earnings forecasting

Earnings Forecasting Models: Adding a Theoretical

Foundation for the Selection of Explanatory Variables

by John E. Sneed

John Sneed is Assistant Professor, College of Business and Technology, Department of Accounting/Finance, University of Nebraska at Kearney, West Center E200,Kearney,NE 68849-4420, USA.

1. Introduction

The purpose of this study is to determine if an earnings forecasting model based on factors hypothesised to result in differential profits across firms (industries) reduces model error relative to the model developed by Ou (1990). Initial research attempting to forecast earnings found that the random walk model, where current year's earnings are the prediction for next year, provides the best forecast of annual earnings (Ball and Watts 1972; Foster 1973; Beaver, Kettler, and Scholes 1970; Albrecht, Lookabill, and McKeown 1977; Brealey 1969). Ou (1990) developed an earnings forecasting model using financial statement information beyond prior years' earnings as the explanatory variables that outperformed the random walk model in predicting annual earnings.

While Ou (1990) identified a set of financial statement variables that improved predictive performance relative to the random walk model, other researchers question the validity of her variable selection process. Greig (1991) argues there is no theoretical support for the accounting descriptors used in Ou's model. The statistical variable selection process originally used by Ou and Penman (1989) and used again by Ou (1990) in developing her earnings forecasting model indicates the potential existence of the "data snooping" bias discussed by Dimson and Marsh (1990). "Data snooping" occurs when the relationships in a data set influence the researcher's choice of model specification. While "data snooping" may be useful in exploratory analysis, the forecast accuracy of models developed in this manner can be overstated.

The lack of theory in selecting the variables also makes it difficult to interpret the results or to determine their significance. It is difficult to predict the effect of variables on earnings without a theoretical basis to determine the expected results. The results could be driven by a causal relationship or by misspecification in the selected models (Greig 1991).

Ou and Penman (1992) state that their earlier analysis (1989) was an empirical analysis, with no contextual basis for the approach. They argue that, without guiding principles, their framework cannot be embraced as a prescription for fundamental analysis. The first objective of this article is to incorporate a theoretical framework in selecting variables to be included in an earnings forecasting model and to determine if this model outperforms Ou's model.

42 Management Research News

Little theory is currently available in the accounting literature for identifying accounting information that is useful in predicting future earnings, with the exception of prior years' earnings. However, the economics literature has identified factors believed to be responsible for the existence of excess profits for some firms/industries in the long-run. Excess profits are defined, in this literature, as profits above the overall market rate of return. The factors responsible for the existence of excess profits in the long-run also should be significant in forecasting future earnings. I will determine if a theoretically developed earnings forecasting model, using the factors believed to be responsible for the existence of excess profits in the long-run as the explanatory variables, reduces model error relative to Ou's model.

Bernard (1993,2) states "the reliance of capital markets research on stock prices to divine Value-relevant' factors is not only unnecessary, but limited in its ability to address at least one of the key issues in financial statement analysis: improving on current profitability as a predictor of future profitability." Some studies have had limited success in predicting changes in return on equity or earnings (Freeman, Ohlson, and Penman 1982; Ou and Penman 1989; Ou 1990). However, much of the success is due to the mean reversion in the earnings measure. The key question is to determine what beyond current return on equity would help in predicting future earnings (Bernard 1993).

Ou's (1990) model incorporates prior years' earnings as well as additional financial statement variables, finding that these additional variables improve the performance of the model. However, as mentioned earlier, the variables were selected using statistical techniques. The second objective of this article is to determine if the theoretically selected variables also improve the performance of the model when added with prior years' earnings.

I will combine the variables in the theoretically selected model with the variables capturing prior years' earnings from Ou's model to determine if the theoretically selected variables add explanatory power to prior years' earnings. I also will compare the accuracy of this model to Ou's model to determine if the theoretically selected variables perform as well as Ou's statistically selected variables after controlling for prior years' earnings.

The results of the analysis indicate that Ou's model, including prior year's earnings, consistently outperforms the theoretically selected model, which does not include prior years' earnings. However, when prior years' earnings are added to the theoretical model, the two models performance is approximately equal. This finding supports the conclusion that the theoretically selected variables perform as well as Ou's statistically selected variables after controlling for prior years' earnings.

2. Importance of the Study

The importance of earnings forecasts is indicated by the significance of earnings expectations in firm valuation, security selection, and cost of capital models. Accurate valuation analysis and cost of capital estimation techniques are depend-

Volume 19 Number 11 1996 43

ent on the accuracy of earnings forecasts (Chatfield, Moyer, and Sisneros 1989). Chang and Most (1980) found earnings and dividends forecasts, and the growth rates in these forecasts, to be key inputs in investor decision models. Because evidence exists that users of accounting information include earnings forecasts in making financial decisions, improved earnings forecasts will improve the information set available to the decision maker. The importance of earnings forecasts has resulted in substantial research attempting to develop an optimal earnings forecasting model.

3. Ou's Earnings Forecasting Model

Ou (1990) developed an earnings forecasting model by statistically selecting variables that were associated with future earnings. Her earnings forecasting model is specified as follows: ROAi,t+1 . = BO + B1GWINVNi,t + B2GWSALEi,t

+ B3CHGDPSi,t + B4GWDEPi,t + B5GWCPXli,t + B6GWCPX2i,t, + B7RORi,t + B8CHGRORi,t + Ei,t

where: ROA = earnings before interest and taxes/total assets;

GWINVN = percentage growth in the inventory to total assets

ratio;

GWSALE = percentage growth in the net sales to total assets ratio;

CHGDPS = change in dividends per share, relative to that of the

previous year;

GWDEP = percentage growth in depreciation expense;

GWCPX1 = percentage growth in the capital expenditures to total assets ratio;

GWCPX2 = GWCPX1, with a one-year lag; ROR = the accounting rate of return, i.e. income before

extraordinary items divided by total owners' equity as of the beginning of the year;

CHGROR = change in ROR, relative to the previous year's ROR;

E = error term;

i = firm;


t = year. Most of these independent variables have been tested previously, either directly or indirectly, in information content studies predicting future firm attributes (Ou 1990).

The future earnings amount (ROA) is defined as earnings before interest and taxes, or "regular income" (Financial Accounting Standards Board (FASB) 1979). The FASB (1979), as part of the conceptual framework project and (1979a) as justification for disclosing holding gains and losses separate from continuing operations, recognised the need for disclosure of and research on the descriptive power of "regular income" based on its decision-usefulness potential (Stewart 1989).

Ou and Penman (1992) argue that the task of determining "intrinsic values" is one of predicting future earnings and assessing the rate at which they should be capitalised. They argue that value should be based on operating activities but be independent of financing and investing activities.

Accurate forecasts of income from continuing operations should provide additional information to the users of financial statement information when making investment decisions. Earnings before interest and taxes is the future earnings amount used in this analysis. This variable is scaled by total assets to permit cross-sectional comparisons. This variable will be the dependent variable for both Ou's model and the theoretically specified model.

4. Theoretical Development of an Earnings Forecasting Model

Having found that differential profits exist across firms and across industries in the long-run, economists have attempted to find an explanation for the persistence of excess profits. Incorporating the factors that result in differential profits into an earnings forecasting model should improve the accuracy of the forecasts. I will include the factors identified by economists as being responsible for differential profits in an earnings forecasting model to determine if they reduce model error relative to Ou's model.

4.1 Improper Measurement of Profits

One explanation of differential profits is that excess profits appear to exist because accountants fail to properly measure profits, and more importantly assets (Weiss 1969; Block 1974; Ayanian 1975). Among other measurement problems, they argue that accountants fail to account for the intangible capital created by advertising and research and development (R&D) expenditures (Megna and Mueller 1991).

These studies assume advertising and R&D expenditures are capital expenditures, where the benefits accrue over multiple periods and exceed the value of the expenditures in the period that they occur. They argue that a proper accounting of the capital-like nature of these expenditures would eliminate observed differences in profitability rates across firms, as well as observed differences in mean industry rates (Megna and Mueller 1991).


However, Megna and Mueller (1991) found that adjusting for the capitallike nature of advertising and R&D expenditures did not eliminate profitability differentials across firms or across industries. Their results supported the assumption that R&D expenditures provide long-term benefits, finding long-term benefits in all four industries examined. However, the results on advertising expenditures are mixed, as the expenditures only provided long-term benefits in two of the four industries examined. Their results suggest that additional factors are responsible, in part, for the existence of excess profits.

4.2 Differential Returns on Intangible Capital

A second potential explanation for the existence of differential profits is that firms may earn different returns on investments in intangible capital, like R&D and advertising. Most prior studies assume the relationship between advertising and R&D expenditures and the benefits they provide is the same across all firms in an industry, and often assume the relationship is the same across industries (Megna and Mueller 1991). This assumption is based on treating intangible capital like physical capital.

For physical capital, with constant returns to scale, each additional machine produces the same output as the previous machine of the same type. If markets are competitive, each additional machine will earn the same revenue as the one before. If all firms have equal access to product and capital goods markets, equalising costs, each firm within an industry receives the same marginal revenues (profits) from capital goods expenditures. If R&D and advertising expenditures have the same effects as capital goods expenditures, each firm/industry should receive the same marginal revenue for the expenditures.

However, the assumptions of constant returns and perfect competition are inappropriate when advertising and R&D are important activities in the competitive process. Advertising and R&D are information creation and distribution activities used to differentiate products. Information is a good whose production and distribution cannot be modeled using constant returns assumptions, since the value of its output is subjective. The absence of constant returns will result in different relationships between firms5 sales or profits and investments in advertising and R&D (Megna and Mueller 1991).

Megna and Mueller (1991) found that advertising and R&D expenditures significantly influence future earnings, with the influence varying across firms and across industries. I will include advertising and R&D expenditures in the earnings forecasting model to capture differential returns on expenditures for intangible capital.

When incorporating these variables in an earnings forecasting model, it is important to match the expenditures to the benefits they provide. Empirical research consistently finds a lagged relationship between the timing of R&D expenditures and when benefits occur (Ravenscraft and Scherer 1982; Branch 1974; Hirschey 1982; Hirschey and Weygandt 1985; Bublitz, Frecka, and McKeown 1985; Bublitz and Ettredge 1989; Megna and Mueller 1991). These


studies consistently find a lagged relationship between the timing of R&D expenditures and the related increases in revenues. Ravenscraft and Scherer (1982) found a lag of four to six years.

Based on the lagged relationship between R&D expenditures and the benefits they provide, I will use the average R&D expense over a five-year period to capture the effects of the lag between the expenditures and the benefits they provide. The five-year period was selected based on the results from earlier studies (Ravenscraft and Scherer 1982; Megna and Mueller 1991). This lag relationship could explain why Lev and Thiagarajan (1991) did not find the anticipated relationship between market returns and R&D expenditures, using only current year expenditures.

Empirical research on the relationship between advertising expenditures and the benefits they provide finds inconsistent results (Schmalensee 1972; Norris 1984). Some recent studies find a lag relationship between advertising expenditures and the benefits they provide (Hirschey 1982; Hirschey and Weygandt 1985). However, later studies extending the earlier studies do not support the longevity of benefits from advertising expenditures (Bublitz, Frecka, and McKeown 1985; Bublitz and Ettredge 1989). Megna and Mueller (1991) found that advertising expenditures did not provide long-term benefits in two of four industries examined. Since most recent studies fail to support the longevity of benefits from advertising expenditures, I will include advertising expense for the year prior to the forecast year in the model.

The advertising and R&D expense variables both will be scaled by sales to allow cross-sectional comparability. Both variables should have a positive relationship with future earnings as firms make these expenditures expecting to increase earnings.

4.3 Existence of Market Power

A third explanation for differential profits is that firms earn excess profits because they have market power that results in less than perfect competition (Collins and Preston 1968; Comanor and Wilson 1967; Porter 1974; Weiss 1974). Prior studies find differences in profitability related to differences in market share, a measure of market power (Shepherd 1972 and 1975; Ravenscraft 1983; Mueller 1986).

Researchers have found that firms with larger market shares earn higher returns on capital expenditures (Ravenscraft 1983; Caves and Pugel 1980). Some argue that this result occurs because larger firms have superior investment opportunities that are not available to smaller firms. Therefore, larger firms should earn excess returns on capital expenditures (Baumol 1967; Hall and Weiss 1967).

If large firms earn excess profits on capital expenditures, due to superior investment opportunities, including capital expenditures in an earnings forecasting model will help capture differences across firms. Since capital expenditures, like R&D expenditures, provide long-term benefits, I will use the five-year


average of capital expenditures in the model. This variable is scaled by net fixed assets to allow cross-sectional comparability. This variable should have a positive relationship with future earnings as larger firms would have superior investment opportunities while having higher levels of capital expenditures.

Other economic studies argue that large firms earn excess profits due to efficiency differences (Demsetz 1973; Carter 1978; Mueller 1986). These studies argue that firms maintain excess profits in the long run because they operate more efficiently than their competitors. The efficiency is usually argued to result from economies of scale, where larger firms achieve lower costs (Hall and Weiss 1967; Scherer 1973).

If larger firms operate more efficiently due to economies of scale, their costs should be lower relative to sales. I will include the cost of goods sold divided by sales variable in the model to capture the effects of firm efficiency. This variable should have a negative relationship with future earnings, since higher costs imply that a firm is operating inefficiently.

4.4 Firm-Specific Risk

A fourth explanation for differential profits is firm-specific risk, where firms arc being rewarded with higher profits for bearing above average risk. Higher risk firms should exhibit greater earnings variation than lower risk firms. Models forecasting earnings need to incorporate a measure of risk to capture this variability.

Different proxies have been used in the literature to measure risk. Based on earlier studies, Megna and Mueller (1991) used the ratio of firms' equity to total assets to measure the effects of risk in firms' returns on assets (Hall and Weiss 1967; Baker 1973; Bothwell, Cooley, and Hall 1984).2 They found that firm-specific risk was positively associated with profits. I expect the relationship between risk and profitability to be positive in my model, as firms will be rewarded for bearing higher levels of risk.

Based upon the above discussion, the earnings forecasting model is specified as follows:

ROAi,t+1 = BO + BlRKi,t + B2RDi,t + B3AEi,t + B4CEi,t + B5CGSi,t + Ei,t

where:

ROA = earnings before interest and taxes/total assets;

RK = equity/total assets;

RD = five-year average R&D expense/sales;

AE = advertising expense/sales;


CE = five-year average capital expenditures/net fixed

assets;

CGS = cost of goods sold/sales;

E = error term;

i = firm;

t = year. This model identifies variables that capture the factors that economists

believe are responsible for differential profits in the long run. If the economists are correct, these variables should be significant in predicting earnings. The RD, AE, and CE variables are expected to have a positive relationship with earnings, as firms are expected to make money on these expenditures. The RK and CGS variables are expected to have a negative relationship with earnings, as the RK variable is an inverse measure of risk. 5. Methodology for the Analysis

Ou (1990) developed an earnings forecasting model, incorporating financial statement information beyond prior years' earnings, that outperformed the random walk model in forecasting annual earnings. However, Ou's model has been criticised in the literature because she statistically selected the variables to be included in the model. The first objective of this study is to theoretically select the variables to be included in an earnings forecasting model and to determine if this model outperforms Ou's model. This issue was examined by comparing the forecast accuracy of Ou's model with the forecast accuracy of the economic model.

Bernard (1993) argues that a key element of financial statement analysis is improving on current profitability as a predictor of future profitability. Ou's model included a measure of the current year earnings (ROR) as well as prior years' earnings (CHGROR). The economic model does not include measures of prior years' earnings, which weakens its predictive ability. The variables capturing prior years' earnings (ROR and CHGROR) were added to the economic model, and the explanatory power of this model also was compared to Ou's model.

The data for the analysis include observations from the oil exploration (SIC 1311), electronic computers (SIC 3571), and eating places (SIC 5812) industries for the years 1979 to 1988. Prior research (Sneed 1995a) indicates that industry-specific models improve forecast accuracy relative to combining firms from different industries in the same model. These three industries were selected for the analysis because there were enough firms in each industry to fit industry-specific models when classifying industry at the four-digit SIC level.


Each of the three models (Ou, Economic, Combined) is estimated on an industry-specific basis for the ten-year period 1979 to 1988. Since the error of each model is an indirect measure of the forecast error that would have occurred if the model had been used to forecast earnings for this period of time, the adjusted R2 is used to measure the accuracy of each model. The adjusted R2 s from the three models are compared for each industry to determine which model provides the best forecast of annual earnings.

Prior research (Sneed 1995 b) also indicates that segmenting earnings forecasting models into shorter time periods reduces model error relative to estimating the model over longer time periods. For this analysis, I segmented each industry-specific model into three time periods: 1986-1988; 1982-1985; 1979-1981. These time periods were selected based upon economic conditions during these periods.

Each of the three industries would have three models, one for each time period, resulting in a total of nine models. However, there were not enough observations to estimate an earnings forecasting model for the electronic computers industry for the 1979-1981 time period, so there are only eight models included in the analysis. The forecast accuracy (adjusted R2 ) of the three models (Ou, Economic, Combined) are compared for each industry/time-pe-riod to determine which model provides the best forecasts of annual earnings.

6. Results and Conclusions

Table 1 presents the adjusted R2 for the three different forecasting models, using industry-specific models. The model for the oil exploration industry used the 511 observations over the 1979 to 1988 period. The 73 observations over the 1982 to 1988 period were used for the model of the electronic computers industry. For the eating places industry, 283 observations from the 1979 to 1988 period were used to estimate the model.

For all industry-specific models analysed, Ou's model substantially outperforms the economic forecasting model. The lowest adjusted R2 for Ou's model is 25.3 percent, while the highest adjusted R2 for the economic model is 20.9 percent. The combined model, adding the ROR and CHGROR variables to the economic model, is more accurate than Ou's model for two of the three industry-specific models. However, the differences between these two models are fairly small.

Table 2 presents the adjusted R2 of the different models for the oil exploration industry, partitioning each model into three time periods. Ou's model substantially outperforms the economic model for all three time periods. Ou's model also outperforms the combined model for two of the three time periods. Again, the differences between the combined model and Ou's model are fairly small.

Table 3 presents the adjusted R2 for the models of the electronic computers industry, using the models partitioned by time. Ou's model outperforms the economic and combined models for the 1986 to 1988 time period, but does


not perform as well as either model for the 1982 to 1985 time period. The interpretation of the results from models in this industry is limited by the small sample sizes for the two time periods.

Table 4 presents the adjusted R2 for the models of the eating places industry, using the models partitioned by time. Ou's model outperforms the economic model in all three time periods. Ou's model also outperforms the combined model in two of the three time periods, with a substantial difference for the 1982 to 1985 period. The average adjusted R2 for each model across all the estimated models is summarised as follows:

Model Ou Economic Combined

Averaged Adjusted R2

.3119

.1683

.3055

The primary conclusion from this analysis is that Ou's model substantially outperforms the economic model in forecasting earnings, providing superior results in ten of the eleven models examined. However, the economic model does not include variables to capture prior years' earnings, which provide the majority of the explanatory power in Ou's model. Of the eleven models examined, Ou's model outperforms the combined model in six cases, while the combined model is superior in the other five. Also, the mean adjusted R2 for the two models across all models estimated are very close. This result suggests that the theoretically selected variables, when combined with variables to capture the effects of prior years' earnings, perform as well as the statistically selected variables. The improvement in the explanatory power of the economic model when the ROR and CHGROR variables are added indicates the importance of including variables to capture prior years' earnings in an earnings forecasting model.


Endnotes

1. For surveys of this literature, see Hopwood and McKeown (1986) and Bao, Leis, Lin and Manegold (1983).

2. They also considered the variance of firms' profitability to proxy for firm-specific risk, but this proxy had weaker explanatory power than the equity to total asset ratio.

3. Concentration ratio had been argued to be a determinant of excess profits. However, Ravenscraft (1983) and Amato and Wilder (1985) find that, when market share (size) is included in the model, the influence of the concentration ratio is weak.

4. As mentioned earlier, the 1979 to 1981 time period was omitted from the analysis for the electronic computers industry since there were only a few observations for this period.

5. There were 42 observations for the 1986 to 1988 period and 31 observations for the 1982-1985 period.


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Table 1: Comparisons of Forecast Accuracy (Adjusted R-Squared) Industry-Specific Models:

1979-1988

Ou's Model Economic Model Combined Model N

Oil Exploration .253 .108 .285 511

Electronic Computers .353 .209 .392 73

Eating Places .272 .099 .236 283

Table 2: Comparisons of Forecast Accuracy (Adjusted R-Squared) Oil Exploration Industry


1986-1988 .201 .144 .281 216

1982-1985 .304 .078 .232 175

1979-1981 .251 .065 .240 120

Table 3: Comparisons of Forecast Accuracy (Adjusted R-Squared)

Electronic Computers Industry


1986-1988 .488 .299 .477 42

1982-1985 .105 .328 .342 31

Table 4: Comparisons of Forecast Accuracy (Adjusted R-Squared)

Eating Places Industry


1986-1988 .235 .233 .328 106

1982-1985 .546 .055 .159 104

1979-1981 .423 .233 .389 73
