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Do Estimates Improve the Usefulness of Financial Information?

By

Baruch Lev*, Siyi Li**, and Theodore Sougiannis**

Please note: This research is still in progress, which explains the somewhat rough and incomplete state of the paper. We apologize for that.

September 2004

*New York University. **University of Illinois, Urbana-Champaign. The authors are indebted to James Ohlson and Shiva Rajgopal for helpful comments.

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Do Estimates Improve the Usefulness of Financial Information?

I. Introduction

Financial statement information, be it balance sheet items, such as net property, plant and

equipment, accounts receivable and inventories, deferred taxes and contingent liabilities, or key

income statement figures, such as revenues, pension expense, and in-process R&D are largely

based on managerial estimates and projections. The economic condition of the enterprise and the

consequences of its operations as portrayed by the financial reports are therefore an intricate and

ever changing mixture of facts and conjectures, where the dividing line between the two is

unknown to information users. With the current move of accounting standard-setters in the U.S.

and abroad toward increased fair-value measurement of assets and liabilities, the role of

estimates and projections in financial reports will further increase.

We ask in this study: What is the effect of managerial estimates underlying accounting

data on the usefulness of financial information? The answer is far from straightforward. On the

one hand, estimates/projections are potentially very useful because they are the primary means

for managers to convey credible forward-looking, inside information to investors. Thus, for

example, the doubtful receivables provision informs investors on expected future cash flows

from customers, restructuring charges predict future severance payments and plant closing costs,

and the capitalized portion of software development costs (SFAS 86) informs investors about

development projects that passed successfully technological feasibility tests and are expected to

provide value to shareholders. This potential contribution of managerial estimates to investors’

assessment of future enterprise cash flows underlies the oft-quoted statement by the FASB in its

Conceptual Framework about the superiority of accruals earnings—practically all accruals are

based on estimates—over current cash flows in predicting future cash flows:

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Information about enterprise earnings based on accruals accounting generally provides a better indication of an enterprise’s present and continuing ability to generate favorable cash flows than information limited to the financial aspects of cash receipts and payments. (FASB, 1978, p. IX).

On the other hand, two major factors cause accounting estimates and projections to

adversely affect the usefulness of financial information: (a) In the current volatile and largely

unpredictable business environment, due to the ever increasing competitive pressures and rapid

technological changes, it is very difficult to make reliable forecasts, or projections. Consider, for

example, the estimated future gain on pension assets—a key component of the pension expense.

This estimate is essentially a prediction of the performance of the stock and bond markets next

year. One wonders about the reliability of such a guess made by managers, or even when made

by “experts”.1 Or, reflect on the impairment charges of fixed assets and acquired intangibles

(including goodwill): The determination of these charges often requires managers to estimate

future cash flows from tangible and intangible assets. In today’s highly competitive and

contested markets which characterize the economic environment surrounding most companies,

the reliability of asset cash flows forecasted over several years is highly questionable.

Accordingly, the multitude of accounting estimates and projections underlying financial

information introduces a considerable and unknown degree of noise, and perhaps bias to

financial information, clearly detracting from their usefulness.2 (b) Add to the above the

1 Consider, for example, the 2001 pension footnotes of Merrill Lynch, Bank of New York, and Charles Schwab which report the following estimates of the expected annual returns on pension assets: 6.60%, 10.50%, and 9.00%, respectively. This is an indication of the widely differing views of experts (lack of objectivity, reliability) about the future performance of capital markets. 2 A recent case in point (Wall Street Journal, August 4, 2004, p. c1): “Investors in Travelers have needed more than that red umbrella protection from what has been raining on them since the company was spun out from Citigroup in early 2002. Late last month, St. Paul Travelers Cos., … announced what Morgan Stanley termed a ‘blockbuster reserve charge’ of $1.625 billion. The charge was about twice as large as analysts have been expecting. The insurer contends that the charge stems largely from the need to reconcile differing accounting treatments at the two companies [Travelers and its acquisition—St. Paul Cos.]. It was just a “reserve valuation adjustment,” the company said…. Sadly there seems to be little reason why Travelers’ executives didn’t anticipate problems with St. Paul’s insurance methodologies… Mr. Benet [Travelers’ CFO] said:…we recognized early on that there was a difference in

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expected and strongly documented susceptibility of accounting estimates to managerial

manipulation, and the potential adverse impact of estimates on the usefulness of financial

information becomes real. Given that it is very difficult to “settle up” with manipulators of

estimates—even if an estimate turns out ex post to be far off the mark, it is virtually impossible

to prove that ex ante the estimate was intentionally manipulated—there are no effective

disincentives for managers to manipulate accounting estimates. Indeed, many of the SEC

enforcement cases alleging financial reporting manipulation concern misestimation of accruals

(e.g., Dechow et al. 1996).

Thus, the impact of the multitude of estimates and projections underlying accounting

measurement and reporting rules on the usefulness of information is an open question, to be

examined in this study. The relevance of this issue cannot be overstated. Accounting estimates

and projections occupy much of GAAP and consume most of standard-setters’ time and efforts.

Just consider the major GAAP issues of recent years—financial instruments, stock options, fixed

assets and goodwill impairment, and the valuation of acquired intangibles, to name a few—all

require major estimates in the process of measurement and reporting. If these and other

estimates do not contribute significantly to the usefulness of financial information, the efforts of

standard-setters, and much more costly—the resources society devotes to the generation of

estimates in the process of accounting measurement and valuation and to their audit—are largely

wasted. Worse yet, if financial information users are led by the estimates-based accounting

information to misallocate resources, an additional dead-weight cost is imposed on society.

We perform in this study three sets of empirical tests, broadly following the underlying

premise of the FASB’s Conceptual Framework that the major purpose of financial information is

some of the methodologies [to estimate reserves] that would have to be addressed.” Thus, different accounting methodologies, to estimate reserves all approved by auditors yield a difference of $1.625 billion.

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to assist investors and other users in predicting future enterprise cash flows.3 The central role of

enterprise cash flows in accounting rules and regulations is not limited to the FASB’s conceptual

framework. Cash flows are at the core of asset and liabilities valuation rules. Thus, for example,

asset impairment (SFAS 121) is determined by expected cash flows, and the lives of acquired

intangibles (SFAS 142) are a function of future cash flows. We admit at the outset to a certain

degree of uncertainty about the specific definition of cash flows used by investors, and

accordingly perform our tests with two, widely-used cash flow constructs: cash from operations

(CFO), and free cash flows (FCF), with a heavier emphasis on the latter. Much of prior related

research focused on CFO. However, these cash flows are not sustainable since they abstract

from the cost of fixed assets. Accordingly, we focus on free cash flows, defined as CFO minus

capital expenditures. Free cash flows are central to practitioners’ valuation models, and play an

important role in research too (e.g., FCF is the central valuation variable in the construct of

Feltham and Ohlson, 1995).

Despite the prominence of cash flows in asset valuation models and in GAAP, there is

not denying that many investors and analysts are using financial data to predict earnings. The

underlying heuristics are somewhat obscured; perhaps investors predict earnings first, and derive

future cash flow estimates from those earnings predictions. In any case, earnings prediction is

prevalent in practice, and we therefore also examine the usefulness of accounting estimates for

the prediction of earnings.

Our three sets of tests, applied to both cash flows and earnings are, in capsule:

(a) Cross-sectional regressions of cash flows (earnings) on lagged values of cash flows

and accruals. The large majority of accounting estimates and projections are

3 We make here the obligatory statement that financial data sometimes have additional uses, such as in contracting arrangements.

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embedded in accruals, and accordingly the focus of this analysis is on the estimated

regression coefficients of accruals components, and their contribution to the

explanation of the cross-sectional variability of subsequent cash flows (earnings).

Such regression analyses are, of course, not reliable examinations of predictive

ability, since they are in-sample tests (see next section). We nevertheless perform

this analysis to both bridge and depart from much of previous related research which

is characterized by the regression approach.

(b) Out-of-sample prediction of future enterprise cash flows (earnings) based on: (i) past

cash flows (the benchmark), and (ii) cash flows plus various components of accruals.

The focus of this analysis is on the improvement in the quality of cash flow (earnings)

prediction brought about by the inclusion of accruals (heavily based on estimates)

among the predictors. These tests are a direct operationalization of the above-quoted

FASB’s postulate about the superiority of earnings over cash flows in predicting

future cash flows.

(c) Portfolio tests, where past and current cash flows, along with accruals, are used to

form portfolios based on predicted changes in cash flows (earnings), and the

abnormal returns on these portfolios are evaluated. The focus here is on comparing

the returns on portfolios constructed on the basis of cash flows and accruals

information, with returns on portfolios constructed strictly on the basis of current cash

flows. The incremental inferences we draw from these portfolio tests over the

prediction tests described in (b) is that the portfolio tests inform about the economic

significance of accruals: The prediction errors (e.g., mean error, mean absolute error,

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etc.) derived from prediction tests inform about the statistical significance of the

differences in predictions and the performance of the underlying models, but

generally not on the economic significance of the differences. The portfolio tests,

focusing on return differentials, inform on the economic significance of alternative

predictors to investors.

Our major findings, based on a sample of all nonfinancial Compustat firms with the

required data—ranging from roughly 3,500 to 4,500 companies per year—spanning the period

1988-2001,4 are as follows: Our three batteries of test—regression analyses, out-of-sample

predictions, and portfolio tests—do not indicate a substantial and consistent contribution of

accruals to the prediction of enterprise cash flows or earnings. In fact, most of the tests do not

show any improvement brought about by the use of accruals, even when they are broken-down to

their various components. Since accounting estimates are deeply embedded in practically all

accruals, we interpret our evidence as consistent with the conclusion that such estimates

currently do not improve the usefulness of financial information to investors. Given the

prevalence of estimates in accounting, this conclusion, if valid, casts a wide shadow on most

measurement and valuation procedures underlying financial reports. A caveat: At this stage of

the analysis we do not fully distinguish between accruals and estimates. To be sure, most

accruals are based on estimates, but to a varying degree (e.g., the change in the estimates-light

accounts payable vs. the pure estimate—bad debt reserve). We are currently exploring such a

distinction.

A brief review of previous related research follows. We are not familiar with empirical

studies that assess the role of accounting estimates in the informativeness of financial

information, but there is a fair number of studies that examine the contribution of accruals to the 4 We start our sample period with 1988, since it is the first year with data on cash from operations.

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prediction of future cash flows, incremental to current and past cash flows. These studies can be

roughly classified into regression-based analyses, and out-of-sample prediction tests. A recent

example of the former is Barth et al. (2001), who regress CFO on lagged values of CFO and

components of accruals (primarily the changes in accounts receivable, inventories, and accounts

payable, as well as depreciation & amortization). The authors report (p. 27) that “each accrual

component reflects different information relating to future cash flows…[and] is significant with

the predicted sign in predicting future cash flows, incremental to current cash flows.” Note that

prediction is assessed in this and most other studies by the significance of the accruals’

regression coefficients and improvement in R2 .

An example of the out-of-sample prediction tests is Finger (1994), who concludes from a

sample of 50 companies with long historical data, that cash flow is marginally superior to

earnings for short-term predictions and performs similar to earnings in long-term cash flow

predictions. Though results of both types of research (regression and prediction) are mixed, and

somewhat contradictory, it appears that by and large the regression-based studies indicate that

certain components of accruals (though not aggregate accruals) are associated with subsequent

cash flows, while the prediction test (with the exception of Lorek and Willinger, 1996) do not

find that accruals contribute to the prediction of cash flows beyond past cash flows. Note that

most previous studies focus on the prediction of cash from operations, while we focus on free

cash flows (as well as cash from operations). No previous study to our knowledge has

performed the combined regression, prediction, and portfolio tests we do.

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II. Methodology: Regressions and Out-of Sample Predictions

Regression analysis of a given variable on lagged values of that variable along with other

variables is commonly used in accounting and finance research to examine prediction

hypotheses. However, as noted by Poon and Granger (2003, p. 492):

“In all forecast evaluations, it is important to distinguish in-sample and out-of-sample forecasts. In-sample forecast, which is based on parameters estimating using all data in the sample, implicitly assumes parameter estimates are stable through time. In practice, time variation of parameter estimates is a critical issue in forecasting. A good forecasting model should be one that can withstand the robustness of an out-of-sample test, a test design that is closer to reality. In our analyses of empirical findings… we focus our attention on studies that implement out-of-sample forecasts.”

A dramatic example of misplaced inferences drawn on the basis of regression analysis is

provided by Goyal and Welch (2004):

“Attempts to predict stock market returns or the equity premium have a long tradition in finance. For example, as early as 1920, Dow (1920) explored the role of dividend ratio. Nowadays, a typical specification regresses an independent lagged predictor on the stock market rate of return, or as we shall do, on the equity premium…The most prominent variables explored in the literature are: The dividend-price ratio and the dividend yield; the earnings price ratio and dividend-earnings ratio; the interest and inflation rates; the book-to-market ratio; the aggregate net issuing activity…we posit that a real-world investor would not have had access to any ex-post information either to construct variables or to the entire-sample gamma regression coefficients. An investor would have had to estimate the prediction equation only with data available strictly before or at the prediction point, and then make an out-of-sample prediction. Therefore, instead of running one single in-sample regression… we must run rolling forecasting regressions…” (pp.1-2).

When Goyal and Welch compare the in-and out-of-sample results they conclude:

“Altogether, we find our evidence sobering: we could not identify a single variable that would have been of solid and robust use to a real-world investor (who did not have access to ex-post information). Our diagnostic shows that any presumed equity premium forecasting ability [claimed by the numerous regression studies cited by Goyal and Welch] was a mirage… most variables are just worse than the prevailing historical equity premium average as a predictor, …In sum, despite good in-sample predictive ability for many of these variables,

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most had consistently poor or zero out-of-sample forecasting ability. (They were essentially noise.)” (pp. 2-3).

This is indeed an important lesson motivating much of our analysis. This analysis is

based on a sample of all nonfinancial Compustat firms with the required data—ranging from

3,500 to 4,500 firms per year—spanning the period 1988-2001. We now turn to a discussion of

our methodologies and results.

III. Regression Estimates

We report in this section on estimates derived from annual, cross-sectional regressions of

free cash flows (FCF) on lagged values of cash from operations (CFO), capital expenditures, and

various components of accruals. At the one extreme of our accruals decomposition we have the

classification of all the accruals in the “operating” section of the cash flow statement into

working capital changes ( WC) and “other accruals” (OA):

EARNINGS

Cash from Operations (CFO)

Working Capital Changes ( WC)

Other Accruals (OA)

ACCRUALS

We break-down accruals to working capital changes ( WC) and other accruals (OA)

because accounting estimates—the focus of our analysis—while present in most accrual items,

are much more influential in the “other accruals” than in most working capital items (inventory

is an exception). Many of the OA components are in fact pure estimates (e.g., depreciation and

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amortization, bad debt reserve, in-process R&D). This and subsequent breakdowns of accruals

are thus intended to allow us to observe the impact of estimates, distinct from accruals, on the

usefulness of financial information.

At the other end of the accruals decomposition we separate out the change in inventory

( INV) from the aggregate changes in working capital items, given the evidence (e.g., Thomas

and Zhang, 2002) that much of the accruals anomaly, probably due to misestimates, resides in

inventory. We further breakout depreciation and amortization (D&A) and deferred taxes (DT)

from other accruals because this identification of individual accruals is possible from Compustat

data over the entire sample period. This decomposition is depicted thus:

EARNINGS

CFO WC* (minus inventory)

Inventory ( INV)

Dep. & Amortization (D&A)

Def. Taxes (DT)

Other Accruals (OA*)

ACCRUALS

We regress free cash flows (FCF) in years t+1 and t+2 on current CFO, capital

expenditures, and various breakdowns of accruals. Regarding the dependent variable—free cash

flows—it is highly unlikely that all investors use a unique, well defined definition of cash flows

in securities’ valuation and analysis. It is also unlikely that the main components of the GAAP

prescribed cash flow statement classification–operating, investing, and financing—map exactly

into investors’ decision model.5 Accordingly, the most one can do in a large-sample empirical

analysis aimed at the prediction of “cash flows” is to focus on a widely-used and persistently

promoted definition of cash flows, and examine the robustness of estimates to alternative cash

5 See the discussion in Nurnberg (1993) and Nurnberg and Largay (1996) for various inconsistencies between the classification of items in the cash flow statement prescribed by SFAS 95, and various concepts of cash flows proposed in the finance literature.

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flow definitions. We, accordingly, focus our analysis on free cash flows, given that it is a

measure of sustainable performance and its wide use in practice and research, and examine the

sensitivity of our estimates to the alternative—cash from operations.

Free cash flow is generally defined as cash from operation minus capital expenditures.6

Since capital expenditures are lumpy, we subtract from CFO in any year the annual average of

capital expenditures reported for the last three years.7 We also include in the extended set of

regressors (several accrual components) the current value of capital expenditures as an

independent variable. This, in fact, serves (along with CFO) as a lagged variable of FCF (the

dependent variable), and it also informs whether the depreciation and amortization expense

proxies for capital expenditures.

Finally, an important methodological note. Researchers often pool data over years and

across firms, and report the pooled coefficient estimates and their t-values. Sometimes, to

account for cross-period correlations due to same firms appearing in consecutive years, mean

yearly coefficient estimates and respective standard errors are reported (“the Fama-MacBeth”

analysis). However, this procedure too does not adequately account for the cross-period

correlations.8 We, accordingly, do not report pooled summary measures of regression estimates.

Rather, we provide graphs of the annual estimated t-values of the coefficients, uncontaminated

by cross-period correlations of the observations. Regression estimates are subjected to the White

correction. All the regression variables are scaled by beginning-of-year market value of the firm.

6 There is no GAAP definition of free cash flows. 7 We have also experimented with an FCF definition based on CFO minus the current value of capital expenditures. This change does not have a noticeable effect on our results. 8 A telling example: In our regressions of next year FCF on current CFO and the detailed breakdown of accruals, the coefficient of “other accruals” (excluding depreciation and amortization, and deferred taxes) was not statistically significant (at the 10% level) in 13 of the 15 annual regressions. Nevertheless, the mean coefficient over the 15 years had an adjusted t-value of –3.64 (adjusted for cross-correlations), conveying the clearly false message that across the sample period the coefficient of “other accruals” was statistically significant.

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Figure 1, Panel A (on page 15) depicts the t-values from annual regressions of year t+1

free cash flows on year t cash from operations (CFO), capital expenditures, working capital

changes, and all other accruals. The top line clearly indicates that the current value of CFO is

strongly and positively associated with subsequent FCF, with t-values typically ranging between

4 and 10. In contrast, the coefficients of the first group of accruals—the aggregate change in

working capital items (middle curve)—ranges in most years between 0 and –2.0, suggesting that

the variable is statistically insignificant (except for the last three years). The coefficient of “other

accruals” (bottom line) is negative and significant in most years.

Figure 1, Panel B portrays the estimates of the regression of year t+2 FCF on the three

independent variables, CFO, WC, and OA (and capital expenditures). Here too, current CFO

is positive throughout the period and highly significant. The change in working capital items is

again mostly insignificant, as is the coefficient of “other accruals” (only marginally significant

in 1989 and 1993).

We conclude from these estimates that over the period 1988-2001, accounting accruals,

aggregated to working capital items and all other accruals, were either unrelated, or only weakly

related (the OA component with next year’s FCF) to subsequent two years’ free cash flows. This

is hardly a resounding affirmation of the FASB postulate (quoted in the Introduction) about the

superiority of accruals earnings over cash flows in predicting future cash flows. When we

substitute cash from operations (CFO) for free cash flows (FCF) as the dependent variable in the

above regressions we obtain very similar estimates.

Panel C of Figure 1 portrays the t-values of next year’s FCF regressed on the extended set

of accruals: CFO, WC* (working capital items excluding the change in inventory), the change

of inventories, depreciation and amortization, deferred taxes, OA* (other accruals excluding

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depreciation & amortization, and deferred taxes), and capital expenditures. We report in the

graph the t-values of CFO, WC*, and OA* only, not to clutter the presentation. Most notably,

OA* (other accruals)—the middle line—is statistically insignificant in every sample year.

Comparing these estimates with those of Panel A (where the OA coefficients were significant in

most years), we note that extracting depreciation & amortization and deferred taxes from OA

renders the latter insignificant. The working capital changes, however, are (after extracting the

change in inventories from them), significant in most years. This is the first clue to the effect of

estimates on cash flow predictability, as distinct from the effect of accruals. Apparently, the

intentional and unintentional misestimates plaguing inventories render the aggregate change in

working capital items unrelated to subsequent cash flows (Panel A, Figure 1). Once inventory is

removed from the aggregate, the other working capital items are significantly associated with

future cash flows. Panel D, referring to t+2 FCF, indicates that other accruals are insignificant in

all years, while the working capital change (minus inventory) is significant in about half the

sample years.

Of the accruals components singled out (as independent variables) for individual

examination (not reported in Figure 1), the change in inventory is insignificant in most years

examined, as are depreciation & amortization and deferred taxes. The insignificance of

depreciation & amortization is due to the presence of capital expenditures in the regression (the

latter is significant in most years). Depreciation & amortization thus proxies to a large extent for

capital expenditures. 9

9 Following is a typical annual regression. For the year 1996, free cash flows in year t+2 (1998) are regressed on 1996 accruals components, yielding the following estimates (t-values below the estimates): Intercept CFO WC* INV D&A DT OA* Cap. Exp. R2 -0.036 0.260 -0.044 -0.178 0.196 -0.029 0.068 -0.482 0.16 -6.69 6.23 -0.56 -1.64 1.71 -0.07 0.76 -9.23

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Figure 1. Year-by-Year T-Statistics for Regression Variables Estimated t-values of Coefficients from Annual Regressions of Cash Flows on Lagged

Values of Cash Flows and Components of Accruals

Panel A. Regressing FCFt+1 on CFOt, WCt, and OAt

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

T-Statistic

CFO DWC OA

Panel B. Regressing FCFt+2 on CFOt, WCt, and OAt

-6

-4

-2

0

2

4

6

8

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

T-Statistic

CFO DWC OA

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Panel C. Regressing FCFt+1 on CFOt, WCt*, INVt, DPAt, CAPEXt, DTt, and OAt*

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

T-Statistic

CFO DWC* OA*

Only t-statistics for CFOt, WCt

*, and OA* are presented.

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Panel D. Regressing FCFt+2 on CFOt, WCt*, INVt, DPAt, CAPEXt, DTt, and OAt*

-6

-4

-2

0

2

4

6

8

10

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

T-Statistic

CFO DWC* OA*

Only t-statistics for CFOt, WCt

*, and OAt* are presented.

FCF and CFO are free cash flows and cash from operations, respectively. WC is the annual change in working capital items; OA is all other operating accruals; INV is the annual change in inventories; DPA is depreciation and amortization, CAPEX are capital expenditures; DT are deferred taxes, and OA* are other accruals excluding DPA and DT.

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Our main conclusion from the cash flow regression analysis is that the association

between accruals, either in groups or broken down to individual items, and free cash flows (or

cash from operations) in the subsequent two years is very weak and inconsistent at best. In most

cases, particularly when year t+2 FCF is the dependent variable, accounting accruals are not

associated with future cash flows. We strongly suspect that the culprit for this weak-to-absent

association are the multitude of estimates underlying accruals. Some estimates are noisy due to

the volatility and unpredictability of the economic environment, and others are intentionally

manipulated by managers, detracting in both cases from the informativeness of financial

information. We thus believe our regression results suggest that the potentially useful attribute

of accruals—a means for managers to impart forward-looking information to investors—is

largely offset by the quality-detracting attribute of accruals, driven by intentional and

unintentional misevaluations10.

We also run regressions where earnings (defined as operating income and alternatively as

income before extraordinary items) are substituted for cash flows (dependent variable) as the

object of prediction. Not surprisingly, in this case, the accruals, aggregated or component-wise,

are in most years significantly associated with subsequent (years t+1 and t+2) earnings.

But, as noted above, in-sample regression analyses are not prediction tests. We, therefore

turn to the latter.

10 Barth et al. (2001) report that components of accruals are significantly associated with subsequent cash flows. Reasons for the difference from our estimates may be our use of free cash flow, relative to their use of cash from operations. More importantly, in the main analysis, Barth et al. (2001) report estimates from pooled regressions (over a 10-year sample). When we run pooled regressions on our data, we also get highly significant coefficients for the accruals components. But our annual regressions tell a different story. It should be noted, however, that Barth et al. (2001, p.52) briefly mention that they get similar (significant) estimates from yearly regressions.

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IV. Prediction Tests

Our prediction tests take the following general form. We predict free cash flows

(earnings) in future years t+1 and t+2 using several sets of predictors: current year CFO only,

current year CFO and total accruals, current year CFO and various components of accruals

(current year capital expenditures are present in all models). Here too the basic idea is intuitive:

to examine whether the addition of accruals to current cash flows improves the prediction of

future cash flows (earnings). The following example (explained thereafter) will clarify the

predictions we perform.

A. Prediction of FCF (t+1)

(a) Benchmark Model CFO only (example for 1989) Estimate cross-sectionally:

εCFOβαFCF +)87(+=)88( Predict: )88(+=)89( CFOβαEFCF , using the above estimated coefficients. Error: )89(FCF - )89(EFCF

(b) Accruals Model (1) Estimate cross-sectionally:

εOAβWCβCFOβαFCF +)87(+)87(∆+)87(+=)88( 321 Prediction and error determination as in (a).

(c) Accruals Model (2)

Estimate cross-sectionally:

εOAβDTβADβINVβWCβCFOβαFCF

+)87(*+)87(+)87(&+)87(∆+)87(*∆+)87(+=)88(

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4321

Prediction and error determination as in (a).

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B. Prediction of FCF (t+2)

(d) Benchmark Model (example for 1989) Estimate: εCFOβαFCF +)87(+=)89( 11 Predict: )88(+=)90( 11 CFOβαEFCF Error: )90(FCF - )90(EFCF

The expanded prediction models incorporating accruals, follow steps (b) and (c), above. Current

year capital expenditures are included as an independent variable in all the models.

Consider the benchmark model (a) above, predicting future 1989 cash flows from current

(1988) cash flows: First we regress free cash flows of 1988 cross-sectionally on CFO of 1987,

and obtain the estimated coefficients α and β . Those coefficients are then used to predict firm

specific free cash flows (EFCF) in 1989, using the firm’s actual CFO of 1988 and the previously

estimated coefficients. In the third stage, a prediction error is determined by comparing the

firm’s actual 1989 FCF with the predicted one. The same procedure is repeated for every firm

and sample year.

Moving to the next example (b)—predicting 1989 free cash flows from CFO, WC, and

OA. First a cross-sectional regression of 1988 free cash flows on the 1987 values of CFO,

WC, and OA is estimated, yielding coefficients ,,, 21 ββα and β3 . Then, firm specific 1989

free cash flows are predicted, using the four coefficients, and the 1988 actual values of CFO,

WC, and OA. Finally, these 1989 FCF predictions (EFCF) are compared with the 1989 actual

free cash flows to determine the prediction error. The same procedure is repeated for each

sample year. Free cash flows are also predicted, using the procedure described above, from the

most detailed accruals breakdown (c): including CFO, inventory change, the aggregate change in

other working capital items, depreciation and amortization, deferred taxes, and the aggregate

remaining other accruals. Derivation of firm-specific FCF predictions, and prediction errors

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follows the above procedure. We repeat the same procedure for year t+2 predictions of FCF.

This is depicted in (d) above. Note the two-year lag in the estimation and prediction processes.

We use the prediction methodology described above to forecast earnings in t+1 and t+2

(income before extraordinary items and operating income). The various prediction models for

earnings are identical to those of free cash flows, except that earnings in T+1 and t+2 are

substituted for FCF in those years.

To evaluate the quality of predictions, we examine three summary measures of prediction

errors derived from the firm- and year-specific prediction errors11: the mean prediction error

(ME), indicating the bias in the forecasts; the mean absolute prediction error (MAE),

disregarding the sign and implicitly assuming that the seriousness (loss) of the error is the same

for positive and negative errors; and the root mean square (RMSE) error, which also abstracts

from the sign of the error and has the same dimension as the predictions and the realizations.

Finally, we form the predictions based on the various predictors (CFO, WC, OA, etc.)

of the most recent year, as in the above example. As a robustness test, we also form predictions

based on the average regression coefficients ,...,, 21 ββα of annual regressions of the most recent

three years. Overall, the predictions based on the most recent year are more accurate than those

based on the last three years, and therefore, the estimates reported and discussed below will be

those based on the most recent year.

Table 1 reports summary prediction errors of the various models we examine, averaged

over all sample firms and years (1989-2001). Here too we focus on the predictive improvement

brought about by the inclusion of the various components of accruals in the predictors. Focusing

on the prediction of next year’s free cash flows (right column of Table 1), we note that the mean

11 The individual prediction error is computed as realized FCF or earnings minus predicted FCF or earnings, divided by market value.

22

error of the predictions which use only CFO (top row, 0.005) is the lowest of all the five models

examined. The addition of accruals to the predictors in fact increases the mean prediction error.

However, when the prediction errors are summarized by the mean absolute error (MAE), and the

root mean square error (RMSE), there is a slight improvement in prediction quality when “other

accruals” are added to the model (prediction models 3-5). For example, the RMSE of model 5

(the most disaggregated accruals), 0.338, is 4.5% lower than the RMSE error of model 1, 0.354,

which does not include any accruals. It is evident, however, that the predictive improvements

brought about by accruals are generally very small, ranging between 0 and 4%.

Considering the prediction of year 2 free cash flows (right column of Table 2), once

more, the mean error indicates that accruals (except for WC in model 2) actually detract from

the predictive ability of CFO. More importantly, in contrast with the prediction of year 1 free

cash flows, where very small improvements can be associated with accruals, both the mean

absolute error, and root mean square error measures do not indicate any improvement in the

prediction of year 2 free cash flows with the use of the various components of accruals. We

obtain, but do not report, very similar results for the prediction of cash from operations (CFO).

Moving to the prediction of subsequent earnings, the two columns to the left of Tables 1

and 2 report summary prediction errors for income before extraordinary items (IBEI) and

operating income (OI). Surprisingly, the results are very similar to those of FCF predictions:

For next year’s earnings, there is generally a very slight improvement when accruals components

are added to the predictors (models 2-5 relative to model 1). These improvements are even

smaller than those of free cash flows (right column). And as was the case for free cash flows,

accruals do not improve the prediction of year t+2 earnings. The findings for earnings prediction

23

TABLE 1 Average Prediction Errors (1988-2001) From Out-Of-Sample Forecasts of Earnings

and Free Cash Flows, Using Various Predictors. One-Year Ahead Predictions

Predictors Income Before Ex Ord. Items

Operating Income

Free Cash Flows

RMSE ME MAE RMSE ME MAE RMSE ME MAE

1. CFO .458 -.017 .217 .371 -.008 .176 .354 .005 .181 2. CFO, WC .455 -.015 .214 .363 -.006 .167 .355 .153 .182 3. CFO, WC,

OACC .442 -.006 .203 .363 -.002 .166 .351 .548 .176

4. CFO, AWC,

INV, D&A, DT

.446 -.008 .206 .365 -.004 .168 .338 .416 .163

5. CFO, AWC,

INV, D&A, DT, OAACC

.442 -.005 .204 .365 -.002 .167 .338 .471 .163

Notes: RMSE, ME, and MAE are root mean square error, mean error, and mean absolute error. The predictors (left column) were defined in notes to Figure 1. OACC are other accruals. OAACC are other accruals minus depreciation & amortization and deferred taxes. All five versions of the prediction models include capital expenditures.

24

TABLE 2 Average Prediction Errors (1988-2001) From Out-Of-Sample Forecasts of Earnings

and Free Cash Flows, Using Various Predictors. Second-Year Ahead Predictions

Predictions

Income Before Ex Ord. Items

Operating Income

Free Cash Flows

RMSE ME MAE RMSE ME MAE RMSE ME MAE

1. CFO .481 -.029 .214 .446 -.016 .191 .344 .026 .174 2. CFO, WC .479 -.029 .211 .439 -.016 .184 .344 .018 .174 3. CFO, WC,

OACC .481 -.026 .208 .437 -.016 .184 .345 .139 .172

4. CFO, AWC,

INV, D&A, DT

.481 -.026 .211 .437 -.014 .186 .354 .403 .170

5. CFO, AWC,

INV, D&A, DT, OAACC

.482 -.025 .210 .436 -.015 .186 .354 .379 .170

25

seem almost the exact opposite of the FASB’s fundamental proposition quoted in the

Introduction. Accrual earnings, by and large, do not seem to improve even the prediction of

earnings, relative to current cash flows, let alone the prediction of cash flows.

Overall, the out-of sample prediction tests do not indicate, in our view, a substantial

contribution of accruals and the underlying estimates to the usefulness of financial information.

It should be noted, of course, that our prediction models are very simple. It may be that more

complex models will yield different results.

V. Portfolio Tests

Poon and Granger (2003, p. 491) note: “Instead of striving to make some statistical

inference, model performance could be judged on some measures of economic significance.” To

gauge the economic significance of the contribution of accruals, and by implication of

accounting estimates, to the usefulness of financial information to investors we perform a series

of portfolio tests. First, we predict years t+1 and t+2 free cash flows (and also cash from

operations), using the procedures described in Section IV. That is, we perform predictions of

subsequent cash flows based on current CFO only, and alternatively on CFO plus components of

accruals. We then use the predicted values of cash flows in years t+1 and t+2 to compute for

each firm and year a predicted change (innovation) in cash flows in t+1 and t+2. We then rank

the sample firms in each year by the expected cash flow change (scaled by beginning-of-year t

market value), and form 10 equal-size portfolios. Finally, we compute abnormal (size, and size

& book-to-market adjusted) returns for each portfolio in years t+1 and t+2, as well as returns on

a zero-investment portfolio (long on the top (positive) FCF change portfolio, and short on the

bottom (negative) FCF portfolio). We focus on these abnormal zero-investment portfolio returns

26

in the evaluation of the contribution of accruals to the usefulness of financial information to

investors.

Figure 2, Panel A presents the size-adjusted returns to various zero-investment (hedge)

portfolios constructed from the prediction of next year’s free cash flows (FCF). The returns

relate to year t+112. (Recall, the ten portfolios are constructed from the ranking of firms each

year on the expected change in next year’s FCF, scaled by beginning-of-year t market value.

The zero-based investment is long on the top portfolio and short on the bottom portfolio.) The

left bar of the graph portrays the return from a perfect prediction of FCF. Thus, if you knew the

value of next year’s FCF for each sample firm, your size-adjusted annual return over the sample

period (1989-2001) would have been 16.3%.13 The second-from-left bar indicates that the size-

adjusted return on a hedge portfolio constructed from the prediction of next year’s FCF based

solely on current CFO would have been 12.4%. The four bars to the right of Panel A present

returns on portfolios constructed from predicted changes in FCF based on various components of

accruals, added to CFO. The four bars reflect, from left to right, returns from FCF predictions

based on current CFO and: (1) WC; (2) WC and OA; (3) WC*, INV, D&A, DT; and

(4) WC*, INV, D&A, DT, OA*, respectively. The definitions of these variables are in

Figure 1, and current capital expenditures is present in the last five models.

Notably, as indicated by the height of the four right bars in Panel A, the addition of

various components of accruals to CFO results in fact in lower size-adjusted returns relative to

those from CFO as the stand-alone predictor. Panel B of Figure 2 presents abnormal returns

12 The return cumulation starts with the fifth month of t+1. 13 The returns presented in Figures 2 and 3 are averages for the years 1989-2002, but exclude the year 1999. For that year, the predictors (CFO and accruals) relate to 1999, and the returns to 2000. In 2000 the stock market bubble burst, and consequently, the returns on all our portfolios are abnormally low, ranging between –60 to –70%. These deeply negative returns distort the portfolios’ performance during 1989-2002, and were therefore excluded from Figures 2 and 3. However, even when the year 1999 is included in the returns, our findings regarding the incremental contribution of accruals to investment outcomes do not change.

27

adjusted for both size and book-to-market effects. As expected, the returns on the five portfolios

based on forecasted FCF are substantially lower than those in Panel A (size-adjustment only),

but the relative performance of the various predictors is largely unchanged: the return on the

portfolio based on the prediction of next year’s FCF from current CFO only (second-from-left

bar) is higher than those from portfolios utilizing various components of accruals, except for the

right-most portfolio which is based on the most disaggregated set of accruals (7.6% vs. 6.9%).

The two panels of Figure 3 present abnormal returns, similarly derived to those of Figure

2, but related to portfolios constructed from the prediction of cash flow changes in year t+2

(relative to t+1). As expected, the returns in Figure 3 are lower than those in Figure 2, reflecting

the increased difficulty of predicting two-years ahead. But the relative performance of the five

portfolios (excluding the perfect foresight) conveys the by now familiar message: the inclusion

of accruals components among the predictors does not improve investment performance. We

obtain very similar results from portfolios based on the prediction of cash from operations, rather

than free cash flows.

We thus conclude that the abnormal returns from predicting future cash flows based on

current cash flows, are equal or higher than the abnormal returns from predicting cash flows

based on current cash flows and various grouping of accruals. These portfolio results, indicating

the economic significance of the prediction models we use, are thus generally consistent with the

out-of-sample prediction results (Section IV): The addition of accruals to cash from operation

does not improve materially the prediction of cash flows.

We end the portfolio tests with estimating abnormal returns on portfolios based on

forecasted earnings. The portfolio construction procedure is essentially the same as the one

described earlier for cash flows. Table 3 presents the abnormal (size and book-to-market

28

Figure 2 Abnormal Returns from Zero-Investment Portfolios Constructed from Forecasted Year

t+1 Cash Flows Based on Current Cash Flows and Various Components of Accruals.

Panel A: Size adjusted returns to hedge portfolios based on actual change in FCF and forecasted changes in FCF from Model 1 to Model 5

Year Actual Model 1 Model 2 Model 3 Model 4 Model 51989 32.0% 5.9% 5.8% 2.5% 8.6% 8.7%1990 13.4% -9.3% -7.8% 3.2% 6.8% 7.3%1991 8.7% 6.4% 9.7% -0.2% 3.6% 8.9%1992 11.5% 28.1% 27.6% 6.9% 9.6% 11.0%1993 17.9% 13.9% 5.2% 2.8% 9.4% 10.1%1994 23.3% 26.1% 22.5% 21.7% 31.0% 27.4%1995 5.1% -33.8% -31.8% -31.3% -20.8% -21.1%1996 19.3% 21.7% 18.1% 15.3% 14.6% 14.9%1997 10.6% 13.5% 16.1% -3.3% -2.9% -2.6%1998 25.4% 6.7% -6.9% -2.1% -3.7% -3.2%2000 12.3% 35.5% 38.8% 36.8% 10.8% 12.4%2001 26.7% 30.2% 29.3% 35.4% 34.1% 36.0%2002 6.4% 15.6% 13.7% 13.5% 17.8% 19.8%

Average 16.3% 12.4% 10.8% 7.8% 9.1% 10.0%Std. Err. 2.3% 5.3% 5.4% 5.1% 4.1% 4.0%

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

Actual Model 1 Model 2 Model 3 Model 4 Model 5

Note to this and subsequent panels: “Actual” refers to returns from perfect foresight of future cash flows. Models 1-5 refer, respectively, to predictions based on current cash flows only; cash flows and working capital changes; cash flows working capital changes and other accruals; cash flows, working capital changes excluding inventories, inventories changes, depreciation and amortization, deferred taxes, and capital expenditures; and lastly (Model 5), the preceding variable plus all the remaining accruals.

29

Panel B: Size and B/M adjusted returns to hedge portfolios based on actual change in FCF and forecasted changes in FCF from Model 1 to Model 5

Year Actual Model 1 Model 2 Model 3 Model 4 Model 51989 30.8% 6.5% 5.8% 2.8% 9.1% 9.2%1990 13.4% -8.9% -7.3% 2.2% 6.1% 6.4%1991 8.8% 4.1% 9.1% -0.9% 2.6% 8.0%1992 12.0% 13.5% 14.9% 4.8% 8.1% 9.8%1993 18.4% 6.5% 0.2% 0.3% 6.7% 7.2%1994 25.0% 19.9% 16.8% 16.5% 27.0% 23.4%1995 5.4% -32.8% -30.8% -30.2% -20.9% -20.4%1996 18.0% 10.5% 10.7% 7.9% 9.6% 11.3%1997 11.1% 8.1% 11.5% -7.3% -6.0% -5.7%1998 23.7% 5.5% -9.2% -1.3% -3.8% -3.3%2000 12.3% 20.1% 20.0% 20.3% 3.9% 4.7%2001 27.1% 23.5% 22.3% 29.8% 28.3% 29.6%2002 6.7% 13.8% 11.4% 11.9% 17.0% 19.2%

Average 16.4% 6.9% 5.8% 4.4% 6.7% 7.6%Std. Err. 2.2% 4.2% 4.2% 4.2% 3.7% 3.6%

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

Actual Model 1 Model 2 Model 3 Model 4 Model 5

30

Figure 3

Abnormal Returns from Zero-Investment Portfolios Constructed Forecasted Year t+2 Cash Flows Based on Current Cash Flows and Accruals Components

Panel A. Size-adjusted returns to hedge portfolios based on actual change in FCF and

forecasted changes in FCF from Model 1 to Model 5: from t+1 to t+2

Year Actual Model 1 Model 2 Model 3 Model 4 Model 5 1990 5.9% -12.7% -14.4% -15.3% -29.4% -27.2%1991 2.9% -8.3% -15.4% -13.8% -5.5% -5.1%1992 35.3% 22.3% 16.9% 27.6% 36.9% 39.8%1993 34.0% 11.5% 12.0% 18.2% 14.7% 14.8%1994 36.8% 17.3% 16.1% 22.7% 15.7% 13.3%1995 -35.2% -37.8% -37.0% -36.4% -33.7% -34.0%1996 47.1% 19.1% 15.6% 18.6% 25.0% 20.6%1997 13.1% -2.8% 1.6% 10.6% 8.0% 7.8%1998 -1.0% -9.9% -16.3% -16.9% 2.9% 1.2%2000 54.8% 36.1% 37.7% 33.9% 24.7% 23.7%2001 73.7% 22.9% 27.0% 26.2% 21.4% 17.0%2002 4.6% 4.0% -13.1% -11.5% -20.1% -15.4%

Average 22.7% 5.1% 2.6% 5.3% 5.1% 4.7%Std. Err. 8.2% 5.7% 6.1% 6.3% 6.3% 6.0%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

Actual Model 1 Model 2 Model 3 Model 4 Model 5

31

Panel B. Size and B/M adjusted returns to hedge portfolios based on actual change in FCF

and forecasted changes in FCF from Model 1 to Model 5: from t+1 to t+2

Year Actual Model 1 Model 2 Model 3 Model 4 Model 5 1990 6.9% -11.6% -12.9% -13.8% -26.8% -24.9%1991 1.4% -9.5% -18.0% -17.1% -9.2% -8.6%1992 21.5% 10.6% 5.4% 13.6% 21.3% 23.8%1993 25.6% 4.0% 3.7% 8.1% 3.3% 3.3%1994 28.3% 9.9% 8.5% 14.6% 8.7% 6.8%1995 -32.1% -36.6% -35.8% -35.4% -32.4% -31.8%1996 32.1% 7.0% 0.9% 3.5% 10.6% 6.9%1997 6.7% -8.5% -5.5% 3.7% 1.5% 1.1%1998 -5.6% -12.3% -19.6% -20.4% -0.9% -3.1%2000 39.7% 18.4% 16.9% 14.7% 10.2% 9.2%2001 64.1% 16.4% 18.7% 17.6% 14.3% 9.8%2002 7.3% 8.5% -11.6% -10.0% -20.9% -12.9%

Average 16.3% -0.3% -4.1% -1.7% -1.7% -1.7%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

Actual Model 1 Model 2 Model 3 Model 4 Model 5

32

adjusted) returns for the two versions of earnings (income before extraordinary items, and

operating income), and two future periods: one and three years. The five models used to predict

future earnings are the same as those in Table 1.

The hedge portfolio returns (long on the top portfolio—highest predicted earnings, and

short on bottom portfolio—lowest predicted earnings) in Table 3 clearly indicate that portfolios

constructed from predicted earnings based on current cash flows yield returns which are as large,

or larger than portfolios of predicted earnings based on cash flows plus accruals. We thus obtain

similar results whether the predicted variable is cash flows or earnings.

VI. Concluding Remarks

Managerial estimates and projections are pervasive in accounting, affecting to an unknown (by

investors) degree practically all income statement and balance sheet items. Estimates and

projections are problematic because their reliability is increasingly challenged in the fast-

changing and ever-intensifying competitive environment, and moreover estimates are easy to

manipulate with impunity. On the other hand, estimates/projections are the major means by

which managers can impart important inside, forward-looking information to investors. Herein,

therefore, lies arguably the most fundamental accounting question: What is the contribution of

accounting estimates to the quality and informativeness of financial information?

We investigate this question by focusing on accounting accruals, where most of the

estimates/projections are embedded, and—following the FASB’s postulate about the predictive

objective of financial information—examine the contribution of accruals to the prediction of both

enterprise cash flows and earnings. Our battery of tests, consisting of regression analyses,

prediction trials, and portfolio tests, do not indicate that accruals, in groups or by individual

33

TABLE 3 Average Abnormal (Size and Book-to-Market Adjusted) Returns on Hedge Portfolios

Based on Predicted Earnings from Current Cash from Operations and Accruals:

Predictors

Income Before Ex. Ord. Items

Operating Income

One Year Three Years One Year Three Years 1. CFO 5.5 17.4 2.5 14.3

2. CFO, WC 4.6 17.0 1.5 14.8

3. CFO, WC, OACC

2.2 9.1 1.2 13.3

4. CFO, WC,

INV, D&A, OT -1.0 3.6 0.5 12.5

5. CFO, AWC,

INV, D&A, DT, OAACC

-1.9 2.0 1.0 14.3

34

components, contribute significantly to the prediction of cash flows, or earnings, beyond current

cash flows. This is obviously a very sober finding for both financial information users and

accounting standard-setters.

Regarding the implications of these findings, we do not propose the elimination of

estimates from accounting measurement and reporting rules, since we believe they can be

substantially improved. Rather, we advocate in a follow up paper procedures that create

incentives for managers to enhance the reliability of estimates, and disincentives to manipulate

estimates. We essentially propose three such procedures: (a) Report the aggregate impact of

estimates/projections on key financial items (e.g., sales, cost of sales, earnings). This will

provide users with important information on the reliability of financial data (e.g., 5% of this

year’s revenues are based on estimates vs. 25% last year ). (b) Compare ex post key estimates

(e.g., provision for bad debts) with realizations. Such comparisons, and the need to explain large

deviations, will provide disincentives to managers to manipulate the estimates. (c) When the

aggregate deviation between estimates and realizations exceeds a cut-off threshold, previously

reported earnings will have to be restated with the realizations replacing the original estimates.

This will provide users with an improved historical context (earnings patterns) of financial

information.

35

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