3. For each year (t), the following pooled (time-series cross-sectional) regression is estimated:
p — = n , , + r t.,T - + e (Eq. 11)
I , - - ' r j J - \
where y ’Qt and y Xt are year-specific parameter estimates, and e2 is an error term (hats denote parameter estimates and prime denotes a parameter based on scaled OI data compared with that based on OI itself). y u is used as an estimate of y x in Eq. 7, and the intercept, y'0 j, is disregarded. On the basis of pooled data from 1976- 1995, DHS report parameter estimates of y'0t equal to 0.01 and y u equal to 0.32. Note that if y'o t is disregarded, the expected value of one-period-ahead OI based on Eq. 11 (i.e., £[v\ ,+1]) is understated and the magnitude of the understatement is equal to y'o t multiplied by the scaling variable, Pj t .
4. For each year (/), firm value is estimated for each firm based on the valuation expression Eq. 8 using book value, RI, estimated OI, the parameter estimates d>u and y u , and an estimate of the cost of equity. Because the estimated OI at time t is a function of the observable analyst-based time t RI forecast for time t+ 1 ( f ta+l) and current RI, the value estimate at time t is equivalently expressed as in Eq. 12 (firm subscript j for variables and time subscript t for parameters are suppressed).
V =b + --- ^ ---X‘ + --- * (Eq. 12)
As shown in Eq. 9 and 11, LID parameters in DHS are estimated based on per-share data scaled by lagged stock price. However, scaling by stock price makes value estimates a function of stock price when applying the 'intercept-inclusive' LID approach, so a fundamental change in the scaling variable is required in this study in order to compare the Ohlson LID-based value estimates with the 'intercept-inclusive' LID-based value estimates. In this study, lagged book value of equity is used as a scaling variable (see Section 3.2.2 for details about the issue of scaling variable).
3.2.2. My procedure
I augment the DHS approach by exploiting the information contained in the estimated LID intercept parameters. As explained in Section 3.1.2, these intercepts capture information concerning average scaled RI. However, practical implementation for valuation requires a fundamental change in the scaling variable, if we are to avoid making value estimates a function of market price. Multiplying Eq. 9 by Pj s_j shows that the conditional expectation of x aj s is a linear combination of x ajt5_x and the scaling variable P. Similarly, from Eq. 11 the conditional expectation of vj s is a linear combination of v. , and P . - . In each case, the weight applied to 1 J 1 P. j in forming the conditional expectation is equal to the respective intercept parameter. Introducing the intercept parameters into the valuation model will therefore cause price to be an input to the valuation model. In order to avoid this circularity, while preserving the scaling of
Chapter 3. D evelopm ent o f the 'intercept-inclusive' linear information dynamics (LID) m odel an d research design
data that is necessary in cross-sectional analysis, I scale by the book value of equity.29
Similar to Ohlson (1995), obtaining a closed form valuation expression for the 'intercept-inclusive' LID model requires me to express conditional expectations of the RI flows for all future time periods in terms of information observable at the valuation date. If the LID intercepts do not equal zero, the conditional expectation of RI for each future period will depend on expected book value at the beginning of the respective period. Therefore, the 'intercept-inclusive' LID requires a model describing the book value dynamics. For simplicity, I assume that book value grows at a constant rate.
My modification of the Ohlson (1995) LID to include intercept parameters for RI and OI, with scaling by book value, leads to the following LID (refer to Eq. 1 for the general LID that allows any scaling variable):
= 0 ) Q + 6 ) x — + — + S ht+1 b, ° 1 bt b, + * £ + *«♦. ( E * 13) b, b, *t± = BG + s bt
where BG is one plus the rate of growth in book value and the s terms are random error terms. From Eq. 13,1 obtain the following expectations:
29 Scaling RI by lagged book value produces the following measure (firm subscript suppressed): x" _ xt - ( R -1)6,_! _ R 0 E _ , R _ ^ } where ROE, denotes Return on Equity at time t, and is equal to
K x K x '
x j b t j . This measure is familiar in the managerial consulting literature as the 'spread', being the excess o f
x \ = K b t + G ) r f + V,
E\yt+A=r'*bt +r,vt
E[bt+l]=BGbt
(Eq. 14)
The model setup closely resembles the Feltham and Ohlson (1995) LIM. However, one important difference is that, from the second equation in Eq. 14, expectations of OI may also depend on book value and may thus deviate from zero on average. The empirical analysis shows that this can be an important difference in practice. In fact, this intercept allows the possibility that expected future RI, conditional on OI, will differ from the average value of RI over the estimation period.
From the RI valuation relationship and Eq. 14, it is straightforward to derive the following valuation expression (refer to Eq. 3 for the general 'intercept-inclusive’ LED model that allows any scaling variable):
30 Recall that OI is defined to be the difference between the analyst-based forecast o f RI and the forecast o f RI derived from a univariate model of RI.
Vt =bt + filX; + f i 2vt +(J33 + 0 4)bt (Eq. 15) where
p —________ y--- r3 (R - BG)(R - co^
Chapter 3. D evelopm ent o f the 'intercept-inclusive' linear information dynamics (LID) m odel an d research design
The coefficients /?3 and on book value in Eq. 15 include the estimated values o f the intercepts in the first two lines of Eq. 13, and arise because book value is the scaling variable in Eq. 13. The Ohlson (1995) valuation model Eq. 8 is a special case: where
ct)'0 = 0 fi3 = 0 and y'Q = 0 -> y?4 = 0.
I estimate the parameters for the first two equations in the modified LID system Eq. 13 using a direct development of the procedures used by DHS. Similar to DHS's procedure shown in Eq. 9, in estimating the first LID equation of Eq. 1 3 ,1 ignore OI and estimate the following regression:
where S'01 and cox t are year-specific parameter estimates, and ex is a random error term.
As mentioned above, OI is defined as the difference between the full information analyst-based forecast of RI (f jt+\) and the implied conditional expectation of RI based on parameter estimates from the univariate model described in Eq. 16.
(Eq. 16)
Note that OI defined for the application of the 'intercept-inclusive' LID approach (Eq. 17) is different from that defined for the application of the Ohlson LID approach (Eq. 10), because cb0 t is differently assumed (non-zero versus zero). Now, the OI dynamics parameters are estimated based on the following regression:
v • v . ,
J ’s n r * y > s —1
, = r k , + r u ~ + evi (Eq. 18)
where y'0j and f l t are year-specific parameter estimates and e2 is a random error term.
Finally, value estimates (Vj t ) are constructed for each firm (j) at each valuation date (t) based on Eq. 15. The following information is required as inputs to the valuation model: RI per share (*£,), estimated OI per share (v; ,), book value per share (bJ t ), the assumed cost of equity, estimates of the LID parameters (bu , yu ) and assumed values of the book value growth rate parameter, BG. Because the estimated OI at time t is a function of observable analyst-based time t RI forecast for time t+l (ft+]), current RI and current book value, Eq. 15 is equivalently expressed as Eq. 19 (firm subscript^ for variables and time subscript t for parameters are suppressed).
Chapter 3. D evelopm ent o f the 'intercept-inclusive' linear