variants also include other accounting variables, such as book value, within the process that generates RI expectations. The intuition is fairly straightforward. The forecasting of RIs for the purpose of valuing a business is likely to involve the analysis of current and past accounting numbers, together with the analysis of other sources of information.
Dechow, Hutton & Sloan (1999) (hereinafter, DHS) devise a novel approach to application of the Ohlson (1995) 'other information-inclusive linear information dynamics (hereinafter, LID) approach to Rl-based valuation, and apply it to U.S. data. DHS compare LID-based value estimates, along with value estimates derived from simpler eamings-based valuation procedures, with observed share prices. A striking feature o f DHS's results is that the Ol-inclusive valuation approach undervalues shares by an average of about 26%.34 This undervaluation is larger than that from a simple valuation model involving the capitalisation of one-year-ahead earnings forecasts. The Ol-inclusive LED approach is also outperformed by this simple procedure on the criterion of mean absolute forecast error (accuracy). DHS's results have raised concerns about the reliability of LID-based valuation models.
This chapter is motivated by this substantial negative bias, reported by DHS, in value estimates from an Ol-inclusive application to U.S. data of the LID approach to Rl-based valuation. It explores one potential source of bias in the LED-based value estimates produced by approaches such as that used by DHS. DHS's LID-based value estimates are constructed in accordance with the Ohlson (1995) LED. The Ohlson (1995) LED is
34 Myers (1999b) uses an Ol-inclusive LID-based approach where order backlog is used to proxy for 01, and reports that the median ratio of value estimate to observed price is 0.648.
parameterised with no intercept parameters, implying that RI is expected to mean revert to zero. Therefore, DHS's value estimates do not reflect the intercept terms from their RI and 01 generating process. Disregard for such intercept terms causes value estimates to be based on the possibly false implicit assumption that the mean of expected future scaled RI is zero. Casual observation of the persistent deviations from unity in market- to-book ratios suggests that it may be inappropriate to make such an implicit assumption. This chapter explores the impact of augmenting the procedure used by DHS such that value estimates impound the information in intercept terms from the RI and 01 generating process. The analysis suggests that small LID intercept terms, such as those reported by DHS, could give rise to theoretical valuation effects of a similar order o f magnitude to the bias reported by DHS. Using U.S. data similar to that used by DHS, this study illustrates empirically the impact of such terms. The evidence confirms that the impact can be comparable in size to, or larger than, the substantial valuation bias reported by DHS. Importantly, for those interested in applying LID model in practical accounting-based equity valuation, the magnitude of the intercept-related valuation component is highly sensitive to the assumed cost of capital and the expected rate of growth in the scaling variable.
The remainder of the chapter is structured as follows. Section 4.2 describes empirical methodology, data and descriptive statistics and Section 4.3 shows empirical results about the magnitude of the impact of the LID-based intercept terms in valuation models. Section 4.4 contains concluding remarks.
Chapter 4. Reliability o f the 'intercept-inclusive' linear information dynamics (LID) model: U.S. evidence
4.2. Empirical methodology and data
4.2.1. Methodology
DHS base their approach on Ohlson's (1995) LID-based valuation approach, and do not incorporate into their value estimates the intercept terms from their LID generating process for RI expectations. Disregard for such intercept terms would cause the omission from value estimates of the effect of non-zero means in expected RI, and could contribute to bias in value estimates. The possibility that omitted intercept terms contribute to bias in LID-based value estimates motivates me to augment the DHS approach by incorporating the intercept terms in LID and scaling data by book value. Scaling by book value rather than by stock price adopted in DHS is to avoid circularity, i.e., making value estimates a function of stock price. The 'intercept-inclusive' LID- based valuation formula is derived as follows (see Chapter 3 for details about the derivation of the 'intercept-inclusive' LID model):
Vt =b, + p t f + J32v,+ (A + P<)b, (Eq. 1) where Vt is the value of equity at time t, bt is the book value of equity at time t, and x at
o). R
and vt are RI and 01 at time t, respectively. p x =— , p 2 -
R - o ) x ( R - o ) x) ( R - y x)
r - _________ arid B = --- and r ' are the LID
A “ ( * - £ G ) ( R - ^ )
(R-BGKR-aMR-n)
° °intercepts corresponding to AR(1) RI and 01 equations, respectively (prime indicates parameters based on scaled data: see below for the parameter estimation procedure), and
cox and y x are the RI and 01 persistence parameters, respectively. R is one plus the discount rate and BG is one plus the rate of growth in book value.
To enable comparison of my results about the 'intercept-inclusive' LID approach with the intercept-exclusive LID (the Ohlson LID) approach, as employed by DHS, I also construct value estimates by ignoring the LID intercept parameters and redefining 01 as in DHS, but using book value as the scaling variable in estimation. Also, in order to facilitate comparison with DHS's results, I construct an additional value estimate in which the one-year ahead earnings forecast is capitalized as a flat perpetuity. Note that the Ohlson LID model is a special case of Eq. 1: where co'0 = y'0 = 0. The model that capitalizes one-year ahead earnings forecasts as a flat perpetuity is also a special case of Eq. 1: where (co'0 = y'0 =cox = 0 ,yl =1) or (d)'0 =y'0 = yx =0,cox =1). Because this model is the same as the 1-year forecast horizon EBO model with the assumption of zero expected future RI growth, I term this model as the 1-year horizon EBO model. The Ohlson LID model and the 1-year horizon EBO model are as follows:
where f t+l is the time t analysts' earnings forecast for time t+1.
Similar to DHS, the LID parameters are estimated using the following AR(1) RI and 01 generating (pooled time-series cross-sectional) regression equations.
Vt =bt + j3 X + fi2vt (Eq. 2)
Chapter 4. Reliability o f the 'intercept-inclusive' linear information dynamics (LID) model: U.S. evidence
+ e, (Eq. 4)
(Eq. 5) where the subscript s is a time index ranging from the first year of available data to year
t, cq'qj , cbxt, y'0t and y Xt are year-specific parameter estimates, and ex and e2 are
random error terms. 01 at time t (vt) is defined as the full information analyst-based RI forecast (f ta+x = f t+x - ( R -1 )bt) less the implied conditional expectation of RI based on parameter estimates from the univariate model described in Eq. 4. Note that vt in the 'intercept-inclusive' LID approach ( f ta+x -a>'0 tbt -cbxtx at ) is different from vt in the Ohlson LID approach (f ta+x - cbx tx at ), so the estimated 01 parameters between two approaches are different.
In this study, Eq. 4 is estimated for each year (t) from 1975 to 1995, using available RI data going back to 1951.35 The a>'0tt and cblt parameter estimates for 1975 and 1976 are used only for estimating 01, while those for 1977 to 1995 are used both for estimating 01 and as direct inputs to the value estimates. The y'ot and y u parameter estimates are estimated based on Eq. 5 for each year (t) from 1977 to 1995, using all available 01 data from 1975 to time t. Using these parameter estimates, value estimates based on Eq. 1 and Eq. 2 are then obtained for each firm at each valuation date (t) from 1977 to 1995.1
35 As in DHS, the range o f years for which Eq. 1 is estimated is determined by the availability o f earnings forecast data for use in constructing 01 estimates.
obtain value estimates for a range of different assumed growth parameter values, and for a range of different assumed costs of equity (see the next section for details).
For each class of value estimate, I calculate scaled differences between the value estimates and the corresponding observed stock prices three months after the balance sheet date (Ptc’3), as follows:
The signed differences (denoted as FE) as in Eq. 6 are used to measure bias in the value estimates. The absolute differences (denoted as AFE) as in Eq. 7 are used to measure accuracy in the value estimates.
4.2.2. Data
The empirical analysis employs U.S. data that is similar to that used by DHS, and that is drawn from a similar period. The data and the sources are detailed below.
Earnings per share and book value o f equity per share
These data are collected from COMPUSTAT from 1950 to 1995. The earnings item is earnings before extraordinary items and discontinued operations available for common stockholders. The book value item is book value of common equity as adjusted by the preferred stockholders' legal claims against the firm. The accounting data relating to the periods prior to 1976 are used only for the purpose of estimating the LID parameters.
(Eq. 6)
Chapter 4. R eliability o f the 'intercept-inclusive' linear