Value Relevance Regression Model Results with Price Change as the Dependent Variable

The pooled and time series results for the value relevance regression models where price change is the dependent variable, regression equations (21) to (23), indicate that current trailing earnings and goodwill amortisation explanatory variables do not explain or forecast subsequent three month price changes (see Tables 4.8 to 4.10).23 The pooled and fixed firm effect adjusted R2s in Tables 4.8 to 4.10 are all 1% or less (effectively zero), for instance, and although the fixed year effect adjusted R2 is somewhat higher (0.099 in the fixed year row in Table 4.8, for instance), almost all of the explanatory power is due to the fixed year effects. All of the pooled and fixed firm or fixed year effect regression coefficients in Tables 4.8 to 4.10 are insignificantly different from zero, thus indicating a random walk of equity prices (for example, the t- statistics for the estimated accounting variable coefficients range from 0.029 in the fixed year row of Table 4.9 to 1.671 for the fixed firm row of Table 4.8).

[Please insert Table 4.8 to 4.10 about here.]

23 _{Sensitivity analysis, reported in Appendices A and B (Tables 4.14 to 4.19), indicates the results remain}

unchanged when a 12 month rather than a three month change in price is employed as the dependent variable in regression equations (21) to (23).

Consistently, the time series regression coefficient results in Tables 4.8 to 4.10 also indicate that, for most firms, there is a random walk of equity prices. Only four firms reveal significant earnings coefficient estimates at the 5% level in any of the three tables (see the rows for COA, HCT, TBL, and SON in Tables 4.8 and 4.10, and HCT, TBL, and SON in Table 4.9). The goodwill amortisation per share (GAPS) coefficient estimates also indicate non-random walk behaviour for three firms (see the rows of MAS, ALOG, and SON in Table 4.9). The most recent prior period’s price coefficient estimate is significant for five firms only (see the rows of COA, HCT, TBL, ALOG and DOW in Tables 4.8 and 4.10 and HCT, TBL, and DOW in Table 4.9). However, only three firms consistently reveal a non-random walk price process in all three tables (see the rows for HCT, TBL, and DOW in Tables 4.8 to 4.10), whereas the other firms reveal mixed (inconsistent) results. No additional information appears to be provided by current trailing earnings, since almost all of the estimated time series coefficients are insignificant at the 5% significance level, a result that is consistent with our earlier results (see Tables 4.8 to 4.10 and compare them to Tables 4.5 to 4.7, respectively).

The adjusted R2s and estimated regression coefficients of the models imply that no significant relationship exists between next period’s price change and the independent explanatory variables (the most recent prior period’s equity price and the current trailing earnings explanatory variables). The results are similar when earnings before goodwill amortization (EBG in equation (21)) and earnings after goodwill amortisation (EAG in equation (23)) are used in the models (see Tables 4.8 and 4.10). Overall, the results indicate no role for current trailing earnings information and only a very limited role (if any) for the most recent prior period’s price when explaining or predicting subsequent price changes. This implies that neither measure of current

trailing earnings is informative, a conclusion that is sharply different from Jennings, LeClere, and Thompson (2001), and is due to improved implementation of regression analysis tests using the Ohlson (1995) value relevance model.

Also of note are the sharply lower adjusted R2s (effectively zero) that are reported when the non-persistent price change dependent variable, rather than the persistent price level dependent variable, is used in the regression analysis (compare Tables 4.8 to 4.10 with Tables 4.2 to 4.7). This indicates, as already noted, that value relevance studies that have price as the dependent variable but do not include the most recent prior period’s price as an explanatory variable are potentially subject to spurious results (see, e.g., Enders, 1995). The sharp decrease in the adjusted R2 in the time series analysis due to switching from price to price change as the dependent variable is due to non-stationarity of equity prices in the time series analysis. The lower adjusted R2 indicates that price change, not price, should be used as the dependent variable in value relevance studies, due to the effect of non-stationarity and the extreme persistence of the price process. When price change is the dependent variable, it is equivalent to having the most recent prior period’s equity price as an additional explanatory variable, since subtracting the most recent prior period’s price Pt from the left hand side of the regression equation (in regression equations (21) to (23)) is equivalent to adding it to the right hand side (as in regression equations (18) to (20)). Further, having price change rather than price as the dependent variable also avoids the spurious regression statistical problems caused by non-stationarity and autocorrelation.

For completeness, Tables 4.11 to 4.13 provide results for value relevance regression tests with price change as the dependent variable but without the most recent prior period’s price as an explanatory variable. The results are roughly the same as in

Tables 4.8 to 4.10, and further indicate, in the pooled regressions and the vast majority of the individual firm time series regressions, that trailing earnings (EBG and EAG) do not explain price changes in value relevance studies. There is, however, one difference that is made by excluding versus including the most recent prior period’s price as an explanatory variable in the price change regression models. Virtually no coefficient estimates are significant when only earnings variables are included in the regression model (see Tables 4.11 to 4.13) but, as noted already, the most recent prior period’s price is sometimes significant in the time series regressions when it is included as an additional explanatory variable (see Tables 4.8 to 4.10). This further indicates that contemporaneous trailing earnings variables are unlikely to provide useful information in value relevance studies.

[Please insert Table 4.11 to 4.13 about here.]