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RATIONAL BIAS IN MACROECONOMIC FORECASTS
by
David Laster, Paul Bennett, and In Sun Geoum
Federal Reserve Bank of New York
Research Paper No. 9617
July 1996
This paper is being circulated for purposes of discussion and comment only.
The contents should be regarded as preliminary and not for citation or quotation without
permission of the author. The views expressed are those of the author and do not necessarily
reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.
Single copies are available on request to:
Public Information Department
Federal Reserve Bank of New York
New York, NY 10045
bnvg
Rational Bias in Macroeconomic Forecasts·
David Laster
· Paul Bennett
In Sun Geoum
Research and Market Analysis Group
Federal Reserve Bank of New York
33 Liberty Street
New York, NY 10045
Tel: (212) 720-5647 (Bennett)
E-mail: paul.bennett@frbny.sprint.com
Current Draft: July 1996
Comments Invited
Abstract
This paper develops a model of macroeconomic forecasting in which a
forecaster's wage is a function of his accuracy as well as the publicity he
generates for his firm by being correct. In the resulting Nash equilibrium,
forecasters with identical models, information, and incentives nevertheless
produce a variety of predictions, consciously biasing them in order to maximize
expected wages. In the case of heterogeneous incentives, the forecasters whose
wages are most closely tied to publicity, as opposed to accuracy, produce the
forecasts that deviate most from the consensus.
We find empirical support for our model using a twenty-year panel of real
GNP/GDP forecast data from Blue Chip Economic Indicators. Although the
consensus outperforms virtually every forecaster, many forecasters choose to
deviate from it substantially and regularly. Moreover, the extent of this deviation
varies by industry in a manner consistent with our model.
•our thanks to Debbie Gruenstein, Lara Rhame, and Alka Srivastava for capable research assistance. Leonardo Bartolini,
Richard Cantor, Arturo Estrella, Linda Goldberg. Ethan Harris, Danyll Hendricks, Bev Hirth~. Jose Lopez, Rick Mishkin, Don
Morgan. Frank Packer, Eli Remolona, Tony Rodrigues, Michael Woodford, Steve Zeldes, and other attendees of the Federa1
Reserve Bank of New York Friday seminar series provided valuable comments. We also wish to thank Robert Eggert for help in
categorizing the organizations represented in his newsletter, Blue Chip Economic Indicators.
The views expressed in this paper arc those of the authors and do not necessarily reflect the position of the Federal Reserve
Bank of New York or the Federal Reserve System.
Empirical tests of the rational expectations hypothesis as it applies to professional
macroeconomic forecasts generally examine whether predictions of a macroeconomic variable are
unbiased and efficient. 1 These analyses presume that, because forecasters have strong economic
incentives to be accurate, the numbers they produce represent their best estimates. Herein lies an
interesting question.· A forecast that best allows a forecaster to achieve his economic goals may
not be "best" in a statistical sense. Indeed, as Zamowitz and Braun (1992) have documented,
group mean ("consensus") forecasts are more accurate than virtually all individual forecasts.
Since consensus forecasts are available publicly on a timely basis, this suggests a conundrum:
Why do firms continue to produce forecasts that are unlikely to be more accurate than the
consensus? A related puzzle, noted by Lamont (1995), is that some experienced forecasters
consistently produce projections that are outliers relative to other professional forecasts. These
observations suggest the possibility that forecasters, when making their projections, may have
goals in mind unrelated to the pure pursuit of accuracy.
In this paper we develop a model in which forecasters' wages are based on two criteria:
their accuracy and their ability to generate publicity for their firms. Accuracy is defined in the
usual sense of minimizing expected forecast error. Publicity comes from having the most accurate
forecast in a given period. The model demonstrates that, even in the case where all forecasters
have identical information and identical incentives, forecasters' efforts to maximize their expected
wage will lead many of them to consciously bias their projections in order to differentiate their
views from the consensus. Thus, in contrast to the standard rational expectations approach, our
model is one of "rational bias." The model has an additional implication for the case where the
1
Tuis is the approach followed by numerous researchers in the empirical rational expectations literature, such as Figlewski and
Wachtel (1981) and Keane and Runkle (1990). For a current discussion of the issues, see Crousbore (1996).
2
incentives forecasters face vary by industry. Forecasters working in industries that value publicity
most will make predictions that deviate most from the consensus.
After examining the model, we test some of its implications using a twenty-year panel of
. forecasts of annual real GDP and GNP growth from Blue Chip Economic Indicators, a widely
used survey of professional forecasters. Sorting the forecasters into six industry categories, we
find that those who work for banks and industrial corporations -- the types of firms that might be
expected to value forecast accuracy -- tend to produce forecasts that are closest to the consensus.
Independent forecasters, who stand to benefit most from favorable publicity, tend to associate
themselves with outlying forecasts.
The plan of this paper is as follows. The first section briefly reviews prior research and
describes the forecasting industry. The next section develops a model of rational bias in
forecasting and examines several of its implications. Empirical support for the model is provided
in the third section. The final section offers a summary and discussion.
I. Background
Previous work
Research examining whether macroeconomic forecasts are consistent with models of
rational expectation has produced mixed results. McNees ( 1978) finds only limited support for
the hypothesis that the forecasts of unemployment, inflation, and real GNP growth by three major
econometric forecasting firms are efficient and unbiased. Figlewski and Wachtel (1981) conclude
that individual inflation forecasts from the Livingston survey are biased and have serially
correlated errors, inconsistent with rational expectations. Critiquing previous empirical studies of
3
the rational expectations hypothesis, Keane and Runkle (1990) perform more carefully controlled
tests. These provide evidence that macroeconomic forecasts from the ASA-NB ER survey of
professional forecasters incorporate full information and are unbiased, " ... salvaging the possibility
that the rational expectations hypothesis is empirically valid" (p. 730).
Bohnam and Cohen
(1995), however, question these results on technical grounds. Jeong and Maddala (1996) reject
the rational expectations hypothesis for a set of interest rate forecasts from the ASA-NBER
survey. In short, a preponderance of statistical evidence calls into question the notion that
professional forecasts are rational in the sense of being efficient and unbiased.
Casting further doubt on how closely forecaster behavior conforms to rational
expectations models are recent studies that suggest that macroeconomic forecasts are colored by
the incentives forecasters face. Ito ( 1990) finds that exchange rate forecasts are systematically
biased toward scenarios that would benefit the forecaster's employer. He terms this bias "wishful
expectations," but leaves unresolved whether it reflects irrational wish-fulfilment or whether it is
the product of rational behavior by individuals responding to corporate incentive structures.
Lamont (1995) hypothesizes that a forecaster's willingness to make predictions that deviate from
the consensus may vary systematically with his level of experience or seniority. Analyzing
forecasts of GNP and GDP from an annual Business Week survey, he finds that forecasters who
have been in the industry longer exhibit a greater willingness to deviate from the consensus.
Ehrbeck and Waldman (1996) develop several models in which forecasters, wishing to signal their
competence, resist changing their forecasts in response to new information. Using data on U.S.
Treasury bill rates, they are unable to find evidence consistent with their model of rational bias.
This paper makes two contributions to the literature on forecaster behavior. First, it
4
develops an original model in which identical forecasters consciously differentiate their
predictions, creating the impression that there is a divergence of views when in fact there is none.
Second, it uses a new panel of data to demonstrate that the extent to which forecasters deviate
from the consensus varies by their industry of employment. Before presenting our model of
forecaster behavior, we briefly discuss the job of the professional forecaster.
The roles of the professional forecaster'
Professional macroeconomic forecasters work for a variety of employers such as banks,
securities firms, nonfinancial corporations, and consulting firms that specialize in econometric
modeling or other types of economic analysis. A key part -- and in some cases the entirety -- of
the forecaster's job is to provide analysis internally: to track economic variables, make
forecasts, and share insights with the organization's decision makers. Providing macroeconomic
forecasts is thus one way the economist supports his firm's efforts for which the accuracy of the
economic analysis and forecasting is crucial.
The other fundamental role of economic forecasters is to provide marketing for their
employers. Through his public speaking engagements, magazine articles, television interviews,
and quotes appearing in the press, the economist keeps his employer's name visible before
important audiences. This external role requires presenting an image of expertise and originality
to the public. In this arena, where the audience is of a broad range of backgrounds, the manner
in which an economist presents his analysis may count as much as its content. The forecaster
operating successfully in this environment provides publicity for his firm.
1
For a more extensive discussion. see Henry (1989).
5
Surveys of professional forecasters
One way for a forecaster to gain publicity for his firm is by participating in surveys of
professional forecasters. These surveys, which appear in the business press as well as in
specialized publications, call attention t_o the firm whose forecasts for the most recent prior
period came closest to the actual outcome. Business Week, for example, has for a number-of
years featured a collection of macroeconomic forecasts by business economists in its year-end
issue. Accompanying the forecasts is a separate write-up on the economist whose prior-year
projection was closest to the mark. The write-up, complete with photograph, also prominently
lists the firm for which the economist works. Similarly, The Wall Street Journal rewards the
most accurate participant in its survey of professional forecasters with a separate article. The
publisher of Blue Chip Economic Indicators, a monthly newsletter compiling dozens of
professional economic forecasts, holds an annual dinner at which the most accurate forecaster
for the previous year is honored.'
In order to survive, a survey must offer benefits to all parties involved: the publication,
its readers, and the participating firms. The publication gains useful data that it can share with
its readers, boosting iL~ circulation. Readers gain information about the outlook for the
economy. Firms that go to the trouble of responding to a survey, offering the fruits of their
labor free of charge, also gain something - media exposure. This includes the chance to receive
the favorable coverage that comes from producing the best forecast in a given period. This
arms-length, high-profile reporting of its forecasting expertise might even be more effective in
2A recent example demonstrates
how significant these contests have become. When Lawrence Meyer was nominated to the
Board of Governors of the Federal Reserve System in February 1996, newspaper accounts noted that his economic forecasting firm
had been cited twice in recent years for having the top forecast in Blue Chip Economic Indicators.
6
attracting new clients than a paid advertisement. Because media citations also enhance a
forecaster's own reputation, he will be particularly willing to help his firm by participating in
these surveys. 3
· II. The Model
We develop a model that shows how forecasters' efforts to balance the twin objectives of
accuracy and publicity can lead them to produce biased macroeconomic forecasts. Heuristically,
if all forecasters have similar information, the pure pursuit of accuracy will lead to forecasts that
cluster tightly around a consensus. Forecasters seeking publicity, however, will not want to be
in the cluster, since their forecasts would then have little or no chance of winning them
widespread attention. Instead, they will select forecast values that have a reasonable likelihood
of occurring but which are not already being forecast by others. As an extension of this
reasoning, those who are especially publicity-conscious should be more inclined to make
unconventional forecasts; those who emphasize accuracy will make projections that cluster
around the most likely outcome. The following sections spell out the details.
Timing and information structure
Assume that there arc N firms, each of which employs an economic forecaster. At date
0, the forecasters announce their predictions of next period's level of a macroeconomic variable
x whose probability distribution function (pdf) is discrete. 4 Forecasters have access to two types
3
Michael Woodford notes that just as these publications have strong incentives to publicize the most successful forecaster, they
a1so have strong incentives not to publicize the poorest performers. This asymmetric media coverage is an efficient mechanism for
encouraging organiultions to participate, and to continue participating. in a survey.
4Toe discreteness assumption renecL'i the way in which widely followed macroeconomic variables are reported. For example,
the real GDP growth rate and the unemployment rate are rounded to the nearest tenth of a percent even though the level of GDP
and the number of people working and looking for work are measured with greater precision.
7
of information, on which they base their predictions of x: (I) the pdf of x, f(x); and
(2) the contemporaneous distribution of forecasts made by those in the profession, denoted n(x).
By assuming the existence of a pdf on which forecasters concur, the model seeks to
explain the dispersion of forecasts without appealing to differences among forecasters'
information sets, methodologies, or abilities. Forecasters in fact rely on extremely similar data
sources; the statistical models they use tend to produce similar near-term forecasts. While some
differences of opinion among forecasters are inevitable, a strength of the model is its ability to
explain how a dispersion of forecasts can occur even in the absence of these differences.
Our other key assumption is that when making their forecasts, each forecaster is aware of
the distribution of contemporaneous forecasts, n(x), a function which meets the condition
(I)
Ln(x) = N.
The assumption that forecasters know n(x) reflects an industry environment in which forecasters
reveal and actively debate their views with one another. The forecasts that appear in the
December issue of Blue Chip Economic Indicators, for example, are very similar to those
appearing in the November issue. Even if important new information has arrived in the interim,
forecasters can generally find out how others in the profession have adjusted their views through
published reports, statements in the press, or personal conversations. Thus, in the model, the
dispersion of published forecasts is due not to differences in information and methodologies, but
to the strategic behavior of forecasters jockeying for position.
At date I the realized value of the variable, x0 , is announced. A forecaster's wage is then
set based on his ex post performance.
8
Forecasters' compensation
A forecaster is paid according to how well he fulfills the roles of internal adviser and
source of media attention. In the first role, the forecaster helps his firm decide such questions as
.how many workers to hire, how much to produce, and how large a stock of inventories to carry. ·
An accurate forecast will enable the firm to plan wisely; a poor forecast will create inefficiencies
and missed opportunities. More specifically, we assume that the opportunity cost L of an
inaccurate forecast is a function of forecast error:
(2)
L(x)
= L(x
0 -
x).
L represents the difference between the profits a firm actually realizes from operations and how
much it would have earned had its forecaster been exactly correct. (This excludes any gains in
profitability due to publicity, which are measured separately). By construction, the function L
achieves a minimum value of zero when its argument is zero.
A forecaster can also contribute to his firm by enhancing its reputation. The firm whose
forecaster is the one who correctly predicts the value of x receives favorable publicity worth P.
But if more than one forecaster predicts this value, the publicity must be shared among all of
their firms. More formally, if the realized value of the forecast variable is x0 , the value of
publicity derived from a forecast of x equals
(3)
A(x) = P/n(x)
A(x) = 0
if x = x0 ; and
otherwise. 5
Forecasters are paid for their contribution to their employers, as measured by their
~ An additional assumption that would make the model more realistic is that if no forecaster correctly predicts the value of x, all
those who come closest will equally share the publicity:
A(x) = P/[n(x) + n(2s0-x))
if n(< 0) =0 and I x-x,I :5 lz-x,I
for all z for which n(z) > 0.
As a practical matter, this will not alter the equilibrium because, as we observe in footnote 12, every value in the range of
possible outcomes will be forecast by someone.
9
accuracy and the advertising they generate. Assuming a linear pay structure, forecaster i earns
i = 1,2, ... ,n
where w; is forecaster i's wage,
V;
is a constant, s, :2: 0 measures how closely forecaster i's pay is
tied to his accuracy, and b; :2: 0 reflects the size of the bonus he receives for making a forecast
that garners publicity by being among the most accurate.
It will simplify the analysis considerably to specify L to be a quadratic loss function.6
Thus, the wage of the ith forecaster, who predicts
X;
when the variable's realized value is x0 ,
equals
(4)
i = 1,2, ... ,N.
If forecasters are assumed to be risk neutral, their optimization problem reduces to choosing the
value of X; that maximizes their expected wage
i = 1,2,... ,N,
where the final term is the expected value of the forecaster's bonus for correctly predicting x.
Lettingµ= E(x 0), this expression simplifies to 7
(5)
where w;* = V; - s;Yar(x). The constant w;*, which is beyond the control of forecaster i, can be
interpreted as his expected base wage, absent bonus, for forecasting the value µ.
The final two terms in equation (5) summarize the trade-off between accuracy and
6
Alternative functional fonns will produce very similar results. If, for example, L were a function of absolute error instead of
squared error. forecasters' expected wage would he pcnali1.ed for deviations from the median of the pdf as opposed to its mean.
The
analysis would be essentially the same.
7Toe key step
is to note that
Etx 0 -x,)2
= El(x0 -µ) + (µ-x 1)]2
= E(x 0-µ) 2 + 2(ft-x,)E(x 0-µ)+(µ-x,)'.
The middle term is zero by definition and U1e first tenn is the variance of x. Substituting,
Ew,(x,) = v, - s,Yar(x) -s,(µ-x,) 2 + b,Pf(x,)/n(x,).
which is equivalent to (5).
10
publicity that a forecaster faces. At one extreme, he can simply forecastµ, the expected value of
x. This will minimize his expected squared error but would rule out the possibility of earning a
large bonus if many others also forecastµ, i.e., if n(µ) is large. Alternatively, to have a chance at
winning a large bonus, he can choose a value of x for which n(x) is small. Such a forecast
would likely be biased, however, thereby raising his expected squared error. The choice that a
given forecaster makes will depend on two factors: differences between the pdf and the
distribution of forecasts, as measured by f(x)/n(x), and the relative emphasis his employer places
on accuracy as opposed to advertising, measured by s/b;. Next we consider the resulting
equilibrium.
Homogeneous Incentives
In the simplest version of the model, every employer places the same emphasis on
advertising and accuracy, so that the parameters b; and S; are the same for all forecasters. We can
therefore omit the subscripL~ from our discussion. There are three possible cases.
Case I: Only accuracy matters (b=0 and s>0).
When only accuracy matters to employers, it follows from equation (5) that, because
b=O, expected wage is maximized when (µ-x) 2 is at a minimum. The optimal forecast of x will
therefore be iL~ expected value µ. This implies that if all employers compensate their forecasters
based solely on accuracy, everyone will make the same forecast.
Case II: Only publicity matters (b>0 and s=0).
The opposite extreme case is where forecasters are all rewarded exclusively for the
publicity they generate for their employers. Since s=O, expression (5) implies that each
11
forecaster will choose the value of x for which f(x)/n(x) is maximized. When all forecasters try
to maximize f(x)/n(x), the resulting distribution of forecasts n(x) will be exactly proportional to
f(x), the pdf of x.
This can be shown through a proof by contradiction. Suppose that the ratio f(x)/n(x)
were not equal to a constant in equilibrium. Then there would e~ist values for x and x such
1
2
that f(x 1)/n(x 1) > f(x 2)/n(x 2). This would not constitute an equilibrium. People forecasting x ,
2
commanding a lower expected wage than those forecasting x 1, would change their forecasts from
x2 to x,. This migration would raise n(x 1) and lower n(x 2), until the discrepancy was eliminated. 8
This general condition of proportionality and equation (I) together imply that when
publicity is all that matters,
(6)
n(x) = Nf(x)
for all x.
What is striking about this result is that even though everyone agrees on which value of x
is most likely to occur, forecasters will nonetheless be drawn to distribute themselves in a
fashion that mimics the pdf of x.
Case Ill: Accuracy and pub/icitv both matter (b>O and s>O).
Having examined the two extreme cases, we next consider the intermediate case, in
which publicity and accuracy both matter. Expression (5) states a forecaster's expected wage Ew
as a function of his forecast of x. For a distribution of forecasts n(x) to constitute a Nash
equilibrium, it must have the property that no forecaster will be able to increase his expected
wage by changing his forecast. What this latter condition implies for equilibrium depends on
whether or not n(x) is assumed to take on only integer values. Provided that n(x) can assume
81bis argument implicitly assumes that n(x) can take on non-integer values. For further elaboration, see the next footnote.
12
any real value, a necessary condition for equilibrium is that all forecasts must yield the same
expected wage w: 9
(7)
Ew(x)
=w
ltx
3
n(x) > 0.
To simplify the analysis, we assume that the mean of f{x) is one of the discrete values
-that x can assume. Reparameterizing so that µ, = 0 and substituting (7) into (5) yields
= w* - sx 2 + bPf(x)/n(x),
w
which can be solved for n:
(8)
n(x)
=
Pfix)
k(w) + rx 2
where k(w) = (w-w*)/b
and
r = s/b.
The expression n(x) represents a distribution of forecasts that will cause all forecasters to
have the same expected wage, w. We will refer to this function as the forecasters' "iso-expected
wage curve" or, more simply, their "iso-wage curve." For this expression to constitute an
equilibrium, it must also satisfy equation (I), which states that there are exactly N forecasters.
There exists a unique market-clearing wage w for which equation (8) characterizes an
equilibrium with N forecasters. To see why, consider the terms on the right-hand side of
equation (8). The pdf f(x) is known and the parameters P (the value of publicity) and r (the
relative emphasis that employers place on accuracy) have fixed values. The only variable in the
expression is k, which is a positive linear function of the market expected wage w. Thus, to each
value of w there corresponds a distinct iso-expected wage curve, which we can label n"'(x)
(Chart 1). Because P, f(x), and r arc all non-negative, it follows from (8) that n"'(x) is
9
lf. however, n(x) is restricted to integer values, a Nash equilibrium will meet a somewhat weaker condition, namely,
Ew(x 1+ I)$ E(Xi)
for all possible forecasts X 1 and Xz·
In this paper we assume that n can a,;sume non-integer values, so that equation (7) applies. The larger the pool of forecasters, the
better an approximation this is. Our analysis of the case in which n is restricted to integer values, not reported here, demonstrates
that the main results continue to hold and that the resulting equilibrium is essentially the same.
(7')
Chart I
A Famil y of_Isowage Curves
8
L n ~ (x)=l09. f10·04
-"'".,'
"' 6
I,
0.03
u
...
&4
i
I\
nw(x)
'0
.,...
0.02
f(x)
~=$75,000
'a::, 2
0.01
z
0
-2.S
-2.0
.lj
-LO
-0.5
0.0
0.5
1.5
2
0
25
8
/\
LD w(x)=65.6
"'
I,
-"'"'
I0.03
6
u
I!:!
~
J:4
c..
IIII
'0
....,
'a 2
0.02
I\
nw(x)
~=$100,000
::,
0.01
z
0
-25
-2.0
.lj
-1.0
-0.5
0.0
0.5
1.5
8
...
"'
B
"'"'I!:!u
&
2
25
0
L" ~ (x)=47.; 1 o.04
I0.03
6
~
c..
4
'0
0.02
.,...
'a
~0.04
::,
z
0
I\
IIII
2
nw(x)
0.01
~ = $125,000
'---'---'--- '---'--'--"- -'--'--'---'- -''--''-''-''- ''-''-''-''-''- ''-''-''-''-''- '._':-"............._._._.._. _.._.._._.
-25
-2.0
-1.5
-1.0
-0.5
0.0
0.5
I
_.._._._._ ._._._.._. ._..._______......._..J...-10
1.5
2
2.5
Notes: The probability distribution function, f(x), is a linear transfonnation of the binomial distribution with n=400, p=q=5.
It is scaled to have zero mean and a variance ofone.
While the distribution of forecasters is sketched here as a curve, it is actually discrete and takes on values at intervals of 0.1.
The isowage curves are constructed for the parameter values [P = $5,000,000; w" = $50,000; s = 50,000; and b=l].
13
monotonically decreasing in w. 10 Moreover, by varying w, In"'(x) can be made arbitrarily large
or small.
11
This implies that for any given number of forecasters N there will exist a market
clearing expected wage wand a unique equilibrium distribution n(x) that satisfies equation (1). 12
The equilibrium will be stable because a forecaster predicting a value of x that is selected
by more than n(x) forecasters will earn a substandard expected wage, prompting him to change
his forecast. Conversely, a value of x chosen by fewer than n(x) forecasters will command an
expected wage above the industry standard. These forces will create incentives for forecasters to
change their predictions until the point where equation (8) holds.
Comparative statics
How does the relative emphasis that employers place on accuracy as opposed to publicity
affect the equilibrium distribution of forecasters? Cases I and II illustrate the notion that the
more employers reward accuracy, the greater will be the tendency for forecasters to cluster.
When r=s/b is high (i.e., employers emphasize accuracy), we would expect the distribution of
forecasts to cluster tightly around its mean. When r is low (i.e., publicity matters relatively
more), the distribution of forecasts should be more dispersed. Proposition I makes the nature of
this relationship more precise.
PROPOSITION 1: Ifn,(x) and n,(x) each represents an equilibrium distribution ofN
forecasters such that n 1 reflects a greater relative emphasis on accuracy than n2 (i.e., r1>r2 ), then
there exists a positive constant a so that n 1(x) > n,(x) - lxl < a.
This proposition states that an increased emphasis on accuracy will raise the number of
tolntuitively, an increase in the reservation wage of forecasters will induce some to leave the business, raising the expected wage of
those who remain (since there will be fewer forecasters with whom to share the available publicity).
11
This is because: Vx. n'\x)--0 as w... cx:; and n"'(O)-"' as w... w*.
12
Expression (8) also implies that for all values of x for which f(x) is positive, n(x) will also be positive. In other words, there
will always be someone forecasting every possible value of x.
14
forecasts of values within a symmetric interval around O and will decrease the number of
forecasts for values outside that interval (Chart 2).
To establish the proposition, first note that (8) implies that
(8')
n;(x)
=
Pt<xl
i=l,2
where subscripts denote the two alternative distributions. Since by hypothesis r > r , it follows
1
2
from (8') that if k 1 ~ k2 , then n1(x) ,; nz(x) for all x, with strict inequality holding for all nonzero
values of x. This would imply that [n 1(x) < [nz(x), which violates the assumption that the two
alternative distributions have the same number of forecasters. So k must be less than k •
1
2
Substituting into (8') for the values i=l,2 and simplifying gives
The desired result follows from setting a= [(k2-k 1)/(r1-r2)]'5 •
The central message of Proposition 1 and equation (8) is that the distribution of forecasts
that we observe for a given period reflects two underlying factors -- the pdf of the variable being
forecast and the relative emphasis that employers place on accuracy. If the incentives forecasters
face don't vary much from year to year then we can interpret a change in the extent to which
forecasters cluster as a symptom that the variable's (unobserved) pdf has changed. Conversely,
secular trends in the incentives that forecasters face, as measured by r, will affect the equilibrium
distribution of forecasts, even absent any changes in the forecast variable's pdf.
Another consequence of Proposition l is that the more employers emphasize accuracy
over publicity, the lower will be the variance of forecasts. 13 But recall from our discussion of
131bis result
follows from the property that, for all c, the sum }.)n 1(xH1:i(x)), wben calculated for •cs:xs:c, is nonnegative. For
further discussion see Mood, Graybill. and Boes ( 1974), pp. 74-75.
Chart2
Comparative Statistics: Equilibrium Distribution of Forecasters
for Varying Degrees of Emphasis on Accuracy
n 1(X)
\ . • - - - accuracy-oriented
•.. -············~- (x;········
.. ··
.. -····
.··
,.-··
2
..·····
•'\
··-...
·•
_
__
....·...
__
...··
...
··•...
··-... ____
publicityj-oriented
·•
....
··-........
..
··----...____________________________ _
..-s••·--··•"'···············/ ... /
-2.5
-2
-1.5
-1
-a-o.5
0
0.5
a
1
1.5
2
Notes: 'The probability distribution function, f(x), is a linear transformation of the binomial distribution with n=400, p=q=.5. It is scaled to have zero mean and a variance of one.
The two alternative equilibrium distributions of forecasters were constructed using the parameter values:
N=
100
P = $5,000,000
r1 =
50,000
5,000
r2 =
Thus, n1 reflects more of an emphasis on accuracy than does n 2 .
While the distributions of forecasters are sketched here as curves, they are actually discrete and take on values at intervals of 0. I.
2.5
15
Case II that when accuracy receives zero weight the distribution of forecasters will be identical
to the pdf of x. These two statements together imply a
COROLLARY: In equilibrium, the forecasts of a given variable will have a variance less than
or equal to that of the variable itself.
Consensus forecast
In this model, the predictions of individual forecasters are often biased. What about the
consensus? Suppose that the pdf of x is symmetric about its mean, which is labeled zero, so that
f(-x) = f(x)
for all x.
This condition together with expression (8) implies that n(x), the distribution of forecasts, will
also be symmetric about 0. From this symmetry it follows that the distribution of individual
forecasts of the variable will have the same mean as the variable's pdf, a result worth
emphasizing:
PROPOSITION 2: If a variable has a probability distribution function symmetric about its
mean, then the consensus (mean) forecast of the variable will be unbiased.
The intuition behind Proposition 2 is that if a large proportion of forecasters opt to make
high forecasts, there will be a strong incentive for some to switch to low forecasts in order to
increase their expected bonuses. This incentive will prompt forecasters to distribute themselves
evenly around the mean of x. While Proposition 2 is premised on a very strong assumption perfect symmetry - it will nonetheless hold approximately true even if f(x) is only approximately
symmetric.
The unbiasedness of the consensus has an important empirical implication, namely, that
the consensus forecast should have the lowest expected root mean squared error. We will return
to this observation in our empirical work below.
16
To summarize, we have shown that in the case where all employers pays their forecasters
according to a common wage function, there exists a stable, unique equilibrium distribution of
forecasts. The variance of this distribution is less than that of the pdf and is an increasing
function of the relative emphasis employers place on publicity. If the pdf is symmetric, the
consensus will be unbiased.
Heterogeneous Incentives
Now consider the more general case, in which the wage parameters w;*,
S;,
and b; can
vary by industry. Forecasters hired to function chiefly as internal advisors have a high value of
S;
relative to b; because accuracy is what matters most. A forecaster employed by a
manufacturer, for example, helps guide the planning process but will not benefit his firm by
winning recognition as the most accurate among a panel of experts. Other employers place
special emphasis on publicity and assign a much higher value to b; relative to S;. The forecasts
produced by an economist working at a fledgling consulting firm (perhaps his own) are a vital
part of the firm's output. The publicity attached to having the best forecast among competitors
can be invaluable to the efforts of such a firm to expand its client base.
The equilibrium we consider is one in which all forecasters receive the same expected
wage. Expected wage is equalized within each industry because any wage inequality will
motivate forecasters to change their forecasts until the disparity is eliminated. Expected wage
will also be equalized across industries provided that forecasters can select the industries in
which they work. 14 This is because forecasters will migrate from low-wage industries to high-
14
Thc analysis readily generalizes to the case where expected wage is equalized within each industry, but not across industries.
17
wage industries until interindustry discrepancies disappear.
Suppose that the pdf f(x), the value of publicity P, the market-clearing expected wage w,
and the wage vector {w;*,s;,b,l are known for each of m industries. Will an equilibrium
distribution of forecasts exist and, if so, what will it be? In particular, how many forecasters will
choose to work in each industry and what values will they forecast?
To solve for the equilibrium, we follow the same approach as in the one-industry
homogeneous incentives case. The isowage curve n(x) in equation (8) states how many
forecasters employed in a given industry will be prepared to forecast each value of x.
Appending subscripts, we can use an analogous expression in the multi-industry case:
(8')
n;(x)
=
Pf(x}
i=l, ... ,m.
where k;(w) = (w-w;*)/b;
and r;
= s/b;.
For any given market-clearing expected wage w, we can aggregate the industry-specific
isowage curves n;(x), to determine the equilibrium distribution of all forecasters. For each
possible forecast value x, the expression n;(X) states how many forecasters compensated
according to the industry i pay scale can predict x and still earn w. It follows that, in equilibrium
the only forecasters who will predict the value x will be those from the industry or industries for
which n;(x) is a maximum. Forecasters from other industries will be crowded out from
predicting the value x because doing so would cause them to earn an expected wage below the
market rate w. The aggregate distribution of forecasters n(x) will therefore be the upper
envelope of the individual industry isowage curves (Chart 3a):
(9)
n(x) = Ml\)( n; (x)
I
i=l ,... m.
Chart 3a
Equilibrium Distribution of Forecasters: Multi-Industry Case
7
In~·~: I
6
..... '\.
!
\
!
\
/industry 2\
5
£.-·-·,·,\
; lndustry3 ,
,:
.:.,,,,.
-
, j
......
1/:
4
\,·,
f
_r
t,
t·
,i \
lndustry4
\
'-.
j ........ •················•·l \. \'
I'
1 ' /:
Industry 5
;·...
·\
,._:.-·· !. -·· .... -·· -·· -•. --..... \ ··-..:., \
~--. -·... ,·.,
.'
,,·,/. /. ---~-:.
.•
3
,·
. --,-·'
.-I ·'
-~--~-
• ,/
.;•=--~-;
2
......
,:" /
... '
,,,
\
··...:\·.\.
~
:
\
i
I
... ·.
,--~·-.
...
•
I
. .... ·.
•
/
\
•,\
'
•,
·.
:
....
✓
/
i
!
.·· .,
~
....
/
••
~'>:::,
''-~
' ·. ,
\
...
\
·~ ..!..
'
1
. - ,>' :: ::~,:·:·: ::.: ..·········/'
0
.·.,;:-·-=t·::.
-2.5
::-1 :C-.1::'
-2
r .J.~·-•····f···t ...r·•·j ..
-1.5
I
I
I
-1
I
I
\ .......... - :_:~-~·:-~;-~ ::' ~" ' ,,...
I
I
-0.5
I
I
I
I
I
I
I
I
I
0
I
0.5
I
I
I
I
I
1
I
I --;····r···+·••l .•.. ~ ••
1.5
.J.:.:J~: t- :r-. ,_;··.::?~,--..
2
2.5
Notes: The probability distribution function, f(x), is a linear transfonnation of the binomial distribution with n:400, p=q=.5. It is scaled to have zero mean and a variance of one.
While the distribution of forecasters is sketched here as a curve, it is actually discrete and takes on values at intervals of0.1.
Pis set equal to $5,000,000. The values of n and N; (the nurnheroffirrns per industry) are assumed to be:
Indus!Q'
i=l
2
3
4
5
.IL
250,000
50,000
25,000
5,000
0
Ni
20
20
20
20
20
18
Equations (8') and (9) together determine the equilibrium distribution of forecasters for
the multi-industry case. The salient characteristic of this equilibrium is the close connection
between the way an industry pays its forecasters and the forecasts that they generate. This is
shown in
PROPOSITION 3: Ifforecaster I is rewarded relatively nwrefor accuracy than is
forecaster 2 (r 1 >r2 ), then their forecasts x1 and x2 will be such that lx1 s;
I lx,I.
The proof of this proposition follows directly from the optimizing behavior of
forecasters. The fact that forecaster I chooses value x 1 rather then x2 implies that
Substituting into (5) and noting that µ=0 yields
which simplifies to
(10)
Similarly, forecaster 2's preference for x2 over x, means that
(11)
Combining (10) and (11) and subtracting gives
The first of these two multiplicative terms is negative by hypothesis. Thus, x/ - x/ must be
negative or zero. The proposition follows as a consequence.
Proposition 3 allows us to characterize the equilibrium distribution for forecasters. If the
employers in each of m industries emphasize accuracy and publicity to varying degrees, we can
number the industries so that
19
fori<j.
The proposition implies that forecasters employed in industry I, which places the greatest weight
on accuracy, will position themselves along a symmetric interval around zero, [-c,,+c1].
Industry 2 forecasters will select values over the intervals [-c2,-c,] and [+c,,-c2], and so forth
(Chart 3b). Finally, industry m forecasters, who receive the greatest relative rewards for
attracting publicity, will position themselves along the tails of the probability distribution, at
We can frame the model in a slightly more realistic way. Until now, we have assumed
that the industry wage parameters {w,*,s,,b,} and the market clearing wage ware exogenous and
that they induce an allocation of forecasters across industries. Another approach is to assume
that each industry adjusts its pay scale to the level needed to attract its desired number of
forecasters. Thus, for each industry, the parameter r, is fixed, while k; can vary. If, in
equilibrium, each industry i employs N, forecasters, where
i=l, .... ,m,
Proposition 3 suggesL~ an algorithm for determining the equilibrium distribution of forecasts
given f(x), and the values of r, and N, for i = l ,... ,m (Appendix !).
To conclude, the multi-industry case of our model has a very strong empirical
implication: the more an industry rewards its forecasters for generating publicity, the greater
15
Tuere could, of course, he two or more industries for which r assumes the same value. In that case, it follows from (8') that the
one with the lowest value of k will bid away the forecasters from the other industries having the same value of r. If two industries
have identical values for both k and r, they can be thought of as constituting a single industry for the purposes of the model.
This discussion implicitly assumes that the wage parameters for the m industries are such that some forecasters will choose to
work in each industry. If. however. the pammeter k1 for a particular industry j is too high (i.e., w;* is too low), forecasters might
choose not to work in that industry. Stated in terms of expression (9), this means that there does not exist a value of x for which n; (x)
is at a maximum when i=j. This in no way affect,; our discussion. We can simply exclude all noncompetitive industries such as j from
the analysis and renumber the remaining industries.
Chart 3b
7,
Equilibrium Distribution of Forecasters: Multi-Industry Case
6
5
4
3
•••
I-
I
Industry I
■
Industry 2
!fil Industry 3
I CJ Industry 4
fl Industry 5
•••••••
1-
I ■
nl I · 111111111 HIn
L
2
,j
11·I
~I II I 111, ll!ll;llillll
I
w,Jt!¢]6; '
,ti -:,,.'
it
I
0
~2.5
-2
-1.5
-C4
-1
-ei
-ei
-0.5
-c,
..., I
0
l:2
0.5
"3
I
1.5
2
2.5
Notes: Tue probability distribution function, f(x), is a linear transformation of the binomial
distribution with n=400, p=q=.5. It is scaled to have zero mean and a variance of one.
Pis set equal to $5,000,000. The values of r; and N; (the numberof firms per industry) are
assumed to be:
Industry
.IL
&
i= I
250,000
20
2
50,000
20
3
25,000
20
4
5,000
20
5
0
20
20
will be the tendency for forecasters in that industry to produce unconventional forecasts.
m.
Empirical Results
In this section we report our statistical findings, which are generally consistent with the
implications of the model. Our data consist of year-ahead forecasts of U.S. real GDP (prior to
1992, GNP) growth p_ublished in Blue Chip Economic Indicators. Participating forecasters were
categorized by industry in consultation with Robert Eggert, the newsletter's editor. These
industry categories are an objective way of grouping together forecasters who work for similar
types of firms and can therefore be expected to face similar incentives regarding accuracy and
publicity. Before presenting our empirical results, we offer a few additional details about the data.
Data
Blue Chip Economic Indicators is a monthly newsletter that compiles several dozen
professional forecasts of widely followed macroeconomic variables. The forecasts are produced
by a variety of participating firms. Once a firm is invited to participate in the survey, it remains a
participant as long as it continues to submit forecasts. While firms are not paid to participate, the
newsletter nonetheless offers them regular public exposure.
Our data consist of the forccasL~ of year-ahead real GNP/GDP growth appearing in the
December issues of the newsletter. During the twenty years in our sample, 1976 through 1995,
the number of forecasters in the panel ranged from 32 to 81. A total of 129 firms contributed real
GNP/GDP forecasts at one time or another. We divide these firms, listed in Appendix 2, into six
industry categories - banks, industrial corporations, econometric modelers, independent
forecasters, securities firms, and other. When analyzing how forecaster behavior is related to
21
industry of employment we use the full panel of data, which consists of 1197 individual forecasts.
When analyzing the forecasts of individual firms, however, we restrict the sample to the forty-one
firms with twelve or more annual real GDP forecasts. Of these, the thirty-eight that published
twelve or more year-ahead December forecasts in years prior to 1995 are used when comparing
forecasts to actuals. The industry breakdown of our sample is as follows:
Categmy
Banks
Securities Firms
Industrial Corporations
Independent Forecasters
Econometric Modelers
Others
Total
# in survey
30
14
18
38
12
-11.
129
# in subsample {>12 annual obs)
12
4
4
9
5
__]_
41
Our analysis also uses the Blue Chip's consensus forecast of real GDP growth. The
consensus is calculated as the mean prediction of forecasters designated as members of the "Blue
Chip panel," rounded to the nearest tenth of a percent. Our sample includes all forecasters
appearing in the newsletter, whether or not they are designated as panel members. Since the
consensus forecast and the mean of our more inclusive sample never differ by more than 0.1
percent, the practical distinction between them is minimal.
The "actual" figures with which we compare the forecasts are the official figures released
in the January following the year in question. For example, the year-over-year "actual" for 1986
was the Commerce Departmen t's January 1987 measure for 1986 constant-dollar GNP, expressed
as a percent change from the January 1987 measure of 1985 constant-dollar GNP, as reported in
the Survey of Current Business. While these figures continue to be revised for several years after
their initial release, we use the first-released figure. McNees ( 1989) convincingly argues that this
22
is the appropriate benchmark against which to measure forecast accuracy.
Consensus forecasts
Researchers have found that consensus forecasts are substantially more accurate than
individual forecasts. Zarnowitz and Braun (1992, Table 9), for example, compare the accuracy of
individual and consensus forecasts of real GNP in the NBER-ASA quarterly surveys for the 196890 period. They find that, over horizons ranging from one to five quarters, the consensus forecast
has a root mean square error ("RMSE") 23 to 27 percent below that of individual forecasts.
Table I, which ranks the individual forecasters in our sample and the consensus by RMSE,
shows a very similar result. The first two columns correspond to subperiods 1977-86 and 198795, and the third column corresponds to the entire sample period. Of thirty-eight firms, four beat
the consensus in the first subperiod, as did ten in the second subperiod. Not one of the firms that
outperformed the consensus in the first subperiod managed to do so again in the second. Only
one firm outperformed the consensus over the entire period. 16
The superior performance of the consensus is consistent with our model. As noted in the
discussion of Proposition 2, the model suggest.~ that the consensus forecast will be unbiased, or
very nearly so. Many individual forecasters, by contrast, will find it in their interest to make
biased forecasts. Our model, therefore, correctly predicts that the consensus will outperform
individual forecasters. Still, the tendency of the consensus to outperform individuals constitutes
at best a weak confirmation of our model. This is because there is an alternative, well-accepted
explanation of why the consensus does so well: averaging the projections of individual
16
Pairwise comparisons between individual forecasters and the consensus yield weaker results. Using a statistic proposed by
Diebold and Lopez ( 1995) we can reject, at the 95 percent significance level, the hypothesis that an individual is a'i accurate as the
consensus for only four of the thirty-eight foreca'iters. This general inability to reject the null seems to be due to the small sample
size.
Table I
Forecasters Ranked by RMSE
Sub~riod I: 1977-86
Firm
RMSE
EC04
EC03
BANI
BAN3
0.91
0.95
0.98
1.03
Consensus 1.04
BAN9
OTH6
OTH2
SEC3
COR3
BAN6
ECOi
EC02
SEC!
BANS
BAN12
OTH4
OTH3
BAN2
BANIO
BANll
SEC2
BAN4
COR2
CORI
BAN5
!ND5
OTHI
INDS
!ND9
IND!
!ND6
BAN7
OTH5
!ND3
OTH7
IND7
IND4
!ND2
Notes:
1.04
1.06
1.08
1.08
1.08
I.II
1.13
1.15
1.15
1.18
1.20
1.21
1.22
1.26
1.26
1.27
1.29
1.32
1.32
1.34
1.38
1.48
1.49
1.50
1.55
1.55
1.58
1.60
1.69
1.77
1.82
1.91
2.63
2.94
Sub=riod 2: 1987-95
"'·3ANII
RMSE
0.72
ND4
0.73
)TH3
0.74
OTH4
0.79
ND!
0.86
IBANl2
0.86
IBAN2
0.91
BAN4
0.91
BAN5
0.93
BANIO
0.96
Consensus 0.96
SEC2
0.99
OTH5
0.99
EC04
0.99
OTH7
1.00
OTHI
1.02
IBAN3
1.03
COR2
1.03
BAN9
1.05
ND7
1.06
BAN6
1.08
ND9
1.08
"ORI
1.09
BAN?
I. I I
ECOi
1.12
~OR3
1.14
OTH6
1.18
EC02
1.20
BANI
1.21
INDS
1.28
SEC3
1.29
OTH2
1.43
IND2
1.44
IND6
1.51
INDS
1.51
BANS
1.52
1.64
ISECI
EC03
1.71
IND3
3.18
Entire Period: 1977-95
Firm
RMSE
EC04
0.96
Consensus 1.01
OTH3
BAN3
BAN9
BAN12
OTH4
BANI
BAN6
BANll
BAN2
COR3
BAN5
OTH6
BANIO
ECOi
BAN4
EC02
SEC2
CORI
SEC3
IND!
COR2
OTH2
OTHI
IND9
OTH5
IND5
BAN7
BANS
EC03
SEC!
OTH7
IND7
INDS
JND6
IND4
IND2
IND3
1.02
1.03
1.05
1.05
1.08
1.09"
1.10
1.10
1.10
1.10
1.11
1.12
1.12
1.13
1.13
1.17
1.18
1.23
1.23
1.23
1.23
1.25
1.28
1.29
1.32
1.33
1.34
1.35
1.36
1.39
1.44
1.46
1.51
1.54
2.04
2.10
2.53
Sample consists or organizations that forecasted real GDP in the December issue of the
Blue Chip Economic Indicators at least twelve times between 1977 and 1995.
Forecasters are labeled by industry sec1or as follows:
BAN= banks
SEC = securities finns
COR = industrial corportations
IND= independent forecasters
ECO = econometric modelers
0TH = other miscellaneous forecasters (financial publications, industry associations,
government bcxlies, insurance companies, and rating agencies).
The correlation coefficient between the RMSEs for the two subperiods is 0.10, not statistically
significant at the 95 percent level.
Sources:
Blue Chip Economic Indicators, Survey of Current Business.
23
forecasters tends to cancel out their idiosyncratic errors.
Another implication of the consensus's strong showing is what it says about forecasters
and their clients. Clients comparing the accuracy of different forecasters should eventually
discover (or read about) how well the consensus performs. Since the consensus forecast is
inexpensive and readily available, there should be no need to hire an in-house economist or an
outside consultant to forecast macroeconomic variables such as unemployment and real GDP
growth.
Firms that do hire their own forecasters assign them roles beyond just making projections.
Professional forecasters explain current developments and the risks they pose to their employers,
provide instant analysis of just-released government statistics, and construct models to estimate
the impact of alternative policy choices. Moreover, many of the variables professional forecasters
predict are regional, industry-specific, or firm-specific. As such, they are not included in surveys
such as the Blue Chip.
But while professional forecasters do more than just predict macroeconomic variables,
those who participate in the Blue Chip survey must still produce some kind of forecast. Why not
just copy the consensus which, as many economists know, tends to perform best over time? The
standard explanation is that different forecasters have different information sets and models. Our
model offers another explanation - strategic behavior in the pursuit of publicity. The next section
provides some evidence that, while necessarily indirect, points to the importance of strategic
behavior.
Deviations from consensus
Chart 4 shows the frequency distribution of the deviations of individual GDP (GNP)
Chart4
Distribution of Individual Year-End
Real GDP/GNP Forecasts Relative to Consensus
Blue Chip Indicators, 1977-1996
120 . - - - - - - - - - - - - - - - - - - - - - - -
------,
100 •-
80
60
40
20
0 I.,,.,. ,, __ ,, ■,
i ■■-i ■,-■-•-■-■
-4.2 -3.8 -3.4 -3.0 -2.6 -2.2 -1.8 -1.4
Source:
Blue Chip Economic Indicators
-1
-0.6 -0.2 0.2 0.6
1.0 1.4
1.8 2.2 2.6 3.0 3.4 3.8 4.2
24
forecasts from the consensus. Are these deviations the result of strategic behavior or do they
mainly reflect idiosyncratic differences in forecast methodologies and information?
One type of bias that does not appear at the industry level is that predicted by the
heterogenous expectations hypothesis as formulated in Ito (1990). Specifically, we do not find
that forecasters' mean deviations from the consensus -- allowing positive and negative values to
cancel -- varies systematically by industry. In Table 2 we regress the deviation of individual
forecasts from the consensus on industry dummies. The OLS results, listed in the left-hand
column of the table, show that five of the six industry categories have mean deviations from
consensus that are less than a tenth of a percent and are statistically insignificant. The only
industry category in which forecasters deviated significantly from the consensus was "other," a
catch-all consisting of financial publications, government agencies, industry associations,
insurance companies, and ratings agencies. When this broad grouping is broken down into its
component subcategories, only the "financial publication" subcategory exhibited a significant
mean deviation from the consensus (right column). All told, industry affiliation explains less than
one percent of the variation in forecasters' deviations from consensus. Using an F-test, we cannot
reject the null hypothesis that industry affiliation has no bearing on these deviations. In short, we
find little support for the hypothesis that the GNP/GDP forecasts by the firms in our sample
exhibit a consistent industry-specific bias. 17
In contrast, the evidence supporting the rational bias theory developed in this paper
appears much stronger. Chart 5 plots the mean deviation from the consensus (rounded to the
17
Tois negative result could be due to the way in which we classify firms. Whereas the profitability of Ito's importers and
exporters are clearly tied to the dollar/yen exchange rate, our data set has no analogous partition between firms that benefit more or
less from strong real GDP growth.
Table 2
Regressions of Deviations from Consensus as a Function of Industry Sector
Dependent variable: (GDP(i)-Consensus)
Sample Period: 1977-1996
Explanatory
Variables:
Coefficient
Constant
PTH
-0.03
-0.01
0.02
-0.03
-0.04
-0.09
0.12*
pp
GOV
-
BAN
COR
ECO
IND
SEC
-1.53
-0.16
0.52
-0.50
-I.I 3
-1.26
2.43
-
IA
-
RAT
INS
R-squared:
F-statistic:
Notes:
t-statistic Coefficient
0.007
1.582
-
-
-
t-statistic
-0.03
-0.01
0.03
-0.03
-0.04
-0.IO
-1.53
-0.25
0.62
-0.56
-I.OJ
-1.32
-
-
0.20*
0.33
0.07
0.21
2.00
1.53
0.74
0.96
0.30
O.Q3
0.009
1.173
Regression was run using panel of 1197 individual forecasts of real GDP appearing
in the December issue of
Blue Chip Economic Indicators from 1977-1996.
Explanatory variables are industry sector dummies, defined as follows, with number
of non-zero
observations in parentheses:
BAN= banks (322)
SEC= securities finns (97)
COR = industrial corporations (163)
IND= independent forecasters (287)
ECO= econometric modelers (142)
0TH = other miscellaneous forecasters ( 186), consisting of:
FP = financial publications (54)
GOV= government agencies (12)
IA= industry associations (57)
INS = insurance companies (51)
RAT= rating agencies (12)
Industry dummies are constrained to have an observation-weighted mean value of zero.
*denotes 95 percent significance; **denotes 99 percent significance.
Source:
Blue Chip Economic Indicators
Chart 5
Histogram: Average Deviation of Individual Real GDP Forecasts
From Blue Chip Consensus, 1977-1996
~
.J.7
• l.6
.1,5
.1,4
.1.3
• l.2
I
. I.I
·l.O
•.9
·.8
•.7
•.6
•.5
•.4
·.3
•.2
·. I
0
.I
.2
.3
.4
.5
.6
.7
.8
.9
1.0
I. I
1.2
I
B
B
C
B
0
b
b
E
b
s
b
b
i
b
C
e
0
b
b
e
e
i
0
C
C
0
0
s
s
s
0
e
B
0
I
I
I
1.3
1.4
1.5
1.6
1.7
Notes:
Includes all organizations that forecasted real GDP/GNP in the December issue of the
Blue Chip Economic Indicators at least twelve times between 1977 and 1996.
Each letter corresponds to a single forecaster.
Forecasters whose letters are bold and capitalized have a bias significant at the 95% level.
Legend: b=banks
s=securities firms
c=industrial corporations
i=independent forecasters
e=econometric modelers
o=other miscellaneous forecasters
Source:
Blue Chip Economic Indicators
25
nearest tenth of a percent) of the forty-one individual forecasters for whom we have at least
twelve observations. Each forecaster is identified with a letter signifying his industry; an
upper
case letter denotes a mean deviation significantly different from zero. What is apparent from
the
chart is that the independent forecasters (the "I's") tend to be more scattered than are forecaste
rs
from other categories. Indeed, the six forecasters with the largest mean deviations from
consensus are all independents. This is consistent with Lamont 's (1995) finding that forecaste
rs
with firms bearing their own names tend to make unconventional forecasts.
Absolute deviations from consensus
We next test the implications of our model more formally. The model suggests two
empirical hypotheses: First, if the relative preference for accuracy versus publicity varies
across
industries but is similar within industries, a forecaster's mean absolute deviation ("MAD"
) from
the consensus should be related to his industry. Second, we can make informed a priori
guesses
about which industries will tend to emphasize publicity most and therefore produce forecasts
that
deviate most from the consensus.
Nonfinancial corporntions, for example, would not be expected to particularly reward
publicity in the sense of having the best forecast in a year, since these firms forecast mainly
for
internal planning and investment purposes, activities for which accuracy counts and publicity
does
not. At the other extreme, a consulting firm or advisory service trying to gain publicity for
its
main product, economic advice, would find the media attention from having the best forecast
in a
given year quite valuable and would place less emphasis on forecast accuracy in the tradition
al
sense.
Other financial firms such as banks or brokerages may welcome favorable publicity as a
Table 3
Regressions of Absolute Deviations from Consensus as a Function of Industry Se,
Dependent variable: IGDP(i)-Consensusl
Sample Period: 1977-1996
Explanatory
Variables:
Coefficient
Constant
0.52**
BAN
-0.11 **
COR
-0.15**
ECO
IND
SEC
0TH
Yl977
Yl978
Yl979
Yl980
Yl981
Yl982
Yl983
Yl984
Yl985
Yl986
Yl987
Yl988
Yl989
Yl990
IYl991
Yl992
Yl993
Yl994
Yl995
Yl996
R-squared:
F-statistic:
Notes:
-0.09*
0.30**
-0.00
-0.07
t-statistic Coefficient
33.89
0.52**
-4.44 -0.12**
-3.93 -0.13**
-2.16 -0,10**
11.01
0.31**
-0.08 -0.02
-1.83 -0.06
-0.16
-0.09
0.08
-
-
-
-
-
-
0.19*
0.23**
0.39**
-
0.10
25.35**
0.16*
-0.13
-0.03
0.15*
0.18**
0.22**
-0.02
0.03
0.11*
-0.02
-0.22**
-0.25**
-0.23**
-0.21 **
I
t-statistic
35.71
-5.14
-3.50
-2.59
11.80
-0.36
-1.76
-1.87
-1.17
1.02
2.56
3.09
5.31
2.14
-1.74
-0.44
2.26
2.71
3.86
-0.34
0.58
1.98
-0.44
-4.06
-4.62
-4.22
-4.46
0.20
12.17**
I
Regression was run using panel of 1197 individual forecasts of real GDP appearing in the December issue of
Blue Chip Economic Indicators from 1977-1996.
Explanatory variables are year dummies and industry sector dummies, defined as follows:
BAN =banks
SEC= securities firms
COR = industrial corporations
IND= independent forecasters
ECO = econometric modelers
0TH = other miscellaneous forecasters (financial publications, industry associations,
government bodies, insurance companies, and rating agencies).
Industry dummies and year dummies are constrained to have an observation-weighted mean value of zero.
•denotes 95 percent significance; .,..denotes 99 percent significance.
Source:
Blue Chip Economic Indicators
26
way of attracting clients, particularly to businesses such as trading services to which economic
forecasting may be complementary. Econometric forecasting firms, much like the banks and
securities firms, need to emphasize.accuracy. But they are also under business pressure to
outperform their competitors in a given year, thereby differentiating their products.
To summarize, we hypothesize that the forecasts produced by different categories of firms
will differ systematically in their mean absolute deviations from the consensus and that these
MADs will be relatively small for industrial corporations; large for independent forecasters; and
somewhere in between for banks, securities firms, and econometric modelers.
Table 3 reports regressions that measure the MAD of forecasts produced by different
categories of firms. The dependent variable is the absolute value of each forecast's deviation from
the consensus. Because the equation includes a constant term, the coefficient for each industry
dummy indicates whether its MAD is greater or smaller than that of the overall sample. The
significance of four industry dummies supports the hypothesis that MADs differ across industry
groups. In particular, industrial corporations and banks deviate least from consensus, followed by
econometric modelers. The securities firms' MAD was appreciably greater. Independent
forecasters, consistent with Chart 5, had the largest MAD. Summing the constant and industry
dummies, we sec just how compelling these differences are. The MAD for independent
forecasters is 0.82, more than double what it is for industrial corporations (0.37). Overall,
industry affiliation alone explains fully ten percent of the variation in absolute deviations from the
consensus. An F-test strongly rejects the null hypothesis that these affiliations are unrelated to
absolute deviations. When year dummies arc included to control for intertemporal changes in the
distribution of GDP/GNP forecasts (second column), the results are essentially the same.
27
IV. Summary and Conclusion
This paper has developed a theory of rational bias in macroeconomic forecasts in which
individual forecasters, hired by firms to project economic variables, have an incentive to
compromise the accuracy of their forecasts in order to gain publicity for their firms. The theory
relies on two key assumptions. First, forecasters are fully knowledgeable about the true
probability distribution of actual outcomes. Second, individual firms assign some combination of
values to statistical accuracy in the traditional sense and to the publicity that accompanies the
"winning" forecast in a given year. The theory predicts that rational forecasts are distributed in a
way that reflects the true probability distribution of the variable being forecast, with the degree of
clustering around the consensus dependent upon the relative value placed on accuracy. The
implication is that different firms with the same information and forecasting skills will produce
different forecasts. The statistical evidence from the real GNP/GDP forecasts of different types of
firms supports the view that there is strategic behavior in positioning forecasts relative to the
consensus forecast, and that firms favoring publicity relative to accuracy will tend to produce
unconventional forecasts.
The main significance of this work is in demonstrating that the observed dispersion of
professional forecasts can be explained purely by strategic behavior. It is not necessary to assume
any differences of fundamental views or information across forecasters. While in fact some such
differences among professional forecasters are inevitable, the contribution of the theory is to
demonstrate that the dispersion of forecasts does not rely on them. Indeed, the inability of
individual forecasters to outperform the consensus over time supports the notion that forecasters
28
often behave strategically when making their projections.
While we develop our theory based on the tradeoff between traditional accuracy and the
publicity value of being the best among all forecasters, there may be other, not necessarily
conflicting, explanations of individual forecaster bias. For example, there may be a chronic
demand for well-articulated forecasts of economic sluggishness coming from bond salesmen or
from journalists seeking a range of views. These would reinforce the incentives to provide
outlying forecasts, in addition to the particular advertising explanation developed in this paper.
Our empirical finding that deviation from the consensus is related to the type of firm for which a
forecaster works is highly supportive of the notion that professional forecasting has a strong
strategic component.
Overall, we conclude that it is fruitful to extend our conception of rational forecasting
behavior beyond the simple notion of individual unbiased projections. Our model supports the
doubts some have held about using survey or published forecast data as a measure of true
individual expectations, while also explaining why the consensus forecasts well.
29
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31
Appendix 1. An algorithm for determining the equilibrium distribution of forecasters given
f(x), {r;}, and {N;), for i=l, ... ,m.
First, provisionally assume a value for n(O), the number of forecasters predicting the
value 0. This value will determine a value of k; and an associated isowage curve n 1(x) for
forecasters in industry I. Working from O outward, assign n1(x) forecasters to values of x until
all sector I forecasters are exhausted, at x=±c1• Then assign enough sector 2 forecasters to ±c,
so that the total number of forecasters predicting these two values are, respectively, n 1(-c ) and
1
n1(c,). The values of n 1(-c 1) and n 1(c 1) will then determine an isowage curve, n2 (x), for sector 2
forecasters. Continuing to move away from the origin, sector 2 forecasters will distribute
themselves along this isowage curve until they too are exhausted. This recursive procedure is
then repeated until either all N forecasters are assigned and some values of x are unaccounted
for, or the entire range of x is blanketed but some forecasters remain unassigned. In either case,
another value of n(O) can be chosen and the procedure repeated until a value of n(O) is found for
which the entire range of values of x is covered and all forecasters are assigned.
Appendix 2
Forecasters Participating in the Blue Chip Economic Indicators
1976-1995
RankslJQl
Bank of America
Bankers Trust Co.
Brown Brothers Harriman
Chase Manhattan Bank
Chemical Banking
Citibank
Comerica
Connecticut National Bank
CoreStates Financial Corp.
First Fidelity Bancorp
First Interstate Bank
First National Bank of Chicago
Fleet Financial Group
Harris Trust and Saving
Irving Trust Company
JP Morgan
LaSalle NationaJ Bank
Manufacturers Hanover
Manufacturers National Bank of Detroit
Marine Midland
Mellon Bank
Nationa1 Chy Bank of Cleveland
Northern Trust Company
PhiladeJphiaNaiional Bank/ PNC Bank
Provident NaUonaJ Bank
Security Pacific Bank
Shawmut National Corp.
United California Bank
U.S. Trust Co.
Wells Fargo Bllllk
Stn1rltia, Finns (14)
American Express/ Shcarson Ldunan Company
Arnhold and S. Blcichrooder
A.G. &;:;bi Becker Associate,,;
A.G. Edwards & Company
Oucago Capital, Inc.
CRT Government Securities
C.J. Lawrence, Inc.
Dean Witter Reynolds, Inc
Goldman, Sachs Co.
Ladenburg, lltalmann, & Co.
Loeb Rhoades, Hornblower, & Co.
Morgan Stanley & Co, Inc
NationsBanc Capital Markets Inc.
Prudential SccuritiC.\, Inc.
Jrulustria\ Cornoraj.lJ>DS O&>
B.F. Goodrich
Caterpillar
Chrysler Corporation
Conrail
Eaton Corporation
DuPont
Ford Motor Company
G~neral Electric Company
General Motors
Machinery & Allied Products
Monsanto Company
Motorola, Inc.
Pennzoil Company
Predex Corp.
Sears Roebuck
Union Carbide
Weyerhaeuser Co.
W.R. Grace
Independent Fow:asteJ'11 (38)
Albert T. Sommers
Argus Research
Anhur D, Lillie
Ben E. Laden Associates
Business Economics, Inc.
Center for Study of American Business
Computer Aided Production Planning Systems, Inc.
D\.Drirace & Associates
DeWolf ~ ,.. _
Econonoclast
F.conoviews International, Inc.
Evans Economics, Inc.
GcorgeGols
Hagerbaumer &:'.:'::oirucs
Mc;nemann Economic Resean.:h
HeJming Group
Herman J. Leibhng & Associates
lnfoMetrica, Inc.
Joel Popkin & Co.
Juodeika Allen & Co.
Leonard Silk, NY Times
MAPI
Morris Cohen & As.wciates
Moseley, Hullganen. & Estabrook
Oxford Economics USA
Peter L. Bernstein, Inc.
Polycononucs
Reeder As.'IOCUlte.~ (Owles)
Robert Genctski and Associutes, Inc.
Rutlegde & Co.
Schroder. Naes.\. and Thomas
Sindhnger Company. Inc.
SOM Economics, Inc.
Stat1s11cal Indicator Associates
Stotler Economics
The Bmuan Group • HHG
Tummg PoinL~ Micromctrics
Wayne Hummer & Company• Chicago
f'.rnnometric MooeleJ'11 (12)
Chase Econometrics
Data Resources, Inc.
Fainnodel•Economics, Inc.
Georgia State University
Gil Heebner, Eastern College
Inforum - University of Maryland
Laurence H. Meyer & Associates
Merrill Lynch Economics
Michigan Quarterly U.S. Model
UCLA Business Forecasting
University of Illinois (B.T.)
Wharton Econometrics /WEFA Group
lllJw:.U7J
Financial Puhlicatiom
Cahners Economics
Financial Times Currency Forecaster
Eggert Economics Enterprises, Inc.
Fortune Magazine
Government Agencies
Bush Administration
Clinton Administration
Congressional Budget Office
Office of Management and Business
Industry Associations
Conference Board
Mortgage Bankers Association of America
National Association of Home Builders
U.S. Chamber of Commerce
Insurance Companies
Equitable Life
Metropolitan Life Insurance Co.
Prudential Insurance Co.
Ratin,:s A,:encies
Dun & Bradstreet
Standard and Poor's Corp.
@FedFRASER