The Ohlson (1995) Value Relevance Model Reformulation

To obtain the Ohlson (1995) value relevance model reformulation, equation (9) can be further rearranged to

( ) ( ) [ ( ) a] ₂[ _{t 1} ( ) _t]. (10) t a 1 t 1 t 1 t t 1 t 1 r P y 1 r y x 1 r x v 1 r v P₊ = + + ₊ − + +α ₊ − + +α ₊ − +

Equations (9) and (10), derived directly from the Ohlson (1995) model price change equation (page 683 of Ohlson, 1995), reveal an important random walk feature of the Ohlson (1995) model. In particular, the time t+1 price (Pt+1) is equal to the future value

of the most recent prior period price ((1+r)Pt) plus adjustments representing innovations

in book value (yt+1 – (1+r)yt), innovations in current abnormal earnings (xt+1 – (1+r) xt),

and innovations in future earnings related value relevant information (vt+1 – (1+r)vt).

The most recent prior period’s price is therefore seen to be a crucial component of the Ohlson (1995) model.

To see this even more clearly, book value (y) can be all but eliminated from equation (10) by substituting in the book value identity (2) as well as the abnormal earnings definition (4). The resulting price equation is

( ) ( ) ( ) a ₂[ _{t 1} ( ) _t]. (11) t 1 a 1 t 1 1 t t 1 t 1 r P d 1 x 1 r x v 1 r v P₊ = + − ₊ + +α ₊ −α + +α ₊ − +

The random walk characteristic of the Ohlson (1995) model is further revealed, since in equation (11) next period’s dividend adjusted price (Pt+1 + dt+1) equals the future value

of the current price ((1+r)Pt) plus innovations in current abnormal earnings and future

earnings related information (xa and v). As we have already argued, market efficiency implies that the current price (Pt) will incorporate expected future earnings related

information. Leaving the most recent prior period’s price out of the Ohlson (1995) model in an empirical set-up will therefore be doubly problematic when other future value relevant variables (v) related to future earnings are left out as well, since both important indicators of expected future abnormal earnings are likely to be highly correlated and will be absent from the model (see also Ohlson, 2001). This can give rise to a missing variable problem, and potentially misleading inferences concerning the value relevance role of current trailing earnings (xt), if current trailing earnings are also

correlated with the most recent prior period’s price Pt (see, e.g., Wooldridge, 2002).

The random walk characteristic of the Ohlson (1995) model, revealed by equation (11), further implies that price change (or return), not price, should be the dependent variable in time series value relevance studies that use Ohlson (1995), since changes in random walk series are stationary whereas the level of the series is not.7 This is an especially important consideration when past price is left out of the value relevance model framework, as is usually the case in value relevance studies, since in a random walk price change process the immediate past price is a crucial determinant of the current price. Jeon and Jang (2004) argue that the first differences in equity prices are a stationary, non-persistent process so, for econometric reasons, change in price (or returns), not price, should be the dependent variable in value relevance studies.8

7 _{Aggarwal and Kyaw (2004) demonstrate, for instance, that the level of equity prices follows an}

autoregressive, non-stationary process.

8 _{The sample period is too short for formal cointegration analysis, but earnings are shown to lose their}

explanatory power when price change (not price) is the dependent variable, thus indicating that the relationship between earnings and prices is potentially spurious (see, e.g., Enders, 1995).

Rearrangement of equation (11) leads to a simplified version of the Ohlson (1995) price change equation (see page 683 of Ohlson, 1995):

( ) ( ) a ₂[ _{t 1} ( ) _t]. (12) t 1 a 1 t 1 1 t t t 1 t P rP d 1 x 1 r x v 1 r v P₊ − = − ₊ + +α ₊ −α + +α ₊ − +

The most recent prior period’s price variable (rPt) on the right hand side of equation

(12) represents the proportionate drift aspect of a random walk price change process and thus represents a potentially important role for past price in the Ohlson (1995) framework even when price change is the dependent variable.

Equations (11) and (12) can be used to derive simplified regression equations for the Ohlson (1995) model that incorporate the potentially important informational role played by the most recent prior period’s price (Pt), current trailing earnings (x), and

future earnings related information (v) in value relevance studies. Three simplifications are required to make the Ohlson (1995) model equations directly comparable with Jennings, LeClere, and Thompson (2001). First, the level of current trailing earnings (x) and future value relevant information (v) are examined, not innovations in the level (see equations (11) and (12)). Secondly, only information that is already available at time t+1 is utilised in the regression model equations.9 Thirdly, the current abnormal earnings variable ( ) is simplified to current trailing earnings (xt), and the regression

equations are further simplified by using the ex-dividend share price Pt+1, thus deleting

the dividend term dt+1 from the regression equation. a

t x

10 _{These simplifications of} equations (11) and (12) lead to the following regression equations for price Pt+1 and

price change ∆P: 1 t 1 t 3 t 2 t 1 0 1 t P x v P₊ =β +β +β +β ₊ +ε₊ (13) and 1 t 1 t 3 t 2 t 1 0 1 t P x v P₊ = + + + ₊ + ₊ Δ θ θ θ θ ε , (14)

9 _{In unreported results, we do not make these first two simplifications, and the results remain unchanged.} 10 _{The dividend term could easily be incorporated in the regression equations.}

where β and θ are coefficients of regression equations (13) and (14), respectively. Equations (13) and (14) explore the incremental role of current trailing earnings (xt) for

explaining subsequent share prices and share price changes, respectively, above and beyond the role played by the most recent prior period’s share price (Pt) as well as by

other forward looking earnings related information (vt+1). This provides a benchmark to

evaluate the information dynamics of current trailing earnings information. When the most recent prior period’s price Pt and forward looking information vt+1 are important

and are correlated, their inclusion together can greatly improve the value relevance model regression equation specification (see value relevance regression equations (13) and (14)).

Current trailing earnings (xt) represent aggregated earnings, but it is also

possible to disaggregate the earnings by extracting goodwill amortisation to directly assess the informativeness of goodwill amortisation. Goodwill is the excess amount beyond the stated value of a firm’s underlying assets. In other words, goodwill can reflect the value of unidentifiable intangibles within the firm (Jennings, LeClere, and Thompson, 2001). Goodwill amortisation is the amount by which goodwill is reduced each year to represent the declining value of intangible assets in a fiscal period. As we intend to assess the additional informativeness of goodwill amortisation, we consider two measures of current trailing earnings, earnings before goodwill amortisation ( =EBGt) and earnings after goodwill amortisation ( =EAGt), as well as goodwill amortisation per share (vt+1 = GAPSt). We employ these earnings variables from Jennings, LeClere, and Thompson (2001) to examine their price value relevance using regression models (13) and (14).

t

4.3.3 Method

We begin our investigation by first replicating the Jennings, LeClere, and Thompson’s (2001) regression models which incorporate various combinations of earnings before and after goodwill amortisation. The Jennings, LeClere, and Thompson’s (2001) regression models do not include the most recent prior period’s price Pt, but are otherwise similar to or identical to value relevance model regression

equation (13) above: Pt+1 = β0 + β1 EBGt+ εt+1 , (15) Pt+1 = β0 + β1 EBGt + β2 GAPSt + εt+1, (16) and Pt+1 = β0 + β1 EAGt+ εt+1 , (17) where

Pt+1 = next period’s end of quarter price,

β0 = intercept of the model,

β1 = coefficient estimate of earnings,

β2 = coefficient estimate of goodwill amortization per share (GAPS), EBGt = annual trailing earnings per share before GAPS for period t, GAPSt = goodwill amortization per share for period t,

EAGt = annual trailing earnings per share after GAPS for period t, and

εt+1 = error term.

Regression models (15) to (17) explore the value relevance relationships between current trailing earnings and subsequent equity prices. Firms cannot disclose accounting information immediately at fiscal year end, so three months duration is

assumed to be the information delay required for the release of a firm’s annual financial statements, as assumed in many studies (e.g., Jennings, LeClere, and Thompson, 2001; Collins, Maydew, and Weiss, 1997), thus explaining why the time t+1 share price is explained by time t trailing earnings information. Trailing twelve months earnings are used in regression equations (15) to (17), as is standard, to avoid the problem of quarterly earnings seasonality. Jennings, LeClere, and Thompson (2001) examine the value relevance of goodwill amortisation for explaining next period’s equity prices in a pooled cross-section. We reproduce their findings within a time series relationship.

The second step to implement regression equations (13) and (14), derived from Ohlson (1995), is to incorporate the most recent prior period’s equity price as an additional value relevance model explanatory variable. Thus, we utilize value relevance regression equation (13) to accommodate the most recent prior period’s equity price Pt

as an incremental explanatory variable by adding it to regression equations (15), (16), and (17) to obtain regression equations (18) to (20). We also utilize value relevance regression equation (14) to modify regression equations (18) to (20) so that they contain price change as the dependent variable in regression equations (21) to (23). The resulting regression equations are as follows:

Pt+1 = β0 + β1 EBGt + β3 Pt + εt+1 , (18) Pt+1 = β0 + β1 EBGt + β2 GAPSt + β3 Pt + εt+1 , (19) Pt+1 = β0 + β1 EAGt+ β3 Pt + εt+1, (20) where

Pt = equity price at time t and

∆Pt+1 = β0 + β1 EBGt + β3 Pt + εt+1 , (21)

∆Pt+1 = β0 + β1 EBGt + β2 GAPSt + β3 Pt + εt+1 , (22) and

∆Pt+1 = β0 + β1 EAGt+ β3 Pt + εt+1 , (23) where

∆Pt+1 = change in equity price (i.e., Pt+1 – Pt).

A three month change in price is utilised in the regression analysis so that the results of regression equations (21) to (23) can be directly compared to the results of regression equations (18) to (20) and (15) to (17).11