# «Leif Atle Beisland University of Agder Dissertation submitted to the Department of Accounting, Auditing and Law at the Norwegian School of Economics ...»

**Cash flow + accruals specification:**

RETi, t = β0 + β1CFi, t + β2 ∆CFi, t + β3ACCi, t + β4 ∆ACCi, t + εi, t

**Cash flow + accruals items specification:**

RETi,t = β 0 + β1CFi,t + β 2 ∆CFi, t + β 3 ∆WC i,t + β 4 ∆∆WC i,t + β 5 DEPi,t + β 6 ∆DEPi,t + β 7 ∆DTi,t + β 8 ∆∆DTi, t + ε i,t where RETi,t is the stock return for company i in year t, EARN is earnings before extraordinary items, CF is cash flow from operations, ACC is total accruals, WC is working capital, DEP is depreciation and impairment, and DT is deferred taxes. ∆ denotes yearly change in the variables. The accounting variables are scaled by the market value of equity at 30 December in year t-1. Coefficients in bold denote a statistical significance at a 5% level using a two sided test.

Panel B presents the results for the negative earnings sample. Now, aggregate earnings and their associated changes are able to explain only 0.64% of the variation in stock return. The results are consistent with prior research (compare to Hayn, 1995). Negative earnings have hardly any explanatory power with respect to stock returns. Neither earnings nor the change in earnings has significant regression coefficients in the most aggregated specification. The explanatory power of the regression increases as earnings are split into cash flow and accruals. The adjusted R 2 is now 2.24%. Cash flow and its associated changes are, however, not significant in the regression. Only change in accruals has a significant coefficient. When the accruals are split into three components, only depreciation and the change in depreciation are significant.17 Furthermore, depreciation (which also includes impairment) has a significantly negative coefficient for the positive earnings sample, while the coefficient is Non-tabulated results show that multicollinearity is not an issue in the regression. I have, as a robustness check, regressed stock return on earnings, change in earnings, depreciation, and change in depreciation when earnings are negative. Even after controlling for earnings and change in earnings, depreciation and change in depreciation remain significantly related to stock return. I have also excluded the earnings change items from the level variables so that the change variables do not appear twice on the right hand side of the regression (i.e., regressed stock return on EARN t −1 + ∆EARN t ). When the most disaggregated regression is run, DEP remains positively associated with stock return and ∆DEP remains negatively associated with stock return when earnings are negative. However, now only the DEP coefficient is significant.

obvious. It may be that for a given amount of negative earnings, investors prefer that the loss can be attributed to a non-cash expense like depreciation instead of “real” cash outflows. It may also be that the larger deprecation expenses for negative earnings companies are due to some kind of “big bath” strategy, and that this kind of strategy is also accepted by investors.

However, even if several of the explanatory variables are insignificant in this specification, the adjusted R 2 increases to 6.50%.

Adjusted R 2 is the chosen metric for analysing value relevance in this study. Table 3 summarises the explanatory power from the regressions run so far. An F-test for restrictions on regression coefficients is provided to test the significance of the differences in adjusted R 2 (Barth et al., 2001, p. 42; Maddala, 2001, p. 155). The explanatory power varies little across specifications for the positive earnings sample. Still, the adjusted R 2 of 13.63% for the most disaggregated model is significantly higher than the adjusted R 2 from the two other specifications. For the negative earnings sample, the explanatory power is highly dependent on specification. The more disaggregated the regression specification, the higher the adjusted R 2. The adjusted R 2 from the three regressions are all significantly different from each other. Overall, the difference in explanatory power between the specifications is far more substantial for the negative than for the positive earnings sample. The p-values are also much smaller for the negative earnings sample. For the negative earnings sample, the increase in explanatory power is 916% from the aggregated to the most disaggregated model, compared to only 5% for the positive earnings sample. However, if the standard deviations of the adjusted R 2 values are large, I cannot really conclude that 916% is, in fact, significantly larger than 5%. I have used bootstrapping to test the significance of the difference, and it turns out that the difference is statistically significant (p-value = 0.024). In this bootstrapping test,

drawn from the negative earnings sample. The procedure is repeated 10,000 times. As 945 and 427 equal the original numbers of observations in the positive and negative earnings samples, respectively, each observation can be drawn several times in each simulation. The adjusted R 2 is computed for both samples in all 10,000 simulations. Only in 236 of these simulations are the relative increases in adjusted R 2 smaller in the negative than in the positive earnings sample.18 The conclusion is that Tables 2 and 3 provide strong support for the proposed hypothesis. Value relevance studies that only analyse aggregate earnings severely understate the value relevance of negative earnings.

Table 3: Comparisons of Models - Explanatory Power Table 3 summarises the adjusted R 2 from the regressions performed in Table 2. Significance levels for differences in R 2 are computed using F-tests for restrictions on coefficients (Barth et al., 2001, p. 42; Maddala, 2001, p. 155).

Earnings may be disaggregated in numerous ways. As a robustness check, I run several regressions using even more disaggregated earnings than in specification (3). First, I split working capital into current assets and current liabilities. Second, I split the current assets into inventory and receivables. Third, I disaggregate the variable “depreciation and impairment” This test involves comparing the adjusted R 2 values between samples, see previously explained critique by Brown et al. (1999) and Gu (2007).

turns out that the adjusted R 2 generally increases as more disaggregated specifications are applied. This is evidence that each earnings item has its unique association (slope) with stock returns. The explanatory power for the most disaggregated specification is equal to 16.68% and 10.45% for the positive and negative earnings samples, respectively. The difference in explanatory power between the two samples has further decreased, both in absolute and relative terms. This is additional evidence for the proposed hypothesis. The results from running the most disaggregated regressions are presented in Table 8 of the Appendix. Because these regressions suffer from multicollinearity the attention should be directed against the explanatory power, not the regression coefficients, of these specifications.

4.2 The Relative Importance of Earnings Disaggregation and the Sign of Earnings The relative importance of earnings disaggregation and the sign of earnings is tested by running regressions (1) to (6) on the total sample. The results are displayed in Table 4. Panel A shows the results from regressions (1) and (4), which are the most aggregated specifications. This panel reveals that the regression model seems far better specified when the sign of earnings is taken into account. The dummy variable D is equal to 1 when earnings are negative and equal to zero for positive earnings. Panel A presents evidence that the intercept is significantly different for negative and positive earnings. The slope coefficients for both earnings and the change in earnings are also highly sign dependent (see the significant interaction terms). D is only dependent on the sign of EARN. The change in EARN may be both positive and negative when D is equal to one. The explanatory power increases from 7.61% to 13.70% as the dummy variable is included in the regressions.

variable D is still equal to 1 when earnings are negative and is not dependent on the sign of cash flow and accruals. Cash flow and accruals and their associated changes all have significant coefficients when the sign of earnings is taken into account. Accruals are barely significant when the dummy variable is excluded, but because its regression coefficient is actually dependent on the sign of earnings, the accruals’ regression coefficient and its associated t-value are both depressed when observations are pooled. The change in accruals is the only explanatory variable that seems to have a coefficient independent of the sign of earnings. As in panel A, the intercept is also highly sign dependent. Again, there is a dramatic increase in explanatory power when the dummy variable is included in the regression. The adjusted R 2 increases from 9.36% to 14.18% when the sign of earnings is taken into account.

The results from the most disaggregated regression specification are found in Panel C. The pattern is the same as in the two former specifications. Most explanatory variables have regression coefficients that differ according to the sign of earnings. The interaction terms for the change in working capital and the change in deferred taxes have p-values slightly above 5%, while the change in depreciation and the “change in change” in deferred taxes appear to have coefficients totally independent of the sign of earnings. The rest of the interaction terms are statistically significant. However, there is some multicollinearity in this regression. The mean variance inflation factor (VIF) is equal to 7.57. Even though this is below the critical limit of 10 proposed by Hair et al. (2006), the individual regression coefficients should be interpreted with some caution (due to their large standard errors). The VIFs of the individual

Table description Table 4 describes the value relevance of earnings for a sample of Norwegian firms from 1992 to 2004. It summarises the regression coefficients (Coefficient), White-adjusted t-values (t-statistic), total explanatory power (adj. R2) and number of observations (n) for the total sample. Possible multicollinearity is examined by mean variance inflation factor (mean VIF – only reported for the most disaggregated earnings specification).

Data is analysed using 3 different earnings aggregation levels.

**Panel A presents the results of the following regressions:**

**Standard specification:**

RETi, t = β0 + β1EARN i, t + β2 ∆EARN i, t + εi, t

**Panel B presents the results of the following regressions:**

**Standard specification:**

RETi, t = β0 + β1CFi, t + β 2 ∆CFi, t + β3ACCi, t + β 4 ∆ACCi, t + εi, t

**Panel C presents the results of the following regressions:**

**Standard specification:**

RETi,t = β 0 + β1CFi,t + β 2 ∆CFi, t + β 3 ∆WC i,t + β 4 ∆∆WC i,t + β 5 DEPi,t + β 6 ∆DEPi,t + β 7 ∆DTi,t + β 8 ∆∆DTi, t + ε i,t

where RETi,t is the stock return for company i in year t, EARN is earnings before extraordinary items, CF is cash flow from operations, ACC is total accruals, WC is working capital, DEP is depreciation and impairment, and DT is deferred taxes. D is a dummy variable equal to 1 when earnings are negative, 0 otherwise. ∆ denotes yearly change in the variables. The accounting variables are scaled by the market value of equity on 30 December in year t-1. Coefficients in bold denote a statistical significance at a 5% level using a two sided test.

Panel D summarises the adjusted R 2 from the regressions. Using F-tests for restrictions on coefficients, it turns out that all adjusted R 2 values are significantly different from each other at the 5% level.

regression coefficients are displayed in Table 9 of the Appendix.19 Still, explanatory power is not biased from multicollinearity. The adjusted R 2 increases from 10.79% to 15.90% when the dummy variable for negative earnings is introduced.

Panel D summarises the explanatory power of all regressions in Table 4. It turns out that all the adjusted R 2 values of Panel D are significantly different from each other, both horizontally and vertically (14.18% is barely significantly different from 13.70%, however).

When the most aggregated model is used and the sign of earnings is not taken into account, the explanatory power equals 7.61%. This number increases to 9.36% when earnings are split into cash flow and accruals, and it increases further to 10.79% when accruals are split into major components. These findings are consistent with Barth et al. (2001). However, when a dummy variable for negative earnings is included in the most aggregated specification, the If CF is excluded from the specification that accounts for negative earnings, mean VIF drops from 7.57 to 4.64 and all individual VIFs are then below 10. The explanatory power is reduced to 14.35%.

explanatory power from disaggregation of earnings is rather modest. Maximum adjusted R 2 is 15.90% for the most disaggregated model. Thus, Panel D indicates that the sign of earnings effect dominates the disaggregation effect. When a dummy variable for negative earnings is introduced in the aggregated specification, explanatory power increases from 7.61% to 13.70%. This is far higher than the explanatory power of 10.79% for the disaggregated model that does not include a dummy variable for negative earnings. Furthermore, when using bootstrapping technique, the increase in explanatory power from introducing a dummy variable for negative earnings is larger than the increase from disaggregating earnings in more than 90% of the cases (10,000 iterations).