Value Relevance Regression Model Results with Price as the Dependent Variable

The value relevance regression model results for price as the dependent variable, regression equations (18), (19), and (20), reveal that the introduction of the most recent prior period’s equity price Pt as an additional explanatory variable greatly increases the adjusted R2 values of the models (see Tables 4.5 to 4.7). More importantly, the results also indicate that the earnings related accounting variables do not tend to explain next period’s price when the most recent prior period’s equity price Pt is included as an explanatory variable in the regression model. The increase in the explanatory power that is obtained using regression equations (18) to (20) is as predicted, since using an autoregressive rather than a non-autoregressive regression equation is important when modeling highly persistent processes like the level of the share price. The non- significance of the earnings coefficient estimates in Tables 4.5 to 4.7 indicates that the exclusion of the most recent prior period’s price in value relevance studies can lead to a potential missing variable problem, since current trailing earnings appear to be a

21 _{Many studies question the compatibility of accounting principles with the concept of goodwill} amortisation (e.g., Smith, 2003; Jennings, LeClere, and Thompson, 2001; Jennings, Robinson, Thompson, Duall, 1996; Duvall, Jennings, Robnson, and Thompson, 1992). Due to dissatisfaction with systematic goodwill amortisation (APB 16, Business Combinations, and APB 17, Intangible Assets), the Financial Accounting Standard Board has superseded APB 16 and APB 17 with new rules (SFAS 141 and SFAS 142 respectively). The new rules state that, from 2002 onwards, firms no longer account for goodwill amortisation in their financial statements, but can report it separately.

spurious proxy for past price in the regression model (compare Tables 4.2 to 4.4 with Tables 4.5 to 4.7).

[Please insert Tables 4.5 to 4.7 about here.]

To illustrate the increase in adjusted R2 obtained by introducing the most recent prior period’s equity price Pt as an additional explanatory variable, it can be noted that the pooled and fixed effect adjusted R2s have all increased to a minimum of 0.946 in Tables 4.5 to 4.7 from a maximum of 0.797 in Tables 4.2 to 4.4. For time series comparisons, recall that three of the firms in Tables 4.2 to 4.4 have time series adjusted R2 values close to zero, and the rest of the firms have adjusted R2 values that range from 0.259 (for the firm BBA in Table 4.2) to 0.879 (for the firm HCSG in Table 4.3). There are no longer any time series model adjusted R2s close to zero in Tables 4.5 to 4.7 (the minimum is now 0.552 in Table 4.6), and the average is now 0.756, much higher than in Jennings, LeClere, and Thompson (2001). All these results indicate that the inclusion of the most recent prior period’s price Pt is highly value relevant, as predicted by the Ohlson (1995) model reformulation (see the discussion of equations (10) and (11)), and it greatly increases the explanatory power of the value relevance regression model.

The pooled and fixed effect coefficient estimate t-statistics are also much higher for the most recent prior period’s price Pt than for the current trailing earnings and goodwill explanatory variables (EBG and EAG). The minimum t-statistic for the most recent period’s price coefficient is 12.772 in the value relevance models (see the fixed firm row in Table 4.6) whereas the maximum t-statistic for any of the earnings explanatory variable coefficients is now 1.671 (see the fixed firm row in Table 4.5). In the pooled and fixed effect regressions, the earnings regression coefficient estimates are

all no longer significant. In the time series regression analysis, the results for 90% of the sample firms indicate that the firms’ current trailing earnings information has already been incorporated into the most recent prior period’s equity price. Trailing earnings information thus does not appear to provide information to investors beyond what is already incorporated in the most recent prior period’s price. The Table 4.5 to 4.7 results are therefore consistent with Marsh and Merton (1987), Ohlson (1995, 2001), and Beaver, Lambert, and Morse (1980), and indicate that the most recent prior period’s equity price of a firm has already incorporated the firm’s contemporaneous accounting information. The results are consistent with the earnings announcement event study literature which demonstrates that equity prices react to the unexpected components of earnings announcements, not the earnings level itself, since the expected level of earnings is already incorporated into the most recent equity price prior to the earnings announcement (see also footnote 17). The Table 4.5 to 4.7 results are also consistent with a random walk price change process, since the most recent period’s price explains the subsequent price.

We have thus demonstrated that a missing variable effect is possible when the most recent prior period’s price is missing from the regression analysis and is highly correlated with earnings, since misleading inference regarding the earnings regression coefficients appears to have occurred when the most recent prior period’s price is not present in the regression model (see, e.g., Wooldridge, 2002). 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.22 Further, it can be noted from the Table 4.5 to 4.7 results that there is a unit root for prices in many of the time series regressions, since many of the past price coefficient estimates are close to one. In this situation, the most recent prior period price coefficient estimate is biased downwards (see Enders, 1995, page 213), thus suggesting that price change should be used as the dependent variable in value relevance studies. For both these econometric reasons we therefore subsequently use change in equity price as the dependent variable to explore the value relevance of current trailing earnings, thus further improving the value relevance model regression equation specification to avoid potentially spurious results.

Before moving on to explore value relevance regression model results with price change as the dependent variable, however, it is important to interpret the Table 4.5 to 4.7 results in relation to the regression scale effect literature (see Brown, Lo, and Lys, 1999). Brown, Lo, and Lys (1999) indicate that there is an increase in R2_{s due to scale} effects when levels regressions are performed. Thus, an equity price – accounting variable relationship, based on a higher R2 value, is unreliable. They document that value relevance of accounting variables is a result of a scale effect, when levels variables are modelled. Because of this scale effect in levels variables in regression models, Brown, Lo, and Lys (1999) suggest that a proxy variable should be incorporated in regression models to control the scale effect. They indicate that there is only a weak relationship between equity price and accounting variables (particularly current trailing earnings and book value of equity) when controlling for the scale effect in levels variables regression models. The Table 4.5 to 4.7 results are consistent with the Brown, Lo, and Lys (1999) results, since the most recent prior period’s price is an

22 _{Earnings and prices could still be cointegrated, but prices would lead earnings, whereas earnings}

appropriate control variable for scale effects (see Brown, Lo, and Lys, 1999). When the most recent prior period’s price is included as an additional explanatory variable then current trailing earnings are no longer value relevant (see Tables 4.5 to 4.7). Employing change in equity price as the value relevance study dependent variable is an even better control for scale effects (see Brown, Lo, and Lys, 1999), thus further justifying the use of price change (not price) in value relevance studies, as outlined below.

4.5.3 Value Relevance Regression Model Results with Price Change as the