Behavior of Accrual Management and Performance of Discretionary Accrual Proxies

Transcription

1 Behavior of Accrual Management and Performance of Discretionary Accrual Proxies Laura Yue Li* Wei Zhu University of Illinois at Urbana-Champaign Current version: 5/27/2015 Abstract This study analyzes how associations between accrual management and firm fundamentals affect the ability of commonly used discretionary accrual proxies (DAP, hereafter) to capture the level of managed accruals. Using a self-collected sample, we directly identify the level of managed accruals from financial restatements using the contrast between originally reported and restated numbers. Our analyses reveal two insights: first, managed accruals are associated with explanatory variables (i.e., sales growth and operating cash flows) in accrual models similar to pre-managed accruals (i.e., in the same direction with similar magnitudes). This mimicking effect results in the exclusion of managed accruals from DAP of a similar degree to the exclusion of premanaged accruals, causing failure in separating discretionary from nondiscretionary accruals even in comprehensive accrual models. Second, firms overstate accruals more often when pre-managed accruals are lower. As a result, overstating firms reported accruals successfully blend in with those of non-overstating populations. Interestingly, the blending in effect is more prominent when reported accruals are below the population median, and, consequently, DAP are significant indicators of accrual overstatement only among firms reporting above median accruals. Our findings provide first evidence on the statistical behavior of accrual management and its significant impact on the performance of discretionary accrual proxies. This manuscript has benefitted from workshop participants at University of Illinois at Urbana- Champaign. We thank Brad Badertscher for sharing his data on GAO restatements. * Corresponding author: Laura Yue Li. Address: 284 Wohlers Hall, 1206 S. Sixth Street, Champaign, Illinois Tel: Fax: liyue@illinois.edu. 1

2 1. Introduction Model-based proxies of discretionary accruals (DAP, hereafter) have long been used to measure and detect earnings management. 1 Despite concerns over the performance of these proxies, they are the only available large sample measurement for the magnitude of earnings management. Therefore, DAP are still actively used by researchers in accounting and finance, 2 and have become the cornerstone of SEC s Robocop, the data-based analytical module to assess the degree of a company s misreporting (Lewis, 2012). Our study examines how statistical behaviors of actual accrual management affect the ability of commonly used proxies to capture the level of accrual management. 3,4 To observe actual accrual management, we collect account-level information from financial restatements and ex post identify the level of managed accruals through originally reported and restated numbers. Such direct observation of accrual management allows us to explore the associations between accrual management and firm fundamentals and to conduct diagnostic analyses on the impact of such associations on the performance of DAP. Our study aims to provide evidence on the statistical behavior of actual accrual management and to aid researchers, investors, and regulators in the use and advancement of proxies for earnings management. 1 Proxies of accrual management are often referred to as discretionary accrual proxies in literature. We use managed accruals and discretionary accruals interchangeably. 2 Recent studies that use these proxies include Fang et al. (2015) and Dou et al. (2015). Earlier studies using these proxies are summarized by Dechow et al. (2010). 3 We examine DAP generated by the following accrual models: Healy (1985) model, Jones (1991) model, modified Jones (Dechow et al., 1995) model, Dechow and Dichev (2002) model, McNichols (2002) model, Ball and Shivarkumar (2006) model, and performance-matched McNichols (Kothari et al., 2005) model. 4 Our study focuses on evaluating DAP that are commonly used to measure accrual management at the firm-year level. Recent innovations on modeling of earnings management are based upon inter-temporal properties of managed vs. pre-managed accruals, (e.g. Dechow et al., 2012; Gerakos and Kovrijnykh, 2013; Nikolaev, 2015) and do not intend to generate firm-year level estimate of accrual management. Therefore, we don t evaluate these models and associated inter-temporal properties of accruals in this study. 2

3 Theoretically, the performance of model-based DAP is determined by how well accrual models capture nondiscretionary accruals, by the amount of noise introduced in the estimation process, and by statistical behavior of managed accruals (Dechow et al., 1995; Dechow et al., 2012). 5 The development of DAP so far has been focused on better modeling of the nondiscretionary accrual process. As more firm fundamentals are added as explanatory variables, the accrual models capture more variations in total accruals. For instance, while the Jones (1991) model explains merely 6.8% of total accrual variation, the McNichols (2002) model has an adjusted R-Square of 38%. Surprisingly, recent studies find that DAP from popular accruals models, even comprehensive models, are not more powerful than unadjusted accruals in predicting the incidence of actual material misstatement (Dechow et al., 2011; Jones et al., 2008). Several recent studies suggest alternative estimation approaches aiming to reduce estimation noise, but achieve limited improvement in predicting actual cases of earnings manipulation (e.g., Ecker et al., 2013; Owens et al., 2015). Among the above three determinants of DAP performance, the statistical behavior of managed accruals specifically, the associations between managed accruals and firm fundamentals have received the least attention. Several researchers conjecture the possibility of such associations and their potential impact on the performance of DAP (McNichols, 2002; Wysocki, 2009; Nikolaev, 2015). However, due to the lack of direct observation of accrual management, there is no empirical evidence on the statistical behavior of managed accruals and whether that behavior significantly impacts DAP performance. Consequently, prior research on accrual models generally assumes 5 Pre-managed accruals are also referred to as nondiscretionary accruals in the literature. We use premanaged accruals and nondiscretionary accruals interchangeably. 3

4 independence between accrual management and firm fundamentals (Dechow et al., 1995; Kothari et al., 2005). Such an independence assumption is likely to be unrealistic, potentially limiting the evaluation and enhancement of discretionary accrual proxies (McNichols, 2002; Dechow et al., 2010; Gerakos, 2012). In our study, we measure DAP performance by using the correlation between the proxy and the actual level of accrual management observed from financial restatements. Through simple derivation, we demonstrate that the statistical behavior of accrual management affects the correlation between the proxy and actual managed accruals through two channels. First, any association between managed accruals and firm fundamentals used as explanatory variables in accrual models can potentially lead to unwanted exclusion or exaggeration of managed accruals from the DAP. Second, the way managed accruals relate to pre-managed accruals affect how prominently managed accruals show up in reported accruals. The more negatively managed accruals associate with pre-managed accruals, the less likely it is for reported accruals to rise with managed accruals. While the first channel influences the separation of discretionary accruals from nondiscretionary accruals in the DAP, the second channel determines the proxy s performance when the separation is not complete. We conduct our analyses on a sample of 606 material misstatement firm-years that are most likely to represent intentional accrual management. We also conduct the same analyses for a sample of 2,173 firm-years that are likely to involve both intentional manipulation and unintentional errors. We get consistent results across the two samples. Our analyses generate the following two key insights. 4

5 1. Mimicking : we find that managed accruals associate with key explanatory variables in commonly used accrual models in the same direction as pre-managed accruals with similar magnitudes. In other words, managed accruals seem to be mimicking the statistical behavior of pre-managed accruals. Specifically, managed accruals are positively associated with a change of sales or cash sales, positively associated with the previous year s operating cash flows, and negatively associated with the current year s operating cash flows. As a result, estimation of these accrual models unintentionally exclude a portion of managed accruals from DAP. This unintended exclusion effect is more severe for comprehensive models, even though the models are also more successful in excluding pre-managed accruals from DAP. The economic magnitude of the unintended exclusion is nontrivial. Except for DAP from the Dechow- Dichev (2002) model (DD model, hereafter), all other model-based proxies exclude a higher percentage of managed accruals than pre-managed accruals. If the unintended exclusion was not present, the correlations between DAP and actual managed accruals would increase by 13% to 102% for the models we examine. 6 In contrast, the impact of estimation noise on DAP performance is trivial, merely decreasing proxy performance by 2 to 14%, except for in the performance-matched model. 7 In summary, the associations between accrual management and explanatory variables in accrual models lead to unintended exclusions of a significant portion of managed accruals from DAP, giving rise to the lack of superior performance of model-based proxies relative to unadjusted accruals. 6 As expected, the increase is higher for more comprehensive models. For example, the increase would be 98% for the McNichols model and 102% for the Ball and Shivakumar model. 7 In the performance-matched model, estimation noise decreases proxy performance by about 70%. 5

6 2. Blending in : we find that firms overstate accruals more often when their premanaged accruals are lower. This negative association between managed accruals and pre-managed accruals liberates overstating firms from reporting higher reported accruals, making it difficult for accrual-based DAP to capture accrual management. This finding confirms the SEC s concern that manipulating firms are blending in instead of standing out (Lewis, 2012). Further analysis shows that the blending in effect is much stronger when reported accruals are below the cross-sectional median than when above the median. Such non-linearity is consistent with prior evidence that upward manipulation in response to negative performance shock is more intensive when reported performance is low. 8 Because of this non-linearity, DAP are significantly less (more) positively related to accrual management when reported accruals are below (above) the cross-sectional median. 9 For instance, the correlation between DAP in the DD model and managed working capital accruals is in the subsample of above-median accruals but in the below-median accruals subsample. Our finding suggests that commonly used DAP are better indicators of accrual management for above-median accrual firms. Further supporting this convexity in DAP s performance, we find that DAP are predictive of the incidence of material misstatement only when reported accruals are above the crosssectional median. 8 Bhojraj et al. (2009) show that firms with lower reported ROA are more likely to miss analyst forecast ex post, implying that pre-managed earnings are more likely to be lower than performance targets for firms reporting lower earnings. Ayers et al. (2006) show that the association between discretionary accrual proxies and earnings intensifies around analyst forecasts, suggesting that the incentive to overstate earnings in response to performance shocks is stronger when pre-managed earnings are below the performance targets. 9 The co-existence of a negative association between managed accruals and pre-managed accruals and a positive association between managed accruals and reported accruals suggests the existence of accrual management that is not driven by earnings performance, e.g., accrual management around seasoned equity offerings (Teoh et al., 2009) and insider trades (Sawicki and Shrestha, 2008). 6

7 Our study contributes to the literature in the following ways. First, we provide the earliest evidence on the relation between accrual management and firm fundamentals. Prior literature using model-based DAP or the incidence of discovered misreporting cannot speak to such a relation due to the confounding factors of pre-managed accruals or the likelihood of misreporting detection. Utilizing ex post identification of managed accruals, our study advances our understanding of accrual management s statistical behavior by providing direct evidence of the association between managed accruals and firm fundamentals. While our current study focuses on the associations between managed accruals and contemporaneous firm fundamentals, which have direct implications for the most commonly used DAP, our self-collected sample on accrual manipulation can potentially be used to examine other statistical behaviors of accrual management, such as the inter-temporal properties of managed accruals, which serves as the foundation for the recent innovations of accrual models (Dechow et al., 2012; Gerakos and Kovrijnykh, 2013; Nikolaev, 2015). Second, our evidence reveals the significant impact of accrual management behavior on DAP performance. While prior literature focuses on better explaining nondiscretionary accruals and reducing estimation noise in accrual models, we find that the mimicking and blending in behavior of accrual management significantly limit the performance of existing DAP. Our findings suggest that better modeling of the nondiscretionary accrual process does not necessarily lead to better DAP and echoes the call for incorporating accrual management behavior in accrual model development (Gerakos, 2012; Nikolaev, 2015). Furthermore, our findings confirm certain assumptions made in the recent development of accrual models that incorporate statistical behaviors of 7

8 accrual management. For instance, our evidence on the blending in effect confirms the negative relation between accrual management and performance shock assumed in Gerakos and Kovrijnykh (2013). Our evidence that managed accruals mimick premanaged accruals in relation to current and past cash flows but not in relation to future cash flows supports the use of a lower conversion rate into future cash flows as the proxy for low accrual quality in White (2012) and Bloomfield et al. (2014). Third, we demonstrate a new approach to evaluate DAP performance: using the correlation with actual managed accruals. This new approach avoids not only the unrealistic assumption of random accrual management (as in simulations), but also the confounding factor of detection risk (as in incidence studies). More importantly, our new approach enables diagnostic DAP analyses by identifying drivers of a proxy s performance and providing critical information regarding the proxy s strengths and limitations. Finally, our findings on the variation of DAP performance provide implications on the use of these proxies. We show that unadjusted accruals and DAP from the DD model delivers equal or better performance than other accrual models. More importantly, we find that DAP are significant indicators of accrual management only when reported accruals are above the median. Future studies using DAP in fraud prediction or accrual management investigation need to incorporate such non-linearity in DAP performance. Our study is subject to several caveats. First, our sample includes misstatements that are subsequently discovered and restated. As a result, our findings are subject to potential sample selection bias. We follow Dechow et al. (2011) to model the incidence of misstatements and use the Heckman (1974) two-stage regressions to control for this 8

9 potential selection bias. After doing so, our results stay the same. Also, our measure of managed accruals by construction excludes accrual management within the boundaries of GAAP, as within-gaap accruals management are not subject to restatements. Consequently, our findings may not be generalizable to aggregate accrual management, including both within-gaap and outside-gaap management. However, to the extent that both management types face similar incentives, we expect aggregate accrual management to exhibit similar statistical behavior to outside-gaap accrual management in relation to firm fundamentals. 2. Study framework and related literature 2.1 Study framework We use the correlation between a DAP and the actual amount of managed accruals to gauge the proxy s ability to capture accrual management. Correlations focus on proxies ability to capture cross-sectional variations in accrual management, ignoring any constant bias, and therefore are most relevant to association studies. In this study, we use a simple framework to illustrate the determinants of such correlation. For each firm and reporting period, accruals include two portions; these are nondiscretionary accruals (NDA) resulting from normal operating activities and discretionary accruals (DA) resulting from accrual management: ACC = DA + NDA (1) A general accrual model aims to separate accruals (ACC) into two portions; these are proxy for discretionary accruals (DAP) and proxy for nondiscretionary accruals (NDAP): 9

10 ACC = DAP + NDAP (2) We further assume DAP to be a linear function of DA and NDA as follows: DAP = Ø * DA +θ * NDA + e (3) where Ø represents the fraction of discretionary accruals captured by DAP, θ represents the fraction of nondiscretionary accruals left in DAP, and e represents estimation noise that is unrelated to managed or pre-managed accruals. the following Using Equations (1)-(3), the correlation between DAP and DA can be written as Corr(DA, DAP) = sign( Std(DA) Std(NDA) θ +Corr(DA,NDA)) Var(e) θ 2 Var(NDA) Corr(DA,NDA)2 ( Std(DA) 2 Std(NDA) θ +Corr(DA,NDA)) (4) Equation (4) suggests that Corr(DA, DAP) consists of two sets of parameters. The first set of parameters, including Ø, θ, and Var(e), are specific to model specification and estimation. If the specification and estimation of an accrual model accurately capture the nondiscretionary accrual process, there would be less nondiscretionary accruals left in DAP (lower θ). A lower θ leads to a higher Corr(DA, DAP). In contrast, a higher Ø leads to a higher Corr(DA, DAP). If the specification and estimation of an accrual model leave all managed accruals intact in DAP, Ø will be one. However, when discretionary accruals are associated with explanatory variables in the accrual model in the same (opposite) direction as nondiscretionary accruals, Ø could be smaller (larger) than one. Such a mimicking ( diverging ) effect will result in an unintended exclusion (exaggeration) of DA from DAP. At the same time, less estimation noise (smaller Var(e)) leads to a higher 10

11 Corr(DA, DAP). We expect a more homogeneous estimation sample of accrual models that leads to lower Var(e). The second set of parameters, including Corr(DA, NDA) and Std(DA) Std(NDA), are independent of the specification and estimation of accrual models. When accrual models fail to separate managed accruals from pre-managed accruals (i.e., value of is not much θ larger than one), Corr(DA, NDA) and Std(DA) Std(NDA) play an important role in determining the performance of DAP; a higher Corr(DA, NDA) or a higher Std(DA) leads to a higher Std(NDA) Corr(DA, DAP). 10,11 If Corr(DA, NDA) is negative, indicating higher accrual overstatement when nondiscretionary accruals are low, the reported accruals of overstating firms may not be higher than that of non-overstating firms, resulting in a blending in effect. A higher value of Std(DA) indicates a larger variation of Std(NDA) discretionary accruals relative to nondiscretionary accruals, making reported accruals more reflective of accrual management. Our framework to evaluate DAP performance is a special case of the general framework proposed in Dechow et al. (1995; 2012). First, we assume DAP to be a linear function of DA and NDA as in Equation (3), while Dechow et al. do not. Using a linear functional form allows us to quantify the extent of exclusion of DA and NDA from DAP. Second, we use a single metric Corr(DA, DAP) to gauge the performance of DAP, while 10 When Ø approaches 1 and θ approaches 0 at the same time, Corr(DA, DAP) will approach 1 regardless of the values of Corr(DA, NDA) and Std(DA) Std(NDA). 11 Strictly speaking, assuming Std(DA) =1, Corr(DA, DAP) increases (decreases) as Corr(DA, NDA) or θ Std(NDA) increases when Corr(DA, NDA) > Std(DA) Std(DA) (Corr(DA, NDA) < ). As Corr(DA, NDA) > Std(NDA) Std(NDA) Std(DA) is satisfied in our sample, we only consider this case in our discussion. Std(NDA) 11

12 the previous study evaluated DAP s specification and power separately in a testing hypothesis of the relationship between DA and a variable of interest PART, e.g., incentive or constraint of earnings management. Because our evaluation uses a limited number of actual observations of managed accruals, we will not be able to evaluate specification and power separately as in simulations. Third, our approach ignores potential correlations between PART and accrual components. Such simplification may limit the generalizability of our conclusions, but it allows us to demonstrate the impact of statistical behaviors of accrual management on DAP performance in a traceable manner. 2.2 Related literature The literature on the measurement of accrual management to date has largely focused on (a) modeling of the nondiscretionary accrual process with the objective of generating DAP with a lower θ (i.e., excluding more nondiscretionary accruals), and (b) a choice of a homogenous estimation sample to reduce θ and Var(e) (i.e., estimation noise). Despite the fact that statistical behaviors of accrual management also affect a proxy s performance as shown in Equation (4), current literature largely ignores such impacts in the development and evaluation of accrual models Development of discretionary accrual proxies The earliest studies use unadjusted accruals or industry-year-adjusted accruals as DAP. Today, commonly used proxies are residuals from accrual models with selected firm characteristics as explanatory variables. Accrual models are typically variants of two basic models: the Jones (1991) model and then DD model. The Jones model includes contemporaneous sales growth as the explanatory variable of nondiscretionary working capital accruals, reflecting the idea that investment in working capital accruals (such as 12

13 accounts receivables and inventories) is required to support firm growth. 12,13 The DD model includes operating cash flows of the adjacent three years as determinants of nondiscretionary working capital accruals, reflecting the accounting principle that working capital accruals should be realized in operating cash flows within an operating cycle. McNichols (2002) suggests adding sales growth as another explanatory variable to the DD model because doing so significantly increases the R 2 of the model. Recent literature generally employs this combination of the Jones and DD models (e.g., Allen et al., 2013). Ball and Shivakumar (2006) further advocate for incorporating accounting conservatism in modeling accruals. They show that accruals are less negatively associated with current period cash flows when cash flows are negative than when they are positive. Finally, Kothari et al. (2005) propose a performance matching approach to further control for potential correlation between nondiscretionary accruals and performance. Other than improving the specification of accrual models, recent literature also suggests alternative approaches to estimate the above models. Most studies estimate the above accrual models by industry-years. However, industry-year estimation samples raise two issues. First, they lead to severe attrition of the sample. Second, firms in the same industry-year may not be homogenous when some of them experience shocks to their business models and, consequently, to the accrual generating process. To solve the first issue, Ecker et al. (2013) recommend estimation samples of firms with similar size. To 12 As our empirical analysis focuses on working capital accruals, we only review determinants of working capital accruals in these models. 13 To reduce the confounding effects of discretionary reporting on the explanatory variables in the accrual models, following research suggests using cash sales growth (Dechow et al., 1995) or employee growth (Zhang, 2007) to capture growth in operations. 13

14 solve the second issue, Owens et al. (2015) suggest excluding firms with largest idiosyncratic volatility from the industry-year estimation samples. 14 One key assumption underlying the above accrual models is that discretionary accruals are independent of nondiscretionary accruals and their determinants (e.g., sales growth and operating cash flows) specified as independent variables in the model. 15 Several researchers questioned this assumption. For instance, Abarbanell and Lehavy (2003) argue that the amount of managed earnings could be positively related to performance and growth, which is used to explain the asymmetry in the distribution of analyst forecast errors. McNichols (2002) argues that accrual management might be correlated with operating cash flows. Dechow et al. (1995) and Kothari et al. (2005) also recognize the possibility of correlations between accrual management and firm fundamentals, such as size and growth. Despite of these conjectures, there is no empirical evidence as to whether and how accrual management relates to firm fundamentals and to what extent such correlations affect DAP performance. Several recent studies on detection of earnings management or measurement of earnings quality avoid assuming independence between managed accruals and contemporaneous firm fundamentals. Instead, they build accrual models based upon certain assumed behaviors of accrual management. Our later empirical findings confirm several assumptions from these recent models. Gerakos and Kovrijnykh (2013) propose a stochastic model of reported earnings that assumes misreporting as a function of 14 Untabulated results show that DAP generated by these alternative estimation samples are not more strongly correlated with DA than those generated by industry-year estimation samples. We also find that the statistical behaviors of managed accruals affect DAP performance similarly across different estimation approaches. As a result, we focus on industry-year estimation samples in our analyses. 15 When accrual models are estimated using OLS regressions, discretionary accruals are also assumed to be independent of nondiscretionary accruals. 14

15 performance shocks. Our finding on the blending in effect confirms their assumption that firms manipulate to offset performance shocks. Our finding also suggests that measure of earnings management inferred from Gerakos and Kovrijnykh (2013) model is likely to perform better when reported accruals are below the cross-sectional median, where accrual manipulation responds to performance shocks significantly more. In addition, our evidence that managed accruals are correlated with current and past cash flows similarly as pre-managed accruals but unrelated with future cash flows supports White (2012) and Bloomfield et al. (2014) on using lower conversion rate into future cash flows as the proxy for lower quality accruals. 16 Our study, however, do not examine the inter-temporal properties of managed accruals that several recent innovations on accrual models base upon. Dechow et al. (2012) propose a new approach to detect earnings management, which exploits the reversal of accrual management (i.e. managed accruals reverse more quickly than premanaged accruals). Gerakos and Kovrijnykh (2013) and Nikolaev (2015) also assume the reversal of managed accruals and the persistence of true performance when developing stochastic models of accrual management. None of these innovations is intended to generate firm-year estimates of DAP. Given that our study focuses on the associations between managed accruals and firm fundamentals that are the foundation of widely-used accrual models generating firm-year estimates of accrual manipulation, we leave the 16 Badertscher et al. (2012) also show that misstated accruals are not associated with future cash flows among a sample of restatement firms that make discretionary accounting choices for opportunistic meet-orbeat reasons. 15

16 evaluation of these recent innovative models and associated inter-temporal behaviors of accrual management to future research Evaluation of discretionary accrual proxies To evaluate DAP performance, the literature generally employs one or both of the following approaches: 1) detection of simulated discretionary accruals and 2) prediction of discovered material misstatements. The simulation approach was first proposed by Dechow et al. (1995) and widely used in later studies (e.g., Kathori et al., 2005; Dechow et al., 2012; Ecker et al., 2013). This approach artificially inserts a fixed amount of accrual overstatement or understatement into randomly selected samples and examines the frequency of rejecting the null hypothesis of DAP being zero. Such simulation mechanically assumes independence between accrual management and any firm characteristic. As a result, conclusions drawn from such simulations can be biased. For instance, accrual models that explain a higher percentage of variations in total accruals in the simulation will mechanically be more powerful in detecting random accrual misstatement. However, these models are not found to be more powerful in predicting real cases of material misstatement (Dechow et al., 2011). Different from simulation, using the incidence of discovered misstatements does not require assumptions on the randomness of accrual management and provides a more realistic assessment of DAP performance (e.g., Dechow et al., 1995; Jones et al., 2008; 17 We are able to infer firm-year estimates of managed earnings using the Gerakos and Kovrijnykh (2013) model, acknowledging that these estimates are not used or recommended by the authors in their paper. We find that these estimates of managed earnings do not perform better than DAP of the DD model (results are available upon request). A possible reason is that their model is estimated in time-series by individual firms, which introduces too much noise in estimating the relationship between accrual management and performance. 16

17 Dechow et al., 2011). 18 However, evaluation through association with misstatement incidence has two major drawbacks. First, the incidence of misstatement is affected not only by the magnitude of accrual management, but also by the detection efforts of external monitors, including whistleblowers, regulators, auditors, and media (Dyck et al., 2010). 19 Second, the incidence of misstatement does not have sufficient information to provide diagnoses of sources driving DAP performance, which is crucial for DAP advancement. To our knowledge, Jones et al. (2008) is the only study that also uses the correlation with observed non-gaap managed accruals to evaluate accrual models. We extend their analyses in two important ways. First, our sample size is much larger than theirs (606 & 2,173 vs. 128). Second, they only examine the overall correlation, while we develop a framework on the determinants of such correlation, examine specific statistical behavior of accrual management, and study its impact on DAP performance. 3. Variable measurement and sample selection 3.1. Discretionary accrual proxies Prior studies employed a wide variety of accrual models to generate proxies for discretionary accruals. Commonly used accrual models aim to capture nondiscretionary accrual process so that the residual value from the model reflects discretionary accruals. 18 The general conclusion is that commonly used DAP are positively associated with incidence of misstatement and that total accruals and the DD model outperform proxies generated by variants of the Jones model. 19 Realistically, these subsequent investigations are not perfect and could potentially vary with firm fundamentals (Gow et al., 2015). For instance, SEC investigations and shareholder lawsuits are more likely for firms that experienced large stock price declines, while restatement firms are biased toward firms that have made a mistake that is not necessarily intentional (Dechow et al., 2011). 17

18 Each accrual model is unique in the list of determinants of nondiscretionary accruals. In this study, we examine variants of the most popular models. Following Dechow and Dichev (2002), we use working capital accruals (ACC) reported on the statement of cash flows as the definition of accruals in our main analysis, since the majority of accrual models are designed to explain the dynamics of working capital accruals instead of non-current accruals. We consider DAP estimated from the following eight models, with an increasing list of hypothesized nondiscretionary accrual determinants (please refer to Appendix A for model specifications): (1) A naïve model that treats all accruals as discretionary; (2) the Healy (1985) model; (3) the Jones (1991) model; (4) the modified Jones model (Dechow et al., 1995); (5) the Dechow - Dichev (2002) model; (6) the McNichols (2002) model; (7) the Ball and Shivakumar (2006) model; and (8) the performance-matched McNichols (Kothari et al., 2005) model Observation of discretionary accruals The direction and amount of discretionary accruals resulting from accrual management are unobservable to outsiders, unless firms subsequently restate their original misrepresented financial statements that are inconsistent with GAAP. In order to gain ex post direct identification of accrual management, we measure discretionary accruals through firms financial restatements. Specifically, for each restated firm-year, we define reported working capital accruals (ACC) as the one reported in the last set of income and cash flows statements filed before the restatement announcement, and nondiscretionary accruals (NDA) as the one restated in the first set of statements filed after the restatement announcement. The level of discretionary accruals (DA), or managed accruals, is defined as reported accruals subtracted by nondiscretionary accruals 18

19 (ACC- NDA). 20,21 Correspondingly, for earnings and other earnings components, we define reported, nondiscretionary, and discretionary values in the same way. Although restatements allow accurate identification of the managed portion of accruals, such identification is nevertheless subject to two limitations. First, our identification by design does not include accrual management within the boundaries of GAAP, as within-gaap accrual management does not trigger subsequent restatements. Consequently, our study is most relevant for research focusing on more material and egregious types of accrual management. In addition, our definition is not observable for accrual management that violates GAAP but is not discovered subsequently by auditors and regulators. We use the Heckman (1974) two-stage estimation method to control for potential sample selection bias caused by these undiscovered cases of accrual management Sample selection Because the focus of our study is the statistical behavior of accrual management, we distinguish accounting misstatements resulting from intentional manipulation from those due to unintentional errors or violation of GAAP for information or contracting purposes. 22 We rely on three sources to identify intentional accounting misstatements: SEC accounting and auditing enforcements (AAER) (Dechow et al., 2011), restatements classified as accounting frauds in audit analytics, and restatements in the Government Accountability Office (GAO) report that are classified as irregular by Hennes et al. 20 A firm-year may be restated more than once. We accumulate managed accruals inferred from each restatement case to find total managed accruals for that firm-year. 21 This definition of discretionary accruals has been used by Jones et al. (2008), Badertscher et al. (2012), and Donelson et al. (2013). 22 Badertscher et al. (2012) and Martin et al. (2015) show that in a significant percentage of restatements, GAAP violation in fact reveals managers private information. 19

20 (2008). As shown in Table 1, a total number of 1,333 firm-years with estimates of DAP are involved in these misstatements. 23 We refer to this sample as the material misstatement sample. For 733 of the above 1,333 firm-years, we are able to collect both the originally reported and restated numbers for the following accounts: sales, net income, cash flows from operations, total accruals, and working capital accruals. 24,25 Because we are interested in accrual manipulation, we require non-zero misstatement of both earnings and working capital accruals. The final sample of material misstatement consists of 606 firm-years for the sample period of We conduct our main analyses on the above material misstatement sample. However, we also repeat the same set of analyses on a sample of restatements not classified as intentional by prior studies (nonmaterial misstatement sample, hereafter), and find highly consistent results across these two samples. It is possible that there remains a significant fraction of intentional accrual management within restatements classified as nonmaterial, which drives the observed similarity between these two samples. An alternative explanation is that unintentional accrual errors exhibit similar associations with firm fundamentals as intentional accrual management. Neither explanation affects our conclusions on the statistical behavior of accrual management and its impact on DAP performance. 23 The GAO report does not indicate fiscal years restated in a restatement case. We thank Brad Badertscher for sharing his data on fiscal years restated in GAO restatements. 24 We define total accruals as net income minus operating cash flows and working capital accruals as change in accounts receivable plus change in inventory minus change in accounts payable minus change in unearned revenue and plus change in other operating assets and liabilities. 25 Some misstatement firm-years are not restated due to bankruptcy, acquisition, etc. We do not observe restated financial statements for these observations. 20

21 4. Empirical results Our empirical analyses start by describing the properties of observed discretionary accruals (DA) and nondiscretionary accruals (NDA) in the material misstatement sample. We then assess DAP performance by estimating the correlation between DAP and DA and decomposing the correlation following our theoretical framework. Next, we empirically explore the two channels through which accrual management behavior affects DAP performance: associations between DA and independent variables in accrual models that affect the separation of DA and NDA, and then the association between DA and NDA that affect DAP performance when the separation is incomplete Descriptive statistics Table 2 presents descriptive statistics for the material misstatement sample. Panel A reports the summary statistics of originally reported earnings and earnings components separately for the material misstatement sample and the Compustat population. 26 The mean (median) originally reported working capital accruals (ACC) is 2.4% (1.4%) of average total assets for the material misstatements sample, which is substantially higher than the 1.2% (0.7%) for the Compustat population. In contrast, reported non-current accruals (NCA), operating cash flows (CFO), and earnings (ROA) are comparable in these two samples. These findings suggest that, among earnings components, reported working 26 The Compustat population includes 89,328 firm-year observations with sufficient data to estimate accrual models at the industry-year levels. To construct this sample, we start with Compustat firm-years satisfying the following data requirements: (1) fiscal years from 1994 to 2011; (2) positive values for CHE, LT, SALE of current and previous years; (3) positive value for AT of the most recent three years; (4) positive value for PPEGT and PPENT; (5) non-missing values for RECT of the most recent three years, IB of the most recent two years, IBC of current year, OANCF of previous, current, and the next year; (6) nonmissing values for at least one of RECCH, INVCH, APALCH, or AOLOCH of current year, (7) nonfinancial firms. We delete firm-years with ROA larger than 1 in magnitude, truncate CFO, TACC, ACC at the bottom and top 0.5% percentiles, and require each two-digit SIC industry-year to have at least 15 observations. 21

22 capital accruals should be most predicative of intentional misstatements, which is confirmed in our later analysis. Panel B reports the summary statistics of discretionary and nondiscretionary earnings components for the material misstatement sample. The mean (median) earnings management DROA equals 1.7% (0.5%) of average total assets, consistent with the material misstatement sample being comprised predominantly of firms where earnings were managed upward. Without upward earnings management, these misstatement firms would have reported a mean (median) level of nondiscretionary earnings NDROA at -2.2% (1.3%), which is equal to (lower than) the mean (median) level of reported earnings in the Compustat population. In addition, these firms increased earnings mainly through management of working capital accruals, which amounts to a mean (median) of 1.2% (0.3%) of average total assets. These results are consistent with the observations by Dechow et al. (2011) and Hennes et al. (2008) that the majority of accounting fraud firms misstated revenue or operating expenses. Table 3 reports the correlations between accruals and accrual determinants in the material misstatement sample. These correlations reveal several important insights. First, nondiscretionary accruals (NDA) and discretionary accruals (DA) are negatively correlated, suggesting that firms manage accruals to blend in among peer firms. This negative correlation may reflect overstatement of accruals to offset negative performance shocks. An alternative interpretation, however, is that the level of nondiscretionary accruals serves as a constraint of overstatement. 27 Moreover, despite of the negative correlation between DA and NDA, reported accruals (ACC) are significantly positively 27 Untabulated results show that managed working capital accruals are also negatively correlated with premanaged operating cash flows. 22

23 associated with discretionary accruals (DA). This finding suggests that the positive association between reported accruals and the incidence of intentional misstatements widely documented in the literature (Dechow et al., 1995; Dechow et al., 2011) is not completely driven by the association between accruals and the detection of misstatements. Third, both nondiscretionary and discretionary accruals are significantly positively associated with contemporaneous sales growth and negatively associated with contemporaneous operating cash flows. This finding confirms the conjecture in the literature that accrual management is associated with accrual determinants specified in the accrual models (McNichols, 2002; Wysocki, 2009). 4.2 The mimicking behavior and unintended exclusion of DA from DAP Correlation between DAP and DA across accrual models Table 4 reports the estimation results of accrual models. Consistent with findings in prior studies, accruals are significantly positively associated with change of revenue, positively associated with prior year and subsequent year cash from operations, and negatively associated with current year operating cash flows. In addition, the negative association between accruals and current year operating cash flows is attenuated when firms have negative operating cash flows, suggesting more timely recognition of losses than gains in accruals (Ball and Shivarkumar, 2006). As expected, a model with a more comprehensive list of accrual determinants has larger explanatory power. Adjusted R 2 increases significantly from 0% for unadjusted accruals (untabulated) to 6.80% for the Jones model, to 30.45% for the DD model, and finally to 38.81% for industry-year 23

24 estimation of the McNichols model. 28 The residuals from these accrual models are proxies for discretionary accruals. Table 5 reports correlations between DAP and DA. All proxies are statistically and economically significantly correlated with the level of observed accrual management, corroborating the use of these proxies to detect accrual management in both literature and practice. Surprisingly, unadjusted accruals (ACC) have a higher correlation with managed accruals (Pearson correlation of and Spearman correlation of 0.241) than all other model-based proxies. Furthermore, DAP generated by accrual models with the most comprehensive sets of accrual determinants, i.e., the McNichols, Ball and Shivarkumar, and performance-matched McNichols models, are least positively associated with DA. These results suggest that accrual models with a larger explanatory power (i.e., adjusted R 2 ) do not lead to a better measure of accrual management. Table 5 also presents the correlations between DAP and the level of earnings management (DROA), which are very similar to those observed above for accrual management. For comparison, we also report the correlations between discretionary total accrual proxies (DTAP) and earnings management. For all accrual models, DAP is significantly more positively associated with DROA than DTAP, suggesting the use of DAP instead of DTAP as the proxy for earnings management. 29 Examining the association between DAP and the level of observed accrual management among restating firms could be problematic because restatement firms were likely caught with their hands in the cookie jar by the SEC, the external auditor, or a 28 Models 5 and 6 are estimated on industry portfolios instead of industry-year portfolios. As a result, these models generate lower adjusted R 2 than Model Our review of the literature suggest that the majority of studies use DTAP instead of DAP as the proxy for earnings management, e.g., Fang et al. (2015) and Dou et al. (2015). A few exceptions include Dechow et al. (2012) and Allen et al. (2013). 24

25 corporate insider. To the extent that the probability of detection is greater when a firm reports higher levels of DAP, the restatement sample may reflect a self-selection bias that distort correlations between these proxies and actual accrual management. Accordingly, we control for self-selection using Heckman s (1974) two-step estimation approach. Specifically, following the prediction model of material misstatements developed by Dechow et al. (2011), we first estimate the likelihood of a particular firm-year being included in our material misstatement sample. 30 The dependent variable in the selection model equals 1 if a firm-year is in our sample of material misstatement, and 0 otherwise. From the selection model, we construct the inverse Mills ratio (IMR) as the self-selection adjustment and include it as a control variable in the second step of estimating the correlation between DAP and DA. Table 6 Panel A presents the results of estimating the selection model with unadjusted working capital accruals (ACC) as DAP. Consistent with the implication of Table 2, ACC is significantly positively associated with the incidence of misstatements, while NCA is not. Panel B reports the results of estimating the selection model with model-based DAP. We find that all DAP are significantly positively associated with the incidence of misstatements, while most NDAP are uncorrelated or even negatively correlated with misstatements. These findings suggest that DAP is the most reliable 30 Our selection model differs from the model in Dechow et al. (2011) in two minor ways: (1) We break down the accrual variable growth of non-cash operating assets into three components: the difference between growth of non-cash operating assets and total accruals (net income minus operating cash flows), working capital accruals (based on cash flows statement items), and non-current accruals (total accruals minus working capital accruals). As we have already included working capital accruals, we drop change of accounts receivables and change of inventory in their model. (2) We add a few variables reflecting the complexity of the firms, including big auditor (BigN), multinational firm indicator (MNC), restructuring indicator (RESTRUCT), and the number of segments (segments). 25

26 predictor of intentional misstatements among earnings components. 31 Table 6 Panel C presents the correlations between DAP and DA after controlling for the inverse Mills ratio (IMR). These correlations are almost identical to those reported in Table 5, indicating that the conclusions we draw from Table 5 are unlikely to be driven by the self-selection bias The unintended exclusion of discretionary accruals from DAP To explain the levels of correlations between DAP and DA observed in Table 5, we decompose these correlations into parameters according to the framework in section 2.1. Table 7 Panel A presents the values of two parameters that are constant across accrual model specifications and estimation approaches: the correlation between discretionary and nondiscretionary accruals (Corr(DA,NDA)) and the relative variance of accrual management ( Std(DA) ). The former equals and the latter equals 0.44 in our Std(NDA) sample of material misstatement. Because Std(DA) is much larger than Corr(DA,NDA) in Std(NDA) magnitude, even unadjusted accruals (ACC) are significantly positively associated with accrual management. 32 Table 7 Panel B presents estimates of three parameters that are specific to accrual model specification and estimation: weight on discretionary accruals (Ø), weight on nondiscretionary accruals (θ), and the variance of estimation noise in the proxy (Var(e)). All DAP have a significantly positive θ, with the minimum value of for DAP from the performance-matched McNichols model (DAPPM). This finding suggests that popular accrual models fail to account for a significant portion of nondiscretionary accruals, 31 Untabulated results show that operating cash flows (CFO) are uncorrelated with misstatements when added to the selection model. 32 Theoretically, Std(DA) could be smaller than Corr(DA,NDA) in magnitude and, thus, ACC could be Std(NDA) negatively correlated with actual accrual management. 26