Researchers frequently use measures of discretionary accruals in tests for earnings management and market efficiency. Following the results in Dechow et al. (1995) and others, the Jones and modified-Jones models are the most popular choices for estimating discretionary accruals. However, previous research shows that both the Jones and modified-Jones models are
severely misspecified when applied to non-random samples of firms (e.g., Dechow et al. 1995 and Guay et al. 1996). Dechow et al. (1995) conclude that all models of discretionary accruals exhibit low power.
We find that the Jones and modified-Jones models reject the null hypothesis excessively in non-random samples and that adjusting the discretionary accruals of these models by the industry mean or median accrual does not improve their performance. On the other hand, tests using performance-matched measures of discretionary accruals are both well specified and quite powerful. We present detailed simulation evidence on the properties of alternative measures of discretionary accruals based on random and non-random samples. We also examine the properties of discretionary accrual models over multi-year horizons and their sensitivity to sample size. Under all circumstances, performance-matched discretionary accrual models are quite well specified and exhibit substantial power. Although a small degree of misspecification using the performance-matched discretionary accrual models in some non-random samples is observed, on balance, performance-matched models are the most reliable from sample-to-sample in terms of Type I error rates and power of the test.
Our study has important implications for future research using measures of discretionary accruals. Adjusting discretionary accruals for the discretionary accruals of another firm matched on the basis of prior performance appears essential to mitigate the concern of misspecification, and therefore spurious rejection of (or failure to reject) the null hypothesis. The results also suggest that use of modified-Jones model adds little to the Jones model so long as performance- matched Jones model discretionary accruals are used.
Our study has at least three limitations. First, we ignore the consequences of the error embedded in estimated total accruals (and therefore in discretionary accruals) as a result of using the balance-sheet approach to estimating total accruals. Collins and Hribar (2000) show that the error in estimated accruals using the balance-sheet approach is correlated with firms’ economic
characteristics. Therefore, the error not only reduces the discretionary accrual models’ power to detect earnings management, but also has the potential to generate incorrect inferences about earnings management. An interesting extension of our study would be to measure total accruals using the balance sheet approach advocated in Collins and Hribar (2000).
Second, while we simulate several event conditions (e.g., multi-year performance, sample size, and various non-random samples), our results may not generalize to research settings that we don’t examine. In addition, we have made certain research design choices like cross- sectional within-industry estimation of the Jones and modified-Jones models, and re-estimation of the models each year as we examine a multi-year horizon that may not be appropriate in all accounting research settings.
Finally, while we find that tests using performance-matched measures do not over-reject the null of zero discretionary accruals even in non-random samples, we cannot be sure that this necessarily indicates that the tests are well specified. Accounting theory suggests non-random sample firms likely engage in earnings management. Therefore, powerful tests should reject the null hypotheses in non-random samples. Performance-matched accrual measures inform whether the extent of discretionary accruals in non-random samples exceeds that in matched samples with similar performance characteristics except the treatment event.
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Table 1
Descriptive statistics for discretionary accrual measures
Panel A reports mean, standard deviation, lower quartile, median and upper quartile values for the entire sample. Panel B reports means and medians for non-random samples formed on the basis of book-to-market ratio, prior year sales growth, earnings-to- price (EP) ratio and firm size (market value of equity). The values reported in Panel B are based the lower and upper quartiles of the variable used to partition the overall sample into the non-random samples which are formed on the basis of select financial characteristics (book/market, past sales growth, etc.). The performance-matched discretionary accrual measures are constructed by precision matching each treatment firm with a control firm based on return on assets in period t-1. Firm-year accrual observations are constructed from the COMPUSTAT Industrial Annual and Research files from 1959 through 1998. We exclude observations if they do not have sufficient data to construct the accrual measures described below or if the absolute value of total accruals scaled by total assets is greater than one. We eliminate observations where there are fewer than ten observations in a two-digit industry code for a given year and we also eliminate observations after 1993 because we examine accruals over a five-year horizon. All discretionary accrual measures are reported as a percent of total assets and all variables are winsorized at the 1st and 99th percentiles. The final sample size is 100,657.
Panel A. Descriptive Statistics for Discretionary Accrual Measures:a
Description Mean STD Q1 Med Q3
Total Accruals -2.78 11.68 -8.16 -3.27 2.12
Jones Model -0.32 10.08 -4.70 -0.08 4.17
Modified Jones Model -0.24 10.44 -4.79 -0.09 4.31
Jones Model with ROA -0.36 9.71 -4.73 -0.20 4.01
Modified Jones Model with ROA -0.27 10.04 -4.80 -0.21 4.12
Discretionary Current Accruals Model 0.04 9.80 -4.11 -0.03 4.04
Performance-Matched Jones Model -0.17 14.07 -6.74 -0.03 6.46
Panel B. Means (Medians) of Discretionary Accrual Measures for Non-Random Sub-Samples:a
Book/Market Past Sales
Growth
E/P Ratio Size
Description Value Growth High Low High Low Large Small
-4.16 -1.66 -0.42 -5.58 -1.59 -6.92 -2.99 -4.42 Total Accruals (-3.89) (-2.33) (-1.67) (-5.07) (-2.49) (-6.52) (-3.56) (-4.27) -1.02 -0.04 0.68 -1.81 0.66 -2.86 0.02 -1.48 Jones Model (-0.46) (0.06) (0.52) (-1.03) (0.44) (-2.11) (0.10) (-0.96) -1.14 0.27 1.12 -2.02 0.72 -3.06 0.11 -1.61
Modified Jones Model
(-0.54) (0.23) (0.73) (-1.2) (0.45) (-2.29) (0.09) (-1.05)
-0.81 0.00 0.42 -1.30 0.14 -1.65 -0.36 -1.02
Jones Model with ROA
(-0.33) (-0.19) (0.25) (-0.73) (0.15) (-1.14) (-0.16) (-0.68)
-0.89 0.33 0.83 -1.42 0.13 -1.67 -0.30 -1.07
Modified Jones Model with ROA
(-0.4) (-0.04) (0.43) (-0.86) (0.09) (-1.17) (-0.18) (-0.8)
-0.98 0.73 1.17 -1.43 0.84 -2.21 0.15 -0.99
Discretionary Current Accruals (DCA)
(-0.6) (0.42) (0.64) (-0.87) (0.37) (-1.65) (-0.01) (-0.76)
-0.39 0.01 0.41 -0.73 0.09 -0.85 -0.37 -0.59
Performance-Matched Jones Model
(-0.13) (0.07) (0.36) (-0.51) (0.00) (-0.65) (-0.08) (-0.39)
-0.50 0.15 0.68 -0.90 -0.01 -0.89 -0.43 -0.71
Performance-Matched Modified Jones
Model (-0.24) (0.13) (0.51) (-0.62) (0.00) (-0.71) (-0.11) (-0.51)
a
Total Accruals (TAit) is defined as the change in non-cash current assets minus the change in current liabilities excluding the current portion of long-term debt minus depreciation and amortization [with reference to COMPUSTAT data items, TA = (∆Data4 - ∆Data1 - ∆Data5 + ∆Data34 - Data14)/lagged Data6]. Cross sectional within-industry discretionary accruals are the residuals from the Jones, modified-Jones model, Jones model including lagged ROA and modified-Jones model including lagged with ROA, respectively. Discretionary accruals from the Jones model are estimated for each industry and year as follows: TAi,t=α0/ASSETSi,t-1 +α1∆SALESi,t+α2PPEi,t+εi,t , where ∆SALESi,t is change in sales scaled by lagged total assets and PPEi,t is net property, plant and equipment scaled by lagged assets. Discretionary accruals from the modified-Jones model are estimated for each industry and year as for the Jones model except that the change in accounts receivable is subtracted from the change in sales. Discretionary accruals from the Jones Model (Modified-Jones Model) with ROA are similar to the Jones Model (Modified-Jones Model) except for the inclusion of lagged ROA as an additional explanatory variable in the model.
Discretionary Current Accruals (DCA) are estimated as in Teoh et al. (1998a) and are based on the following model estimated by industry and year: TA_NODEPit=β0/ΑSSETSit-1 + β1∆SALESit+eit, where TA_NODEPit is total accruals excluding depreciation expense. Using the estimated parameters of this model, Nondiscretionary accruals are calculated as: NDAit =
β0/ΑSSETSit-1 + β1(∆SALESit-∆ARit). Discretionary Current Accruals are equal to TA_NODEPit - NDAit. To measure performance matched discretionary accruals, we precision match firms in period t-1 based on return-on-assets. To calculate a performance-matched Jones model (Modified-Jones model) discretionary accrual for firm i we subtract the Jones model (Modified-Jones model) discretionary accrual of the firm with the closest return-on-assets in the same industry as firm i.
Serial correlation in return on assets (ROA), total accruals and discretionary accrual measures for the entire sample and non- random subsaples of firms from 1959-1993
The table reports the mean value of the slope coefficient of the following annual regression: Xit = α + βXit-1 + εit, where Xit (Xit-1) is the value (lagged value) of the particular variable of interest. Xit is ROA, Total Accruals, Jones Model Discretionary Accruals, Modified-Jones Model Discretionary Accruals, Performance- Matched Jones Model Accruals or Performance-Matched Modified-Jones Model Accruals. Results are reported for the full sample (all firms) and non-random samples based on select financial performance measures (e.g., book-to-market, past sales growth, earnings-to-price ratio and firm size). The performance-matched discretionary accrual measures are constructed by precision matching each treatment firm with a control firm based on return on assets in period t-1. Firm-year accrual observations are constructed from the COMPUSTAT Industrial Annual and Research files from 1959 through 1998. We exclude observations if they do not have sufficient data to construct the accrual measures described below or if the absolute value of total accruals scaled by total assets is greater than one. We eliminate observations where there are fewer than ten observations in a two-digit industry code for a given year and we also eliminate observations after 1993 because we examine accruals over a five-year horizon. All variables are winsorized at the 1st and 99th percentiles. The final sample size is 100,657.
All Firms Book/Market Past Sales Growth E/P Ratio Size
Descriptiona Value Growth High Low High Low Large Small
ROA 0.687 ** 0.674 ** 0.669 ** 0.661 ** 0.628 ** 0.621 ** 0.568 ** 0.761 ** 0.600 **
Total Accruals 0.161 ** 0.061 ** 0.197 ** 0.173 ** -0.010 0.102 ** -0.002 0.279 ** 0.077 **
Jones Model Accruals -0.001 -0.053 ** 0.033 0.028 -0.071 * -0.074 ** -0.115 0.105 ** -0.055 **
Modifed Jones Model Accruals 0.018 * -0.042 * 0.058 * 0.043 ** -0.052 * -0.061 ** -0.133 0.121 ** -0.035 *
Performance-Matched Jones -0.019 ** -0.016 -0.008 -0.006 -0.077 ** -0.056 ** -0.041 0.025 -0.039 *
Perfomance-Matched Modified Jones -0.012 * -0.006 0.002 0.000 -0.064 ** -0.046 * -0.036 0.026 -0.028
a
Return on Assets (ROA) is net income (COMPUSTAT data item 18) scaled by lagged total assets. Total accruals is defined as the change in non-cash current assets minus the change in current liabilities excluding the current portion of long-term debt minus depreciation and amortization [with reference to COMPUSTAT data items, TA = (∆Data4 - ∆Data1 - ∆Data5 + ∆Data34 - Data14)/lagged Data6].
Cross sectional within-industry discretionary accruals are the residuals from the Jones and modified Jones models, respectively. Discretionary accruals from the Jones model are estimated for each industry and year as follows: TAi,t=α0/ASSETSi,t-1 +α1∆SALESi,t+α2PPEi,t+εi,t , where TAit (Total Accruals) is as defined above,
∆SALESi,t is change in sales scaled by lagged total assets (ASSETSi,t-1), and PPEi,t is net property, plant and equipment scaled by ASSETSi,t-1. Discretionary accruals from the modified-Jones model are estimated for each industry and year as for the Jones model except that the change in accounts receivable is subtracted from the change in sales.
For performance matched discretionary accruals, we precision match in period t-1 based on return-on-assets. To obtain a performance-matched Jones model discretionary accrual for firm i we subtract the Jones model discretionary accrual of the firm with the closest ROA that is in the same industry as firm i. A similar approach is used for the modified Jones model.
Type I error rates of discretionary accrual measures for the full sample and upper and lower quartiles of non-random samples formed on the basis of financial characteristics [book-to-market ratio, sales growth over the prior year, earnings-to-price (EP) ratio and firm size (market value of equity)]
The table reports the percentage of 250 samples of 100 firms each where the null hypothesis of zero discretionary accruals is rejected at the 5% level (upper and lower one- tailed tests). The significance of the mean discretionary accrual in each of the 250 random samples is based on a cross-sectional t-test. The performance-matched discretionary accrual measures are constructed by precision matching each treatment firm with a control firm based on return on assets in period t-1. Firm-year accrual observations are constructed from the COMPUSTAT Industrial Annual and Research files from 1959 through 1998. We exclude observations if they do not have sufficient data to construct the accrual measures described below or if the absolute value of total accruals scaled by total assets is greater than one. We eliminate observations where there are fewer than ten observations in a two-digit industry code for a given year and we also eliminate observations after 1993 because we examine accruals over a five- year horizon. All variables are winsorized at the 1st and 99th percentiles. The final sample size is 100,657.
Panel A. Accruals over one year:a HA: Accruals < 0
HA: Accruals > 0
Book/ Market
Sales
Growth EP Ratio Size
Book/ Market
Sales
Growth EP Ratio Size All
Firms Value Growth High Low High Low Large Small All
Firms Value Growth High Low High Low Large Small
Jones Model:
Cross sectional within-industry Jones model 7.2 33.2 6.4 2.0 53.6 0.4 72.8 3.6 34.0 2.4 0.4 5.2 13.2 0.0 21.6 0.0 4.8 0.4
Industry median adjusted discretionary accruals
6.8 31.2 5.2 2.0 49.6 0.8 69.6 4.0 30.0 2.4 0.4 6.4 12.8 0.0 20.8 0.0 4.8 0.4
ROA included in accrual estimation equation 9.6 22.0 8.4 2.4 32.4 4.4 40.4 18.4 24.4 2.0 0.8 7.6 10.8 0.0 7.6 0.0 0.0 0.8
Performance matched discretionary accruals 8.0 6.0 4.0 2.4 10.8 5.2 6.8 12.8 8.8 3.6 4.0 7.6 4.4 0.8 4.0 2.8 3.6 3.6
Modified Jones Model:
Cross sectional within-industry Jones model 5.2 36.8 4.0 0.8 58.4 0.0 76.8 2.4 35.6 2.8 0.4 6.8 19.6 0.0 23.2 0.0 6.0 0.4
Industry median adjusted discretionary accruals
4.8 36.0 3.6 0.4 52.8 0.4 72.4 2.8 32.4 4.0 0.4 10.0 21.6 0.0 21.6 0.0 6.0 0.4
ROA included in accrual estimation equation 8.0 24.0 6.0 1.2 35.2 4.4 39.6 15.6 22.8 3.2 0.8 12.0 14.8 0.0 7.6 0.0 0.4 0.8
Panel B. Accruals over three years:a H A: Accruals < 0 HA: Accruals > 0 Book/ Market Sales
Growth EP Ratio Size
Book/ Market
Sales
Growth EP Ratio Size
All
Firms Value Growth High Low High Low Large Small All
Firms Value Growth High Low High Low Large Small
Jones Model:
Cross sectional within-industry Jones model 10.8 9.2 10.0 12.4 21.6 5.2 30.8 10.0 12.4 1.2 2.0 2.4 2.0 1.6 6.8 0.0 2.8 2.8
Industry median adjusted discretionary accruals 10.8 9.2 9.2 11.2 21.2 6.8 27.6 10.4 11.2 1.6 2.0 4.0 2.4 2.0 5.2 0.4 2.8 2.8
ROA included in accrual estimation equation 11.2 9.6 13.6 14.4 14.8 10.0 18.0 26.0 8.4 1.6 2.8 1.2 1.2 2.0 2.0 0.8 0.0 4.0
Performance matched discretionary accruals 5.6 3.2 5.2 4.4 4.4 6.0 6.0 6.0 2.8 6.8 5.6 6.4 4.8 6.8 4.8 3.2 3.2 7.2
Modified-Jones Model:
Cross sectional within-industry Jones model 10.8 9.2 8.8 10.4 25.6 5.2 33.6 11.2 11.6 1.6 2.0 3.6 2.0 2.0 6.4 0.0 2.8 1.6
Industry median adjusted discretionary accruals 8.4 9.2 7.6 10.0 24.8 6.0 28.4 10.4 10.4 1.2 2.0 4.0 2.4 2.4 6.0 0.0 3.2 1.6
ROA included in accrual estimation equation 11.2 9.2 11.6 11.2 16.8 9.6 17.6 25.2 7.6 2.8 3.2 1.2 1.2 2.0 2.0 0.8 0.0 4.4
Performance matched discretionary accruals 6.0 3.6 5.2 4.4 6.0 6.0 5.6 7.2 2.8 6.0 6.0 6.4 4.8 5.2 4.0 3.6 2.8 6.4
Panel C. Accruals over five years:a
Jones Model:
Cross sectional within-industry Jones model 15.2 6.0 16.4 18.8 17.2 11.6 19.6 16.8 13.2 1.6 2.8 2.4 1.6 1.2 1.6 0.4 0.8 0.8
Industry median adjusted discretionary accruals 12.4 6.8 14.4 18.0 13.2 10.0 15.6 14.8 12.4 2.0 3.6 3.2 1.6 1.6 1.6 1.2 0.8 1.6
ROA included in accrual estimation equation 12.4 9.6 21.6 25.2 16.4 10.8 16.4 28.8 11.6 1.2 2.0 0.0 1.2 1.6 2.0 0.8 0.0 0.8
Performance matched discretionary accruals 5.2 3.2 4.8 5.6 8.0 7.6 6.0 6.0 4.0 3.2 4.4 4.8 3.6 2.0 4.4 5.6 2.8 6.4
Modified-Jones Model:
Cross sectional within-industry Jones model 15.6 6.4 15.2 16.8 17.6 11.2 20.4 20.4 14.0 1.6 2.0 3.2 1.6 0.8 2.0 0.8 0.4 0.8
Industry median adjusted discretionary accruals 13.6 7.2 12.0 15.2 16.8 8.4 15.2 16.4 12.0 2.4 3.2 4.0 2.0 1.2 1.2 1.6 0.4 1.2
ROA included in accrual estimation equation 10.8 9.6 20.4 20.4 16.0 12.0 12.8 30.8 12.0 1.6 2.0 0.0 2.0 0.8 2.0 0.8 0.0 1.2
a
Cross sectional within-industry discretionary accruals are the residuals from the Jones and modified Jones models, respectively. Discretionary accruals from the Jones model are estimated for each industry and year as follows: TAi,t=α0/ASSETSi,t-1 + α 1∆SALESi,t+ α2PPEi,t+εi,t , where TAit (Total Accruals) is defined as the change in non- cash current assets minus the change in current liabilities excluding the current portion of long-term debt minus depreciation and amortization [with reference to COMPUSTAT data items, TA = (∆Data4 - ∆Data1 -∆Data5 + ∆Data34 - Data14)/lagged Data6], ∆SALESi,t is change in sales scaled by lagged total assets (ASSETSi,t-1), and PPEi,t is net property, plant and equipment scaled by ASSETSi,t-1. Discretionary accruals from the modified-Jones model are estimated for each industry and year as for the Jones model except that the change in accounts receivable is subtracted from the change in sales. Discretionary accruals from the Jones Model (Modified-Jones Model) with ROA are estimated similar to the Jones Model (Modified-Jones Model) except for the inclusion of lagged ROA as an additional explanatory variable in the accruals regression.
For performance matched discretionary accruals, we precision match in period t-1 based on return-on-assets. To obtain a performance-matched Jones model discretionary accrual for firm i we subtract the Jones-model discretionary accrual of the firm with the closest return-on-assets that is in the same industry as firm i. Both the sample and control firm must survive for five subsequent years to be included in the sample.
Table 4
A comparison of the power of the discretionary accrual models to detect abnormal accruals when they have been seeded into the data
For each sample the indicated seed level is simply added to the mean discretionary accrual of the sample. The table reports the percentage of 250 samples of 100 firms each where the null hypothesis of zero discretionary accruals is rejected at the 5% level (upper and lower one-tailed tests). The significance of the mean discretionary accrual of each of the 250 random samples is based on a cross-sectional t-test. The performance-matched discretionary accrual measures are constructed by precision matching each treatment firm with a control firm based on return on assets in period t-1. Firm-year accrual observations are constructed from the COMPUSTAT Industrial Annual and Research files from 1959 through 1998. We exclude observations if they do not have sufficient data to construct the accrual measures described below or if the absolute value of total accruals scaled by total assets is greater than one. We eliminate observations where there are fewer than ten observations in a two-digit industry code for a given year and we also eliminate observations after 1993 because we examine accruals over a five-year horizon. All variables are winsorized at the 1st and 99th percentiles. The final sample size is 100,657.
Panel A. HA: Accruals < 0:
Book/
Market Sales EP Ratio Size
Seeded Abnormal
Accrual All Firms
Value Growth High Low High Low Large Small
Jones Model: a
-1% 21.2 21.2 13.6 10.4 23.2 20.8 16.0 41.2 14.4
-2% 43.2 44.0 34.8 29.2 45.6 49.6 33.2 76.8 32.4
Performance matched discretionary accruals
-4% 88.0 92.0 78.8 72.0 86.4 91.2 74.8 98.8 74.8
-1% 18.8 20.4 18.8 12.8 32.0 20.0 18.8 43.6 18.0
-2% 44.8 50.0 36.0 32.4 52.8 50.8 37.6 78.0 35.6
Performance matched discretionary accruals