5. MARCO REFERENCIAL
5.5. MARCO HISTÓRICO
This section demonstrates that the most recent prior period’s equity price can play a very important role in the Ohlson (1995) model, and reveals that price change or return, not price, should be the dependent variable in Ohlson (1995) model value relevance empirical implementations.
7 Ohlson (2001) does not, however, give specific examples of future value relevant earnings information.
Examples of future value relevant information could include research and development expenditures and earnings forecasts.
To demonstrate the role of the most recent prior period’s price in the Ohlson (1995) value relevance model when price is the dependent variable, the Ohlson (1995) model price change equation (9) can be rearranged to
( ) ( ) [ ( ) ] 2[ t 1 ( ) t]. (10) a 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 + − +
Equation (10), derived directly from the Ohlson (1995) model price change equation (page 683 of Ohlson, 1995), reveals 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 ,
and innovations in future earnings related value relevant information (vt+1 – (1+r)vt).
The most recent prior period’s price can therefore be a crucial component of the Ohlson (1995) model. ) ) ( ( ta a 1 t 1 r x x+ − +
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
( ) ( ) ( ) 2[ t 1 ( ) t]. (11) a 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 and future earnings related
information (xa and v). We will argue below that market efficiency implies that the most recent prior period’s 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 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 earnings (xt), if current earnings are also correlated with the most recent
prior period’s price Pt (Wooldridge, 2002).
The random walk characteristic of the Ohlson (1995) price valuation model, revealed by equation (11), further implies that price change or return, not price, should be the dependent variable in value relevance studies that use Ohlson (1995), since changes in random walk series are stationary whereas the level of the series is not.8 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. Aggarwal and Kyaw (2004) demonstrate that the level of equity prices follows an autoregressive, non-stationary process. 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.
Rearrangement of equation (11) leads to a simplified version of the Ohlson (1995) price change equation (see page 683 of Ohlson, 1995):
Pt+1 −Pt =rPt −dt+1+(1+α1)xta+1−α1(1+r)xta +α2[vt+1−(1+r)vt]. (12)
8 Earnings and equity prices are both non-stationary, so they move together over time, thus potentially
creating a spuriously significant statistical relationship between current trailing earnings and next period’s price when a non-autoregressive empirical model is used to explain prices (see, e.g., Enders, 1995). Earnings and price could still be cointegrated, but it will be shown in later chapters that earnings lose their explanatory power when price change (not price) is the dependent variable, so levels regression between earnings and prices can be potentially spurious.
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 (see also equation (14) below) and thus represents a potentially important role for past price in the Ohlson (1995) framework even when price change is the dependent variable. Further rearrangement of equation (12) leads to a returns version of the Ohlson (1995) value relevance model:
t t 1 t 2 t a t 1 t a 1 t 1 t 1 t t 1 t P v r 1 v P x r 1 P x 1 r P d P P+ − + + = +( +α ) + −α ( + ) +α [ + −( + ) ] . (13) The most recent prior period’s period price inversely enters equation (13), thus creating a value effect for returns.
Equations (11), (12), and (13) are used to derive simplified regression equations for the Ohlson (1995) model that incorporate the role of past price and future value relevant information, once the market efficiency literature is reviewed to further reveal the potentially important informational role played by the most recent prior period’s price in value relevance studies.