The Ohlson Model: Contribution to Valuation Theory,Limitations, and Empirical Applications*

Kin Lo

Faculty of Commerce and Business Administration University of British Columbia

and Thomas LysJ. L. Kellogg Graduate School of Management Northwestern University

Abstract

The work of Ohlson (1995) and Feltham and Ohlson (1995) had a profound impact on accounting research in the 1990s. In this paper, we first discuss this valuation framework, identify its key features, and put it in the context of prior valuation models. We then review the numerous empirical studies that are based on these models. We find that most of these studies apply a residual income valuation model, without the information dynamics that are the key feature of the Feltham and Ohlson framework. We find that few studies have adequately evaluated the empirical validity of this framework. Moreover, the limited evidence on the validity of this valuation approach is mixed. We conclude that there are many opportunities to refine the theoretical framework and to test its empirical validity. Consequently, the praise many empiricists have given the models is premature.

*This paper has benefited from informal discussions with our colleagues at the Kellogg Graduate School of Management, Northwestern University, comments received from seminar participants at the Simon School, University of Rochester, Jeffrey Callen, Jerry Feltham, Jim Ohlson, Jerry Zimmerman, an anonymous referee, and participants of the 1999 Conference of the Journal of Accounting, Auditing, and Finance.

The Ohlson (1995) and Feltham and Ohlson (1995) studies stand among the most important developments in capital markets research in the last several years. The studies provide a foundation for redefining the appropriate objective of [valuation] research. Bernard (1995, 733).

1. Introduction

Rarely has an accounting paper received as much and early laudation as Ohlson (1995).1 Bernards flattering characterization of the Ohlson model (OM) is widespread. For example, Lundholm writes: The Ohlson (1995) and Feltham and Ohlson (1995) papers are landmark works in financial accounting. (1995, 749), and Dechow, Hutton, and Sloan state: Existing empirical research has generally provided enthusiastic support for the model. (1998, 2).Not surprisingly, this enthusiasm is also evident in the impact of the model on contemporary accounting literature. For example, to date (May 12, 1999) we found an average of 9 annual citations in the Social Sciences Citation Index (SSCI) for Ohlson (1995). If this citation rate continues, Ohlsons work is not just influential, but will become a classic.2What are the reasons for this enthusiasm for the OM? A survey of the accounting literature

reveals five possible reasons. First, it appears that there is consensus among accounting researchers that one of the desirable properties of the OM is its formal linkage between valuation and accounting numbers: Ohlson and Feltham present us with a very crisp yet descriptive representation of the accounting and valuation process (Lundholm: 1995, 761).

1 Although our analysis primarily focuses on Ohlson (1995), by reference, we also include related contributions such as Feltham and Ohlson (1995, 1996). We will make specific references to those works when we address issues beyond the basic model.2 Brown (1996) characterizes articles with an average annual SCCI of 4 or more (the range is 4.00 to 8.35) as

classics, those with an average annual SCCI between 3.00 and 4.00 as near classic, and the rest of the top 100 most

10Second, researchers appreciate the versatility of the model: [the residual income valuation] model should be an integral part of a broader solution to the problem of accounting diversity (Frankel and Lee, 1996, 3). [E]mpirical results . . . illustrate the resilience of the model to international accounting diversity (Frankel and Lee, 1996, 2).Third, the enthusiasm with the OM appears to be a response to Levs (1989) challenge that traditional approaches used in accounting research find a very weak linkage (low R2) between value changes and accounting information. In contrast, analyses that rely on the OM find that [I]n most countries, our estimate [from the residual income valuation model] accounts for more than 70% of the cross-sectional price variation (Frankel and Lee, 1996, 2).Fourth, and related to the previous point, the high R2 found in analyses that rely on the OM is interpreted to suggest that little value relevance is related to variables other than book value of equity, net income, and dividends. For example, using firm-level regressions Hand and Landsman obtain R2 in excess of 80% and conclude that: [T]he role in setting prices of information outside key aggregate accounting numbers in current financial statements may be more limited than previously thought (Hand and Landsman, 1998, 24).Finally, the very high explanatory power of the models leads researchers to conclude that the OM can be used for policy recommendations: [T]he Ohlson model has stimulated a growing body of policy-relevant work examining the link between firms equity market values and amounts recognized and/or disclosed in financial statements . . . the Coopers & Lybrand Accounting Advisory Committee (1997) advocates that empirical research evaluating financial reporting standards promulgated by standard setting bodies is best conducted through the Ohlson framework (Hand and Landsman, 1998, 2).

influential papers in accounting have an average annual SCCI of 2.14 - 2.89 (Table 1, 726-8).

But is this enthusiasm justified? As the remainder of this discussion will reveal, we believe the excitement is at a minimum premature and, more likely, unjustified. We revisit the OM, its application, and its contributions to accounting research. The purpose of our discussion then is to provide both a better understanding of the OM and its limitations.

residual income valuation (RIV)Section 2 of the paper discusses, the precursor to the OM. We note that, given clean surplus accounting, there is a one-to-one equivalence between RIV and the dividend discount model. That is, rejecting RIV is logically equivalent to concluding thatstock prices do not represent the present value of expected cash flows. Moreover, we show that RIV imposes data requirements that are impossible to meet in actual empirical settings. As a result, tests of RIV will necessarily require approximation of the models requirements.However, the consequences of such approximations on the models predictions are very difficult to assess. As a result, rejection of RIV will lead readers to conclude that the test approach was flawed or the data were bad but not that the model is wrong. Thus, RIV is both untestable and, in most researchers minds, almost surely true!Section 3 investigates Ohlsons (1995) information dynamics, Ohlsons application of the RIV. We show that the OM provides additional structure linking the RIV model to testable propositions. Note, however, that testing the OM is a joint test of RIV and Ohlsons information dynamics. Thus, based on the preceding paragraph, a rejection of the OM will be interpreted as a rejection of the information dynamics and not of RIV and the dividend discount model. Insection 3.3, we discuss how the OM relates to the Gordon dividend growth model, which precedes the OM by four decades. Although the Gordon models (implicit) information dynamics differ somewhat from Ohlsons, we show that the Gordon model can be restated to a formulation that is surprisingly similar to that of the OM. In section 3.4 we discuss the Feltham

and Ohlson (1995) extension of the OM. Then, we extend the OM in section 3.5 for instances where researchers use dirty surplus earnings or when they decompose earnings into different parts such as income from operations, special items, and extraordinary items. Based on the previous discussion, we summarize in section 3.6 our evaluation of the OMs contribution to valuation theory.Section 4 investigates the empirical applications of the OM. The analysis is divided into three subsections. Section 4.1 discusses papers that incorporate none of the informationdynamics, that is research that implicitly test or use RIV rather than the OM. Section 4.2 reviews tests of the information dynamics, that is the OMs assumptions. Section 4.3 analyzes research that evaluates the models predictions. The discussion of existing research is complemented with our own analysis. We find that the empirical evidence to date indicates that, while the information dynamics are possibly descriptive, the OM does not perform significantly better than existing valuation approaches. However, in the OMs defense, we also conclude that to date there have been few attempts to empirically incorporate Ohlsons information dynamics. In Section 5, we discuss studies that inappropriately implement RIV and the OM. Finally, Section 6 provides summary and conclusions.

2. Residual Income Valuation: The Precursor to the Ohlson Model

To understand the contribution of Ohlson (1995) to valuation theory, it is useful to decompose the OM into two parts: Residual Income Valuation (RIV) and Ohlsons (1995) information dynamics. We begin our analysis by discussing RIV as the precursor to the Ohlson Model in section 2.1. Section 2.2 discusses the empirical implications of RIV. In short, we point out that RIV is logically equivalent to the hypothesis that investors price securities as the expected present value of future dividends. Then, section 2.3 discusses testability of RIV.

2.1 RIV

Although RIV is an integral part of what is commonly referred to as the OM, it predates Ohlsons work by over fifty years.3 Specifically, RIV can be found in the literature as early as 1938 (see Preinreich, 1938, 240), but there are indications that the relation was known much earlier than that.4 RIV rests on a single hypothesis: asset prices represent the present value of all future dividends (PVED):

pt =

=1

tR E (d

t+ )

(PVED)

where pt is market price of equity at date t, dt symbolizes dividends (or net cash payments) received at the end of period t, R is unity plus the discount rate r, and Et is the expectation operator based on the information set at date t.5,6

To derive RIV from PVED, two additional assumptions are made. First, an accounting system that satisfies a clean surplus relation (CSR) is assumed:

bt = bt 1 + xt d t .

(CSR)

Commonly, bt is assumed to represent the book value of equity at date t, xt denotes the earnings in period ending at date t. However, CSR does not require that the accounting system

3 Ohlson is careful at pointing out that RIV was known in the thirties.

4 Relying on Pratt (1986), Bernard (1995) reports that the Internal Revenue Service used RIV as early as 1920 to estimate the impact of prohibition on the value of breweries (page 741, and footnote 8).5 Notice that RIV is frequently applied to equity valuation (where pt represents stock prices and dt dividends,

respectively). However, the analysis that follows can equally be conducted in settings where pt represents corporate value and dt net cash payments to all claimholders.6 One can generalize PVED to allow for time-varying discount rates.

be of the form that we typically imagine. Any two variables satisfying CSR will do. That is, CSR is merely used to substitute x and b for d in PVED. We will return to this point below.Second, a regularity condition is imposed, namely that the book value of equity grows at a rate less than R, that is

R E (b

) 0.

tt +

These two assumptions are used to restate (PVED) as a function of book value and discounted expected abnormal earnings:

p = b +

R E (x a )

(RIV)

tt =1

tt +

twhere x a

xt r bt1 . For the subsequent discussion it is important to note that, given the two

assumptions, PVED and RIV are mathematically equivalent. In other words, rejecting RIV is logically equivalent to rejecting the hypothesis that investors price securities as the present value of all expected future cash flows. Conversely, if PVED is false, then so must be RIV. A useful analogy to the relation between PVED and RIV is Rolls critique of tests of the Capital Asset Pricing Model: Use of a minimum variance benchmark portfolio is logically equivalent to linearity between the security return and the return on the benchmark portfolio (see Roll, 1977). We discuss the empirical implications and the testability of RIV next.

2.2 Empirical Implications

At first glance, the empirical implications of RIV seem straightforward: stock prices are a linear function of only the book value of equity and expected abnormal earnings, albeit an infinite series of the latter. Moreover, the coefficient on the book value of equity is unity, and the coefficients on expected abnormal earnings follow a geometric series in the inverse of the discount factor. Finally, the model imposes clean surplus as the sole restriction on the

accounting system.

RIV is attractive, because it links value to observable accounting data. But does RIV really require accounting in the common sense of the word? As suggested above, the answer is no! Any accounting system satisfying CSR will do. But it is important to note that satisfying CSR does not necessarily result in an accounting system accountants typically think off. Specifically, the model uses two variables, x and b, but imposes only one (time series) restriction (i.e. CSR).In other words, either x or b can be chosen arbitrarily, and CSR defines the other variable. While x defined as accounting earnings and b as the accounting book value of equity works, a system that defines b equal to zero, or the CEOs social security number will also satisfy RIV as long asx is defined to satisfy the time series property CSR.

However, this shortcoming of the model is also it strength. Specifically, even in cases where the accounting system does not satisfy CSR (e.g., US GAAP), it is possible to restate earnings in terms of comprehensive income, that is change in the book value of equity minus net capital contributions.7 Thus, all that is required by RIV is articulation between bt and xt. The price of this versatility, however, is that at least one of the two variables may not correspond toany number that appears in actual financial statements. Although this may seem to be a minor point, CSR is necessary to derive RIV from PVED. Thus, the model requires adding back of gains and losses that circumvented the income statement to net income. More importantly, the model calls for comprehensive income and not income from operations, or net income before extraordinary items, gains and losses, effects of accounting changes, etc.But do actual financial statements satisfy CSR? To provide evidence on this issue, we

7 For example, US GAAP treatment of foreign currency translations (SFAS 52) violates CSR. See Johnson, Reither, Swieringa (1995) or Frankel and Lee (1996) for dirty surplus items in US GAAP.

examined the difference between reported income and comprehensive income, a number calculated to satisfy CSR given reported retained earnings and dividends. Comprehensive income is defined as the change in retained earnings (Compustat item #36) excluding common and preferred dividends (#21 and #19). Dirty surplus is the absolute value of the difference between comprehensive income and a particular measure of income.8Table 1 provides statistics on dirty surplus for Compustat firms in the period 1962-1997.9

We find that, while the median deviation of US GAAP from CSR is only 0.40%, the mean deviation is 15.71% and a full 14.4% of the company-years have CSR violations that exceed 10% of comprehensive income. (Similar results are obtained relative to book value of equity and total assets.) Not surprisingly, CSR violations are more pronounced if xt is defined as income before extraordinary items and even more so for income before extraordinary and special items (two income definitions often used in valuation): 22% and 28% or observations have deviations of more than 10% of comprehensive income, respectively. Thus violations of clean surplus may be substantial under GAAP. This, in turn implies that rejections of RIV using GAAP netincome, income before extraordinary items, or income before extraordinary items and special items can be dismissed because they do not satisfy CSR.

8 Dhaliwal, Subramanyam, and Trezevant (1998) also use this method to calculate comprehensive income. However, common and preferred dividends according to Compustat do not include the value of stock dividends.Although stock dividends are typically small and infrequent, to the extent that retained earnings are affected by stock dividends, our statistics on dirty surplus are overstated.9 We quantify CSR violations as the absolute value of the difference between net income and comprehensive

income, divided by the absolute value of comprehensive income. We obtain similar results (see Table 1) when we replace the absolute value of comprehensive income in the denominator by either the book value of equity or bytotal assets.

Although dirty surplus items in historical accounting earnings may be substantial, what matters for RIV is that book values and expected earnings satisfy CSR. Of course, book values and expected earnings are likely to be affected by historical realizations and use of simple earnings forecasts may be inadequate. In section 3.5 we address how dirty surplus can be incorporated into RIV and the OM. Holding CSR violations aside, is RIV testable? We discuss this issue next.

2.3 Testing RIV

Setting aside measurement issues, a closer look reveals that RIV is not a good candidate for testing. Recall that RIV relies on only one hypothesis: investors price securities as the expected present value of future dividends. Thus, a rejection of RIV is logically equivalent to prices not being equal to the present value of expected future dividends. Few researchers would be willing to draw this inescapable conclusion and indeed are more likely to fault the research method. This denial will be easy, as by the very nature of the model, tests of RIV will be flawed.Specifically, empirical tests necessarily require truncation of the infinite series of abnormal earnings and the use of proxies for investor expectations. In other words, the empirical tests rely on approximations of the models constructs. As a result, the regression R2 will be less than unity and the coefficients will deviate from their predicted values. Yet it is almost impossible to theoretically derive the magnitude of those deviations. Therefore, it is very difficult to derive objective criteria for rejecting RIV. For example, consider Bernard (1995) implicit test of RIV, which results in a regression R2 of 68%. Although this is a high R2, the model predicts that the value ought to be 100%. Obviously, one reason 68% was obtained is because Bernard had to truncate the infinite series. But given the truncation, is 68% high enough? In other words, how

low could the regression R2 be before one would have to conclude that RIV is false?10

To see this more explicitly, first rewrite RIV to separate the portion of abnormal earnings in the finite horizon from the remainder being truncated at date T:

Tp = b +

R E ( xa ) +

R E ( x a )

tt =1T

tt +

T

=T +1

tt +

(1)

= bt + t

+ t

Now, to estimate the finite horizon version of this equation, we need to introduce three other notations: subscripts for firm identifiers, an error term to substitute for the portion of abnormal earnings being truncated, and coefficients for the remaining terms. For simplicity, we use only one coefficient for the sum of discounted abnormal earnings over the forecast horizon. Also, we do not introduce the additional complication of firm-specific discount rates. Thus, we write the following regression equation:

p =

+ b +

TR E (x a

) +

it0

1 it2 =1T

ti ,t +it

(2)

= 0 + 1bit + 2it +it

The difficulty of deriving an appropriate benchmark for testing RIV is evident by examining the difference between (1) and (2) above. The theoretical values of the coefficients and R2 will depend on a number of factors other than the forecast horizon T. First among these factors is the

itvariance of T

, which is unobserved. This effect, however, is mitigated by the covariances of

TTit with it and with bt. The explanatory power of the model will be increased to the extent

10 For comparison purposes, Bernard (1995) estimates a regression with dividends as the independent variable. That regression has a lower R2. The reason for this may not be the superiority of RIV vs. dividend discount model in finite data series, however. Rather, it is likely that Bernards results reflect the bias in R2 that results when unscaled variables are used in the estimation (see Brown, Lo, and Lys, 1999). We will return to this issue below.

itthat the included variables ( T

and bt) captures information in the omitted variable ( T

). That

itis, the higher the magnitude of these covariances, the higher the resulting regression R2. Third, serial correlation in abnormal earnings will result in 1 and 2 deviating from their theoretical values of 1. Finally, measurement error in the proxy for expectations will reduce the magnitude of estimated coefficients and explanatory power. Given all these factors, it is indeed a difficult task to come up with a theoretical benchmark for testing RIV.Abarbanell and Bernard (1994) illustrate the difficulty of testing RIV. The study relies on RIV to investigate whether the U.S. stock market is myopic, valuing short-term earnings more than they should, and long-term earnings less than they should. Their regression results show that the coefficient on the forecasted price-to-book premium (their proxy for long-term earnings) was at 0.53 compared with a predicted value of one, reliably too low. However, the paper then proceeds through a series of tests and discussions that attribute the result to measurement error, and concludes that there is no market myopia. Indeed, the rejection of RIV is so unappealing, that researchers will naturally search for alternative conclusions.In summary, any rejection of RIV would be associated with a critique of the implementation

of the tests, as opposed to the empirical validity of the model (i.e., that investors do not price securities as the expected present value of future dividends). In other words, RIV is not rejectable. Thus, while RIV may have seemed as an ideal topic for empirical testing, that first impression was misleading. The assumptions of PVED and CSR are not rejectable because RIV offers no guidance on how to proxy for the infinite series of expected abnormal earnings.

3. The Ohlson Model and Its Contribution to Valuation Theory

As suggested in the Section 2, the OM builds on the foundations provided by RIV. But saying

this is not to somehow diminish Ohlsons contribution: as we have discussed in Section 2, RIV is neither implementable nor testable. Thus, beyond the issue whether the OM is empirically valid, Ohlsons contribution is the linkage between RIV and testable propositions provided by the additional structure imposed. Section 3.1 describes Ohlsons application of RIV, while section3.2 provides an interpretation of the model and discusses empirical propositions. In section 3.3, we discuss how the OM relates to the Gordon dividend growth model. We also compare the OM with the model of Feltham and Ohlson (1995) in section 3.4. Section 3.5 extends the OM for cases where researchers use income definitions that are not consistent with CSR. Finally,Section 3.6 discusses Ohlsons contribution to valuation theory.

3.1 Ohlsons Information Dynamics

Ohlsons (1995) contribution comes from his modeling of the information dynamics. The model postulates the time-series behavior of abnormal earnings via two equations:aa

xt +1 = xt

+t + t +1

(ID1)

and

t +1 = t +t+1

(ID2)

where t = value relevant information not yet captured by accounting (i.e. events that have not

yet affected bt, xt), t ,t

are mean zero disturbance terms, and 0 , < 1 . (The lower bound of

this restriction is dictated by economic reasoning or empirical observation; the upper bound is required to achieve stationarity.) These two equations imply the following restrictions: abnormal earnings follow an AR(1) process; other information begins to be incorporated into earnings with exactly one lag; and the impact of other information on earnings is gradual, following an AR(1) process.For purposes of interpretation, one can rewrite equations ID1 and ID2 so that abnormal

.earnings is a function of the disturbance terms only:

t +1 a

t +1

t t

ts s

(ID)

xt+1 = =1

+ =1

s=

Based on RIV and ID1 and ID2, Ohlson obtains the valuation function:

tt1 tp = b + x a

+ 2t

where 1 = /( R )2 = R /( R )(R ).

(3)

Equivalently, the valuation function can be written so that earnings replaces abnormal earnings:

pt = (1 k)bt + k(xt dt ) +2t

where k = 1r = r/( R ) = R / r

(4)

Note that while RIV requires expected future abnormal earnings, the additional structure of the information dynamics allows value to be expressed as a function of contemporaneous data. In addition to the two price levels equations (3 and 4), Ohlson (1995) derives an equation describing returns as a function of shocks to earnings and other information:

Ret t = R + (1 +1 )t / pt1 +2t / pt 1

where Rett = ( pt + dt ) / pt1

(5)

The attractiveness of the OM to empiricists is that it provides a testable pricing equation that identifies the roles of accounting and non-accounting information, and only three accounting constructs are required to summarize the accounting component. Moreover, whether such a separation is empirically valid is a testable proposition. Equation (4) provides roles for book value and earnings, both of which have been used extensively, either separately or jointly, in prior empirical research. Furthermore, equation (5) is consistent with existing work on the relation between (abnormal) returns and earnings. Finally, the two parameters and are sufficient to characterize processes where earnings are purely transitory to processes where earnings are highly persistent. In sum, the OM provides an internally consistent set of valuation

equations for price levels and returns in place of a number of ad hoc models used in the last three decades. More importantly, the model is sufficiently tractable to allow derivation of specific predictions and rejection criteria.

3.2 Interpretation and Analysis of the Model

The discussion in this section focuses on that part of the OM that goes beyond RIV. That is, we will consider the information dynamics ID1 and ID2 and the related results. We take this approach because the assumptions underlying RIV are uncontroversial.Analysis of the First Information Dynamic

On the surface, the AR(1) structure for abnormal earnings is quite appealing. It is parsimonious; it is easy to interpret; it is roughly consistent with empirical observation; and it leads to simple, close form solutions. A closer look at ID1, however, reveals some implicit assumptions.Consider the unconditional expectation of abnormal earnings. Given (i) the autoregressive

nature of the stochastic process, (ii) the disturbance term having mean zero, and (iii) other information having mean zero, it follows that abnormal earnings are zero unconditionally;

tE(x a ) = 0 . Therefore, unconditional goodwill, defined as the difference between pt and bt, is also zero. For this to occur, firms cannot on average earn more than the cost of capital. If the accounting system uses historical cost (the primary basis of GAAP in most industrialized counties), this is equivalent to saying that all projects (not just marginal projects), must have zero expected net present value (NPV).11 This suggests that the model does not provide for project selection by managers.One solution to this problem is to allow dirty surplus for the expected NPV of projects. For

11 A sufficient condition for projects to have zero expected net present value is that the market for real assets is perfect.

example, if a firm invests in a project with positive expected net present value, then the assets

and equity of the company would be marked up to reflect the positive NPV. However, the mark- up must bypass the income statement to maintain a zero mean for abnormal earnings. While allowing for dirty surplus ensures the validity of ID1, the equivalence of RIV and PVED nolonger holds, so this solution is unappealing. Another solution one might propose is to allow for conservative accounting as in Feltham and Ohlson (1995), since understating book value relative to market value is commonly considered conservatism. However, this is not so. One can readily verify that any clean surplus accounting system must generate positive abnormal earnings onaverage if projects on average have positive NPV.12 A simpler though ad hoc solution is to

modify ID1 to allow for a constant term, so that expected abnormal earnings are positive. A more complete solution would extend ID1 to include a model of project selection, see Yee (2000).Analysis of the Second Information Dynamic

On the surface, the second information dynamic looks innocuous; it is again a standard AR(1) process. Because of the apparent simplicity, and the elusive nature of other information, few researchers have devoted attention to this assumption. Even Ohlson (1995) provides almost no discussion of this dynamic.First, we find the terminology problematic in the context of the model. Ohlson (1995, 668) indicates that t is information other than abnormal earnings. A standard economic

12 The reasoning is as follows : Recall that under RIV, unconditional goodwill is zero if and only if unconditional expected abnormal earnings is zero. Applying RIV on a project-by-project basis, NPV > 0 if and only if pt exceedsinvestment cost (i.e., goodwill > 0). Since goodwill > 0 if and only if E(xta) > 0, then NPV > 0 if and only if E(xta) >

0. Hence for any CSR accounting system, zero expected abnormal earnings implies and is implied by zero expected NPV investments.

ttttinterpretation of this phrase would lead one to conclude that t is independent of x a. In fact, researchers have argued that a constant term can proxy for t because t is (incorrectly) argued to be uncorrelated with x a. (See, for example, an early draft of Dechow et al, 1998). However, a close examination of the two dynamics together reveals that this is the case only in the boundary case of = 0. Positive values of result in a positive correlation between t and x a. To see this, note that t-1 affects both t and x a. This correlation is important from an empirical standpoint because one cannot simply omit t in estimating the model; t constitutes a correlated omitted variable.In addition to the dependence of other information and abnormal earnings, the AR(1) structure of ID2 results in some interesting and possibly unintuitive patterns of abnormal earnings when considered in conjunction with ID1. (For this discussion, we will set aside theabove concerns about the first dynamic.) In a single equation dynamic, the effect of disturbances diminish at the rate of unity minus the AR(1) coefficient (or ). However, the two dynamics work in such a way that the effect of a shock to other information (t) increase over time before dissipating. It is clearly evident that each t results in a sequence of t that diminish toward zero with time. However, note that the sequence of t (not just a single t) then feeds into the first dynamic, so that the effect of each t shock on abnormal earnings grows for some time before diminishing. This effect can be readily verified by examining the second term of equation (ID), and is depicted in Figure 1. To illustrate, we introduce a one time shock to at t = 1. As illustrated in Figure 1, the effect of this one time shock increases for several periods, before declining toward zero. This occurs because ID2 feeds back into ID1. In contrast, shocks to decay in a geometric fashion. Thus, for a given size shock (and given and ), ID2 has a more lasting impact on the time-series of abnormal earnings than ID1.

The role of accounting

Accounting enters the model through the information dynamics. In other words, the sole determinant of the accounting system are the specific time-series properties specified in the information dynamics. However, another interesting feature of the OM is that the Modigliani and Miller (MM) assumptions are satisfied. In perfect markets, there is no substantive role for accounting as there are no information asymmetries. If stock price already incorporates all available information, financial statements provide no added value. Moreover, absent agency costs, there is no demand for monitoring. This fact has been recognized in previous literature.For example, Verrecchia (1998) states: If firm value is common knowledge, however, why does

anyone care whether it can be summarized as an expression that involves only earnings and assets? In other words, what is the advantage of an accounting process that achieves parsimony? (115).Thus, this literature needs to move away from MM assumptions in order to make any substantive statements about accounting.

3.3 Relation to the Gordon Model

Ohlsons model is related to Gordons dividend growth model (see Gordon and Shapiro, 1956). Gordons model is stated in terms of dividends, so it may not appear that the OM is all that closely related to it. However, as we see below, the two models are remarkably similar.The Gordon growth model starts with PVED as does the OM. Other assumptions include specification of the processes for earnings and dividends. The Gordon growth model assumes the following relationships for the firms dividend policy and accounting rates of return:13

13 The model of Gordon and Shapiro (1956) does not address uncertainty explicitly. Rather, Gordon and Shapiro describe their model using expected values: a corporation is expected to earn a return of [] on the book value of its common equity (105). Strictly speaking, this is an over-simplification because the evolution of book values,

d t+

= (1 )xt+

(6)

xt+

= bt + 1

(7)

In these two equations, is the portion of earnings retained, or the plowback ratio, and is the book return on equity. Although not explicitly stated, Gordon also assumes CSR. These assumptions lead to the following evolution of book value, earnings, and dividends, where g = is the growth rate:

bt+1 = bt + xt +1 dt +1 = bt + xt +1 = bt + bt= (1 + g)bt

(8)

xt+1 = bt

= (1+ g )bt1

(9)

= (1 + g)xt

d t+1 = (1 ) xt +1 = (1)(1 + g) xt= (1 + g)dt

In addition, we can write the abnormal earnings dynamic in the Gordon growth model as:

(10)

xa t+1

= xt +1

rbt

= (1 + g) xt rbt= (1 + g)( x a + rb

) rb

(11)

tt 1t

= (1 + g) xa + r(1 + g)b

rb

t

t= (1 + g) xa

t 1t

Notice this dynamic is very similar to ID1, except for Ohlsons inclusion of other information t. One need only replace (1 + g) by . In Gordons model, it is typically assumed that g 0, in contrast to Ohlson.

earnings, and dividends depend on the realized values, not expectations, if clean surplus is to be satisfied. If one incorporates an error term into (7), one way for the results of the Gordon model to hold is to set the dividend policy to pay out an amount at t equal to (1-)Et-1(xt) + t, where t is the innovation in earnings. This approach works because the earnings shock is not permitted to affect end-of-period book value and thus future earnings are notaffected by the current earnings shock via the accounting rate of return assumption.

Based on the assumptions on dividend policy, accounting rates of return, and CSR, Gordon obtains the pricing equation familiar to most readers:

pt =

dt +1r g

(1 + g)dt=.r g

(12)

Because of the tight linkage Gordon imposes between dt, xt, and bt, this pricing equation can be equivalently stated in terms of earnings or book value:

(1 )(1 + g) xtpt =r g

or(13)

(1 )btpt =.r g

(14)

Thus, the Gordon dividend growth model can also be considered an earnings growth model or a book value growth model. In fact one can also convert Gordons pricing equation to involve both earnings and book value by recognizing that (1+g) in equation (11) corresponds to in Ohlsons notation. That is, (11) corresponds to ID1 when = 0. Hence, we can rewrite the Gordon pricing equation as:

tt1 tp = b + xa

which is exactly Ohlsons valuation function (3) without t. Although her derivation differs somewhat from ours, Morel (1998) obtains a similar expression, showing that the Gordon Model is nested in Ohlson. In addition, she compares Gordon and Ohlson and finds Gordon wanting.While the valuation functions of Gordon and Ohlson are similar, there is one important distinction. The Gordon model specifically links dividends, earnings, and book value via the dividend policy and the accounting rate of return. In other words, Gordon imposes one more constraint on the model than does Ohlson. As a result, the model, in general, does not satisfy dividend irrelevancy. This is apparent from (15) as the growth rate (g = -1) in the valuation function depends on the plowback ratio parameter . In contrast, the OM specifies the abnormal

(15)

earnings dynamic independently of dividend policy so does not depend on dividend policy.

3.4 The Feltham-Ohlson Extension

Feltham and Ohlson (1995) expand the OM by separating a firms net assets into financial and operating assets. The distinguishing feature is that the former is assumed to be fairly valued on the balance sheet such that abnormal earnings for financial assets is always zero. One can simplify the Feltham and Ohlson model (henceforth FOM) by focusing exclusively on operating assets, that is valuing the operating assets only. Making this simplification, no modifications are required to PVED, CSR, or RIV.14What distinguishes the FOM from the OM are the information dynamics. The FOMs

dynamics consist of the following four equations, with our relabeling of operating assets as book value and operating earnings as total earnings.

x= x+aat +11 tbt +1 = 1,t +1 = 2,t +1 =

1bt +2 bt +

1,t + 2,t + 11,t + 22,t +

1,t+1 2,t+1 1,t+1 2,t+1

(ID3)(ID4)(ID5)(ID6)

with the following restrictions: |1|, |2| < 1, 0 1 < 1, 1 0, and 1 2 < R.

A comparison of ID3 - ID6 with ID1 and ID2 shows that the difference between the two models is twofold: (i) the addition of a book value dynamic (ID4 and ID6), and (ii) the dependence of abnormal earnings on book value. The coefficients on book value have the

14 It is not entirely clear what constitutes financial assets in the FOM. Specifically, a strict interpretation is that financial assets such as cash play no role in the value creation process. However, under this interpretation,shareholder value would be unaffected if those assets were distributed. Possibly a more realistic view is that financial assets facilitate value creation of operating assets, for example by allowing the firm to be liquid. Underthis interpretation, FOM arbitrarily assigns the abnormal earnings created by financial assets to the operating assets.

following interpretation: 1 parameterizes accounting conservatism, with a value of 1 = 0 ( > 0) corresponding to unbiased (conservative) accounting; 2 parameterizes the growth in book value.The valuation function under the dynamics of the FOM is as follows:

tt11 tp = b + x a

+ 12bt + 211,t + 222,t

(16)

where

11 =

1R 1

(= 1 )

21 =

R( R 1 )( R 1 )

(= 2 )

12

=1 R(r 1 )(R 2 )

22 =

12R 2

The immediately apparent difference between the valuation functions in the FOM and the OM is the additional weight (12) put on bt. The OM valuation function obtains as a special case when 12 = 0 (accounting is unbiased).Introducing the book value dynamic into the model allows Feltham and Ohlson to make

statements regarding the effect of conservatism and growth on valuation. Briefly, we summarize the main results (with some looseness in language for the sake of brevity):1. When accounting is conservative (1 > 0), and there is growth in book value (2 > 1), then value grows faster than (capitalized) earnings. (Proposition 5)2. When accounting is conservative and there is growth in book value, the expected change invalue over a period is larger than the expected earnings for the period. (Proposition 6)3. If accounting is conservative and there is no growth, then price will be higher relative tobook value, but not relative to (capitalized) earnings. If accounting is conservative and thereis growth, price is higher relative to both book value and earnings.4. If accounting is conservative, then:accrued earnings affect value more than cash earnings; and accrued earnings affect future earnings more than cash earnings.

In summary, the FOM is distinct from the OM not because of the separation of operating and financing activities, as the title of Feltham and Ohlson (1995) would suggest (Valuation and Clean Surplus Accounting for Operating and Financing Activities), but rather, because of the analysis of conservatism and growth.

3.5 Allowing for Dirty Surplus Accounting

xaIn this section, we analyze how dirty surplus affects the OM and how researchers can compensate for dirty surplus accounting. In the original model, xt is comprehensive (clean surplus) income. Now, denote yt as an alternate measure of income and zt = xt - yt as the dirty surplus corresponding to income measure yt. We define abnormal dirty surplus earnings as

yat = yt rbt1 . Abnormal clean surplus earnings is then

t = xt rbt 1 = yt + zt rbt1

t= y a

+ zt . This extension allows us to rewrite RIV as:

pt = bt + R =1

E ( x)att +

a

(RIV)

= bt + R

Et ( yt + ) + R

Et (zt + )

=1

=1

tt(RIV) indicates that using abnormal dirty surplus earnings while omitting zt creates two problems. First, as long as the correlation between y a and zt is less than unity, omission of zt from (RIV) will bias the regression R2 downwards. The magnitude of that bias will be a function of the variance of the omitted variable relative to the two included variables. Second, as

long as the correlation between either of the two included variables

y a or bt and the omitted

variable zt is not zero, the omission will bias the coefficients of the included variables. Thus,

teven if researchers were to use an infinite series of

y a s, either the regression R2 or the

coefficients, or both will be biased leading to a rejection of RIV. Next, we derive the consequences of dirty surplus accounting for the OM. To do this, we must make an assumption

tabout the time series properties of y a .

Researchers use dirty surplus measure of income yt presumably because such a measure has different information about future earnings then the dirty surplus item zt. For instance, one

chooses to define yt as income before extraordinary items and zt as extraordinary items because extraordinary items are considered (more) transitory. Thus, it is more reasonable to assume that yt and zt follow different processes.

Suppose that

y a follows ID1 (with appropriate substitution of

y a for x a ). Let zt follow the

ttt

AR(1) process:

zt +1 = zt + t +1 ,

0 < 1

(ID7)

In this dynamic, it is reasonable to assume that the dirty surplus item (e.g., extraordinary items) is not affected by non-accounting information t. Using this assumption, the valuation function then becomes:

p = b +

R E (x a )

tt =1

tt+

a

(3)

= bt + 1Et ( yt ) +2t + 3 zt

where 3 = / (R-). Stated in term of earnings instead of abnormal earnings, the valuation function is:

pt = (1 k)bt + k (yt dt ) + 2t + (k +3 ) zt

(4)

Note that, other than the substitution of one income definition for another (y for x) the only change from (3) and (4) to (3) and (4) are the additional terms 3zt and (k+3)zt, respectively. As indicated by (4), only when (k+3) = 0 does omission of zt bias neither the coefficient estimates nor the regression R2. That is, all income must be transitory such that = = 0. For example, while extraordinary items are likely to be well approximated as transitory, using only income before extraordinary items in applying the OM is incorrect, because k and 3 are likely to be non-zero. For dirty surplus items that are not completely transitory, such as unusual items, and 3 will be greater than 0, so zt should not be omitted from the equation, regardless of the

value of and k.

The above also points to an approach to generalize Ohlsons valuation equations to use items of the income statement other than comprehensive income. That is, the model can be expanded to allow numerous categories of income. For example, we can define yt as operating income after taxes, z1t as gains and losses from asset disposals, z2t as unusual items, and z3t as extraordinary items. Each of these components of income can then have their own AR(1) coefficients. The valuation implications of the zs will enter into the valuation equationadditively. The only requirement is that all of the income categories used must add up to comprehensive income.

3.6 Ohlsons Contribution

We consider Ohlsons contribution to be threefold. First, Ohlson (1995) revived the use of residual income in valuation research at a time when the approach could be more readily implemented. The availability of analyst forecasts since the 1980s and the easy access to computational resources allowed researchers to implement RIV. Poor timing may explain the lack of success of prior proponents of residual income, such as Edward and Bell (1961). Thus, while RIV cannot be attributed to Ohlson, the contribution of revitalizing interest in the model should not be underestimated. The move from a focus on value distribution to value creation, and the support for using accrual accounting numbers in valuation are both beneficial in research and in the classroom.Second, the information dynamics provides a way to link the dividend discount model to observable accounting variables. Here again, Ohlson revives an existing model (i.e., the Gordon- Shapiro dividend growth model). There are several distinctions between the two models, the main difference is that Ohlson is consistent with Modigliani and Miller dividend irrelevancy

while Gordon-Shapiro generally is not. However, the basic result of the two models is identical: price is the sum of book value and a multiple of abnormal earnings.Third, the model provides a framework to understand the different ad-hoc valuation approaches used in the past. For example, it helps to understand the discussion of whether earnings changes or earnings levels are appropriate in earnings-returns specifications.

4. An Evaluation of the Empirical Evidence Related to the Model

Any test of the OM (1995) is a joint test of the three main assumptions: PVED, CSR, and the information dynamics. We structure our discussion in three parts. First, we discuss research that, while referring to Ohlson (1995), ignores the information dynamics. This research is equivalent to testing RIV. We follow this by a discussion of research that test the information dynamics independent of the remainder of the model. Finally, we discuss research that tests the models predictions.

4.1 Testing RIV

A growing list of research is dedicated to RIV. Most of that research, however, does not purport to provide formal tests of RIV. Rather, the aim is to document how useful RIV is for security valuation. One reason that no formal tests of RIV are presented, is due to the fact that, as indicated above, it is not possible to specify the appropriate benchmark for testing RIV. As a result, most research has focused on documenting the RIVs superior explanatory power relative to alternative models.Bernard (1995) examines the explanatory power of RIV with a forecast horizon of four years

and finds that the approach explains 68% of the variation in per share equity values, much higher than the 29% obtained based on forecasted dividends. (Other studies too numerous to list find similar levels of R2s even using only historical book values and earnings.) Bernard further

concludes that [t]here is evidently little to be gained by forecasting earnings and book value beyond four years! However, conclusions such as this are likely premature given the specifications used in such analyses. Brown, Lo, and Lys (1999) show that levels regressions (i.e., regression where the dependent variable includes a scale factor) result in R2s that are higher than the R2 that would be obtained if the regression were not affected by scale. (In the subsequent discussion we refer to this phenomenon as the scale effect.) Furthermore, the higher R2 of the RIV approach relative to the discounted dividend approach is likely due to book value and earnings forecasts being more closely associated with scale (i.e. share size), than are dividends. This is particularly true for firms paying no dividends. Thus, the conclusion drawn in this class of studies that RIV is a powerful tool even with a short (or null) forecast horizon issuspect.

Frankel and Lee (1998) implement RIV by computing estimates of the intrinsic value Vt by

the following equation:

Vb

T E [x

(R 1) b

1 ]E [ x

( R 1) b1 ]

=+ Tttt =1

t+R

t + +t

t +TRT

( R 1)

t +T ,

(17)

The second term on the RHS of (17) represents abnormal earnings in the first T periods and the third term on the RHS of (17) represents the terminal value, proxied by the abnormal earnings of period t + T, discounted in perpetuity. Expected earnings and book values are computed using consensus analyst forecasts and realized accounting data.15 Frankel and Lee estimate (17) for

15 In reality, Frankel and Lee (1999) rewrite (17) in terms of exp ected returns on equity. That expression can be obtained from (17) through a simple transformation, yielding:

Vkt= bt

k [FROE+ t +=1

( R 1)] bt+ 1R

+ [ FROE t +k 1 ( R 1)] bt+ k 1 ,R k 1 (R 1)

where FROE is expected return on equity, computed using the IBES consensus earnings forecast.

jtjtvalues of T = 1, 2, and 3. They then proceed to compute the correlation between pjt and V T . Notice that that the square of the correlations corresponds to the R2 in a regression of pjt on V T . The results (shown in their Table 2, p 293) indicate a correlation of 0.80, 0.81, and 0.82 for T = 1, 2, and 3, respectively. The correlations using historical earnings substituting for earnings forecasts are about 0.69 for all three horizons. Moreover, bjt alone yields a correlation of 0.60.While the correlations reported in their Table 2 are high, the results raise some concerns.

First, we have no benchmark against which to judge those correlations (recall that the book value of equity alone provides a correlation of 0.60). Second, adding more than one-year ahead forecasts has no material effect on the correlation. One possibility is that analyst forecasts beyond one year are so noisy that inclusion of those forecasts adds very little. Alternatively, bjt may be explaining most of the cross-sectional variation, and the valuation incorporating earnings adds next to nothing. This latter interpretation is consistent with the results of Myers (1999).To further investigate this issue, we replicate in Table 2 some of the analyses of Frankel and Lee (1998) using actual earnings. This perfect foresight analysis is first performed using reported earnings and book values, and a discount rate of 12%.16 The results indicate a correlation of 0.97 using book value of equity alone (or 0.64 when securities with stock prices exceeding $1000 per share are excluded). Moreover, that correlation declines as more residual earnings numbers are added. Notice that the high correlation is consistent with the analysis ofBrown, Lo, and Lys (1999) who document that increasing the coefficient of variation of the scale factor increases the correlation. Thus, the correlations reported in our Table 2 (and in Table 2 of Frankel and Lee) are inflated due to the scale effect. However, although the scale effect

16 Frankel and Lee (1998) calculate V using both fixed discount rates (11, 12, and 13%) and discount rates estimated by Fama and French (1997). Their results are robust with respect to the discount rates used, however.

increases the regression R2, the magnitude of this increase is difficult to assess. However, one indication of its existence is the drop in correlation by 34% (0.64/0.97 1) when 12 observations with a price exceeding $1000 (Berkshire Hathaway) are excluded. This exclusion reduces the cross-sectional coefficient of variation of the scale variable and therefore reduces the size- induced inflation. Another indication is that book value based on cash accounting -- where there are no accruals even for capital investments and debt financing -- also explains 61% of the cross- sectional variation of prices.17 Thus, the correlations of price with estimates of intrinsic value measured on a per share or firm level basis are highly sensitive to the degree that scale effects exist in the data.Frankel and Lee (1998) also document several trading rules based on the ratio of V/P. Based on the evidence that portfolios with high V/P have higher returns than those with low V/P, they conclude that V/P is a good predictor of cross-sectional returns. Alternatively, one can argue that the discount rates used do not adequately proxy for expected returns. That is, a high V/P could simply indicate that the discount rates used were too low. It is then not surprising that realized returns are higher than another firm with a low V/P. By construction, using the wrong discount rate will lead to V/P predicting returns. Put another way, if the correct discount rates were used, then V/P should not explain cross-sectional returns at all, under the assumption of market efficiency.Taking a similar approach to Frankel and Lee (1998), Lee et al. (1999) examine the ability of

V to predict the prices of Dow 30 stocks. However, in this paper, they do not maintain the

17 Another observation from Table 2 is that estimates of V based on cash accounting earnings perform less well that value estimates based on accrual earnings, suggesting that the latter is more useful. However, this inference must be tempered by our caution regarding this methodology.

assumption of market efficiency. Lee et al. interpret the returns predicted by V/P as abnormal returns instead of expected returns, in contrast to Frankel and Lee. It remains to be seen which is the correct interpretation.Other studies that evaluate the usefulness of the RIV approach include Penman and

Sougiannis (1997) and Francis et al. (1997). Both studies compare the accuracy of valuation models based on RIV, dividend discounting, and free cash flow. The primary difference in the two studies is the proxy for expectations: the first study uses average realizations in portfolios while the latter uses Value Line forecasts. Accuracy is operationalized as the (absolute) difference between the estimated and the actual price divided by the actual price. Both studies conclude that the RIV approach dominates the other two approaches.

4.2 Testing the Lag Structure of the Information Dynamics

Another approach taken in the literature is to directly test the empirical validity of Ohlsons information dynamics. For example, Bar-Yosef, Callen, and Livnat (1996) (BCL) examine the empirical validity of the AR(1) assumption in the OM. A similar approach is followed by Morel (1999).18 BCLs evidence does not support the single-period lagged linear autoregressive relationships among dividends, earnings, and book values. (207). The analysis involves estimating a system of vector autoregressive linear equations (VAR) as follows:

18 To test the lag structure of the information dynamic, Morel also estimates the valuation equation in addition to the earnings dynamic. However, we are not convinced of the efficacy of comparing the estimates from the twoequations to evaluate the internal consistency of the model. In general, one cannot evaluate internal consistency of a model using empirical data. Rather, internal consistency should be evaluated analytically. The estimates from one equation could differ with those from the other because, for example, the market is inefficient that is, prices do not appropriately reflect the lag structure of earnings.

bt= 1bt 1xt= 2 bt 1d t= 3bt1

+ 1 xt 1+ 2 xt1+ 3 xt1

+ 1 dt1+ 2 dt1+ 3dt 1

+ 1t+ 2t+ 3t

(18)

The first point to note regarding BCLs approach is that, invalidation of a models assumption(s) does not invalidate the model, nor does it necessarily make the model not descriptive of the reality.19This philosophical point aside, there also appears to be some substantial problems with the

studys methodology, particularly the sample selection procedure. BCL excludes from estimation any firm that has one or more nonstationary series in book values, earnings, or dividends. This would seem to generate an unusual sample: it is well known that managers hold dividends stable and tend to increase them over time, and even casual observation suggests that book value and earnings are not stationary for most companies (and tend to drift upwards). Confirming this unusual sampling, BCL obtains only 118 firms for their analysis. Besides potentially producing a sample that is not representative of the population, this small sample also does not provide enough power to test the hypotheses.20 For example, under the assumptions of CSR and ID1 (and ignoring t), the second equation in the VAR is as follows, with corresponding results from BCLs Table 1:

xt =xt =t stat :

(1 )r 0.0138(0.09)

bt 1 bt 1

+R+ 0.3428(1.09)

xt1 xt1 +

r0.0128(0.00)

dt 1dt 1

+ t

(19)

Notice that the coefficient on xt-1, although economically plausible in the OM, is statistically

19 For example, even though the assumption of a frictionless world is surely false, the models for the trajectories of, say, cannon balls, in a vacuum are well accepted, and the predictions can be quite accurate in a world with air.20 Interestingly, BCL (208) indicate that similar results obtain using a larger sample that includes firms with non- stationary time series.

insignificant. For the coefficient to be significant with the given sample size, the estimated coefficient must be almost twice as large. Given the upper bound imposed by the stationarity requirement, it is unlikely that the coefficient can be much higher than 0.6.21 Thus, it seems that there is almost no room for the coefficient on xt-1 to attain significance in the sample.The insignificance of the other coefficients merits some comment as well. The OM predicts the coefficients on bt-1 and dt-1 to be an order of magnitude smaller than that of xt-1 if the discountfactor is around 10-12% and is not too close to 0 or 1. Thus, the predictions of the OM are not

ruled out (nor supported) by BCLs results. In sum, we find BCLs evidence inconclusive with respect to the information dynamics of the OM.

4.3 Tests of the Ohlson Model Including Information Dynamics

Two recent examples that test the predictions of OM are Myers (1999) and Dechow, Hutton, and Sloan (1998). Myers (1999) implements four different time-series models of linear information dynamics. The first one excludes other information t from the model. Two other versions are modifications to the model based on Feltham and Ohlson (1995, 1996) that take account of accounting conservatism. The final model (labeled LIM4) used by Myers is the only one thatcan be considered to be a test of the Ohlson (1995) model, because it explicitly attempts to

incorporate non-accounting information. Myers uses order backlog to proxy for t. The evidence shows that valuation estimates based on these implementations of the OM are not better than those using book values alone.Dechow, Hutton, and Sloan (1998) find support for the information dynamics. Based on the suggestion of Ohlson (1999), they use analyst earnings forecasts to proxy for non-accounting information, The AR(1) coefficients for both ID1 and ID2 are within the range specified by the

21 Recall that BCL retain only firms for which non-stationarity could be rejected.

OM: is estimated to be 0.62 and is 0.32. Furthermore, coefficients on additional lags in ID1 are not large, suggesting that the AR(1) specification sufficiently captures the salient effects. However, the paper also shows that the OM provides only slight improvements over existing models based on capitalizing short-term earnings forecasts. In summary, the little evidence that there is on the usefulness of the Ohlson (1995) model suggests that it is not a substantial improvement over existing models.

5. A Critique of Past Applications of the Model

As discussed above, both the revival of RIV and the information dynamics of the OM are important contributions to the valuation literature. However, many researchers misapply the OM, and there are also many instances in which researchers give too much credit to the OM. This section will discuss such application of the model. Before proceeding with this discussion, we need to describe what is in our view the correct way to empirically implement the OM.

5.1 Translating Theory to Empirical Analysis

The OM is written as a model for a single firm. To estimate the model cross-sectionally, one needs to convert the model for multiple firms. This conversion may seem trivial, but it is often overlooked. The obvious adjustments required to the model are to allow for discount rates and information dynamic parameters that are firm specific. Thus,=+a+*

p jt

b jt

R j =1

Et (x j,t+ )

jt

(RIV )

aa*

x j,t +1 = j x jt + jt + j ,t +1

(ID1 )

j,t+1 = j jt +j ,t +1

(ID2*)

One factor that results in the cross-sectional variation in the parameters of the information

dynamics is differences in accounting systems. Thus, in contrast to RIV, each specification of the OM is specific to the accounting methods employed. This factor appears to have been overlooked in the literature. Specifically, cross-sectional aggregation is inappropriate where firms differ in earnings persistence or accounting systems.The second adjustment is not so obvious. Examining the above equations, it appears that we have exhausted all possibilities in allowing for cross-sectional differences. However, empirical analysis requires that one isolate the effect due to the variables of interest from those that result from differences in initial conditions. For example, consider a simple experiment in which a researcher is interested in the effects of sunlight on plant growth. In such an experiment, the researcher would take every effort to ensure that factors other than sunlight are the same for each experimental group or explicitly control for it. In particular, the researcher would not deliberately choose plants of different species (e.g., mixing sunflowers with redwoods) or use plants at different stages of maturity (e.g., mixing seedlings and mature redwoods). Similarly, theresearcher would not consider one observation to be one redwood, and another observation to be

a group of 100 redwoods. Doing so is likely to result in biased coefficients and explanatory power because the scale of the observations can vary so widelyThis problem, of course, has been recognized in the accounting literature. Often termed as the scale effect See Gordon 1959, Lev and Sunder, 1981, Christie 1987, Landsman and Magliolo, 1988, Kothari and Zimmerman, 1995, Barth and Kallapur 1995, Easton, 1998, and Brown, Lo, and Lys 1999. The effect of scale on the estimated coefficients as we discussed above is, fundamentally, the omitted correlated variable problem in the econometrics literature (see, for example, Greene 1993). That literature offers two basic remedies: avoid the problem by designing the experiment to be free of omitted correlated variables (i.e., meaning that

observations must be similar along the relevant dimensions), or adjust for the biases by including one or more proxies for the omitted variables.Focusing on the first remedy in the context of valuation models, researchers need to satisfy the ceteris paribus condition. However, it is quite controversial how this is to be achieved. Firms do not start out with the same values, and shares do not start with the same prices, no matter how far back in their history one goes. While this seems to leave accounting researchers in an impossible position, it does not. What is different between plants and investments is that the latter is (roughly) infinitely divisible. Thus, one solution to satisfy the ceteris paribus condition is not to find a point in time where firms were the same value, but to ensure that the starting values of the investments are the same at a point in time (e.g., $1). In other words, researchers should be dividing the variables used in the valuation equations by the value of the firm at the beginning of the investment horizon. This approach, has been recommended in the

jtliterature (e.g., Lev and Sunder, 1981, Christie, 1987, Kothari and Zimmerman, 1995, Barth and Kallapur, 1996, and Brown et. al., 1999). Using this approach, cross-sectional estimation of

equations (RIV*), (ID1*), and (ID2*) requires that each of variables

p jt

, b jt

, xa , and

v jt

are

interpreted to be ex-dividend returns, book-to-lag-price ratio, abnormal earnings-to-lag-price ratio, and other information-to-lag-price ratio. Alternatively, the researcher can control for scale by including a scale proxy as a control variable.These two recommendations are warranted because scale in theory affects the dependent variable linearly. As a first approximation, investments have constant returns-to-scale. That is, a$100 investment is expected to end up 100 times as valuable as a $1 investment over the same period of time. Of course, risks of the investments will affect values to some extent, but is clearly of second order importance. However, one of the unavoidable drawbacks of these

recommendations is that they may change the nature of the experiment. For example, deflating by market value purges the left hand side variable of any information contained in lagged market value. Similarly, including a scale proxy as a control variable captures the information up to the beginning of the investment horizon.In the accounting literature, a common practice to control for a variable not relevant to the research question is to form portfolios by partitioning the sample based on that variable (see for example Chang, 1999). However, such a procedure is ineffective in controlling scale effects. In fact, we are unaware of any respectable econometrics literature that suggests this approach to be a solution for the omitted correlated variable problem. This procedure is not an effective solution because if scale affects the entire sample, then it will also be present in each partition. Consider the extreme case when the dependent variable is linearly and positively related to scale and is completely explained by the scale variable. The plot of the dependent variable on the scale variable forms an upward sloping straight line. Slicing the chart into two, ten, or any number of partitions using the x-axis in no way diminishes the positive relationship between the dependent variable and scale. It is straight-forward to see that the same result holds when variation is added around the straight line just plotted.

5.2 Empirical Misapplications

The accounting literature is replete with valuation studies that draw inappropriate conclusions because no attempt is made to asses the impact of the scale effect on parameter estimates and regression R2s. We have already discussed the problems with some specific sections of the analyses in Bernard (1995) and Frankel and Lee (1998). Other studies that at one point or another make similar methodological errors include Frankel and Lee (1996), Francis, Olsson,and Oswald (1997), Hand and Landsman (1998), Dechow, Hutton, and Sloan (1998), and a long

list of studies in the value relevance genre that look at the association of prices with book value and earnings.22We also conjecture that this methodology has led researchers to erroneously conclude that it is not necessary to use firm-specific discount rates and information dynamic parameters because doing so does not appear to make a big difference. This is likely a result of the pervasive scale effects in the model dominating the other effects. Beaver (1999) laments [i]t is remarkable that the assumption of constant discount rates across firms and time is the best we can do.The problems of the lack of control for the scale effect can be appreciated by examining Hand and Landsman (1998) as an illustration. That study is an application of the OM with both information dynamics. Hand and Landsman find that a firm level regression of price on book value, earnings, and dividends results in a positive coefficient on dividends. Since the OM predicts a negative value for this coefficient (-k, see equation 4), Hand and Landsman go on to conclude that the OM is rejected and the reason being that dividends provides a signal about future prospects of the firm. However, we show below that this result is caused by biases inherent in the levels approach.Table 3 replicates some of the Hand and Landsman analyses. Specifically, we analyze the relation between the market value of equity and contemporaneous book value of equity, earnings, and dividends in the spirit of equation (4). As in Table 3 of Hand and Landsman (1998), these regressions do not include a term for other information, t. (We only report the results for one year (1996), although results from several other years analyzed were similar.) We

22 Note that our criticism is not meant to apply to these studies in their entirety. We only disagree with the specific portions of the analyses that interpret coefficients and explanatory power from levels specifications. The overall contribution of each study may in fact overshadow the one shortcoming we identify.

exclude from the analysis observations with negative book value, and those identified as outliers by studentized residuals.Model 1 is a replication of the results of Hand and Landsman. When variables are measured on an aggregate firm level, the coefficient on dividends is positive, opposite the prediction of the OM. In addition, the coefficient is 3.03. This suggests a money-making machine - for each $1 increase in dividends, the firm value increase by $3. Obviously, something is wrong! Finally,the explanatory power of the model is an astounding 95%. This result is even more impressive, once we realize that this equation assumes that discount rates and abnormal earnings persistence are cross-sectionally constant. Taken at face value, this indeed leaves very little to be explained by information other than summary accounting measures. One is also tempted to conclude that all firms have the same discount rate and/or persistence, or at least that the cross-sectional variance in those attributes are sufficiently low. Model 2 repeats this analysis with variables measured on a per share basis, with the same result of a positive coefficient on dividends. However, the levels specification of Model 1 and Model 2 result in biased coefficient values andR2 (see Barth and Kallapur, 1995, and Brown, Lo, and Lys, 1999). To explore the direction and

magnitude of these biases, we re-estimate (4) after deflating all variables in model 1 (except the constant term) by the lagged value market of owners equity.23 As is reported in the third row of Table 3, the coefficient on dividends reverses in sign when the variables are deflated by market value of equity.24 Also, the R2 is a more modest 41%. Finally, Model 4 re-estimates the Hand and Landsman specification with size as an additional control variable (see Barth and Kallapur,

23 Note that the original equation (4) has no intercept. Rather, the intercept was added in the estimation. Therefore, the constant term need not be deflated.24 The coefficient is more negative than the lower bound of -1 predicted by the model, but not significantly so. However, the coefficient on net capital distributions is significantly less than -1.

1995). Again, the results indicate that the coefficient on dividends is negative (although the estimated value is reliably less than the value of 1 implied by the OM).This example underscores our argument that levels regressions such as Models 1 and 2 are likely to result in biased coefficient estimates and R2 values due to omission of a (cross- sectionally variable) scale factor. The bias in coefficients from a levels approach was so severe that the dividend coefficient had the wrong sign. The direction of the bias is actually quite predictable in this instance. Based on the casual observation that large firms tend to pay large dividends, and small firms tend to pay little or no dividends, one reasonably conjectures that the coefficient on dividends in Model 1 would be positive. In fact, the annual dividends paid by theaverage firm in the largest decile exceeds the market value of any firm in the smallest five deciles. Clearly, firm size and dividends are correlated - indeed, the pearson correlation between annual dividends and market value is 0.83.The same reasoning would lead one to conjecture that almost any variable positively correlated with firm size, such as operating expenses, will result in a positive coefficient. For example, we re-estimate equation 4 replacing dividends by cost of goods sold. Again, cost of goods sold has a positive coefficient of 0.06 (t = 14.2). In sum, we conclude that when one does not control for the size effect, the dividends variable captures some of that size effect. Thus, just as in the case of cost of goods sold, we find unconvincing Hand and Landsmans interpretation that dividends provide a signaling role.While the change in the dividend coefficient is most obvious because of the change in sign, other coefficients also change substantially when scale is controlled for. The coefficients on book value and earnings are much lower controlling for scale, reducing in magnitude by at least 60%. These changes in coefficients also reflect the bias induced by scale in the firm level and

per share regressions.

A final observation is that the explanatory power in the appropriately deflated regression is not as high as others have claimed. This suggests that we can improve the models implementation. In particular, there is ample opportunity to increase the explanatory power of the model by incorporating the heterogeneity of discount rates and persistence in abnormal earnings. There is also plenty of room for other information (accounting or non-accounting) to play a role in valuation.

6. Conclusion

Our review of the Ohlson Model suggests that it extends the literature on valuation. The revival of residual income valuation is notable on its own. Added to that, the parsimonious information dynamics translates expectations of the future to current observables. While the models core has been known for many decades, the OM is built upon the more solid foundation of Modigliani and Miller. Finally, the model is elegant and lends itself to extensions that analyze accounting issues such as conservatism and growth, as demonstrated by Feltham and Ohlson (1995).In contrast to the theoretical contribution of the OM, our review of the empirical results does not warrant the enthusiasm shown by many researchers. We find that most studies implement the model incorrectly. First, many studies refer to Ohlson (1995) but do not include the information dynamics. Thus, these studies are little more than tests or implementations of RIV. Second, studies typically use levels data in their analyses. However, such approaches are likely to have biased slope coefficients. Even more importantly, the R2 in such regressions are upwardly biased. As a result, researchers generally assign more credit to the model than it really deserves. Thus, we find much of the evidence that overwhelmingly supports the model suspect. This skepticism is particularly well founded in light of evidence in the few studies that do test the

model with scale-free data, which find that the model does not perform better than existing (simpler) models.However, in light of the inadequate implementation of the tests, the lack of empirical support for the Ohlson Model is not sufficient reason to abandon it. The model is just the starting point. The model has been developed in the context of perfect capital markets, and so is not meant to be entirely descriptive of the real world. Just as our colleagues in finance have taken away the MM assumptions one by one, we can do the same with the Ohlson Model. The model could be enhanced to incorporate the effects of taxes, bankruptcy costs, agency costs, asymmetric information, and so on. Given the evidence from the finance literature that these market imperfections do matter, we surely cannot be content with a model based on MM assumptions. As Bernard states: [the Ohlson Model] represent the base of a branch [for] capital market research . . . Ohlson (1995) and Feltham and Ohlson (1995) return to step one and attempt to build a more solid foundation for further work. Our challenge is clear.

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Descriptive Statistics on Dirty Surplus Itemsa

Table 1

Income Definition Income Before

Income Before

GAAP Net

Extraordinary

Extraordinary and

IncomeItemsSpecial Items

Dirty surplus as % ofMeanb15.7121.8228.65

|comprehensive income|Median0.403.069.00

% of obs > 10%14.4121.5728.02

Dirty surplus as % ofMeanb3.585.608.30

equity book valueMedian0.060.401.13

% of obs > 2%11.0917.8424.59

Dirty surplus as % ofMeanb1.472.253.43

total assetsMedian0.020.140.45

% of obs > 1%9.7716.0022.43

% of firm-years with dirty surplus > $1MM24.6129.8835.14

Number of firm-years157,661157,665144,428

a Comprehensive income is defined as the change in retained earnings (Compustat item #36) excluding common and preferred dividends (#21 and #19). Dirty surplus is the absolute value of the difference between comprehensive income and a particular measure of income. GAAP net income is item #172, income before extraordinary items is #18, income before extraordinary and special items is #18 plus #17. Data includes all firm-years between 1962 and 1997 subject to data availability in Compustat, except for observations with non-positive values of assets, book value, or |comprehensive income|.

b Means calculated based on ratios winsorized to a maximum value of 1.

Correlation of Stock Prices with Estimates of Intrinsic Valuea

Table 2

Data

Book

Residual Income Values Estimates

Accounting System

IncludedN

ValueT=1T=2T=3

GAAP book value andAll obs98,5460.970.940.880.81

earningsbp < $1,00098,5340.640.530.500.47

Cash accountingcAll obs95,3270.61- 0.13- 0.12- 0.11

p < $1,000 95,3150.200.100.100.11

a Includes on firm-years between 1962 and 1994 with sufficient data to implement each valuation model. Residual income value estimates are calculated using realized earnings to proxy for expected earnings, a constant discount rate of 12%, and forecast horizons of one, two, and three years, denoted T=1,2,3, respectively. All variables are per share values.

b GAAP book value is book value of equity (Compustat items #60) and earnings is income before extraordinary items (#18).

c Cash accounting book value is cash and short-term investments (#1) and earnings is defined to satisfy clean surplus, being casht - casht -1 + dividendst . Dividends include common and preferred dividends (#21 and #19).

OLS Regression of Market Value on Book Value, Earnings, and Dividends (t-statistics in italics below coefficients)a

NetCapitalR2 ModelConstantBook ValueEarningsDividendsDistributionN

Prediction if t = 0

1. Firm levelb--

111.740 1-k 1

1.01k 0

8.68-1 -k 0

3.03-1 -k 0

0.91

94.64%

7.8879.0575.6513.996.485741

2. Per sharec5.970.993.401.85-0.8563.68%

31.5049.3230.037.55-9.075744

3. Deflatedd1.010.340.63-1.16e-1.8341.22%

65.3222.3920.07-5.68-43.505776

4. Firm level with-13.700.221.03-1.90-0.8498.74%

size controlf-3.0129.1318.75-18.68-12.855137

a Regression includes Compustat firms with fiscal years ending in 1996, except for firms with negative book value. For each specification, 5794 firms were used in a preliminary regression. Reported results are for regressions excluding observations with |studentized residuals| > 4. Results of several other years in the 1990s were similar.

b Variables measured at aggregate firm level. Dependent variable is market value of equity at fiscal year-end (number of shares x price -- Compustat item #25 x #199). Book value is book value of common equity (#60), earnings is income before extraordinary items (#18), dividends is common dividends (#21), and net capital distributions is purchase of common and preferred stock (#115) less sale of common and preferred stock (#108).

c Variables measured on a per share basis. Dependent variable is stock price at fiscal year-end (#199). Book value per share is book value of common equity divided by number of shares (#60/#25), earnings is EPS before extraordinary items (#58), and dividends is common dividends per share (#21 / #25).

d Variables correspond to those used in the firm level regression, each divided by market value of common equity as of the preceding fiscal year-end (lag of (#25 x #199)).

e Coefficient is not significantly smaller than 1.0 (t = -0.78).

f The lagged market value (see d above) is added as an additional independent variable. That variable has a coefficient of 0.91 with a t-statistic of 171.17.

Table 3

Figure 1

t+Effect of a 1 unit shock to at t = 1 on abnormal earnings x a

3

Omega=0.9, Gamma=0.9 Omega=0.9, Gamma=0.7 Omega=0.7,Gamma=0.7

2

1

0

02468101214161820

Time Periods