An association between the revision coefficient and the predictive value of quarterly earnings in financial analysts' earnings forecasts.

Jin, Jongdae ; Lee, Kyungjoo ; Huh, Sung K. 等

ABSTRACT

This study provides further evidence regarding the predictive value of quarterly earnings in improving the forecasts of annual earnings. It is hypothesized that the revision coefficient is positively related to the predictive value of quarterly earnings information. The revision coefficient is a magnitude of earnings forecast revision in response to actual quarterly earnings information releases, which is measured by a regression coefficient of forecast errors over forecast revisions. The predictive value is a measure of quarterly earning information's impact on the accuracy of annual earnings forecasts, which is measured by total improvement (TI) in the accuracy of annual earnings forecasts for one year and by relative improvement (RI) in the accuracy of annual earnings forecasts for each quarter.

Empirical tests on this hypothesis are conducted using the Value Line analysts' earnings forecast data about 235 sample firms over a five-year period. The test results show the followings. First, the accuracy of annual earnings forecasts increases as additional quarterly reports become available, which is consistent with many previous studies on this issue (see Lorek [1979], Collins and Hopwood [1980], Brown and Rozeff [1979b],and Hopwood, McKeown and Newbold [1982]). Second, the revision coefficient is positively related to both of TI & RI, which supports the hypothesis. These results are robust across different forecast error metrics, and statistical methods.

INTRODUCTION

Ever since Green and Segall [1966,1967] did pioneering works, numerous researchers in accounting have examined the predictive value of quarterly earnings in forecasting annual earnings (E.G., Abdel-Khalik and Espejo [1978] and Brown, Hughes, Rozeff and Vanderweide [1980], Lorek [1979], Collins and Hopwood [1980], and Brown and Rozeff [1979b] and Hopwood, McKeown and Newbold [1982]). Using various time-series models and data, these studies found that the accuracy of analysts' annual earnings forecasts improves with the release of quarterly earnings information, which is intuitively appealing because annual earnings are temporal aggregation of four quarterly earnings. Previous studies also identified systematic and time persistent differences in analysts' earnings forecast accuracy, but have not explained why the differences exist. In other words, how quarterly earnings affect the forecast accuracy was not well documented in the previous research (E.G., Clement [1999], Hope [2003], Clement et. al. [2003], Gleason & Lee [2003]).

Thus, the objective of this study is to examine this issue of how quarterly earnings affect the accuracy of analysts forecasts. To be specific, it is to investigate the impact of the revision coefficient on the predictive value of quarterly earnings. The revision coefficient is a magnitude of earnings forecast revision in response to actual quarterly earnings information releases, which is measured by a regression coefficient of earnings forecast errors over earnings forecast revisions. This coefficient may vary with the quality and quantity of new information revealed through the quarterly earnings announcement. The predictive value is a measure of quarterly earning information's impact on the accuracy of annual earnings forecasts, which is measured by total improvement (TI) in the accuracy of annual earnings forecasts for one year and by relative improvement (RI) in the accuracy of annual earnings forecasts for each quarter.

It is hypothesized that the revision coefficient be positively related to the predictive value of quarterly earnings information.

Empirical tests on this hypothesis are conducted using the Value Line analysts' earnings forecast data about 235 sample firms over a five-year period. The test results are consistent with the hypothetical prediction that the revision coefficient is positively related to the predictive value of quarterly earnings (i. e., positive relationships with both of TI & RI). Besides it, the results show that the accuracy of annual earnings forecasts increases as additional quarterly reports become available, which is consistent with many previous studies on this issue (see Lorek [1979], Collins and Hopwood [1980], Brown and Rozeff [1979b], Hopwood, McKeown and Newbold [1982]). These results are robust across different forecast error metrics, and statistical methods.

The remainder of this paper is organized as follows. Chapter 2 describes hypotheses development, which is followed by a discussion on sample selection and methodology for testing the hypotheses in Chapter 3. Empirical results from the hypotheses tests are presented in Chapter 4, while some concluding remarks appear in Chapter 5.

HYPOTHESES DEVELOPMENT

Financial analysts revise their annual earnings forecasts as new quarterly earnings information is released, because earnings forecasts for a reporting quarter, an integral part of annual earnings forecasts, are replaced by the actual earnings for the same quarter. This revision may vary with the quality and quantity of new information revealed through the actual quarterly earnings announced.

The quantity of new information in the actual quarterly earnings can be measured by the difference between the projected earnings for the reporting quarter and its corresponding actual earnings (i.e., quarterly earnings forecast error), because more news in the actual quarterly earnings causes the bigger difference. The bigger the quarterly earnings forecast error, the bigger the revision on annual earnings forecasts. In other words, an association between the quarterly earnings forecasts error and the revision on annual earnings forecasts (i.e., the revision coefficient) should be positive.

The quality of new information in the actual quarterly earnings may be reflected on the sensitivity of annual earnings forecast revisions with respect to a given magnitude of quarterly earnings forecast error. Financial analysts place heavier weights on the high quality information than on low quality information when they revise their forecasts on the annual earnings. Thus, the higher the quality of new information in the actual quarterly earnings, the bigger the revision on the annual earnings forecasts. In other words, the revision coefficient should be positively related to the quality of quarterly earnings information.

With the revision, the accuracy of annual earnings forecasts improves, because uncertainties in the annual earnings forecasts decrease as the predicted quarterly earnings in annual earnings forecasts is replaced by the corresponding actual quarterly earnings. And the higher the revision coefficient due to higher quality of quarterly earnings information, bigger the revision on annual earnings forecasts which, in turn, leads to higher accuracy of annual earnings forecasts.

In sum, the predictive value of quarterly earnings, a measure of quarterly earnings' impact on the accuracy of annual earnings forecasts, is positively related with the revision coefficient. This predictive value can be measured either by total improvement in the accuracy of annual earnings forecasts due to all four quarterly earnings (i.e., annual earnings) information (TI) or by relative improvement in the accuracy of annual earnings forecasts due to an individual quarterly earnings information (RI). Since TI is a temporal aggregation of four quarterly RI's, both TI and RI should be positively related to the revision coefficient. Therefore, testable hypotheses herefrom would be H1: The total improvement (TI) is positively related to the revision coefficient of quarterly earnings. H2: The relative improvement (RI) is positively related to the revision coefficient of quarterly earnings

METHODOLOGY

This chapter describes sample selection, empirical measures of predictive values and time-series parameters, and statistical methodology used to test the hypotheses.

Sample Selection

Each firm included in this study should satisfy the following selection criteria. (1) Quarterly earnings per share (EPS) data are available in the Value Line Investment Survey over the entire estimation and testing period (10 years for estimation and 5 years for testing). (2) Quarterly earnings forecasts are available in the Value Line during the estimation and testing period. (3) Sufficient daily return data are available on the CRSP tape. (4) Each firm's financial information must be included in the COMPUSTAT tapes. (5) Each firm has a fiscal year ending on December throughout the estimation and testing period. And (6) each firm must be in the manufacturing industry with two-digit SIC code between 10 and 39.

The first criterion is used to have enough EPS data for estimating the time-series models. The second criterion to estimate revision coefficients of the time-series model implied by analysts' forecasts. The criteria (3) and (4) are required to ensure the availability of necessary financial and market data. The fifth and sixth criteria are imposed to ensure the comparability of earnings series across firms. The firms in the regulated industries such as Banking, Utilities and Transportation are excluded because they may have earnings processes quite different from the manufacturing firms. As is typical with time-series research in accounting, the familiar 'survivorship bias' applies to the sample because it includes only those firms that have existed for at least 18 years.

The above selection criteria yielded a sample of 235 firms. Table 1 shows the breakdown of the sample firms by industry (two-digit SIC code). Twenty-three industries are represented in the sample. There is clustering in particular industries, notably Chemicals (SIC=28) and Electric Machinery (SIC=36), which account for 15.7% and 13.6% respectively, of the sample firms.

Measuring Predictive Values of Quarterly Earnings

The term 'predictive value' is defined here as the improvement in the accuracy of annual earnings forecasts with the release of actual quarterly earnings information. The improvement in the forecasts is measured by the reduction in forecast errors. Two forecast error metrics are used; absolute forecast error (AFE) and squared forecast error (SFE) which are specified as:

AFE[([Q.sub.[tau]]).sub.iy] = [absolute value of [A.sub.iy] - E[(A|[Q.sub.[tau]]).sub.iy]]

SFE[([Q.sub.[tau]]).sub.iy] = ( [A.sub.iy] - E[[(A|[Q.sub.[tau]]).sub.iy]).sup.2]

where [A.sub.iy] = actual annual earnings for firm i and year y, and

E[(A|[Q.sub.[tau]]).sub.iy] = forecasted annual earnings conditional on [tau] quarter's earnings for firm i and year y, [tau] =0,1,2,3.

These two forecast error metrics are used in this study (i) to examine the sensitivity of the results to different measures of forecast error, and (ii) to be comparable with previous studies which employed this measure. Hereafter, SFE([Q.sub.[tau]]) will be used for exposition purposes.

The total improvement (TI) in the accuracy of annual earnings forecasts during a year relative to the beginning of the year due to the release of actual quarterly earnings is measured by:

[TI.sub.iy] = [SFE[([Q.sub.0]).sub.iy] - SFE[([Q.sub.3]).sub.iy]]/SFE[([Q.sub.0]).sub.iy]

Similarly, the relative improvement (RI) in the accuracy of annual earnings forecasts due to an individual quarterly earnings is measured by:

RI[([Q.sub.[tau]]).sub.iy] = SFE[([Q.sub.[tau]-1]).sub.iy] - SFE[(Q[tau]).sub.iy]/SFE[([Q.sub.0]).sub.iy] - SFE[([Q.sub.3]).sub.iy]

The forecasts of annual earnings at the end of each quarter E(A|[Q.sub.[tau]]) are obtained by summing the remaining quarterly earnings forecasts of the year with the actual quarterly earnings of current and previous quarters.

Measuring Revision Coefficient

Recent studies have provided empirical evidence suggesting the superiority of financial analysts over the three 'premier' time-series models in forecasting future earnings (e.g., Collins and Hopwood [1980] and Brown, Hagerman, Griffin and Zmijewski [1987]). Therefore, it would be appropriate to use analysts' earnings forecasts data to measure the revision coefficient and examine the association between the revision coefficient and the predictive value of quarterly earnings. Analysts' forecast data from the Value Line Investment Survey were used in this study.

To obtain the revision coefficient, the following regression model was estimated:

[REV.sub.[tau]] (t) = [??] + [??](t)[FE.sub.[tau]] + e (1)

where [REV.sub.[tau]] (t) = the revision of t-quarter ahead Value Line forecast at quarter [tau],

[FE.sub.[tau]] = the forecast error for quarter [tau]; actual earnings minus the most recent Value Line Earnings forecast for quarter [tau].

[??](t) = the revision coefficient.

This adaptive expectation model was used for the following reasons. First, the process by which analysts form their forecasts has not been established in the literature. The model has been used in previous studies to investigate analysts' revision process of annual earnings forecasts (Givoly [1985]) as well as quarterly earnings forecasts (Abdel-Khalik and Espejo [1978] and Brown and Rozeff [1979c]).

Equation (1) was estimated for each firm using immediately preceding 10 years' forecast data to obtain the revision coefficient for each testing year. Both one-quarter and two-quarters ahead forecast revisions were used as dependent variables for all sample firm over five-testing years, which results in total of 2,350 estimates for the dependent variable (2x235x5).

Table 2 presents summary statistics on the estimation results of equation (1) using initial 10 years' forecast data. Panel A reports the mean, standard deviation, and quartile distributions of intercept and slope coefficients, their t-statistics, and [R.sup.2]s using one-quarter ahead forecast revisions as the dependent variable. The results suggest that in most of the sample firms, the adaptive expectation model adequately represents the analysts' forecast revision process. First, the mean [R.sup.2] value of 0.221 indicates that a significant portion of forecast revision is explained by the most recent one-quarter ahead forecast error. Second, the estimated intercepts are small and insignificantly different from zero. Third, the average slope coefficient is 0.329 and it is significant in 190 of the 235 regressions. Furthermore, except for nine firms, the revision coefficients are positive and most of them lie between zero and one.

Panel B of Table 2 shows the summary statistics on the estimates of equation (1) using two-quarter ahead forecast revisions. As expected, there is a decrease in [R.sup.2] (an average value of 0.101). Although the descriptive statistics on the revision coefficients using two-quarter ahead forecasts are less informative, they can be used to draw an inference as to which time-series model is most concordant with analysts' forecast revision process.

Testing Hypotheses

It was hypothesized that both total (H1) and relative (H2) predictive value of quarterly earnings are positively related to the revision coefficient of quarterly earnings. To test these hypotheses, the following pooled cross-sectional and time-series regression models are estimated:

[TI.sub.iy] = [a.sub.0] + [a.sub.1][PARA.sub.iy] + [a.sub.2]ln[(SIZE).sub.iy] + [[??].sub.iy] (2)

RI[([Q.sub.j]).sub.iy] = [b.sub.0] + [b.sub.1][PARA.sub.iy] + [b.sub.2]ln[(SIZE).sub.iy] + [[??].sub.iy] (3)

where TI = total improvement in the accuracy of annual earnings forecasts from incorporating all four actual quarterly earnings,

PARA = revision coefficient of a given quarterly earnings time-series model,

ln(SIZE) = natural logarithm of firm size measured by the market value of equity,

RI([Q.sub.j]) = relative improvement in the accuracy of annual earnings forecasts by the Quarter j's actual earnings,

i, y = firm and year index, respectively.

Under these regression models, the hypotheses can be stated as follows: H1: [H.sub.0] : [a.sub.1] = 0, [H.sub.a] : [a.sub.1] > 0 H2: [H.sub.0] : [b.sub.1] = 0, [H.sub.a] : [b.sub.1] > 0

Firm size is used as a controlling variable for the following reasons. First, the superiority of financial analysts' forecasts over those by univariate time-series models suggests that information other than publicly available earnings data is useful for forecasting earnings. In fact, several studies have used firm size as a proxy for the availability of other information sources and found that firm size is positively related to the accuracy of earnings forecasts (e.g., Brown, Richardson and Schwager [1987] and Collins, Kothari and Rayburn [1987] among others). Second, evidence by Bathke, Lorek and Willinger [1989] suggests that firm size is positively related to both revision coefficients and the accuracy of one-quarter-ahead earnings forecasts. Thus, the firm size effect should be controlled for to examine the net effect of the revision coefficient on the predictive value of quarterly earnings. The controlling variable, SIZE, is measured by the market value of equity.

As an additional test on H1 and H2, two-way analysis of variance (ANOVA) design was also employed by dichotomizing sample firms according to the magnitude of revision coefficient (high(H) versus low(L) revision coefficient firms), and the firm size (small(S) versus big(B) firms). Under this 2x2 factorial design, H1 and H2 can be stated in null form as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

EMPIRICAL RESULTS

Table 3 presents descriptive statistics of annual earnings forecast errors, which are reported for each conditioning quarter and for both absolute forecast error (AFE) (Panel A) and squared forecast error (SFE) (Panel B). Mean values of AFE and SFE decrease every quarter, which implies that the accuracy of annual earnings forecasts improves, as additional quarterly reports become available. The F-values are 70.562 and 55.499 for the AFE and SFE, respectively. The corresponding [chi square] statistics from the Kruskal-Wallis tests are 455.50 and 454.94, which is statistically significant. Standard deviation of forecast errors decreases as the year-end approaches, which means that analysts converge to a consensus on annual earnings forecasts as more quarterly earnings become available. All these results are robust with respect to the choice of forecast error metric. In sum, the results presented in Table 3 are consistent with the previous studies that the accuracy of annual earnings forecasts increases, as additional quarterly earnings become available.

One-way ANOVA was conducted using analysts' forecasts to test H1 and H2, and the results are reported in Table 4. Panel A provides evidence about the effect of revision on the predictive values of quarterly earnings. The result shows that firms with higher revision coefficients have larger TI's as well as RI([Q.sub.j])'s than the firms with lower revision coefficients. The differences are statistically significant ([alpha]<0.10) using either the F-tests or the Wilcoxon tests. Also, the result is not sensitive to the choice of forecast error metric. Panel B of Table 4 shows the relationship between firm size and predictive values of quarterly earnings. Large firms exhibit consistently larger predictive values (both TI and RI([Q.sub.j])) than smaller firms. However, the differences are statistically significant ([alpha]<0.10) only when AFE was used.

Table 5 presents the results from 2x2 ANOVA to test the effect of revision coefficients on the total predictive value (Panel A) and the relative predictive value (Panel B) after controlling for firm size. Consistent with the univariate results, revision coefficient has a significantly positive effect on both TI and RI([Q.sub.j]). Although the significance level is somewhat low ([alpha]<0.10), this result lends support to H1 and H2 even after controlling for the effect of firm size.

Results from estimating regression model (2) and (3) are presented in Panel A of Table 6. The regression coefficients of the revision coefficient variable, [a.sub.1] and [b.sub.1], have the expected positive signs and are statistically significant at the [alpha] level of 0.05 for AFE and 0.01 for SFE. The regression coefficients of the firm size variable, [a.sub.2] and [b.sub.2], also have the predicted positive sign but are not statistically significant except for the RI([Q.sub.1]) when SFE was used. Regressions models (2) and (3) were again estimated using rank data, and the results are reported in Panel B of Table 6. The general tenor of conclusion remains the same; significantly positive relation of revision coefficient to both total and relative predictive values, which supports H1 and H2. Diagnostic tests for multicollinearity and heteroskedasticity were also conducted using the procedure introduced by Belsley, Kuh and Welsch [1980] and White [1980], respectively. Test results indicate that neither of these problems presents in our data.

In sum, results show that annual earnings forecasts become more accurate as additional quarterly reports become available and revision coefficients of quarterly earnings are positively related with both total and relative predictive values of quarterly earnings (TI and RI). These results are robust with respect to the choice of forecast error metric, statistical methodology, forecast data and revision coefficients used.

CONCLUSIONS

This study examines the effect of quarterly earnings and their revision coefficients on their predictive value. It is hypothesized that the revision coefficient is positively related to the predictive value of quarterly earnings information. The revision coefficient is a magnitude of earnings forecast revision in response to actual quarterly earnings information releases, which is measured by a regression coefficient of forecast errors over forecast revisions. The predictive value is a measure of quarterly earning information's impact on the accuracy of annual earnings forecasts, which is measured by total improvement (TI) in the accuracy of annual earnings forecasts for one year and by relative improvement (RI) in the accuracy of annual earnings forecasts for each quarter.

This hypothetical relationship was empirically tested using the Value Line analysts' forecast data about 235 sample firms over the five-year period. Empirical results are consistent with the hypothetical relationship between the revision coefficients and the predictive value of quarterly earnings. First, annual earnings forecasts become more accurate as additional quarterly reports become available, suggesting that quarterly earnings are useful for improving the accuracy of annual earnings forecasts. Second, revision coefficients of quarterly earnings are positively related with both total and relative predictive values of quarterly earnings (TI and RI). These results are robust with respect to different forecast error metrics and statistical methods.

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Jongdae Jin, William Paterson University

Kyungjoo Lee, Cheju National University

Sung K. Huh, California State University-San Bernardino Table 1: Industry Classifications of Sample Firms Two-Digit Industry Description Number of Firms SIC Code 10 Metal Mining 9 12 Coal Mining 3 13 Oil and Gas Extraction 5 14 Nonmetal Mineral 1 16 Heavy Construction 2 20 Food and Kindred 10 21 Tobacco 3 22 Textile Mill 3 24 Lumber and Wood 2 25 Furniture and Fixtures 2 26 Paper 11 27 Printing and Publishing 7 28 Chemicals 37 29 Petroleum Refining 18 30 Rubber 7 32 Stone, Clay and Glass 11 33 Primary Metal 15 34 Fabricated Metal 9 35 Industrial Machinery 21 36 Electric Machinery 32 37 Transportation Equipment 19 38 Instruments 7 39 Miscellaneous Goods 1 Total 235 Table 2: Descriptive Statistics of Adaptive Expectations Model Estimates Using Analysts' Forecasts (a) [REV.sub.t](t) = [??] + [??](t)[FE.sub.t] + [??] b Panel A. One-Quarter Ahead Forecast Revisions Estimates Mean Standard Quartiles Deviation 0.25 0.50 0.75 [??] -0.015 0.049 -0.021 -0.006 0.003 t([??]) -0.478 1.243 -1.352 -0.652 0.328 [??] 0.329 0.257 0.171 0.326 0.465 t([??]) 2.926 2.850 1.539 2.782 4.421 [R.sup.2] 0.221 0.186 0.068 0.177 0.359 Panel B. Two-Quarter Ahead Forecast Revisions Estimates Mean Standard Quartiles Deviation 0.25 0.50 0.75 [??] 0.001 0.039 -0.006 0.003 0.014 t([??]) 0.291 1.308 -0.599 0.409 1.235 [??] 0.148 0.246 0.011 0.116 0.236 t([??]) 1.194 1.509 0.124 1.177 2.118 [R.sup.2] 0.101 0.121 0.009 0.055 0.146 (a) The summary statistics are based on 235 sample firms. (b) [REV.sub.t](t) = the revision of t-quarter ahead Value Line forecast at quarter t. [FE.sub.t] = the forecast error for quarter t; actual EPS minus the most recent Value Line forecast for quarter t. Table 3: Descriptive Statistics of Annual Earnings Forecast Errors Using Analysts' Forecasts (a) Panel A. Absolute Percentage Error (b) Quarters Mean Standard Quartiles Reported Deviation 0.25 0.50 0.75 0 0.543 0.803 0.06 0.177 0.624 1 0.430 0.712 0.042 0.127 0.413 2 0.310 0.599 0.029 0.084 0.266 3 0.173 0.419 0.013 0.038 0.130 Panel B. Squared Percentage Error (c) Quarters Mean Standard Quartiles Reported Deviation 0.25 0.5 0.75 0 0.517 0.962 0.004 0.031 0.390 1 0.390 0.848 0.002 0.016 0.171 2 0.258 0.693 0.001 0.007 0.071 3 0.129 0.498 0.000 0.001 0.017 (a) The summary statistics are based on 235 sample firms over 5 year testing period. (b) The absolute percentage error (APE) is defined as APE=[absolute value of (A-E(A))/A], where A and E(A) are actual and forecasted annual earnings, respectively. APE greater than 3.00 were truncated to 3.00. (c) The squared percentage error (SPE) is defined as SPE= [((A-E(A))/A).sup.2]. SPE > 3.00 were also truncated to 3.00. Table 4: Effect of Revision coefficient and Firm Size on the Predictive Values of Quarterly Earnings: One-Way ANOVA Using Analysts' Forecasts (a, b) Panel A. The Effect of Revision coefficient Absolute Forecast Error Parameter TI RI([Q.sub.1]) Small 0.622(0.407) 0.408(0.286) Large 0.782(0.304) 0.526(0.235) F-value 5.82 * 6.31 * Wilcoxon Z 2.24 * 2.12 * Panel B. The Effect of Firm Size Absolute Forecast Error Firm Size TI RI([Q.sub.1]) Small 0.649(0.393) 0.426(0.278) Large 0.764(0.337) 0.515(0.259) F-value 2.91 (x) 3.24 (x) Wilcoxon Z 2.03 * 1.71 (x) Panel A. The Effect of Revision coefficient Squared Forecast Error Parameter TI RI([Q.sub.1]) Small 0.793(0.386) 0.556(0.300) Large 0.908(0.259) 0.667(0.237) F-value 5.84 * 8.07 ** Wilcoxon Z 1.62 (i) 2.69 ** Panel B. The Effect of Firm Size Squared Forecast Error Firm Size TI RI([Q.sub.1]) Small 0.805(0.379) 0.568(0.299) Large 0.883(0.291) 0.644(0.251) F-value 2.51 3.63 (x) Wilcoxon Z 0.99 1.57 (a) Analyses are based on pooling data across 235 sample firms and over 5 year testing period. Observations in middle parameter group are excluded. (b) The numbers reported are mean values with the standard deviation in parentheses. Revision coefficients are the slope coefficients of the regression model (7) and firm size is measured by the market value of equity. ** Significant at a<0.01; * Significant at a<0.05; (x) Significant at a<0.10. Table 5: Effect of Revision coefficient and Firm Size on the Predictive Values of Quarterly Earnings: Two-Way ANOVA Using Analysts' Forecasts Panel A. Total Predictive Value Absolute Forecast Error Source SS F-value p-value Parameter 0.400 3.57 0.0625 Size 0.247 2.20 0.1420 Error 8.509 R-square 0.071 Panel B. Relative Predictive Value Absolute Forecast Error Source SS F-value p-value Parameter 0.224 3.61 0.0611 Size 0.233 3.76 0.0561 Error 4.703 R-square 0.088 Panel A. Total Predictive Value Squared Forecast Error Source SS F-value p-value Parameter 0.356 3.69 0.0570 Size 0.258 2.67 0.1046 Error 12.258 R-square 0.047 Panel B. Relative Predictive Value Squared Forecast Error Source SS F-value p-value Parameter 0.234 3.44 0.0660 Size 0.347 5.09 0.0258 Error 8.650 R-square 0.061 Table 6: Effect of Revision coefficient and Firm Size on the Predictive Values of Quarterly Earnings a: [TI.sub.iy] = [a.sub.0] + [a.sub.1][PARA.sub.iy] + [a.sub.2] ln[(SIZE).sub.iy] + [[??].sub.iy] (2) RI[(Qj).sub.iy] = [b.sub.0] + [b.sub.1][PARA.sub.iy] + [b.sub.2]ln[(SIZE).sub.iy] + [[??].sub.iy] (3) Panel A. Ordinary Regression Analysis Absolute Forecast Error Variables TI RI[(Q1.sub.1)] Intercept 0.77 (6.298) ** 0.54 (6.076) ** PARA 0.22 (2.511) * 0.15 (2.402) * ln(SIZE) 0.024 (1.323) 0.021 (1.544) [R.sup.2] (%) 3.42 4.58 F-value 4.135 * 4.195 * Panel B. Rank Regression Analysis (c) Absolute Forecast Error Variables TI RI[(Q1.sub.1)] Intercept 84 (8.264) ** 85 (8.351)** PARA 0.19 (2.589) ** 0.18 (2.408)* ln(SIZE) 0.13 (1.752) [zeta] 0.13 (1.752) [zeta] [R.sup.2] (%) 5.49 5.00 F-value 5.086 ** 4.602 ** Panel A. Ordinary Regression Analysis Squared Forecast Error Variables TI RI[(Q1.sub.1)] Intercept 0.90 (10.404) ** 0.69 (9.856) ** PARA 0.17 (2.723) ** 0.17 (3.262) ** ln(SIZE) 0.019 (1.444) 0.022 (2.094) * [R.sup.2] (%) 3.22 4.99 F-value 4.702 ** 7.432 ** Panel B. Rank Regression Analysis (c) Squared Forecast Error Variables TI RI[(Q1.sub.1)] Intercept 139 (10.764) 00** 135 (9.856) ** PARA 0.10 (1.732) [zeta] 0.18 (3.037) ** ln(SIZE) 0.07 (1.197) 0.12 (2.072) * [R.sup.2] (%) 1.54 4.56 F-value 2.220 [zeta] 6.767 ** (b) TI = total improvement in the accuracy of annual earnings forecasts from incorporating all four actual quarterly earnings, PARA = revision coefficient of a given quarterly earnings time-series model, ln(SIZE) = natural logarithm of firm size measured by the market value of equity, RI([Q.sub.j]) = relative improvement in the accuracy of annual earnings forecasts by the Quarter j's actual earnings, i, y = firm and year index, respectively. (c) Ranks of both dependent and independent variables are used. ** Significant at a <0.01; * Significant at [alpha] <0.05; [zeta] Significant at [alpha] <0.10.