A Modified Ohlson (1995) Model and Its Applications

In this paper, I explore a modified Ohlson (1995) model, which incorporates future positive net present value (NPV) investments. I first utilize an approach to simultaneously estimate the parameters in the linear information dynamic alongside the cost of equity capital, then evaluate the model’s performance in equity valuation and return prediction. Contrary to the systematic undervaluation of the Ohlson (1995) model reported in prior literature, I find that there is no systematic undervaluation of stock prices by using the modified Ohlson (1995) model. The out-of-sample median valuation bias estimated with this new approach is only 3.3% compared with 34.8% achieved when carrying out the estimation using existing methods. I also find that using a time-varying cost of equity capital reduces valuation bias and improves valuation accuracy. Furthermore, the expected return estimates developed from the model generate a monotonic decile ranking of future realized stock returns.


Introduction
The residual income valuation (RIV) model is one of the major earnings-based equity valuation models. To implement the model, in the seminal paper 'Earnings, Book Values, and Dividends in Security Valuation,' Ohlson (1995) proposes a parsimonious linear information dynamic (LID) and establishes a link between stock values and accounting fundamentals. The LID model with its neat closed-form solution has made a significant impact on both theoretical and empirical work in equity valuation. However, the LID model is developed in an unbiased accounting framework and it is argued to be inconsistent with firms having nonzero net present value (NPV) investment projects. Existing empirical evidence seems to lend only limited support for the model. It leads to an obvious question: how can the deficiency of the model be overcome, and in particular, how can the LID model be extended and implemented in equity valuation?
In this paper, I explore a modified Ohlson (1995) LID model, which can in theory incorporate conservative accounting and future nonzero NPV investments. I propose a new approach to estimate simultaneously the modified LID parameters alongside the cost of equity capital. I find that the out-of-sample median valuation bias is substantially reduced compared with those in the 664 P. Wang existing literature applying the Ohlson (1995) model. The valuation inaccuracy can be improved when a time-varying cost of equity capital is utilized. I also find that the expected return estimates based on the model generate a monotonic decile ranking of future realized stock returns.
The modified LID as proposed in Ohlson (2003) involves the same two variables as in Ohlson (1995): residual income (or abnormal earnings) and 'other information' (henceforth OI) that can be useful to forecast future residual incomes. However, it permits firms' economic profits to persist in the long run with positive NPV investments by allowing the persistence of OI to be greater than or equal to one. In contrast to prior literature that applies a sequential procedure to estimating the two persistence parameters in the LID, I simultaneously estimate the LID parameters. These estimates are internally consistent as they are grounded in a no-arbitrage condition. 1 Estimating on both a year-by-year basis and an industry-year basis, I find that on average the persistence of OI is indeed between one and one plus the cost of equity capital, while the persistence of residual income remains between zero and one. This suggests that the parameter restrictions in the modified LID are justified and competition may not necessarily drive out firms' economic profits even in the long run. 'Asset light' companies in this digital era might be such an example. Firms with strong brands and other human capital may generate economic profits for a prolonged period. After estimating the industry LID parameters including the cost of capital and growth rate, I then evaluate the modified model's out-of-sample performance in equity valuation. In contrast to the systematic undervaluation of the Ohlson (1995) model reported in prior literature, I find that the systematic undervaluation using the modified model disappears. Defining valuation bias as the mean difference between the observed stock price and model predicted value scaled by price, the median bias estimated with this new approach is only 3.3% compared with 34.8% achieved when carrying out the estimation using existing methods. Contrary to Dechow et al. (1999), my results suggest that stock prices are not systematically overstated relative to their intrinsic values, and investors do not place too high a weight on the one-year ahead forecasts of earnings relative to the theoretical coefficients attached to forward earnings.
The new approach allows the implied discount rate to change over time and to be industryspecific. The results show that using the implied time-varying industry-specific cost of equity capital further improves valuation accuracy. This is in contrast to Beaver (1999, p. 37) who suggests that '(it) is remarkable that the assumption of constant discount rates across firms and time is the best we can do.' I also apply the model to estimate a proxy of firm-specific expected returns. When regressing realized returns on the proxy of the expected returns, I find that the coefficient of the proxy is positive and statistically different from zero. In addition, not only are realized stock returns sensitive to both cash flow news and discount rate news with the predicted signs, but the coefficients are also closer to their theoretical values than those reported in prior studies. Furthermore, the expected return estimates generate a monotonic decile ranking of future realized stock returns. This paper makes three main contributions. Firstly, it extends the Ohlson (1995) model to a parsimonious model that incorporates positive NPV investments and is supported by empirical evidence in equity valuation. Secondly, it offers a new approach to estimate simultaneously the parameters in the linear information dynamic, in sharp contrast to the sequential procedure applied in the existing literature. Thirdly, it provides an addition to the set of tools for estimation of the implied cost of equity capital (ICC). The new approach starts from a linear information dynamic and the mapping between accounting information dynamic and stock prices. To my knowledge, it is the first paper to adopt this approach to estimate the implied cost of equity capital. I extend it to develop a proxy for the firm-specific expected returns.

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argue that if we assume the persistence of OI is greater than or equal to one, then the Ohlson (1995) model allows for positive NPV projects, even when the persistence of residual income is between zero and one. It permits that firms' economic profits persist in the long run with NPV > 0 investments arising from either competitive advantages or accounting conservatism while the persistence of abnormal earnings disappears over time due to market competition. In contrast to FO (1995FO ( , 1996, the modified Ohlson (1995) model does not require any additional assumption on the book value dynamic in developing a closed-form valuation, hence it improves the practicability of implementation of the model. Under the assumptions of this modified model, we can establish a one-to-one mapping between the one-year ahead forecasts of earnings and current stock value. This mapping is important because it links a firm's performance in its product market to the capital market and may avoid potential violation of no-arbitrage condition. Myers (1999, p. 6) argues 'adopting information dynamics that seem reasonable in isolation can generate rather subtle inconsistencies when evaluated within the totality of the model linking information to firm value.' Like the original Ohlson (1995) model, the modified model requires the input of less information than most other existing equity valuation models in its implementation. 5 Although the Ohlson (1995) model has the virtue of parsimony in its description of the LID, implementing the LID model has proved to be challenging because OI is unidentified. The existing empirical studies are subject to the criticism that they fail to adequately model for the OI variable in either the Ohlson (1995) or the FO (1995FO ( , 1996 framework. Dechow et al. (1999) were among the first to provide a comprehensive empirical assessment of the model. They use a sequential procedure to estimate two parameters in the Ohlson (1995) LIDs. First, they estimate the persistence of abnormal earnings on a year-by-year basis as if abnormal earnings follow an autoregressive process, AR(1). Second, they estimate the persistence of OI by using the one-year ahead analysts' forecasts of earnings and the unconditional persistence of abnormal earnings estimated from the first stage. This effectively assumes that the role of OI in valuation is subordinate to that of abnormal earnings. They report that the Ohlson model underestimates equity value on average by more than 25%. Lo and Lys (2000) argue that this sequential procedure is problematic because the correlation between abnormal earnings and OI is important from an empirical standpoint. OI constitutes a correlated omitted variable when we simply omit OI in estimating the persistence of abnormal earnings in the model. Attempts to use some accounting variables as a proxy for OI may be helpful in forecasting future abnormal earnings, but this could still potentially be misleading by omitting important value relevant information. For example, Myers (1999) considers a firm's capital expenditure and order backlog as a proxy for OI. This results in a substantial undervaluation bias with a median of 35.6%. In addition to a possible misidentification of OI, there are other reasons in the existing literature that may lead to systematic underestimates of stock values using the Ohlson (1995) model. For instance, empirical studies on panel data often assume that all sample firms have the same constant cost of capital when implementing the model. The existing literature often assumes a constant cost of capital of 12% as in Dechow et al. (1999). However, if 12% as a discount rate is too high for some firms, then future economic profits for those firms will be too low or even negative for given values of earnings and assets. A high cost of capital not only influences the calculation of the present value of residual incomes, but also on the numerator itself in residual income valuation. The present value of expected future economic profits will be too low if the assumed cost of capital is higher than the true cost of capital. Furthermore, Dechow et al. (1999) also suggest that there is a possibility that stock prices may not reflect rational expectations and are overstated relative to the intrinsic values generated from the Ohlson (1995) model because investors place 'too low a weight on book value and too high a weight on the analysts' forecast of next year's earnings.' Overall, the existing empirical evidence lends little support to the use of the Ohlson (1995) model as a valuation model and empirical evidence suggests that it leads to a systematic undervaluation of equity shares.
In the spirit of Easton et al. (2002) and Ashton and Wang (2013), I utilize a regression approach to simultaneously estimate the LID parameters alongside the cost of equity capital on an industryyear basis in the modified Ohlson (1995) model, rather than to estimate the LID parameters in a sequential procedure and assume a constant cost of capital. 6 It relies on one-year ahead forecasts of earnings, which are expected to be more accurate than the multi-period ahead forecasts. Dividend payout policy is redundant when estimating the implied cost of capital. This is in contrast to existing ICC literature that often requires multiperiod forecasts of earnings or price targets and assumes a dividend payout policy over a finite forecast horizon in addition to assume a long-term growth of variables of interest. 7 In addition to assessing the valuation bias and valuation inaccuracy, I also develop a proxy for the expected stock returns and investigate the validity of the proxy. It establishes how accounting fundamentals governed by conservative principles effectively convey the risk of future expected growth (Penman & Yehuda, 2019;Penman & Zhang, 2020). Prior literature that assesses the validity of firm-specific estimates of expected returns has been motivated on the predictability of future realized returns. Given that there is often an insignificant or negative relation between the proxy and future realized stock returns after controlling for cash flow news and discount rate news, I evaluate the expected return proxy on the predictability of future realized returns in the Easton and Monahan (2005) framework.

The Modified Ohlson (1995) Model and Its Estimation Procedure
In this section, I outline the modified Ohlson LID model and its estimation procedure. I first follow Ohlson (1995) in making two standard initial assumptions. (1) Assume that the equity is valued in an arbitrage-free market with RP t = E t [P t+1 + d t+1 ], where P t is the ex-dividend equity value at time t, R equals one plus the cost of equity capital, and E t [.] is the expectations operator based on information available at time t. This assumption leads to the well-known dividend discount valuation model. (2) Assume that the clean surplus accounting relation (CSR) where x t is earnings and b t is the book value of equity at time t. That is, changes in the book value of equity must go through earnings. I also assume the following restrictions originating in the accounting for owners' equity: ∂x t /∂d t = 0 and ∂b t /∂d t = −1 indicating dividends do not affect contemporaneous earnings but reduce the book value of equity dollar-for-dollar. The well-known residual income valuation model (RIV) then directly follows from the above two assumptions (Edwards & Bell, 1961;Peasnell, 1982). RIV shows that market value of equity equals to the sum of book value and the present value of all expected future abnormal earnings. 6 O'Hanlon and Steele (2000) were among the first to use a regression approach to estimate simultaneously the cost of equity capital and the growth rate of abnormal earnings. Wang (2018) also applies a similar approach to directly estimate valuation parameters. 7 Claus and Thomas (2001) assume that firms retain 50% of earnings each period. Gebhardt et al. (2001) use up to three years of forecasts of earnings and assume that firms have a 100% dividend payout ratio beyond the forecast horizon. Easton et al. (2002) are based on up to four years of earnings forecasts and assume that the expected dividends in the forecast period are equal to current dividends. A more recent comprehensive review of the research using the implied cost of capital (ICC) methodology can be found in Echterling et al. (2015).

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Following Ohlson (1995Ohlson ( , 2003, I assume the following linear information dynamics (LID): where x a t = x t − (R − 1)b t−1 is residual income or abnormal earnings, OI t is 'other information' that has not yet been captured by current abnormal earnings but is useful in predicting future abnormal earnings. ε x,t+1 and ε OI,t+1 are mean zero random error terms, and ∂OI t /∂d t = 0. To explicitly incorporate the firm's future growth opportunities and accounting conservatism, I allow for 0 ≤ ω < 1 and 0 ≤ γ < R. The last inequality ensures convergence of the model. I call the system defined by equations (1) and (2) the modified Ohlson (1995) LID. 8 Note that abnormal earnings do not asymptotically approach to zero if the firm has NPV > 0 investments with γ > 1, even if ω < 1 or the persistence of abnormal earnings disappears over time. 9 Therefore, accounting is conservative with respect to book value and the value relevance of current abnormal earnings is negligible in the long run. The following propositions follow: Proposition 1 Given the residual income valuation model (RIV) and information dynamic (2), abnormal earnings dynamic (1) holds if, and only if the following valuation equation holds: Ohlson (1995) actually shows the 'only if' part of the proposition regardless of the LID parameter restrictions. Equation (3) intuitively demonstrates that the coefficient of residual income is the declining-perpetuity term ω/(R − ω). The coefficient of OI reflects a discounted compounding effect, and can be written as (1 + ω/(R − ω))(1 + γ /(R − γ ))/R = R/((R − ω)(R − γ )). Proposition 1 further shows that the reverse is also true. All proofs can be found in the Appendix. Under the assumptions, abnormal earnings dynamic (1) is a necessary condition for valuation model (3). In other words, there is a one-to-one mapping between the one-year ahead forecasts of abnormal earnings and current stock value. This is consistent with Ohlson (1999) and Pope and Wang (2005), who demonstrate that valuation of equity and forecasting of future earnings are interlinked. The model maintains the MM dividend policy irrelevancy, ∂P t /∂d t = −1. 10 The OI term represents the value of growth opportunities captured by current stock value. Accordingly, (γ − 1) can be interpreted as the growth rate based on current available information.
Proposition 2 Given the residual income valuation model (RIV), any two of the following three statements imply the third: (i) abnormal earnings dynamic (1) holds; (ii) equity value is given by 8 The extension of γ from original (0, 1) to (0, R) allows abnormal earnings and OI to be nonstationary, like the dividend growth assumption in the Gordon growth model. As Lo and Lys (2000) point out, '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).' 9 Abnormal earnings dynamics (1) and (2) imply E t [x a t+n ] = ω n x a t + ((γ n − ω n )/(γ − ω))OI t . If 0 < ω < 1, then ω n → 0 (n → ∞). Abnormal earnings eventually capture value relevant information included in OI > 0 that reflects a firm's new investment opportunities and future prospects. Ohlson (2003) shows that the LID model allows for positive NPV projects when 0 < ω < 1 and γ = 1. 10 This is in contrast with FO (1995FO ( , 1996, who separate operating activities from financial activities and assume that paying dividends is a financial activity, whereas financing activities are zero NPV investments. However, distinguishing between operating and financial assets can be arbitrary and all assets may be operating assets (Callen & Segal, 2005).

equation (3); (iii) abnormal earnings satisfy:
Note first that statements (i) and (ii) are independent without information dynamic (2). While Proposition 1 builds a mapping between forecasting of future earnings and stock value, Equation (4) establishes explicitly a link between stock value and the one-period ahead forecasts of earnings. Combining (4) with either (1) or (3) implies the other. It shows that the expected one-year ahead abnormal earnings can be written in terms of current abnormal earnings, book equity and stock value. Comparing information dynamic (4) with (1), it is clear that 'other information' OI can be inferred from accounting goodwill (the difference between market value and book value of equity) and current abnormal earnings. In other words, unlike abnormal earnings dynamic (1) and valuation equation (3), information dynamic (4) expresses future (abnormal) earnings in terms of observables if stock price is a good proxy for its intrinsic value. It builds a foundation for the following empirical examination. The intrinsic relations in Propositions 1 and 2 link a firm's financial performance in its product market to the capital market. It is intuitive to assume ω < 1 in (1) in a competitive economic market, though the two persistence parameters in (4), ω and γ , have symmetric roles.
Since (4) can be written in terms of earnings as (5) It suggests that stock prices can be a leading indicator of future earnings (Beaver et al., 1980(Beaver et al., , 1987(Beaver et al., , 1997. If we know market expectation of the firm's one-period ahead earnings (E t [x t+1 ]) and stock prices, Equation (5) can be used to estimate the LID parameters and the cost of equity capital. Following Ashton and Wang (2013), to reduce nonstationarity and minimize the effects of endogeneity, I divide both sides of information dynamic (5) by price and transform the information dynamic of future earnings into a dynamic of the forward earnings-to-price ratio as below: It establishes a nonlinear relationship between the forward earnings-to-price and the LID parameters. The importance of this observation is that we can estimate simultaneously the LID parameters, ω, γ and the cost of equity capital (R-1) by running a nonlinear regression. This approach contrasts sharply with existing studies that estimate the Ohlson style LID parameters in a sequential procedure, whereby estimates are first made of ω and these are used to estimate γ . Equation (5), in turn, implies that stock value can be written in terms of earnings, book value, dividends and the expected one-period ahead earnings as below, 670 P. Wang Therefore, value is a nonlinear function of (ω, γ , R), whose values must be estimated. Since both ω and γ < R, the coefficient of future earnings is expected to be positive and larger than the other coefficients in (7) reflecting the paramount importance of future earnings in valuation.
Consistent with long-standing financial analysts' practice, I use industry-year value drivers and value multiples as proxies for those of individual firms in the industry. By running a nonlinear regression based on (6), I can estimate simultaneously the LID parameters, the persistence of abnormal earnings (ω), and value drivers: growth rate (γ − 1) and the cost of equity capital (R-1) for each industry-year portfolio given market expectation of firms' one-year ahead earnings.
It then follows from (7) that equity value can be estimated as are the theoretical coefficients of earnings, book value, dividends and one-period ahead forecasts of earnings for individual firms in industry i in year t respectively. It is worth emphasizing that the above simultaneous procedure uses fundamental accounting information as well as stock prices in estimating the cross-sectional LID parameters. The resulting estimates of the theoretical values of the coefficients of book value, earnings, dividends and the one-year ahead forecasts of earnings in (9) contain information included in stock price at time t. Therefore, I compare valuation biases 'out-of-sample' from different estimation procedures. Specifically, to eliminate the effect of time t stock price information in estimating the LID parameters, I use the lagged one-year industry average theoretical values of the coefficients of book value, earnings, dividends and the one-year ahead forecasts of earnings to calculate intrinsic value at time t. 11 These estimates determine valuation multiples ( , B, , ) in (9) and the intrinsic value given by (8).
Applying valuation model (8), we can compare the valuation bias and valuation inaccuracy in different approaches to estimating the LID parameters, (ω, γ , R). Following prior studies, valuation bias is defined as the mean difference between the observed stock price and model predicted value, scaled by price. Valuation inaccuracy is defined as the mean absolute value of the difference between the observed stock price and model predicted value, scaled by price.
Furthermore, we can use industry-year specific parameters to represent firm-year specific parameters to develop a proxy for the firm-specific expected stock returns. 12 Specifically, It shows that the coefficients of current earnings and forward earnings in return expression (10) are negative and positive respectively under the model assumptions. If γ it ≥ 1, then the coefficient of current book value is also negative. It suggests that the recognition of current earnings implies lower risk, and similarly booked assets have lower risk (Penman, 2016;Penman & Yehuda, 2019). A lower (higher) earnings realization implies higher (lower) expected returns. It is also consistent with Penman and Zhang (2020) who show that, in conservative accounting, the higher expected future earnings are at risk, hence are associated with higher expected returns. Firms expense investment when outcomes are uncertain reducing current earnings and pushing earnings to the future. Accounting fundamentals governed by conservative principles effectively convey the risk of future expected growth. Return expression (10) provides a theoretical representation of these insights. It incorporates risk aversion and conservative accounting, and demonstrates the time-varying property of stock returns reflecting the arrival of new information.

Data Description
The sample includes all listed securities in NYSE, Amex and Nasdaq. Data is extracted from the CRSP monthly returns file, the Compustat industrial annual file and forecasts of earnings from the Institutional Brokers Estimate System (I/B/E/S) from 1979 to 2015. The adjusted number of shares outstanding and adjusted price at the end of the fiscal year, and adjusted price of equity three months after the fiscal year-end are collected from CRSP. The cumulated adjustment factors for number of shares and stock prices are collected from CRSP to calculate the adjusted number of shares outstanding and the adjusted prices. Stock prices three months after the fiscal year-end are used to ensure that information about the prior year financials have been incorporated in the analysts' forecasts of earnings. Relevant accounting data are collected from Compustat. Firms with negative book values (CEQ) are deleted. Earnings are measured as net income before extraordinary items (IB). For the purpose of comparison, I use the one-year ahead analysts' forecasts of earnings (feps t+1 ) as a proxy of the market's expectation of the firm's future earnings. The median consensus forecasts of earnings per share at the first month after the corresponding I/B/E/S-reported prior-year earnings announcements are used. All total variables used in the estimation are divided by the adjusted number of shares outstanding to reduce heteroskedasticity and increase comparability across time. In constructing the data set, 1% at the top and bottom stock prices, (price deflated) book value, (price deflated) earnings and dividends and (price deflated) analysts' consensus forecasts of earnings are deleted to avoid the influence of extreme observations. Panel A of Table 1 presents the descriptive statistics of the sample firms. These are largely consistent with those reported in previous studies. Panel B of Table 1 shows the annual crosssectional correlations for 98,955 observations over the 35-year period from 1980 to 2014. The upper (lower) right triangle of the matrix presents Spearman (Pearson) correlations. These correlations show that current prices and earnings are the variables with the largest correlation coefficients with forecasts of earnings.

Evaluating the Performance of the Modified Ohlson (1995) Model
In this section, I investigate the valuation implications by using the simultaneous approach to estimate the LID parameters in the modified Ohlson (1995) model. I evaluate the out-of-sample valuation bias and valuation inaccuracy as well as the valuation effects by using a time-varying cost of equity capital. I also assess the validity of the proxy for the expected stock returns.

Estimation of the LID Parameters
I use analysts' consensus earnings forecasts as a proxy for the market's expectation of future earnings, and stock prices as a proxy for the intrinsic value to estimate the modified LID parameters. I run the following cross-sectional nonlinear regressions based on (6): where feps t+1 is the one-year ahead analysts' forecasts of earnings for each year k = 1981, . . . ,2014. 13 Table 2 reports the average estimated LID parameters (ω, γ − 1) and the implied cost of capital R-1 (≡ ICC) as well as their t-statistics on a year-by-year basis. 14 Table 2. Simultaneous estimation of the LID parameters and cost of capital (ICC) Year  Table 2 reports the modified Ohlson (1995) LID parameters (ω, γ ), the cost of equity capital (R-1 = ICC), and their t-statistics on a yearly basis between 1981 and 2014. The LIDs are: is abnormal earnings and OI is 'other information.' x t , and b t are earnings and book value at time t respectively. A nonlinear least squares procedure is used to estimate simultaneously three parameters (ω, γ , R) from the following cross-sectional nonlinear regressions: where feps t+1 is the one-year ahead analysts' forecasts of earnings, and P t is stock price at time t.
The most noteworthy feature of the results in Table 2 is that on average, 1 < γ < R , with the mean (median) of γ = 1.018 (1.017). 32 out of the 34 observed values of γ are significantly greater than 1. Only in 2006-2007, are the values of γ significantly less than 1. It suggests lack of significant growth opportunities in the few years before the 2008 global financial crisis. The mean (median) of the persistence of abnormal earnings, ω, is 0.21 (0.20). These values are similar to those reported in Myers (1999). Consistent with Ashton and Wang (2013), the cost of equity capital falls almost monotonically from a high of 14.9% in 1981 to 4.8% in 2006-2007. It is more than 10% in 1980s and is between 4.8% and 6% after 2004. All are lower than 9% after 1992. The mean and the median values are 8.3% and 7.7% respectively. Comparing the trend of the implied cost of capital with ten-year U.S. government bond yields, we see that the cost of capital generally declines with the risk-free rate. However, Figure 1 shows that the risk premium increases from 2006 to 2012.
The summary statistics of the estimated parameters, the persistence of abnormal earnings and the growth rate, (ω, γ − 1), are presented in Panel A of Table 3.
Prior literature assumes empirically a temporally and cross-sectional constant discount rate in the model application. To see the impact of a fixed cost of equity capital for each firm-year on the LID parameters estimation and valuation, I follow prior literature and assume a constant discount rate in the model implementation. Specifically, I run cross-sectional nonlinear regressions with a constant R-1 = 9% based on Equation (11). 15 I simultaneously estimate (ω, γ ) each year and refer to two LID parameters (ω, γ ) as (ω , γ ), where the dashes denote estimates using a constant cost of capital. Panel B of Table 3 reports these summary statistics of the implied persistence of abnormal earnings (ω ) and growth rate (γ − 1) as well as their t-statistics. Note that the persistence of OI satisfy: 1 < γ < R for all sample years. Both the mean and the median of persistence of abnormal earnings (ω ) are close to 0.23. In general, the magnitudes of ω (γ ) in Panel B and ω(γ ) in Panel A are similar.
For the purpose of comparison, I also estimate the LID parameters in a sequential procedure as is normally adopted in the existing literature. The procedure effectively sets OI t = 0 in estimating  Table 3 reports the summary statistics of the modified Ohlson LID parameters estimated from different estimation procedures and alternative discount rates between 1981 and 2014 on a yearly basis. The summary statistics include mean, standard deviation, minimum, the 1st quartile, median, the 3rd quartile, maximum and the Fama-MacBeth t-statistic. Panel A presents the summary statistics of LID parameters, (ω, γ − 1), reported in Table 2.
In Panel B, the same nonlinear least squares procedure as in Panel A is used to simultaneously estimate two parameters, (ω, γ − 1), but a constant R-1 = 9% is assumed for every firm each year. Panel C reports the summary statistics of the LID parameters, (ω, γ ), estimated from the sequential estimation procedure assuming R-1 = 9% for every firm each year. ω is the regression coefficient from the following cross-sectional regressions: x a t+1 /P t = ω 0 + ωx a t /P t + ε x,t+1 , where x a t+1 = x t+1 − (R − 1)b t is calculated by using realized earnings. ω 0 is the intercept term. γ is estimated from the following cross-sectional regressions: OI t+1 /P t = γ 0 + γ OI t /P t + ε OI,t+1 , where 'other information': OI t = feps t+1 − (R − 1)b t − ωx a t , and feps t+1 is the one-year ahead analysts' forecasts of earnings. γ 0 is the intercept term. Panel D shows the summary statistics of the difference of the LID parameters, when using different estimating procedures (the simultaneous estimation vs. sequential estimation) and different discount rates (R-1 = ICC vs. 9%).
the LID parameter ω, ignoring the possibility that OI t constitutes a correlated omitted variable in the LID. Again, I assume R-1 = 9% in information dynamics (1) and (2), and run cross-sectional regressions. Specifically, I first estimate an unconditional value of ω from an abnormal earnings autoregression on a year-by-year basis (ignoring OI t ). I then use the unconditional ω estimated to calculate OI as: , and finally estimate γ from regressions based on information dynamic (2). I report the summary statistics of the estimates (ω, γ ) in Panel C of Table 3. For the purpose of my presentation, I refer to (ω, γ ) as (ω , γ ), where the double dashes denote their values based on the sequential estimates of the parameters. It shows that values of ω and γ are very similar to those reported in Choi et al. (2006). 16 The mean value estimates for the persistence of abnormal earnings and OI are 0.473 and 0.603 respectively. ω is in a range of 0.377-0.568, while γ is between 0.46 and 0.731. While the sequential estimation procedure produces values of the persistence (γ ) of OI that are significantly less than 1, in striking contrast, γ estimated from the simultaneous 676 P. Wang estimation procedure is significantly greater than 1 in each of the sample years as reported in Panel B.
Finally, a formal comparison of parameter estimates is presented in Panel D of Table 3, which reports the summary statistics in differences between LID parameters estimated by using different discount rates and different estimation procedures. It shows that both persistence of abnormal earnings and OI from the simultaneous estimation procedure when assuming a constant discount rate are statistically significantly larger than those when using the time-varying discount rate, the mean of (ω − ω) is 0.018 and mean of (γ − γ ) is 0.006. It suggests that on average LID parameter estimates (ω , γ ) may be upwardly biased when using a constant discount rate of 9% relative to using the time-varying implied cost of capital as a discount rate. I will show that this result has implication in estimating the intrinsic value of equity. Panel D also shows that the persistence of abnormal earnings is larger and the persistence of OI is much smaller when using the sequential estimation procedure than those when using the simultaneous estimation procedure. The mean of (ω − ω) is 0.263 and mean of (γ − γ ) is − 0.415. The impact of these differences on valuation is shown in the analysis next.

Valuation Bias and Inaccuracy by Using Different Estimation Procedures and Alternative Estimates of Discount Rates to Determine the LID Parameters
Because the cost of capital varies by industry and competition is mainly between firms in the same industry, I estimate the modified Ohlson LID parameters and the time-varying industryspecific cost of equity capital by running industry-year regressions when examining the valuation biases in this section. This allows the LID parameters to reflect variation in economic and accounting environment across industries and over years (Barth et al., 2005;Fama & French, 1997). Since some industries only have a limited number of observations in some sample years, firms are grouped into five industries based on the industry classification from Ken French's website and pooled cross-sectional nonlinear regressions are run in a four-year rolling window. 17 For each year k = 1981, . . . ,2014, the model is estimated using only data that are available in years between k-3 and k. The estimated parameters from the regressions are then used as year k parameters in the following analysis. Since the proposed approach utilizes time t information contained in stock prices, I make an out-of-sample comparison of valuation biases and valuation inaccuracies with those generated from existing approaches. Three parameters (ω it , γ it , R it − 1) for industry i in year t are estimated either by a simultaneous estimation procedure or a sequential procedure. When applying a sequential procedure, I assume R it − 1 = 9% for each firm-year. The persistence of abnormal earnings (ω it ) is the regression coefficient from pooled cross-sectional four-year rolling window regressions on an industry-year basis: x a t+1 /P t = ω 0 + ωx a t /P t + ε x,t+1 , where x a t+1 = x t+1 − (R − 1)b t is calculated by using realized earnings. ω 0 is the intercept term. The persistence of OI (γ it ) is also estimated from fouryear rolling window regressions on an industry-year basis: OI t+1 /P t = γ 0 + γ OI t /P t + ε OI,t+1 , where 'other information': OI t = feps t+1 − (R − 1)b t − ωx a t , and feps t+1 is the one-year ahead analysts' forecasts of earnings. γ 0 is the intercept term. When applying a simultaneous procedure, I use information up to time (t-1) and estimate (ω it , γ it , R it − 1) for industry i in year t based on (11). 18 I also estimate (ω it , γ it ) for industry i in year t by assuming R it − 1 = 9% from regressions on (11). 17 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. Industry 'Healthcare, Medical Equipment, and Drugs' has a small number of observations in the earlier sample period. I use 4-year rolling window to increase the industry-year sample observations. The results are similar if I run regressions in a three-or five-year rolling window. 18 Strictly speaking, Dechow et al. (1999) have also implicitly used time t price information when they use price as a deflator in estimation.

A Modified Ohlson (1995) Model and Its Applications 677
With different sets of LID parameters estimated using different estimation procedures and different discount rates, Equation (8) gives different sets of intrinsic values of equity shares. Following prior literature, the extreme 1% of the model predicted values are deleted and negative predicted equity values are set to zero (Barth et al., 2005). Moreover, the extreme 1% of biases and inaccuracies are winsorized. Table 4 reports the valuation bias and valuation inaccuracy from the LID model with the theoretical coefficient of each variable in (9) estimated at time t information from the sequential approach, and with the theoretical coefficients of relevant variables estimated at time t-1 information from the simultaneous approach. Panel A of Table 4 shows that the intrinsic value estimated from the sequential procedure understates stock prices on average by 25.7%, which is similar to those reported in the existing literature. On the other hand, the intrinsic value estimated from the simultaneous procedure overstates stock prices on average by 9.9% to 10.5% depending on whether the discount rate is time-varying or assumed constant. The median bias from the sequential procedure is 34.8%. In sharp contrast, it is between 3.3% and 6.4% from the simultaneous procedure. When using the simultaneous procedure and a constant discount rate of 9%, equity value is overstated more than that when using the time-varying implied cost of capital as a discount rate. This is consistent with Panel D of Table 3 since LID parameter estimates (ω , γ ) are upwardly biased relative to (ω, γ ). The smallest median bias is based on the LID with the time-varying industry-specific discount rate. There is no evidence of systematic undervaluation or overvaluation of stock prices from the LID model based on the simultaneous estimation procedure. This leads to higher standard deviations of valuation biases relative to that from the sequential procedure. Panel A of Table 4 also reports the pairwise t-tests for the valuation biases across different estimation procedures and different discount rates. While the means of valuation inaccuracies are comparable from different estimation approaches, Panel B of Table 4 shows that the first quartile, the median and the third quartile valuation inaccuracy using the simultaneous estimation procedure are all lower than those from the sequential estimation procedure. In particular, the LID model estimated from the time-varying discount rate generates the most accurate valuation. The median valuation inaccuracy is 29.5%, which is significantly smaller than 40.4% when the sequential estimation procedure is used. Panel B of Table 4 also reports the pairwise t-tests for the valuation inaccuracies across different estimation procedures and different discount rates. The pairwise t-tests show that these differences in valuation biases and valuation inaccuracies are statistically significant. These results suggest that we should estimate simultaneously both LID parameters (ω, γ ) and the time-varying cost of equity capital in implementing the RIV valuation model. It suggests that OI is not subordinate to the abnormal earnings in valuation.

Theoretical Weights and Those Investors Place on Short-Term Earnings Forecasts
The intrinsic values estimated by the Ohlson (1995) model based on the sequential estimation procedure substantially understate stock prices. The magnitude of underestimation reported in Table 4 is similar to that documented by Dechow et al. (1999), who argue that investors may overreact to the short-term forecasts of earnings since too high (low) a weight is placed on oneperiod ahead earnings (book value) relative to the theoretically predicted value. In a rational capital market, stock value is determined by the present value of expected future earnings (cash flows). We should expect the theoretical coefficient of future earnings ( ) in (8) to be positive and larger than the coefficients of current earnings, dividends and book value.
As in the last subsection, I apply the simultaneous procedure to estimate (ω it , γ it , R it − 1) for industry i in year t from pooled cross-sectional nonlinear regressions based on equation (11) on an industry-year basis. I calculate the implied values of the theoretical coefficients attached to book value, earnings, dividends and the one-year ahead forecasts of earnings for each industry-year as   Table 4 shows the valuation bias and valuation inaccuracy using different estimating procedures: sequential estimation (SEQ) or simultaneous (SIM) estimation, to estimate the modified Ohlson LID parameters and alternative discount rates, 9% or the implied cost of equity capital (ICC). The number of observations, mean, standard deviation, the first quartile (Q1), median and the third quartile (Q3) are reported. Panel A reports the valuation bias and Panel B reports the valuation inaccuracy. The results on pairwise t-tests for the valuation bias and inaccuracy across different estimation procedures and discount rates are also reported. The value of equity is given by: are the theoretical coefficients of earnings (x t ), book value (b t ), dividends (d t ) and one-period ahead forecasts of earnings (feps t+1 ) for individual firms in industry i in year t respectively. Three parameters (ω it , γ it , R it − 1) are estimated either from a simultaneous estimation procedure or a sequential procedure. When applying a sequential procedure, I assume R it − 1 = 9% for each firm and each year. The persistence of abnormal earnings (ω it ) for industry i in year t is the regression coefficient from 4-year rolling window regressions: is calculated by using realized earnings. ω 0 is the intercept term. The persistence of OI (γ it ) for industry i in year t is estimated from 4-year rolling window regressions: and feps t+1 is the one-year ahead analysts' forecasts of earnings. γ 0 is the intercept term. When applying a simultaneous procedure, I use information up to time (t-1) and estimate (ω it , γ it , R it − 1) for industry i in year t from the following pooled cross-sectional nonlinear 4-year rolling window regression on an industry-year basis: The To investigate what weight investors place on each of book value, earnings, dividends and the one-year ahead analysts' forecasts of earnings, I next regress stock prices on these variables on an industry-year basis: Table 5 columns 6-9 report regression coefficients of price on book value, earnings, dividends and the one-year ahead analysts' forecasts of earnings over the same sample period across 5-industry. The average regression coefficients (the Fama-MacBeth t-statistic) of book value, earnings, dividends and forecasts of earnings are: 0.323 (14.0), − 0.871 ( − 6.86), 0.517 (1.89) and 6.845 (20.56) respectively. The last four columns of Table 5 report the difference between the corresponding theoretical coefficients and regression coefficients over the sample period. Contrary to Dechow et al. (1999), the difference between the theoretical coefficients and regression coefficients of future earnings (book value) is positive (negative) in each sample year. These differences are statistically significant. It suggests that investors neither place a too high weight on the one-year ahead forecasts of earnings, nor place a too low weight on book value. While the one-period ahead forecasted earnings are short term and may not be realized, investors effectively put a conservative weight on it and anchor the stock price to book value. The theoretical coefficients of earnings are less than the regression coefficients in each sample year. On the other hand, the theoretical valuation coefficients put almost all (positive) weights on the forecasts of future earnings reflecting that assets are valued based on the expected future earnings (cash flows). In other words, future earnings subsume value relevant information in book value and current earnings. Note also that the difference between the theoretical coefficients and regression coefficients of dividends is not statistically different from zero supporting dividend irrelevancy.

Prediction of Stock Returns
If we use the one-year ahead analysts' forecasts of earnings as a proxy for the market expectation of firms' one-period ahead earnings, Equation (10) can be used to estimate the expected stock returns. That is, a proxy for the expected stock return for firm j in industry i at time t is where the industry-year LID parameters (ω it , γ it ) and discount rate (R it − 1) are estimated simultaneously as described in section 5.2. To evaluate the usefulness of the proxy, I follow prior literature and test whether it can predict realized future stock returns. Based on two tautologies, the log-transformed realized t + 1 period returns are usually decomposed into three components: 'true' expected return, cash flow news (CFN) and discount rate news (DRN) at t + 1. Denote R t = ln(1 + RET t ) the log of the realized one-period ahead stock returns (RET t ), and ER t = ln(1 + MPR t ) the log of model (12) predicted returns, where MPR t = E t [P t+1 + d t+1 ]/P t − 1. When future realized cash flows or earnings are greater (less) than the expected cash flows or earnings, time t + 1 realized return will be greater (less) than the expected return, all else being  Notes: Table 5 columns 2-5 report the mean theoretical coefficients attached to book value (b), earnings (x), dividends (d) and one-period ahead analysts' forecasts of earnings (feps) across 5-industry over 34-year between 1981 and 2014 in the following model: . Three parameters (ω, γ , R − 1) are estimated simultaneously on an industry-year basis from the following regression: Columns 6-9 report regression coefficients of price on book value, earnings, dividends and the one-year ahead analysts' forecasts of earnings over the same period: P t = β 0 + β 1 b t + β 2 x t + β 3 d t + β 4 feps t+1 + ε t . The last four columns report the difference between the corresponding theoretical coefficients and regression coefficients. The average value, standard deviation and the Fama-MacBeth t-statistic are also reported.
equal. When future discount rates are upwardly (downwardly) revised, time t + 1 realized return will be lower (higher) than the expected return, all else being equal. By definition, the two news components are unpredictable ex ante. Vuolteenaho (2002) suggests that the proxy for discount rate news should be a function of the time t + 1 change in the implied expected returns and firmspecific. Hence, consistent with Monahan (2005, 2016), time t + 1 discount rate news is proxied by DRN t+1 = resER t+1 /(1 − 0.98κ), where resER t+1 is the residual from the following firm level model predicted return regression: ER t+1 = constant + κER t + resER t+1 and κ is the slope. 19 It captures firm-specific discount rate shocks. Cash flow news is defined as actual earnings per share for year t + 1 less analysts' forecasts of one-year ahead earnings per share or 'earnings surprise,' scaled by stock price at time t. It intends to capture firm-specific cash flow shocks. Therefore, I examine the relationship between the realized one-period ahead stock returns and model (12) predicted returns after controlling for CFN and DRN. In the following regression: where XRET t+1 = R t+1 − ln(1 + r f ) and XER t+1 = ER t+1 − ln(1 + r f ) are the one-year ahead excess realized stock returns and the excess model predicted returns respectively, and r f is the 10-year US government bond yield, δ 1 and δ 2 are expected to be close to one and δ 3 is expected to be close to minus one if the model predicted returns (MPR) are a good proxy for the expected returns. Since the proxy of expected return is measured with error, the coefficients of XER, CFN and DRN are expected to differ from their theoretical values. Table 6 Panel A reports the summary statistics of the one-year ahead excess realized stock returns (XRET), the model predicted excess returns (XER), cash flow news (CFN) and discount rate news (DRN). It shows that XRET is much more volatile than XER. The mean of XRET is much smaller than its median, while the mean and the median of XER are similar.
Panel B presents regression coefficients (t-values) of the one-year ahead excess realized stock returns (XRET) on the model predicted excess returns (XER). Two-way cluster-robust standard errors are used to correct for both cross-sectional and time series dependence. The coefficient of XER in the univariate regression is 1.41, which is significantly different from zero (t-statistic 29.06). 20 In the multivariate regression, the coefficient of XER is 2.31 with t-statistic of 49.3. It suggests that ER is a downward biased measure of the expected return as documented in the ICC literature. The results in Table 6 are, however, in contrast with findings in Easton and Monahan (2005) who find that many popular ICC measures are negatively associated with realized returns after controlling for CFN and DRN. The coefficients on proxies for CFN and DRN are positive (1.246) and negative ( − 0.992) respectively with theoretically predicted signs. In particular, the coefficient of DRN is statistically indifferent from minus one. Panel C reports the cross-sectional regression results based on Fama and MacBeth (FM 1973) method. I report the average estimates in the sample period. While the coefficient of XER is less (greater) than one in the univariate (multivariate) regression, both CFN and DRN have correct signs. They are closer to their theoretical values than those reported in prior studies. 21 19 In order to estimate the firm level discount rate news, I delete all firms with less than 6 observations in the firm level regressions. As a result, sample firms reduce from 10759 to 4696. 20 Guay et al. (2011) report that the coefficients of most ICC measures are between -0.33 and 0.43 in univariate crosssectional regressions and they are not statistically distinguishable from zero at conventional levels. 21 Studies show that realized stock returns are often insensitive to discount rate news when regressing realized returns on a proxy of the expected return, CFN and DRN (Easton & Monahan, 2005;Nekrasov & Ogneva, 2011;Gode & Mohanram, 2013). I also document the model predicted returns' out-of-sample predictive ability with respect to future realized stock returns by sorting firms into deciles of the model predicted return distribution at the end of each financial year in Table 7.
For each portfolio, the mean buy-and-hold returns for the next 12-, 24-and 36-months are calculated. It exhibits a strictly monotonic relationship with future realized returns for all three horizons. The hedge returns, the differences in realized returns over 12-, 24-and 36-month between the top and bottom deciles of the predicted expected stock returns are equal to 13%, 23.8% and 35.3% respectively. In addition, Table 7 appears to suggest that the monotonic relation with future realized returns is associated with the book-to-market ratio and firms' market capitalization (Fama & French, 1992, 1993. It is also almost monotonically positively associated with the Sharpe ratio, though it cannot be explained by the CAPM beta. 22

Robustness Tests
In the above analysis, I use the one-year ahead analysts' forecasts of earnings from the I/B/E/S as a proxy for the market expectation of firms' one-period ahead earnings in estimating the modified  Table 7 reports the mean of 12-, 24-and 36-month ahead realized returns from models' predicted return decile sorted portfolios based on 61265 firm-year observations between 1981 and 2014. B/M is the book-to-market ratio and Mktcap is the log of price per share multiplied by the number of share outstanding. Beta is the CAPM beta estimated via the market model using the value weighted NYSE/Amex market index return applying at least 18 and up to 60 months of lagged monthly returns. The Sharpe ratio is the difference between bhr1 and 10-year US treasury bond yield divided by the standard deviation of annual stock returns. bhr1-, bhr2-and bhr3 are 12-, 24-and 36-month buy-and-hold returns for each firm after the financial year end respectively. The model predicted return is given by: Parameters with subscript it stand for the average for industry i at year t. feps t+1 is the one-year ahead analysts' forecasts of earnings. x t , b t and P t are earnings, book value and price at time t respectively. The parameters (ω, γ , R-1) are estimated simultaneously from the following regression on an industry-year basis: Ohlson LID parameters in stock valuation. However, it is well documented that the I/B/E/S analysts' forecasts are upwardly biased and only available for large and financially healthy firms, especially in the earlier sample years. To examine whether the underrepresented small firms and financially distressed firms affect the results in valuation bias and valuation inaccuracy, I use the Heckman two-stage correction to account for the endogeneity in this selection bias. I estimate the probability of being included in the I/B/E/S consensus forecast as a function of the control variables presented in (6) and firm size in the first stage. While size is assumed to affect the probability of analysts' following, it is not supposed to influence earnings per share. Table 8 reports the descriptive statistics of the estimated modified Ohlson LID parameters (ω it , γ it , R it − 1) for industry i in year t alongside the inverse Mills ratio (λ) between 1981 and 2014. They are estimated from the pooled cross-sectional nonlinear regressions on an industryyear basis by applying the simultaneous procedure on (11). It shows that these LID parameters are compatible with those reported in Table 2. The mean and the median of λ are significantly positive. However, this is mainly because all λ are significantly positive from 1981 to 2003. In fact, all λ are not significantly different from zero after 2008. It suggests that unobserved factors that make the I/B/E/S forecasts are more likely to be associated with upwardly biased forecasts in the earlier sample years. Table 8 also reports the descriptive statistics of the valuation bias and valuation inaccuracy based on the Heckman two-stage correction model. It shows that the magnitudes are similar to those reported in Table 4.
The above analyses are based on the 5-industry classification to grouping firms. The 5-industry classification can provide sufficient numbers of observations within each cross-section to ease the concern that finite-sample estimates from the generalized method of moments (GMM) may fall  N 130,191 130,191 130,191 130,191 130,191 130,191 130,191 130,171 Table 8 reports the descriptive statistics of the modified Ohlson (1995) LID parameters (ω, γ ), the cost of equity capital (R-1 = ICC), their t-statistics alongside the inverse Mills ratio (IMR). The LIDs are: x a t+1 = ωx a t + OI t + ε x,t+1 , 0 ≤ ω < 1, and OI t+1 = γ OI t + ε OI,t+1 , 0 ≤ γ < R, where x a t = x t − (R − 1)b t−1 is abnormal earnings and OI is 'other information.' x t , and b t are earnings and book value at time t respectively. A nonlinear least squares procedure is used to estimate simultaneously three parameters (ω, γ , R) from the following pooled cross-sectional nonlinear regression on an industry-year basis in a four-year rolling window: where feps t+1 is the one-year ahead analysts' forecasts of earnings, and P t is stock price at time t. 5-industry is based on the classification from Ken French's website. Firm size is included in the first-stage regression.
far from their asymptotic values, but it may not achieve sufficient homogeneity. To mitigate this concern, I replicate the above results based on the Fama-French 12-industry classification. The results not tabulated are generally consistent with those based on the 5-industry classification. However, the valuation inaccuracies appear to be slightly improved, which may reflect a more homogeneous grouping in parameter estimations. In principle, the simultaneous estimation procedure on (11) can be applied at the individual firm level if the firm has sufficient time series data. When I delete all firms with less than 10 observations in the firm level regressions to estimate valuation parameters for each firm, I find that the mean and the median of all three parameters are slightly greater than those presented in Table 2. The valuation biases are comparable with those shown in Table 4 in the industry-year analysis. The valuation accuracy is slightly improved. It may reflect a survivorship bias since sample firms only include those having a long history in the market place. 23

Conclusion
In implementing the residual income valuation model, Ohlson (1995) proposes a parsimonious information dynamic LID. However, it is argued that the LID does not consider conservative accounting and fails to capture a firm's nonzero NPV investment projects. Existing empirical studies document that the model systematically undervalues equity shares. In this paper, I study a modified LID model in which the information dynamics incorporate firms' accounting conservatism and allow for possible future growth. The modified model does not assume any additional assumption on the book value dynamic and the modification remains consistent with MM dividend irrelevancy. It offers benefits in terms of practicability of implementation relative to the Ohlson (1995, 1996) models. I provide an approach to estimate simultaneously the LID parameters alongside the cost of equity capital from a one-to-one mapping between the oneyear ahead forecasts of earnings and current stock prices. The one-to-one mapping is important 686 P. Wang because it links a firm's performance in the capital market to its product market. The approach provides a new tool for the estimation of the implied cost of equity capital.
The empirical results show that on average the persistence of 'other information' is greater than one suggesting that the modified LID parameters indeed reflect companies' future growth and investment opportunities. The out-of-sample median valuation bias and valuation inaccuracy are substantially reduced compared with results in the existing literature. There is no systematic undervaluation of stock prices using the modified LID model. The empirical results are further strengthened if a time-varying industry-specific cost of capital is used. Relative to its theoretical value, I find that investors do not place too much a weight on the short-term future earnings. I also find that the model predicted return as a proxy for the expected return measure exhibits a monotonic relation with future realized stock returns.
Intuitively, it is important to estimate parameters in information dynamics using homogeneous firms in a simultaneous estimation procedure. The main results in this paper are based on industry portfolios because industry classification is convenient to group firms sharing similar economic and accounting characteristics, and ensures a relative stability of parameter estimates. However, analysis based on an industry classification has its drawbacks. For example, industries can be very widely based, and a company may operate in two or more different industries. Future research may form homogeneous portfolio from other grouping such as from text analysis of firm 10 K product descriptions to improve valuation bias and valuation inaccuracy.

Appendices Appendix 1. Definition of the Variables with the Relevant Mnemonics
Variable/notation Definition LID Linear information dynamic OI 'Other information' in LID ω The persistence of abnormal earnings in LID γ The persistence of OI in LID P t Stock price at time t b t Book value of equity at time t x t Earnings at time t d t Dividends at time t x a t The abnormal earnings (residual income) at time t feps t+1 The one-year ahead analysts' forecasts of earnings R One plus cost of equity capital E t [.] Expectation operator based on time t information ICC Implied cost of capital RIV Residual income valuation model ω it The persistence of abnormal earnings in LID for industry i in year t γ it The persistence of OI in LID for industry i in year t R it − 1 The cost of equity capital for industry i in year t Coefficient of x t in valuation after controlling for b t , d t and x t+1 . B Coefficient of b t in valuation after controlling for x t , d t and x t+1 . Coefficient of d t in valuation after controlling for x t , b t and x t+1 . Coefficient of x t+1t in valuation after controlling for x t , b t and d t . CSR Clean surplus relation CFN Cash flow news DRN Discount rate news RET t The realized one-period ahead stock returns at time t R t ln(1 + RET t ) MPR t The model predicted rate of returns ER t ln(1 + MPR t ) resER t+1 The residual in the firm level model predicted return regression XRET The one-year ahead excess realized stock returns XER The model predicted excess returns λ The inverse Mills ratio Assumption 1 and (2) then imply that Rb t + (1 + α 1 )E t [x a t+1 ] + α 2 γ OI t = RP t . (3) further implies Rb t + (1 + α 1 )E t [x a t+1 ] + α 2 γ OI t = R(b t + α 1 x a t + α 2 OI t ), or Reorganizing terms, the expected future abnormal earnings can be written as E t [x a t+1 ] = ωx a t + OI t . Therefore, information dynamic (1) holds. (1) and (3) imply (4). Equation (1) can be rewritten as

Proof of Equation (10):
Given (3) and the clean surplus relation, the total stock return can be expressed as It follows from (2) that Note E t [x a t+1 ] = E t [x t+1 ] − (R it − 1)b t and x a t = x t − (R it − 1)b t−1 . For firm j in industry i at time t, if we use industry-year specific parameters (ω it , γ it , R it ) as proxies for firm-specific A Modified Ohlson (1995) Model and Its Applications 691 parameters, we have the expected return for firm j at time t: