Discussion of the quality of accruals and earnings: the role of accrual estimation errors.

I. INTRODUCTION

The paper by Dechow and Dichev (2002) (hereafter DD) proposes a measure of the quality of accruals and earnings based on the extent to which accruals map into cash flow realizations in contemporaneous and adjacent time periods. Underpinning their measure of earnings

quality is the notion that accruals are estimates of future cash flow realizations, so that the quality of accruals and earnings is an inverse function of the precision of these estimates. Economic and structural factors can cause variation in the precision of accruals estimates (across accounts for a given firm, for a given firm over time, and across firms), regardless of the presence or absence of managerial interventions in the reporting process. In addition, managerial expertise will affect the precision of estimates, even if other factors that affect precision are held constant. As a result, a less-than-perfect mapping between accruals and cash flows in adjacent periods can reflect firms that report honestly but face uncertain economic environments, firms whose managers are less expert at estimation, and or firms whose managers intervene in the process to manipulate accruals. My discussion aims to shed light on the contribution of DD's paper by characterizing its innovation and limitations, and by putting it in the context of related literature. My discussion concludes with suggestions for future research on earnings quality.

H. DECHOW AND DICHEV'S DEFINITION OF EARNINGS QUALITY

The accounting literature includes several definitions of earnings quality. Some define earnings as high quality if earnings are persistent, an attribute based solely on the time-series properties of earnings. Some define earnings as high quality if earnings accurately represent the economic implications of underlying transactions and events. Some, and this includes DD, define earnings quality in terms of the relation between accruals and cash flows. DD's definition does not distinguish among the various factors that influence this relation--the uncertainty in the firm's environment, the ability of management, the extent to which accruals are manipulated--but some approaches to defining earnings quality do. (1)

DD characterize the linkage between current accruals and cash flows in the immediately adjacent periods. Recognizing that accruals may arise following some cash flows and in anticipation of others, they develop a model that reflects estimation error in anticipated cash flows. (2) They characterize aggregate accruals as the sum of opening and closing deferral and accrual entries. Specifically:

(DD4) [A.sub.t] = C[F.sub.t-1.sup.t] - (C[F.sub.t.sup.t+1] + C[F.sub.t.sup.t-1]) + C[F.sub.t+1.sup.t] + [[epsilon].sub.t+1.sup.t] - [[epsilon].sub.t.sup.t-1]

where:

[A.sub.t] = current accruals recognized in period t;

C[F.sub.t.sup.s] = cash from operations realized in period t and recognized in period s; and

[[epsilon].sub.t.sup.s] = estimation error associated with accruals recognized in period s and cash flows realized in period t.

The first and fourth terms reflect recognition of cash flows realized in t-1 and to be realized in t+1. The second term defers recognition of cash flows realized in t that are to be recognized in t+1, and the third term reflects cash flows realized in t that were recognized in t-1. The fifth and sixth terms reflect the estimation error in period t's opening accrual that will be realized in t+1 and the closing error for period t-1 realized in period t.

Estimation error is defined as the difference between the amount accrued and the amount realized. Therefore period t's earnings include the opening error that will be realized in t+1 when the related cash flows are realized and the reversing error from the cash flows realized in period t that differ from the amount accrued in period t-1. DD define the quality of accruals and earnings as the magnitude of these errors.

Cash flow realizations in periods prior to t-1 and subsequent to t+1 are assumed to be beyond the horizon reflected in current accruals. That is, the approach they take requires an estimated coefficient for every period in which there is a pertinent accrual. In a model of, say, deferred taxes or depreciation, this is a long series of leads/lags indeed, and the model is not operational. The approach requires that the key element of accruals/earnings quality is in the current accruals. This is a significant assumption that limits the applicability of their approach to firms with operations that are shorter-term in nature.

The DD definition of earnings quality differs from that of Comiskey and Mulford (2000) who define earnings as high quality if the contemporaneous cash flows are greater (less) than the recognized revenues or gains (expenses or losses), and low quality if the associated cash flows are less than (greater than) the recognized revenues or gains (expenses or losses). This view considers a firm with significant unearned revenue and deferred expenses to have high-quality earnings, and a firm with significant accrued revenue and prepaid expenses to have low-quality earnings. In contrast, DD define earnings to be of equal quality for firms with high vs. low realizations of the sum of the error terms in Equation (4) if the variance of the sum of the errors for the firms is equal. Their notion of earnings quality assumes a symmetric loss function, that investors are indifferent between estimation errors that overstate and understate future cash flow realizations by an equal amount.

The estimation errors are assumed to be independent of each other and of the cash flow realizations. The discussion in the paper suggests this assumption is plausible, but this arises from the focus on the behavior of total accruals. DD do not separately consider how total accruals might be affected by the behavior of discretionary accruals. Prior literature suggests that estimation errors caused by management discretion are not likely to be independent of each other and of the cash flow realizations, and therefore suggests that DD's analytical model and predictions may not apply in a context of great interest, where management intervenes in the financial reporting process to alter perceptions of the firm's underlying performance.

For example, Demski and Frimor (1999) develop a model in which discreteness in the payoffs to the agent causes the magnitude of manipulation to be nonlinear in what might be called pre-managed earnings. Healy (1985) suggests discretionary and nondiscretionary accruals will be uncorrelated when pre-managed earnings are less than the earnings target and management cannot manipulate upward sufficiently to achieve positive results, but will be negatively correlated when earnings are greater than the target. McCulloch and Black (2002) show that, if management alters accruals in response to fluctuations in nondiscretionary accruals to achieve a smoother income series, then nondiscretionary and discretionary accruals will be negatively correlated. Furthermore, they argue that discretion in accruals can induce correlation in errors across years, as managers exercise income-increasing (-decreasing) discretion in low- (high-) earnings years and reverse this discretion in subsequent high- (low-) earnings years.

Empirical evidence also documents that discretionary accrual estimates are correlated with earnings performance. Dechow et al. (1995) and Kasznik (1999) find that firms with higher (lower) earnings exhibit significantly positive (negative) discretionary accruals, suggesting earnings management varies with earnings or that the Jones (1991) model used to estimate nondiscretionary accruals is misspecified. Beaver et al. (2002) find that property and casualty insurance firms' loss reserve errors are significantly more negative for firms with large positive earnings than for firms in other regions of the earnings distribution, suggesting firms in this industry with large positive earnings use discretion to lower earnings. Thus, the theory and evidence suggests incorporating management's incentives to exercise discretion over accruals in the model will result in different implications than those of the present model.

III. EMPIRICAL IMPLEMENTATION

DD characterize the "empirical version" of Equation (4) as:

[DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] CF[O.sub.t-1] + [b.sub.2] CF[O.sub.t] + [b.sub.3] CF[O.sub.t+1] + [[epsilon].sub.t]

and measure earnings quality as the standard deviation of the residual. This section discusses three issues raised by the empirical implementation of the DD earnings quality measure: the standard deviation of the residual as a proxy for earnings quality, the difference between reported cash from operations and the cash flows related to period t, and the implications of common firm transactions for the residual term.

First, the standard deviation of the residual, in theory, is the estimated square root of the variance of the dependent variable conditional on the explanatory variables. This measure therefore reflects absolute variation in the residual rather than variation relative to the variation in accruals. Holding the [R.sup.2] of the model constant, firms with more variable accruals will have a higher standard deviation of the residuals, so firms with greater underlying volatility in earnings are classified as having lower quality earnings. In this sense, the empirical results in the paper relating DD's empirical proxy to the absolute magnitude of accruals, and to the standard deviations of sales, cash flows, accruals, and earnings, are likely to be induced mechanically, in that variability in the residual is increasing in variability in accruals, which in turn is correlated with variability in sales, cash flows, and earnings.

The inverse empirical measure of quality in the paper is the standard deviation of residual accruals, but, and given the mechanics of OLS regression, this measure will be larger for firms with large absolute accruals holding relative estimation error constant. The results would be more readily interpretable if the relative variance of the errors were shown to be associated with proxies for environments in which it is difficult to forecast. In other words, for firms where the [R.sup.2] in DD's empirical equation is high (low), one would expect, other things equal, an environment where forecasting ability is great (small).

A second issue with the empirical specification, which DD note, is that the cash from operations data available to researchers includes cash flows realized in a period that are recognized in multiple periods, in contrast to the theoretical specification, which includes only cash flows recognized in period t but realized in periods t-1 or t+1, and cash flows realized in t but recognized in periods t-1 and t+1. Their empirical specification has error in the independent variables, leading to biased coefficients. They analyze this issue in Appendix B and their simulations indicate that the effect of the measurement error is to bias downward the coefficients on all three cash from operations variables in their equation.

However, in addition to the amounts included in cash from operations that are outside the model, a number of other items can affect the analysis. For example, to the extent sample firms participate in mergers and acquisitions, or in divestitures, the accrual data in one period may not correspond to the cash flow data in another. Collins and Hribar (2001) provide evidence that these transactions are fairly common during their sample period 1988-1997, with over a third of their sample engaging in mergers and or discontinued operations. These transactions can cause current accruals to be based on a different entity than future cash flows. A related issue arises for rapidly growing firms. The cash from operations in t+1 may be greater than amounts accrued in t due to growing sales. In this case, cash from operations in period t+1 contains additional measurement error, as it includes the cash flow effects of sales for period t+1 as well as for period t, and is therefore likely biased downward further.

IV. EARNINGS QUALITY AND DISCRETIONARY ACCRUALS

The purpose of this section is to link the DD analysis of earnings quality to the literature on discretionary accruals, and in particular, the Jones (1991) model. Jones' intent was to separate discretionary accruals (DA) from nondiscretionary accruals (NDA). DD's intent is to assess accruals as a whole--they do not attempt to separate management-induced effects (the analog of DA) from all other effects. Linking the approach taken by DD with that taken by Jones (1991) has the potential to strengthen both approaches, and to calibrate the errors associated with Jones' measure of discretionary accruals and DD's measure of earnings quality.

As discussed in McNichols (2000), there are many reasons to suspect that the estimated discretionary accruals from the Jones model reflect nondiscretionary forces rather than pure discretion. In particular, the Jones model assumes accruals react to the current change in sales, but that lagged and future changes are not relevant. Counter to this assumption are the assumptions in Bernard and Stober (1989) and Dechow et al. (1998) that accruals do not fully adjust to a contemporaneous sales shock; rather, adjustment occurs over succeeding periods. Furthermore, anticipation of future sales growth is likely to influence management's estimates, as reflected in accruals. Consistent with this, McNichols (2001) documents that analysts' long-term earnings growth forecasts have significant explanatory power for residuals estimated using the Jones model, suggesting that growth is a significant correlated omitted variable in this model.

The estimation results in DD suggest that including cash flows in the Jones model might reduce the extent to which the model omits variables that are correlated with sample firms' economic fundamentals. Relatedly, measurement error in DD's estimation may preclude them from controlling for the fundamental factors influencing accruals. Therefore, including sales in the DD model provides a useful specification check on the magnitude of measurement error in their cash flow variables. To assess this, I compare the incremental explanatory power of the independent variables in each of these models for the other, to provide evidence on the validity of each specification.

To test for a relation between discretionary accrual estimates from the Jones (1991) model and cash flows, I examine a sample of all nonfinancial firms on the Compustat annual research files during 1988-1998. (3) This sample period permits me to use SFAS No. 95 (FASB 1987) statement of cash from operations data to estimate accruals, rather than a balance sheet approach. Given the findings of Collins and Hribar (2000), I exclude companies with mergers, acquisitions, or discontinued operations, as indicated by Compustat footnote 1. (4)

To examine whether cash flows have explanatory power for accruals after controlling for the change in current period sales and the level of plant and equipment, and vice versa, I estimate the following equations:

(1) [DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] CF[O.sub.t-1] + [b.sub.2] CF[O.sub.t] + [b.sub.3] CF[O.sub.t+1] + [[epsilon].sub.t]

(2) [DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] [DELTA][Sales.sub.t] + [b.sub.2] PP[E.sub.t] + [[epsilon].sub.t]

(3) [DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] CF[O.sub.t-1] + [b.sub.2] CF[O.sub.t] + [b.sub.3] CF[O.sub.t+1] + [b.sub.4] [DELTA][Sales.sub.t] + [b.sub.5] PP[E.sub.t] + [[epsilon].sub.t]

where [DELTA]W[C.sub.t] is defined as in DD to include the change in accounts receivable (item 302), the change in inventory (item 303), the change in accounts payable (item 304), the change in taxes payable (item 305) and change in other assets (item 307); CF[O.sub.t] is cash from operations from the SFAS No. 95, Statement of Cash Flows, (item 308); and the [DELTA][Sales.sub.t]. (item 12) and PP[E.sub.t] (item 7) are the change in sales and the level of property, plant, and equipment, respectively. (5) Equation (1) is DD's empirical model, as characterized by their Equation (5) and Equation (2) is the Jones model. Equation (3) includes the explanatory variables from Equations (1) and (2), to assess whether included variables in either of Equations (1) or (2) have explanatory power for the other equation.

The estimation results for the above equations are in Table 1. The findings confirm that, consistent with DD, accruals are significantly positively associated with prior year, current year, and subsequent year cash from operations; the [R.sup.2] is .20. The coefficient estimates are 0.0543, -0.2214, and 0.1312, with associated t-statistics of 23.33, -60.18, and 41.72, respectively. Consistent with DD, the strongest association is with current cash from operations.

The next set of estimation results is for the Jones model; these results indicate significant explanatory power, with an adjusted [R.sup.2] of .07 and F-statistic of 592.3, but substantially less than the estimation based on DD's model. Accruals and the change in sales are significantly positively associated, as indicated by a coefficient of 0.0802 and t-statistic of 33.74.

The third set of estimation results combines cash flow variables from DD's model with Jones model variables. The findings indicate that both models are likely significantly misspecified, in that both the cash flow variables and the change in sales remain highly significant; the [R.sup.2] increases to .30. The coefficient on the change in sales is 0.0966 with a t-statistic of 45.93.

The findings in Table 1 suggest misspecification in both the Jones and DD models. Specifically, the estimation results for Equation (3) indicate that the residual from Equation (1) is significantly correlated with the change in sales, consistent with cash from operations being a noisy proxy for the cash flows recognized in accruals. The findings in Table 1 also indicate that the residual from Equation (2), the Jones model, is significantly associated with lagged, current, and future cash flows. Because these variables most likely reflect fundamentals to a greater extent than discretion, the findings indicate that estimates of discretionary accruals based on the Jones model likely include a substantial nondiscretionary component.

The findings indicate that researchers should consider the implications of both the DD and Jones models to develop more powerful approaches to the estimation of earnings quality and the role of management discretion in influencing earnings quality. As McNichols and Wilson (1988) discuss, to the extent a proxy for discretionary accruals contains measurement error that is correlated with the partitioning variables in a study's research design, inferences are affected. This holds for studies of earnings quality as well. Taken as a whole, the findings suggests that further modeling of the relation between accruals and cash flows could yield substantial improvements in our ability to understand the factors that influence earnings quality. This should also yield substantial improvements in our ability to test for management's exercise of discretion over accruals.

V. CONCLUDING REMARKS

In my view, the paper by Dechow and Dichev (2002) makes two contributions. First, it provides a characterization of the relation between accruals and cash flows that captures an important element of earnings quality--estimation error in accruals. This paper extends the modeling in Dechow (1994), Dechow et al. (1998), and Barth et al. (2001) by incorporating the role of estimation error, and by drawing an explicit link to earnings quality.

The second contribution is to operationalize this characterization empirically and provide some evidence on its validity. Prior literature has provided evidence on the contemporaneous relation between accruals and cash flows (Rayburn 1986; Bowen et al. 1986; McNichols and Wilson 1988; Bernard and Stober 1989; Dechow 1994; Dechow et al. 1998). Prior literature has also provided evidence on the relation between accruals and future cash flows (Finger 1994; Dechow et al. 1998; Barth et al. 2001). The present paper corroborates many of the findings in these earlier studies. In addition, it suggests a rationale for an empirical specification relating accruals to cash flows from the prior, contemporaneous, and subsequent periods.

The approach taken in this paper suggests several future research directions. The first direction is to enrich the modeling by specifying the process generating cash flows, the information available to management, management's estimation task, and the consequences of these estimates. One can then incorporate management's incentives to report objective vs. biased accruals, and determine the implications of these enrichments for the relation between accruals and cash flows. The second direction is to focus on specific accruals rather than aggregate accruals. The complexity associated with modeling the estimation errors in aggregate accruals is daunting, and the construct validity associated with a proxy based on aggregate accruals seems low. A focus on specific accruals can permit a more complete characterization of the relation between accruals and cash flows, and can potentially result in a better understanding of the role played by estimation error. For example, studies in the property and casualty insurance area (e.g., Petroni 1992; Petroni et al. 2000; Beaver and McNichols 1998, 2001) focus directly on loss reserve errors, which reflect the change in management's estimates of claim loss reserves over time. The potential to develop models of specific accruals such as restructuring reserves, warranty liabilities, and specific components of current accruals is largely untapped. Such development can potentially allow better understanding of the forces shaping management's choices and their relation to the measurement error in earnings.

TABLE 1
Estimation Results from Regression of Changes in Working Capital on
Cash Flows, Change in Sales and Plant and Equipment

This table presents estimation results for the sample of 15,015
firm-year observations with available data from the Compustat Annual
Industrials and Research file, with SIC codes 2000-3999 for years
1988-1998. Observations with merger and acquisitions, accounting
changes, fiscal year changes, and discontinued operations are excluded.

(1) [DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] CF[O.sub.t-1] + [b.sub.2]
CF[O.sub.t] + [b.sub.3] CF[O.sub.t+1] + [[epsilon].sub.t]

(2) [DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] [DELTA][Sales.sub.t] +
[b.sub.2] PP[E.sub.t] + [[epsilon].sub.t]

(3) [DELTA]W[C.sub.t] = [b.sub.0] + [b.sub.1] CF[O.sub.t-1] + [b.sub.2]
CF[O.sub.t] + [b.sub.3] CF[O.sub.t+1] + [b.sub.4] [DELTA][Sales.sub.t]
+ [b.sub.5] PP[E.sub.t] + [[epsilon].sub.t]

Esti-
mation   Intercept   CF[O.sub.t-1]   CF[O.sub.t]   CF[O.sub.t+1]

  1       0.0154         0.0543         -0.2214        0.1312
         27.57          23.33          -60.18         41.72

  2       0.00951
          0.57

  3       0.0096         0.0645         -0.2409        0.1251
         12.18          29.41          -69.31         42.48

Esti-       [DELTA]                    Adjusted
mation   [Sales.sub.t]   PP[E.sub.t]   [R.sup.2]   F-value     n

  1                                     0.2011     1260.9    15015

  2          0.0802        -0.0052      0.0730      592.26   15015
            33.74          -5.57

  3          0.0966        -0.0027      0.3009     1293.38   15015
            45.93          -3.32

Variable definitions:

[DELTA]W[C.sub.t] = changes in working capital accounts as disclosed on
the statement of cash from operations, measured as the increase in
accounts receivable (Compustat data item #302) plus the increase in
inventory (#303) plus the decrease in accounts payable and accrued
liabilities (#304) plus decrease in taxes accrued (#305) plus the
increase (decrease) in other assets (liabilities) (#307), deflated
by beginning total assets;

CF[O.sub.t] = cash from operations in year t (Compustat data
item #308);

[DELTA]SALES = change in sales (data item #12) deflated by beginning
total assets (data item #6); and

PPE = property, plant, and equipment deflated by beginning total
assets (data item #6).

I gratefully acknowledge the helpful comments of participants at The Accounting Review Conference on Quality of Earnings. I also especially appreciate the comments of Stephen Ryan and Katherine Schipper, and the able research assistance of Yulin Long.

(1) See for example, Jonas and Blanchet (2000) for discussion of dimensions of financial reporting quality, Penman and Zhang (2002) for discussion of the role of accounting choices and estimates on the sustainability of earnings, and the literature on earnings management, (e.g., Healy [1985], Moses [1987], McNichols and Wilson [1988], Schipper [1989], Bernard and Skinner [1996], Demski and Frimor [1999], Healy and Wahlen [1999] for discussion of management's incentives to intervene in the financial reporting process).

(2) Their model does not consider however, subsequent revision of a prior accrual, such as an inventory impairment.

(3) The sample includes firms with SIC codes from 2000-3999.

(4) Specifically, all firm-year observations coded by Compustat as experiencing an accounting change, merger or acquisition, or discontinued operations or a fiscal year change that affected sales were excluded.

(5) Jones (1991) includes depreciation in her measure of accruals, but to allow for consistency with DD, the measure of accruals adopted here excludes depreciation.

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Maureen F. McNichols
Stanford University