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

The Ohlson Model: Contribution to Valuation Theory, Limitations, and Empirical Applications* Kin Lo Faculty of Commerce and Business Administration...

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 Lys J. 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 1990’s. 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 Bernard’s 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, Ohlson’s work is not just influential, but will become a “classic.”2 What 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 1  Second, 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 Lev’s (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). 2  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. Section 2 of the paper discusses residual income valuation (RIV), 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 that stock 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 model’s requirements. However, the consequences of such approximations on the model’s 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 Ohlson’s (1995) information dynamics, Ohlson’s 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 Ohlson’s 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. In section 3.3, we discuss how the OM relates to the Gordon dividend growth model, which precedes the OM by four decades. Although the Gordon model’s (implicit) information dynamics differ somewhat from Ohlson’s, 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 3 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 OM’s 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 information dynamics, 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 OM’s assumptions. Section 4.3 analyzes research that evaluates the model’s 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 OM’s defense, we also conclude that to date there have been few attempts to empirically incorporate Ohlson’s 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 Ohlson’s (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. 4 2.1 RIV Although RIV is an integral part of what is commonly referred to as the OM, it predates Ohlson’s 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): ∞ p t = ∑ R −τ E t ( d t +τ ) (PVED) τ =1 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, x t 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 p t represents stock prices and d t dividends, respectively). However, the analysis that follows can equally be conducted in settings where p t represents corporate value and d t net cash payments to all claimholders. 6 One can generalize PVED to allow for time-varying discount rates. 5 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 −τ Et (bt +τ ) τ → 0. →∞ These two assumptions are used to restate (PVED) as a function of book value and discounted expected abnormal earnings: ∞ p t = bt + ∑ R −τ Et ( xta+τ ) (RIV) τ =1 where x ta ≡ xt − r × bt −1. 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 Roll’s 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 6 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 CEO’s social security number will also satisfy RIV as long as x 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 x t. The price of this versatility, however, is that at least one of the two variables may not correspond to any 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. 7 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.8 Table 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 x t 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 net income, 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 by total assets. 8  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 model’s 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 9 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: T ∞ p t = bt + ∑ R −τ E t ( xta+τ ) + ∑R −τ Et ( xta+τ ) τ =1 τ =T +1 (1) = bt + Ω + ∆ T T 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: T p it = α0 + α1bit + α2 ∑ R −τ Et ( xia,t +τ ) + ψit τ =1 (2) = α0 + α1bit + α2 Ω + ψit T 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 variance of ∆Tit , which is unobserved. This effect, however, is mitigated by the covariances of ∆Tit with Ω Tit 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 Bernard’s 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. 10 that the included variables ( Ω Tit and bt) captures information in the omitted variable ( ∆Tit ). That is, the higher the magnitude of these covariances, the higher the resulting regression R2. Third, serial correlation in abnormal earnings will result in α1 and α2 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 11 this is not to somehow diminish Ohlson’s contribution: as we have discussed in Section 2, RIV is neither implementable nor testable. Thus, beyond the issue whether the OM is empirically valid, Ohlson’s contribution is the linkage between RIV and testable propositions provided by the additional structure imposed. Section 3.1 describes Ohlson’s application of RIV, while section 3.2 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 Ohlson’s contribution to valuation theory. 3.1 Ohlson’s Information Dynamics Ohlson’s (1995) contribution comes from his modeling of the information dynamics. The model postulates the time-series behavior of abnormal earnings via two equations: x ta+1 = ωxta +ν t + εt +1 (ID1) and νt +1 = γνt + ηt +1 (ID2) where νt = value relevant information not yet captured by accounting (i.e. events that have not yet affected bt, x t), εt ,ηt are mean zero disturbance terms, and 0 ≤ ω,γ < 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 12 earnings is a function of the disturbance terms only: t +1 t  t  x ta+1 = ∑ ωt −τ +1 ετ + ∑  ητ × ∑ ωt − s γ s −τ . (ID) τ =1 τ =1  s =τ  Based on RIV and ID1 and ID2, Ohlson obtains the valuation function: p t = bt + α1 x ta + α2νt where α1 = ω /( R − ω) (3) α2 = R /( R − ω)( R − γ ). Equivalently, the valuation function can be written so that earnings replaces abnormal earnings: p t = (1 − k ) bt + k (ϕxt − d t ) + α2νt where k = α1 r = r ω/( R − ω) (4) ϕ = R/r 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 + α1 )εt / p t −1 + α2ηt / pt −1 where Ret t = ( p t + d t ) / p t −1 (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 ω and γ 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 13 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; E ( xta ) = 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. 14 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 no longer 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 on average 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 νt 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 p t exceeds investment cost (i.e., goodwill > 0). Since goodwill > 0 if and only if E(xt a ) > 0, then NPV > 0 if and only if E(xt a ) > 0. Hence for any CSR accounting system, zero expected abnormal earnings implies and is implied by zero expected NPV investments. 15 interpretation of this phrase would lead one to conclude that νt is independent of x ta. In fact, researchers have argued that a constant term can proxy for νt because νt is (incorrectly) argued to be uncorrelated with x ta. (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 γ = 0. Positive values of γ result in a positive correlation between νt and x ta. To see this, note that νt-1 affects both νt and x ta. This correlation is important from an empirical standpoint because one cannot simply omit νt in estimating the model; νt 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 the above 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 (ω or γ). However, the two dynamics work in such a way that the effect of a shock to other information (ηt) increase over time before dissipating. It is clearly evident that each ηt results in a sequence of νt that diminish toward zero with time. However, note that the sequence of νt (not just a single νt) then feeds into the first dynamic, so that the effect of each ηt 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 ν 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 ε decay in a geometric fashion. Thus, for a given size shock (and given ω and γ), ID2 has a more lasting impact on the time-series of abnormal earnings than ID1. 16 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 Ohlson’s model is related to Gordon’s dividend growth model (see Gordon and Shapiro, 1956). Gordon’s 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 [ρ] on the book value of its common equity” (105). Strictly speaking, this is an over-simplification because the evolution of book values, 17  d t +τ = (1 − φ) x t +τ (6) x t +τ = ρbt +τ −1 (7) In these two equations, φ is the portion of earnings retained, or the plowback ratio, and ρ 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 = φρ is the growth rate: bt +1 = bt + xt +1 − d t +1 = bt + φxt +1 = bt + φρbt (8) = (1 + g )bt x t +1 = ρbt = ρ(1 + g )bt −1 (9) = (1 + g ) x t d t +1 = (1 − φ) xt +1 = (1 − φ)(1 + g ) xt (10) = (1 + g ) d t In addition, we can write the abnormal earnings dynamic in the Gordon growth model as: x ta+1 = xt +1 − rbt = (1 + g ) xt − rbt = (1 + g )( xta + rbt −1 ) − rbt (11) = (1 + g ) x + r (1 + g )bt −1 − rbt a t = (1 + g ) xta Notice this dynamic is very similar to ID1, except for Ohlson’s inclusion of other information νt. One need only replace (1 + g) by ω. In Gordon’s 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-φ)Et-1 (x t ) + εt , where εt 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 not affected by the current earnings shock via the accounting rate of return assumption. 18  Based on the assumptions on dividend policy, accounting rates of return, and CSR, Gordon obtains the pricing equation familiar to most readers: d t +1 (1 + g ) d t pt = =. (12) r−g r −g Because of the tight linkage Gordon imposes between dt, x t, and bt, this pricing equation can be equivalently stated in terms of earnings or book value: (1 − φ)(1 + g ) xt pt = or (13) r−g (1 − φ) ρbt pt =. (14) r−g 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 Gordon’s pricing equation to involve both earnings and book value by recognizing that (1+g) in equation (11) corresponds to ω in Ohlson’s notation. That is, (11) corresponds to ID1 when γ = 0. Hence, we can rewrite the Gordon pricing equation as: p t = bt + α1 xta (15) which is exactly Ohlson’s valuation function (3) without νt. 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 = ω -1) in the valuation function depends on the plowback ratio parameter φ. In contrast, the OM specifies the abnormal 19 earnings dynamic independently of dividend policy so ω does not depend on dividend policy. 3.4 The Feltham-Ohlson Extension Feltham and Ohlson (1995) expand the OM by separating a firm’s 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. 14 What distinguishes the FOM from the OM are the information dynamics. The FOM’s dynamics consist of the following four equations, with our relabeling of operating assets as book value and operating earnings as total earnings. xta+1 = ω1 x ta + δ1 bt + ν1, t + ε1, t +1 (ID3) bt +1 = δ2 bt + ν2 , t + ε 2 , t +1 (ID4) ν1,t +1 = γ1ν1, t + η1, t +1 (ID5) ν 2 ,t +1 = γ 2ν2 , t + η2 , t +1 (ID6) with the following restrictions: |γ1 |, |γ2 | < 1, 0 ≤ ω1 < 1, δ1 ≥ 0, and 1 ≤ δ2 < 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. Under this interpretation, FOM arbitrarily assigns the abnormal earnings created by financial assets to the operating assets. 20 following interpretation: δ1 parameterizes accounting conservatism, with a value of δ1 = 0 ( > 0) corresponding to unbiased (conservative) accounting; δ2 parameterizes the growth in book value. The valuation function under the dynamics of the FOM is as follows: p t = bt + α11 x ta + α12 bt + α21ν1, t + α22ν 2 ,t (16) ω1 R where α11 = ( = α1 ) α21 = ( = α2 ) R − ω1 ( R − ω1 )( R − γ 1 ) δ1 R α12 α12 = α22 = (r − δ1 )( R − δ2 ) R −γ2 The immediately apparent difference between the valuation functions in the FOM and the OM is the additional weight (α12 ) put on bt. The OM valuation function obtains as a special case when α12 = 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 (δ1 > 0), and there is growth in book value (δ2 > 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 in value 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 to book value, but not relative to (capitalized) earnings. If accounting is conservative and there is 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. 21 3.5 Allowing for Dirty Surplus Accounting In this section, we analyze how dirty surplus affects the OM and how researchers can compensate for dirty surplus accounting. In the original model, x t is comprehensive (clean surplus) income. Now, denote yt as an alternate measure of income and zt = x t - yt as the dirty surplus corresponding to income measure yt. We define abnormal dirty surplus earnings as y ta = yt − rbt −1. Abnormal clean surplus earnings is then x ta = xt − rbt −1 = y t + z t − rbt −1 = y ta + z t. This extension allows us to rewrite RIV as: ∞ p t = bt + ∑ R −τ E t ( xta+τ ) τ =1 (RIV’) ∞ ∞ = bt + ∑ R E t ( y −τ a t +τ ) + ∑ R E t ( z t +τ ) −τ τ =1 τ =1 (RIV’) indicates that using abnormal dirty surplus earnings while omitting zt creates two problems. First, as long as the correlation between y ta 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 ta or bt and the omitted variable zt is not zero, the omission will bias the coefficients of the included variables. Thus, even if researchers were to use an infinite series of y ta ‘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 about the time series properties of y ta. 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 22 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 ta follows ID1 (with appropriate substitution of y ta for x ta ). Let zt follow the AR(1) process: z t +1 = θz t + µt +1 , 0 ≤θ 10% 14.41 21.57 28.02 Dirty surplus as % of Meanb 3.58 5.60 8.30 equity book value Median 0.06 0.40 1.13 % of obs > 2% 11.09 17.84 24.59 Dirty surplus as % of Meanb 1.47 2.25 3.43 total assets Median 0.02 0.14 0.45 % of obs > 1% 9.77 16.00 22.43 % of firm-years with dirty surplus > $1MM 24.61 29.88 35.14 Number of firm-years 157,661 157,665 144,428 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. 44  Table 2 Correlation of Stock Prices with Estimates of Intrinsic Valuea Data Book Residual Income Values Estimates Accounting System Included N Value T=1 T=2 T=3 GAAP book value and All obs 98,546 0.97 0.94 0.88 0.81 earningsb p < $1,000 98,534 0.64 0.53 0.50 0.47 Cash accountingc All obs 95,327 0.61 - 0.13 - 0.12 - 0.11 p < $1,000 95,315 0.20 0.10 0.10 0.11 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). 45  Table 3 OLS Regression of Market Value on Book Value, Earnings, and Dividends (t-statistics in italics below coefficients)a Net Capital R2 Model Constant Book Value Earnings Dividends Distribution N Prediction if νt = 0 -- 0 ≤ 1-k ≤ 1 kϕ ≥ 0 -1 ≤ -k ≤ 0 -1 ≤ -k ≤ 0 1. Firm levelb 111.74 1.01 8.68 3.03 0.91 94.64% 7.88 79.05 75.65 13.99 6.48 5741 2. Per sharec 5.97 0.99 3.40 1.85 -0.85 63.68% 31.50 49.32 30.03 7.55 -9.07 5744 3. Deflatedd 1.01 0.34 0.63 -1.16e -1.83 41.22% 65.32 22.39 20.07 -5.68 -43.50 5776 4. Firm level with -13.70 0.22 1.03 -1.90 -0.84 98.74% size controlf -3.01 29.13 18.75 -18.68 -12.85 5137 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 1990’s 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. 46  Figure 1 Effect of a 1 unit shock to ν at t = 1 on abnormal earnings x ta+τ 3 Omega=0.9, Gamma=0.9 Omega=0.9, Gamma=0.7 Omega=0.7,Gamma=0.7 2 1 0 0 2 4 6 8 10 12 14 16 18 20 Time Periods 47