PROBABILISTIC NATURE OF ACCOUNTING EARNINGS:
MACROECONOMIC INFLUENCE
AND EX ANTE PREDICTION
BY
PAUL R. WELCH
A DISSERATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
1981
Copyright 1981
by
Paul R. Welch
TABLE OF CONTENTS
PAGE
LIST OF TABLES ................... ...........*********************** vii
LIST OF FIGURES .............................************** x
ABSTRACT....................************************ xi
CHAPTER
ONE INTRODUCTI ON ...........................********** 1
Background and purpose of the research.............. 1
Motivation.................................. 1
Earnings prediction problems................... 2
Problems of prior studies................. 2
Problems in evaluating earnings forecasts. 3
Research Contribution.............................. 3
Influence of macroeconomic variables.......... 3
Timeseries model performance update........... 4
OverLview............................. ******** 5
Scope of the research.......................... 5
Important Definitions.......................... 6
Chapter organization........................... 8
TWO LITERATURE REVIEW ................................***** 9
Background and motivation........................... 9
Literature on the time series properties of earnings 13
Empirical works................................ 14
Annual results............................ 14
Quarterly results......................... 15
Predictions of management and analysts.... 16
Synthesis of time series research.............. 18
Use of economic variables and index models.......... 20
Prior support for use of macros................ 20
Hopwood................................. 21
Lev...................................... 23
Econometric models........................ 24
Causal modeling approach............................ 26
Note to Chapter Two...,.............................. 28
THREE EPISTOMOLOGICAL ISSUES................................... 29
Evaluation of forecasts............................. 29
Management forecasting systems................ 30
Review of financial forecasts.................. 31
Interaction of reported information
and future events......................... 33
Issue of accountant interference............... 34
Types of probabilistic data.................... 36
Practical issues in earnings forecasting............ 41
The model versus the method.................... 41
Interaction of economic events................. 42
Practical issues..............................* 43
FOUR METHODOLOGY AND PRELIMINARY INVESTIGATION................ 51
Overview of research methodology.................... 51
Distributed lag methodology features........... 52
Updating process............................... 54
Model comparison statistics.................... 55
Hypotheses................................. 56
Nature of the data sets............................. 60
Experimental samples........................... 60
Annual sample #1.......................... 60
Annual sample #12....................,..... 60
Quarterly sample.......................... 61
Macro economic data............................ 62
Annual macro data set..................... 63
Quarterly macro data set.................. 63
Research design.................................... 63
Annual research design......................... 63
Annual DLWM model......................... 65
Predicting the exogenous macroeconomic
variables............................ 66
Comparison models......................... 70
Procedures for sample #1.................. 71
Procedures for sample #2.................. 73
Annual hypotheses......................... 74
Quarterly research design...................... 78
Quarterly DLWM models........,............. 78
Prediction of quarterly macro variables... 79
Comparison models......................... 80
Procedures............................... 81
Quarterly hypotheses...................... 82
Computing systems utilized..................... 83
Notes to Chapter Four................................ 83
FIVE EMPIRICAL WORK AND RESULTS............................... 85
Annual sample #F1 results............................ 86
Overview...................... ................. 86
MSE results................................... 91
Specific industry results................. 91
Sensitivity of M~SE results................ 97
MAbsE results................................ 98
Specific industry results................. 98
Error truncation findings.................102
Summary of annual sample #1....................102
Annual sample #2 results............................118
Industry 3531 results..........................118
Results based on mnean square error.......118
Results based on absolute error..........120
Results based on absolute percent error..120
Industry group 3550/3560 results...............123
Results based on mean square error.......123
Results based on absolute error..........125
Results based on absolute percent error..125
Industry group 3711/3713 results...............127
Results based on mean square error.......127
Results based on absolute error..........129
Results based on absolute percent error..129
Summary of annual sample #2 results............129
Summary of industry 3531..................132
Summary of industry group 3550/3560.......137
Summary of industry group 3711/3713.......137
Quarterly results..................................14
Industry 3531 results..........................148
Results based on mean square error.......148
Results based on absolute error..........151
Results based on absolute percent error..151
Industry 3550 results..........................152
Results based on mean square error.......152
Results based on absolute error..........155
Results based on absolute percent error..155
Industry 3560 results.........................,.157
Results based on mean square error.......157
Results based on absolute error..........157
Results based on absolute percent error..157
Industry 3711/3713 results.....................159
Results based on mean square error.......159
Results based on absolute error..........159
Results based on absolute percent error..159
Summary of the quarterly results...............162
Summary of empirical work and results...............171
SIX SUMMARY AND CONCLUSIONS ................... ...............189
Summary.................................8
Dyerview of results....,........................189
Evaluation of the results......................190
Conclusions...................................19
Value of the approach..........................193
Extensions.................................. 19
Extensions relating directly to
limitations of the currect study.....193
Extensions relating to further model
specification........................195
Specific Conclusions...........................195
BIBLIOGRAPHY...... ....................***************9
APPENDIZCE S
A LIST OF FIRMS IN ANNUAL SAMPLE #1...........................211
B LIST OF FIRMS IN ANNUAL SAMPLE #2...........................214
C LIST OF FIRMS IN QUARTERLY SAMPLE...........................215
D ANNUAL HYPOTHESES.....................................21
E QUARTERLY HYPOTHESES................................... 21
F SAMPLE #2 RESULTS WITH STANDARD DEVIATIONS ..................2 19
G PROGRAM TO PRODUCE ANNUAL PREDICTIONS (Sample #2)...........222
H PROGRAM TO PRODUCE QUARTERLY NON BOXJENKINS PREDICTIONS....227
BIOGRAPHICAL SK~ETCH.........................................23
LIST OF TABLES
Table Page
31 Industry Ranking by Energy Consumption .............******* 47
32 Selected Industry Lapact of Restatement ...~................ 48
33 Mean Absolute Percentage Error by Industry ................ 49
34 Systhesis of Economic Literature ...................... 50
41 Summary of Empirical Work ........................... 59
42 Annual Four Stage Least Squares for PRW10 and PRW11 ....... 67
43 Annual Models .....................********************** 68
44 Annual Sample #1 Design ................................... 69
'45 Annual Sample #2 Design .................******************* 76
46 PRW11 Prediction Equations ................**************** 77
47 Summary of the Prediction Quarters and Horizons ........... 84
48 Sample Size for Each Stratum of Quarterly Sample #2 ....... 84
51 Mean Squared Error for Each Stratum of Sample #1 .......... 92
52 Summary of MSE Results for Sample #1 ...........*********** 94
53 Annual Sample #1 Mean Square Error Rankings for Each Model. 95
54 Mean Absolute Error for Each Stratum of Sample #1 ......... 99
55 Annual Sample #1
Mean Absolute Error Rankings for Each Model ..........100
56 Mean Squared Error for Each Stratum of Capital/Durable
Goods Firms ...................*********************.10
57 Mean Squared Error for Each Industry/Horizon Combination ..104f
58 Mean Squared Error for Each Stratum of Sample #1
Absolute Error less than $100 ............*************10
59 Mean Squared Error for Each Industry/Horizon Combination
Absolute Error less than $100 ...................107f
vii
Table Page
510 Sensitivity Test 2 on MSE Results..............*************109f
511 Mean Absolute Error for Each Stratum of Capital/Durable
Goods Firms ......*********************************** 111
512 Mean Absolute Error for Each Industry/Horizon Combination 112f
513 Mean Absolute Error for Each Stratum of Sample #1
Absolute Error less tah $100 .................... 114
514 Mean Absolute Error for Each Industry/Horizon
Combination Absolute Error less than $100 ......... 115f
515 Mean Absolute Error Outlyer Firms Eliminated ........... 117
516 MSE Wilcoxon Significance Tests Industry 3531 ............ 119
517 MAbsE Wilcoxon Significance Tests Industry 3531 ........ 121
518 MSE Wilcoxon Significance Tests Industry 3550 and 3560 .. 124
519 MAbsE Wilcoxon Significance Tests Industry 3550 and 3560 126
520 MSE Wilcoxon Significance Tests Industry 3711 and 3713 .. 128
521 MAbsE Wilcoxon Significance Tests Industry 3711 and 3713 130
522 Ranking of Each Model for all Strata of Sample #2 ........ 131
523 H~ypothesis Summary MSE (legend p. 134) .................. 133
524 HIypothesis Summary MAbsE ............................... 135
525 Mean Squared Error Industry 3531 ........................ 139
526 Mean Absolute Error Industry 3531 ........................ 140
527 Mean Absolute Percent Error Industry 3531 ............... 141
528 Mean Squared Error Industry 3550 and 3560 ............... 142
529 Mean Absolute Error Industry 3550 and 3560 ............... 143
530 Mean Absolute Percent Error Industry 3550 and 3560 ....... 144
531 Mean Squared Error Industry 3711 and 3713 ................ 145
532 Mean Absolute Error Industry 3711 and 3713 ............... 146
533 Mean Absolute Percent Error Industry 3711 and 3713 ....... 147
534 MSE Wilcoxon Tests Industry 3531......................... 150
viii
Table Page
535 MAbsE Wilcoxon Tests Industry 3531 ...................... 153
536 MSE Wilcoxon Tests Industry 3550 ....................... 154
537 MAbsE Wilcoxon Tests Industry 3550 ...................... 156
538 MSE Wilcoxon Tests Industry 3560 ......................... 158
539 MAbsE Wilcoxon Tests Industry 3560 ...................... 160
540 MSE Wilcoxon Tests Industry 3711 and 3713 ................ 161
541 MAbsE Wilcoxon Tests Industry 3711 and 3713.............. 163
542 Summary of Quarterly Results: Rankings .................. 164
543 Summary of Hypothesis Testing Industry 3531 (legend p.167) 166
544 Summary of Hypothesis Testing Industry 3550 .............. 168
545 Summary of Hypothesis Testing Industry 3560 .............. 169
546 SuImmary of Hypothesis Testing Industry 3711 and 3713 ..... 170
547 Mean Squared Error Industry 3531 ........................ 172
548 Mean Absolute Error Industry 3531 ........................ 173
549 Mean Absolute Percent Error Industry 3531 ................ 174
550 Mean Squared Error Industry 3550 ....................... 175
551 Mean Absolute Error Industry 3550 ........................ 176
552 Mean Absolute Percent Error Industry 3550 ................ 177
553 Mean Squared Error Industry 3560 .......................... 178
554 Mean Absolute Error Industry 3560 ........................ 179
555 Mean Absolute Percent Error Industry 3560 ................ 180
556 Mean Squared Error Industry 3711 and 3713 ................ 181
557 Mean Absolute Error Industry 3711 and 3713 ............... 182
558 Mean Absolute Percent Error Industry 3711 and 3713 ....... 183
LIST OF FIGURES
Figure Page
1 Relationship Between the Hypotheses and the Models ...... 75
2 Distribution of Absolute Percent Error for Each
Annual Model (Legend p. 88) ........................ 87
3 Distribution of Signed Percent Error for Each
Annual Model (title p. 89).......................... 90
4 Distribution of Absolute Percent Error for Each
Quarterly Model Industry 3531 ................. 184
5 Distribution of Absolute Percent Error for Each
Quarterly Model Industry 3550 (title p. 185)...... 186
6 Distribution of Absolute Percent Error for Each
Quarterly Model Industry 3560 ................. 187
7 Distribution of Absolute Percent Error for Each
Quarterly Model Industry 3711 and 3713 ........... 188
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fufillment of the
Requirements for the Degree of Doctor of Philosophy
PROBABILISTIC NATURE OF ACCOUNTING EARNINGS:
MACROECONOMIC INFLUENCE AND EX ANTE PREDICTION
BY
Paul R. Welch
December 1981
Chairman: Shih Cheng Yu
Major Department: Accounting
The primary contribution of this research is to ascertain the
value of macroeconomic variables to the accounting earnings
forecasting process. In particular the author posits the use of an ex
ante causal modeling approach to earnings prediction. Over the years
there has been considerable research on the nature of the earnings
process, especially its timeseries properties. However, there are
unresolved questions with respect to both the value of nonaccounting
information in forecasting earnings and the probabilistic nature of
earnings in general.
This study discusses many prediction issues as well as conducts
empirical work to test the value of a causal modeling approach to
earnings forecasting. Drawing from theory and available empirical
evidence, a regressionbased model is developed to predict earnings
before extraordinary items. An ex ante distributed lag with macro
(DLWM) variables model is chosen because of its ability to provide a
true forecast as opposed to the "forecast" of correlational regression
models. Predictions of this model and a number of models suggested by
current literature are obtained for a sample of capital goods, durable
goods and drug firms both on an annual and a quarterly basis. The
models' forecast accuracies are compared and the results used to help
establish the value of macroeconomic variables to the earnings
prediction process.
A secondary contribution is an update of timeseries model
prediction performance. The work presents comparative evidence of the
predictability of numerous wellknown models using fairly recent
prediction periods. The results indicate that the causal modeling
approach is a more accurate predictor of annual earnings before
extraordinary items in many industries studied and is at least as
accurate in predicting quarterly earnings in the same context.
BoxJenkins models were found to be no more accurate than a DLWM model
in all industries at all prediction horizons tested above one quarter.
One quarter ahead prediction did show statistically significant
superior performance of the timeseries models, but not always those
estimated using the BoxJenkins procedure.
The findings demonstrate the viability of DLWM methods in
combating the explosive nature of earnings predictions experienced in
recent years.
CHAPTER ONE
INTRODUCTION
Background and Purpose of the Research
Motivation
Accounting earnings play a major role in investment analysis,
especially financial statement analysis. An investor considering a buy
or hold strategy regarding a particular stock is concerned with
evaluating the prospects of future stock price, among other things.
Information relating to the overall economy and industry conditions is
relevant to his investment decision. Both earnings and security returns
are affected significantly by outside events. The accuracy of earnings
prediction is of interest to researchers for such purposes as testing
the various models of firm valuation, the relationship between
unanticipated earnings and stock prices, and the information content of
disclosures of earnings forecasts by management. The nature of the
earnings process and the impact of external events on earnings
forecasts are of direct interest to those responsible for the
independent evaluation of prediction disclosures generated by corporate
management.
Over the years there has been a considerable amount of research on
the nature of the earnings process, especially its timeseries
properties. However, there are unresolved questions with respect to
both the value of nonaccounting information in forecasting earnings and
the probabilistic nature of earnings in general.
In predicting earnings, or any other unknown future quantity, it
is important to know the probability mechanism which underlies the
forecast. Consideration must be given to interactions with relevant
factors that are judged to be causal. Realization of a specific
earnings number is necessarily contingent upon the relationship between
the process of income generation specific to the firm and the influence
exerted by relevant macroeconomic forces. The probabilistic nature of
accounting earnings is apparent when one considers the uncertainty
associated with these major causal forces in future periods.
Earnings Prediction Problems
Problems of prior studies. The nature of the results obtained in
prior studies does not provide sufficient information upon which to
base judgments as to the reasonableness of forecasts of earnings.
There still remains the question of the individual model which best
describes the earnings for a particular industry or firm. With no
premier model yet established as a bench mark from which to judge the
adequacy of forecasts made by other models or by management, there
continues to be a need for further research. This is especially true
in light of the results of recent quarterly studies which indicate a
weakness in the BoxJenkins (BJ) methodology when applied to more
recent data sets. These recent findings have created renewed interest
in methods for forecasting earnings.
Past studies have attempted to validate and compare various
earnings predictions by using ex post error measurement, but
inconsistent results across industries and time have made the
evaluation process a difficult one. The fact one set of models worked
in one time frame and another set of models performed better in a
different time frame means both sets failed to consider fully the
probabilistic nature of the process generating the time series of
earnings during the two periods. Therefore, no conclusions can be
drawn concerning a global representation of the properties of earnings
nor of the appropriate prediction system.
Problems in evaluating earnings forecasts. Questions remain as to
the nature and the extent of the Certified Public Accountant's (CPA)
review of the forecasting process. Current guidelines are very general
and therefore do not provide a systematic procedure to follow. Many of
the CPA's information sources are left open to judgment or to the
suggestions of future research.
Considering both the need for future evidence and the general lack
of bench marks, it is natural to consider including nonaccounting
information in the prediction process. However, previous research has
been limited in establishing the value of macroeconomic factors as
inputs to a forecasting model. This is especially true if one
considers the need to judge forecasts at the time they are made (ex
ante) as well as subsequent to the actual earnings number being
realized (ex post).
Research Contribution
Influence of Macroeconomic Variables
The primary contribution of this research is to ascertain the
value of macroeconomic variables to the accounting earnings
forecasting process. Once established, the influence of these
variables can be incorporated to express more fully the probabilistic
nature of accounting earnings and can be used to evaluate directly
management forecasts, both ex ante and ex post.
In order to accomplish the goal of determining the value of
macroeconomic factors (macros, henceforth), a particular earnings
prediction methodology is proposed. This causal modeling approach uses
the economic variables to help predict earnings by using a procedure
which allows specification of the causal nature of the macros visavis
the earnings series.
There are four reasons for developing this causal modeling
approach. First, the theory of the firm under uncertainty (micro level
theory) is not well developed. Second, the prediction of micro level
variables for subsequent use in ex ante forecasting is more difficult
than earnings prediction itself. Third, determining a more complicated
earnings structure, based on macroeconomic theory, is illfounded.
Fourth, such a structure has a high possibility of being estimation
period specific thereby reducing predictive performance.
A compromise is developed which both avoids overfitting by
limiting the number of independent macro variables and uses a versatile
regression (very general structure) formulation, including the use of
lagged economic variables, to render ex ante predictions possible.
Thus, the proposed major contribution would be the evidence obtained
from testing the predictability of the causal model.
Timeseries Model Performance Update
A secondary contribution of this research is to provide an update
of timeseries models' prediction performance. Wellknown models are
compared to the causal modeling approach using fairly recent prediction
periods. Therefore, evidence is supplied relevant to the current
predictability of BJ timeseries and nonBJ timeseries models as well
as the causal models. The study is capable of resolving some of the
inconsistencies created by past research.
The two major contributions sought here are (1) to assess the
value of nonaccounting (macro) information in the earnings forecasting
process and (2) to provide information from which to judge the adequacy
of the forecasts made by various models. The ex ante nature of the
causal model and its development also provide the necessary bench mark
for reviewers to evaluate management forecasts.
Overview
Scope of the Research
This study discusses many prediction issues and conducts empirical
work to test the value of a causal modeling approach to earnings
forecasting. Drawing from theory and available empirical evidence, a
regressionbased model is developed to predict earnings before
extraordinary items. An ex ante distributed lag model with macro
variables is chosen because of its ability to provide a true forecast
as opposed to the ex post "forecast" of correlational regression
models. Predictions of this model and a number of alternative models
suggested by current literature are obtained for a sample of capital
goods, durable goods, and drug firms on both an annual and a quarterly
basis. The forecast accuracy of the models is compared and the results
of this comparison are used to help establish the value of
macroeconomic variables to the earnings prediction process.
Any conclusions are considered preliminary because (1) alternative
structures have not been explored, (2) relatively crude methods are
used to predict the macroeconomic variables, and (3) only macro
variables are used instead of industry or firmspecific variables. Of
course, if predictions of such models can outperform, or perform as
well as, competitive ones, then the value of the procedure would be
demonstrated clearly; thus, an independent reviewer (e.g., an auditor)
would be supplied with additional evidence with which to judge the
adequacy of corporate management's financial forecasts of earnings.
Important Definitions
There are three types of events which affect a firm's financial
performance. These are (1) firm specific occurrences, (2) industry
events, and (3) overall macroeconomic conditions. Yet some macro
phenomena, such as the inflation of energy costs, impact certain
industries much more than others. These factors are considered to be
macro for the purpose of this study.
The following critical distinction between ex post and ex ante
forecasts is important to this study:
In terms of timeseries models, both forecasts predict values
of a dependent variable beyond the time period in which the
model is estimated. However, in an ex post forecast the
forecast period is such that observations of both endogenous
variables and the exogenous explanatory variables are known
with certainty. Thus, any ex post forecasts can be checked
against existing data, and provide a means of evaluating a
forecasting model. An ex ante forecast predicts values of
the dependent variable beyond the estimation period, using
explanatory variables which may or may not be known with
certainty, depending on the nature of the data and the length
of the lags associated with explanatory variables. (Pindyck
and Rubinfeld, 1976, p. 157)
Macroeconomic forces in year tR influence the performance of
corporate earnings in year t. The lingering effect or prolonged impact
of economic downturns, for example, means that past (lagged) macro
activity can be used to predict future earnings realizations.
Most ex ante forecasting requires explanatory (right side)
variables to be predicted, before a single equation regression model
can be used to forecast. The predicted nature of these independent
variables leads to a forecast of the dependent variable which is less
reliable than if known explanatory variables were used, but not
necessarily less reliable than models omitting important explanatory
variables.
In an unconditional forecast, values for all the explanatory
variables in the forecasting equation are known with certainty. Any ex
post forecast is, therefore, an unconditional forecast. In order to
produce an unconditional ex ante forecast, the explanatory variables
must be known with certainty for the entire forecast period, i.e.,
sufficient lags. In a conditional forecast, values for one or more
explanatory variables are not known with certainty, so that guesses
(extrapolations or forecasts) of them must be substituted. For a
forecasting equation with no lags, every ex ante forecast is a
conditional forecast.
Regressions with stochastic explanatory variables are common, if
not predominant, in a field such as econometrics where the problem has
been studied to a great extent. In many studies, the values of the
explanatory variables are determined (along with those of the dependent
variable) as a result of some probability mechanism rather than being
controlled by the experimenter.
The typical accounting timeseries literature deals with
unconditional forecasting. A "good" model in terms of unconditional
forecasting may perform poorly when conditional forecasting is
attempted. One should not be too quick to reject a model with a high
forecast error if the primary component of that error is due to the
prediction involved in the determination of explanatory values during
the forecast period. The ex ante approach taken here does not rely on
any information which is not actually available at the time of
prediction. The implication of this strategy is that the derived
"forecasts" are truly forwardlooking and consequently are useful to
those who (1) require information about future earnings or (2) wish to
evaluate various other forecasts prior to the actual realization date.
As a bench mark for the evaluation of the conditional forecasts
produced in this study, an alternative method of deriving the
explanatory values is employed. In combination, these two procedures
allow for the analysis of the contribution of the model itself. Two
methods of macroeconomic variable prediction reveal the sensitivity of
the model to the quality of macro forecast and isolate the component of
forecast error due to macro prediction.
Chapter Organization
Chapter Two discusses the current stateoftheart of earnings
forecasts, reviews the statistical literature and summarizes the
importance of the topic. Building on this foundation, a number of
specific issues are established and discussed in Chapter Three; the
synthesis contained therein provides a basis for the empirical work
which follows. The justification of the particular approach used
requires a substantial concatenation and constitutes a major portion of
the development of the model. After the rationale for the general
approach to the model is established, the specific forms of the model
are developed in Chapter Four. The results are presented in Chapter
Five, and conclusions and extensions are given in Chapter Six.
CHAPTER TWO
LITERATURE REVIEW
This chapter discusses the prior accounting and statistics
literature concerning prediction models. Forecasting methods can be
grouped into two sets depending on whether or not a model incorporates
variables other than past observations of the earnings stream. Methods
which use only the past time series of earnings are pure time series
models. Methods which include other variables can also be of a time
series nature and are fit over the series of past observations of some
set of variables which may possibly include earnings.
The chapter also provides a rationale for the empirical work
presented in Chapters Four and Five. This review raises several
issues, some of which are discussed further in Chapter Three. Chapter
Two begins with background material and motivation for the current
study.
Background and Motivation
Earnings forecasting is of interest to those testing valuation
models, the relationship between unanticipated earnings and stock
prices, or the information content of earnings disclosures. There are,
however, two schools of thought concerning the importance, or lack
thereof, of earnings prediction. The study of accounting income time
series per se without first establishing the theoretical interest in
such series has come under attack by Revsine (1971) and Lauderback
(1971). On the other hand, Foster (1978), Gonedes (1973), and Gray
(1973) have supported the importance of such research as have Beaver
(1970) and May and Sundem (1976) and others.
The main criticism of the numerous predictability studies
conducted to date is that the various models and methods of prediction
have been applied to earnings (an artifact of historical cost
accounting) instead of to some more relevant variable, such as cash
flow. It is argued that what is really needed are empirical tests of
the ability of the various methods to generate reasonable estimates of
cash flows and that the results of predictability studies thus far are
devoid of meaning in that they do not establish a correspondence
between income forecasts and future values of cash flow. This
dissertation does not address this issue directly, and its results must
be viewed with this caveat in mind. Revsine (1971) argues that
...only one justification for income prediction survives;
that is, such forecasts are useful only insofar as the income
concept being predicted is a reasonable indicator of some
real events) [cash flows, for example] of concern to users.
(p. 488)
Yet a great deal of research continues relevant to the timeseries
properties of earnings. The work of Watts (1975), Griffin (1977),
Foster (1977), Brown and Rozeff (1979), Lorek (1978), and Hopwood
(1980) have attracted considerable interest.
Some reasons for this interest are: (1) the potential
use of forecasts of accounting numbers as inputs to decision
models; (2) the need to secure proxies for unobservable
expectations in order to test economic theories; (3) the need
to use such statistical models within the context of studies
dealing with the predictive ability of information content of
accounting numbers, subjects that have been receiving
increased attention during the past few years; (4) the
growing interest in examining the forecasting success of, for
example, managers and financial analysts relative to
statistical models that are "appropriate" for the accounting
number series of interest, and (5) the need to use accounting
numbers in testing hypotheses regarding industrial
organization (e.g., market concentration), profitability, and
the growth and decline of firms. (Gonedes, 1973, p. 212)
Statements such as the following are among the primary motivators
of this dissertation.
Although the most frequently mentioned forecast
accounting numbers are probably net income and earnings per
share, they are probably more difficult to predict and also
the least reliable. This results from the fact that a
projection of accounting income depends on many subjective
variables and many assumptions regarding the firm and the
economy . .. With a publication of the forecast of
financial accounting information and other information
relating to the firm, it is necessary that the basic
assumptions relating to the economy and external factors be
disclosed so that the users of the forecasts can better
evaluate its reliability. Such assumptions should include
expectations regarding the industry as well as assumptions
regarding changes in economic conditions. (Hendriksen, 1977,
p. 549)
Research on the probabilistic nature of earnings ultimately may
help users of financial statements to evaluate the imprecise nature of
reported income and of earnings forecasts disclosed in annual reports
to stockholders just as current primary and fully diluted earnings per
share (EPS) indicate a range of possible outcomes. The Executive
Committee of the Management Advisory Services Division of the American
Institute of Certified Public Accountants (AICPA) created a task force
in 1973 to develop standards for a CPA's association with the reporting
of financial forecasts. Somewhat earlier (and continuing on through
1979) the Securities and Exchange Commission (SEC) issued a series of
releases refining its position with regard to management forecast
disclosures. The final link in the entire process was the issuance in
October 1980 of the "Guide for a Review of a Financial Forecast,"
prepared by the Financial Forecasts and Projections Task Force of the
AICPA. The contents include definitions, scope of the review,
procedures to evaluate assumptions, and sample report formats; reprints
of an SEC Release on Disclosure of Projections of Future Performance;
and other AICPA technical pronouncements.
Independent CPAs are now allowed (permitted, but not required) to
review and to report on estimates of the most probable financial
position for one or more future periods although "traditionally
projections have been given for three items .. of primary interest
to investors: sales or revenue, net income, and earnings per share"
(p. 76). Among the suggestions mentioned in the guide are two of
interest to this study:
The accountant should obtain knowledge of the entity's
business and the key factors upon which its future financial
results depend, focusing on such areas as .. factors
specific to the industry, including competitive conditions,
sensitivity to economic conditions . .. (p. 6,7)
The accountant's standard report on a review of a
financial forecast should include .. a statement regarding
whether the underlying assumptions provide a reasonable basis
for management's forecast. (p. 21)
The guide also encourages but does not require subsequent comparison of
actual results with those forecasted, but error metric issues are not
addressed. No questions of percent error vs. raw error or of absolute
error vs. signed error are raised.
Evaluation of earnings forecasts is possible at two distinct
points in time. Before observing the actual outcome of some future
event there is the possibility of ex ante scrutiny either by analysis
of the basis of the forecast or by establishing an ex ante statistical
confidence interval around the point estimate by formal (discussed in
Chapter Three) or informal means as suggested by Daily:
Investors should be expected to anticipate minor
variations between a forecast and actual results because of
the nature of forecasting, and variations within the range of
10 percent to 15 percent or less should be explainable to the
satisfaction of most investors. (1971, p. 688)
After the actual has been observed, comparison can be made with either
the range mentioned above or the point forecast itself. It is the
second comparison which gives rise to the ex post error measure and to
the volume of literature to date concerning the predictability of
various forecasting models.
The accuracy of earnings forecasts has received a major
effort in the literature. The need for more accurate
forecasts provided the impetus for perfecting some mechanical
forecasting models. At first comparisons were made of the
relative accuracy of various mechanical models. Research
technology evolution and more data availability allowed
comparison of accuracy of forecasts made by rigorous time
series models with those made by managements. It was hoped
that these comparisons would provide some inferences as to
the relative value of privately gathered and nonaccounting
information. Unfortunately, the evidence to date is
inconclusive. In some industries, mechanical models were
found to be as good forecasters as managements or better than
mechanical models on the average. It is striking, however,
that analysts and managements did not continuously outperform
mechanical models. We feel that both the properties of
earnings forecasts and the question of their value continue
to be a fertile area for research. (AbdelKhalik and
Thompson, p. 202)
Literature on the TimeSeries Properties of Earnings
Although many articles refer to the importance of macros or the
influence of economic conditions, the vast majority of the accounting
literature has not dealt with these factors. These works are labeled
here as timeseries research studies. Use of timeseries methodologies
transforms the work from the discovery of explanatory exogenous
variables underlying the earnings process to the detection of
timeseries patterns in the earnings data itself. However, "the issue
of whether there are systematic patterns in the annual earnings series
of individual firms that can be exploited for forecasting is very much
an unresolved question" (Foster, 1978, p. 123). It is the predictive
ability criterion which provides the motivation for most of these
studies.
The time series of earnings literature can be organized according
to a number of different schemes depending on the emphasis of the
studies classified. There are annual as well as quarterly studies.
There are studies dealing with timeseries properties and with the
accuracy of various timeseries models. There are comparisons among
predictions made by models, managements, and analysts. There are
studies which describe alternative earnings series, alternative
prediction horizons, alternative time periods being forecast,
alternative industries, alternative error measures, and alternative
updating techniques. Finally, some studies use quarterly forecasts to
predict annual forecastsGreen and Segall (1966) and Lorek (1979).
Three good sumrmaries of this literature are Abdelkhalik and Thompson
(197778), Lorek (197778), and Foster (1978).
Empirical Works
The main body of literature is concerned with the relative
accuracy of the various models as well as comparisons of predictions
made by management and financial analysts. There are a number of
different model types. Naive (ad hoc) models include extrapolations,
random walks, simple autoregression, mean reverting, and some
combinations of these. BoxJenkins models are characterized by three
steps: identification, estimation, and forecasting. This algorithm
allows for the flexibility of the autoregressive integrated moving
average (ARIMA) family. For a more complete explanation of the BJ
technique, refer to Mabert and Radcliffe (1974), Nelson (1973), or Box
and Jenkins (1970).
Annual results. Past studies concerning the timeseries behavior
of annual earnings include Beaver (1970), Ball and Watts (1972),
Lookabill (1976), Foster (1977), Watts and Leftwitch (1977), and
Albrecht, Lookabill, and McKeown (1977). The results of these research
efforts are reasonably consistent and allow one to concentrate on the
summarizing nature' of the last two articles. Watts and Leftwitch state
that the random walk (martingale)1 model is still a good description of
the process generating annual earnings (p. 28). More specifically, the
random walk with drift (submartingale) is appropriate for nondeflated
income while a noisy random walk works for earnings per share. These
conclusions are based on ex post error measures in comparison with
other timeseries models only. Thus, the random walk with drift model
is the preferred choice among the time series subset of annual earnings
forecast models. The Allbrecht et al. (1977) formulation of this model
is discussed further in Chapter Four and will be used as a comparison
in the annual research.
Quarterly results. Accounting literature has distinguished two
types of applications of BJ techniques. One method (parsimonious
models) relies on prior research on the earnings series to establish
the parameters of the model, thus creating a socalled nonspecifically
identified "premier" model. When used, this procedure omits the
regular identification stage and adopts whatever model form is deemed
appropriate under the circumstances. The other major application of
the BJ technique, individually fitted/firm specific BJ models, is
achieved through use of all three stages in the iterative process.
Three parsimonious model forms have been offered as contenders for
the premier title. They have come to be known by the names of the
authors who have championed them:
(1) Foster (1977),
(2) Watts (1975) and Griffin (1977), and
(3) Brown and Rozeff (1979).
Research using data through 1975 prediction quarters indicates the
dominance of parsimonious BJ models over firmspecific BJ models as
well as naive models. This literature uses data sets culminating with
1975 and, therefore, does not address the explosive error problem
encountered in more recent studies. However, these quarterly results
do not resolve the question of superiority of the various parsimonious
models themselves, nor could they speak to the lack of superiority
which emerged when studies began to predict later time periods [e.g.,
Hopwood, Hillison, and Lorek (1980), Kee (1980), and Abdulkader
(1979)]. These newer results show extremely high ex post error measures
for all BJ model predictions and leave open the question of any
longterm validity of the timeseries properties of earnings using
these methods. In addition, the explosive nature of the errors invokes
statistical questions as to the appropriateness of these techniques.
BJ models require constant variance over time, which clearly is not the
case empirically. Thus, one of the critical assumptions of the
methodology is violated. These and similar issues are discussed
further in Chapters Three and Four.
Predictions of management and analysts. Researchers also have
studied the accuracy of financial analysts' and managements' (experts)
predictions of earnings. However, few conclusions can be drawn. Among
the studies which deal with this area are Elton and Gruber (1972),
McDonald (1973), Daily (1971), Barefield and Comiskey (1976), Lorek,
McDonald, and Patz (1976), and Brown and Rozeff (1978).
The forecasts made by management/analysts can be compared to the
predictions of timeseries models or to any other mo~del type which does
not benefit from their experience or inside knowledge. Two viewpoints
can be taken with regard to this comparison. First, a naive model can
be used to evaluate the reasonableness of an expert's ex post forecast
error. Conversely, management or analyst forecasts can be used as
standards by which to evaluate types of naive forecasting, including
timeseries Imodels. If used in this second way, it must be assumed
that an expert forecast is some upper bound on forecast accuracy due to
additional information available to them.
Unfortunately, past research has shown that management forecasts
are not necessarily better than those of the models. Abdelkhalik and
Thompson (197778) summarize:
Researchers disagree as to whether earnings forecasts
made by management and/or analysts are more accurate than
forecasts which rely on mechanical forecasting models. Most
of the studies conclude that analysts and mechanical models
perform. about equally well.
The evidence to date does not show that information
available to management and analysts (beyond that required by
historically based time series models) is particularly
valuable for making more accurate forecasts.
The evidence also suggests that the ability to forecast
a firm's earnings is dependent, to some degree, on the
industry in which it operates.
Security analysts seem to utilize and adapt to the new
information contained in earnings time series. (p. 192)
As a result of these findings, one can conclude that the value of
comparing timeseries models with management forecasts is in the
ability of the models to help evaluate the quality of management's
disclosures. Research results can be especially helpful in providing
evidence of the relative difficulty of the forecasting process in
different industries and, to some extent, in providing information on
bias tendencies of over or underprediction in certain industries.
Synthesis of TimeSeries Research
The inconclusive nature of the predictability research evokes a
number of questions. The question of further fruitful timeseries
endeavors is indicated perhaps by a suggestion made by Foster in his
book (1978, p. 107): "An interesting extension of Foster (1977) would
be to compare model 5 visavis model 6 when the parameters of both are
reestimated each quarter." His model 6 is the parsimonious BJ model
referenced earlier under his name. The model 5 he mentions is the same
general model, but is estimated using nonBJ procedures. Questions of
the appropriateness of parsimonious BJ models can be answered only by
conducting more empirical research. Recent studies indicate poor
performance of BJ techniques and raise serious methodological questions
for the continued use of these models in the earnings context.
Foster mentions a number of statistical issues with regard to the
use of BJ models in accounting earnings studies. Foster (p. 106),
Lorek (1979, p. 192) and Griffin (1977, p. 75) allude to the
overfitting problem of firmspecific BJ models. Another problem
concerns the fitting period for these models. Unfortunately, the
length of time required to estimate BJ models increases the likelihood
of structural change since there is an opportunity for the process
generating earnings to change due to some real event. Most timeseries
applications need a rather large number of observations, say fifty or
more. "Unfortunately, this extension of the time period increases the
likelihood of structural change, since there is a greater opportunity
for the time series of earnings to change from one stationary process
to another because of some real event, such as a merger" (Watts and
Leftwich, 1977, p. 255). Depending on the type of model used, the
question of such nonstationarity can be a critical issue. Some
formulations are much more susceptible to structural change than are
others. The more the conditions of overfitting exist with a particular
method, the more likely the model will have difficulty beyond the
sample period. Forecasts with such models are subject to extreme
variability, and the ex post error measure can be expected to fluctuate
widely. Thompson and Kemper state it this way: "Variability arises
because (1) the process which generates the data is stochastic and/or
(2) the estimating process is imperfect" (1965, p. 575).
Nonstationarity can be classified into two types: gradual and
jump. Primary examples of the first type are changing consumer tastes
and subtle changes in the economy. Examples of the second type are
generally firm specificsuch as new products, a change in leadership,
sudden inflation, and new cost interrelationships such as much higher
energy costs relative to other costs. The use of a confidence interval
for a forecast is especially important when there is a question of
nonstationarity. This fact is pointed out by Biruberg and Slevin
(1976, p. 157): "[the] condition where the interval statement may be
useful is when the underlying process changes."
No prediction model can incorporate all factors for practical
reasons and because reduced forecastability can be expected to result.
On the other hand, lack of consideration of essential elements
affecting future earnings also can have a detrimental impact on
forecast performance. This is especially important if one agrees that
the earnings generation process is not a function of the timeseries
properties of reported earnings but results from production, marketing,
and finance decisions as well as from changes in the economy.
Lorek (197778) frequently reminds us of the caveat that most
accounting timeseries models are devoid of economic variables.
However, of timeseries research, he states: "In essence, we examine
an impact of several economic variables on the series by allowing the
series itself to provide clues regarding the expectation model" (1979,
p. 191). The synthesis points to the need to (1) eliminate statistical
weaknesses generally; (2) directly compare alternative models, both
timeseries models (e.g., Foster's model 5, model 6) and other model
forms; and (3) study models which incorporate exogenous economic
factors. The application of models such as those of Foster,
GriffinWatts, and Brown and Rozeff to data of recent years has left
the value of their methods open to considerable question due primarily
to the large prediction errors which have resulted. This raises the
issue of other variables being used in the prediction.
Use of Economic Variables and Index Models
Prior Support for Use of Macros
In general, the importance of these factors is not disputed:
Those who use financial information for business and
economic decisions need to combine information provided by
financial reporting with pertinent information from other
sources, for example, information about general economic
conditions or expectations, political events and political
climate, or industry outlook. (SFAC #1, 1978, p. 10)
Empirical support for the use of macroeconomic factors is also
available. Among the many (primarily accounting) studies which have
utilized economic variables are the following: Allbrecht and McKeown
(1976), Brown and Ball (1967), Elliott and Uphoff (1972), Foster
(1978), Gonedes (1973), Gould and Nelson (1974), Hopwood (1980), King
(1966), Lev (1980), Magee (1974), Prakash and Rappaport (1974), and
Saunders (1978). The pages which follow dwell heavily on this
literature for both the theory given and the empirical results
obtained.
One of the first studies to examine the importance of economy and
industry factors on earnings was Brown and Ball (1967). They
determined that ". . on average, approximately 3540% of the
variablilty of a firm's annual earnings numbers can be associated with
the variability of earnings numbers averaged over all firms; .. on
average, a further 1015% can be associated with the industry average"
(p. 65). Another study which dealt with the impact of marketwide
factors demonstrated that these factors were statistically important
determinants of firms' operating results [Gonedes (1973), p. 235].
These economywide studies attempt to describe crosssectional
dependencies with respect to firms' accounting numbers. Some specific
potential sources of crosssectional dependencies are changes in the
economy's production technology, the effects of economic stabilization
policies, and the resource flows and relative price changes associated
with general equilibrium forces. "All firms in the economy are
affected to some degree by monetary policy or changes in interest
rates. The factors shared by firms in a given industry would include
the demand for the products of the industry and the movements of other
firms into and out of the industry" (Brown and Ball, 1967, p. 56).
Hopwood. In a procedure which incorporates industrywide and
economywide factors, Hopwood (1978) distinguishes models by the data
sets utilized and defines three distinct data sets (p. 13):
(1) data internal to the firm (earnings excluded, i.e., ratios);
(2) data external to the firm; and
(3) earnings data.
He then derives a set of uncorrelated indices computed from ratio,
market, and industry data in an attempt to improve earnings per share
predictability. His procedure is a firmidentified, multivariable,
longitudinal model utilizing simultaneously internal, external, and
earnings data sets. In a refinement of this research, Hopwood (1980)
investigates the relative forecast accuracy of a basic ARIMA model and
an index model using EPS data taken from Moody's Handbook. This second
model is a singleinput transfer function (TF) with an market or
industry price index used as the input variable. The indices were
Standard and Poor's (S+P) Composite Index and S&P's Air Transportations
Industry Index.
Using both indices, "the TF forecasts are not significantly
different than the ARIM~A forecasts" (p. 82). However, Hopwood found
that "if a transfer function outperformed an ARIMA model for the first
three periods in the forecast horizon, then there was a high
probability that it would do the same for periods four through ten" (p.
88). Hopwood's work suggests:
that for about onehalf of the firms studied, at least one of
the TF models provided a better descriptive forecast model of
the underlying earnings process. Evidence of the superiority
of these TF models was that those which dominated the ARIMA
models for the first three periods could be expected, with
significant probability, to continue to do so over the next
seven periods.
One implication of this result is that about onehalf of
the ARIMA models were suboptimal. We should not jump
immediately, however, to the conclusion that the result is an
artifact of the transferfunction modeling process and not
the predictive value of the input series. This possibility
was investigated before economic explanations were
considered. (p. 85)
I conclude there is insufficient evidence to attribute
the improved forecasts of the TF models to the predictive
value of the input series. (p. 86)
The evidence here is not sufficient to determine whether
industry and price indices have predictive value in
themselves. First, the present study is subject to the use
of the TF methodology and it is possible that an alternative
methodology might be more sensitive. Future research is
needed on comparisons of alternative methodologies for
measuring the predictive value of multivariate time series.
(p. 86)
Hopwood also had the explosive error problem with 10 percent of the
absolute percent error measures more than three standard deviations
from the mean and "a large number" in excess to twentyfive standard
deviations (p. 81).
Lev. In another 1980 study, Lev examined the predictability of
models such as
Et = B + B Mt and Et = 80 + B Mi~
i1
where Mt is gross national product (GNP) or total corporate profits
(TCP) after taxes in current dollars. He found these index models to
be mlore accurate predictors of annual sales, operating income, and net
income than a random walk with drift at a oneyear forecast horizon.
Although Lev states that "conditional oneyearahead predictions of the
firms' variables were generated from the estimated index models and
from forecasts of the indexes," he also states:
For each of the seven years 19681974, predictions of sales,
operating income, and net income for each sampled firm were
made from the estimated index model parameters and the GNP
and TCP forecasts (independent variables) published in August
of each predicted year. (p. 532)
This finding and the preceding one are consistent with the
hypothesis underlying this study (and with available
evidence), that firms' financial variables are
contemporaneously closely associated with economywide
indexes. (p. 531)
Thus, his forecasts are neither causal nor a full oneyear forecast
horizon, although they do come at yearly intervals. The model was
reestimated each year. Industries studied included packaged food,
paper, chemicals, air transport, retaildepartment stores, retailfood
chains and oil integrateddomestic.
A two factor model also included industry sales or industry net
income predictor variables. Because predictions of industry indexes
for the years 196874 were not available, Lev restricted the prediction
tests of the twofactor models to one year only, 1968.
It can be reasonably concluded, therefore, that incorporation
of an industry factor improved the predictive ability of the
index models, particularly for the operating and net income
series.
To summarize, the predictive ability tests of the
singlefactor difference index models for the three
accounting series examined were found to be, in general,
superior to both the levels index models and the
submartingale benchmark models. (p. 535)
Lev also points out that index models generate more skewed (than
bench mark) error distributions, thus resulting in a high number of
large errors (p. 535). Evidently to avoid this explosive error
problem, Lev based his findings on median prediction errors. His major
conclusion is expressed thusly:
It appears that the relationship between firm variables and
economywide indexes is stronger for nondurable and service
industries than for durable good industries. This is
probably explained by the fact that demand for nondurables
and services is more stable over time than demand for durable
goods. (p. 531)
Based on mean square error MSE, for instance, his results might have
been much different.
Not all researchers support the use of macro factors, especially if
the mechanism used is regression based. Mandelbrot (1963, p. 409)
discusses specifically the failure of leastsquares method in
forecasting, and Albrecht and McKeown (1976)
have provided evidence to show that (1) regression analysis
was inappropriate to analyze economic data where the time
series observations were not independent .. (2) the
bivariate BoxJenkins time series analysis is a methodology
capable of articulating the nature of the relationship
between two variables when the data are available in a time
series. (p. 13)
Econometric models. A category of methods which is broader than
"One motivation in
regression models is the set of econometric models.
using an econometric model for forecasting a firm's earnings, sales,
etc., is to exploit more information than is available in the past
sequence of the variable being forecast" (Foster, 1978, p. 111).
Econometric models rely on established statistical procedures and
economics. One or more equations is used, based on the existing or
assumed relationship or structure among the variables. Often the
parameters are estimated using a regression technique such as ordinary
least squares. A linear regression using economic forces, such as GNP,
etc. as exogenous independent variables, would be an econometric model
with a very informal structureindex model form.
The reason for considering linear models is the same as that for
many other existing model forms. These techniques have the ability to
capture relationships between variables and can be applied easily.
General linear models are important to the accounting applications
considered in this project because of the presence of numerous
variables and because of the need to deal with the resulting
complexity. A complication arises when lagged values of the dependent
variable are on the right side of the prediction equation. This test
does not have the common interpretation nor is it valid under these
circumstances (Elliott and Uphoff 1972, and Johnston 1963),
Any use of regressionbased probabilistic models hopefully would
be based on adequate prior theory. Thomas (1974) gives the following
example of the danger of employing correlational regressions for the
purposes of prediction while disregarding causal explanations:
...one who has concluded that soda is intoxicating because
he or she has become drunk on bourbon and soda, rye and soda,
and rum and soda may be disappointed by ice cream sodas, (p. 77)
An assumption in building singleindex or multiindex models is
that economywide or industrywide factors are useful in predicting an
individual firm's accounting numbers. An important consideration is
the ease with which the properties of the economy or of the industry
variables themselves are identified. "Most work on building such
structural econometric models has been done at the economy or industry
level .. In comparison, work on causal modeling of the financial
series of individual firms is relatively less developed" (Foster, 1978,
p. 82).
The use of simultaneous equation econometric models in an
accounting context is rare. Elliott and Uphoff (1972) is the only
example in the accounting literature, although they indicate three
other studies which dealt with "predicting elements of financial
performance" (p. 260). They apply econometric techniques to forecast
elements of the income statement using industry and market data and
give examples of uncorrelated indices (p. 261).
Causal Modeling Approach
The application of models such as those of Foster, GriffinWatts
and Brown and Rozeff to data of recent years has left the value of
their methods open to considerable question due primarily to the large
prediction errors which have resulted. This raises the issue of other
variables being used in prediction and brings to mind an observation by
Revsine
To be a useful predictor, an income concept need not be
relatively stable from period to period. If the variable for
which a prediction is desired is volatile, then the best
possible prediction would be similarly volatile with a
reasonable lead. (1971, p. 4889)
Prior accounting studies have relied on correlational relation
ships as well as crosssectional methodologies. Consequently, their
success in forecasting has been very limited since prediction requires
intertemporal validation (ex ante), whereas explanation requires only
crossvalidation (ex post). The correlational nature of a formulation
such as Lev (1980) does not give rise to the causal or temporal impact
of any macroeconomic factor which might influence future earnings.
Given the aim of this paper to incorporate macroeconomic
variables into the prediction model, it becomes necessary to find a
model form which does not suffer from the shortcomings of a statistical
nature as discussed earlier. A form of time series regression is the
most obvious choice, but there are some problems. When a
regressionbased model is estimated using data over time, there exists
the possibility of autocorrelation of the residuals. Two other
difficulties are underestimation of the sample variances and
inefficient predictions. Regression studies have been criticized for
lack of consideration of this problem, e.g., Godfrey (1973), Godfrey
(1974), Granger (1974), Howrey et al. (1974), and Jensen (1979).
Variations to the standard regression, which solve this problem, have
been developed; in particular, the suggestions of Feldstein (1971),
Fuller (1976), Pindyck and Rubinfeld (1976), Granger and Newbold
(1977), and Johnston (1963) apply. The alternatives to basic
regression include distributed lag, dynamic regression, and spectral
analysis. Spectral analysis, like the BoxJenkins methodology, is an
example of the statistical modeling approach.
The distributed lag methodology, when it includes lagged values of
both the dependent and the independent variables, is an example of the
causal modeling approach to econometric modeling. In this approach,
predictions are obtained using historical values of endogenous and
exogenous variables and projected values of exogenous variables. The
technique is explained by Wallis (1967), Johnston (1963, p. 315320),
and Fuller (1976, p. 429446).
The usefulness of macroeconomic variables for forecasting
purposes remains an empirical question to be addressed in this
dissertation.
Unfortunately, econometric models have as yet failed to
demonstrate higher predictive power than the previously
mentioned extrapolative models. Much more research is
necessary on structural specification and parameter
estimation before the potential of this forecasting tool is
more fully realized. (Lorek, 197778, p. 215)
Having reviewed the relevant literature involving both timeseries
earnings prediction and the use of econometric formulations, there
remain major epistomological issues which impinge on one's ability to
improve earnings forecasting. Some of these issues relate to the
nature of the information; others relate to the incorporation of these
data metholologically/statistically. The following chapter provides an
indepth discussion of a number of these issues.
Note to Chapter Two
1. Both a martingale and a pure random walk are modeled as
Et = Et~ + e .
Thus the expected earnings (E) number in year t is the earnings in
year t1. The only difference between the two models is that the
martingale model has no distributional assumptions on the error
term, et'
CHAPTER THREE
EPISTOMOLOGICAL ISSUES
This chapter deals with a number of epistomological issues and
raises certain questions with regard to numerous relationships and
interactions. These interactions include those between management and
the reviewer of earnings forecasts made by management, between earnings
models and prediction accuracy, between the various elements of the
economy, and between the disclosure of financial information and future
events.
Given the oftenstated importance of earnings prediction in
the investment and financial analysis literature, it is
surprising how little analysis of (and evidence pertaining
to) prediction issues is contained in this literature.
(Foster, 1978, p. 80)
Evaluation of Management Forecasts
This section deals with a number of issues related to the
production and evaluation of forecasts made by management and by
various models used to predict earnings. The emphasis is on the impact
of interaction effects which result because of the nature and type of
information used to formulate and communicate the forecast and its
accuracy. Resolving these issues requires subjective judgments on the
part of the researcher as well as independent reviewers. The American
Institure of Certified Public Accountants (AICPA) already has taken
note of the subjective nature of the assumptions which management must
make in creating a financial forecast.
29
Management Forecasting Systems
No matter what the nature of a management forecasting system,
management and the independent reviewer must exercise judgment with
regard to some uncertain event or events. In arriving at these
judgments, it is desirable to be as formalized as possible. However,
if some decisions have little or no hard evidence on which to proceed,
making the evaluation of this information as objectively as possible is
important. It also is important to keep in mind the assumptions made
during the construction of a forecasting system. The assumptions which
underlie financial forecasts are "extensive in number and
nonproportional in their impacts on net income . ." (Williams, 1977,
p. 29). This point also is made by Elgers, Clark and Speagle (1974).
Williams points out that one must be "particularly careful of
important, but often subtle, relationships between the assumptions
embedded in the base case when changes are introduced into the model"
(p. 24).
Evaluating the impact of forecasting systems, which is a necessary
task of both management and the reviewer, depends on the complexity and
design of the system itself, The most formal systems may be
computerized models. Decision makers constantly face uncertain
situations which require action based on estimates of relevant
variables, which are not known at the time of the decision and
consequently must be predicted. If a management forecasting system is
sufficiently complex, then it might rely on some techniques which have
been successful in econometrics and statistical decision theory. Other
systems could be more of the seatofthepants variety and may be based
on no more formalized a system than a series of reasonable judgments
derived logically from management's past experience. The use of either
extreme involves inherent difficulty in evaluating the impact of
external events as well as internal events.
Because of the complexity of most economic inter
relationships, there is probably no quantitatively based
technique that could monitor this potential shortcoming.
Management and/or staff analysts estimated these
relationships when the model was initially constructed, and
they should remain sensitive to all potentially major
ramifications of them on their "what if" questions.
(Williams, 1977, p. 24)
Review of Financial Forecasts
Independent review of management's earnings forecasts by a CPA is
a relatively new phenomenon, especially with respect to compliance with
the recently issued AICPA guide on the subject. In all likelihood,
part of the assessment the reviewer makes concerning the forecast and
its underlying assumptions will be the formulation, in the reviewer's
mind, of some notion as to the likelihood that the company can reach
the estimated earnings number. This evaluation undoubtedly will be
judgmental in nature, arrived at through a probabilistic thought
process.
In order to make this probabilistic notion operational, there must
be an interval placed around a point forecast. The reviewer can form
one in his mind or can require management to produce one for his use in
evaluating the assumptions of the model. Whether this information is
reported to the public is also an issue here because
.. investors cannot assume that all reported quantitative
data have the same probability of accuracy. Therefore,
research in accounting should focus on the method of
measuring and reporting probabilistic data rather than
deterministic amounts. (Hendriksen, 1977, p. 547)
From a theoretical standpoint, quantifying the uncertainty around
economic variables is a more accurate way of reflecting economic
reality and more closely portrays the results of the measurement
process. From a normative viewpoint, the disclosure of uncertainties
should increase the value of financial statements by indicating the
inherent differences in reliability attached to various pieces of
information. In either case, financial data (including forecasts)
should not be presented in such a way as to imply a misleading degree
of precision or reliablilty. Comparability is weakened if
uncertainties which vary significantly among companies and industries
are obscured or ignored.
To satisfy individual preferences for predicting and controlling
the impact of uncertain events on enterprise earning power, some
apparently simple quantifications, such as net income, need to be
supplemented to represent their actual complexities by disclosing
ranges of precision, reliability, or probability distributions over
relevant variables. At present, both primary earnings per share (EPS)
and fully diluted EPS are required in financial statements in order to
provide the reader with more than the simple net income, thus giving a
range from an expected to a worstpossible situation.
Accountants need a statistical methodology in order to express the
stochastic nature of financial accounting numbers, especially earnings
forecasts; and users need variability data in order to determine the
risk involved in their decisions. In most situations, no single bit of
informationstockholders' equity, net income, cash flows, or capital
positioncan provide all the necessary input for a decision.
Ultimately, the question involves projections of future events and the
related uncertainty of them.
The information provided by financial reporting often results
from approximate, rather than exact, measures. The measures
commonly involve numerous estimates, classifications,
summnarizations, judgments, and allocations. The outcome of
economic activity in a dynamic economy is uncertain and
results from a combination of many factors. Thus, despite
the aura of precision that may seem to surround financial
reporting in general and financial statements in particular,
with few exceptions the measures are approximations, which
may be based on rules and conventions, rather that exact
amounts. (Statement of Financial Accounting Concepts No. 1,
1978, p. 9)
Even if interval data are not publicly disseminated, the independent
reviewer should request management to provide an estimation of the
sensitivity of the forecast to the assumptions.
It would seem that a complete estimate of future uncertain
earnings would include both a point estimate and a confidence interval
around it. This point is made by a AAA committee which stated:
The treatment of uncertainty in accounting should perhaps be
divided into two facets. First, there is the analytical
process of observing certain selected characteristics of a
factual situation for the purpose of assessing the degree of
uncertainty which is inherent in the situation. Second,
there is the process of designing financial reports so that
the accountant's assessment of uncertainty is conveyed in the
financial statements. (Committee on Concepts and Standards
External Financial Reporting, 1974, p. 204)
Interaction of Reported Information and Future Events
If any reported financial data have relevance or usefulness to
users, it must be assumed that there is an interaction between that
disclosure, stock prices, and consumer behavior. Consider the current
situation of Chrysler Motors. Due to their tenuous financial position
there is a lack of consumer confidence in their products. People may
not be willing to buy a car from a company which may not be around to
provide future service. Assume it develops that Chrysler's point
forecast of future earnings is reasonably good and that the "proper"
interval is relatively large due to Chrysler's uncertain future. Would
the disclosure of this good forecast alter the value of the interval or
otherwise change consumer confidence from what it would have been had
the information not been disclosed? If confidence can be altered, then
34
the situation is similar to the problem in which the act of measurement
alters the system being measured.
Issue of Accountant Interference
Since what accountants report can have an impact on future events
involving a business entity, it is natural to question whether the link
creates fluctuations in earnings. Prior research indicates that
accounting does not necessarily accentuate business fluctuations (Ray,
1960). However, even if accountants do not contribute to changes in
the level of relevant variables, the measurement process may
contribute, to some extent, to the uncertainty if there is interaction
over time.
In terms of economic reality and the measurement problem, all the
various elements of the process are related. When management prepares
financial statements or forecasts, certain judgments and measurements
relating to the economics of the firm are made. No matter what the
purposes of such reports, the information collected can have an impact
on the future operations of the enterprise because of the interaction
between the accountant's measures and the system in which he is taking
the measurement. The object of accounting research may be to clarify
the relationship between economic events affecting an entity and the
information recorded about that entity. The relationship is mutual, in
the sense that research may be directed toward the process in which
information is generated from economic events, or it may be directed
toward the reverse process in which economic events are affected by
information.
Accounting can learn a great deal from work done previously in
other fields of endeavor which have faced similar problems.
A committee of the American Accounting Association (AAA) touched on
this fact in 1966:
Another aspect of multiple valuations involves the use of
nondeterministic measures or quantum ranges with or without
probabilistic measures. In view of uncertainties surrounding
business activities and the measurement of their impact, the
use of such nondeterministic measures is likely to become a
part of an expanded accounting discipline of the future.
(Committee to Prepare a Statement of Basic Accounting Theory,
p. 65)
Other disciplines long have studied the problems of uncertainty, and
the use of the word "quantum" here suggests a look at the statistical
problems of physics.
One of the foundations of modern physics is the quantum theory.
When first introduced in the scientific community, it marked a
significant breakthrough in the measurement process of physical
phenomena. An investigation of both the issues involved and the
resulting forms of measurement has potential for accounting.
The concept acknowledges measurement difficulties and, therefore,
uncertainties with regard to the position and movement of subatomic
particles. The conflict in classical physics between the wave theory
and the particle theory remained unresolved for many years. Heisen
berg (1958) proposed the uncertainty principle which states that it is
impossible to measure simultaneously with perfect accuracy both
position and momentum. This is because of interaction between the
observer and what is being observed; i.e., it is impossible to separate
the behavior of atomic objects from their interaction with the
measuring instruments.
The application of the quantum concept to accounting seems
obvious. The study of business and economy does not deal with isolated
systems. If what is reported now will influence the future, then it
may create a change in the degree of uncertainty in the forecasted
earnings value itself. In terms of the measurement and reporting of
earnings as well as the production of forecasts by either management or
the concerned researcher, all this is conjecture. The form of
interaction possibly could be explained through information inductance
or as selffulfilling prophecies.
Types of Probabilistic Data
"The concept of probability has always been elusive and lies at
the heart of whatever any of us understand by statistical theory today"
(Savage, 1964, p. 175). According to the Laplacian view, all knowledge
has a probable character, simply because people lack the requisite
skill and information to forecast the future and to know the past
accurately. Therefore, a degree of probability is a measure of the
amount of certainty associated with a belief. Formal logic, as a
science, investigates the rules whereby one proposition can be inferred
necessarily from another. By applying this method to subjective
probability, it is possible to investigate the rules whereby the degree
of one's belief of a proposition varies with the degree of one's belief
of other propositions with which it is connected (Venn, 1964, p.
1920).
What about the measurement of a probability if it is described as
a degree of belief? According to Venn:
There is a large body of writers, including some of the most
eminent authorities upon this subject, who state or imply
that we are distinctly conscious of such a variation of the
amount of our belief, and that this state of our minds can be
measured and determined with almost the same accuracy as the
external events to which they refer . .. we have a certain
amount of belief of every proposition which may be set before
us, an amount which in its nature admits of determination,
though we may practically find it difficult in any particular
case to determine it. (1964, p. 19)
A system which derives the measurement could be a person, a
group of people, a mathematical model, computer simulation, or any
number of things. I.J. Good calls a system an "org" when he
defines four types of probabilities:
(1) Physical (material) probability, which most of us regard
as existing irrespective of the existence of orgs. For
example, the unknown probability that a loaded, but
symmetricallooking, die will come up 6.
(2) Psychological probability, which is the kind of
probability that can be inferred to some extent from your
behavior, including verbal communications.
(3) Subjective probability, which is a psychological
probability modified by the attempt to achieve consistency,
when a theory of probability is used combined with mature
judgment.
(4) Logical probability which is hypothetical subjective
probability when you are perfectly rational, and therefore
presumably infinitely large. (1962, p. 319320)
For those persons who have been exposed to an axiomatic definition of
probability, the relationship of the above to these axioms is that
physical probability automatically obeys the axioms, subjective
probability depends on axioms, psychological probability neither obeys
axioms nor depends very much on them. There is a continuous gradation,
depending on the "degree of consistency" of the probability judgments
with a system of axioms, from psychological probability to subjective
probability and, beyond, to logical probability, if it exists.
According to Good, "every measure of a probability can be interpreted
as a subjective probability" (p. 320). For example, the physical
probability of a six with a loaded die can be estimated as equal to the
subjective probability of a six on the next throw, after several
throws. Further, if one becomes aware of the value of a logical
probability, he would adopt it as his subjective probability.
Therefore, a single set of axioms should be applicable to all kinds of
probability (except psychological probability), namely the axioms of
subjective probability. Finally, it must be said that there is no such
thing as probability in the abstract, for probability only exists in
relation to a particular body of knowledge.
To some, the use of the word "probability" to refer to both a
concept and the index number by which that concept is measured is akin
to circular reasoning or using a word in its own definition, but
There is nothing unusual about making a word do double
service in this way. We do it habitually in all matters of
measurement. Thus, the word "length" is used either for the
abstract concept of extension in space, or for the number
which measures it. (Fry, 1934, p. 207)
When speaking of the probabilistic nature of accounting earnings,
one is concerned with formalizing the process by which these forecasts
are properly reviewed. Based on past experience, the skilled user of
financial statements already possesses a notion of the relative size of
the interval around the point estimate. Therefore, the question is
whether there is some means by which the extent of uncertainty about
such numbers can be made more objective.
We have emphasized here the subjective or personal judgmental
aspects. Savage points out, "At first glance, such a concept seems to
be inimical to the ideal of scientific objectivity, which is one major
reason why we statisticians have been slow to take the concept of
personal probability seriously." (1964, p. 176)
It is appropriate to mention the judgmental influence which has
always existed in accounting measurements. Nothing prohibits the
ultimate results of a reviewer's mentation from being either objective
or subjective as long as it is based on the information available at
the time. If the final result contains an element of "degree of
belief," then it emphasizes the fact knowledge is limited.
This type of probability is not new to accounting (Toba, 1975, p.
11). The word "probability" refers to both the fundamental concept and
the index number by which that concept is measured. The probability of
an event happening is an estimate of one's ignorance about the event.
Sometimes it is important to view uncertainty about an event as the
amount one does not know rather than the amount that is known. In this
way, one may think of probability as the degree of assurance warranted
by a state of partial knowledge or lack of knowledge (e.g., allowance
for doubtful accounts used to bring the valuation of accounts
receivable to an expected value and bad debt expense is estimated).
The alternative to subjective probability is the relative
frequency approach, which is based on observing the portion of outcomes
of one type in an infinite number of experiments to determine the
numerical value of a particular probability. Accounting has few
instances which occur often enough under similar circumstances to
warrant the use the relative frequency approach. However, if
accountants could rely on this method, then the benefit would lie in
its being relatively more objective than other concepts of probability.
The interplay between the concepts of objectivity and subjectivity
in statistics is interesting if sometimes confusing. Since
frequentists usually strive for, and believe that they are in
possession of, an objective kind of probability and since personalists
declare probability to be a subjective quantity, it would seem natural
to call frequentists objectivists and personalists subjectivists.
Churchman demonstrates in a very subtle analysis that the measurement
of relative frequency by necessity also introduces value judgments:
"the operation of verifying the theory of sampling is based on
judgment; the verification of a theory of the generation of events is
based on judgment" (1961, p. 168). Whichever means is chosen, it is
essential that data collected under the other be adjustable. Relative
frequencies must agree with judgment probabilities and judgment
probabilities must agree with relative frequencies when only those data
are available.
In order to maintain relative objectivity, one must adhered to
specific guidelines. In reporting the results of an analysis involving
estimation of parameters, it is important to provide at least (1) a
detailed discussion of the stochastic model assumed to generate the
observations, (2) a full discussion of prior assumptions about
parameter values, (3) the sample information, and (4) information about
posterior probability density functions (pdf) for parameters of
interest. Of course, when using experimental data as a basis for
logical inference, one must mix the statistics with common sense.
When the honest statistician gives you an indirect answer, it
is because he is evaluating the experimental evidence common
to both of you, and allowing you to add the common sense for
yourself. (Fry, 1934, p. 213)
When reporting the results of analyses of scientific studies, the
following must be considered. With respect to the stochastic model for
the observations, subject matter considerations should be reviewed to
justify its form and stochastic assumptions. In the case of earnings
prediction, if theory fails to specify completely the relationship
between variables, the researcher must identify properly his
assumptions as well as those instances where judgments are employed.
If databased information is used, then this fact should be noted
and the sources of the information should be provided. If
nondatabased information is used, it should be examined and
explicated carefully. In this way, the reader will understand what
information, if any, is being added to the sample information. For the
researcher attempting to model the timeseries properties of earnings,
it would be beneficial to disclose the subjective nature of the process
of examining the autocorrelation function in deriving identified
BoxJenkins (BJ) firmspecific models.
Practical Issues in Earnings Forecasting
The Model versus the Method
This section discusses the source of forecast accuracy
differential when alternative formulations are compared. Basically
there are two reasons for this difference: one involving the
functional form (the method) and the other involving the specific
variables included. Any prediction equation is based on a specific set
of statistical procedures which is the method employed (for instance,
ordinary least squares [0LS] versus least absolute value [LAbsV]
criterion). Within the use of a particular method there also exist
differences in accuracy resulting from the set of specific independent
explanatory variables selected.
A method describes the particular procedures which are to be
performed and how they are to be performed. The statistical
forecasting method determines how the parameters are estimated to
develop the forecasting equation or model. The components of the model
and the manner in which they are determined differ with each
statistical method. However, there are many similarities in the
resulting models across methods. The end product may be capable of
being expressed mathematically as a series of parameter coefficients
and model variables not unlike linear regression:
Y =81 1 ;2 2+ 83 3'
Although it resembles OLS, this example could be the output of any
method. Once determined, the model itself can be characterized
independent of the method generating it; i~e., in the above example,
there are three independent variables. The differences and
similarities among methods are important to the questions of fitting
the model to the data and making ex ante judgments generally.
Itwo different BJ forecasting equations share the same method, but
have a different resulting model. An OLS regression with three
independent variables and an OLS regression with five independent
variables are two different models, but here again, they share the same
statistical estimation method. A forecast using a parsimonious BJ
technique versus a distributed lag with macros (DLWM) would be a
comparison of both different methods and different models. Comparing
Foster's (1978) "model 5" and "model 6," as mentioned in Chapter Two,
is an example of different methods (0LS versus ad hoc), but the same
model:
Yt B1 t versus Yt = 1(Yt
A third type of difference is possible. This difference results
from a data availability factor. If one forecaster has information not
available to another, then there can be a difference in prediction even
if both use the same model and the same method. This third case
concerns information availability rather than information use.
Interaction of Economic Events
The business environment can be viewed either as the economy as a
whole or in terms of some segment of it. Trends in the general economy
or the future course of the industry play a significant role in
determining future performance of smaller units. Macro forces (e.g.,
the level of economic activity and other prevailing factors) have an
impact on the individual operations at the microlevel. The extent of
the influence of these factors depends a great deal on the industry
involved. Firms from one group may be affected much less than others
by overall economic trends.
As an example of this phenomenon, consider the impact of the
energy crisis on various industries. Table 31 shows the ranking by
twodigit Standard Industrial Classification (SIC) code of the 2XXX and
3XXX code groups according to the consumption of energy in a recent
year. Obviously there is a great divergence just among the subgrouping
of these two broad industry groups.
Another example of differential economic influence is the change
in certain financial statement items as a result of accounting for
changing prices. Table 32 presents the specifies. Among all the
industries presented in the Arthur Young (1980) study, the drug
industry has the smallest impact of restatement. On the other hand,
broadcasting, airlines, railroads, and tire and rubber each have
impacts of restatements of more than 100%. Similar results hold for
the percent increase in net assets as a result of restatement. Thus,
"understanding the implications of major economic events should be of
considerable value in attempting to forecast earnings changes"
(Brealey, 1969, p. 111).
Practical Issues
The ability to predict earnings also varies considerably depending
on the industry involved. Gray states:
The accuracy of forecasting is strongly influenced by the
nature of the industry to which the firm whose results are
being forecasted belongs. Certain industries, such as
automotive, aerospace, and steel, are much more difficult to
forecast than other industries, such as food, oil, and drugs.
(1974, p. 70)
Gray also summarizes forecasts made by security analysts for ten
industries in terms of mean absolute percentage error (MAbsE). The
results are presented in Table 33. This is a doubleedged sword.
Although the auto industry may be more difficult to forecast than the
other industries mentioned, theoretically it reacts the most to the
macroeconomic factors contemplated in this paper. (see Samuelson 1961,
Chapter 14) Therefore, such an industry is of particular interest to
the current research question.
The question of which specific forces have an impact also is an
issue. Appropriate economic variables to consider are:
(1) Production aggregates (level of economic activity)
(a) real gross national product (GNP); levels or deviation
from trend
(b) real personal disposable income (PDI)
(c) real gross private domestic investment (GPDI)
(d) index of industrial production
(2) Measures of monetary stimulus
(a) real interest rates (interest rate X):
(where X = expected inflation or actual inflation)
(b) money growth relative to trend
(c) unanticipated money growth.
The theoretical basis for selecting GNP is rather obvious: it isa
measure of overall economic activity. The industries that should be
affected are determined primarily by which industry's profits are most
sensitive to the business cycle. (see Samuelson, p. 290291) Good
candidates are capital goods and consumer durables. GPDI is related to
the profitability of industries such as capital goods and may be
indicative of the profitability of cyclical industries in general, if
one believes that investment demand drives the business cycle. This
idea is supported by Samuelson (p. 281, 295 and 299) as well as by
Ackley (1961, p. 337338).
Other forces are influential. Brown and Ball posit that "All
firms in the economy are affected to some degree by monetary policy or
changes in interest rates" (1967, p. 56). Economic theory supports the
notion that real interest rates are a principal determinant of
investment demand. As such, they also are good indicators for capital
goods industries. PDI is thought to be a good barometer for consumer
expenditure, thereby affecting consumer goods industries. The theory
behind the idea of unanticipated money growth is more recent. Barro
(1967) presents a valuable theoretical study of this topic. He argues
that only unanticipated movements in money affect real economic
variables. "Moreover, forecasts of such macroeconomic variables are
generally available, continuously revised on the basis of current
information, and their predictive quality is being extensively
investigated" (Lev, 1980, p. 529).
A synthesis of the economic literature results in a selection of
possible industries and relevant economic variables for each. These
industry/economic variable combinations are listed in Table 34. Up to
this point, the discussion has concentrated on the influence of
macroeconomic factors. The theory supporting these impacts is
relatively strong. As a result, it is foreseen that macro variables
can be incorporated easily into a causal model to predict earnings. On
the other hand, a review of some articles on the use of micro variables
suggests their use to be fruitless. Never the less, two accounting
studies do rely tangentially on micro theory (Brown and Ball, 1967; and
Elliot and Uphoff, 1972), although as Cyert states, "They do not
develop any systematic theory but rely implicitly on propositions of
micro and macro economics" (1967, p. 78).
In general, one would expect a firm's level of activity and,
perhaps, profit to be dependent upon a number of micro factors such as
the following among others:
(1) Output considerations
(a) product mix and price activity
(b) extent of vertical integration
(2) Costs
(a) discretionary expenditures for research and
development, advertising, etc.
(b) inventory method, since LIFO would tend to
smooth the income stream
(c) energy consumption
(d) others
(3) Policies
(a) dividend payout ratio
(b) desire for growth, etc.
(c) nonrecurring events, among others.
While earnings, in the short run, are dominated by the last item
nourecurring eventsthe others on the list (if known or predictable)
would have to be considered in any prediction model which incorporates
microeconomic factors. The problems with these variables lie both in
both their predictability and in lack of knowledge as to the mechanism
by which they might impact earnings. Futhermore, firmspecific data on
these variables are very hard to acquire. The practicality of using
microeconomic variables is doubtful since "the specification of a
complete economic theory of the firm under uncertainty is not available
presently . ." (Lorek, 1979, p.191). Therefore, micro variables are
not considered in this project.
This chapter has identified a number of issues; the next chapter
addresses their resolution. To the extent possible, the model
formulation seeks to follow available theory, while at the same time
avoiding pitfalls where possible.
TABLE 31
Industry Ranking by Energy Consumption
Billions kwh
SIC Equivalent Purchased
Code Rank Industry Fuels & Electric
28 1 Chemicals, allied products 814.7
33 2 Primary metals 654.9
29 3 Petroleum and coal products 397.8
26 4 Paper and allied products 354.6
32 5 Stone, clay, glass products 339.8
20 6 Food and kindred products 268.8
34 7 Fabricated metal products 107.6
37 8 Transportation equipment 101.9
35 9 Machinery, except electrical 96.8
22 10 Textile mill products 90.0
24 11 Lumber and wood products 67.2
36 12 Electric, electronic products 66.7
30 13 Rubber, misc. plastic products 66.5
27 14 Printing and publishing 25.5
38 15 Instrument, related products 20.4
23 16 Apparel, other textile products 16.4
25 17 Furniture and fixtures 13.6
39 18 Mise. manufacturing 13.1
31 19 Leather, leather products 6.6
21 20 Tobacco products 5.5
Source: 1975 Annual Survey of Manufacturers
Nominal Dollar IFCO
175% gain
3% loss
24% gain
21%; gain
135% gain
39% gain
Company, 1980, p. 11)
(Arthur Young and
TABLE 32
Selected Industry Impact of Restatement
Frame 1 Impact on Income from Continuing Operations(IFCO)
Percent Change in Percent Change in
IFCO as a result of IFCO as a result of
constant $ restatement .current cost restatement
Drugs 25 decrease 16 decrease
Equipment 28 decrease 39 decrease
Motor
Vehicle
All non
financial
38 decrease
42 decrease
42 decrease 49 decrease
(Arthur Young and Company, 1980, p. 9)
Frame 2 Purchasing Power Gain/Loss as % of
Airlines
Drugs
Equipment
Motor Vehicle
Utilities
All nonfinancial
TABLE 43
Gray (1974) Results
Mean Absolute Percentage Error
by Industry
Percentage
Industry
4.5%
6.0
7.0
8.0
8.5
12.0
13.5
17.0
18.0
29.0%
Utilities
Drugs
Retail Trade
Paper and Containers
Food and Household Products
Building Construction
Machinery
Aerospace
Automobiles and Parts
Metals
SReported also in Abdelkhalik and Thompson (A+T) [197778, p. 188.]
"Forecasts made over a ten year period by security analysts employed at
a large brokerage house" (A+T, p.188).
TABLE 34
Synthesis of Economic Literature
Industry Variables*
Capital goods industries
Construction.....,...................... G, V, R, S
Materials.............................. M, D, S, R
Heavy Equipment........................ M, D, S, R, V
Consumer durables industries
Automobiles............................ G, V, R, S
Appliances............................. I, M, D, S
Consumer goods industries
Retail sales........................... I, D
Services............................... G
Drugs............................. None
*Key:
G Gross National Product
I Personal Disposable Income
R Real Interest Rate
M Unanticipated Money Growth
D Implicit Price Deflator for GNP
V Gross Private Domestic Investment
S Money Stock(M2)
This table was compiled with the assistance of Professor William
Baumberger, Ph.D., Department of Economics, University of Florida.
CHAPTER FOUR
METHODOLOGY AND PRELIMINARY INVESTIGATION
This chapter describes the research design employed. It contains
the specification of the earnings models utilized, the industries
selected, the earnings variable chosen, and the hypotheses generated.
The chapter is organized in four parts. The first section gives a
methodological overview. The second indicates the nature and sources
of the data used. The third section delineates the procedures utilized
in the annual prediction research, and the last contains the quarterly
methodology. As the procedures are described, the results of some
preliminary investigation are given.
Overview of Research Methodology
A causal modeling approach is taken to predict income before
extraordinary items (IBEI) on both an annual and a quarterly basis.
Forecasts of this earnings number are made for the following subset of
the industries discussed in Chapter Three:
Industry Standard Industrial Classificatiion
(1) Dr~ugs.......... .******** ********** ********* 2830
(2) Construction Machinery and Equipment........... 3531
(3) Special Industry Machinery................... 3550
(4) General Industrial Machinery and Equipment..... 3560
(5) Motor Vehicles, car, truck, and bus bodies..... 3711 and 3713.
The forecast accuracy of a series of models is compared to help
establish the value of both the causal modeling approach and the use of
52
macroeconomic factors in earnings prediction. An explanation of the
particular causal modeling approach, the distributed lag model, is
presented first.
Distributed Lag Methodology Features
The primary methodology employed is an autoregressive, time
series regression model. Three distinct features of this forecasting
model are described below.
1. The model contains negatively lagged (hereafter, lagged)
values of the earnings variable "on the righthand side". The model
also includes exogenous explanatory variables, including a time
variable and, possibly, powers of it. The results of this formulation
achieve many of the same statistical goals of pure timeseries models
in that (1) stationarity is achieved by the inclusion of the time
variables instead of by taking differences and (2) timeseries
properties of past earnings are somewhat captured, depending on the
selection of lags of dependent variables. The method is similar to
naive models because of the ad hoc selection of the lags and, thus, is
unlike the datadetermined iterative process of the BJ technique.
2. Most importantly, the model has the ability to contain lagged
values of macroeconomic variables on the (explanatory) right side.
These exogenous factors are included because of their causal nature
and, hopefully, for their predictive ability. In order to accomplish
both of these objectives, it is necessary for the lags to be "minus
lags" only. In other words, if one is regressing Yt on a set of right
side variables, X1 then the only appropriate values of R are t1, t2,
t3, etc. The fact that the XQ's are lagged in this way gives them the
capability of having a causal (temporal) impact on Yt. However, there
53
arises the question of predictability if the forecast horizon exceeds
the smallest lag. In this case, the lagged variables must themselves
be forecast or the "forecast" is made ex post, with data not really
available at the time the forecast is desired. In the present study,
only negatively lagged variables are used in order to obtain a true ex
ante forecast.
3. The parameters of the model are estimated more than once to
eliminate autoregressive tendencies in the data. The model is fit
using ordinary least squares (0LS) resulting in parameter coefficients
which are efficient and unbiased. The general form of the resulting
equation looks like:
m n p q, 9
Y = Y Y + C 8 k .k~ + aLcn tt
t i= ti j1k1 kj, =
where: i's and j's are lags (up to m and n lags respectively),
some Skj and/or6a may be zero,
Xk's are the macros, and
L's are the powers of the time variable, t.
The resulting model becomes a distributed lag with macros (DLWM) model.
In order to implement this methodology and make statements of
relative accuracy, a few other issues relating to the specific
application of the models must be resolved. As seen from the equation
above, the possibility exists of an unlimited number of lags of both
endogenous and exogenous variables. In this study, an attempt is made
not to overfit the model and thereby to try to capitalize on fitting
the model to the data. The rationale is based on three points: (1)
fewer right side variables allow for more generalizability to other
industries and other time periods; (2) prudent restriction on the
54
number of factors incorporated results in better actual predictability;
and (3) correlation coefficients between various lags of the various
macros (and first differences of macros) indicate multicollinearity.
All choices except one are made ex ante; that is, in selecting
lags of the right side variables, all decisions are made before any
predictions or any comparisons with the actual are made. The one
exception is the selection of the powers of the independent variable
time. Previous annual studies show a high number of biased predictions
with existing timeseries models. The published prediction errors
(predictedactual) are mostly negative, indicating underprediction in
most cases. This underprediction results because the naive models
assume a linear trend which does not capture the temporal nature of the
time series. The general increase in earnings (19571977) has not been
linear for many firms. Instead, it has been somewhat upward curving.
This fact is confirmed by plotting the data used in this study.
Updating Process
In applying the distributed lag model in this dissertation,
"adaptive updating" has been chosen. Prior research has shown the
relative accuracy of BJ updating techniques from best to worst to be
(1) reidentification (not a possibility for the parsimonious
application of BJ techniques), (2) reestimation, and (3) adaptive
forecasting. The DLWM prediction process also can be updated by either
reestimation or adaptive procedures. Under these circumstances, a DLWM
comparison to parsimonious BJ models will make the strongest case for
the latter if the BJ models are reestimated and the causal modeling
approach is updated using adaptive procedures. Therefore, one can make
more definitive statements as to the value of the model/macros under
these circumstances.
All forecasts typically are made for periods beyond an initial
estimation period. The data available in this estimation period
constitute the base upon which forecasts of "future" period's earnings
are to be made. However, if a researcher desires to make forecasts of
one year ahead at more than one point in the future, updating the data
beyond the initial data base is required. There are three recognized
updating procedures: reidentification, reestimation, and adaptive
forecasting. All three rely on data beyond the initial base period,
but vary with regard to the extent to which a statistical methodology
is reapplied. Reidentification is the most severe since this updating
technique has the possibility of changing the model as well as always
requiring reestimation. Reestimation alone merely requires the
parameter coefficients of the previously established model to be
estimated on the expanded data base.
Adaptive updating requires minimal procedures. No reestimation
takes place. An additional data point (actual) is compared to the
forecast already made for that point in time (based on the initial data
set). The difference between the two, a new residual, is used in the
same manner as other residuals are used in that particular method.
Prior research (see McKeown and Lorek, 1978) has shown, in the context
of BJ forecasting, that reestimation is more accurate than adaptive
updating. Reidentification has also been shown to be more accurate
than only reestimating for those who deal with firmspecific models.
When working with parsimonious BJ models, reidentification does not
apply.
Model Comparison Statistics
To measure forecast accuracy, a comparison statistic is required.
As described in each of the following sections of this chapter, various
model forms are used to evaluate the DLWM approach. Forecasts of each
model are obtained for each firm. The relative accuracy of the models
is determined by comparing the ex post errors of each model. Three
different error metrics are used:
Let E = error (predicted actual) and A = actual, then
MSE = 1 C (Ei)2 (mean square error)
n
M~bsE = 1E E (mean absolute error)
n i=1
n I
MAbsE = 1 C I;i (mean absolute percent error)
n i=1 1i
where n = the number of predictions for an industry, a
forecasting horizon, etc.
To test the difference between means of any two models, a Wilcoxon
matched pairs significance test is performed. The test hypotheses are
described below.
Hypotheses
A number of different hypotheses have been generated for
subsequent empirical testing. Some of the hypotheses will be tested by
comparison of the error metrics and significance tests. Others will be
addressed without significant measures provided. Some specific
hypotheses are presented in subsequent sections of this chapter, along
with the procedures used to test them. The general hypothesis is:
The distributed lag model with macros is at least as
accurate as relevant models from the literature.
To perform hypothesis testing, the following stratifications of
the data are considered:
(1) Data Base
(a) Annual sample #1
(b) Annual sample #2
(c) Quarterly sample
(2) Indus tries : 2830, 3531, 3550, 3560, and 3711/3713
(3) horizons: 13 years or 15 quarters
(4) Error measures
(a) MSE
(b) MAbsE
(c) MAbsE.
For 192 of the strata indicated in Table 41, a set of specific
hypotheses is to be tested. These specific hypotheses depend on the
sample used and, therefore, on the relevant comparison model suggested
by the literature. An "X" in the table indicates that ex post accuracy
measurements are taken for each model. A "W" indicates that, in
addition, a Wilcoxon significance measure is employed.
If the following assertions hold, the value of the causal modeling
approach will be clearly demonstrated:
(1) an ex ante unconditional DLWM model performs as well as
a random walk with drift (RWWD) in predicting annual
earnings, and
(2) an ex ante unconditional DLWM model performs as well as
univariate BJ models in forecasting quarterly earnings.
If the influence of macroeconomic variables on earnings is in
fact a causal one, then predictions based on actual macros should be
more accurate than predictions based on predicted macros, i.e., an
unconditional model should outperform a conditional model.
For each stratification indicated in Table 41, the alternative
hypotheses for annual samples #1 and #2 are (null hypothesis in each
case is "is equally accurate.":
Al: DLWM (unconditional) is at least as accurate as IWWD
A2: DLWM (ex ante conditional) is at least as accurate as RWWD
A3: Distributed lag (DL) without macros is at least as accurate
as a RWWD)
A4: DILWM (unconditional) is at least as accurate as DLWM
(conditional)
A5: DLWM (unconditional) is at least as accurate as DL without
macros.
For sample #1 only, there are also alternative hypotheses:
A6: OLS (with macros and without intercept) is at least as
accurate as RWWD
A7: OLS (with macros and without intercept) is at least as
accurate as OLS (with macros and with intercept).
For the quarterly sample, the alternative hypotheses are:
Q14: D]LWM (conditional) is at least as accurate as each of the
four models suggested by relevant quarterly research
Q58: DLWM (unconditional) is at least as accurate as each of the
four models suggested
Q9: DLWM (unconditional) is at least as accurate as DLWM
(conditional).
Two broad categories of data are needed to test these hypotheses.
The first is the object of prediction, the earnings number. Earnings
before extraordinary items has been chosen. The second category
includes the macroeconomic predictor variables. The nature and
sources of these data are described below.
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Nature of the Data Sets
Annual earnings before extraordinary items data are taken from
Compustat Annual Industrial (CAI) tapes. Earnings data for 1958
through 1977 are contained on the 1978 CAI tape. Earnings for 1978 are
taken from the 1979 CAI tape so there are potentially 21 years of data
available. ITwo samples are utilized to test the accuracy of the annual
prediction models. Both samples require firms to be listed on the 1978
CAI: tape and to have earnings figures available by at least 1964. This
cutoff is necessary in order to have sufficient observations to perform
the estimation phase of model construction. It is assumed that the set
of firms contained on the CAI tape is representative of each of the
industries chosen.
Experimental Samples
Annual sample #1. The 1978 CAI tape lists a total of 109 firms
within the five industry groups under study (85 capital/durable goods
and 24 drugs). Only 19 of the 24 firms in the drug industry satisfy
the data availability requirement. Likewise, for the construction
machinery and equipment industry, the special industry machinery
industry, the general industrial machinery and equipment industry, and
the motor vehicles, car, truck, and bus bodies group: there are 9 of
11, 20 of 22, 30 of 38, and 13 of 14 firms, respectively, which m~eet
this requirement. (See Table 55, Frame 1) Thus, the annual sample #11
consists of 91 firms, 72 of which are in the capital/durable goods
industries. See Appendix A for listing of the firms.
Annual sample #2. A subset of the first sample is taken to form
annual sample #2. This new sample consists of all 9 firms of the
construction machinery and equipment industry (3531); a random sample
of 10 firms from industrial machinery group consisting of special
industry machinery (3550) and general industrial machinery and
equipment (3560); and all 13 firms of the motor vehicles, car, truck,
and bus bodies group (3711 and 3713). This sample has been selected in
order to conduct extended forecasting on capital/durable goods firms
and to test further the value of the DLWM approach. A list of these
firms is contained in Appendix B.
Quarterly sample. The 1978 Compustat Quarterly Industrial (CQI)
tape is the source of quarterly earnings before extraordinary items.
Potentially there are 40 quarters of data on this tape; however, data
are missing at both ends. The first quarter listed is normally the
first quarter of 1968, 681. The last quarter listed is normally 771,
so that 37 quarters typically are available.
Because of a peculiarity of one of the quarterly models (to be
described later), it is necessary for all firms of the sample to have
data beginning at the same point in time; thus, cutoff similar to the
annual sample is necessary. In order for a firm to be selected, it
must have data as of the beginning of the tape, i.e., 681. As a result
of this criterion, 14 of the 85 capital/durable goods firms have been
omitted.
The resulting 71firm sample consists of 9 firms from the
construction machinery and equipment industry, 18 firms from the
special industry machinery industry, 31 firms from the general
industrial machinery and equipment industry, and 13 firms from the
motor vehicles, car, truck, and bus bodies group. Appendix C contains
a listing of these firms.
Macro Economic Data
Real GNP, real personal disposable income (PDI), and gross private
domestic investment (GPDI) are available quarterly over a long period
of time. Interest rate data likewise, are widely available. The rate
on treasury debt of various maturities is available on a weekly basis
through the Federal Reserve Bulletin. The rate on corporate debt of
various ratings is available as well. The above macro variables, money
stock data, and a listing of the implicit price deflator for GNP are
available in Survey of Current Business and 1975 Business Statistics.
If one wishes to determine a real rate of interest, a measure of
expected inflation must be subtracted from the interest rate. One
solution is to subtract the actual inflation rate. A theoretical basis
for using actual inflation as a measure of expected inflation is
contained in Fama (1975). Another way to measure expected inflation is
to use survey data. There is a survey of economists, businessmen, etc.
regarding forecasts of future inflation which has been collected by J.
A. Livingston since 1947 and is contained in Carlson (1977).
Money growth is available on a monthly basis from the federal
reserve, and Barro has calculated unanticipated money growth annually
for 1941 to 1975. Economic Outlook USA, of the Survey Research Center
of the University of Michigan, has on a quarterly basis (with
projections and prediction interval) the following: GNP, GPDI, and
personal consumption expenditures.
In this study the major sources of macroeconomic data are the
Survey of Current Business (various monthly issues through June 1979)
and its 1975 statistical supplement, Business Statistics 1975. Other
sources include Barro (1977) for unanticipated money growth and Carlson
63
(1977) for expected inflation. Therefore, the following variables have
been collected:
(1) The four production aggregates are real gross national
product (GNP), real personal disposable income (PDI), real gross
private domestic investment (GPDI), and the GNP implicit price deflator
(IPD), where 1972 = 100.
(2) The measures of monetary stimulus are interest rate data,
unanticipated money growth, and the money stock.
For nominal interest rate data, two yields on U.S. Government
taxable securities have been obtained. The first is the rate on three
month new issues (INTM) and the second is the open market rate on
three to fiveyear issues (INTY). For the measure of the money stock,
the variable "M2" has been chosen, defined as currency, private demand
deposit, and bank time and savings deposits (other than large
negotiable certificates of deposit). For a measure of real interest
rates, an estimate of expected inflation is subtracted from the nominal
rate (INTY). This measure of inflation is obtained from J. A.
Livingston's survey of economists and businessmen; see Carlson (1977).
The availability of these data is discussed in the following two
sections.
Annual macro data set. The data for GNP, GPDI, PDI, iPD, M2,
INTM, and INTY are gathered for the period 1947 through 1978. These
figures represent the revised series as indicated in the July 1977 (p.
16) and July 1978 (pp. 24 and 36) issues of the Survey of Current
Business.
Expected inflation data are gathered for 1947 through 1977.2
Therefore, real interest (RINT) [= INTY expected inflation] is
available 1947 through 1977. Unanticipated money growth has been
obtained for 1947 through 1975. Since data for 19761978 might be
needed, an extrapolation is conducted to generate these years
artificially:
Mt 1Gt+ B2 t+ t1
where M = unanticipated money growth,
G = gross national product,
I = personal disposable income, and
D = implicit price deflator for GNP.
Quarterly macro data set. The quarterly series of GNP, GPDI, PDI,
IPD, INTM, and INTY have been obtained for the first quarter 1947 (471)
through the first quarter 1979 (791). M2 is obtained for the period
511791. Unanticipated money growth does not have a quarterly series.
Expected inflation, while being available semiannually, does not have a
quarterly series. The sources and nature of the earning variables are
discussed in the next section.
Research Design
Annual Research Design
In order to test the value of the causal modeling approach and
specifically the DLWM methodology, a number of further specifications
must be stated. For the annual study, the following aspects must be
determined:
(1) macro exogenous variables;
(2) lags of each macro, or powers of time variable;
(3) comparison modelss;
(4) periods, horizons, bases, industries predicted;
(5) error measures; and
(6) significance measures and sensitivity checks.
Annual DLWM model. As discussed previously, the distributed lag
methodology is quite flexible as to particular model form. For the
purpose of the annual predictions, three macroeconomic factors have
been chosen as exogenous variables and only the first negative lag is
selected for each of these. The variables selected for the capital
durable goods industries are real GPDI, real interest, and money stock
(M2). Two macroeconomic variables hare been selected for the drug
industryGNP and PDI in their first lag only. These choices are based
on economic theory which indicates the influence of these factors [see
Samuelson (1961) and other references discussed in Chapter Three].
This negative lag has been chosen because of the causal implications of
negative lags and because of the need to limit the number of terms (to
avoid overfitting). However, the judgments made are somewhat ad hoc.
The model itself is ex ante in the sense that the model form is
determined in advance and contains only negative lags. This
formulation eliminates the correlational nature of contemporaneous
approaches, such as Lev (1980) and others, which are not true ex ante
forecasts.
The delineation of the DLWM model requires two more specifi
cations. First, both the first and the second power of the time
variable is used to capture the general increase in earnings over time
which has been greater than linear. Second, a problem arises as to
where one acquires the values of the lagged macrovariables beyond a
oneyear prediction horizon. Since these ordinarily are not known at
the time of a forecast for a two or more year horizon, either the
macros are predicted prior to their use, or in a research setting,
actuals are used to make "predictions" after the fact. Predicting in
both these ways helps to isolate the factors which lead to good
predictability: "In practice, the predictive ability of an econometric
model will be jointly dependent on the structure of the model and the
ability to forecast the exogenous variables" (Foster, 1978, p. 123).
In order to evaluate the power of the DLWM methodology, it is
necessary to separate the predictability of the method from the
predictability of the macros. Therefore, two DLWM models are utilized
throughout the research. The first model (unconditional), PRW10,
incorporates actual values of the macros. The second model
(conditional), PRW11, requires independent prediction of the macros.
The forecasting methodology for PRW10 and PRW11 requires a multistep
statistical procedure. This technique is the fourstage least squares
suggested by Fuller, Johnston, and Wallis and described earlier in the
chapter. For the annual model, the formalization is presented in Table
42.
Predicting the exogenous macroeconomic variables. In order to
generate predictions based on the PRW11 model, the values of the
macroeconomic factors for horizons of two years or more themselves
must be predicted. Numerous methods are available for such prediction.
Viewed on a continuum, these methods vary from extremely sophisticated
(assumed to be most accurate), on the one hand, to crude (assumed to
lack accuracy) on the other. If it were possible to predict perfectly
the macros, one would have PRW11 = PRW10. Hence, the example of the
accurate extreme is PRW10. It is natural, therefore, to select a
method of predicting the macros for PRW11 which sets this model
reasonably apart from PRW10. Based on such reasoning, a reasonably
crude method of predicting the macros is selected. This method is an
extrapolative regression:
67
TABLE 42
Annual Four Stage Least Squares for PRW10 and PRW11
Stage 1: To get estimate of Et1, regress
2 3
E = f(t t t M M. intercept)
t1 i 1
t1 t2
Stage 2: To obtain residuals, regress
Et = f(Et_ t t M. intercept)
t1
then generate residuals: zt = Et Et
tt t t
Stage 4: To obtain efficient estimates of the coefficients, make
following transformations using estimate of rho:
^ 2 2 ^2
Et = E PE,, t = t 0(t1)
1 1P p t =t 9(t1)
M. M. pM E = E pE
1 i t1 t1 t2
t t t1
Then regress
3 5*
** (i3)
Et =1 + yE + C B M. + C B t +6*z and set
t t1 ii i t1
i=1 t 1i=4
p = 6+p. Then obtain predictions as follows:
3^^ ^2 ^ *
E = YE + B Mi + ,T + 8 T + B, + p *z
1976 1975 1 1975
i=1 1975
3h 2
E = YE + B Mi + 8 T +B 5 T2. B P**z
1977 1976 ii 1975
i=1 1976
3 *3
E = YE + B Mi + 8 T + T2 P**z
1978 1977 1 0 1975
i=1 1977
1. Et = predicted annual earnings.
2. Albrecht, Lookabill and Mckeown model from their Autumn 1977
Journal of Accounting Research article.
TABLE 43
Annual Models
Note
1
Model Model Type
Last Stage Model Form
Et = Et1 + (Et1
ALM
RWWD
 EO)/(t2)
DLWM
actual
macros
St4t + B5t + E Si i
i it1
4 Bt + 85t + C BIii
i=1 t1
E, = YEt1
Et = YEt1
^ 8
0 8
PRW10
DLWM
PRW11 predicted
macros
DL
with out
macros
OLS using
ALM time
trend
OLS using
AILM time
trend
OLS using
ALM time
trend
Et = YE,, + B
^ ^ 2
+ 8 t + 8 t
PRW30
8 ALMt + B $.M
i=1 t1
= C B M.
i=1 i t1
= fi3BE 6 M. + B
Et 0 At
Et ALM
PRW40
PRW41
PRW42
Notes:
3. The M
t1
are the actual values of macro variables: gross private
domestic investment, money stockM2 and real interest.
4. The M, is actual value for the 1976 prediction and predicted
t1 values for the 1977 and 1978 predictions.
5. ALM is the prediction from the ALM model. Each of the PRW4x models
is "with macros".
6. This model form is used to get better estimates of the beta
coefficients. The prediction equation would be of the same form
as model PRW40.
Number of Firms in Sample 1
TABLE 44
Annual Sample #1 Design
Frame 1 Data Availability
Industry Number
Capi tal/
Durable
Goods:
3531
3550
3560
3711/3713
times years predicted
predictions
less missing actuals
9
20
30
13
72
x 3
216
 22
Drug:
2830
19
x 3
57
 3
54
248 predictions.
Statistics based on
Frame 2 Years Predicted
Horizon
1 2 3
Base Period
Ending
1975 predicted: 1976 1977 1978
Mt = 1t 82t
This particular model has been chosen because plots of the macros
indicate an upward sloping graph. Likewise, a log function could have
been chosen. The predictions are within 10% accuracy based on absolute
percent error.
There are two more reasons for choosing a crude method of
predicting the macros. First, if PRW11 (with crude macro prediction)
should prove to be more accurate than a RWWD, then stronger conclusions
can be made with respect to the value of the methodology. Second, in
order for the procedure to be valuable in practice (as part of the
reviewer's ex ante analysis of management forecasts) it must be easy to
apply and must not rely on unavailable technology or models.
Comparison models. As stated in Chapter Two, the consensus of the
annual earnings prediction literature indicates that the RWWD model
appears to exhibit the best predictability. Therefore, a particular
form of this model, the Albrect, Lookabill and McKeown (1977) random
walk with drift model (ALM), has been selected as a primary comparison
model:
E = E + [(E E)/(t2]
t t1 
As defined here, the drift term within the brackets is the average
increase in prior years' earnings from the first year available to the
previous year, t1. All random walk methods are inherently similar in
that the ex post errors of these models have relatively little variance
across predictions. As a result, they have proved accurate across many
industries. Among the other strengths of the ALM model are its
parsimonious nature, fewer data needs, and its prevalence in the
literature.
On the other hand, RWWD models have the following drawbacks. First,
the method usually underestimates. Second, the methodology could be
called "seatofthepants" and, therefore, is not an efficient
statistical procedure, especially with regard to estimating a linear
trend.
In addition to these models, five other models hare been created.
Four of these and the original three are listed in Table 43. Another
model, PRW20, is so numbered, but never utilized. This model is:
3
E, = 80~ 4t +Bgt +C E i Mi
i=1 t1
That is, the same as PRW10 except for no YEt1. The PRW40 model also
is excluded from the analysis. Essentially, this model is a mechanical
combination of ALM with macros. This model and PRW41 contain the same
explanatory variables. PRW41 achieves better statistical results due
to a more efficient estimation of the B 's.
The utilization of the PRW30 model is important to this research
because it helps to isolate the causes of any superiority of the DLWEM
models which ultimately might occur. If DLWM models are better, it
could be due to the nature of the statistical methodology or because
DLWM models rely on a larger data set than does ALM (inclusion of
macros in DLWM).
Procedures for sample #1. Predictions are made from six models
based on the first annual sample and ex post error measures are taken
over a threeyear holdout period1976, 1977, and 1978. The model
parameters are estimated using an 18year base period (19581975).
With 19581975 as a basis, oneyearahead forecasts of 1976, twoyear
ahead forecasts of 1977, and threeyearahead forecasts of 1978 are
made for the five industries. In each industry, the predictions of
each of the six models are generated, except no PRW11 predictions are
produced for the drug industry.
Accuracy is judged on the basis of two error metrics: ~MSE and
MAbsE. In both cases, a series of stratifications of the results is
emp loyed. (See Table 41.) Total sample error means are calculated as
well as means for each industry, each forecast horizon, and each
industry/horizon combination.
Because of the possible sensitivity of the results to a few large
errors, prediction sensitivity procedures are conducted based on
analysis of the error distributions which result. This is a check on
the sensitivity to a few large errors. No significance tests are run
on the results of this sample. However, bar graphs showing the
distribution of the MAbs%E's for each model are presented in Chapter 5.
Since data are missing at the end of the CAI tape and since the
years 19761978 are predicted in all cases, all ex post accuracy
statistics involving the use of the actual (i.e. error = actual 
predicted) are based on the predictions which have an accompanying
actual available. The breakdown of the availability is shown in Frame
1 of Table 44.
As indicated by Frame 2 of Table 44, there is only one base
period (1975) for all of the predictions made using sample #1 data.
This means that, among other things, oneperiodahead forecasts predict
only 1976 earnings. The results of sample #1 should be highly
sensitive to this restriction. Therefore, it is necessary to have
forecasts generated from a base period other than 1975. In order to
accomplish this, another annual sample is chosen.
Procedures for sample #2. Because of base period sensitivity,
further testing is undertaken. However, only four models are now
utilized and only three industry groupings are involved. A second
series of predictions constitutes the major annual analysis and is, in
reality, an extension of the forecasting which used sample #1. The
nature of the extension is in the number of base periods used to make
predictions. Although the drug industry and PRW40 and PRW41 are not
included, there is considerable benefit of predicting at more than one
base period. In addition, the results are compared more easily to
other research which utilize ten firm samples from twodigit SIC code
industry groups (e.g., Abdulkader (1979)]. The analysis also can
highlight the comparison between the RWWD and the two DLWM models.
Three sets of predictions now are made. First, with 1975 as a
base, 1976, 1977, and 1978 earnings are predicted. Second, with 1976
as a base, 1977 and 1978 are predicted. And third, with 1977 as a
base, 1978 is predicted. This gives three sets of oneyearahead
forecasts, two sets of twoyearahead forecasts, and one set of
threeyearahead forecasts. The years predicted and the forecast
horizons involved are presented in Table 45, Frame 2. In each case,
the models (ALM, PRW10, PRW11, and PRW30) are fitted in the base period
with prediction years held out.
For the distributed lag models (PRW10, PRW11, and PRW30), the
following forecasting procedures are used. For the predictions based
on 1975, the model parameters are estimated using data from 19581975
(18 years; same as sample #1). For the predictions based on 1976, data
from 1958 to 1976 (19 years) are used. The final set of predictions,
based on 1977, are generated using updated 1976 base data, i.e., the
models are not reestimated that year; the updating technique used is
adaptive forecasting. Table 46 contains the prediction equations for
the PRW11 model.
The stratification of the data in this sample is somewhat similar
to that employed in annual sample #1. However, no overall sample
results are calculated. MSE, MAbsE, and MAbsE are calculated for each
industry group, base period, and forecast horizon. This results in 24
strata for which summary error statistics are calculated. Of these, 21
are subject to Wilcoxon matched pairs significance tests based on MSE.
(See again Table 41.) The sample size for each stratum is presented
in Table 45, frame 1.
Annual hypotheses. Comparing the relative performance of PRW10
and PRW11 to ALM is the primary purpose of the research conducted here.
Any superiority of one versus the other can be attributed to either
the difference in method or the difference in the model. If ALM proves
to be more accurate than PRW11, then another possibility exists; that
is, the need to predict better future values of the macro variables
used with PRW11. Therefore, two other comparisons are in order.
First, a comparison of PRW10 and PRW11 indicates the value of more
accurate prediction on the macros and demonstrates the decline in
predictability due solely to their prediction. Second, a comparison of
PRW10 and ALM directly provides the answer to the question of the value
of the DLWM approach. Any difference here again can be due to both
differences in statistical method and the set of independent variables
utilized, i.e., the model.
Other comparisons made include: PRW10 versus PRW30, to isolate the
value of the macros separate from any difference in method; and PRW41
versus ALM, to test the same question. Finally, a comparison of PRW30
and ALM shows the value of the distributed lag method since neither
model contains macros. These comparisons are presented graphically in
Figure 1 and are listed below in accordance with the numbering system
given in the overview to this chapter:
B~Eypothesis Tests for
Al: PRW10 is at least as accurate as ALM [value of DLWM method]
A2: PRW11 is at least as accurate as ALM [difference in model
and method]
A3: PRW30 is at least as accurate and ALM [value of DL approach]
A4: PRW10 is at least as accurate as PRW11 [goodness of macro
prediction]
A5: PRW10 is at least as accurate as PRW30 [value of macros only]
A6: PRW41 is at least as accurate as ALM [value of macros only]
A7: PRW41 is at least as accurate as PRW42 [difference in esti
mating OLS regression
coefficients]
Models With Macros
 >PRW10
A4
HDTI
Models Without Macros
Distributed Lag
Methodology
Non , PRW41
Distributed Lag A6
Models
ALM A7
PRW42
Relationships Between the Hypotheses and the Models
Figure 1
TABLE 45
Annual Sample #2 Design
Frame 1 Sample Size for Each Stratification of Annual Sample #2
Industry Group
(number of firms)
Base
(10)
10
9
7
26
9
7
16
7
26
16
7
49
(13)
13
11
10
34
11
10
21
10
34
21
10
65
(32)
32
29
26
87
29
26
55
26
87
55
26
168
Ending
1975
(9)
9
9
9
27
9
9
18
9
27
18
8
54
1976
1977
All
Frame 2 Years Predicted and Horizons
Horizon:
Base Period
Ending
1975
1976
1977
3
1978
1977
1978
1976
1977
1978
Period Horizon 3531 3550/ 3711/ All
~
I
1
2
3
All
1
2
All
1
1
2
3
All
TABLE 46
PRW11
Prediction Equations
Parameters estimated on data 19581975 (i.e. Base = 75):
E M
1 1 ~
+ B T + T2+ + P Z
4 5 01975
1975
E
1976
=IY1975 +
(one year hoizon)
i=1
E1977 Y1976 +
(two year horizon)
B Mi + B T + B T + BO + 9
1976
.Z
1975
3
1978 Y1977+
(three year horizon)
*3
1975
B Mi +B T + 8T2 8
1977
Parameters reestimated on data 19581976 (i.e. Base = 76):
3
E = yE + C +B T +~gZ 8 T
1977 1976 Bii 4 50
i=1 1976
(one year horizon)
1976
8.Mi + 8 T + i$ TZ+ B + P
1977
E = YE +
1978 1977
(two year horizon)
.Z
1976
Data base updated for 1977 atualy (i.e. Base = 77):
3
c B M +B BT +f T2 B
ii 4 5 0
i=1 1977
E1978 Y1977 +
(one year horizon)
1977
Quarterly Research Design
To evaluate the generalizability of the predictive value of macro
factors, models utilizing quarterly data also are studied. To test the
hypotheses listed below, six model forms from three distinct
methodologies are utilized. A quarterly PRW10 and a quarterly PRW11
are generated as the primary models for study. For comparison
purposes, four other models are selected. The first three of these are
the parsimonious BJ models of Foster; Brown and Rozeff; and Watts
Griffin. The last model is the regression equivalent of Foster's BJ
model, which was suggested by him in his book as well as in his
article.
Quarterly DLWM models. In order to maintain the causal nature of
the models (as with the annual study), only negatively lagged values of
the macros are utilized. Within the framework of the DLWM model (and
after economic theory has suggested which macros), there still remain
many specification alternatives which must be made based on the
researcher's judgment. While a macroeconomic variable such as GPDI
theoretically does affect capital goods businesses, predicting
quarterly earnings using quarterly observations of macros gives rise to
the question of time needed (allowed by researcher) for the macro to
take effect. If the GPDI of a year ago is important, then the model
should include a lag of t4. If the GPDI of the preceding year is
important, then possibly the sum of the last four quarters is
appropriate. Personal judgment is required, since the literature does
not contain the necessary refinement. Three basic differences between
the annual and quarterly model can be identified.
First, for the quarterly research a smaller set of macro variables
must be used since the quarterly data base consists typically of 37
observations, 7 of which are in a hold out sample. There is serious
concern for enough data points to estimate properly the number of model
parameters needed in the quarterly DLWM model; hence, the least
theoretically supportable macro variable is emitted. For the capital
and durable goods industries, no real interest variables are
incorporated into the quarterly model.
Second, for the causal impact of GPDI and M2 fully to take place,
the last four quarters of these variables are summed. In order for the
model fitting process to identify turning points, a t2 lag of GPDI is
included and the money stock (M2) variable remains at t1 lag as in the
annual work. This lag combination is selected judgmentally.
The remainder of the model includes two lags of the dependent
variable, t1 (the previous quarter) and t4 (the same quarter last
year). Both time and time squared are included as before. For the
identity of the particular quarter involved, three dummy variables are
added. Thus, quarterly earnings are a function of time, prior
earnings, the quarter being predicted, and macroeconomic forces. The
complete formulation of PRW10 is presented below:
Et = 80 + B T + B T2+ YIE~ + YZE~ + D1 + D2 + D) +
S 4 4 2 
+ 8( M, ) + B ( EM ) +t ( B M )
i1ti i=1 ti i=1 ti
where M1 = money stock, and M2 = gross private domestic investment.
Prediction of quarterly macro variables. As with the annual
formulation, the values of the macro variable beyond a oneperiodahead
horizon must be predicted independently for subsequent use in the
horizon must be predicted independently for subsequent use in the
quarterly version of PRW11. The manner of prediction and the rationale
are the same as that of the annual research. The macro variables are
predicted using an extrapolative regression: Mt ~ it + B2t This
somewhat crude prediction methodology allows for ease of application
and for reasonable differentiation from PRW10 (where the values of the
macros are supplied ex post and, therefore, are 100% accurate).
Comparison models. Three BJ models are estimated so that
comparison accuracy is available to evaluate the predictions of the
PRW10 and PRW11 models. The three BJ models are (in the customary
notation):
Model
BJF
BJBR
BJWG
where
The prediction
P D) Q Prior work by
0 1 0 Foste (arins
0 1 1 Brown and Rozeff (EPS)
0 1 1 WattsGriffin (earnings)
autoregressive ,
differencing,
moving average,
autoregressive,
differencing, and
moving average parameters.
each can be expressed as
ypd ]
1 0 0
S0 0
0 1 1
P P seasonal
D = seasonal
Q = seasonal
p = ordinary
d =I ordinary
q = ordinary
equation for
BJ: =E + (E E )+a+
BJ: t t4 1 t1 t5) +t + 0
BJBR: Et = Et + 1(Et E ) + at 8 *at
~~ Et5 t6*t1 1*at4 1 1*at5
BJWG: Et =Et4, + (Et1
where $1 is a seasonal autoregessive parameter,
60 is deterministic trend constant,
81 is seasonal moving average parameter,
61 is moving average parameter,
and the a 's are disturbance terms.
Each model is fit using an additional drift term, although Brown and
Rozeff and WattsGriffin did not use one in their original research.
The last comparison model, designated FOST, is
E = E + B(E E ) + 6 where 6 is a drift term.
t t4 t1 t5
Although Foster used BJ techniques to estimate both B and 8, it is
possible to fit this model using OLS. To do so, one must regress
[Et Et 6J = B(Et Et
with the proper definition of the drift term, 8. For the current
research, the average change in quarterly earnings is used:
6i = (Et E E8+)/4(t4 (681 + i))
where i = 1 for first quarter,
= 2 for second quarter,
= 3 for third quarter, or
= 4 for fourth quarter.
The analysis proceeds with the use of these six models.
Procedures. For each firn for each model, 15 forecasts are made:
a set of 5 forecasts at 3 points in time. One, two, three, four,
and fivequarterahead forecasts are made with 752, 753, and 754,
respectively, as the base quarter. Data from 681 to 752 are used to
make the original estimate of the parameter. Then updated forecasts
are needed for those based on 753 and 754. PRW models and the FOST
model are updated using adaptive forecasts. BJ models are reestimated
each time. Thus, the first set of predictions is based on data from
681752 inclusive, i.e., 30 quarters. The second set is based on 31
quarters and the last on 32 quarters. The 15 forecasts and horizons
are listed in Table 47.
For each stratification of the quarterly sample, the three summary
error statistics calculated are MSE, MAbsE, and MAbsE. In the case of
the MSE and MAbsE calculations, a statistical significance of the
difference between models is also determined. This measure of
difference is again the Wilcoxon matched pairs test. For the MAbs%E
results, bar graphs are presented in Chapter 5 to give an indication of
the error distribution for each model.
As indicated by the sample size data of Table 48, missing actuals
exist in both industry 3560 and in the 3711/3713 group. For industry
3560, there are two fourthquarter 1976 (764) actuals missing and three
771 actuals missing. For the 3711/3713 group, there are two missing
actuals in both quarters 764 and 771.
Quarterly hypotheses. Based on the information contained in the
three individual error statistics, the quarterly hypotheses can be
formulated and tested. The following nine hypotheses are tested many
times with each of the three error measures. In terms of the notation
used in this section, the hypotheses can be stated as follows:
Hypothesis
Q1: PRW11 is at least as accurate as FOST.
Q2: PRW11 is at least as accurate as BJ1.
Q3: PRW11 is at least as accurate as BJ2.
QA: PRW11 is at least as accurate as BJ3.
Q5: PRW10 is at least as accurate as FOST.
Q6: PRW10 is at least as accurate as BJF.
Q7: PRW10 is at least as accurate as BJBR.
Q8: PRW10 is at least as accurate as BJWG.
Q9: PRW10 is at least as accurate as PRW11.
Computing Systems Utilized
The majority of the data are analyzed using the Statistical
Analysis System on an Amdahl 470 V/611 with OS/MVS release 3.8 and
JES2/NJE release 3. Computing uses the facilities of the Northeast
Regional Data Center of the State University System of Florida, located
on the campus of the University of Florida in Gainesville. Additional
computing is accomplished using the Florida State University Computer
Center's Control Data Corporation cyber 170, model 730 with NOS
operating system. The results of these calculations are presented in
the next chapter.
Notes to Chapter Four
1. Such an extension would not necessarily carryover to another
industry unless its "true" model was quite similar.
2. Carlson's data are through December 1975. I obtained 1976 and 1977
data from Professor William Baumberger, department of economics,
University of Florida. Data beyond 1977 are available by
contacting Donald Mullineaux at the Federal Reserve Bank of
Philadelphia.
3. As is the case with all DLWMI forecasts, the final term in the
prediction equation uses the residual from the last year of the
base period. For a 1978 forecast this would be the residual from
the prior year. However, the data set used to generate the
estimate of the parameter coefficients did not include data for
1977, so that there is no residual for the prior year, 1977. In
order to have a onestep ahead forecast, it was, therefore,
necessary to artificially gererate this residual. This process of
updating is basically adaptive forecasting as opposed to
reestimation.
TABLE 47
Summary of the Prediction Quarters and Horizons
Base
Estimation
Period
Updated for
Quarter
Predicted
(horizon)
681 752
581 752
681 752
753 + 754
761(1)
762(2)
763(3)
764(4)
771(5)
753
754(1)
761(2)
762(3)
763(4)
764(5)
753(1)
754(2)
761(3)
762(4)
763(5)
TABLE 48
Sample Size for Each Stratification of the Quarterly Sample
Industry
3531 3550 3560 371X
Stratification
Industry
Horizon 1
135
270 458 189
27 54 93 39
27 54 93 39
27 54 93 39
27 54 91 37
5
Total
Base 752
27
135
45
54 88 35
270 458 189
90
155
65
63
61
189
753
45 90 153
754
Total
45
135
90 150
270 458
CThe number of firms in each industry is 9, 18, 31, and 13 respectively.
CHAPTER FIVE
EMPIRICAL WORK AND RESULTS
The results of the annual and quarterly samples appear to
indicate, to varying degrees, that the value of the distributed lag
with macros (DLWM) approach has been established. Accuracy
measurements are not consistent across industries and across firms
within an industry. However, the number of times that one of the two
DLWM models is more accurate than the comparison model, or is not
significantly less accurate, forms a large portion of the results. The
relative accuracy is not consistent at any levelindustry, horizon, or
data setalthough the DLWM model generally performs worse based on one
error metric, mean absolute percent error (MAbsE).
With so many specific hypotheses tested, instances can be found in
which the aull is rejected at a significant level almost by chance.
Many findings of one stratification are contradicted in another stratum
which share many of the same characteristics. Despite the mixed
results, it is possible to make some general observations, conclusions,
and trend analyses. Specific results are discussed below according to
the sample to which they pertain. After the second annual sample
results are presented, a preliminary synthesis is offered. Then, the
quarterly results are delineated, followed by an overall comparison of
the findings of all three samples. Final conclusions are reserved for
Chapter Six.
Annual Sample #1 Results
Dyerview
The results of the sample #~1 predictions are mixed. While there
is overall indication that macro forces are useful in predicting
earnings, the specific industry results show this is not always the
case. Generally, the use of macro factors is legitimate in the mean
square error (MSE) metric case, although not with the DLWM models
(PRW10 and PRW11) for some of the capital goods industries. Even for
the two industries (drugs and general industrial machinery and
equipment) where macro factors do not perform well, the distributed lag
(DL) model without macros (PRW30) outperforms the Albrecht, Lookabill
and McKeown (ALM) model. Due to large standard deviations, most
differences in MSE should not be significant.
Originally DLWM models were compared to ALM because a random walk
with drift (RWWD) is considered the best annual prediction model
according to current literature; never the less, it appears the ALM
version can be bettered in every industry studied. Of the six models
compared by industry, ALM is never the one with the smallest MSE,
although ALM comes in a close third in the Special Industry Machinery
and Equipment Industry (3550).
A frequency distribution for absolute percent error (Abs%E) of
each of the six models is presented in Figure 2. The vertical
dimension represents the number of predictions from the capital/durable
goods industries which fall within the 19 ranges of AbsE plotted on
the horizontal axis. Any prediction error greater than 300% in
absolute value is not plotted. The size of the ranges on the
horizontal axis changes.
87
AL.'4 
?RW30
Ditibto of Abolt Pecn Ero
fo ah oe
Fiur 2
Range
Legend to Figure #2
SCALE FOR HORIZONTAL AXIS
Width of
the Range
2%
2
2
2
20
10
10
10
10
10
10
10
10
10
25
25
25
100
Range
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
or more but les than
2%
4
6
8
10
20
30
40
50
60
70
80
90
100
125
150
175
200
300
6
8
10
20
30
40
50
60
70
80
90
100
125
150
175
200
