non-zero option grants. We further restrict the sample for Panel B to include only rms that granted options in 2004, 2005, 2006, and 2007. 16 Our results are qualitatively similar if we do not restrict the sample such that each rm appears in both the pre- and post-SFAS 123R periods. Heaping of Executive Compensation193 Journal of Management Accounting Research Volume 32, Number 1, 2020 consistent with the round compensation we observe resulting from heaping: when boards increase the effort they expend in setting compensation, they are less likely to provide round compensation grants. Round Compensation and Compensation Levels To test H3, that compensation is higher when boards grant round compensation, we test whether, controlling for economic determinants of compensation and determinants of rounding, the level of compensation is higher when compensation is round. To do so, we estimate the following equation: Compensation t¼aþb 1PercentRound tþb 2Dual tþb 3Insiders tþb 4AppointedByCEO tþb 5SDROA tþb 6SDReturns t þb 7Digits tþb 8NumComponents tþd 1 8 CompensationControlsþYearFEþIndustryFEþe t ð2Þ In our primary analysis, we estimate Equation (2) with the dependent variable measured as performance-based compensation (PerformanceCompensation), which is the sum of non-equity incentive plan compensation, the value of option grants, and the value of stock grants. We also report results using the dependent variableDiscretionaryCompensation,de ned as the sum of salary and discretionary bonus, and asTotalCompensation,de ned as the sum of all compensation components. We again expect our results to be weaker for discretionary compensation than performance-based compensation. All compensation measures are in logs.PercentRoundrefers toPercentRoundPerformance, PercentRoundDiscretionary,and PercentRoundAllmeasured as discussed above. If round compensation is consistent with heaping, and the corresponding lack of board effort in setting compensation allows self-interested managers to gain excess compensation, thenb 1will be greater than 0 for performance-based compensation. We include controls for the probability of rounding, as in Equation (1),Dual, Insiders, AppointedByCEO, Digits, NumComponents, SDROA,andSDReturns,which are likely also correlated with the level of compensation. In addition, we include common economic predictors of compensation levels (Core et al. 2008).ROA t(ROA t 1 ) is return on assets measured as earnings before interest and taxes scaled by average total assets measured in yeart(t 1).RET t(RET t 1 ) is the 12-month buy- and-hold market return for scal yeart(t 1).LogSales t 1 is the log of sales in yeart 1.BTM t 1 is the book value of assets divided by market value of assets in yeart 1.LogTenureis the log of CEO tenure.PercentOwnedis the percent of total shares owned by the executive, as reported in ExecuComp. We again include year and industry xed effects. Table 5 presents the results of estimating Equation (2). We nd that the coef cient ofPercentRoundPerformance,reported in Column 1, is positive and signi cant ( p,0.01, one-tailed), which is consistent with our hypothesis that, controlling for rm performance and other economic determinants of compensation, round compensation is higher than non-round compensation. The coef cient of 0.084 implies that performance-based compensation is 8.4 percent higher when all its components are rounded compared to when no components are rounded. 17 In Column 2, the association between discretionary compensation rounding and the level of discretionary compensation is not statistically different from zero. However, re ecting the performance-based compensation results, the coef cient ofPercentRoundAllis signi cantly positive in Column 3. These associations are consistent with heaping leading to round compensation: when boards are less informed or expend less cognitive effort in setting compensation, both round compensation and excess compensation result. Round Compensation and Firm Performance The above analyses are consistent with heaping occurring when boards determine executive compensation. We observe abnormally high levels of round compensation values, and round compensation is consistent with a lack of information acquisition and processing regarding compensation. In our nal analysis, we test whether round compensation is associated with future rm performance, controlling for common predictors of performance and determinants of rounding. We estimate the following equation using OLS regression: ROA tþ1 ¼aþb 1PercentRound tþb 2Dual tþb 3Insiders tþb 4AppointedByCEO tþb 5SDROA tþb 6Compensation t þb 7ROA tþb 8LogSales tþ1 þYearFEþIndustryFEþe t ð3Þ We proxy for future rm performance using ROA from the period after which compensation is granted (ROA tþ1 ), measured as earnings before interest and taxes scaled by average total assets measured in yeartþ1. We measure rm performance using ROA following prior literature that demonstrates an association between current year compensation and 17 Since the independent variable in Equation (2) is natural logarithm of performance-based compensation, the economic magnitude of moving PercentRoundPerformancefrom 0 to 1 is calculated as: 8.8 percent¼exp(0.084 ) 1. 194Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 TABLE 5 Associations of Round Compensation with Compensation Levels Compensation t¼aþb 1PercentRound tþb 2Dual tþb 3Insiders tþb 4AppointedByCEO tþb 5SDROA tþb 6SDReturns t þb 7Digits tþb 8NumComponents tþd 1 8 CompensationControlsþYearFEþIndustryFEþe t ð2Þ Predicted AssociationCompensationRefers to: Performance CompensationDiscretionary CompensationTotal Compensation PercentRoundRefers to: PercentRound PerformancePercentRound Discretionary PercentRoundAll PercentRoundþ0.084*** 0.018 0.177*** (3.24 ) ( 1.04 ) (6.83) Dualþ0.031** 0.021 0.006 (1.73) (1.06 ) (0.31) Insidersþ 0.139* 0.129 0.178** ( 1.56 ) ( 1.19) ( 1.99) AppointedByCEOþ0.014 0.064 0.040 (0.28) ( 1.14 ) (0.79) SDROAþ 0.083 0.174 0.007 ( 0.36 ) ( 0.67 ) (0.03) SDReturnsþ0.040 0.040 0.016 (1.27 ) ( 1.22) (0.58) Digitsþ1.836*** 1.408*** 1.415*** (53.56 ) (11.47 ) (11.93) NumComponents? 0.107*** 0.088** 0.161*** (10.38) (1.89) (16.68) ROA t þ0.042 0.250** 0.099 (0.31) ( 1.77 ) ( 0.73) ROA t 1 þ 0.276** 0.467*** 0.067 ( 2.16 ) (3.23) ( 0.50) RET t þ0.039*** 0.002 0.057*** (2.40) ( 0.12) (2.94 ) RET t 1 þ0.007 0.039*** 0.016 (0.52) (3.23) (1.14 ) LogSales t 1 þ0.107*** 0.067*** 0.131*** (11.00) ( 2.64 ) (5.35) BTM t 1 0.304*** 0.197*** 0.267*** ( 6.21) (4.01) ( 4.33) LogTenureþ0.002 0.009 0.025 (0.10) ( 0.34 ) (1.13) PercentOwned? 0.002 0.014*** 0.008*** ( 0.86 ) ( 4.09) ( 3.54 ) Constant 5.660*** 1.929*** 3.215*** ( 28.45) ( 3.48) ( 4.71) Observations 9,785 10,277 10,299 Adj. R 2 0.887 0.680 0.767 ***, **, * Indicate statistical signi cance at the 1 percent, 5 percent, and 10 percent levels (one-tailed), respectively. (continued on next page) Heaping of Executive Compensation195 Journal of Management Accounting Research Volume 32, Number 1, 2020 future year ROA (e.g.,Core, Holthausen and Larcker 1999;Hayes and Schaefer 2000). If round compensation re ects signi cant rent extraction by CEOs, then we should nd a negative association between the frequency of rounding and future rm performance (b 1,0). If, instead, heaping results from ef cient allocation of board attention, we will not detect an association between round compensation and future rm performance (b 1not different from 0). We include several controls for determinants of future ROA. We measureROA tandSDROAas previously discussed. We measureLogSales tþ1 as the log of sales in yeartþ1. We also include the level of compensation as a control to address concerns about mechanical associations about the frequency of rounding and levels of compensation. We include industry and year xed effects in all speci cations. We present the results of estimating Equation (3) in Table 6. We nd that round performance-based compensation is signi cantly positively associated with future rm performance. This result is consistent with ef cient allocation of board attention. This positive association could result if current-period performance-based compensation re ects the board’s private information about performance in periodtþ1, as proposed inHayes and Schaefer (2000). Further, this positive association might arise if current period performance-based compensation is viewed as a‘‘gift exchange’’between the board and the executive proposed byAkerlof (1982). We note the signi cantly negative association between round discretionary compensation and future rm performance. As we report in Column 2 of Table 5, we do not nd that discretionary compensation is higher when CEOs receive round discretionary compensation components. Thus, we interpret this negative association between round discretionary compensation components and future rm performance as indicating the presence of agency con icts, rather the direct cost of excess compensation when compensation is round. When we consider total compensation in the third column, we nd no evidence that the percentage of round compensation components is associated with future performance. We therefore caution that this result does not resolve whether round compensation re ects ef cient or inef cient allocation of effort in setting compensation. VI. ADDITIONAL TESTS Changes in Non-CEO Compensation One concern with our cross-sectional analysis of the change in round compensation frequency following passage of compensation-related regulations is that boards may respond to regulation by expending effort to change only the most visible compensation—that of the CEO. If so, we may observe different patterns in the response to compensation regulation for CEOs than for other executives. To address this concern, we perform our analyses of changes in rounding around Say on Pay again, but we construct the samples to include the CEO and the Chief Financial Of cer (CFO). We test whether the effect of the regulation change was stronger for the most visible executive, the CEO, than for other executives. Again,Jagolinzer (2009) TABLE 5 (continued) Compensationrefers toPerformanceCompensation(Column 1),DiscretionaryCompensation(Column 2), orTotalCompensation(Column 3). PerformanceCompensationis the sum of compensation from the four performance-based compensation components, as reported in ExecuComp, in thousands of dollars.DiscretionaryCompensationis the sum of salary and discretionary bonus compensation from ExecuComp, in thousands of dollars. TotalCompensationis compensation as reported in ExecuComp, in thousands of dollars (TDC1). Following prior literature, we use the natural logs of compensation variables in our empirical analyses.PercentRoundrefers toPercentRoundPerformance(Column 1),PercentRoundDiscretionary(Column 2), orPercentRoundAll(Column 3), as de ned in the notes to Table 1. The sample size for this table is 10,299 CEO-years from 2007 to 2014. We estimate Equations (2) and (3) using OLS regression. Standard errors are clustered by rm. This analysis includes industry and year xed effects. Variable De nitions: Dual¼an indicator variable set to 1 if the CEO is also the chairman of the board and 0 otherwise; Insiders¼the percentage of board members who are insiders; AppointedByCEO¼the percentage of outside board members appointed by the CEO; ROA t(ROA t 1)¼return on assets measured as EBIT/average total assets measured in yeart(t 1); SDROA¼the three-year standard deviation ofROA t; SDReturns¼the standard deviation of the prior 36 months of returns, ending in the year for which compensation is granted; Digits¼the number of digits in values ofPerformanceCompensation, DiscretionaryCompensation,orTotalCompensation,respectively; NumComponents¼the number of performance-based compensation components (Column 1), the number of discretionary compensation components (Column 2), or the number of compensation components in a compensation package (Column 3); RET t(RET t 1)¼the 12-month buy-and-hold market return for scal yeart(t 1); LogSales t 1 ¼the log of sales in yeart 1; BTM t 1 ¼the book value of assets divided by market value of assets in yeart 1; LogTenure¼the log of CEO tenure; and PercentOwned¼the percentage of total shares owned by the executive, as reported in ExecuComp. 196Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 notes that such analyses control for rm-year characteristics by design because we match CEOs and CFOs within the same rm and for the same year. We present the results of these analyses in Table 7. This analysis includes only rms where the CEO and CFO of a rm were granted each type of compensation in both 2009 and 2011, which allows us to make within rm-year comparisons. 18 We exclude rst-year CEOs and rst-year CFOs from our sample. Table 7 provides evidence that CFOs are statistically signi cantly less likely to receive rounded compensation grants both before and after Say on Pay than are CEOs. Table 7 also reveals that rounding of CFO compensation generally decreased around Say on Pay for performance-based compensation. TABLE 6 Associations of Round Compensation with Future Firm Performance ROA tþ1 ¼aþb 1PercentRound tþb 2Dual tþb 3Insiders tþb 4AppointedByCEO tþb 5SDROA tþb 6Compensation t þb 7ROA tþb 8LogSales tþ1 þYearFEþIndustryFEþe t ð3Þ Predicted AssociationPercentRoundRefers to: PercentRound PerformancePercentRound Discretionary PercentRoundAll PercentRound? 0.003** 0.002** 0.000 (1.65) ( 1.69) (0.12) Dual 0.001 0.001 0.001 (1.00) (0.64 ) (0.68) Insiders 0.014*** 0.013*** 0.012** (2.52) (2.42) (2.20) AppointedByCEO 0.002 0.001 0.002 ( 1.01) ( 0.62) ( 0.66 ) SDROA? 0.018 0.014 0.014 (0.39) (0.35) (0.35) Compensation? 0.000 0.000 0.001* (0.19) ( 0.55) ( 1.36 ) ROA t þ0.824*** 0.822*** 0.823*** (38.68) (41.08) (41.06 ) LogSales tþ1 þ0.003*** 0.003*** 0.004*** (5.06 ) (6.77 ) (6.51) Constant 0.020*** 0.016*** 0.013** ( 2.76 ) ( 2.47 ) ( 1.98) Observations 9,785 10,279 10,299 Adj. R 2 0.634 0.638 0.638 ***, **, * Indicate statistical signi cance at the 1 percent, 5 percent, and 10 percent levels (one-tailed), respectively. PercentRoundrefers toPercentRoundPerformance(Column 1),PercentRoundDiscretionary(Column 2), orPercentRoundAll(Column 3), as de ned in the notes to Table 1.Compensationrefers toPerformanceCompensation(Column 1),DiscretionaryCompensation(Column 2), orTotalCompensation (Column 3), as previously de ned. Following prior literature, we use the natural logs of compensation variables in our empirical analyses. The sample size for this table is 10,299 CEO-years from 2007 to 2014. We estimate Equation (4 ) using OLS regression. Standard errors are clustered by rm. This analysis includes industry and year xed effects. Variable De nitions: ROA tþ1 (ROA t)¼return on assets measured as EBIT/average total assets measured in yeartþ1(t); Dual¼an indicator variable set to 1 if the CEO is also the chairman of the board and 0 otherwise; Insiders¼the percentage of board members who are insiders; AppointedByCEO¼the percentage of outside board members appointed by the CEO; SDROA¼the three-year standard deviation ofROA t; and LogSales tþ1 ¼the log of sales in yeartþ1. 18 We use only one year pre- and post-Say on Pay for this analysis because when we restrict our sample to include each type of compensation for each executive in all four years from 2009 through 2012 our sample is extremely limited. Heaping of Executive Compensation197 Journal of Management Accounting Research Volume 32, Number 1, 2020 Taken together, the results in Tables 3, 4, and 7 offer strong support for H2, that regulations governing compensation reduce the prevalence of round compensation. Sensitivity Analyses Our main results are robust to several sensitivity tests. In our analyses, we do not differentiate between exactly $1 million salary observations and other round salary observations. Many of these salary observations are likely round not because of heaping but because the Internal Revenue Code limits the deductibility of non-incentive-based compensation to $1 million (Rose and Wolfram 2000,2002). We obtain qualitatively and quantitatively consistent results for all hypotheses when we treat these observations as non-round. Finally, we assume that boards choose numbers of options or shares to grant for compensation, rather than choosing a value of grants and calculating the number of options or shares necessary to provide a desired level of compensation. When we assume that boards grant dollar values of option or equity compensation, we nd that the dollar value of options is evenly divisible by $10,000 in 3.5 percent of cases and that the dollar value of equity grants is evenly divisible by $10,000 in 4.5 percent of cases. This is consistent with some boards roundingdollar valuesof option and equity grants, instead ofnumbersof option and equity grant shares. If some boards grant round dollar values of option or equity grants, the corresponding number of options or shares would also be round only if the fair value of the option or share is also round. This implies that results of TABLE 7 Test of the Association between Round Compensation Grants and Passage of Say on Pay for CEOs and CFOs Panel A: Percent of Round Performance-Based Components CEO CFOCompare CEO to CFO t-statistics Pre-Say on pay % rounded 22.7% 14.8% 6.606*** Observations 1,309 1,309 Post-Say on pay % rounded 17.2% 9.6% 7.534*** Observations 1,309 1,309 Pre- versus Post- t-statistics 4.510*** 5.230*** Panel B: Percent of Round Discretionary Components CEO CFOCompare CEO to CFO t-statistics Pre-Say on pay % rounded 34.5% 24.6% 6.353*** Observations 1,513 1,513 Post-Say on pay % rounded 34.2% 22.3% 7.731*** Observations 1,513 1,513 Pre- versus Post- t-statistics 0.200 1.631* Panel C: Percent of Round Components CEO CFOCompare CEO to CFO t-statistics Pre-Say on pay % rounded 27.4% 19.2% 8.120*** Observations 1,518 1,518 Post-Say on pay % rounded 23.8% 15.0% 9.590*** Observations 1,518 1,518 Pre- versus Post- t-statistics 3.400*** 4.693*** *** Indicate statistical signi cance at the 1 percent level (one-tailed). The frequencies reported refer toPercentRoundPerformance(Panel A),PercentRoundDiscretionary(Panel B), orPercentRoundAll(Panel C ), as de ned in the notes to Table 1. The pre-SOP period is 2009, and the post-SOP period is 2011. The initial sample size for this table is 7,156 CEO- or CFO-years from 2009 and 2011; we exclude rst-year CEOs and rst-year CFOs. We only include matched pairs of CEOs and CFOs, both of whom receive non-zero compensation in the pre- and post-periods. Finally, we require rms to be present in both 2009 and 2011. The resulting sample sizes for each analysis are included in panels above. 198Jorgensen, Patrick, and Soderstrom Journal of Management Accounting Research Volume 32, Number 1, 2020 our tests of the frequency of rounding option and equity grants (Figure 1, Panels D, E, and F, and Table 2) are likely understated. We nd that our results in Tables 3 through 7 are qualitatively similar when we use the dollar value of options or shares granted instead of the number of options or shares granted. VII. CONCLUDING REMARKS We investigate whether round CEO compensation results from heaping, which is the tendency of imperfectly informed individuals to report round estimates of discrete, quantitative data (Turner 1958). We document that round compensation is quite common. Since boards may possess imperfect information due to a lack of investment in information acquisition and processing, we investigate whether round compensation is associated with various proxies for board inattention to compensation, including proxies for weak board monitoring, shareholder pressure, and excess compensation. Consistent with our expectations, we nd evidence that rounding is positively associated with proxies for weak board monitoring. We also nd that the incidence of round compensation decreases after passage of compensation-related regulation (i.e., Say on Pay and SFAS 123R), which is consistent with these regulations providing incentives for boards to exert greater effort to reduce uncertainty when determining compensation. Additional results provide evidence that round compensation tends to be higher than non-round compensation. This association suggests that round compensation could signal to shareholders that boards who grant round compensation are less attentive to compensation than other boards. As expected, our results are driven by performance-based compensation rather than discretionary compensation. We also investigate the association of heaping of compensation with future rm performance, but do not nd consistent evidence. While we interpret our ndings from the perspective of heaping as de ned in the accounting literature, we acknowledge that other elds de ne heaping as a broader phenomenon that might also explain our results. Our study is the rst to investigate whether heaping explains the distribution of executive compensation, but several questions remain for future research. For example, we measure stakeholder pressure using changes in regulation. Other sources of stakeholder pressure may also affect how boards set compensation and the effects of behavior on compensation. Prior literature documents that publicity (e.g.,Johnson et al. 1997;Core et al. 2008), shareholder proposals (e.g.,Thomas and Martin 1999,Ertimur et al. 2011), and proxy advisor recommendations (e.g.,Ertimur et al. 2018) affect how boards set compensation. Future research could further investigate whether these sources of pressure have similar effects on compensation. 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