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Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values
Mary E. Barth William H. Beaver
Graduate School of Business Stanford University
John R. M. Hand
Wayne R. Landsman Kenan-Flagler Business School
University of North Carolina at Chapel Hill
September 2004
We appreciate funding from the Financial Research Initiative, Graduate School of Business, Stanford University, Center for Finance and Accounting Research at UNC-Chapel Hill, Stanford GSB Faculty Trust, and Bank of America Research Fellowships. We also thank workshop participants at Lancaster University and the University of Utah for helpful comments, and Brian Rountree, Steve Stubben, Qian Wang, and Rui Yao for able research assistance. Corresponding author: William H. Beaver, Graduate School of Business, Stanford University, 518 Memorial Way, Stanford, CA 94305-5015, (650) 723-4409, [email protected]
Accruals, Accounting-Based Valuation Models, and the Prediction of Equity Values
Abstract
This study uses out-of-sample equity value estimates to determine whether earnings
disaggregation, imposing valuation model linear information (LIM) structure, and separate
industry estimation of valuation model parameters aid in predicting contemporaneous equity
values. We consider three levels of earnings disaggregation: aggregate earnings, cash flow and
total accruals, and cash flow and four major components of accruals. For pooled estimations,
imposing the LIM structure results in significantly smaller prediction errors; for by-industry
estimations, it does not. However, by-industry prediction errors are substantially smaller,
suggesting the by-industry estimations are better specified. Mean squared and absolute
prediction errors are smallest when disaggregating earnings into cash flow and major accrual
components; median prediction errors are smallest when disaggregating earnings into cash flow
and total accruals. These findings suggest that (1) If concern is with errors in the tails of the
equity value prediction error distribution, then earnings should be disaggregated into cash flow
and the major accrual components; otherwise earnings should be disaggregated only into cash
flow and total accruals. (2) Imposing the LIM structure neither increases nor decreases
prediction errors, which provides support to the efficacy of drawing inferences from valuation
equations based on residual income models that do not impose the structure implied by the
model. (3) Valuation of abnormal earnings, accruals, accrual components, equity book value,
and other information varies significantly across industries.
Accruals, Accounting-Based Valuation Models, and the Prediction of Equity
Values
1. Introduction
There is a large literature examining how accounting amounts, including earnings, and
earnings disaggregated into cash flow and accruals, relate to contemporaneous equity values.1
Ohlson (1995, 1999) and Feltham and Ohlson (1995, 1996) develop valuation models that link
accounting amounts and equity values by assuming a link between equity values and the linear
information structure of the accounting amounts. Although such models have been the subject of
empirical testing, few studies test whether they aid in predicting equity values. The objective of
this study is to determine whether and the extent to which disaggregation of earnings and
imposing valuation model linear information structure aid in predicting contemporaneous equity
values out of sample. We also determine whether and the extent to which basing such
predictions on separate industry estimation of valuation model parameters affects their accuracy.
A primary goal of financial reporting is aiding investors in making economic decisions.
A primary economic decision investors make is assessing the value of firms in which they are
invested or consider investing. The Financial Accounting Standards Board (FASB) recognizes
this motivation for financial reporting by noting in Statement of Financial Accounting Concepts
No. 1, paragraph 34, “financial reporting should provide information that is useful to present and
potential investors, and creditors, and other users in making rational investment, credit, and
similar decisions.” Although the FASB recognizes the importance to investors of financial
statement amounts, the concepts statements provide little guidance as to how the amounts are to
be used. In contrast, accounting-based valuation models incorporating accounting accruals based
1 Throughout we use net income and earnings interchangeably.
on the Feltham-Ohlson framework provide this guidance. We use this framework to provide
empirical evidence on our research questions.
The first empirical question we address is whether disaggregating earnings into cash flow
and total accruals, and into cash flow and the major components of accruals, result in differences
in equity value predictive ability. We do this because several studies find that cash flow and
accruals differ in their ability to forecast future earnings and to explain cross-sectional variation
in equity values. The second empirical question we address is whether accounting-based
valuation models incorporating accruals aid investors in predicting equity market values.
Accounting-based valuation models have been the focus of studies in several contexts, including
examining whether such models are descriptively valid, and assessing the value relevance of
accounting amounts. Some studies use accounting-based valuation models to predict equity
values for purposes of exploiting differences between theoretical and actual equity values.
However, they only consider aggregate earnings and do not address whether imposing the
model’s linear information structure affects predictability. The third empirical question we
address is whether basing predictions on separate industry estimation of valuation model
parameters affects equity market value predictions. Valuation parameters can differ across
industries because the relative mix of accrual components can differ across industries, and
because earnings forecastability or persistence of particular accrual components can differ across
industries.
To address our research questions, we use a sample of Compustat firms from 1987 to
2001. We predict contemporaneous equity market values using out-of-sample estimates, i.e., we
use cross-sectional valuation equations that for each year exclude each firm from the equations
used to predict its equity value that year. Hereafter, we use the term predictions to refer to these
2
out-of-sample equity market value predictions. To test whether earnings disaggregation affects
equity value predictive ability, we predict equity values using three linear information valuation
models (LIMs) employing three levels of earnings disaggregation. LIMs comprise forecasting
equations for abnormal earnings and each earnings component considered separately, and an
equity valuation equation. The LIM structure provides links between multiples in the valuation
equation and those in the forecasting equations. The first LIM is based on aggregate earnings.
The second, following Barth, Beaver, Hand, and Landsman (1999), disaggregates earnings into
cash flow and total accruals. The third, introduced here, disaggregates earnings into cash flow
and the four major components of accruals−change in receivables, change in inventory, change
in payables, and depreciation.
We develop equity value predictions for each LIM using two estimation procedures. The
first procedure is an equity valuation equation that includes accounting amounts as explanatory
variables, but does not impose the structure of the LIM implied by the level earnings
disaggregation. The second procedure imposes the LIM structure. To test whether earnings
disaggregation aids in predicting equity values, we compare prediction errors across the three
LIMs. To test whether imposing the LIM structure aids in predicting equity values, we compare
mean and median squared and absolute prediction errors from estimations when the LIM
structure is imposed to those from when it is not. To test whether basing predictions on separate
industry estimations of valuation model parameters affects equity value predictions, we compare
prediction errors from pooled and separate industry estimations for each LIM.
The effect of imposing the LIM structure on out-of-sample prediction errors cannot be
predicted. This contrasts with in-sample prediction errors, where for a given LIM, the errors
obtained when the LIM structure is not imposed are guaranteed to be no larger than those
3
obtained when it is imposed. There are two reasons why imposing the LIM structure can result
in smaller out-of-sample prediction errors. First, using knowledge of the interrelation of
accounting amounts in structuring the LIM should, other things equal, enhance the equity
valuation equation’s ability to predict equity value. Second, imposing the LIM’s structure
mitigates the extent to which the equity valuation equation overfits the data. However, imposing
the LIM structure can result in larger out-of-sample prediction errors because of inefficiency in
estimating the additional forecasting parameters.
One might also expect equity value prediction errors to decrease as the level of earnings
disaggregation increases. This is because as the level of earning disaggregation increases,
different components of earnings are permitted to have different valuation multiples. However,
earnings disaggregation can be costly in terms of increasing prediction errors. First, out-of-
sample prediction errors can increase as the level of earnings disaggregation increases because of
the potential for data overfitting. Second, as the level of earnings disaggregation increases, so
does the extent of structure imposed by the LIM on the forecasting and valuation relations. In
other words, although earnings disaggregation relaxes constraints on valuation coefficients by
permitting them to differ, it adds constraints on the valuation coefficients when the LIM structure
is imposed. As a result, the predictive ability of each LIM relative to the others could differ
depending on whether the LIM structure is imposed.
Before addressing our first research question by comparing prediction errors based on
different levels of earnings disaggregation, i.e., different LIMs, we address our second research
question by comparing prediction errors within each LIM to determine whether imposing the
LIM structure affects prediction errors. We find that for all three LIMs, imposing the LIM
structure results in significantly smaller prediction errors for pooled estimations. However,
4
prediction errors do not differ significantly when the LIM structure is or is not imposed for the
by-industry estimations. These finding support the efficacy of drawing inferences from
valuation equations based on residual income models that do not impose the structure implied by
the model because doing so neither increases nor decreases prediction errors. A striking result
from the within LIM prediction error comparisons is that, consistent with our prediction relating
to our third research question, prediction errors based on the by-industry estimations are
substantially smaller than those based on the pooled estimations. This finding suggests that
valuation of abnormal earnings, accruals, accrual components, equity book value, and other
information varies significantly across industries. This finding also suggests that inferences
relating to whether imposing the LIM structure reduces prediction errors should be based on by-
industry estimation.
Regarding our first research question, we find evidence of some reduction in mean
prediction errors from disaggregating earnings into cash flow and total accruals, and some
additional reduction from disaggregating total accruals into its four major components. Evidence
from median prediction errors portrays a somewhat different picture. In particular, whereas
mean prediction errors generally support disaggregation of earnings into cash flow and the four
major accrual components, median prediction errors generally support disaggregation of earnings
only into cash flow and total accruals. These findings suggest that if when predicting equity
market values the concern is with errors in the tails of the prediction error distribution, then net
income should be disaggregated into cash flow and the four major accrual components.
However, if the concern is not with errors in the tails of the prediction error distribution, then
earnings should be disaggregated only into cash flow and total accruals. Thus, accrual
5
components appear to provide additional information incremental to that in total accruals helpful
to predicting equity values when considering firms with more extreme prediction errors.
The remainder of the paper is organized as follows. Section 2 develops the research
design. Section 3 describes the sample and data, and section 4 presents the findings. Section 5
summarizes and concludes the study.
2. Research Design
2.1 LINEAR INFORMATION MODELS
Our tests of equity value prediction errors use equity value estimates from three linear
information models (LIMs) based on the Feltham-Ohlson framework. Each LIM reflects a
different level of earnings disaggregation. Our first research question is whether successively
disaggregating earnings into cash flow and total accruals, and cash flow and four major accrual
components aids in prediction equity values. Our second research question is whether imposing
the LIM structure aids in predicting equity values.
The first linear information model, LIM1, is based on Ohlson (1995), and comprises three
equations. Equations (1a) – (1c) are forecasting equations, and equation (1d) is the valuation
equation implied by the linear information dynamics of the forecasting equations. For example,
Ohlson (1995) shows that the abnormal earnings valuation coefficient in equation (1d), α1, is a
nonlinear function of ω11 and the discount rate, r.
itititait
ait BVNINI 111311211110 ενωωωω ++++= −−− (1a)
ititit BVBV 212220 εωω ++= − (1b)
ititit 313330 ενωων ++= − (1c)
itititaitit uBVNIMVE ++++= ναααα 3210 (1d)
6
MVE is market value of equity, NIa is abnormal earnings defined as earnings minus the normal
return on equity book value, BV, the εks and u are error terms, and the i and t subscripts denote
firm and year.2 tν , other information, is defined as 11 −− − tt MVEMVE , where 1−tMVE is the
fitted value of based on a version of equation (1d) that does not include 1−tMVE tν . Thus, tν
captures the extent to which the accounting variables do not explain market value of equity
(Feltham and Ohlson, 1995; Ohlson, 1995). We include equity book value in equation (1a) and
the abnormal earnings and component forecasting equations for LIM2 and LIM3 to enhance
stationarity of the forecasting equations (Barth, Beaver, Hand, and Landsman, 1999). LIM1
implicitly assumes that all earnings components have equal weight in forecasting abnormal
earnings and hence have equal weight in the valuation equation.
We estimate LIM1 because it focuses on aggregate earnings and plays a prominent role in
the empirical accounting literature. Several studies (Bernard, 1995; Lundholm, 1995; Barth,
Beaver, Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999; Myers, 1999) find that
LIMs using aggregate earnings are descriptively valid. In light of this, a rather robust literature
uses specifications based on LIM1 to examine how accounting amounts relate to
contemporaneous equity values to obtain inferences about these accounting amounts, i.e., their
value relevance (Barth, Beaver, and Landsman, 2001; Holthausen and Watts, 2001). Other
studies (Frankel and Lee, 1998; Lee, Myers, and Swaminathan, 1999) use models similar to
LIM1 to estimate theoretical prices to exploit differences between theoretical and actual equity
values to find mispriced securities.
The second, LIM2, is that estimated in Barth, Beaver, Hand, and Landsman (1999). It
relaxes the assumption that the total accruals, ACC, and cash flow components of earnings have
2 We use the same notation for coefficients and error terms across the three LIMs to facilitate exposition. They
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the same model parameters.3 LIM2 can be viewed as a version of the model in Ohlson (1999),
which models the transitory component of earnings, although the model applies to any earnings
component. LIM2 comprises four equations, where equations (2a) through (2d) are forecasting
equations, and equation (2e) is the valuation equation implied by the linear information dynamics
of the forecasting equations. Thus, relative to LIM1, by adding an additional forecasting
equation, LIM2 imposes additional assumptions on the valuation parameters.
ititititait
ait BVACCNINI 111411311211110 ενωωωωω +++++= −−−− (2a)
itititit BVACCACC 212312220 εωωω +++= −− (2b)
ititit BVBV 313330 εωω ++= − (2c)
ititit 414440 ενωων ++= − (2d)
ititititaitit uBVACCNIMVE +++++= νααααα 43210 (2e)
We estimate LIM2 because it focuses on the cash flow and total accrual components of
earnings and several studies find that these components differ in their ability to forecast future
earnings and to explain cross-sectional variation in equity values (Dechow, 1994; Sloan, 1996;
Barth, Beaver, Hand, and Landsman, 1999; Barth, Cram, and Nelson, 2001).
The third, LIM3, further relaxes the assumptions relating to earnings components by
permitting the model parameters for four major accrual components to differ from one another as
well as from those on other components of earnings, including cash flow. LIM3 comprises
seven equations. Thus, relative to LIM2, by adding three additional forecasting equations, LIM3
imposes additional assumptions relating to the valuation parameters.
itititititititait
ait BVDEPAPINVRECNINI 111711611511411311211110 ενωωωωωωωω ++++∆+∆+∆++= −−−−−−− (3a)
likely differ.
8
ititititititit BVDEPINVRECREC 212712612512312220 ενωωωωωω ++++∆+∆+=∆ −−−−− (3b)
ititititititit BVDEPAPINVRECINV 313613513413313230 εωωωωωω +++∆+∆+∆+=∆ −−−−− (3c)
ititititit BVAPINVAP 414614414340 εωωωω ++∆+∆+=∆ −−− (3d)
itititit BVDEPDEP 515615550 εωωω +++= −− (3e)
ititit BVBV 616660 εωω ++= − (3f)
ititit 717770 ενωων ++= − (3g)
itititititititaitit uBVDEPAPINVRECNIMVE ++++∆+∆+∆++= ναααααααα 76543210 (3h)
REC∆ is annual change in receivables, INV∆ is change in inventory, AP∆ is change in
payables, and DEP is depreciation and amortization expense.
We estimate LIM3 because it focuses on earnings disaggregated into cash flow and four
major accrual components and findings in Barth, Cram, and Nelson (2001) indicate these
components differ in their ability to forecast future cash flows and explain cross-sectional
variation in equity values. In addition, Barth, Beaver, Hand, and Landsman (1999) finds that
LIM2 may be mispecified, which suggests that disaggregating accruals into its major
components could enhance our ability to predict equity values.
Appendix A describes how we develop LIM3 and presents findings from estimating the
LIM forecasting equations for all three LIMs. Appendix B develops the algebraic relation
between the valuation coefficients and the forecasting equation coefficients for LIM3. As
explained in Appendix B, the signs and magnitudes of the αjs in equation (3h) depend on the ωs
in equations (3a) through (3g). The relations among the αjs and the ωs are complex because of
the number of explanatory variables in equation (3h), each of which has its own forecasting
3 Note that permitting a different coefficient for total accruals in equations (2a) and (2e) implicitly permits the
9
equation. The complexity of the relations is exacerbated because equations (3a) through (3g) do
not have a triangular structure. For example, with a triangular structure, the signs of α1 and α2
are determined solely by the signs of ω11 and ω22, respectively (Myers, 1999). Although it can
be shown that the sign of α1 is determined by the sign of ω11, the sign of each of the remaining
αs is not determined by any single ω.
The third research question we address is whether estimating valuation parameters using
separate industry estimation aids in predicting equity market values. Valuation parameters can
differ across industries for two reasons. The first is that the relative mix of accrual components
can differ across industries. For example, manufacturing firms have substantial investments in
inventory, but service firms do not. With respect to LIM3, if this is the only difference, then all
valuation and forecasting parameters will be the same across industries. However, because
inventory is aggregated with other accruals in LIM1 and LIM2, valuation and forecasting
parameters will differ across industries for these LIMs. The second is that earnings
forecastability or persistence of particular accrual components can differ across industries. For
example, manufacturing firms are likely to have more persistent receivables than retail firms. To
the extent that firms within the same industry face similar economic conditions, including cost of
capital, and have similar accounting practices, including level of conservatism, the valuation and
forecasting parameters for firms within a given industry will be the same. But, the parameters
can differ across industries as a result of differences in economic environment and accounting
practices. Separate industry estimation permits all valuation and forecasting parameters to
reflect systematic variation in economic and accounting environments across industries, e.g.,
coefficients on cash flow, i.e., ω11 and α1, to differ from those on accruals, i.e., ω11 + ω12 and α1 + α2.
10
differential persistence in abnormal earnings. It also permits the level of conservatism and the
cost of capital associated with abnormal earnings to vary by industry.4
2.2 OUT-OF-SAMPLE PREDICTION
We use a jack-knifing procedure to generate contemporaneous out-of-sample equity
market value predictions. The principal reason for using jack-knifing is that we seek to obtain
equity value predictions for each firm without using that firm’s data to generate its predicted
equity value.5 Jack-knifing also results in our obtaining statistics for hypothesis testing that do
not rely on unknown parametric distributions, e.g., normality (Noreen, 1989).6
The prediction of firm i’s equity value in year t is the predicted value from the valuation
equation in each LIM, i.e., equations (1d), (2e), and (3h), using estimated coefficients from the
valuation equation and all firms’ data except firm i’s in year t. Because firm i’s data in year t are
not used to estimate the coefficients, each prediction is out-of-sample. We set to zero negative
predicted equity market values because equity market values cannot be negative.7
Imposing the structure implied by the LIM constrains the estimated valuation coefficients
to be related to the estimated forecasting equation coefficients in the manner specified by the
particular LIM. When we impose the LIM structure, we exclude firm i’s data in year t when
4 As explained in section 3.1, when we estimate equations pooling sample firms across industries, we use industry and year fixed-effects. This permits intercepts to vary across industries and years, but restricts slope coefficients to be the same. 5 Another motivation for using out-of-sample predictions is to help distinguish between two alternative interpretations for the finding in Barth, Beaver, Hand, and Landsman (1999) that imposing the structure of LIM2 results in greater in-sample equity value prediction errors. In particular, one interpretation of that finding is that LIM2 not correctly specified. Another is that LIM2 is correctly specified and it overfits the data. That is, it is possible that imposing the structure implied by LIM2 results in estimated valuation coefficients that are closer to unobservable valuation multiples at the expense of lower explanatory power relative to an estimation in which the structure is not imposed. It is difficult to determine which interpretation is correct without out-of-sample prediction tests. 6 The jack-knife procedure assumes that parameter estimates are generated from a sample that was collected randomly and that observations in the sample are independent.
11
estimating all of the LIM’s equations. For example, when generating the LIM1 prediction for
firm i in year t without imposing the LIM structure, we estimate equation (1d) using the data for
all firms except firm i in year t. When generating the LIM1 prediction for firm i in year t with
imposing the LIM structure, we estimate equations (1a) through (1d) using the data for all firms
except firm i in year t and restricting the coefficients in equation (1d) to equal those implied by
equations (1a) through (1c), e.g., . )/( 11111 ωωα −= R
2.3 PREDICTION ERROR TESTS
For each LIM, we construct two distributions of prediction errors, one generated without
imposing the LIM structure and one with. For each distribution, we calculate two commonly
employed prediction error metrics, absolute percentage error, AE, and squared percentage error,
SE:
AE = ititit MVEMVEMVE )/ predicted abs( − and (4a)
SE = . (4b) 2))/ predicted (( ititit MVEMVE MVE −
To assess the statistical significance of differences in prediction errors, we compare both means
and medians for AE and SE.8 This results in a total of eight error metrics for each LIM. For
tests comparing means, MeanAE and MeanSE, we assume unequal variances when tests of
variance equality reject the null. For tests comparing medians, MedAE and MedSE, we use a
nonparametric paired sign test that does not require symmetry of paired differences in the ranks.
To address our first research question, whether earnings disaggregation aids in predicting
equity values, we compare prediction errors across the three LIMs, when the LIM structure is
7 The number of negative predicted equity market values is approximately 10 percent in each estimated LIM. Not surprisingly, the firms with negative predicted equity values are concentrated among firms with small equity market values. 8 The term significant indicates statistical significance at the 0.05 level or less using a one-sided test for signed predictions, and a two-sided test otherwise.
12
imposed and when it is not. To address our second research question, whether imposing the LIM
structure aids in predicting equity values, within each LIM, we compare predictions from
estimations when the LIM structure is imposed to those from when it is not. To address our third
research question, whether basing predictions on separate industry estimations of valuation
model parameters affects equity value predictions, we compare prediction errors from pooled
and separate industry estimations for each LIM, when predictions are based on imposing the
LIM structure and when they are not.
3. Data and Descriptive Statistics
3.1 DATA
We obtain data for 1987−2001 from the Compustat Primary, Secondary, and Tertiary,
Full Coverage, and Research Annual Industrial Files. Our sample period begins in 1987
because prior to that date cash flow from operations disclosed under Statement of Financial
Accounting Standards No. 95 (FASB, 1987) is unavailable. To mitigate the effects of outliers,
for each variable, by year and within each industry, we treat as missing observations that are in
the extreme top and bottom one percentile (Collins, Maydew, and Weiss, 1997; Fama and
French, 1998; Barth, Beaver, Hand, and Landsman, 1999), and observations for which the
absolute value of any accrual component used in LIM3 divided by total revenue is greater than
one. To avoid the influence of small firms, we restrict the sample to firms with total assets in
excess of $10 million. To facilitate comparisons across LIMs, we require sample firms to have
full data to estimate all forecasting and valuation equations, which results in a sample common
across LIMs. All variables are measured as of fiscal year end, including equity market value,
and are expressed in millions of dollars.
13
Net income, NI, is income before extraordinary items from the statement of cash flows.
Although defining NI in this way violates the clean surplus assumption of Ohlson (1995), it
eliminates potentially confounding effects of large one-time items and is consistent with prior
research (e.g., Dechow, Hutton, and Sloan, 1999).9 Findings in Hand and Landsman (2004)
suggest that violating clean surplus should have little effect on our findings. In calculating
abnormal earnings, NIa, we set R − 1 ≡ r = 12%, the long-term return on equities (Barth, Beaver,
Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999).10 Totals accruals, ACC, equals
NI minus cash flow from operations.
We estimate all equations with untabulated year fixed-effects, and with untabulated
industry fixed-effects, when applicable, pooling available firm-year observations from all sample
years. We use data from the current and most recent four prior years when estimating valuation
and forecasting equations.11 Because lagged amounts appear as explanatory variables in the
forecasting equations, estimation of these equations uses data from six years. This reflects a
tradeoff between efficiency and parameter stationarity, where presumably the former (latter) is
increasing (decreasing) in years included in the estimating equations.
We base our industry classifications on those in Barth, Beaver, and Landsman (1998) and
Barth, Beaver, Hand, and Landsman (1999), and include food; textiles, printing and publishing;
chemicals; pharmaceuticals; extractive industries; durable manufacturers; computers; retail; and
services. We subdivide durable manufacturing firms into seven industries: rubber; plastic,
leather, stone, clay & glass; metal; machinery; electrical equipment; transportation equipment;
instruments; and miscellaneous. We also subdivide retail firms into three industries: wholesale;
9 It also is consistent with one-time items having zero persistence with respect to future abnormal earnings (Ohlson, 1999). 10 None of our experimental inferences is affected by assuming alternative values for r, ranging from 8 to 14 percent.
14
miscellaneous retail; and restaurant. We subdivide the durable manufacturers and retail
industries to increase the likelihood that parameters are the same within each industry, and to
help balance the number of sample firms across industries. However, we exclude financial
institutions and those firms in the insurance and real estate industries. We do so to ensure that
the accrual components on which we focus are meaningful for our sample firms. For example,
inventory is not a predictor of future earnings for financial institutions. We estimate all
equations using unscaled data (Barth and Kallapur, 1996).12
3.2 DESCRIPTIVE STATISTICS
Table 1 presents descriptive statistics for each variable used in the estimating equations.
Panel A reports distributional statistics, panel B contains Pearson and Spearman correlations, and
panel C describes the industry composition of the sample. Panel A reveals that, on average, the
market value of equity exceeds the book value of equity, indicating that equity book value alone
is insufficient to explain equity market value. Consistent with prior research, (Sloan, 1996;
Barth, Beaver, Hand, and Landsman, 1999; Barth, Cram, and Nelson, 2001), panel A also reveals
that, on average, total accruals is negative. This is attributable to depreciation expense being
included in accruals, but capital expenditures being included in investing cash flows. In
particular, mean depreciation and amortization expense, $27.45 million, is more than three times
greater than mean change in receivables, $5.59 million, the next largest accrual component. To
provide insight into the relative size of each accrual component, panel A also includes
distributional statistics for the absolute value of each component divided by total revenue.
Findings indicate that all four accrual components comprise a non-trivial proportion of total
11 As noted above, we exclude firm i’s data in year t when predicting year t’s equity market value. However, we use firm i’s data for years prior to year t because they are known when predicting equity market value for year t.
15
revenues, with depreciation and amortization expense being the largest component (mean =
5.98% of total revenues), and change in inventory being the smallest (mean = 2.36% of total
revenues).
Panel B reveals that most of the variables are highly correlated with each other. Panel C
reveals that industries with the largest concentrations of firm-year observations are Computers,
15.32%, Textiles, printing & publishing, 9.49%, and Services, 9.18%.
4. Results
4.1 SUMMARY STATISTICS FROM LIM ESTIMATIONS
Table 2, panels A through C, present regression summary statistics for the equity market
value equations for the three LIMs, equations (1d), (2e), and (3h).13 These statistics are not
based on the jack-knifing procedure described in section 2.2. We present these statistics to
provide descriptive evidence on the magnitudes and signs of the valuation parameter estimates
and the effects on the estimates of imposing the LIM structure, and to facilitate comparison with
prior research. The first two lines in each panel report statistics based on pooling all
observations. The remaining lines report statistics from industry-by-industry estimations,
specifically means, minimums and maximums, number of industries for which coefficients are
significantly positive and negative, and number of industries for which the coefficients estimated
with and without imposing the LIM structure differ significantly. For example, the mean α1
estimate in table 2, panel A, 6.82, is an average of the 17 industry mean values. The test of
12 Untabulated findings from regressions using a variety of controls for scale differences across firms result in inferences similar to those from the tabulated findings. 13 We employ seemingly unrelated regressions when estimating each system of equations. Thus, parameter estimates from the valuation equations reflect the effects of permitting regression errors from each of the forecasting equations to be correlated with those in the valuation equation.
16
whether each mean coefficient differs from zero is based on the standard deviation of the 17
industry means (Fama and MacBeth, 1972).
The findings relating to LIM1 in panel A are consistent with prior research (Barth,
Beaver, Hand, and Landsman, 1999; Dechow, Hutton, and Sloan, 1999). In particular, the
valuation coefficients on abnormal earnings and equity book value, α1 and α2, are significantly
positive in the pooled sample and in all industries (and therefore the mean coefficients across
industries are also significantly positive), both with and without imposing the LIM structure.
The valuation coefficient, α3, on other information, ν , also is always significantly positive. For
example, without imposing the LIM structure, the pooled estimation coefficient estimates (t-
statistics) for α1, α2, and α3 are 9.45, 2.52, and 0.69 (69.75, 143.44, and 80.38). The large range
in coefficient estimates across the 17 industries, as evidenced by the minimums and maximums,
suggest equity predictions based on separate industry estimation rather than pooled estimation
may be more accurate. For example, without imposing the LIM structure, estimates of α1 across
industries range from 2.02 to 21.84.
Panel A also reveals that the valuation coefficients, α1, α2, and α3, estimated with and
without imposing the LIM structure differ significantly for virtually all industries. For example,
for 8 (7) industries, α1 estimates are significantly larger when the LIM structure is not (is)
imposed, leaving only two industries for which the α1 estimates do not differ significantly. This
raises the possibility that predictions of equity market value based on coefficients estimated with
and without imposing the LIM structure could differ significantly.
Turning to LIM2, the findings in panel B also are consistent with prior research (Barth,
Beaver, Hand, and Landsman, 1999). In particular, for the pooled sample and for all industries,
the valuation coefficients on abnormal earnings and equity book value, α1 and α3, are
17
significantly positive. The incremental valuation coefficient on total accruals, α2, is significantly
negative in most (all) industries when the LIM structure is not (is) imposed. The means across
industries of α1, α2, and α3 without imposing the LIM structure are 7.43, −2.18, and 2.10, which
compare to means across industries of 8.95, −1.94, and 1.87 in Barth, Beaver, Hand, and
Landsman (1999). The fact that the coefficient on total accruals differs from that on other
components of abnormal earnings suggests that disaggregating earnings into cash flow and total
accruals can enhance equity valuation prediction. As for LIM1, the valuation coefficient for
other information, α4, is significantly positive in all cases.
Panel B also reveals that the valuation coefficients estimated with and without imposing
the LIM structure differ significantly for almost all industries. For example, for 10 (5) industries,
α2 estimates are significantly larger when the LIM structure is not (is) imposed, leaving only two
industries for which the α2 estimates do not differ significantly. As with LIM1, this again raises
the possibility that predictions of equity market value based on coefficients estimated with and
without imposing the LIM structure could differ significantly.
Findings in panel C relating to LIM3, which permits separate coefficients for the four
accrual components, indicate substantial differences in coefficients across the components, as
well as substantial inter-industry differences in coefficients for each component. Regarding
cross-component differences, results from the pooled estimation without imposing the LIM
structure indicate each of the incremental coefficients on change in inventory, change in
payables, and depreciation, α3, α4, and α5, is positive, and that on change in receivables, α2, is
negative. However, only the incremental coefficient on change in payables is significantly
different from zero. The pooled α2, α3, α4, and α5 coefficient estimates (t-statistics) are −0.22,
0.48, 1.20, and 0.21 (−0.68, 1.15, 3.34, and 1.10).
18
Results from the pooled estimation with imposing the LIM structure indicate that the
incremental coefficients on change in payables and depreciation, α4, and α5, are significantly
positive, and those on changes in receivables and inventory, α2, and α3, are significantly
negative. The pooled α2, α3, α4, and α5 coefficient estimates (t-statistics) are −1.40, −2.70, 1.17,
and 0.84 (−7.63, −11.69, 5.90, and 4.61). In addition, untabulated findings from a test of
equality of coefficients across the four accrual components indicate the coefficients differ
significantly from each other. These findings indicate that the total coefficients on depreciation
and changes in receivables, inventory, and payables significantly differ from those on the cash
flow and other accrual components of earnings when the LIM structure is imposed. Thus,
relating to our first research question, these findings suggest that disaggregation of total accruals
into its four major components can aid in predicting equity values when the LIM structure is
imposed. Relating to our second research question, finding different coefficients with and
without imposing the LIM structure raises the question of whether equity value prediction is
enhanced when the LIM structure is imposed.
Turning to the separate industry estimations, table 2 reveals that inferences relating to the
mean coefficients across industries differ from those from the pooled regressions. In particular,
when the LIM structure is not imposed, none of the incremental accrual component coefficient
estimates of α2, α3, α4, and α5 is significantly different from zero. When the LIM structure is
imposed, only the coefficient on change in inventory, α3, is significantly different from zero.
Also, table 2, panel C, indicates there is substantial cross-industry variation in the
coefficients on each accrual component. For both with and without LIM structure-imposed
estimations, the incremental valuation coefficient, αj, on each accrual component is significantly
positive for some industries and negative for others. For example, when the LIM structure is not
19
imposed, the coefficient on change in payables, α4, is significantly positive in five industries, and
significantly negative in five industries. This contrasts with the coefficients on the other
components of abnormal earnings, which includes cash flow, α1, equity book value, α6, and
other information, α7, which are significantly positive in all industries. The incremental
valuation coefficients on change in receivables, α2, and change in payables, α4, are more
consistently positive than those on change in inventory, α3, and depreciation, α5, which are more
evenly split as to their signs.
Collectively, table 2, panels A, B, and C, yield three key findings that potentially have
implications for equity value predictions. First, the valuation coefficient on net income differs
from that on total accruals, and the valuation coefficients on the major accrual components differ
from each other. Second, the signs and magnitudes of the accrual component valuation
coefficients depend on whether the LIM structure is imposed. Third, accrual component
valuation coefficients differ across industries. The next section examines the extent to which
these differences affect equity value prediction.
4.2 COMPARISON OF OUT-OF-SAMPLE EQUITY VALUE PREDICTIONS
4.2.1 Within LIM comparison of equity value prediction errors
Table 3 presents mean (median) squared and absolute errors, MeanSE and MeanAE
(MedSE and MedAE), for equity market value predictions obtained from estimations in which
model parameters are estimated with and without imposing the LIM structure, using the jack-
knifing procedure described in section 2.2. Significant differences are denoted by boldface font.
For each comparison, table 3 presents findings based on prediction errors from pooled and
separate industry estimations. Two comparisons are presented for the industry estimations. The
first is based on aggregating all errors from separate industry estimations. The second is based
20
on the mean and median error metrics for each of the 17 industries. Table 3 also lists the number
of industries for which the error metrics differ significantly. Panels A, B, and C present the
findings relating to LIM1, LIM2, and LIM3.
Findings relating to pooled estimations for all three LIMs reveal that imposing the LIM
structure results in significantly smaller MeanSEs, MeanAEs, MedSEs, and MedAEs. For
example, for LIM1, panel A reveals that imposing the LIM structure significantly reduces the
MeanSEs (MeanAEs) from 75.94 to 65.25 (2.72 to 2.64) based on pooled estimation. However,
for LIM1 and LIM2, this finding does not obtain in the by-industry estimation. In particular,
with one exception, all four error metrics based on by-industry estimations are significantly
larger when the LIM structure is imposed. For example, for LIM1, panel A reveals that
imposing the LIM structure significantly increases the MeanSEs (MeanAEs) from 34.04 to 35.98
(1.76 to 1.79). For LIM3, the results are mixed in that when the LIM structure is not imposed,
median prediction errors are significantly larger, but mean prediction errors are significantly
smaller. However, for all three LIMs, none of the error metrics relating to the mean (median) of
industry means (medians) differs significantly when the LIM structure is or is not imposed.
Consistent with this, for all three LIMs, the number of industries for which MeanSEs (MeanAEs)
are significant smaller with or without imposing the LIM structure is approximately the same,
although there is some evidence that imposing the LIM structure is marginally beneficial for
LIM2. Taken together, these findings suggest that imposing the LIM structure neither
consistently increases nor consistently decreases prediction errors. Thus, these findings support
the efficacy of drawing inferences from valuation equations based on residual income models
that do not impose the structure implied by the model.
21
A striking result in table 3 relates to the comparison of findings between the pooled and
the by-industry estimations. First, consistent with our prediction that the relation between equity
market value and accounting amounts differs across industries, each of the four error metrics is
significantly and substantially larger based on the pooled estimation.14 For example, the
MeanSEs and MeanAEs based on the pooled estimation are almost twice as large as those based
on by-industry estimation. Recall that the pooled estimations include industry fixed-effects.
Had we restricted the intercept to be the same across industries in the pooled estimations, the
differences between the pooled and by-industry estimations likely would be even greater.
Second, inferences relating to whether imposing the LIM structure reduces prediction errors
differ depending on whether the inferences are based on comparisons of error metrics from
pooled or by-industry estimation. Whereas the error metrics based on pooled estimation are
significantly smaller when the structure is imposed, the reverse is true in the by-industry
estimation.
4.2.2 Cross-LIM comparisons of equity value prediction errors
Table 4 presents comparisons of the four error metrics across the three LIM estimations.
Panel A (B) presents comparisons of MeanSE and MeanAE without (with) imposing the LIM
structure; panel C (D) presents analogous statistics for MedSE and MedAE. Significant
differences between (1) LIM1 and LIM2, (2) LIM1 and LIM3, and (3) LIM2 and LIM3 error
metrics are denoted by an asterisk (*), italics font, and boldface font, respectively. For each
pairwise comparison of the LIMs, table 4 also lists the number of industries for which the error
metrics differ significantly.
14 MeanSE, MeanAE, MedSE, and MedAE values for pooled estimations are significantly larger than each comparable industry-based value at less than the 0.0001 level. Consistent with these findings, Barth, Beaver, Hand, and Landsman (1999) provides descriptive evidence that accrual and cash flow earnings components vary across
22
Comparison of MeanSE and MeanAE based on LIM1 and LIM2 in panels A and B
reveals that disaggregation of earnings into cash flow and total accruals aids in predicting equity
market values. In 11 of 12 comparisons, the error metrics for LIM2 are smaller than those for
LIM1. However, only four of these differences are significant, three of which obtain when the
LIM structure is imposed. In particular, panel B reveals that when the LIM structure is imposed,
three of six error metrics are significantly smaller for LIM2 than LIM1, and none is significantly
smaller for LIM1. The significant reductions are in MeanSE, 65.25 to 58.13, based on pooled
estimation, and in MeanAE, 2.64 to 2.58 and 1.79 to 1.76, based on pooled and by-industry
estimation. In addition, there is a greater number of industries for which LIM2 results in a
reduction in MeanSE (MeanAE), 4 versus 3 (7 versus 5).
Regarding comparison of prediction errors from LIM2 and LIM3, panels A and B reveal
that LIM3 evidences smaller prediction errors than LIM2 when the LIM structure is not imposed.
For example, panel A reveals that when the LIM structure is not imposed, disaggregating
earnings into cash flow and the four major accrual components significantly decreases MeanSE
from 33.97 to 31.66 based on by-industry estimation, and MeanAEs from 2.69 to 2.66 and 1.75
to 1.68, based on pooled and by-industry estimation. However, panel B reveals that when the
LIM structure is imposed, MeanSEs and MeanAEs increase significantly when using LIM3,
from 58.13 to 64.20 and 2.58 to 2.63, based on pooled estimation. For only MeanAE based on
by-industry estimation is there a significant decrease in prediction error from LIM2 to LIM3
when the LIM structure is imposed.
In addition, table 4, panels A and B reveal that the efficacy of disaggregating total
accruals into its four major components appears to be industry-specific. In particular, when the
industries, but does not test whether constraining the components’ coefficients to be the same across industries is binding.
23
LIM structure is not imposed, panel A reveals there are 2 (3) industries for which LIM2 results in
significantly smaller MeanSEs (MeanAEs), and 4 (7) industries for which LIM3 results in
significantly smaller MeanSEs (MeanAEs). When the LIM structure is imposed, panel B reveals
the number of industries for which LIM2 or LIM3 has significantly smaller MeanSEs and
MeanAEs is evenly split.
Although comparison of error metrics based on LIM2 and LIM3 fails to reveal a
consistent benefit to additional disaggregation of earnings into cash flow and the four major
accrual components, comparison of mean prediction errors from LIM1 and LIM3 reveals a
somewhat clearer picture. In particular, in all 12 possible cases, error metrics for LIM3 are
smaller than those for LIM1. When the LIM structure is (is not) imposed, 4 of 6 (2 of 6) of the
differences are significant. For example, panel A reveals that when the LIM structure is not
imposed, there is a significant reduction in MeanSE (MeanAE) from 75.94 to 73.96 (2.72 to
2.66), based on pooled estimations, and from 34.04 to 31.66 (1.76 to 1.68), based on by-industry
estimations. Panel B reveals that when the LIM structure is imposed, there are significant
reductions in MeanAEs only, from 1.79 to 1.71 based on pooled estimations, and from 1.72 to
1.64, based on by-industry estimations.
Also, table 4, panels A and B, reveal that the efficacy of disaggregating earnings into
cash flow and the four major accrual components appears to be compelling for a greater number
of industries, whether or not the LIM structure is imposed. In particular, panel A reveals that
whereas there are 3 (8) industries for which LIM3 results in significantly smaller MeanSEs
(MeanAEs) when the LIM structure is not imposed, and panel B reveals there are 8 (9) industries
when it is, there are only 1 (2) industries for which LIM3 results in significantly larger MeanSEs
(MeanAEs) when the LIM structure is not imposed, and 2 (3) industries when it is.
24
Taken together, the findings in panels A and B based on mean error prediction metrics
suggest there is some reduction in prediction error when earnings are disaggregated into cash
flow and total accruals, and some additional reduction when total accruals are disaggregated into
its four major components. However, the total reduction in prediction error obtained from
disaggregating net income into cash flow and the four major accrual components is more
substantial than is apparent from the two sequential disaggregations. In other words, although
there is some separation in predictive ability between LIM2 and LIM1, and some additional
separation between LIM3 and LIM2, the total separation between LIM3 and LIM1 is more
apparent.
Turning to the median statistics presented in table 4, panels C and D, comparison of
prediction errors across the three LIMs portrays a somewhat different picture from the
comparisons based on mean statistics presented in panels A and B. In particular, whereas the
mean prediction errors and industry count statistics in panels A and B generally support
disaggregation of earnings into cash flow and the four major accrual components, the median
prediction errors generally support disaggregation of earnings only into cash flow and total
accruals. Furthermore, this conclusion holds whether or not the LIM structure is imposed. For
example, panel C reveals that when the LIM structure is not imposed, disaggregation of net
income into cash flow and total accruals significantly reduces the MedSEs (MedAEs) from 0.85
to 0.79 (0.92 to 0.89) based on pooled estimation, from 0.36 to 0.34 (0.60 to 0.59) based on by-
industry estimation. In addition, whereas the number of industries for which LIM2 results in
smaller MedSE (MedAE) is 6 (6), the number for which LIM1 results in smaller MedSE
(MedAE) is only 2 (3).
25
Comparison of error metrics for LIM2 and LIM3 reveals that disaggregation of total
accruals is not beneficial. For example, panel C reveals that when the LIM structure is not
imposed, MedSEs (MedAEs) increase from 0.79 to 0.84 (0.89 to 0.92) based on pooled
estimation, and from 0.34 to 0.36 (0.59 to 0.60) based on separate industry estimation, although
only the by-industry differences are significant. As with the mean statistics in panel B, the
efficacy of disaggregating earnings into cash flow and the four major accrual components based
on median error metrics appears to be industry-specific, with a virtual tie in terms of number of
industries for which LIM2 or LIM3 results in significantly smaller error metrics.
Finally, the comparison of median error metrics for LIM1 and LIM3 in table 4, panels C
and D reveal some evidence that LIM3 results in smaller median prediction errors than LIM1.
Most notably, the number of industries for which LIM3 results in significantly smaller error
metrics than LIM1 largely reflects the benefits of disaggregating net income into cash flow and
total accruals, i.e., LIM2. However, disaggregation of total accruals into its four major
components yields only a modest increase in the number of industries for which there are smaller
error metrics than is obtained when disaggregating net income into cash flow and total accruals.
Thus, in contrast to the evidence from the mean statistics, the evidence from the median statistics
indicates that equity market value predictive ability improves primarily only when
disaggregating net income into cash flow and total accruals.15
15 As explained in Appendix A, the LIM3 we develop and estimate is based on a model we believe appropriately captures the interrelation among accrual components. However, it is possible that our conclusions regarding the relative merit of disaggregating total accruals into its four major components is the result of the version of LIM3 that we selected. To examine this possibility, we estimated three alternative LIMs using the four major accrual components. The first modifies equations (3b), (3c), and (3d) to include only the lagged value of the component being forecasted and equity book value. The second does not treat depreciation as a separate accrual component, thereby eliminating equation (3e) and eliminating DEP from the remaining equations. The third does not treat change in inventory as a separate accrual component, thereby eliminating equation (3c) and eliminating ∆INV from the remaining equations. None of the inferences relating to LIM3 is affected when these alternative LIMs are used.
26
Taken together, the evidence in table 4 suggests that if when predicting equity market
values one is concerned about errors in the tails of the prediction error distribution, then one
should disaggregate net income into cash flow and the four major accrual components.
However, if one is less concerned about errors in the tails of the prediction error distribution,
then one should disaggregate net income only into cash flow and total accruals. That is, if the
firms for which one is predicting equity values are similar—in terms of valuation implications of
their accruals—to firms on which the predictions are based, then it is not necessary to base
predictions on a model that includes accrual components. However, if the firms for which one is
predicting equity values are unlike firms on which the predictions are based, then predictions are
more accurate when based on a model that includes accrual components rather than total
accruals.
6. Summary and Concluding Remarks
This study determines whether and the extent to which disaggregation of earnings and
imposing valuation model linear information structure aid in predicting equity values. It also
determines whether and the extent to which basing predictions on separate industry estimation of
valuation model parameters affects equity market value predictions.
Using a sample of Compustat firms, we predict out-of-sample contemporaneous equity
market values using a jack-knifing procedure. To test whether earnings disaggregation affects
equity value predictive ability, we predict equity values using three linear information valuation
models (LIM) employing three levels of earnings disaggregation. The first LIM is based on
aggregate earnings, the second disaggregates earnings into cash flow and total accruals, and the
third disaggregates earnings into cash flow and the four major components of accruals−change in
receivables, change in inventory, change in payables, and depreciation.
27
We develop equity value predictions for each LIM using two estimation procedures, one
that does not impose the structure of the LIM on the equity valuation equation, and a second that
does. To test whether earnings disaggregation aids in predicting equity values, we compare
prediction errors across the three LIMs. To test whether imposing the LIM structure aids in
predicting equity values, we compare predictions from estimations when the LIM structure is
imposed to those from when it is not. To test whether basing predictions on separate industry
estimations of valuation model parameters affects equity value predictions, we compare
prediction errors from pooled and separate industry estimations for each LIM.
Regarding our research question whether imposing the LIM structure aids in predicting
equity values, we find that for all three LIMs, imposing the LIM structure results in significantly
smaller prediction errors, based on pooled estimations. In contrast, we find that prediction errors
do not differ significantly when the LIM structure is or is not imposed in by-industry estimation.
This finding suggest that research designs based on residual income models need not impose the
model structure because doing so neither increases nor decreases prediction errors. Thus, this
finding supports the efficacy of drawing inferences from valuation equations based on residual
income models that do not impose the structure implied by the model. Relating to our research
question whether by industry estimation aids in predicting equity values, we find that prediction
errors based on by-industry estimation are substantially smaller than those based on pooled
estimation. This finding suggests that valuation of abnormal earnings, accruals, accrual
components, equity book value, and other information varies significantly across industries. It
also suggests that inferences relating to whether imposing the LIM structure reduces prediction
errors should be based on by-industry estimation.
28
Regarding our research question relating to whether disaggregating earnings aids in
predicting equity values, we find some reduction in mean prediction errors when earnings are
disaggregated into cash flow and total accruals, and some additional reduction when total
accruals are disaggregated into its four major components. However, the total reduction in mean
prediction errors obtained from disaggregating net income into cash flow and the four major
accrual components is more substantial than is apparent from the two sequential disaggregations.
In contrast, evidence from median prediction errors support disaggregation of earnings only into
cash flow and total accruals. These findings suggest that if when predicting equity market values
the concern is with errors in the tails of the prediction error distribution, then earnings should be
disaggregated into cash flow and the four major accrual components. However, if there is less
concern with errors in the tails of the prediction error distribution, then earnings should be
disaggregated only into cash flow and total accruals. Thus, for firms with more extreme
prediction errors, accrual components appear to provide additional information incremental to
that in total accruals that is helpful to predicting equity values.
29
APPENDIX A
LIM Forecasting Equations
ACCRUAL COMPONENTS AND FUTURE EARNINGS
LIM3 focuses on four major components of accruals, change in receivables, ∆REC,
change in inventory, ∆INV, change in payables, ∆AP, and depreciation and amortization, DEP,
because we expect them to have different implications for forecasting abnormal earnings and
equity valuation. The first accrual component, ∆REC, reflects information about current sales
and cash receipts. To the extent that current sales are positively related to future sales, ∆REC
will be positively related to future sales and thus future earnings (Stober, 1992).16 However,
because ∆REC is negatively related to cash receipts, change in receivables can be negatively
related to futures sales. This negative relation occurs because low current cash receipts can be an
indication that product demand will decrease in the future because there is a drop in product
demand as a result of or unrelated to general economic conditions.
The second accrual component, ∆INV, can be negatively or positively related to future
sales. Assuming constant inventory costs, an increase (decrease) in inventory can result from an
increase (decrease) in current sales, if management cannot immediately adjust inventory in
response to sales shocks. As with receivables, to the extent that recent sales positively predict
future sales, ∆INV is negatively related to future sales because of the negatively relation with
current sales. However, because inventory levels reflect management’s private information
about future demand, ∆INV can be positively associated with future sales. If management adopts
an inventory policy that requires the firm to maintain a target inventory level based on
16 For the sake of parsimony, development of our predictions regarding the relations among accrual components and future earnings focuses on sales and not expenses. Untabulated findings from regressions based on equations (3a)
30
anticipated sales, that is, they partially respond to current sales shocks, observing inventory
increases (decreases) reveals management’s expectations about future demand increases
(decreases) (Bernard and Noel, 1991; Dechow, Kothari, and Watts, 1998; Barth, Cram, and
Nelson, 2001). Holding inventory quantity constant, increases in inventory can reflect increases
in factor-input prices, which results in higher current expenses and lower current earnings. To
the extent that current expenses predict future expenses, increases in inventory are negatively
associated with future earnings.
As with inventory, the third accrual component, ∆AP, can be negatively or positively
related to future sales. Holding factor-input prices constant, increases in payables can reflect
increases in inventory attributable to purchases, and hence, are positive in indicators of future
sales increases. Holding quantity of inventory purchases, increases in payables can reflect
increases in factor-input prices, which result in higher current expenses and lower current
earnings. To the extent that current expenses predict future expenses, increases in payables are
negatively associated with future earnings.17
The final accrual component of earnings, DEP, is likely to be positively associated with
future sales because management increases purchases of noncurrent assets in anticipation of
increased production, and increases in noncurrent assets result in higher depreciation (Feltham
and Ohlson, 1996). Although depreciation and amortization expense reduces earnings,
management would not invest without expecting a positive return on its investment.
Although it is not an accrual component of earnings, as in LIM1 and LIM2, we include in
LIM3 equity book value, BV, in the abnormal earnings equation to permit the effects of
through (3h) expanded to permit the coefficients on sales and expenses to differ reveal that coefficients differences generally are insignificantly different from zero.
31
conservatism to manifest (Feltham and Ohlson, 1995; 1996) and to relax the assumption that the
cost of capital associated with calculating abnormal earnings is a predetermined cross-sectional
constant. BV will be positively related to future abnormal earnings if earnings are conservative.
BV will be negatively related to future abnormal earnings if the normal return on equity book
value is less than the return we assume in our empirical tests, which, consistent with prior
research, is 12 percent.
Although each accrual component should aid in predicting future abnormal earnings,
except for DEP, the sign of the relation between each component and future abnormal earnings is
not predictable. More importantly, as the discussion above suggests, the relations likely differ
across the components. Thus, LIM3 permits each accrual component to have a different
forecasting relation with future abnormal earnings.
Table A1, panels A, B, and C, present the abnormal earnings prediction equation
summary statistics for LIM1, LIM2, and LIM3. For LIM1, findings relating to regressions in
which we do not impose the LIM structure reveal the mean coefficient across industries on
lagged abnormal earnings, ω11, is 0.56, which is similar to that reported in prior research. The
mean coefficients are all significantly positive, and range from 0.18 to 1.03, indicating there is
substantial cross-industry variation in the persistence of abnormal earnings. Findings relating to
regressions in which we impose the LIM structure are similar except that the industry means are
substantially larger in magnitude. For all 17 industries, the mean coefficients differ from those
obtained from the estimations without imposing the LIM structure.
Panel B reveals the incremental coefficient on ACC, lagged total accruals, ω12, in the
abnormal earnings forecasting equation is negative, on average, for all industries and
17 The same prediction can result by relating payables with expenses unrelated to inventory, such as components of selling, general, and administrative (SGA) expense. For example, holding factor-input prices constant, increases in
32
significantly negative for all but four. The industry mean coefficient values of –0.17 and –0.22,
are similar in sign and magnitude to the industry mean of –0.25 reported in prior research (Barth,
Beaver, Hand, and Landsman, 1999).
Panel C indicates there is substantial cross-industry variation in the coefficients on each
accrual component of earnings, change in receivables, ∆REC, change in inventory, ∆INV, change
in payables, ∆AP, and depreciation and amortization, DEP. First, for all four components, the
incremental abnormal earnings forecasting coefficients, ω12, ω13, ω14, and ω15, on each accrual
component are significantly positive for some industries and negative for others. This contrasts
with the coefficients on the other components of abnormal earnings, which includes cash flow,
and equity book value, which are significantly positive in virtually all industries. The
incremental abnormal earnings forecasting coefficients on change in receivables, ∆REC, change
in payables, ∆AP, and depreciation, DEP, are more consistently positive than those on change in
inventory, ∆INV, which are more consistently negative.
Notably, with the exception of one industry for ∆AP, the incremental abnormal earnings
forecasting coefficients obtained with and without imposing the LIM structure do not
significantly differ from one another. This suggests that imposition of the LIM structure is not
binding in the estimation of LIM3. This contrasts with the findings for LIM1 and LIM2 in
panels A and B, which indicate that the forecasting coefficients on abnormal earnings and total
accruals obtained with and without imposing the LIM structure are significantly different from
one another. Thus, the more disaggregate LIM, LIM3, results in estimated abnormal earnings
forecasting coefficients that are more consistent with the valuation coefficients reported in table
2. Recall, however, that because of the complexity of LIM3, consistency of coefficients between
AP can reflect increases in purchases of other factor inputs that are components of SGA.
33
incremental forecasting and valuation coefficients does not necessarily imply consistency in their
signs.
ACCRUAL COMPONENT PREDICTION EQUATIONS
For LIM3, equations (3b) through (3e) specify a prediction equation for each component.
Consistent with Ohlson (1999), each component is assumed to follow an autoregressive process.
Thus, each component prediction equation includes the lagged value for that component.
Because we expect accrual components to be positively autocorrelated, based on Ohlson (1999)
and findings relating to total accruals in Barth, Beaver, Hand, and Landsman (1999), we predict
ωjj > 0 for each component. We do not predict ωjj ≤ 1, as would be required for stationarity if
equations (3a) through (3g) included only the lagged value of each component. Rather,
stationarity of equations (3a) through (3g) requires only the Eigenvalue for the system of
equations given by equations (3a) through (3g) be less than 1.
The receivables prediction equation, equation (3b), also includes ∆INV and DEP because,
as described above, each of these earnings components predicts future sales, which in turn affects
future change in receivables. Equation (3b) does not include ∆AP because we expect any
relation between change in payables and future change in receivables associated with future sales
to be captured by change in inventory.
As in equation (3b), because change in receivables and depreciation predict future sales,
which in turn affects future change in inventory, the inventory prediction equation, equation (3c),
includes ∆REC and DEP. Because payables are used to purchase inventory, we expect change in
payables to predict future change in inventory. Thus, equation (3c) also includes ∆AP. To the
extent that change in inventory is persistent, we expect change in inventory to predict future
change in payables. Thus, equation (3d), the payables prediction equation, also includes ∆INV.
34
Because we do not expect any earnings component to have any first order predictive ability for
depreciation, equation (3e) only includes lagged DEP and equity book value.
Table A2 presents the earnings component prediction equation summary statistics for
LIM2 in panel A, and for LIM3 in panels B through E. Panel A reveals the industry mean
coefficients on total accruals, ACC, in its own forecasting equation, ω22, 0.59 and 0.60, are
similar to the industry mean of 0.48 reported in prior research (Barth, Beaver, Hand, and
Landsman, 1999). Even though the there is a wide range of coefficients across industries,
virtually all are significantly positive. Panel A also reveals that the LIM structure is binding for
only 3 of the 17 industries.
Turning to LIM3, the findings reported in panels B, C, D, and E generally indicate that
the coefficient on each component’s lagged value, ωjj, is positive and significant. In addition,
lagged values of the other components also are often significant explanatory variables in each of
the component forecasting equations, although their signs are more industry-specific. Notably,
consistent with the findings reported for the LIM3 abnormal earnings forecasting equation
reported in table A1, panel C, panels B through D indicate that the LIM structure is not binding
for most of the component forecasting equation coefficients.
35
APPENDIX B
Derivation of Valuation Coefficients for LIM3
This appendix derives the valuation coefficients in equation (3h) in terms of the ωjk in
equations (3a) through (3g). Our derivation is similar to that in Ohlson (1995) and Myers
(1999). Following Ohlson (1995), market value of equity, MVE, is defined as the sum of current
equity book value, BV, and expected future abnormal earnings, NIa, discounted at a constant rate,
r:
⎥⎦
⎤⎢⎣
⎡
++= ∑∞
=+
1 )1(E
t
at
ttt rNI
BVMVE ττ (A1)
Define M={ωjk), a six by six matrix of the ω coefficients in equations (3a) through (3g),
X={ω11, ω12, …, ω16}, a one by six row vector comprising the coefficients relating to equation
(3a), and = { , , , tZ atNI tREC∆ tINV∆ tAP∆ , , }, a six by one column vector
comprising the explanatory variables in equation (3h). Using this notation, equation (3a) can be
rewritten as , or more generally, . Noting that ,
. Thus, equation (A1) can be re-expressed as:
tDEP tBV
tXZ=+atNI 1 1−++ = ττ tXZa
tNI tMZZ =+1t
tZXM 1−+ = τ
τatNI
⋅⋅⋅++
++
++
+= 3
2
2 )1()1()1( rrrBVMVE ttt
ttZXMXMZXZ
(A2a)
tt rrrBV ZMΜIX
⎥⎦
⎤⎢⎣
⎡⋅⋅⋅+
++
++
++= 2
2
)1()1()1( (A2b)
Assuming the Eigenvalues of )1( r+
M are all less than one in absolute value, then the bracketed
36
term in equation (A2b) equals 1
)1(
−
⎥⎦
⎤⎢⎣
⎡+
−r
MI .18 This implies that
ttt rrBVMVE ZMIX
1
)1()1(
−
⎥⎦
⎤⎢⎣
⎡+
−+
+= (A3)
Define T={0, 0, 0, 0, 0, 1}, a one by six row vector, and α={α1, α2, α3, α4, α5, α6}, also a one by
six row vector, then equation (A3) can be rewritten as:
ttt rrMVE ZMIXTαZ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎥⎦
⎤⎢⎣
⎡+
−+
+==−1
)1()1( (A4)
Thus,
1
)1()1(
−
⎥⎦
⎤⎢⎣
⎡+
−+
+=rr
MIXTα (A5)
Absent restrictions on M, e.g., triangularity of the linear information dynamics, the closed form
solution for α is complex.
18 This assumption is a generalization of the assumption in Ohlson [1995] that , which ensures that time-series processes are stationary.
1|| <jjω
37
References
Barth, M.E., W.H. Beaver and W.R. Landsman (1998). “Relative Valuation Roles of Equity
Book Value and Net Income as a Function of Financial Health.” Journal of Accounting and
Economics 25: 1-34.
Barth, M.E., W.H. Beaver and W.R. Landsman (2001). “The Relevance of the Value Relevance
Literature for Accounting Standard Setting: Another View.” Journal of Accounting and
Economics 31: 77-104.
Barth, M.E., W.H. Beaver, J.M. Hand, and W.R. Landsman (1999). “Accruals, Cash Flows, and
Equity Values.” Review of Accounting Studies 3: 205-229.
Barth, M.E., D.P. Cram, and K.K. Nelson. (2001). “Accruals and the Prediction of Future Cash
Flows.” The Accounting Review 76: 27-58.
Barth, M.E., and A.P. Hutton. (2004). “Analyst Earnings Forecast Revisions and the Pricing of
Accruals.” Review of Accounting Studies 9: 59-96.
Barth, M.E., and S. Kallapur (1996). “Effects of Cross-Sectional Scale Differences on
Regression Results in Empirical Accounting Research.” Contemporary Accounting Research
13: 527-567.
Bernard, V.L. (1995). “The Feltham-Ohlson Framework: Implications for Empiricists.”
Contemporary Accounting Research 11: 733-747.
Bernard, V.L., and J. Noel. (1991). “Do Inventory Disclosures Predict Sales and Earnings?”
Journal of Accounting, Auditing, and Finance 6: 145-181.
Collins, D.W., and P. Hribar. (2000). “Earnings-based and Accrual-based Market Anomalies: One
Effect or Two?” Journal of Accounting and Economics 29: 101-123.
Collins, D.W., Maydew, E.L., and I.S. Weiss. (1997). “Changes in the Value-Relevance of
38
Earnings & Equity Book Values Over The Past Forty Years.” Journal of Accounting and
Economics 24: 39-67.
Dechow, P.M. (1994). “Accounting Earnings and Cash Flows as Measures of Firm Performance:
the Role Accounting Accruals.” Journal of Accounting and Economics 18: 3-42.
Dechow, P.M., Hutton, A.P., and R.G. Sloan. (1999). “An Empirical Assessment of the Residual
Income Valuation Model.” Journal of Accounting and Economics 26: 1-34.
Dechow, P.M., S.P. Kothari, and R.L. Watts. (1998). “The Relation between Earnings and Cash
Flows.” Journal of Accounting and Economics 25: 133-168.
Fama, E.F., and K.R. French. (1998). “Taxes, Financing Decisions, and Firm Value.” Journal of
Finance 53: 819-843.
Fama, E.F., and J.D. MacBeth. (1973). “Risk, Return, and Equilibrium: Empirical tests.” Journal
of Political Economy 81: 607-636.
Feltham, G.A., and J.A. Ohlson. (1995). “Valuation and Clean Surplus Accounting for Operating
and Financial Activities.” Contemporary Accounting Research 11: 689-732.
Feltham, G.A., and J.A. Ohlson. (1996). “Uncertainty Resolution and the Theory of Depreciation
Measurement.” Journal of Accounting Research 34: 209-234.
Financial Accounting Standards Board. (1987). Statement of Financial Accounting Standards
No. 95: Statement of Cash Flows (FASB, Stamford, CT).
Frankel, R.M., and C.M.C. Lee (1998). “Accounting Valuation, Market Expectation, and the
Cross-Sectional Stock Returns.” Journal of Accounting and Economics 25: 283–319.
Hand, J.R.M., and W. Landsman. (2004). “The Pricing of Dividends and Equity Valuation.”
working paper, University of North Carolina, forthcoming, Journal of Business Finance and
Accounting.
39
Lee, C.M.C, J.N. Myers, and B. Swaminathan (1999). “What is the Intrinsic Value of the Dow?”
Journal of Finance 54: 1693-1741.
Lundholm, R.J. (1995). “A Tutorial on the Ohlson and Feltham-Ohlson Models: Answers to
Some Frequently Asked Questions?” Contemporary Accounting Research 11: 749-761.
Myers, J.N. (1999). “Implementing Residual Income Valuation with Linear Information
Dynamics.” The Accounting Review 74: 1-28.
Noreen, E.W. (1989). Computer Intensive Methods for Testing Hypotheses: An Introduction.
Wiley: New York, NY.
Ohlson, J.A. (1995). “Earnings, Equity Book Values, and Dividends in Equity Valuation.”
Contemporary Accounting Research: 66-687.
Ohlson, J.A. (1999). “On Transitory Earnings.” Review of Accounting Studies 3: 145-162.
Sloan, R.G. (1996). “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows
About Future Earnings?” The Accounting Review 71: 289-315.
Stober, T.L. (1992). “The Incremental Information Content of Receivables in Predicting Sales,
Earnings, and Profit Margins.” Journal of Accounting, Auditing, and Finance, 447-473.
Xie, H. (2001). “The Mispricing of Abnormal Accruals.” The Accounting Review 76: 357-373.
40
TABLE 1 Descriptive Statistics for 17,601 Compustat Firm-year Observations, 1988–2001
Panel A: Distributional Statistics (in $millions) Variable Mean Median Std. Dev. Market value of equity MVE 661.95 122.63 1,887.53 Book value of equity BV 227.85 72.88 453.21 Abnormal earnings NIa –0.54 –0.78 56.44 Total accruals ACC –27.59 –4.88 84.60 Change in inventory ∆INV 3.69 0.31 19.93 Change in receivables ∆REC 5.59 1.02 28.92 Change in payables ∆PAY 4.03 0.65 25.48 Depreciation + amortization DEP 27.45 6.45 68.54 Other information ν –290.65 –212.48 980.21 |∆INV| / revenues 2.36% 1.21% 3.78%|∆REC| / revenues 3.49% 1.88% 5.15%|∆PAY| / revenues 2.80% 1.61% 4.49%|∆DEP| / revenues 5.98% 3.96% 7.61% Panel B: Correlations, with Pearson (Spearman) Correlations above (below) the Diagonal MVE BV NIa ACC ∆INV ∆REC ∆PAY DEP ν MVE 0.75 0.42 –0.52 0.29 0.35 0.29 0.63 0.47 BV 0.90 0.20 –0.68 0.28 0.30 0.24 0.83 0.27 NIa 0.30 0.17 0.07 0.27 0.29 0.25 0.13 0.24 ACC –0.40 –0.47 0.15 0.01* –0.04 –0.18 –0.84 –0.19 ∆INV 0.25 0.22 0.25 0.23 0.31 0.39 0.21 0.14 ∆REC 0.35 0.29 0.33 0.15 0.28 0.58 0.27 0.23 ∆PAY 0.27 0.21 0.22 –0.11 0.30 0.43 0.20 0.20 DEP 0.78 0.87 0.09 –0.62 0.15 0.22 0.18 0.23 ν 0.11 0.09 0.17 –0.03 0.04 0.10 0.07 0.08
41
TABLE 1 (continued)
Panel C: Industry Composition Industry Description Primary SIC Codes Obs. %
Food 2000 – 2111 592 3.36Textiles, printing & publishing 2200 – 2780 1,670 9.49Chemicals 2800 – 2824, 2840 – 2899 695 3.95Pharmaceuticals 2830 – 2836 726 4.12Extractive industries 2900 – 2999, 1300 – 1399 796 4.52Durable manufacturers Rubber, plastic, leather, stone, clay & glass 3000 – 3299 768 4.36 Metal 3300 – 3499 904 5.14 Machinery 3500 – 3569, 3580 – 3599 1,048 5.95 Electrical equipment 3600 – 3669, 3680 – 3699 1,149 6.53 Transportation equipment 3700 – 3799 534 3.03 Instruments 3800 – 3899 1,548 8.79 Miscellaneous manufacturers 3900 – 3999 298 1.69Computers
7370 – 7379, 3570 – 3579, 3670 – 3679 2,697 15.32
Retail Wholesale 5000 – 5199 921 5.23 Miscellaneous retail 5200 – 5799, 5900 – 5999 1,266 7.19 Restaurant 5800 – 5899 373 2.12Services
7000 – 8999, excluding 7370 – 7379 1,616 9.18
Total 17,601 100.00 MVE is market value of equity at fiscal year end; BV is book value of equity at fiscal year end; NI is income before extraordinary items and discontinued operations; NIa is abnormal earnings, defined as NIt – rBVt–1, where r = 12%. ACC is total accruals (NI – cash flow from operations). ∆INV, ∆REC, and ∆PAY are annual change in inventory, receivables, and payables. DEP is depreciation and amortization expense. ν represents other information. *p-value = 0.45. All other correlations in panel B are significantly different from zero (α = 0.01).
42
TABLE 2 Regression Statistics for Sample of 14,128 Compustat Firm-year Observations, 1988–2001
Panel A: ititit
aitit uBVNIMVE ++++= ναααα 3210
Without LIM Structure With LIM Structure α1 α2 α3 R2 α1 α2 α3 R2
Pooled 9.45 2.52 0.69 0.73 10.38 2.58 0.56 0.73t-statistic 69.75 143.44 80.38 81.67 147.86 72.00
By Industry
Mean 6.82 2.36 0.87 0.85 7.12 2.45 0.74 0.85FM t-statistic 4.87 12.84 14.32 5.15 12.45 10.54
Minimum 2.02 1.20 0.47 0.59 1.25 0.26Maximum 21.84 4.37 1.28 22.16 4.72 1.31# sig. positive 17 17 17 17 17 17 # sig. negative 0 0 0 0 0 0 # sig. larger 8 1 13 7 9 2
43
TABLE 2 (continued)
Panel B: ititititaitit uBVACCNIMVE +++++= νααααα 43210
Without LIM Structure With LIM Structure α1 α2 α3 α4 R2 α1 α2 α3 α4 R2
Pooled 9.69 –1.77 2.29 0.67 0.73 10.79 –3.18 2.18 0.54 0.73t-statistic 68.49 –14.27 96.96 78.51 81.53 –33.42 101.67 69.52
By Industry
Mean 7.43 –2.18 2.10 0.85 0.86 8.00 –2.83 2.11 0.72 0.86FM t-statistic 5.02 –3.23 14.90 13.96 5.46 –3.94 14.58 10.44
Minimum 1.62 –9.05 1.21 0.44 0.82 –11.19 1.21 0.25Maximum 24.09 1.66 3.63 1.27 24.59 –0.35 3.88 1.30# sig. positive 17 2 17 17 17 0 17 17 # sig. negative 0 10 0 0 0 17 0 0 # sig. larger 8 10 5 13 7 5 7 2
44
TABLE 2 (continued)
Panel C: itititititititaitit uBVDEPAPINVRECNIMVE ++++∆+∆+∆+= νααααααα 7654321
Without LIM Structure With LIM Structure α1 α2 α3 α4 α5 α6 α7 R2 α1 α2 α3 α4 α5 α6 α7 R2
Pooled 9.34 –0.22 0.48 1.20 0.21 2.48 0.68 0.73 10.50 –1.40 –2.70 1.17 0.84 2.52 0.56 0.73t-statistic 66.58 –0.68
1.15 3.34 1.10 83.29 79.49 81.19 –7.63 –11.69 5.90 4.61 88.97 72.80
By Industry
Mean 6.52 0.27 –1.57 –1.33 0.11 2.30 0.86 0.86 7.25 –0.63 –1.51 0.08 0.49 2.35 0.73 0.85FM t-statistic 4.55 0.42 –1.46 –0.69 0.10 9.48 14.21 5.16 –1.45 –2.66 0.15 0.44 9.86 10.97
Minimum 1.64 –5.73 –7.43 –29.93 –14.17 1.14 0.47 0.69 –5.55 –7.83 –6.02 –14.80 1.20 0.30Maximum 22.04 5.30 7.65 5.94 6.98 5.61 1.29 22.95 1.92 2.42 3.90 7.77 5.56 1.30# sig. positive 17 5 3 5 6 17 17 17 2 1 5 7 17 17# sig. negative 0 3 7 5 3 0 0 0 6 8 2 3 0 0# sig. larger 6 11 6 7 3 6 15 9 2 7 9 9 6 1 Variable definitions are as in table 1. Panels A, B, and C are estimations based on LIM1, LIM2, and LIM3. LIM1, LIM2, and LIM3 are linear information dynamics systems of equations based on aggregate net income, net income disaggregated into cash flows and total accruals, and net income disaggregated into cash flows and the major components of accruals, respectively. The pooled regression is estimated with year and industry fixed-effects, which are not tabulated. Separate industry regressions are estimated with year fixed-effects, which are also not tabulated. By industry mean (minimum, maximum) represents the mean (minimum, maximum) of the 17 industry coefficient estimates. FM t-statistic is the Fama-MacBeth (1973) t-statistic of the mean of the 17 industry coefficient estimates. # sig. positive (negative) is the number of industries with coefficient estimates significantly greater (less) than zero. # sig. larger is the number of industries where the model without or with LIM structure produces a significantly larger coefficient estimate.
45
TABLE 3 Comparison of Out of Sample Equity Market Value Forecast Errors
Without Compared to With Imposing LIM Structure (N = 14,128) Panel A: LIM1 MeanSE MeanAE MedSE MedAE w/o with w/o with w/o with w/o withPooled 75.94 65.25 2.72 2.64 0.85 0.81 0.92 0.90By Industry
Mean (median) 34.04 35.98 1.76 1.79 0.36 0.38 0.60 0.61Mean (median) of industry means (medians)
29.31
31.31
1.71
1.72
0.36
0.36
0.60
0.60
# of industries sig. lower without or with LIM
3
7
5
7
6
6
6
7
Panel B: LIM2 MeanSE MeanAE MedSE MedAE w/o with w/o with w/o with w/o withPooled 71.42 58.13 2.69 2.58 0.79 0.74 0.89 0.86By Industry
Mean (median) 33.97 36.05 1.75 1.76 0.34 0.35 0.58 0.59Mean (median) of industry means (medians)
27.63
29.53
1.68
1.68
0.36
0.37
0.60
0.61
# of industries sig. lower without or with LIM
3
8
5
8
6
9
6
9
Panel C: LIM3 MeanSE MeanAE MedSE MedAE w/o with w/o with w/o with w/o withPooled 73.96 64.20 2.66 2.63 0.84 0.80 0.92 0.89By Industry
Mean (median) 31.66 35.20 1.68 1.71 0.36 0.35 0.61 0.60Mean (median) of industry means (medians)
27.45
28.82
1.64
1.64
0.33
0.36
0.57
0.60
# of industries sig. lower without or with LIM
3
3
5
5
5
3
4
3
Bold denotes significant differences (α = 0.05) without and with imposing the LIM structure. “w/o” (“with”) represents estimation without (with) imposing the LIM structure. LIM1, LIM2, and LIM3 are linear information dynamics systems of equations based on aggregate net income,
46
net income disaggregated into cash flows and total accruals, and net income disaggregated into cash flows and the major components of accruals, respectively. The major components of accruals are changes in receivables, inventory, and payables, and depreciation and amortization expense. MeanSE (MeanAE) is the mean squared (absolute) equity value prediction error. MedSE (MedAE) is the median squared (absolute) equity value prediction error. Pooled regressions are estimated with year and industry fixed-effects. Separate industry regressions are estimated with year fixed-effects.
47
TABLE 4 Cross-LIM Comparisons of Out of Sample Equity Market Value Prediction Errors (N = 14,128)
Panel A: Model Estimates Without Imposing LIM Structure – Mean Prediction Errors
MeanSE
MeanAE LIM1 LIM2 LIM3 LIM1 LIM2 LIM3Pooled 71.42 75.94 73.96 2.72* 2.69* 2.66 By Industry
Mean
33.97 34.04 31.66 1.76 1.75 1.68 Mean of industry means 29.31 27.63 27.45 1.71 1.68 1.64
# of industries sig. lower: LIM1 compared to LIM2 4 2 6 6 LIM2 compared to LIM3 2 4 3 7 LIM1 compared to LIM3 1 3 2 8
Panel B: Model Estimates With Imposing LIM Structure – Mean Prediction Errors
MeanSE
MeanAE LIM1 LIM2 LIM3 LIM1 LIM2 LIM3
Pooled 58.13*65.25* 64.20 2.64* 2.58* 2.63By Industry
Mean 36.0535.98 35.20 1.76* 1.79* 1.71 Mean of industry means 31.31 29.53 28.82 1.72 1.68 1.64
# of industries sig. lower: LIM1 compared to LIM2 3 4 5 7 LIM2 compared to LIM3 4 4 5 5 LIM1 compared to LIM3 2 8 3 9
48
TABLE 4 (continued)
Panel C: Model Estimates Without Imposing LIM Structure – Median Prediction Errors
MedSE
MedAE
LIM1 LIM2 LIM3 LIM1 LIM2 LIM3Pooled 0.79* 0.85* 0.84 0.92* 0.89* 0.91 By Industry
Median
0.34* 0.37* 0.36 0.61* 0.58* 0.60 Median of industry medians 0.36 0.36 0.33 0.60 0.60 0.57
# of industries sig. lower: LIM1 compared to LIM2 2 6 3 6 LIM2 compared to LIM3 4 5 4 5 LIM1 compared to LIM3 2 8 2 7
Panel D: Model Estimates With Imposing LIM Structure – Median Prediction Errors
MedSE
MedAE LIM1 LIM2 LIM3 LIM1 LIM2 LIM3
Pooled 0.74*0.81* 0.80 0.90* 0.86* 0.89 By Industry
Median 0.35* 0.38* 0.35 0.61* 0.59* 0.60 Median of industry medians 0.36* 0.37* 0.36 0.60* 0.61* 0.60
# of industries sig. lower: LIM1 compared to LIM2 4 8 4 7 LIM2 compared to LIM3 6 6 6 6 LIM1 compared to LIM3 3 8 3 9
Asterisk (Italics, Bold) denotes a significant difference between values for LIM1 and LIM2 (LIM2 and LIM3, LIM1 and LIM3) at significance level α = 0.05. LIM1, LIM2, and LIM3 are linear information dynamics systems of equations based on aggregate net income, net income disaggregated into cash flows and total accruals, and net income disaggregated into cash flows and the major
49
components of accruals, respectively. The major components of accruals are changes in receivables, inventory, and payables, and depreciation and amortization expense. MeanSE (MeanAE) is the mean squared (absolute) equity value prediction error. MedSE (MedAE) is the median squared (absolute) equity value prediction error. Pooled regressions are estimated with year and industry fixed-effects. Separate industry regressions are estimated with year fixed-effects.
50
TABLE A1 Regression Statistics for Sample of 14,128 Compustat Firm-year Observations, 1988–2001
Panel A: ititit
ait
ait BVNINI 111311211110 ενωωωω ++++= −−−
Without LIM Structure With LIM Structure ω11 ω12 ω13 R2 ω11 ω12 ω13 R2
Pooled 0.64 0.00 0.00 0.32 1.02 –0.02 0.01 0.17t-statistic 85.52 –0.85 1.94
929.02 –19.68 40.69
By Industry Mean 0.56 0.00 0.01 0.37 0.91 –0.02 0.02 0.19FM t-statistic 9.77 –0.28 2.16 24.84 –3.56 8.80
Minimum 0.18 –0.03 –0.02 0.41 –0.05 0.01 Maximum 1.03 0.04 0.03 1.07 0.02 0.04# sig. positive 17 4 10 17 1 17# sig. negative 0 6 3 0 12 0# sig. larger 0 15 2 17 1 14
51
TABLE A1 (continued) Panel B: itititit
ait
ait BVACCNINI 111411311211110 ενωωωωω +++++= −−−−
Without LIM Structure With LIM Structure ω11 ω12 ω13 ω14 R2 ω11 ω12 ω13 ω14 R2
Pooled 0.72 –0.17 –0.02 0.00 0.34 1.03 –0.14 –0.04 0.01 0.22t-statistic 105.36 –26.33 –19.61 2.76
969.85 –30.96 –32.36 41.28
By Industry Mean 0.63 –0.17 –0.02 0.01 0.41 0.94 –0.22 –0.04 0.02 0.26FM t-statistic 11.85 –4.53 –3.55 2.59 29.63 –5.35 –6.84 8.10
Minimum 0.23 –0.59 –0.08 –0.01 0.51 –0.66 –0.09 0.00Maximum 0.98 0.03 0.02 0.02 1.08 –0.02 0.00 0.04# sig. positive 17 0 2 10 17 0 0 17# sig. negative 0 13 11 3 0 17 15 0# sig. larger 0 11 13 2 17 4 2 14
52
TABLE A1 (continued) Panel C: ititititititit
ait
ait BVDEPAPINVRECNINI 111711611511411311211 ενωωωωωωω ++++∆+∆+∆+= −−−−−−
Without LIM Structure With LIM Structure ω11 ω12 ω13 ω14 ω15 ω16 ω17 R2 ω11 ω12 ω13 ω14 ω15 ω16 ω17 R2
Pooled 0.66 –0.06 –0.25 0.14 0.08 –0.01 0.00 0.32 1.02 –0.13 –0.25 0.11 0.01 –0.02 0.01 0.19t-statistic 90.85
By Industry
–3.68 –11.89 8.06 7.84 –5.66 2.35 950.61 –8.09 –11.78 6.63 3.90 –14.89 42.09
Mean 0.57 –0.02 –0.21 0.14 0.06 –0.01 0.01 0.41 0.92 –0.17 –0.24 0.05 0.03 –0.02 0.02 0.20FM t-statistic 9.63 –0.38 –2.05 2.57 1.14 –1.12 2.53 27.21 –1.52 –2.67 0.70 1.23 –3.34 8.34
Minimum 0.13 –0.35 –0.93 –0.39 –0.31 –0.05 –0.01 0.46 –1.81
–1.09 –0.46 –0.08 –0.05 0.00
Maximum 1.02 0.34 0.72 0.41 0.60 0.04 0.02 1.07 0.31 0.50 0.43 0.30 0.02 0.05# sig. positive 17 2 2 11 7 5 10 17 1 1 5 5 1 16# sig. negative 0 5 11 2 4 8 4 0 7 9 3 2 11 0# sig. larger 0 10 10 9 8 9 1 17 2 6 5 7 4 14 Variable definitions are as in table 1. LIM1, LIM2, and LIM3 are linear information dynamics systems of equations based on aggregate net income, net income disaggregated into cash flows and total accruals, and net income disaggregated into cash flows and the major components of accruals, respectively. The major components of accruals are changes in receivables, inventory, and payables, and depreciation and amortization expense. The pooled regression is estimated with year and industry fixed-effects, which are not tabulated. Separate industry regressions are estimated with year fixed-effects, which are also not tabulated. By industry mean (minimum, maximum) represents the mean (minimum, maximum) of the 17 industry coefficient estimates. FM t-statistic is the Fama-MacBeth (1973) t-statistic of the mean of the 17 industry coefficient estimates. # sig. positive (negative) is the number of industries with coefficient estimates significantly greater (less) than zero. # sig. larger is the number of industries where the model without or with LIM structure produces a significantly larger coefficient estimate.
53
TABLE A2 Regression Statistics for Sample of 14,128 Compustat Firm-year Observations, 1988–2001
Panel A: itititit BVACCACC 212312220 εωωω +++= −−
Without LIM Structure With LIM Structure ω22 ω23 R2 ω22 ω23 R2
Pooled 0.59 –0.07 0.64 0.60 –0.07 0.64t-statistic 78.77
–54.18 81.18 –53.25
By Industry
Mean 0.45 –0.08 0.56 0.45 –0.08 0.56FM t-statistic 9.14 –10.73 9.03 –10.60
Minimum –0.04 –0.13 –0.04 –0.12 Maximum 0.86 –0.03 0.87 –0.03# sig. positive 16 0 16 0 # sig. negative 0 17 0 17 # sig. larger 0 0 3 2
54
TABLE A2 (continued)
Panel B: itititititit BVDEPINVRECREC 2126125123122 εωωωω +++∆+∆=∆ −−−− Without LIM Structure With LIM Structure ω22 ω23 ω25 ω26 R2 ω22 ω23 ω25 ω26 R2
Pooled 0.09 –0.02 0.03 0.01 0.12 0.09 –0.01 0.03 0.01 0.12t-statistic 10.84 –1.48 6.43 15.71 11.98 –1.14 5.96 15.76
By Industry
Mean 0.08 –0.03 0.02 0.01 0.16 0.08 –0.02 0.01 0.01 0.16FM t-statistic 1.95 –0.49 0.72 5.53 1.94 –0.42 0.60 5.35
Minimum –0.27 –0.52 –0.20 0.00 –0.22 –0.42 –0.22 0.00 Maximum 0.44 0.41 0.19 0.04 0.44 0.39 0.18 0.04# sig. positive 7 4 3 14 8 5 2 11# sig. negative 1 5 1 1 2 5 1 1# sig. larger 1 3 1 1 4 3 2 1
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TABLE A2 (continued)
Panel C: ititititititit BVDEPAPINVRECINV 3136135134133132 εωωωωω +++∆+∆+∆=∆ −−−−− Without LIM Structure With LIM Structure ω32 ω33 ω34 ω35 ω36 R2 ω32 ω33 ω34 ω35 ω36 R2
Pooled 0.05 0.05 0.06 –0.01 0.01 0.12 0.05 0.05 0.06 –0.01 0.01 0.12t-statistic 6.96 5.26 8.16 –2.82 16.75 7.32
5.32 8.09 –2.73 16.57
By Industry
Mean 0.08 –0.04 0.08 –0.04 0.01 0.16 0.09 –0.03 0.07 –0.03 0.01 0.16 FM t-statistic 2.89 –0.94 2.72 –1.76 3.42 3.52 –0.59 2.65 –1.61 3.32
Minimum –0.19 –0.37 –0.16 –0.22 0.00 –0.12 –0.36 –0.14 –0.21 –0.01 Maximum 0.24 0.29 0.25 0.11 0.04 0.23 0.30 0.26 0.11 0.04# sig. positive 11 4 8 3 9 10 4 9 3 10# sig. negative 2 7 3 6 0 1 6 2 6 0# sig. larger 2 1 3 3 2 2 3 4 3 2
56
TABLE A2 (continued)
Panel D: ititititit BVAPINVAP 4146144143 εωωω ++∆+∆=∆ −−− Without LIM Structure With LIM Structure ω43 ω44 ω46 R2 ω43 ω44 ω46 R2
Pooled –0.13 0.13 0.01 0.09 –0.12 0.14 0.01 0.09t-statistic –11.06 17.19 26.23 –10.48 17.80 25.78
By Industry
Mean –0.14 0.11 0.01 0.15 –0.16 0.14 0.01 0.15 FM t-statistic –2.79 2.66 6.84 –3.57 3.15 6.85
Minimum –0.73 –0.16 0.00 –0.62 –0.14 0.00 Maximum 0.15 0.40 0.03 0.10 0.44 0.03# sig. positive 1 10 15 1 12 15 # sig. negative 10 3 0 10 3 0# sig. larger 2 0 1 2 7 0
57
TABLE A2 (continued)
Panel E: itititit BVDEPDEP 5156155 εωω ++= −− Without LIM Structure With LIM Structure ω55 ω56 R2 ω55 ω56 R2
Pooled 1.03 0.01 0.96 1.04 0.01 0.96t-statistic 385.18
17.52 393.72 16.64
By Industry
Mean 1.00 0.01 0.97 1.01 0.01 0.97 FM t-statistic 80.65 5.82 78.63 5.43
Minimum 0.91 0.00 0.92 0.00 Maximum 1.09 0.03 1.10 0.02# sig. positive 17 15 17 13 # sig. negative 0 0 0 0 # sig. larger 0 6 7 0
Variable definitions are as in table 1. LIM1, LIM2, and LIM3 are linear information dynamics systems of equations based on aggregate net income, net income disaggregated into cash flows and total accruals, and net income disaggregated into cash flows and the major components of accruals, respectively. The major components of accruals are changes in receivables, inventory, and payables, and depreciation and amortization expense. The pooled regression is estimated with year and industry fixed-effects, which are not tabulated. Separate industry regressions are estimated with year fixed-effects, which are also not tabulated. By industry mean (minimum, maximum) represents the mean (minimum, maximum) of the 17 industry coefficient estimates. FM t-statistic is the Fama-MacBeth (1973) t-statistic of the mean of the 17 industry coefficient estimates. # sig. positive (negative) is the number of industries with coefficient estimates significantly greater (less) than zero. # sig. larger is the number of industries where the model without or with LIM structure produces a significantly larger coefficient estimate.
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