Asymmetric Behavior of Accruals

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1 Asymmetric Behavior of Accruals Rajiv D. Banker * Temple University Shunlan Fang Kent State University Byunghoon Jin Temple University This Draft February 2015 Please do not quote. ABSTRACT Estimated discretionary accruals are commonly used in accounting research as a primary indicator of earnings management. Many studies use the residuals from Jones-type expectation models to measure discretionary accruals. These models assume that accruals have a linear relation with sales change but ignore the asymmetry in the impact of managers operating decisions on accruals that differ when sales decrease. By forcing a linear model on an inherently non-linear relation, the modified Jones model underestimates discretionary accruals when firms experience an extreme sales change and overestimates them when firms experience a moderate sales change. Extensive simulation analysis documents that this bias results in substantial Type I error in tests of positive discretionary accruals, except at the extremes of the sales growth distribution when Type II error dominates. This non-linearity of the bias explains why the inclusion of a linear control variable does not adequately address the problem but performance matching (Kothari, Leone and Wasley, 2005) does much better. As a further consequence of this non-linear bias, we document significant upward bias in estimated discretionary accruals for firms with low sales volatility. We also document that, unlike for small profit firms, positive discretionary accruals are significant for small loss firms relative to other firms only in the extreme ends of the sales growth distribution. * Corresponding Author. Department of Accounting, Fox School of Business and Management. Temple University, 1801 Liacouras Walk, Philadelphia, PA

2 1. Introduction Measurement of discretionary accruals relative to a baseline model of expected accruals, such as the modified Jones model (Dechow et al. 1995), has been at the core of many studies of earnings management. 1 Ball (2013) questions these studies pointing to our limited knowledge of the determinants of accounting accruals under the null hypothesis of no earnings management. We document that the modified Jones model is misspecified because it assumes a linear relation between accruals and changes in sales when managers operating decisions affecting their accruals (e.g., credit sales terms, credit purchase terms and inventory policies) are asymmetric with respect to the direction of sales change. Ignoring the asymmetry in the relationship and forcing a linear model on a non-linear relation, the modified Jones model underestimates discretionary accruals when firms experience an extreme sales change and overestimates them when firms experience a moderate sales change. The bias in the estimation of discretionary accruals is systematic and has a predictable non-linear pattern. In our sample from 1988 to 2013, discretionary accruals (scaled by beginning assets) measured using the modified Jones model average for firms in the bottom two deciles of sales growth and for firms in the top decile of sales growth, but for firms with moderate sales growth. Simulations confirm that this bias results in substantial Type I error in tests of positive discretionary accruals, except at the extremes of the sales growth distribution when Type II error dominates. The non-linearity of the bias explains why the inclusion of ROA or sales growth as simply a linear control term in the modified Jones model 1 Even during the recent four years , as many as 30 papers (excluding literature review papers) were published in Journal of Accounting and Economics, Journal of Accounting Research and The Accounting Review that used the modified Jones model or its variants. Of these, 12 used the modified Jones model as the main model to estimate discretionary accruals, 7 used an extended version of the modified Jones model that includes ROA as an additional control variable, 5 used a matching approach following Kothari et al. (2005), and 6 used other variants of the Jones model. 2

3 does not eliminate the bias, but performance matching suggested by Kothari, Leone and Wasley (2005) does. Ball (2013) suggests that accrual management detected in accounting research seems to be too prevalent to be true. The non-linear bias in discretionary accruals estimated by the modified Jones model creates the risk of false positives in detecting income-increasing accruals management. We illustrate this risk by documenting that estimated income-increasing accruals have a mechanical negative association with sales volatility. Firms with low sales volatility are more likely to exhibit moderate sales growth and therefore exhibit significantly more positive discretionary accruals due to the non-linear bias in estimating discretionary accruals. In addition, we also show that the systematic bias we document in estimating discretionary accruals provides deeper insights into the results of Dechow, Richardson and Tuna (2003), who show that discretionary accruals for small profit are not significantly different from those for small loss firms. Instead, we find that positive discretionary accruals in small loss (but not in small profit) firms relative to other firms is primarily driven by the underestimation of discretionary accruals for firms in the extreme ends of the sales growth distribution. The bias in the modified Jones model results from the fact that the model ignores the impact on accruals of managers operating decisions that change with the direction of sales change. Normal (or non-discretionary) accruals behave asymmetrically with respect to sales changes because non-cash working capital accounts have asymmetric response to sales shocks. Consider each of the three main working capital accounts: accounts receivable, inventory and accounts payable. Accounts receivable generally increase as a firm s sales increase but decrease to a lesser extent when the sales decrease because managers are more likely to relax credit policies when sales decline in order to attract customers. Similarly, inventory account grows if a 3

4 firm s sales are expected to increase, but a decline in sales is likely to result in a proportionately smaller decrease in inventory because rebalancing inventory levels takes time. Also, if managers expect the sales decline to be temporary, they are not likely to dispose off all excess inventory (Bernard and Noel 1991). In a similar way, accounts payable behave asymmetrically in that they increase as sales increase but do not decrease in the same proportion as sales decline because managers may seek to postpone payments to alleviate the cash crunch caused by a sales decline. We posit that, on average, working capital accounts on the liability side tend to be less sensitive to sales changes than those on the asset side because of the timing difference in managerial operating decisions. For a typical operating cycle, managers make production plans according to their sales projections. They acquire inputs and hire labor to initiate the production process before sales occur. Thus, production related decisions precede the sales realization. Accruals associated with current liabilities (e.g., accounts payable, wages payable) are more likely to be generated with production decisions while accruals related to current assets (e.g., accounts receivable, inventory) are more likely to be associated with sales decisions. Due to the timing difference, managers are likely to have greater discretion in adjusting accruals related to current assets than they do in adjusting accruals related to current liabilities. When there is a negative sales shock, managers can extend additional credit to customers and inventory unsold production (e.g., Emery 1984; Lee and Stowe 1993). However, accruals related to current liabilities are less likely to be sensitive to negative sales shocks than those related to current assets because transactions related to production typically precede the realization of sales shocks. Empirically, the asymmetry in the impact of operating decisions on working capital accounts translates into a non-linear relationship between total accruals and cash sales (or total sales). We document robust evidence showing that total accruals are significantly more sensitive 4

5 to changes in cash sales when sales are down, implying a steeper decrease in total accruals as sales decline. Forcing a linear relation between total accruals and changes in cash sales as in the modified Jones model creates significant bias in estimating discretionary accruals. Discretionary accruals estimated as residuals from the modified Jones model are understated when there is a large sales change and are overstated when there is a moderate sales change (see Figure 1). In other words, when there is an extreme sales change, tests of discretionary accruals based on the modified Jones model are less likely to support incomeincreasing accruals management. In contrast, when there is a moderate sales change, these common tests of discretionary accruals are more likely to support a hypothesis of incomeincreasing accruals management. Extensive simulation analysis documents that this bias results in substantial Type I error in tests of positive discretionary accruals, except at the extremes of the sales growth distribution when Type II error dominates. The evidence also provides a conceptual explanation for why using the performance matching approach proposed by Kothari, Leone and Wasley (2005) mitigates the bias in estimating accruals using the modified Jones model. The inclusion of just a linear control for performance (be it return on investments (ROA) or sales growth) cannot eliminate the bias in estimating discretionary accruals that is negative, followed by positive, and followed finally by negative again. Because the bias in estimating discretionary accruals is not linear with respect to sales growth, matching firms on performance outperforms a modified Jones-type regression model that simply controls for performance. Our simulation study confirms that performance matching on ROA substantially reduces the bias in estimating discretionary accruals using the modified Jones model (Kothari et al. 2005), and that matching on sales growth provides further improvements. 5

6 Next, we consider the implications of the bias we document in estimating discretionary accruals for tests of earnings management using the modified Jones model. We posit and document that firms with low sales volatility exhibit significantly more positive discretionary accruals estimated using the modified Jones model than those with high sales volatility. There are no compelling economic reasons why firms with relatively low sales volatility should manage earnings upward. The pattern we document is likely to be driven by the artifact that firms with low sales volatility are less likely to experience the extremes of sales growth when the modified Jones model underestimates discretionary accruals. There are important implications for other studies of earnings management as well. We reexamine Dechow, Richardson and Tuna s (2003) analysis of discretionary accruals by firms with small losses and small profits compared to other firms. They document that firms with small losses are similar to firms with small profits in exhibiting discretionary accruals greater than for other firms. We confirm their result overall, but find that unlike for small profit firms, this result for small loss firms is primarily driven by only those firms experiencing the extremes of either large sales decline or very high sales growth. The remainder of the paper is organized as follows. In Section 2, we provide the economic intuition underlying the asymmetric relation between change in sales and total accruals and present empirical results to support it. In Section 3, we present simulation results by sales growth deciles on the bias in estimating discretionary accruals using the modified Jones model and the performance matched model of Kothari et al. (2005). In Section 4, we examine the implications of this bias on tests of earnings management for firms with low sales volatility and for firms with a small loss. We conclude in Section 5 with a summary of our results and some thoughts for future research. 6

7 2. Asymmetric Behavior of Accruals and Bias in Measuring Discretionary Accruals 2.1. Economic Explanation for Asymmetric Behavior of Accruals Accruals refer to the non-cash component of earnings. Non-discretionary accruals reflect normal managerial operating decisions under the prevailing business conditions, whereas discretionary accruals are often considered opportunistic, driven by managers earnings management incentives. Many accounting research studies (e.g., McNichols 2002; Larcker and Richardson 2004; Francis et al. 2005; Doyle et al. 2007) have relied on discretionary accruals estimated using Jones-type models (e.g., Jones 1991; Dechow et al. 1995; Sloan 1996) as the primary indicator of accrual management. Much of the prior literature has estimated discretionary accruals in the following two steps. First, normal (non-discretionary) accruals are estimated using an accruals expectation model such as the modified Jones model. Second, discretionary accruals are defined as the difference between the actual and the expected normal accruals. 2 For instance, the Jones model assumes that normal accruals are proportional to sales changes, controlling for total assets and property, plant and equipment: TACC t = β 1 (1/ASSET t-1 ) + β 2 ΔREV t + β 3 PPE t + ε t, (1) where TACC t = total accruals in year t. Following Hribar and Collins (2002), total accruals (TACC) are measured as earnings before extraordinary items and discontinued operations less operating cash flows from continuing operations. ΔREV t is revenue in year t less revenue in year 2 Discretionary accruals defined as residuals are the unexplained portion of total accruals. Not all of the unexplained portion can be attributed to earnings management. However, unmodeled earnings management may change the conditional mean of the residuals for some firms. It is important, therefore, to have an unbiased accruals expectation model to assess the differential impact of earnings management. 7

8 t-1 and PPE t is gross property, plant, and equipment in year t. TACC t, ΔREV t and PPE t are scaled by total assets at year t-1. While the Jones model implicitly assumes that all revenue is non-discretionary, Dechow et al. (1995) assume that the entire change in credit sales results from earnings management. They provide a modified version of the Jones model where the change in revenue is adjusted for the concurrent change in accounts receivable: TACC t = β 0 + β 1 (1/ASSET t-1 ) + β 2 (ΔREV t ΔAR t ) + β 3 PPE t + ε t, (2) where ΔAR t = accounts receivable in year t less accounts receivable in year t-1 scaled by total assets at year t-1. Ball (2013, p.851) criticizes these standard accruals expectation models for treating working capital accruals as deterministic (Gerakos 2012) when, in fact, working capital is stochastic changing in response to operating conditions and expectations. In this paper, we consider sales growth or decline as an important source of stochasticity. We posit that both the original and the modified Jones models suffer from substantial bias in estimating discretionary accruals because these models ignore the asymmetric impact of managers operating decisions on accruals. The change in accruals depends on the direction of change in sales. The accruals in earnings management studies typically refer to non-cash working capital accounts that are likely to reflect shocks to supply and demand (Ball 2013, p ). We focus on three major working capital accounts (i.e. accounts receivable, inventory and accounts payable) to illustrate this point. Accounts receivable depend on the credit a firm extends to its customers. The level of accounts receivable generally increases when the firm s sales activities increase and decreases when the sales activities decrease. Granting credit is expected to enhance a firm s sales by 8

9 mitigating customers financial frictions (Meltzer 1960), reducing transaction costs (Ferris 1981; Emery 1987), signaling product quality (Lee and Stowe 1993; Emery and Nayar 1998), reducing information asymmetry (Smith 1987; Long et al. 1993; Pike et al. 2005), providing a mechanism of price discrimination between cash and credit customers (Brennan et al. 1988; Petersen and Rajan 1997), and improving supplier-customer relation (Ng et al. 1999; Wilner 2000; Cuñat 2007). When sales decline, managers are more likely to relax credit policies in order to attract customers and increase the company s competiveness in the market (Emery 1984; Lee and Stowe 1993). As a result, receivables decrease at a lower rate than they increase in response to sales change. Similarly, the level of inventory typically increases as demand increases but decreases to a lesser extent when sales decline. Favorable market environment (e.g., increasing sales) may motivate firms to build inventory for future sales and minimize inventory stock-out costs (Lev and Thiagarajan 1993). Normal inventory increase is considered a positive signal for a firm (e.g., Lev and Thiagarajan 1993; Abarbanell and Bushee 1997, 1998; Sun 2010) because it suggests the firm s sales are expected to increase. A decline in sales is more likely to result in inventory build-up because rebalancing inventory takes time (see Ball 2013, p.851). 3 In addition, if managers expect the sales decline to be temporary, they are not likely to dispose off all excess inventory. Accounts payable are created when a firm purchases goods or services using trade credit. Payables also behave asymmetrically in that they increase as sales increase but do not decrease 3 Ball (2013, p.851) describes this vividly as follows: Under the work-horse Jones model, working capital in the absence of manipulation is proportional to sales, and hence, according to this simplistic model, a negative shock to sales should engender a proportional non-discretionary decrease in inventory. The actual effect of a negative sales shock on inventory in the absence of manipulation is positive: the firm has an unexpected amount of unsold inventory at year-end. Thus, behavior that in fact is not manipulative is classified as an income-increasing discretionary accrual, even though no discretion has been exercised. 9

10 proportionately as sales decline. This is because managers may seek to postpone payments to alleviate the cash crunch caused by a sales decline, if necessary through renegotiation of contract terms. A firm could renegotiate with suppliers about the timing in paying the bills because it is less costly to delay payment to suppliers than to acquire external financing (Danielson and Scott 2004). 4 Such actions would result in a smaller decrease in accounts payable when sales decline. We further posit that, on average, working capital accounts on the asset side are more sensitive to sales changes than those on the liability side because of timing differences in the operating cycle. In a typical operating cycle, managers make production plans according to their sales projections. They need to acquire inputs (e.g., hire labor, purchase material) to initiate the production process before making sales so that decisions related to production typically precede those related to actual sales. Accruals related to current liabilities (e.g., accounts payable) are more likely to be generated based on production decisions while accruals related to current assets (e.g., accounts receivable and inventory) are more likely to be generated based on sales outcomes. Therefore, accruals related to current liabilities are typically determined at an earlier stage of the operating cycle while those related to current assets at a later stage. Due to this timing difference, accruals related to current liabilities are likely to be less sensitive to negative sales shocks than accruals related to current assets. Accordingly, net accruals are likely to decrease more steeply with a sales decline than they increase with a sales growth. This asymmetric accrual behavior implies that the discretionary accruals estimated by the modified Jones model exhibit non-linear bias with respect to sales growth. Simply adding a 4 Danielson and Scott (2004) argue that vendors may allow a delay in payments (when banks will not) because 1) the short-term nature of trade credit allows vendors to continually monitor a firm s payment pattern and to adjust sale prices or terms accordingly, 2) the collateral value of a firm s inventory is likely to be higher to trade creditors, and 3) foregone discounts provide a high effective interest rate, compensating vendors for the risk of eventual nonpayment. A typical example is Walmart. The company has a provision in its vendor agreement that makes suppliers share the risk of lower sales volume. 10

11 linear control for sales growth or earnings performance in expectation models cannot fully address the non-linearity of accruals. Since the relation between total accruals and sales change or sales growth is non-linear, a matching approach will mitigate the model misspecification problem more effectively than simply adding more control variables in the accruals expectation model. This explains why the performance matching approach proposed by Kothari, Leone and Wasley (2005) significantly reduces the bias in estimating discretionary accruals using the modified Jones model. Kothari et al. (2005) suggest that performance-matching mitigates concerns about the correlation between performance and residuals from the Jones-type accruals expectation models. They identify a control firm in the same industry-year with the closest level of ROA to that of each sample firm and subtract the control firm s discretionary accruals from those of the sample firm to generate performance-matched discretionary accruals. Their primary motivation in using ROA as the matching variable as opposed to other candidates (e.g., size, sales or earnings growth, earnings yield, market-to-book) comes from prior studies that analyze long-run abnormal stock return performance and abnormal operating performance and find matching on ROA results in better specified and more powerful tests compared to other matching variables (e.g., Barber and Lyon 1996, 1997; Lyon et al. 1999; Ikenberryet al. 1995). Our theory suggests that using sales growth as the matching variable instead of ROA will better address the asymmetry in accruals with respect to sales growth Empirical Evidence Our initial sample consists of 219,284 firm-year observations over the fiscal years from Compustat Fundamentals Annual Files. We exclude firms in financial (SIC codes between 6000 and 6999) and regulated (SIC codes between 4000 and 4999) industries from the 11

12 sample. This restriction reduces the sample by 55,814 observations. We further exclude 25,074 observations which do not have sufficient data to compute the variables used in our main analysis. We also remove the top and bottom 1% of the observations with extreme values in all financial variables used in our main analysis. The final sample consists of 128,910 observations for 15,479 firms. [TABLE 1] Table 1 provides descriptive statistics for our sample data. The average ratio of total accruals to beginning total assets is -11.0%, -9.7%, and -14.1% for the overall sample, sales-up firms, and sales-down firms, respectively. Changes in individual working capital accounts, earnings (before extraordinary items and discontinued operations), and cash flow from operations are all significantly larger in firms with increasing sales than in those with decreasing sales. About 30.9% of overall sample observations are firms with decreasing sales. To document the asymmetric relation between changes in working capital accounts and changes in sales, we run the following regression: WC t = β 0 + β 1 (ΔREV t ΔAR t ) + β 2 (ΔREV t ΔAR t ) DEC t + Year/Industry Fixed Effects + ε t, (3) where WC t stands for each working capital account (e.g., accounts receivable, inventory, accounts payable). DEC t = 1 if revenue in year t is less than revenue in year t-1 and = 0 otherwise. The regression results are shown in Tables 2, 3, and 4. We find that the coefficient on ΔREV t ΔAR t is positive while that on (ΔREV t ΔAR t ) DEC t is negative for each working capital 12

13 account, indicating a reduced slope on the relation between changes in accounts receivable and changes in sales. 5 [TABLE 2] The asymmetric relation between current assets change and revenue change are reported in Table 2. Column (1) shows that change in accounts receivables (ΔAR) and change in sales are positively associated (β 1 = 0.117, t = 38.96) as expected. 6 The negative coefficient on the interaction term (β 2 = , t = -8.80) suggests that the positive relation between change in sales and change in accounts receivable is dampened by 38.5% (= / 0.117) when sales decrease. Similarly in Column (2), change in inventory (ΔINVT) and change in sales are positively associated (β 1 = 0.095, t = 38.68), consistent with the premise that firms hold more inventory when sales increase. As suggested by the negative β 2 (= , t = -3.46), the positive relation is also mitigated by 13.7% (= / 0.095) when sales decrease. Column (3) exhibits the regression result for change in other current assets (ΔOCA) which includes prepaid expenses. For ΔOCA, the positive relation of change in other current assets to change in sales (β 1 = 0.025, t = 24.51) is completely canceled out when sales decrease (β 2 = , t = ). Consistent with results shown in Columns (1), (2) and (3), the positive relation between change in revenues and change in total non-cash current assets (ΔNCCA) in Column (4) is mitigated by 35.9% ( = / 0.237) when sales decrease. Overall, the results shown in Table 2 indicate that the positive relation between change in sales and change in non-cash current assets is mitigated when sales decrease, consistent with our prediction. [TABLE 3] 5 The results are robust when an independent DEC t dummy is also included. 6 The change in receivables (and also in other components of working capital) is substantially less than the change in sales (β 1 < 1) indicating the extent of normal accrual adjustments corresponding to sales change is on average less than the sales change. 13

14 Results reported in Table 3 document the asymmetric relation between current liabilities change and revenue change. Column (1) shows that change in accounts payables (ΔAP) and change in revenues are positively associated (β 2 = 0.085, t = 32.46) as expected and that the positive relation is mitigated by 55.3% (= / 0.085) when sales decrease. Columns (2) and (3) exhibit regression results for change in income tax payables (ΔTXP) and change in other current liabilities (ΔOCL) which includes accrued expenses, respectively. Similar to the results for other working capital accounts, the positive response in income tax payables and in other current liabilities to change in revenues is mitigated by 60.0% (= / 0.005) and by 71.0% (= / 0.077), respectively, when sales decrease. Consistent with results shown in Columns (1), (2) and (3), the positive relation between change in sales and change in total current liabilities excluding current portion of long-term debt (ΔCL_DLC) in Column (4) is mitigated by 62.5% ( = / 0.168) when sales decrease. The overall results shown in Table 3 indicate that the positive relation between change in revenues and change in current liabilities (excluding debt) is also mitigated when sales decrease, consistent with our prediction. [TABLE 4] Table 4 presents result of the regression of total accruals on change in revenues. In particular, Columns (4) and (5) show the asymmetric relation of balance sheet accruals (TACC_BS = ΔNCCA ΔCL_DLC DP) and cash flow accruals (TACC) to change in revenue. For both TACC_BS and TACC, the coefficient on the interaction term (β 2 ) is highly significant and positive, which suggests that sales-down effect on the liability-side working capital accounts dominates that on the asset-side working capital accounts, consistent with our prediction. 14

15 To capture the asymmetry in the relation between expected total accruals and change in sales, we incorporate the sales-down effect by including an interaction term (between the salesdown dummy and the change in adjusted sales revenue) in the modified Jones model: TACC t = β 0 + β 1 (1/ASSET t-1 ) + β 2 (ΔREV t ΔAR t ) + β 3 (ΔREV t ΔAR t ) DEC t + β 4 PPE t + Industry/Year Fixed Effects + ε t. (4) While both cross-sectional regression (e.g., DeFond and Jiambalvo 1994) and panel regression (e.g., Dechow et al. 2012) are commonly used in the existing literature, we present results for the latter with two-digit SIC industry and year fixed effects for our main analysis in order to directly examine whether the coefficients are statistically different between sales-up firms and salesdown firms. As a robustness check, we confirm that using cross-sectional regressions yields similar results. The results are robust also when we include a stand-alone binary variable for the DEC t dummy. [TABLE 5] Table 5 reports regression results for the basic modified Jones model and the accruals expectation model after allowing for asymmetric response to sales decisions. Column (1) presents the result of estimation of the basic modified Jones model. Prior studies generally do not make a prediction on the sign of the coefficient on revenue change because total accruals increase with change in current assets and decrease with change in current liabilities and both change in current assets and change in current liabilities increase with sales change. We find a positive coefficient on change in sales (β 2 ). The significant negative coefficient on PPE (β 4 ) is consistent with the negative relation between total accruals and depreciation expense. 15

16 Column (2) shows the estimation result when the effect of decreasing sales are incorporated in the modified Jones model. Consistent with our prediction, we find a significantly positive coefficient on the interaction term between the sales-down dummy and change in revenue (β 3 ), indicating that total accruals decrease more steeply with decreasing sales. Specifically, the relation between sales change and total accruals is insignificant in firms with increasing sales (β 2 = , t = -0.34), but this relation is significantly more positive in firms with decreasing sales (β 3 = 0.110, t = 9.54). The result also suggests that the positive coefficient on sales change documented in previous studies (e.g., Jones 1991) is driven primarily by firms with decreasing sales Robustness Checks We perform several sensitivity analyses to confirm our findings. First, we incorporate the sales-down effect into accrual models other than the modified Jones model to see if our findings are robust to the selection of a base model. Specifically, we incorporate the sales-down binary variable into (1) the original Jones model where the change in revenues is not adjusted for the change in accounts receivable, (2) an advanced version of the modified Jones model which includes book-to-market ratio and cash flows from operations to control for expected growth in the firm s operations and current operating performance, respectively (Larcker and Richardson 2004), and (3) the forward-looking modified Jones model which includes only the unexpected portion of the change in accounts receivable in discretionary accruals and controls for future sales growth and the lagged value of total accruals (Dechow et al. 2003). 7 We also estimate our 7 For the forward-looking modified Jones model, we first regress the change in accounts receivable on the change in sales revenue for each two-digit SIC-year group as follows: ΔAR t = α + k ΔREV t + ε t, 16

17 main regression model (without fixed effects) individually for each of the two-digit SIC industry-year groups with at least 10 observations instead of using a panel regression. In a further check, we define the dummy for decreasing sales based on sales change adjusted for accounts receivable change instead of unadjusted sales change (i.e., DEC t = 1 if ΔREV t ΔAR t < 0). Untabulated results show that our findings are robust to these alternative specifications. We also conducted spline regression analysis (Greene 2012, Chapter 6) to verify the robustness of the non-linear relation estimated in our principal models (see Figure 2) Bias in Estimating Discretionary Accruals We depict in Figure 1 the relation between expected total (non-discretionary) accruals and the magnitude of sales change estimated with both the modified Jones model and the asymmetric accruals expectation model. 8 Figure 2 displays a similar relation estimated using spline regression analysis. As discussed earlier, the expected accruals estimated from the modified Jones model is a linear function of sales change, based on the estimation result reported in Column (1) of Table 5. In contrast, the non-discretionary (or normal) accruals estimated from the asymmetric accruals expectation model exhibit a piece-wise relation between nondiscretionary accruals and revenue change, based on the estimation results in Column (2) of Table 5. When sales increase, non-discretionary accruals are weakly and negatively associated where k captures the expected change in accounts receivable for a given change in sales. In the accrual estimation, we subtract the full amount of the change in accounts receivable and add back the expected change (which is k multiplied by the change in sales) as follows: TACC t = β 0 + β 1 ((1+k)ΔREV t ΔAR t ) + β 2 DEC t + β 3 ((1+k)ΔREV t ΔAR t ) DEC t + β 4 PPE t + β 5 TACC t-1 + β 6 GR_SALES t + Year/Industry Fixed Effects + ε t, where GR_SALES t is the future sales growth (which is the change in sales in year t+1 scaled by sales in year t). 8 The graphs in Figure 1 are obtained by inserting the mean values of 1/ASSET t-1, PPE t, and year/industry dummies into the regression results shown in Columns (1) and (2) of Table 5.The range of x-axis values shown in Figure 1 is approximately between the 5th and 95th percentiles of the x-variable, REV A/R. 17

18 with sales change. However, when sales decline, non-discretionary accruals are positively associated with sales change. [FIGURES 1, 2] Figures 1 and 2 show that the modified Jones model underestimates (overestimates) discretionary accruals when there is a large increase or decrease in sales (a small change in sales), compared with those estimated from the asymmetric accruals expectation model. Statistical evidence is consistent with the implication of Figures 1 and 2. Discretionary accruals estimated with the modified Jones model (DACC MJ ) are significantly (p < 0.01) lower for firms in the bottom two deciles (mean = ) or the top decile (mean = ) of sales growth compared to those for the other seven deciles (mean = ). 3. Simulation Analysis of Bias in Discretionary Accruals 3.1. Test of Type I Error Rates for Discretionary Accrual Measures The non-linear relation between expected accruals and the magnitude of sales change implies that an earnings management test based on the modified Jones model will be misspecified in a systematic and predictable manner. For firms with a relatively large (positive or negative) change in sales, the modified Jones model will underestimate discretionary accruals and work against finding income-increasing earnings management. That is, for the null hypothesis of zero discretionary accruals, the alternative hypothesis of positive discretionary accruals is more likely to be rejected while the alternative hypothesis of negative discretionary accruals is more likely to be supported. In contrast, for firms with a relatively small change in 18

19 sales, the modified Jones model will overestimate discretionary accruals and more likely to find income-increasing earnings management. The alternative hypothesis of positive discretionary accruals is more likely to be supported, while the alternative hypothesis of negative discretionary accrual is more likely to be rejected. To test our prediction, we perform a Monte Carlo simulation experiment to examine Type I error rates of earnings management test based on the modified Jones model by the following steps: 1) Observations in the sample are organized into 10 portfolios based on sales growth, where decile 10 consists of firms with highest sales growth. 9 2) From each sales growth decile, 100 observations are randomly selected. 3) The null hypothesis of no earnings management is tested at the 5% level against each of the alternative hypotheses of income-increasing and income-decreasing earnings management after estimating discretionary accruals as residuals from the modified Jones model. 4) As in Kothari, Leone and Wasley (2005), steps 2 and 3 are repeated 250 times. 5) For each earnings management test, the rate of rejection of the null hypothesis (i.e., Type I error rate) is calculated Simulation Results The results of the simulation experiment are shown in Table 6. The evidence is consistent with our predictions on how bias in estimating discretionary accruals using the modified Jones model is related to sales change. For the test of the null hypothesis with the alternative 9 Sales growth is defined as REV t / REV t-1. 19

20 hypothesis of positive discretionary accruals (income-increasing earnings management), the rates of rejection of the null hypothesis of zero discretionary accruals are higher in the middle sales growth deciles where we predict that discretionary accruals are overestimated and lower in the extreme sales growth deciles where discretionary accruals are underestimated. The Type I error rates for positive discretionary accruals presented in Panel A of Table 6 show that the rejection rates are substantially greater than the 5% normal rejection rate in the middle deciles (Deciles 3 to 9) and are close to zero in the extreme deciles (Deciles 1 and 10). For the test of the null hypothesis against the alternative hypothesis of negative discretionary accruals (income-decreasing earnings management), the rejection rates are lower in the middle deciles where discretionary accruals are predicted to be overestimated and higher in the extreme deciles where discretionary accruals are underestimated using the modified Jones model. The Type I error rates for negative discretionary accruals presented on Panel B of Table 6 show that the rejection rates are significantly greater than the 5% normal rejection rate in the two extreme deciles (Deciles 1 and 10) and are close to zero in the middle deciles (Deciles 3 to 9). We graphically summarize the simulation results in Figure 3. [TABLE 6] [FIGURE 3] Next, we examine whether the model misspecification problem is mitigated when the relation between expected accruals and sales growth is incorporated in the estimation of discretionary accruals. To control for the omitted variable bias, we employ two approaches: First, as in Das et al. (2011), Francis and Michas (2013) and Hoi et al. (2013), we include the sales growth in the accruals expectation model as a control variable. Second, we use the matching 20

21 approach of Kothari et al. (2005) because the relation between expected accruals and sales growth is non-linear. For discretionary accruals estimated using the modified Jones model for each firm-year observation, we subtract the discretionary accruals of the firm with the closest sales growth in the same two-digit SIC industry and fiscal year to obtain discretionary accruals matched on sales growth. The results (also in Table 6) show that simply adding a linear control for sales growth to the modified Jones model does not result in an improvement. 10 However, the rejection rates are much closer to the 5% nominal rejection rate with performance matching, suggesting that matching on sales growth mitigates the misspecification problem of the modified Jones model. We also examine whether the misspecification problem is mitigated by matching on ROA (Kothari et al. 2005) which is widely used in recent studies. Interestingly, the results (also in Table 6) show that the bias is mitigated to a considerable extent when discretionary accruals are matched on ROA, perhaps because deciles of ROA are significantly correlated (r = 0.24, p < 0.01) with deciles of sales growth. 11 The mean absolute deviation from the 5% benchmark to test for positive discretionary accruals over the ten deciles is 33.7% for the modified Jones model (with or without linear control for sales growth) but only 2.1% for performance matching on ROA and 1.6% for matching on sales growth. For tests of negative discretionary accruals, the mean absolute deviations are 12.3%, 4.6% and 1.1%, respectively. 10 Discretionary accruals estimated using the modified Jones model with a control for sales growth are highly correlated with those based on the modified Jones model without a control for sales growth (r = 0.99, p < 0.01), and the rejection rates for the two discretionary accrual measures are almost identical to each other. 11 However, the results also show that the rejection rates matching on ROA are relatively lower (higher) in the middle deciles and higher (lower) in the extreme deciles for the positive (negative) earnings management test although the variations are much smaller in magnitude compared to the rejection rates before matching, suggesting that matching on ROA tends to overcorrect the misspecification problem of the modified Jones model. 21

22 4. Implications of Bias in Estimating Discretionary Accruals on Detecting Earnings Management 4.1. Sales Volatility Hribar and Nichols (2007, Table 2) report a significant negative correlation between sales volatility and signed discretionary accruals estimated using the modified Jones model. However, to our knowledge, no study has explored the reason for the negative correlation. 12 As there is no obvious economic reason to expect a negative relation between sales volatility and signed discretionary accruals, we consider the possibility that the negative relation is driven by the systematic bias we document in estimating discretionary accruals using the modified Jones model. As discussed earlier, the modified Jones model underestimates (overestimates) discretionary accruals when firms experience extreme (moderate) sales changes and therefore works against (for) finding positive discretionary accruals. Since low sales volatility implies that extreme sales changes are less likely to be realized, positive discretionary accruals (leading to inference of income-increasing earnings management) are more likely to be estimated for firms with low sales volatility when using the modified Jones model. To test our prediction, we define sales volatility (VOLATILITY) as the standard deviation of sales revenue for each firm and examine its relation with discretionary accruals (DACC MJ ) estimated using the modified Jones model. 13 The Pearson correlation between DACC MJ and VOLATILITY is significant and negative (-0.025, p < 0.01), consistent with our prediction. The (untabulated) univariate t-test result shows that firms in the high sales volatility tercile exhibit 12 Since sales volatility was not their focus, Hribar and Nichols (2007) simply report the negative relation between sales volatility and signed discretionary accruals in the descriptive statistics for their sample, but do not provide an economic reason. 13 Firms with fewer than 5 observations are excluded from the sample. 22

23 significantly (p < 0.01) lower discretionary accruals (mean DACC MJ = ) than firms in the low sales volatility tercile (mean DACC MJ = 0.003), which is also consistent with our prediction. Next, we conduct a simulation experiment to examine Type I error rates for the earnings management test separately for each sales volatility decile. We divide the sample into 10 portfolios based on sales volatility, where decile 10 consists of firms with the highest sales volatility. For each sales volatility decile, we follow the simulation steps described in Section 3. [TABLE 7] The simulation results for discretionary accruals estimated using the modified Jones model are shown in Table 7. The results are consistent with our expectation. Specifically, Panels A and B of Table 7 show that in the Type I error rate for positive earnings management generally decreases as sales volatility increases while the Type I error rate for negative earnings management increases as sales volatility increases. The results suggest that when sales are more volatile, the alternative hypothesis of positive discretionary accruals is less likely to be supported over the null hypothesis of zero discretionary accruals, and the alternative hypothesis of negative discretionary accruals is more likely to be supported. In contrast, when sales are less volatile, the alternative hypothesis of positive discretionary accruals is more likely to be supported, and the alternative hypothesis of negative discretionary accruals is less likely to be supported. Table 7 also shows that the rejection rates are much closer to the 5% nominal rejection rate when matching on sales growth is used, suggesting that incorporating the relation between estimated accruals and sales growth mitigates the misspecification problem of the modified Jones model. Similar to the simulation results using sales growth deciles, matching on ROA also mitigates the bias to a considerable extent, but not as much as when matching on sales growth. 23

24 As before, simply including a linear control for sales growth to the modified Jones model does not adequately mitigate the bias when using that model Firms with Small Losses Dechow et al. (2003) document that similar to firms with small profit, those with small loss also exhibit significantly higher discretionary accruals compared to other firms. Although high discretionary accruals in small profit firms are consistent with firms incentives to manage earnings to avoid a loss (Burgstahler and Dichev 1997), high discretionary accruals in small loss firms are inconsistent with the loss avoidance story. The Dechow et al. results suggest that a kink in the earnings distribution at zero cannot be fully explained by managerial incentives to avoid a loss. However, Dechow et al. do not provide a specific economic explanation for the high discretionary accruals in small loss firms. The bias with the modified Jones model documented in the previous sections suggests the possibility that the Dechow et al. findings are driven by this bias. To obtain deeper insights into the findings of Dechow et al., we replicate their study and compare estimated discretionary accruals for small profit firms, small loss firms, and other firms, separately for firms in the bottom two deciles of sales growth (i.e., firms with a large sales decrease), those in the top decile of sales growth (i.e., firms with a large sales increase), and those in the seven middle deciles of sales growth (i.e., firms with a small sales change). Following Dechow et al., we limit the sample period to the years , and measure discretionary accruals using the cross-sectional forward-looking modified Jones model. 14 For the 14 Results in this section are robust when (1) the sample period is extended to , (2) a panel regression with fixed effects is used instead of a cross-sectional regression, or (3) the modified Jones model is used instead of the forward-looking modified Jones model. 24

25 forward-looking modified Jones model, we first regress the change in accounts receivable on the change in sales revenues for each two-digit SIC-year group measured as: ΔAR t = α + k ΔREV t + ε t, (5) where k captures the expected change in accounts receivable for a given change in sales. In the accruals estimation, we subtract the full amount of the change in accounts receivable and add back the expected change (which is k multiplied by the change in sales) as follows: TACC t = β 0 + β 1 ((1+k)ΔREV t ΔAR t ) + β 2 PPE t + β 3 TACC t-1 + β 4 GR_SALES t + ε t, (6) where GR_SALES t is the future sales growth (which is the change in sales in year t+1 scaled by sales in year t). Firms are classified as small profit (loss) firms if net income scaled by beginning market value of equity is between 0 and 0.01 (-0.01 and 0). Untabulated descriptive statistics show that our replicated sample (n=54,648) is comparable to the original sample (n=47,847) used in Dechow et al. (2003). Results of the discretionary accruals comparison in Table 8 document that overall, both small loss firms and small profit firms exhibit significantly greater discretionary accruals (DACC FWD ) based on the forward-looking modified Jones model compared to the other firms, consistent with Dechow et al. However, the results for each decile group based on sales growth provide a new insight into how the result for the small loss firms is different from the result for the small profit firms. In particular, Panel A of Table 8 shows that the difference in mean discretionary accruals between small loss firms and the others is statistically significant only for firms with a large sales increase or decrease, and not significant for firms in the middle deciles, suggesting that the finding of Dechow et al. (2003) is driven by firms with an extreme sales change. In contrast, Panel B of Table 8 shows that small profit firms exhibit significantly greater discretionary accruals than others for all decile groups based on sales growth, suggesting that the 25

26 previous finding that small profit firms exhibit higher discretionary accruals is relatively well supported even after considering the bias in the estimation of discretionary accruals related to sales growth. In summary, the results reported in this section provide examples of how earnings management tests based on discretionary accruals estimated using Jones-type models are affected by the systematic bias related to sales growth in a non-linear manner. This bias cannot be addressed simply by adding sales growth to a linear model, but performance matching mitigates the bias to a considerable extent. We conclude that research on earnings management should carefully check the robustness of results for different levels of sales growth. [TABLE 8] 5. Conclusion In this paper, we document the asymmetric behavior of accruals with respect to the direction of change in sales. Both asset-side and liability-side components of working capital become less sensitive to sales change when a firm experiences a sales decline. However, accruals related to current liabilities are less sensitive to negative sales shocks than those related to current assets because transactions related to production occur at an earlier stage of the operating cycle and precede sales shocks. As a result, total accruals decrease more steeply with decreasing sales than they increase with increasing sales. We provide robust empirical evidence of such asymmetric behavior of accruals. We also show that the modified Jones model is misspecified in a systematic and predictable manner because it ignores the asymmetry in the relation between accruals and sales 26

27 change. By forcing a linear model on a non-linear relation, the modified Jones model underestimates discretionary accruals when firms experience an extreme sales change and overestimates them when firms experience a moderate sales change. The bias in estimating discretionary accruals implies that tests of discretionary accruals based on the modified Jones model are less likely to support a hypothesis of income-increasing accruals management when firms experience an extreme sales change and more likely to support it when the magnitude of sales change is relatively small. Our simulation study documents that the Type I error rates for positive discretionary accruals are much higher than expected for firms with moderate sales growth while the rates for negative discretionary accruals are much higher than expected for firms with extreme sales growth. We also show that the bias in testing for earnings management using the modified Jones model is substantially mitigated when discretionary accruals are matched on sales growth (or even ROA) to control for the non-linear relation between expected total accruals and sales growth (Kothari et al. 2005). Our study strongly supports the use of performance matching in tests of earnings management when using the modified Jones model. The systematic bias we document in estimating discretionary accruals provides important insights also for other studies of earnings management. While there is no obvious economic reason for any relation between sales volatility and signed discretionary accruals, the systematic bias in estimating discretionary accruals using the modified Jones model implies that estimated discretionary accruals are higher for firms with lower sales volatility that are more likely to exhibit moderate sales growth. We also reexamine Dechow, Richardson and Tuna s (2003) analysis of discretionary accruals by firms with small losses and small profits compared to other firms. We document that, unlike for small profit firms, positive discretionary accruals are 27

28 significant for small loss firms relative to other firms only in the extreme ends of the sales growth distribution. Above all, our study highlights the fact that how accruals behave when there is no earnings management is not yet understood well (Ball 2013). We introduced a step in the direction of developing more dynamic representation of accruals behavior by recognizing the asymmetry of total accruals with how sales change. Ignoring this asymmetry results in significant predictable non-linear bias when estimating discretionary accruals. In untabulated results, we also find similar but smaller non-linearities with respect to other potential determinants of accruals such as ROA, size, earnings growth, earnings yield and market-to-book. Understanding the determinants of accounting accruals and the functional form representing the behavior of accruals presents an important avenue for future research. Until we obtain a more precise understanding of how accruals behave, performance matching seems to be the best alternative for tests of earnings management, but researchers are well-advised to carefully check the robustness of their results for different levels of sales growth. 28

29 REFERENCES Abarbanell, J., and B. Bushee Fundamental analysis, future earnings, and stock prices. Journal of Accounting Research 35(1): Abarbanell, J., and B. Bushee Abnormal returns to a fundamental analysis strategy. The Accounting Review 36(1): Ball, R Accounting informs investors and earnings management is rife: Two questionable beliefs. Accounting Horizons 27(4): Barber, B. M. and J. D. Lyon Detecting abnormal operating performance: The empirical power and specification of test statistics. Journal of Financial Economics 41(3): Barber, B. M. and J. D. Lyon Detecting long-run abnormal stock returns: The empirical power and specification of test statistics. Journal of Financial Economics 43(3): Bernard, V. and J. Noel Do inventory disclosures predict sales and earnings? Journal of Accounting, Auditing & Finance 6(2): Brennan, M., V. Maksimovic, and J. Zechner Vendor financing. Journal of Finance 43: Burgstahler, D., and I. Dichev Earnings management to avoid earnings decreases and losses. Journal of Accounting and Economics 24(1): Cuñat, V Trade credit: Suppliers and debt collectors as insurance providers. Review of Financial Studies 20(2): Danielson, M. G. and J. A. Scott Bank loan availability and trade credit demand. Financial Review 39(4): Das, S., K. Kim, and S. Patro An analysis of managerial use and market consequences of earnings management and expectation management. The Accounting Review 86(6): Dechow, P. M., A.P. Hutton, J. H. Kim, and R. G. Sloan Detecting earnings management: A new approach. Journal of Accounting Research 50(2): Dechow, P. M., R. G. Sloan, and A. P. Sweeney Detecting earnings management. The Accounting Review 70: Dechow, P. M., S. Richardson, and I. Tuna Why are earnings kinky? An examination of the earnings management explanation. Review of Accounting Studies 8: DeFond, M. L., and J. Jiambalvo Debt covenant effects and the manipulation of accruals. Journal of Accounting and Economics 17: Doyle, J., W. Ge, and S. McVay Accruals quality and internal control over financial reporting. The Accounting Review 82(5):

30 Emery, G. W A pure financial explanation for trade credit. Journal of Financial and Quantitative Analysis 19(3): Emery, G. W An optimal financial response to variable demand. Journal of Financial and Quantitative Analysis 22(2): Emery, G. W. and N. Nayar Product quality and payment policy. Review of Quantitative Finance and Accounting 10(3): Ferris, J. S A transactions theory of trade credit use. The Quarterly Journal of Economics 96(2): Francis, J., R. LaFond, P. Olsson, and K. Schipper The market pricing of accruals quality. Journal of Accounting and Economics 39: Francis, J. R., and P. N. Michas The contagion effect of low-quality audits. The Accounting Review 88(2): Gerakos, J. J Discussion of: Detecting Earnings Management: A New Approach. Journal of Accounting Research 50: Greene, W. H Econometric Analysis. 7th edition. Upper Saddle River, NJ: Prentice Hall. Hoi, C. K., Q. Wu, and H. Zhang Is corporate social responsibility (CSR) associated with tax avoidance? Evidence from irresponsible CSR activities. The Accounting Review 88(6): Hribar, P., and D. Collins Errors in estimating accruals: Implications for empirical research. Journal of Accounting Research 40: Hribar, P., and D. C. Nichols The use of unsigned earnings quality measures in tests of earnings management. Journal of Accounting Research: 45: Ikenberry, D., J. Lakonishok, and T. Vermaelen Market underreaction to open market share repurchases. Journal of Financial Economics. 39(2): Jones, J Earnings management during import relief investigations. Journal of Accounting Research 29: Kothari, S. P., A. J. Leone, and C. Wasley Performance matched discretionary accrual measures. Journal of Accounting and Economics 39: Larcker, D. F. and S. A. Richardson Fees paid to audit firms, accrual choices, and corporate governance. Journal of Accounting Research 42(3): Lee, Y. W. and J. D. Stowe Product risk, asymmetric information, and trade credit. Journal of Financial and Quantitative Analysis 28(2). Lev, B., and R. Thiagarajan Fundamental information analysis. Journal of Accounting Research 31:

31 Long, M. S., I. B. Malitz, S. A. Ravid Trade credit, quality guarantees, and product marketability. Financial Management 22: Lyon, J. D., B. M. Barber, and C. L. Tsai Improved methods for tests of long-run abnormal stock returns. The Journal of Finance 54(1): McNichols, M. F Discussion of the quality of accruals and earnings: The role of accrual estimation errors. The Accounting Review 77: Meltzer, A. H Mercantile credit, monetary policy, and size of firms. The Review of Economics and Statistics 42: Ng, C. K., J. K. Smith, and R. L. Smith Evidence on the determinants of credit terms used in interfirm trade. Journal of Finance 54: Petersen, M., and R. Rajan Trade credit: Theory and evidence. Review of Financial Studies 10(3): Pike, R., N. S. Cheng, K. Cravens, and D. Lamminmaki Trade credit terms: asymmetric information and price discrimination evidence from three continents. Journal of Business Finance & Accounting 32(5 6): Sloan, R Do stock prices fully reflect information in accruals and cash flows about future earnings? The Accounting Review 71(3): Smith, J. K Trade credit and informational asymmetry. Journal of Finance 42: Sun, Y Do MD&A disclosures help users interpret disproportionate inventory increases? The Accounting Review 85(4): Wilner, B. S The exploitation of relationship in financial distress: The case of trade credit. Journal of Finance 55:

32 FIGURE 1 Relation Between Total Accruals and Revenue Change Note: The graphs in Figure 1 show the following functions: TACC t = (ΔREV t ΔAR t ) (Modified Jones model); TACC t = (ΔREV t ΔAR t ) (Asymmetric accruals expectation model for sales-up firms); TACC t = (ΔREV t ΔAR t ) (Asymmetric accruals expectation model for sales-down firms) where the functions are obtained by inserting the mean values of 1/ASSET t-1, PPE t, and year/industry dummies into the regression results shown in Columns (1) and (2) of Table 5. Deciles of ΔREV t ΔAR t are shown on the x-axis. 32

33 FIGURE 2 Spline Regression of Total Accruals and Revenue Change Note: Figure 2 shows the five splines of the modified Jones model estimated for each quintile of ΔREV t ΔAR t, where the functional values are obtained by inserting the mean values of 1/ASSET t-1, PPE t, and year/industry dummies into the regression results. Deciles of ΔREV t ΔAR t are shown on the x-axis. 33

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