By Tim Keefe ,CFA (Contact Author | Biography)
Using the raw accrual amounts as a proxy for earnings management is a simple method to evaluate earnings quality because firms can have high accruals for legitimate business reasons, such as sales growth. A more complicated proxy can be created by attempting to categorize total accruals into nondiscretionary and discretionary accruals. The nondiscretionary component reflects business conditions (such as growth and the length of the operating cycle) that naturally create and destroy accruals, while the discretionary component identifies management choices. The result of pulling discretionary accrual amounts from the total accrual amount is a metric that reflects accruals that are due to management's choices alone; in other words, there appears to be no business reason for these accruals. So, discretionary accruals are a better proxy for earnings quality.
There are many approaches used in an attempt to estimate this nondiscretionary accrual proxy, but estimating the nondiscretionary component of accruals typically involves a regression model. Identifying discretionary accruals by regression can be difficult in practice, and different approaches differ in practically every respect: how to measure the dependent variable (total net accruals or net operating accruals), what to use as independent variables and whether to use a cross-sectional model or a time-series model.
Measuring the Dependent Variable
Either total net accruals or net operating accruals can be used as the dependent variable. Recall from above that we have defined both of these dependent variables from the cash flow statement as:
And
Many studies have used the balance sheet to calculate total net accruals or net operating accruals, but due to non-articulation issues, the cash-flow approach is better suited to describing accruals in all situations, and we will not detail how to calculate accruals from balance sheet data here.
Choosing Independent Variables
The independent variables are data items that should have some relationship to nondiscretionary accruals. For example, normal accruals driven by sales, PP&E, expected sales growth and current operating performance. A simple (and one of the most commonly used) model to estimate the nondiscretionary accrual component is the Modified Jones Model (1991). It may or may not be the best model. It surely isn't perfect, but other variables can be added to the equation in an attempt to increase the model's precision. In addition, a fourth variable such as the life-cycle score may capture relationships in total net accruals or operating net accruals that the current three variables in the regression fail to capture. The model can be represented as follows:
Or
Where:
TNA= Total net accruals
NOA= Net operating accruals
ATA = Average total assets
ΔSales = Change in sales
ΔRec= Change in accounts receivable
GPPE = Gross PP&E
Each β is the estimated relationship of the independent variable to the dependent variable, and the error term represents the composite effect of all variables not explicitly stated as an independent variable.
Using Cross-Sectional or Time-Series
The model can be employed by regressing accrual data from many firms in the same industry for one time period (cross-sectional) or by regressing accrual data from the same firm across several time periods (time-series). There are disadvantages to both methods, but the cross-sectional analysis is probably a better method for the following technical reasons:
If any of these issues above is true, it is impossible to make valid statistical inferences from the regression results obtained with time-series analysis.
Time-Series Analysis
To estimate the nondiscretionary accrual amounts, firm-specific amounts for each independent variable are used for each period/year over a sequence of periods/years. In essence, think of each data item [(TNA / ATA), (1/ATA),(ΔSales – ΔRec / ATA) and (GPPE / ATA )] as coming from the same firm, with each data set being from a different time period. For example, the data set might be one firm with accounting data from each year between 1977 and 2007.
The error term, ε, is the estimate of discretionary accruals. This discretionary accrual estimate for the firm can then be used to rank the firm with respect to its peers and all other firms in the universe. A high level of discretionary accruals relative to peers would indicate that earnings quality is relatively low. Meanwhile, a low level of discretionary accruals would indicate that earnings quality is relatively high.
Cross-Sectional Analysis
In a cross-sectional analysis, the model is a two-stage model. This means that results from the first part of the analysis are plugged into the next stage to get the needed estimate.
To estimate the nondiscretionary accrual amounts, firm-specific amounts for each independent variable are used for a particular period across several different firms. In essence, think of each data item [(TNA / ATA), (1/ATA),(ΔSales – ΔRec / ATA) and (GPPE / ATA )] as coming from the same time period with the next data set being from a different firm. For example, the data set might be 45 different firms with accounting data for the year ending 2007.
Once β0, β1, β2 and β3 have been estimated for the cross-section of firms for the period (which is calculated by the computer running a regression equation), we have denoted these estimates as β0, β 1, β 2, β 3. Use these cross-sectional coefficients along with a specific firm's data to estimate the individual firm's nondiscretionary accruals for the period. After processing, the calculation results in an estimate for nondiscretionary accruals scaled by average total assets, represented by NDA / ATA below.
Total discretionary accruals are the difference between the individual firm's scaled total net accruals and its estimated total nondiscretionary accrual amount.
If, instead, the regression is run with net operating accruals as the dependent variable, the equations would yield an estimate for just the operating component of nondiscretionary accruals.
The discretionary-accrual estimate for the firm, whether it is based on total net accruals or net operating accruals, can then be ranked against the discretionary accrual estimates of the firm's peers and all other firms in the universe. This ranking is a comparative measure of the size of discretionary accruals, and it is a proxy for the quality of the firm's earnings. A high amount of discretionary accruals indicates lower-quality earnings and is a red flag that management may be using aggressive accounting to overstate earnings.
Earnings Quality: Conclusion
Using the raw accrual amounts as a proxy for earnings management is a simple method to evaluate earnings quality because firms can have high accruals for legitimate business reasons, such as sales growth. A more complicated proxy can be created by attempting to categorize total accruals into nondiscretionary and discretionary accruals. The nondiscretionary component reflects business conditions (such as growth and the length of the operating cycle) that naturally create and destroy accruals, while the discretionary component identifies management choices. The result of pulling discretionary accrual amounts from the total accrual amount is a metric that reflects accruals that are due to management's choices alone; in other words, there appears to be no business reason for these accruals. So, discretionary accruals are a better proxy for earnings quality.
There are many approaches used in an attempt to estimate this nondiscretionary accrual proxy, but estimating the nondiscretionary component of accruals typically involves a regression model. Identifying discretionary accruals by regression can be difficult in practice, and different approaches differ in practically every respect: how to measure the dependent variable (total net accruals or net operating accruals), what to use as independent variables and whether to use a cross-sectional model or a time-series model.
Measuring the Dependent Variable
Either total net accruals or net operating accruals can be used as the dependent variable. Recall from above that we have defined both of these dependent variables from the cash flow statement as:
| Total Net Accruals = Net Income - ΔCash - Cash Dividends - Stock Repurchases + Equity Issuance |
And
| Net Operating Accruals = Net Income - Cash Flow from Operations |
Many studies have used the balance sheet to calculate total net accruals or net operating accruals, but due to non-articulation issues, the cash-flow approach is better suited to describing accruals in all situations, and we will not detail how to calculate accruals from balance sheet data here.
Choosing Independent Variables
The independent variables are data items that should have some relationship to nondiscretionary accruals. For example, normal accruals driven by sales, PP&E, expected sales growth and current operating performance. A simple (and one of the most commonly used) model to estimate the nondiscretionary accrual component is the Modified Jones Model (1991). It may or may not be the best model. It surely isn't perfect, but other variables can be added to the equation in an attempt to increase the model's precision. In addition, a fourth variable such as the life-cycle score may capture relationships in total net accruals or operating net accruals that the current three variables in the regression fail to capture. The model can be represented as follows:
| TNA / ATA = β0 + β1(1/ATA) + β2(ΔSales – ΔRec / ATA) + β3(GPPE / ATA ) + ε |
Or
| NOA / ATA = β0 + β1(1/ATA) + β2(ΔSales – ΔRec / ATA) + β3(GPPE / ATA ) + ε |
Where:
TNA= Total net accruals
NOA= Net operating accruals
ATA = Average total assets
ΔSales = Change in sales
ΔRec= Change in accounts receivable
GPPE = Gross PP&E
Each β is the estimated relationship of the independent variable to the dependent variable, and the error term represents the composite effect of all variables not explicitly stated as an independent variable.
Using Cross-Sectional or Time-S
The model can be employed by regressing accrual data from many firms in the same industry for one time period (cross-sectional) or by regressing accrual data from the same firm across several time periods (time-series). There are disadvantages to both methods, but the cross-sectional analysis is probably a better method for the following technical reasons:
- Time-series analysis may not have enough enough observations in the estimation period to obtain reliable parameter estimates for a linear regression.
- The coefficient estimates on ΔSales and GPPE may not be stationary over time.
- The self-reversing property of accruals may result in serially correlated residuals.
If any of these issues above is true, it is impossible to make valid statistical inferences from the regression results obtained with time-series analysis.
Time-Series Analysis
To estimate the nondiscretionary accrual amounts, firm-specific amounts for each independent variable are used for each period/year over a sequence of periods/years. In essence, think of each data item [(TNA / ATA), (1/ATA),(ΔSales – ΔRec / ATA) and (GPPE / ATA )] as coming from the same firm, with each data set being from a different time period. For example, the data set might be one firm with accounting data from each year between 1977 and 2007.
The error term, ε, is the estimate of discretionary accruals. This discretionary accrual estimate for the firm can then be used to rank the firm with respect to its peers and all other firms in the universe. A high level of discretionary accruals relative to peers would indicate that earnings quality is relatively low. Meanwhile, a low level of discretionary accruals would indicate that earnings quality is relatively high.
Cross-Sectional Analysis
In a cross-sectional analysis, the model is a two-stage model. This means that results from the first part of the analysis are plugged into the next stage to get the needed estimate.
To estimate the nondiscretionary accrual amounts, firm-specific amounts for each independent variable are used for a particular period across several different firms. In essence, think of each data item [(TNA / ATA), (1/ATA),(ΔSales – ΔRec / ATA) and (GPPE / ATA )] as coming from the same time period with the next data set being from a different firm. For example, the data set might be 45 different firms with accounting data for the year ending 2007.
Once β0, β1, β2 and β3 have been estimated for the cross-section of firms for the period (which is calculated by the computer running a regression equation), we have denoted these estimates as β0, β 1, β 2, β 3. Use these cross-sectional coefficients along with a specific firm's data to estimate the individual firm's nondiscretionary accruals for the period. After processing, the calculation results in an estimate for nondiscretionary accruals scaled by average total assets, represented by NDA / ATA below.
| NDA / ATA = β 0 + β 1(1/ATA) + β 2(ΔSales – ΔRec / ATA) + β 3(GPPE / ATA ) + ε |
Total discretionary accruals are the difference between the individual firm's scaled total net accruals and its estimated total nondiscretionary accrual amount.
| TDA = TNA / ATA – NDA / ATA |
If, instead, the regression is run with net operating accruals as the dependent variable, the equations would yield an estimate for just the operating component of nondiscretionary accruals.
| ODA = NOA / ATA – NDA / ATA |
The discretionary-accrual estimate for the firm, whether it is based on total net accruals or net operating accruals, can then be ranked against the discretionary accrual estimates of the firm's peers and all other firms in the universe. This ranking is a comparative measure of the size of discretionary accruals, and it is a proxy for the quality of the firm's earnings. A high amount of discretionary accruals indicates lower-quality earnings and is a red flag that management may be using aggressive accounting to overstate earnings.
Earnings Quality: Conclusion
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