248407

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The Explanatory Power of Earnings for Stock Returns Author(s): Norman Strong and Martin Walker Source: The Accounting Review, Vol. 68, No. 2 (Apr., 1993), pp. 385-399Published by: American Accounting AssociationStable URL: http://www.jstor.org/stable/248407Accessed: 25-08-2015 10:34 UTC

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THE ACCOUNTING REVIEW Vol. 68, No. 2 April 1993 pp. 385-399

The Explanatory Power of Earnings

for Stock Returns

Norman Strong Martin Walker

University of Manchester, England

SYNOPSIS AND INTRODUCTION: In a thorough review of market- based research on the information content of accounting earnings, Lev (1989) concludes that the explanatory value of earnings for stock returns, and therefore the usefulness of earnings disclosures, tends to be embar- rassingly low. A number of nonmutually exclusive explanations have been advanced for these disappointing results, including: (1) poor specification of the estimating equation, such as a failure to allow for cross-sectional variation in the regression parameters; (2) inappropriate choice of the assumed proxy for expected earnings; (3) the availability of more timely sources of the value-relevant information in earnings statements (Beaver et al. 1980); and (4) poor informational properties (quality) of reported earnings because of biases induced by accounting measurement practices or creative "abuses" of the earnings measurement process.

Lev (1989) speculated that the last of these explanations was the most likely cause of the poor statistical performance consistently found in returns-earnings research. In contrast, the present study shows that a considerable improvement in statistical performance can be achieved by working with a more general specification of the returns-earnings relation. Lev's article has resulted in serious questioning of the contribution of market-based research, but we believe that the present study provides grounds for a more positive assessment.

We use a panel regression approach to examine the association between annual stock price returns and reported earnings figures of industrial companies in the United Kingdom. We combine several recent advances in

We are grateful to members of the Centre for Empirical Research in Accounting and Finance at the Uni- versity of Manchester for comments on this research. An early version of the paper was presented at the 1991 Finance and Market Based Accounting Research Conference held at the University of Manchester; we are grateful for comments received from participants at that conference. John O'Hanlon and Peter Pope made a number of helpful suggestions on a previous version of the paper. We would particularly like to acknowledge the comments of the editor, an associate editor, and the anonymous referees; their comments resulted in a sub- stantial improvement in the focus and exposition of the paper. The financial support of the ICAEW and the ESRC (grant number R000233813) is also gratefully acknowledged.

Submitted August 1991. Accepted December 1992.

385



386 The Accounting Review, April 1993

market-based acounting research design to produce a specification of the relation between earnings and price changes that subsumes the following key features:

1. Contemporaneous earnings yield is included in addition to the deflated first difference in earnings that is normally included in models of the returns-earnings relation.

2. Regression parameters are allowed to vary both cross-sectionally and over time.

3. Parameter values are allowed to vary across components of earnings to accommodate differences in the degree of persistence; in particular, we model the explanatory power resulting from attempts by accountants to distinguish extraordinary and exceptional items from the other components of earnings.

We introduce these features in a general model in a way that allows us to assess the incremental explanatory power of each individually as well as the joint effects of two or more combined. Each methodological improvement contributes significantly to our ability to explain security price changes, and we show that the best fit is achieved by incorporating all three features in a single general model. In moving from the standard model, which regresses a measure of abnormal returns on earnings changes, to the most general model, the adjusted R-squared increases from 0.10 to 0.38.

Key Words: Stock returns, Earnings yield, Earnings disaggregation, Panel regression.

Data Availability: A list of the sample firms is available from the authors upon request. The rest of the data are available from sources identified in the text.

Tp HE article is organized as follows. We introduce the general earnings response model in section I and provide details of the sample of observations and definitions of variables in section II. Section III contains a statistical analysis of the

variables included in the study. The principal results are reported in section IV, and we offer our conclusions in the final section.

L. Earnings Response Models

The standard model of the relation between abnormal returns and accounting earnings can be represented as:

CARi,=a Rb Eit-=Eib ( 1i)

where:

a= an intercept parameter to be estimated, b = a slope parameter to be estimated (generally referred to in the literature as

the earnings response parameter),



Strong and Walker-Power of Earnings 387

CAR i= the cumulative abnormal return of company i in period t, Ei,=the earnings of firm i in period t,

Vit-1 =the market value of equity at the start of period t, and ui= a conventional, mean zero, disturbance term.

Recent advances in the market-based accounting literature have attempted to extend this basic model in a number of ways. Theoretical work by Ohlson (1989) has suggested that earnings yield might be added as a second independent variable to allow for transitory components in earnings, and Easton and Harris (1991) have further high- lighted the potential of the yield variable to explain stock returns.' In addition, a number of recent studies based on U.S. data have documented statistically significant varia- tions in the earnings response coefficient, both across firms and over time. Kormendi and Lipe (1987) and Collins and Kothari (1989) show that earnings response coefficients are positively related to the persistence of earnings and exhibit cross-sectional and intertemporal variation. Easton and Zmijewski (1989), adopting a random coefficients regression model, and Board and Walker (1990), employing a fixed coefficients (dummy-variable) regression approach, support these findings. Other studies have shown that it may be possible to increase the explanatory power of earnings response models by identifying various components of earnings as separate independent variables (see, e.g., Lipe 1986).

Collectively, these considerations suggest the following generalization of equation (1):

CAR,= a,+t(bi+b . + C+(c +c+) E (2) X1= Vit- 1 i=1 Vit-

where:

a,= a time-varying intercept parameter, Ej,=the jth component of the earnings of firm i in period t,2

bJ and bi = firm-varying response parameters associated with the change in Et c8 and ca- firm-varying response parameters associated with the level of E cj and c=are firm-varying response parameters associated with the level of Em;,,

and other variables are as defined previously. Equation (2) adds an intercept term that is allowed to vary over time to equation

(1). In addition, the model disaggregates earnings into I components and allows the response parameters to vary across components and over time. Finally, equation (2)

'The standard earnings response model represented by equation (1) assumes that earnings follow a random walk. The potential value of including an earnings yield variable can be seen, if we instead assume that earnings follow a first-order autoregressive process of the form,

El, - j&=,(Ejj - A) +e;,.

Then expected earnings in period t is, u+ (E,- u), and the returns-earnings relation becomes,

CAR,,=a+ b( -1) +b_ __ ___ +b(1-0) u,. 'vir1 it-1Vi-

2 Throughout this article, superscripts are used exclusively to denote earnings components and the parameters associated with these components. Thus, E2 denotes the second earnings component, not earnings squared.




incorporates a yield variable for each component of earnings, with the response parameter being allowed to vary across firms, over time, and across components.3 In its most general form, the model requires estimation of (I x 7 + 3 x T) parameters, where T is the number of years for which data are available. For 200 firms and 20 years of data per firm, the estimation of 1,460 parameters from 4,000 observations would be required.

We present empirical evidence for equation (2) and for several restricted versions that were carefully selected to highlight the incremental effects of: (1) allowing for cross-firm variation in the parameters, (2) introducing the yield variable into the specification, and (3) separately identifying the exceptional and extraordinary components of earnings. Following suggestions in a number of recent studies, we also present results for raw returns as well as for abnormal returns as the dependent variable.

II. Sample Selection and Data Definitions

The study is based on a random sample of 416 companies selected from the 1987 list of all U.K.-quoted industrial companies in Datastream.4 From this starting sample, we selected all companies with December to April financial year-ends.5 We carefully checked the sample to exclude any companies that changed their accounting year-end during the relevant period. Further companies were excluded by the following data requirements: (1) At least 10 consecutive years of accounting data had to be available on Datastream within the period 1971 through 1986 and (2) we also required a complete set of 16 years of returns data on the London Business School Share Price Database (LSPD). The 16 years correspond to the 10 years for which the accounting data was available, plus five years preceding the first year of accounting data (used to estimate the market model for the first year of the study) and one year following the last year of accounting data.

These criteria generated a final study sample of 146 U.K.-quoted companies and 2,036 observations. Though slightly biased toward the larger companies, the size distribution of the sample at the end of 1980, when all sample firms were trading, was reasonably representative of the population of firms recorded as being traded at the end of 1980 by the LSPD. Sixty percent of both the sample and the population of companies fell in the size range of ?2 through ?38 million ($4.8 through $91.2 million). However, the percentage of companies with a market capitalization of less than ?2 millon was only 10 percent in the sample, compared to 20 percent in the entire population. At the other end of the size distribution, 30 percent of the sample firms had a market capitalization greater than ?38 million, compared to only 20 percent in the population. The industrial composition of the sample is reported in table 1 and is reasonably representative of the population of industrial companies in the United Kingdom.

The values of two return metrics were computed for each company year of data.6

An econometric restriction implicit in equation (2) is that the cross-firm and intertemporal sources of parametric variation are assumed to be additive in their effects.

4 Datastream is an extensive on-line system of data bases covering, inter alia, domestic (United Kingdom) and international company accounts.

I In the regression analysis, the months January to April were grouped with the preceding December in defining period t.

6 The statistical analysis used abnormal return calculated according to the capital asset pricing model as a third return metric. The results were virtually identical to those for the market model abnormal return and are not separately reported.




Table I Industrial Composition of the Study Sample

Industrial Classification N Percent

Industrial and building material 17 11.6 Contracting, construction 9 6.2 Electricals and electronics 4 2.7 Miscellaneous mechanical engineering 16 11.0 Other capital goods 21 14.4 Brewering, catering, and leisure 9 6.2 Food 7 4.8 Newspaper, publishing, and printing 10 6.8 Stores and other retailing 10 6.8 Health and household products 7 4.8 Chemicals and oil 5 3.4 Shipping and transport 10 6.8 Miscellaneous industrials 7 4.8 Overseas trade 6 4.1

2 1.4

Total 146 100

MMCAR is the cumulative monthly market model abnormal return from May of year t through April of year t+ 1, and RETURN is the cumulative monthly stock return from May of year t through April of year t + 1.7 Both return metrics implicitly assume that the earnings news for year t (for a December year-end company) is released no earlier than May of year t and no later than April of year t+ 1.

The empirical analysis focuses on three components of earnings: earnings before exceptional and extraordinary items, denoted E' and referred to as "pre-exceptional earnings"; exceptional earnings, denoted E2; and extraordinary earnings, denoted E3. The following important aggregations of these earnings components are also examined:

Ordinary earnings E I + E2, (3)

and

All-inclusive earnings E 1 + E2 + E3. (4)

In the United Kingdom, ordinary earnings comprise the reported earnings number on which earnings per share calculations are currently based.8

7 The dates for estimating benchmark returns, for cumulating (abnormal) returns, and for deflating earnings components refer to December year-end companies. For company financial years ending January to April, dates are successively adjusted forward by one month. The market model abnormal return was calculated by fitting the market model to the continuously compounded company and market returns (Financial Times All Share Index) for the 60 months immediately prior to year t. The abnormal returns from May of year t to April of year t + 1 were then derived as the prediction errors from the market model, conditional on the realized value of the market index for that month. All return data were taken from the LSPD.

* The distinctions between pre-exceptional, exceptional, and extraordinary earnings were established in the early 1970s by the United Kingdom's Accounting Standards Committee (ASC) and were formalized in Statement of Standard Accounting Practice 6 (SSAP6) in 1974. Extraordinary items were defined as "those items which derive from events or transactions outside the ordinary activities of the business and which are both material and expected not to recur frequently or regularly. They do not include those items which, though




Corresponding to the definitions, the following five accounting variables were assembled from Datastream company accounts data for each company year:

El + E2 =Ordinary earnings (Datastream item 175), E2 = Exceptional items (Datastream item 194), E3= Extraordinary items (Datastream item 193), EI=Earnings before Exceptional Items (Datastream items 175 minus

194), and El + E2+ E3= All-inclusive earnings (Datastream items 175 plus 193).

For each of these earnings components, we then defined and calculated the "deflated first difference" as the value of the component in year t minus the value in year t -1 divided by the market capitalization on April 30 of year t (May 31 for January year-end companies, etc.). We also calculated an earnings yield variable for each component as the value of the component reported for year t divided by the market capitalization on April 30 of year t. Dummy variables were constructed to allow the regression parameters to vary both across firms and over time in accordance with equation (2).9 The time dummies allow for a different response parameter for each year (corresponding to an average coefficient for all firms in that year). The (time-invariant) firm dummies allow for a different response parameter for each firm.10

III. Data Analysis

Before conducting the panel regressions, we completed a number of separate analyses on the materiality of the earnings components, the correlation structure of the main variables involved in the study, and the time-series properties of the three earnings components.

Materiality of the Earnings Components in Relation to Market Capitalization

This was assessed by examining the key descriptive statistics of the three components of all-inclusive earnings yield (see table 2). The pre-exceptional earnings yield averaged about 13 percent over the sample period, with a standard deviation of 20 percent. There was no marked skewness. The median values and the 25th and 75th per-

exceptional on account of size or incidence (and which therefore may require separate disclosure), derive from the ordinary activities of the business. Neither do they include prior year items simply because they relate to a prior year." This definition implicitly considers exceptional items as arising from the ordinary activities of the business and requiring separate disclosure because of their size or incidence.

Successive surveys of published accounts showed that SSAP6 succeeded in rapidly establishing the required practice of separate disclosure of extraordinary and exceptional items and the practice of calculating earnings per share figures according to earnings after exceptional but before extraordinary items (see, e.g., ICAEW 1977, sec. 7). However, several surveys also showed considerable inconsistencies in the way similar items were accounted for by different companies, the main difficulty being that of deciding whether a particular item derived from the ordinary activities of the business. In an attempt to reduce the incidence of such inconsistencies, the ASC issued a revised version of SSAP6 in 1986. To avoid complications caused by the changed definition of extraordinary items, we restrict our attention to the period preceding the revision.

9 Judge et al. (1985, chap. 13) gives a helpful discussion of the basic technique. 10 We found that 37 companies reported extraordinary items in fewer than six years. In regressions with

extraordinary items separately identified, the corresponding firm-varying regression parameters were restricted to be constant across these companies. A similar procedure was followed for 21 companies that reported exceptional items in fewer than six years.




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Table 3 Median Time-Series Correlations of MMCAR and RETURN

with the Independent Variables

Dependent Variable

Independent Variables MMCAR RETURN

Pre-exceptional earnings yield 0.39 0.34

Pre-exceptional first difference 0.44 0.37

Exceptional earnings yield 0.00 -0.01

Exceptional first difference -0.04 -0.01

Extraordinary earnings yield 0.01 0.06

Extraordinary first difference 0.17 0.16

Note: The variables comprise the three components of all-inclusive earnings, each expressed in levels and first-difference form. Each is deflated by opening equity capitalization. N=all 146 companies.

centiles of the exceptional and extraordinary earnings yields show that many of these reported values are close to zero-50 percent are less than or equal to 1 percent in absolute value. It is also noteworthy that the extraordinary items have a negative skew, in contrast to the positive skew of exceptional items, which suggests a tendency to report large positive items as exceptional and large negative items as extraordinary.

Correlation Structure

The median time-series correlations of MMCAR and RETURN with the three earnings yield and three first-difference variables are given in table 3. The median value of the correlations for the two pre-exceptional variables are both appreciably greater than zero. Moreover, the 25th percentiles of the distributions are also positive. In contrast, the correlations of the variables for the extraordinary and exceptional items tend to be much lower. The median correlations for the two exceptional earnings variables are close to zero; although positive for the two extraordinary earnings variables, they are appreciably lower than the corresponding correlations for pre-exceptional earnings.

The median time-series correlation matrix for the six independent variables (table 4) exhibits four significant features:

1. The median correlations between the exceptional and extraordinary variables (levels and first differences) are all close to zero.

2. The median correlation between the first difference of pre-exceptional earnings and the pre-exceptional earnings yield, at 0.64, is moderately high.

3. The two exceptional variables have a tendency to be negatively correlated with the two pre-exceptional earnings variables. The extraordinary variables, however, exhibit a positive association. These are the kind of associations one would expect if exceptional and extraordinary items are used to "smooth" reported earnings per share.

4. The median correlation between the yield and difference variables is high for both exceptional and extraordinary items. Multicollinearity could prove to be a problem here.11

"In particular, it would be quite possible for the yield and differences variables to be jointly significant but for both individual t-statistics to be insignificant.




Table 4 Median Time-Series Correlation Matrix of the Main Independent Variables

Pre-Exceptional Exceptional Exceptional Extraordinary Extraordinary Difference Yield Difference Yield Difference

Pre-exceptional yield 0.64 -0.36 -0.22 0.14 0.09

Pre-exceptional difference -0.39 -0.52 0.04 0.11

Exceptional yield 0.74 0.00 0.01

Exceptional difference 0.01 0.01

Extraordinary yield 0.74

Note: The variables comprise the three components of all-inclusive earnings, each expressed in levels and first-difference form. Each is deflated by opening equity capitalization. N=all 146 companies.

Time-Series Properties

The first-order serial correlations of the three main earnings variables (undeflated levels) are shown in table 5. In contrast to pre-exceptional earnings, which exhibit strong positive serial correlation with a median value of 0.63, the exceptional and extraordinary items exhibit a median serial correlation close to zero. Moreover, the 75th percentiles of the distributions for the exceptional and extraordinary items lie below the 25th percentile of the corresponding distribution for pre-exceptional earnings. As an alternative test for persistence, we estimated the first-order serial correlations for the corresponding first differences. The median first-difference correlation for pre-exceptional earnings is - 0.01, close to zero. For exceptional and extraordinary earnings, the corresponding median correlations are -0.41 and -0.35, respectively, which shows strong evidence of mean reversion."2

The results suggest that pre-exceptional earnings exhibit a high degree of persistence but that the other two components are highly transitory. In conformance with the ideas of Kormendi and Lipe (1987) and Collins and Kothari (1989), these persistence comparisons lead us to hypothesize that, on average, the relation between stock price movements and extraordinary items should be broadly similar to the corresponding relation for exceptional items. Moreover, both of these relations should differ from the corresponding relation for pre-exceptional earnings. Because of these considerations, our general model separately identifies the exceptional and extraordinary components of earnings by allowing the response parameters to vary across components.

IV. Regression Results

The main findings of the study are reported in two subsections. The first shows the improvements in explanatory value achieved by successively moving toward the general econometric specification previously outlined. The second examines the signs and significance levels of the parameter estimates generated by our most general econometric model.

12 We also employed nonparametric procedures to test whether the distribution of the first-order serial correlations differed between the three earnings variables. Kolmogorov-Smirnov and Kuiper statistics, based on the empirical distribution function, rejected the null hypothesis that the distribution of first-order serial correlations for pre-exceptional earnings is the same as that for either exceptional or extraordinary earnings, at a significance level of 0.1 percent. The same test statistics were unable to reject the null hypothesis that the distributions of first-order serial correlations for exceptional and extraordinary items are the same (at well above standard significance levels).




Table 5

First-Order Serial Correlations of the (Undeflated) Earnings Variables

25th 75th Percentile Median Percentile

Pre-exceptional earnings 0.31 0.63 0.85

Exceptional earnings -0.17 0.01 0.24

Extraordinary earnings -0.09 0.05 0.29

Table 6

A Summary of the Differences Between Models for Which Adjusted R2 are Reported in Table 7

Time- Firm- Levels Model Varying Varying Variable Earnings

Number Parameters Parameters Included Disaggregated

MO No No No No Ml Yes No No No M2 Yes No Yes No M3 Yes No No Yes-tEIl, IE21, JEI1 M4 Yes Yes No No M5 Yes No Yes Yes-tElJ, tE2l, tE3l M6 Yes Yes No Yes-tE'J, tE2l, JE31 M7 Yes Yes Yes No M8 Yes Yes Yes Yes-tElJ, tE2+EI3 M9 Yes Yes Yes Yes-tE'+E2J, tE3l

M10 Yes Yes Yes Yes-tElJ, tE2l, tE3l

Model Selection

The 11 models for which results are reported are presented in figure 1 and summarized in table 6. The starting point for our analysis is MO, the basic earnings response model given by equation (1). This model was fitted to the entire (pooled) sample of observations with the first difference in all-inclusive earnings as the independent variable. The resulting R-squared values are reported in table 7 and provide a benchmark for comparison with the more refined models, Ml to M10.

The first refinement is given by model Ml, which allows the regression parameters of the basic model to vary over time. A number of researchers have established theoretical grounds for time-series variation in the earnings response parameter (see, e.g., Board and Walker 1990; Collins and Kothari 1989). In addition, the earnings response parameter will vary over time if the expectation benchmark for earnings is more accurate in some years than in others.

A comparison of the findings for Ml with those for MO reveals a marked improvement in R-squared under both MMCAR and RETURN. The improvement for MMCAR




Figure 1

A Summary of the Panel Regression Models

Given below is the full set of regression equations used in the research. All equations were estimated with both annual cumulative abnormal return (MMCAR) and annual unadjusted return (RETURN) as the dependent variable (denoted below as RiJ. The components of earnings identified are pre-exceptional earnings, El, exceptional earnings, E2, and extraordinary earnings, El. Where appropriate, the equations are given in increasing order of generality.

3

E (El,,-El,-,) R,,=a+b ri +ui (MO)

'1it-1

3

(El,- -E1) R,,=a,+b,

i +u,, (Ml)

3 3

1 E',,-E',-,) E El, R,, = a.,+ b, j 1 +ct i-1 + u,, (M2)

V'it- Vl.-1

Ri =at+ (bf hi- + it+ (M3)

33

(E',,-E',-, )

R,=a, +(b,+b) j1 +(u,, (M4)

R,=, EJf Ei-EJi 3

SC EJ, 5 =1 V,.~~-1 l V,

R., =a, + E (b', +t b>) Ec + u, , ( M6)

}s 1 V ,,_1 Vi=2

Ri,=a,+ E~bJ iJ-I- + U(b(+b)

3 3

1: (E E',t- E',,S ) El,,

R,.=a.+ (b,+b,) V= + (c,+c, CJj- +u,, (M7)

Vit-1 Vit-I 3

E~~~~ E f,

+ it , + C + ( C_ + +u (M8) E it ji

R,,-,+(,+b) =1 +(b,3+b,) " + (c,'+ c,) ~~+ (c,3+c3 " + U1, (M9) Vit -I Vt1-

2 v-it-i~ ~~~33StEi-

II~a+~b+~ + C'+(c) t+c +Uh (M1O)




Table 7

Adjusted H-Squared Values of the Models

Dependent Variables

Regression Models MMCAR RETURN

MO 0.1028 0.0659 Ml 0.1943 0.3753 M2 0.2083 0.3920 M3 0.2195 0.3940 M4 0.2386 0.4141 M5 0.2412 0.4134 M6 0.3059 0.4758 M7 0.2737 0.4796 M8 0.3142 0.5069 M9 0.3359 0.5240 M10 0.3823 0.5454

Note: The independent variables comprise various disaggregations of all-inclusive earnings, in first difference or levels form or both. These are deflated by opening equity capitalization, and various degrees of temporal and cross-sectional variation are modeled.

is broadly consistent with the findings of previous studies based on U.S. data. A more dramatic increase in R-squared occurs with RETURN as the dependent variable because, in addition to the factors that cause the regression parameters to vary under MMCAR, a considerable proportion of the time-series variation in individual company returns is "explained" by the market; in model Ml, the temporal variation in the market return is captured by the time-varying intercept.

The remaining results for models M2 to M10 in table 7 incorporate various combi- nations of refinements over and above those captured by model Ml. These results allow us to assess the individual and joint effects of incorporating (1) firm variation in the independent variable response parameters, (2) earnings yield variables, and (3) earnings disaggregation. We first consider the individual effects of these three additional refinements, then the joint effects of incorporating two or more of the refinements.

Comparing the findings for models M2, M3, and M4 with those for model Ml shows that moderate improvements in R-squared are achieved by all three methodological refinements under both MMCAR and RETURN. Conventional analysis of covariance (F-) tests confirmed that the increases in R-squared of models M2, M3, and M4 over Ml are significant at the 1 percent level under both MMCAR and RETURN.13

Models M5, M6, and M7 show the joint effect of introducing two of the three model refinements. Analysis of covariance tests were performed to compare these models with their nested counterparts in models M2, M3, and M4.14 These tests showed that significant improvements in explanatory power at the 1 percent level are achieved for both dependent variables in M5 over M2 and M3, M6 over M3 and M4, and M7 over M2 and M4.

13 See Harvey (1990, 61-64) for further details. 14 A model is a nested version of another if it can be derived by imposing appropriate restrictions on the

parameters of the other model. See Judge et al. (1985, chap. 21), for details,




The effect of incorporating all three methodological refinements into our general model was assessed by comparing model M10 with models M5, M6, and M7. Analysis of covariance tests rejected M5, M6, and M7 in favor of model M10 at a significance level of 1 percent for both MMCAR and RETURN. Thus, adding any one of the three methodological refinements yields a further significant improvement in explanatory power. Overall, these tests identify M10 as the most appropriate model of the relation between returns and earnings. Moreover, the improvement in explanatory power generated by moving from the basic earnings response model, MO, to the general model, M10, suggests that the low R-squared values reported in the research surveyed by Lev (1989) can, to a significant extent, be attributed to the restrictive research designs in early studies.

Finally, for sake of completeness, we investigated the comparative explanatory value of three alternative forms of earnings disaggregation via comparisons of model M10 with models M8, which aggregates exceptional and extraordinary items but sepa- rates these from pre-exceptional earnings, and M9, which distinguishes between ordinary and extraordinary earnings. Examination of M8 is motivated by our earlier results on the time-series properties of the three earnings components; examination of M9 follows from the standard accounting practice in the United Kingdom of separating extraordinary items from ordinary earnings. Conventional analysis of covariance tests selected M10 over both M8 and M9 under both MMCAR and RETURN at a significance level of 1 percent. These results suggest that the market-pricing process for exceptional items is different from the pricing process for both pre-exceptional earnings and extraordinary items.15

Parameter t-Values and Hypothesis Tests

Since the number of parameter values generated by M10 is large (869), the analysis focuses on hypothesis tests relating to the average value of the parameters across firms and over time. Table 8 shows the significance of the average values, across firms and time, of the regresssion slope parameter estimates generated by fitting model M10.16 The results are similar under both dependent variables.17 The significance of both pre- exceptional earnings yield and pre-exceptional first difference suggests that the specification of the conventional earnings response model is improved by incorporating a yield variable.

None of the other four variables is significant at conventional levels under either MMCAR or RETURN, a result apparently contradicting the earlier finding that model M10 provides a better fit to the data than model M8. One possible reason for this lack of significance is the multicollinearity noted in the discussion of table 4. To test this, we conducted further t-tests for the joint significance of the yield and first-difference pa-

1S For completeness, we also ran the alternative regression to M8 and M9 by aggregating pre-exceptional earnings (El) and extraordinary items (E3) but separating exceptional earnings (E2). The R-squared for this regression was 0.3066 for MMCAR and 0.5012 for RETURN.

16 Bernard (1987, 13) discusses the severe problems for hypothesis testing that arise from cross-sectional dependency in the residuals when models impose cross-sectional homogeneity in the response coefficient. By allowing for cross-sectional variation, M10 should substantially reduce the problem of cross-sectional dependence.

17 The remaining problem of serial correlation in the residuals could lead to upwardly biased t-values when RETURN is the dependent variable. However, the similarity of the findings for RETURN and MMCAR is reas- suring.




Table 8

Average Values of the Regression Slope Parameters for Model M1O

Dependent Variable

Independent Variable(s) MMCAR RETURN

Pre-exceptional earnings yield 1.59** 1.67**

Pre-exceptional earnings difference 1.85** 1.92**

Exceptional earnings yield 1.48 0.49

Exceptional earnings difference 2.51 3.85

Extraordinary earnings yield -0.37 0.90

Extraordinary earnings difference 0.60 -0.60

Exceptional earnings yield and difference 2.00* 2.17**

Extraordinary earnings yield and difference 0.11 -0.05

Note: The test determines whether the average firm slope parameter corresponding to a particular independent variable (or variables) is significantly different from zero when the slope parameter for an individual firm is given by its firm-varying component for those years the firm was in the sample. All tests used the full variance-covariance matrix of parameter estimates from model M10.

rameters for both exceptional and extraordinary earnings (see table 8). The important additional result to emerge is rejection of the null hypothesis that the exceptional yield and difference variables taken jointly are, on average, insignificantly different from zero.18

V. Conclusions

The evidence in this study suggests that a significant improvement in the statistical performance of models of earnings and returns can be achieved by allowing for time- series and cross-sectional variation in the regression parameters, by including an earnings yield variable along the lines suggested by Ohlson (1989), and by partitioning all- inclusive earnings into pre-exceptional, exceptional, and extraordinary components. The evidence that the pre-exceptional earnings yield variable is statistically significant on average further suggests that pre-exceptional earnings exhibit both permanent and transitory features and that models of the relation between earnings and returns that focus exclusively on the deflated first difference of earnings are misspecified,

18 Shortly before publication we found that Datastream Item 175 excluded certain exceptional items in some of our sample company years. We re-estimated the models using Datastream Item 182, which includes all exceptional items. Model M10 still emerged as the best model with R-squared values marginally higher than those reported in table 6. The pre-exceptional earnings yield variable was more significant than reported above and was the only variable to be statistically significant on average. Further details are available from the authors on request.



Strong and Walker- Power of Earnings 399

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