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Journal of Business & Economic Statistics

ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20

Forecasting Professional Forecasters
Eric Ghysels & Jonathan H. Wright
To cite this article: Eric Ghysels & Jonathan H. Wright (2009) Forecasting Professional
Forecasters, Journal of Business & Economic Statistics, 27:4, 504-516, DOI: 10.1198/
jbes.2009.06044
To link to this article: http://dx.doi.org/10.1198/jbes.2009.06044

Published online: 01 Jan 2012.

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Forecasting Professional Forecasters
Eric G HYSELS
Department of Finance, Kenan–Flagler School of Business and Department of Economics, University of North
Carolina, Gardner Hall CB 3305, Chapel Hill, NC 27599-3305 (eghysels@unc.edu)

Jonathan H. W RIGHT

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Department of Economics, Johns Hopkins University, Baltimore, MD 21218 (wrightj@jhu.edu)
Surveys of forecasters, containing respondents’ predictions of future values of key macroeconomic variables, receive a lot of attention in the financial press, from investors and from policy makers. They are
apparently widely perceived to provide useful information about agents’ expectations. Nonetheless, these
survey forecasts suffer from the crucial disadvantage that they are often quite stale, as they are released
only infrequently. In this article, we propose MIDAS regression and Kalman filter methods for using asset

price data to construct daily forecasts of upcoming survey releases. Our methods also allow us to predict
actual outcomes, providing competing forecasts, and allow us to estimate what professional forecasters
would predict if they were asked to make a forecast each day, making it possible to measure the effects of
events and news announcements on expectations.
KEY WORDS: Forecast evaluation; Kalman filter; Mixed frequency data sampling; News announcements; Survey forecasts.

1. INTRODUCTION
Surveys of professional forecasters are released, typically on
a quarterly or monthly basis, containing respondents’ predictions of key macroeconomic variables. These releases get wide
coverage in the financial press and many of the forecasters being surveyed have a large clientele base paying considerable
sums of money for their services. The sources and methods that
these forecasters use are somewhat opaque, but a large quantity of their information is economic news that is in the public
domain. Through the market process of price discovery, this
economic news is also impounded in financial asset prices.
In this article, we propose methods for using asset price data
to construct daily forecasts of upcoming survey releases. Our
methods also allow us to estimate what professional forecasters
would predict if they were asked to make a forecast each day,
making it possible to measure the effects of events and news
announcements on expectations. The empirical models we construct also readily become competing forecasting models and

we show that they indeed provide accurate forecasts of the actual outcomes, competing with survey forecasts, while being
more timely.
There are various reasons why we are interested in measuring professional forecasters’ expectations at a daily frequency.
First, agents’ expectations are of critical importance to policy
makers, and policy makers apparently perceive surveys of forecasters to be providing useful information about those expectations. Monetary policy communications, such as the minutes of
the Federal Open Market Committee, frequently point to survey
expectations of inflation. Policy makers, monitoring the economy in real time, would presumably like to be able to measure
these expectations at a higher frequency than the current infrequent survey dates. The methods that we propose allow us
to measure expectations immediately before and after a specific event (e.g., macroeconomic news announcements, Federal
Reserve policy shifts, or major financial crises) and so measure the impact of such events on agents’ expectations. Second,
expectations in a multiagent economy involve “forecasting the

forecasts of others” (to paraphrase Townsend 1983) and, therefore, private sector agents would likewise also wish to obtain
higher frequency measures of others’ expectations. A third reason (closely related to the first two) is that surveys may be (approximately) rational or efficient forecasts of future economic
data and may thus contain information for policy makers not
just about agents’ expectations, but also about likely future outcomes. In this article we do not, however, make an assumption
that surveys represent rational conditional expectations.
While there are many reasons for measuring professional
forecasters’ expectations at high frequency, the task itself, as
noted before, is not so trivial. One may first of all wonder which

data would be most suitable to use. The task is very much related to the construction of leading indicators, or the extraction
of a common factor as in, for example, Stock and Watson (1989,
2002). We could use low-frequency macroeconomic data, or
high-frequency asset price data. But the latter will allow us to
make predictions at any point in time, which is our goal in this
article. Thus, in this article we use daily asset price data.
A priori, it is not clear how to use daily financial market data
to formulate a parsimonious model. The challenge of formulating models to accomplish these tasks is that financial data
are abundant and arrive at much higher frequency than the releases of macroeconomic forecasts. It quickly becomes obvious
that, unless a parsimonious model can be formulated, there is no
practical solution for linking the quarterly forecasts to daily financial data. A simple linear regression will not work well as
it would entail estimating a large number of parameters and the
estimation uncertainty would nullify any underlying predictable
patterns that might exist. Matters are further complicated by the
fact that there is some fuzziness in the timing of the surveys:
although we have a notional date for each survey (the deadline for submission of responses), we have no way of knowing

504

© 2009 American Statistical Association

Journal of Business & Economic Statistics
October 2009, Vol. 27, No. 4
DOI: 10.1198/jbes.2009.06044

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Ghysels and Wright: Forecasting Professional Forecasters

505

whether the forecasters actually formed their predictions on the
survey deadline date or several days earlier. To allow for this we
might want to use more than two months of data. We resolve the
challenge by using mixed data sampling, or MIDAS regression
models, proposed in the recent work of Ghysels, Santa-Clara,
and Valkanov (2005, 2006). MIDAS regressions are designed
to handle large high-frequency datasets with judiciously chosen
parameterizations, tightly parameterized yet versatile enough to
yield predictions of low frequency forecast releases with daily
financial data.

In addition to using these regression models to predict upcoming survey releases, we consider a more structural approach
in which we use the Kalman filter to estimate what forecasters
would predict if they were asked to make a forecast each day,
treating their forecasts as “missing data” to be interpolated (see,
e.g., Harvey and Pierse 1984; Harvey 1989; Bernanke, Gertler,
and Watson 1997). As a by-product, this also gives forecasts of
upcoming releases. Again, however, we have to contend with
the fact that although we have a notional date for each survey,
agents likely formed their expectations sometime earlier. Again,
we resolve this problem by using mixed data sampling methods.
In our empirical work we use the median forecasts of output growth, inflation, unemployment, and interest rates, from
the Survey of Professional Forecasters (Croushore 1993). The
financial market data that we use to predict these forecasts are
daily changes in interest rates. We find that these asset price
changes give us considerable predictive power for upcoming
Survey of Professional Forecasters releases. Having obtained
estimates of agents’ daily forecasts, we can then relate these
to macroeconomic news announcements. For example, we can
measure the average effect of a nonfarm payrolls announcement
that is 100,000 better-than-expected on agents’ forecasts. We

find economically meaningful and statistically significant news
impact estimates.
The remainder of this article is organized as follows. In Section 2 we present a theoretical framework that succinctly represents the salient features of predicting forecasters with financial
data and present the empirical methods. Empirical results appear in Section 3. Section 4 discusses the impact of news on
expectations. Section 5 concludes the article.
2. FORECASTING AND FINANCIAL
MARKET SIGNALS
In this section we show, in a very stylized setting, how if asset prices and forecasts both respond to news about the state of
the economy, we can use asset returns to glean high-frequency
information about agents’ forecasts. As we want to keep the
model in this section simple, we make compromises with regards to generality and do not aim at matching all salient
data features that will appear in our empirical analysis. We
also present the empirical methods, both regression-based and
Kalman filter, as they relate to the stylized model.
Assume that we observe forecasts of some future macroeconomic variable yt (e.g., inflation four quarters hence) once
a quarter and suppose, for simplicity, that these are observed
on the last day of each quarter. Moreover, let the underlying
process for yt be AR(1):
yt+1 = a0 + a1 yt + εt+1 .

(1)

Let ftt+h denote the forecast of yt+h made on the last day of
quarter t. We focus on h period ahead forecasts as professional
forecasters produce multiple period ahead predictions, which
are in turn of most interest to forward-looking policymakers or
investors. If the forecaster knows the DGP, knows yt at the end
of quarter t (when the forecast is being made), and is constructing a rational forecast then this h-quarter-ahead forecast will
be:
ftt+h = a0

h−1


j

a1 + ah1 yt ,

(2)

j=0

which is related to the previous h-quarter-ahead forecast and the
shock εt as follows:


h−1

j
t−1+h
h
t+h
a1 + a1 ft−1
+ a1h−1 εt . (3)
ft = a0 a1 − (a1 − 1)
j=0

We are interested in predicting ftt+h at some time between the
end of quarter t − 1 and the end of quarter t. During the quarter
news is released pertaining to the macroeconomic variable yt ,

which is impounded into financial asset returns. Although the
errors εt occur quarterly, we construct a fictitious set of daily
t
shocks εt ≡ ld=l
vd , where lt denotes the last day of quart−1 +1
ter t. While there are many financial assets traded, we focus on
a single asset and assume that its price on day τ relates to the
fictitious shocks as follows:
pτt = p0t +

τ


vd + ω τ ,

(4)

d=lt−1 +1

where p0t is the price at the beginning of the quarter t. Equation (4) tells us that daily prices provide a noisy signal of the

underlying economic shocks. Assume that the fictitious shocks
vd are Gaussian with mean zero and variance σv2 and that the
noise is also Gaussian with mean zero and variance σw2 and is
orthogonal to the vd process. We make these assumptions for
convenience, but will comment on them later. The two related
problems we then consider are: (1) predicting ftt+h during quarter t with concurrent and past daily financial market data via
a regression model, or (2) treating agents’ h-quarter-ahead expectations during the quarter as “missing” values of a process
only observed at the end of the quarter. There is a fundamental difference between predicting ftt+h , during the quarter, and
“guessing” ϕτh , the unobserved h-quarter-ahead expectation on
day τ . The former is a prediction problem that can be formulated via a regression, whereas the latter is a filtering problem.
Asset prices embed both forecasts of future (macro) factors
and also prices of risk, and there is substantial evidence in the
finance literature that the prices of risk are time-varying. Our
simple reduced form model does not attempt to split these out.
One remedy would be to replace the “plain” return series used
in our model by so-called economic tracking portfolios (see,
e.g., Breeden, Gibbons, and Litzenberger 1989, or more recently Lamont 2001 and Christoffersen, Ghysels, and Swanson 2002). Lamont (2001) in particular, constructed tracking
portfolios for future economic variables, and used only the unexpected component of returns (not total returns) in constructing the tracking portfolios. In principle, one could use tracking

506

Journal of Business & Economic Statistics, October 2009

portfolio returns and this might further improve the forecasting performance that we document in this article, but constructing these portfolios involves estimation error and evidence on
their out-of-sample forecasting power is mixed. Besides the additional complications pertaining to estimation error, it should
also be noted that data vintage issues play a role in the construction of economic tracking portfolios (see, e.g., Christoffersen,
Ghysels, and Swanson 2002 for further discussion). The virtue
of using plain return series is, therefore, the avoidance of additional estimation error and data revision issues. The downside
is that we cannot separate movements in risk premia from expected future macro factors that both affect the return processes
feeding into our prediction models.

form regressions that do not explicitly hinge on the specifics of
the DGP.
Our empirical specification uses regression models for predicting ftt+h . Let dt denote the survey deadline date for quarter t:
survey respondents submit their forecasts on or before this day:
the survey results are released a few days later. We suppose that
the researcher wishes to forecast ftt+h using asset return data on
days up to and including day τ . Our forecasting model is:
ftt+h

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Equation (4), the partial sums process Sτ =
From
τ
d=lt−1 +1 vd behaves like a random walk and, therefore, the
asset price pτt behaves like a random walk plus noise (in practice stock prices are not a random walk, but this is one of our
simplifying assumptions). To predict ftt+h , we would like to
know εt+1 , and the best predictor on day τ would be Sτ which
is not observed but can be extracted from asset returns. In particular, in Appendix we show that conditional linear prediction
given daily returns, denoted P can be approximated as:
P[ftt+h |rd , d = lt−1 + 1, . . . , τ ]


h−1

j
h
a1
≈ a0 a1 − (a1 − 1)
j=0

lt−1 +1
t−1+h
+ a1 ft−1

+ ah−1
1



(1 − (−ζ )τ −d+1 )rd ,

(5)

d=τ

where ζ is a function of the signal-to-noise ratio q = σv2 /σw2
[see Equation (A.2) in the Appendix] and rd is the asset return
on day d for days lt−1 + 1, . . . , τ during quarter t.
The stylized model presented so far is based on a number
of simplifying assumptions. It is worth discussing some of the
critical assumptions and how they can be relaxed. Firstly, the
above analysis assumes that forecasters have rational expectations and know the DGP. The analysis in the remainder of
the article will not exclude the possibility of rational forecasting, and that would clearly strengthen the motivation for realtime forecasting of the forecasters. Nevertheless, our empirical
model does not rely on such an assumption and, throughout this
article, we remain strictly agnostic about the rationality of forecasters’ expectations.
Secondly, to derive Equation (5) we assumed Gaussian errors. The resulting prediction formula only depended on the
signal to noise ratio q and the linear prediction is optimal in
a MSE sense. With the Gaussian distributional assumptions, we
are, in fact, in the context of the Kalman filter, the topic of the
next subsection. Here we consider Equation (5) as a linear projection or regression equation. Obviously, this regression equation is tightly parameterized because the analysis has been kept
simple for the purpose of exposition. In particular, the process yt
was assumed to be a random walk and this yielded convenient
formulas in this example. In practice, we prefer to have reduced

+

nA


βj γ (L)rτj + εt ,

(6)

j=1

j

2.1 The Regression Approach

=α

t−1+h
+ ρft−1

where rτ denotes the return on day τ for asset j, nA denotes the
number of assets and γ (L) is a lag polynomial of order nl so that
j
γ (L)rτ is a distributed lag of daily returns on asset j over the nl
days up to and including day τ = dt−1 + θ (dt − dt−1 ), where
0 < θ ≤ 1. In empirical work we will consider θ = 1, 2/3,
and 1/3 corresponding to forecasts for ftt+h made on the survey deadline date, about one month earlier, and about two
months earlier, respectively. Equation (6) uses mixed frequency
t−1+h
data: ftt+h and ft−1
are observed at the quarterly frequency,
t = 2, . . . , T, while the returns are at the daily frequency, but
there is only one observation of the distributed lag of daily rej
turns, γ (L)rτ , in each quarter. Hence, as suggested by Equation (5), asset returns up to a fraction θ of the time from the
quarter t − 1 survey deadline date to the quarter t survey deadline date are used to predict the quarter t survey. We run a
different regression for each θ and so should strictly put a θ A
subscript on α, {βj }nj=1
, ρ, and γ (L) in Equation (6), but do not
do so, in order to avoid excessively cumbersome notation. In order to identify βj in this equation, we constrain the polynomial
γ (L) to have weights that add up to one. Following Ghysels,
Sinko, and Valkanov (2006) we use a flexible specification for
γ (L) with only two parameters, κ1 and κ2 , using their “Beta
Lag” specification. It should be noted that Ghysels, Sinko, and
Valkanov (2006) discussed various schemes besides the Beta
Lag specification. Similar results can be obtained with other
polynomials, but the beta lag specification is convenient because it can capture the hump-shaped weighting function that
we consistently find in empirical applications with just two parameters.
We consider three MIDAS regression models for the prediction of ftt+h . The first, which we refer to as model M1,
is simply given by Equation (6) with unknown parameters α,
A
{βj }nj=1
, ρ, κ1 and κ2 . The second, model M2, imposes that
κ1 = κ2 = 1, implying that the weights in γ (L) are equal. In
j
this case, γ (L)rτ is simplythe average return over the nl days
nl
up until day τ and γ (L) = j=1
(1/nl )Lj−1 . Lastly, we consider
an equal-weighted MIDAS regression in which the average returns from day dt−1 to
τ are used to predict the upcoming
day
τ
release, i.e., γ (L) = nj=1
(1/nl )Lj−1 and nτ = τ − dt−1 . We
refer to this as model M3. The difference between models M2
and M3 is that model M2 has a fixed lag length parameter, nl ,
while model M3 will always use returns from exactly day dt−1
to day τ . We estimate MIDAS models M2 and M3 by OLS and
M1 by nonlinear least squares.

Ghysels and Wright: Forecasting Professional Forecasters

507

2.2 The Filtering Approach
We now turn to the second problem, namely how to extract ϕτh . For this, it is very natural to specify and estimate a
state space model using the Kalman filter to interpolate respondents’ expectations (see, e.g., Harvey and Pierse 1984; Harvey
1989; Bernanke, Gertler, and Watson 1997). It is worth noting
that the regression approach of the previous subsection can be
viewed as less “structural” in the sense that we do not need to
specify an explicit state space model. The Kalman filter applies
to homoscedastic Gaussian systems, assumptions we make here
for analytic convenience. To be specific, let us reconsider Equation (3) and apply it to a daily setting:

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ϕτh ≈ ϕτh−1 + ãvτ .

(7)

The shocks vτ are not directly observable, only the returns are.
The above equation, therefore, holds the ingredients for a state
space model to determine ϕτh , namely daily returns are a noisy
signal of daily changes in ϕτh :
rτ = φ(ϕτh − ϕτh−1 ) + ε̃τ1 ,

(8)

where at the end of each quarter we observe ftt+h = ϕlht , giving
an explicit state space model.
The Kalman filter applies to homoscedastic Gaussian systems and this assumption is clearly inadequate for financial
data. However, the Kalman filter provides optimal linear prediction even with non-Gaussian errors. We consider two thoughtexperiments that go beyond the simple stylized example. The
first is that forecasters form expectations each day, but only
send these expectations into the compilers of the survey once
a quarter, on survey deadline dates. Thus, we observe respondents’ expectations on survey deadline dates, but these expectations must be interpolated on all other days. We let ϕτh denote the respondents’ h-quarter-ahead expectations on day t and
write the following model
rτ = φ(ϕτh − ϕτh−1 ) + ε1τ ,

(9)

ϕτh = μ0 + μ1 ϕτh−1 + ε2τ ,

(10)

ftt+h = ϕdht ,

(11)

where ((ε1τ )′ , ε2τ ) is iid normal with mean zero and diagonal variance-covariance matrix. This model is clearly a linear Gaussian model in state-space form with ϕτh as the unobserved state, Equation (10) as the transition equation, and Equations (9) and (11) as the elements of the measurement equation.
Note that we avoid here a direct mapping between the parameters of the stylized model. Instead, we proceed with a generic
state space model, similar to the generic MIDAS regressions
considered in the previous section.
As discussed earlier, there is some uncertainty about the exact timing of respondents’ expectations that it seems we should
allow for. We can do so by amending Equation (11) to specify
instead that
ftt+h = γ (L)ϕdht ,

(12)

where γ (L) is a MIDAS polynomial. Thus the second thoughtexperiment is that individual respondents form their expectations each day, but that some of these get transmitted to the
compilers of the survey faster than others, with the compilers

of the survey using the latest numbers from each respondent to
construct the survey releases once a quarter, on survey deadline
dates. Our objective is to back out our estimates of respondents’
underlying expectations given by ϕτh . Of course, the model in
which surveys correspond exactly to respondents’ expectations
on survey deadline dates is nested within this specification, as
we can specify that κ1 = 1 and κ2 = ∞, implying that γ (L) = 1.
We refer to the simple Kalman filter model [Equations (9),
(10), and (11)] as model K1. We refer to the MIDAS Kalman filter model [Equations (9), (10), and (12)] as model K2. In either
case, we can use the Kalman filter to find maximum-likelihood
estimates of the parameters, giving filtered estimates of ϕτh and
forecasts of ftt+h (made a fraction θ of the way through the
prior intersurvey period) as by-products. We can also use the
Kalman smoother to obtain estimates of ϕτh conditional on the
entire dataset. The simple Kalman filter model has been used in
several mixed-frequency applications such as Zadrozny (1990),
who was concerned with the problem of using observed quarterly GNP and other monthly data to interpolate monthly GNP
numbers. But the MIDAS Kalman filter model is new and its
greater flexibility may be helpful in our application of interpolating survey predictions at the daily frequency.
3.

EMPIRICAL RESULTS

The survey that we consider in the empirical work is the
Survey of Professional Forecasters (SPF), conducted at a quarterly frequency. The respondents include Wall Street financial
firms, banks, economic consulting groups, and economic forecasters at large corporations. Prior to 1990, it was a joint project
of the American Statistical Association and the National Bureau of Economic Research; now it is run by the Federal Reserve Bank of Philadelphia. We use median SPF forecasts of
real GDP growth, CPI inflation, three-month T-Bill yields, and
the unemployment rate at horizons one-quarter through fourquarters ahead. Real GDP growth and CPI inflation are constructed as the annualized growth rates from quarter t − 1 to
quarter t + h, where t is the quarter in which the survey is taken
and h is the horizon of the forecast (h = 1, 2, 3, 4). Three-month
T-Bill yields and the unemployment rate are simply expressed
in levels. In the notation of the previous section, ftt+h refers to
the forecast made in the quarter t SPF forecast for any one of
these variables in quarter t + h and our forecasting models are
the MIDAS and Kalman filter models exactly as defined earlier.
We start with the forecasts made in 1990Q3 and end with forecasts made in 2005Q4 for a total of 62 forecasts. For each of
these forecasts we have the survey deadline dates that are about
in the middle of each quarter. The survey deadline date is not
the date that the survey results are released, but is the last day
that respondents can send in their forecasts. We do not use SPF
forecasts made before 1990Q3 because we do not have the associated survey deadline dates. Besides, the use of a relatively
recent sample minimizes issues of structural change that seem
to be very important using data that spans earlier time periods
(Ang, Bekaert, and Wei 2007 and Stock and Watson 2003). In
the working paper version of the article we also report results
covering the Consensus Forecasts, a survey that is conducted
at a monthly frequency by Consensus Economics (see Ghysels
and Wright 2006).

508

We can use daily asset prices to predict the upcoming releases of the survey, using MIDAS regression models M1, M2,
and M3, or our Kalman filter models K1 and K2. We consider models with the following daily asset returns: (a) the
daily changes in three-month and ten-year Treasury yields, and
(b) the daily change in two-year Treasury yields, using the constant maturity yields (H-15 release). The number of assets, nA ,
is thus either 1 or 2 and these assets represent the level and/or
slope of the yield curve. Results with other assets are reported
in Ghysels and Wright (2006).

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3.1 MIDAS Regression Results
In MIDAS models M1 and M2, the lag length nl is a fixed
parameter that we set to 90. As our data are at the business
day frequency, this corresponds to substantially more than one
quarter of data. We do this because we have no way of knowing
whether the forecasters actually formed their predictions on the
survey deadline date or several days earlier, and because preliminary investigation revealed that this choice of nl generally
gave the best empirical fit.
We evaluate the forecasts by comparing the in-sample and
pseudo-out-of-sample root mean-square prediction error (RMSPE) of each of the models M1, M2, M3, K1, and K2, used
to predict the upcoming survey release, relative to the RMSPE
from fitting an AR(1) to the survey releases [an “AR(1)” forecast]. The empirical results for predictors (a) and (b) are reported in Tables 1 and 2, respectively. Both tables give the insample and pseudo-out-of-sample RMSPE of models M1, M2,
M3, K1, and K2, used to predict the upcoming survey release,
relative to the AR(1) benchmark, for θ = 1, 2/3, 1/3. The first
observation for out-of-sample mean square prediction is the
first observation in 1998, with parameters estimated only using data from 1997 and earlier, and prediction then continues
from this point on in the usual recursive manner, forecasting in
each period using data that were actually available at that time.
Note that because we are working with asset price data and survey forecasts (rather than actual macroeconomic realizations),
we have no issues of data revisions to contend with; the outof-sample forecasting exercise is a fully real-time forecasting
exercise.
We first discuss the simple regression results (models M1,
M2, and M3). The in-sample relative RMSPEs from MIDAS
models M1, M2, and M3 are by construction less than or equal
to one, and are generally well below one. Not surprisingly, relative RMSPEs are higher in the pseudo-out-of-sample forecasting exercise. Survey forecasts of the unemployment rate and
T-Bill yields appear to be generally the most predictable out-ofsample, but out-of-sample relative RMSPEs are in many cases
below one for GDP growth and CPI inflation forecasts as well.
The results are similar for both predictors, but the better outof-sample results mostly appear to obtain for predictors (a) (the
daily changes in the three-month and ten-year Treasury yields).
On average, across all four variables and all four horizons, the
pseudo-out-of-sample relative RMSPE from MIDAS model M1
with θ = 1 and predictors (a) is 0.77. However, using predictors (b) (the daily changes in two-year Treasury yields alone)
generally gives better out-of-sample predictions for real GDP
growth forecasts, which is consistent with the work of Ang, Piazzesi, and Wei (2006) who found that the level of short-term

Journal of Business & Economic Statistics, October 2009

interest rates alone has more predictive power for growth than
any term spread.
Even though MIDAS model M1 involves estimation of two
additional parameters, it generally gives smaller out-of-sample
RMSPEs than models M2 or M3. Thus, perhaps in part because
the surveys represent agents’ beliefs at a substantial lag relative
to the survey deadline date (a lag that furthermore varies by
respondent), allowing for nonequal weights in γ (L) appears to
result in improved forecasting performance. The improvement
is quite substantial in many cases.
Not surprisingly, the relative RMSPE is generally somewhat
smaller for forecasts made using asset price data up through the
survey deadline date (θ = 1) than for forecasts made earlier in
the intersurvey period (θ = 2/3, 1/3).
3.2 Kalman Filtering Results
We next discuss the results using the Kalman filter (models
K1 and K2). The patterns are similar. Again, the best results obtain when predicting the forecasts for three-month T-Bill yields
and the unemployment rate, and when using predictors (a).
Model K2, which allows for surveys to represent respondents’
beliefs at a substantial lag relative to the survey deadline date,
generally gives smaller out-of-sample RMSPEs than model K1,
and the improvement is quite substantial in many cases, even
though it involves estimation of two additional parameters. This
reinforces the evidence that surveys represent agents’ beliefs at
a considerable lag to the survey deadline date.
Models K1 and K2 on average give slightly less good forecasts of what the upcoming survey release is going to be than
the reduced form MIDAS regression models M1, M2, and M3.
Nonetheless, they have the useful feature of allowing us to estimate forecasters’ expectations on a day-to-day basis, [ϕτh in
the notation of Equation (9)] and these estimates can be either conditional on past data (filtered estimates) or the whole
sample (smoothed estimates). We cannot precisely accomplish
these tasks with the reduced form MIDAS regression models.
As an illustration, in Figure 1, we show the time series of
Kalman smoothed estimates of two-quarter-ahead real GDP
growth expectations from models K1 and K2, using predictors (a), over the period since January 1998. In the companion working paper (Ghysels and Wright 2006) we also reported
Kalman filtered estimates. SPF releases of actual two-quarter
real GDP growth expectations are also shown on the figure
(dated as of the survey deadline date). The Kalman filter estimates jump on each survey deadline date as the information
from the survey becomes incorporated in the model, but the
jumps are quite a bit smaller in magnitude than the revisions to
the survey forecasts, consistent with the results in Tables 1 and 2
on the RMSPE of the Kalman filter forecasts relative to that of
the AR(1) benchmark. As expected, the Kalman smoothed estimates adjust more smoothly than the Kalman filtered estimates.
3.3 Parameter Estimates
Across all combinations of predictors, forecast horizons, and
models that we have estimated, the number of parameters is
very large. As an illustration of these parameter estimates, Table 3 reports the estimates from fitting model M1 to the SPF

Downloaded by [Universitas Maritim Raja Ali Haji] at 17:33 12 January 2016

Horizon
(Qtrs.)

θ =1

θ = 2/3

θ = 1/3
K2

M1

M2

M3

K1

K2

AR(1) RMSE
(memo)

0.819
0.957
0.886
0.915

M2
M3
K1
Real GDP growth (in-sample)
0.931
0.871
0.878
0.957
0.920
0.926
0.979
0.955
0.962
0.988
0.973
0.981

0.856
0.915
0.955
0.974

0.862
0.929
0.954
0.950

0.990
0.991
0.986
0.981

0.899
0.945
0.968
0.990

0.951
0.984
1.011
1.023

0.910
0.951
0.979
0.995

0.680
0.488
0.352
0.282

0.928
0.883
0.884
0.895

0.916
0.875
0.873
0.866

CPI inflation (in-sample)
0.925
0.918
0.941
0.894
0.887
0.907
0.890
0.891
0.907
0.885
0.894
0.908

0.928
0.883
0.882
0.888

0.897
0.859
0.852
0.849

0.947
0.927
0.923
0.914

0.923
0.900
0.894
0.894

1.004
0.973
0.959
0.957

0.923
0.880
0.877
0.902

0.315
0.237
0.214
0.194

0.325
0.412
0.473
0.590

0.266
0.362
0.433
0.567

0.311
0.368
0.427
0.530

0.517
0.559
0.575
0.617

T-Bill (in-sample)
0.507
0.484
0.542
0.520
0.583
0.566
0.649
0.646

0.402
0.455
0.505
0.599

0.507
0.522
0.553
0.624

0.672
0.708
0.718
0.744

0.676
0.665
0.686
0.737

0.741
0.742
0.760
0.813

0.645
0.654
0.676
0.743

0.484
0.496
0.464
0.440

0.721
0.695
0.760
0.741

0.704
0.674
0.741
0.728

0.659
0.648
0.733
0.707

0.630
0.654
0.719
0.672

Unemployment rate (in-sample)
0.741
0.744
0.745
0.767
0.751
0.739
0.853
0.816
0.811
0.844
0.770
0.778

0.677
0.692
0.796
0.748

0.700
0.735
0.798
0.776

0.825
0.857
0.909
0.914

0.783
0.798
0.839
0.822

0.853
0.833
0.862
0.865

0.765
0.775
0.844
0.823

0.238
0.228
0.235
0.208

0.856
0.957
1.030
1.062

0.866
0.964
1.057
1.103

0.890
1.004
1.121
1.150

0.813
0.958
1.065
1.115

0.878
0.976
1.085
1.187

Real GDP growth (pseudo-out-of-sample)
0.946
0.889
0.936
0.846
0.993
0.975
1.020
0.968
1.054
1.066
1.107
1.059
1.088
1.137
1.136
1.106

0.921
1.106
1.117
1.116

1.030
1.045
1.073
1.088

0.917
0.979
1.017
1.077

0.984
0.997
0.985
0.987

0.925
1.004
1.047
1.096

0.791
0.548
0.366
0.286

0.948
0.927
0.920
0.920

0.914
0.896
0.900
0.905

0.962
0.931
0.936
0.944

0.948
0.897
0.887
0.901

0.963
0.929
0.880
0.877

1.014
0.951
0.937
0.932

CPI inflation (pseudo-out-of-sample)
0.908
0.940
0.900
0.960
0.890
0.912
0.855
0.914
0.889
0.924
0.857
0.863
0.887
0.942
0.873
0.857

0.963
0.939
0.928
0.939

0.947
0.933
0.923
0.913

0.953
0.949
0.949
0.954

0.896
0.880
0.886
0.895

1.021
0.975
0.914
0.907

0.309
0.246
0.226
0.205

1
2
3
4

0.267
0.378
0.435
0.592

0.322
0.410
0.459
0.590

0.257
0.352
0.384
0.548

0.251
0.336
0.373
0.531

0.276
0.381
0.458
0.606

0.380
0.412
0.456
0.596

0.398
0.463
0.517
0.619

0.508
0.517
0.563
0.676

0.688
0.715
0.715
0.735

0.631
0.634
0.666
0.740

0.650
0.666
0.691
0.752

0.619
0.655
0.690
0.760

0.548
0.558
0.516
0.486

1
2
3
4

0.717
0.762
0.763
0.720

0.695
0.692
0.736
0.755

0.709
0.700
0.723
0.727

0.680
0.672
0.705
0.732

0.687
0.674
0.753
0.741

0.743
0.789
0.727
0.670

Unemployment rate (pseudo-out-of-sample)
0.854
0.795
0.702
0.673
0.835
0.835
0.720
0.702
0.883
0.829
0.774
0.770
0.882
0.774
0.754
0.742

0.744
0.762
0.856
0.834

0.868
0.858
0.914
0.938

0.692
0.746
0.805
0.824

0.753
0.756
0.799
0.812

0.702
0.726
0.806
0.801

0.236
0.239
0.25
0.231

M1

M2

M3

K1

K2

M1

1
2
3
4

0.814
0.905
0.940
0.964

0.877
0.953
0.989
0.998

0.865
0.932
0.975
0.990

0.846
0.918
0.965
0.983

0.824
0.908
0.953
0.972

1
2
3
4

0.901
0.865
0.861
0.853

0.935
0.901
0.899
0.894

0.933
0.907
0.905
0.906

0.946
0.915
0.911
0.911

1
2
3
4

0.259
0.347
0.409
0.524

0.330
0.418
0.467
0.563

0.346
0.432
0.486
0.584

1
2
3
4

0.637
0.661
0.748
0.675

0.688
0.686
0.768
0.759

1
2
3
4

0.861
0.962
1.109
1.075

1
2
3
4

T-Bill (pseudo-out-of-sample)
0.615
0.579
0.423
0.648
0.606
0.460
0.658
0.624
0.495
0.686
0.685
0.580

509

NOTE: The regressors in Equations (6) and (9) are changes in three-month and ten-year Treasury yields. The entries are ratios relative to an AR(1) Forecast. We start with the forecasts made in 1990Q3 and end with 2005Q4. The first observation for
out-of-sample mean square prediction is 1998Q1, with parameters estimated only using data from 1997 and subsequently updated.

Ghysels and Wright: Forecasting Professional Forecasters

Table 1. In- and pseudo-out-of-sample root mean square error of predictions of the SPF

510

Table 2. In- and pseudo-out-of-sample root mean square error of predictions of the SPF
θ =1

θ = 2/3

θ = 1/3
K2

M1

M2

M3

K1

K2

AR(1) RMSE
(memo)

0.848
0.917
0.951
0.975

M2
M3
K1
Real GDP growth (in-sample)
0.900
0.873
0.888
0.957
0.927
0.934
0.987
0.961
0.967
0.996
0.980
0.986

0.850
0.914
0.955
0.976

0.880
0.931
0.950
0.969

0.973
0.991
1.000
0.998

0.900
0.936
0.965
0.989

0.937
0.978
1.011
1.023

0.887
0.936
0.970
0.989

0.680
0.488
0.352
0.282

0.950
0.911
0.903
0.897

0.950
0.914
0.903
0.896

CPI inflation (in-sample)
0.959
0.956
0.980
0.928
0.925
0.949
0.925
0.917
0.935
0.922
0.916
0.931

0.955
0.916
0.905
0.897

0.939
0.910
0.895
0.888

0.969
0.944
0.940
0.934

0.954
0.933
0.920
0.916

1.023
0.998
0.982
0.978

0.944
0.911
0.903
0.896

0.315
0.237
0.214
0.194

0.643
0.615
0.626
0.699

0.544
0.506
0.528
0.624

0.516
0.480
0.493
0.573

0.563
0.553
0.555
0.602

T-Bill (in-sample)
0.634
0.651
0.609
0.623
0.621
0.629
0.677
0.691

0.591
0.563
0.572
0.641

0.618
0.598
0.614
0.677

0.716
0.726
0.731
0.759

0.718
0.686
0.699
0.752

0.797
0.779
0.790
0.839

0.721
0.711
0.727
0.781

0.484
0.496
0.464
0.440

0.865
0.820
0.863
0.882

0.839
0.792
0.835
0.854

0.788
0.746
0.800
0.790

0.774
0.740
0.805
0.797

Unemployment rate (in-sample)
0.783
0.809
0.845
0.763
0.770
0.794
0.840
0.840
0.851
0.839
0.827
0.856

0.806
0.751
0.824
0.811

0.818
0.789
0.854
0.839

0.859
0.848
0.894
0.899

0.854
0.809
0.865
0.849

0.883
0.839
0.874
0.872

0.823
0.778
0.844
0.819

0.238
0.228
0.235
0.208

0.830
0.919
0.975
1.006

0.868
0.920
0.961
0.995

0.844
0.915
0.971
1.010

0.774
0.924
0.998
1.057

0.825
0.952
0.999
1.047

Real GDP growth (pseudo-out-of-sample)
0.880
0.848
0.876
0.837
0.947
0.905
0.938
0.943
0.996
0.952
0.985
1.007
1.024
1.003
1.022
1.056

0.887
0.941
0.994
1.018

0.974
0.997
1.028
1.043

0.884
0.919
0.959
1.017

0.941
0.971
0.965
0.972

0.893
0.972
1.027
1.065

0.791
0.548
0.366
0.286

0.951
0.921
0.905
0.905

0.944
0.917
0.906
0.905

0.963
0.940
0.928
0.928

0.982
0.940
0.908
0.894

0.986
0.924
0.885
0.860

0.950
0.932
0.926
0.927

CPI inflation (pseudo-out-of-sample)
0.931
0.922
0.979
0.983
0.899
0.893
0.929
0.918
0.898
0.890
0.895
0.875
0.898
0.897
0.882
0.844

0.957
0.939
0.920
0.924

0.955
0.931
0.926
0.923

0.945
0.940
0.933
0.938

0.940
0.933
0.929
0.929

1.034
1.015
0.943
0.915

0.309
0.246
0.226
0.205

1
2
3
4

0.536
0.484
0.488
0.596

0.596
0.554
0.556
0.611

0.642
0.593
0.572
0.622

0.630
0.572
0.560
0.631

0.577
0.532
0.538
0.625

0.569
0.548
0.539
0.614

0.611
0.570
0.569
0.627

0.624
0.605
0.618
0.704

0.717
0.720
0.714
0.732

0.708
0.674
0.682
0.738

0.761
0.748
0.763
0.810

0.736
0.731
0.746
0.794

0.548
0.558
0.516
0.486

1
2
3
4

0.781
0.772
0.798
0.811

0.802
0.814
0.823
0.843

0.827
0.813
0.846
0.879

0.825
0.813
0.844
0.882

0.796
0.817
0.822
0.812

0.856
0.807
0.857
0.859

Unemployment rate (pseudo-out-of-sample)
0.846
0.795
0.845
0.812
0.824
0.807
0.812
0.812
0.872
0.862
0.866
0.845
0.870
0.834
0.883
0.836

0.972
0.841
0.919
0.920

0.907
0.851
0.899
0.917

0.827
0.771
0.836
0.838

0.862
0.827
0.861
0.872

0.838
0.840
0.858
0.844

0.236
0.239
0.25
0.231

M1

M2

M3

K1

K2

M1

1
2
3
4

0.854
0.913
0.948
0.973

0.867
0.942
0.980
0.994

0.894
0.943
0.975
0.990

0.872
0.933
0.971
0.990

0.809
0.892
0.941
0.971

1
2
3
4

0.942
0.905
0.894
0.887

0.965
0.937
0.927
0.921

0.977
0.958
0.945
0.941

0.981
0.956
0.940
0.936

1
2
3
4

0.512
0.471
0.486
0.577

0.577
0.547
0.560
0.627

0.667
0.637
0.645
0.698

1
2
3
4

0.775
0.736
0.805
0.798

0.811
0.778
0.834
0.845

1
2
3
4

0.818
0.923
0.977
1.007

1
2
3
4

T-Bill (pseudo-out-of-sample)
0.616
0.670
0.660
0.592
0.634
0.607
0.578
0.624
0.605
0.599
0.667
0.656

NOTE: The regressors in Equations (6) and (9) are changes in two-year Treasury yields. The entries are ratios relative to an AR(1) Forecast. The entries are ratios relative to an AR(1) Forecast. We start with the forecasts made in 1990Q3 and end with
2005Q4. The first observation for out-of-sample mean square prediction is 1998Q1, with parameters estimated only using data from 1997 and subsequently updated.

Journal of Business & Economic Statistics, October 2009

Downloaded by [Universitas Maritim Raja Ali Haji] at 17:33 12 January 2016

Horizon
(Qtrs.)

Downloaded by [Universitas Maritim Raja Ali Haji] at 17:33 12 January 2016

Ghysels and Wright: Forecasting Professional Forecasters

511

Figure 1. Kalman smoothed estimates of 2-Quarter GDR growth forecasts with predictors (a) (Actual SPF forecasts are shown by dots).

data using predictors (a), the daily changes in three-month and
ten-year Treasury yields. The coefficients β1 and β2 (corresponding to the three-month and ten-year yields, respectively)
are both estimated to be positive for real GDP growth and CPI
inflation and negative for the unemployment rate, meaning that
rising yields are associated with stronger forecasts for economic
activity and inflation. For inflation and GDP growth forecasts
at longer horizons, the coefficient on the three-month yield is
smaller than that on the ten-year yield, meaning that a steepening yield curve is associated with faster growth and inflation
forecasts. F-statistics testing the hypothesis that β1 = β2 = 0
are significant in every case except for GDP growth at the three
or four quarter horizons. The R-squareds from these regressions
are extremely high, but this largely reflects the slow-moving
nature of the forecasts (the high value of ρ). Finally, the table
shows likelihood ratio (LR) tests of the hypothesis that the MIDAS polynomial is degenerate or flat (i.e., κ1 = κ2 = 1). These
can be thought of as LR tests of the null of model M2 against
the alternative of model M1. The hypothesis is rejected in most
cases, showing the need for some flexibility in the distributed

lag polynomial, which is to be expected given that model M1
generally has better forecasting power than model M2, even
out-of-sample. Figure 2 plots the MIDAS polynomials γ (L)
corresponding to the estimates of κ1 and κ2 , illustrating clearly
that the elements of γ (L) are far from equal and showing humpshaped polynomials.
3.4 Forecasting Future Outcomes
Although our main motivation in this article is to construct high-frequency predictions of infrequently-released survey forecasts, it seems natural to assess both our predictions
and the surveys themselves as forecasts of actual future outcomes. As a simple comparison, we computed the RMSPEs of
the predictions from models M1, M2, M3, K1, and K2 made
just before the survey deadline date (θ = 1)—viewed as predictions of actual realized values of the data—relative to the RMSPEs of the subsequently-released survey forecasts themselves.
In this exercise, we used the changes in three-month and tenyear Treasury yields as the predictors in Equations (6) and (9).
The results are shown in Table 4.

Variable
Horizon
α
SE

Real GDP growth

CPI inflation

T-Bill

Unemployment rate

1
1.46
(0.27)

2
0.97
(0.25)

3
0.70
(0.20)

4
0.55
(0.18)

1
0.45
(0.16)

2
0.29
(0.13)

3
0.24
(0.12)

4
0.20
(0.11)

1
0.10
(0.05)

2
0.13
(0.07)

3
0.11
(0.08)

4
0.10
(0.11)

1
0.09
(0.13)

2
0.23
(0.14)

3
0.28
(0.18)

4
0.17
(0.14)

β1
SE

36.58
(12.58)

12.88
(7.52)

3.58
(5.73)

1.10
(4.43)

3.34
(5.34)

7.34
(4.19)

5.89
(3.75)

5.11
(3.37)

53.69
(2.59)

47.34
(3.48)

41.17
(3.83)

34.91
(4.68)

−19.99
(3.08)

−20.18
(3.18)

−19.45
(3.69)

−15.96
(2.20)

β2
SE

8.24
(9.40)

12.24
(7.42)

10.68
(6.16)

7.82
(5.19)

12.89
(5.19)

10.55
(4.54)

10.32
(4.13)

9.86
(3.70)

15.15
(2.90)

22.30
(3.86)

22.86
(4.25)

22.51
(5.19)

2.92
(2.47)

−3.68
(3.46)

−0.81
(3.95)

1.12
(2.25)

ρ
SE

0.52
(0.09)

0.68
(0.09)

0.77
(0.07)

0.82
(0.06)

0.83
(0.06)

0.89
(0.04)

0.91
(0.04)

0.92
(0.04)

0.98
(0.01)

0.98
(0.02)

0.98
(0.02)

0.99
(0.02)

0.97
(0.02)

0.95
(0.03)

0.94
(0.03)

0.96
(0.03)

0.00

0.00

0.12

0.24

0.01

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

F (pval)
LR (pval)

0.01

0.04

0.04

0.12

0.11

0.08

0.07

0.06

0.00

0.00

0.00

0.01

0.01

0.10

0.19

0.00

R2

0.62

0.64

0.73

0.78

0.80

0.88

0.90

0.92

0.99

0.99

0.98

0.97

0.97

0.97

0.95

0.97

NOTE: This table reports the parameter estimates from fitting model M1 to the SPF forecasts using changes in three-month and ten-year Treasury yields (see Table 1). Standard errors are shown in parentheses. The row labeled F (pval) reports the
p-values from F-tests of the hypothesis that β1 = β2 = 0. The row labeled LR (pval) reports the p-values from likelihood ratio tests of the hypothesis that the MIDAS polynomial is degenerate (κ1 = κ2 = 1).

Journal of Business & Economic Statistics, October 2009

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Table 3. Parameter estimates MIDAS regression model M1

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Figure 2. Estimated MIDAS polynomials γ (L) from fitting model M1 with predictors (a).
Table 4. Forecasting actual macroeconomic series
In-sample
Horizon
(Qtrs.)

Pseudo-out-of-sample
Survey RMSE
(memo)

M2

M3

K1

K2

Survey RMSE
(memo)

0.996
0.989
0.968
0.950

1.004
0.993
0.971
0.953

1.007
0.997
0.971
0.956

0.996
0.981
0.956
0.934

2.141
1.738
1.642
1.497

1.008
0.983
0.980
0.995

1.005
0.974
0.967
0.990

0.989
0.959
0.945
0.973

0.986
0.957
0.943
0.966

0.986
0.960
0.955
0.978

1.272
1.081
0.986
0.922

1.107
1.103
1.072
1.034

1.089
1.087
1.063
1.030

1.032
1.049
1.042
1.022

1.037
1.066
1.048
1.024

1.073
1.077
1.070
1.042

0.446
0.804
1.183
1.552

Unemployment rate
0.234
1.254
0.344
1.194
0.459
1.078
0.564
1.090

1.176
1.055
1.033
1.045

1.255
1.082
1.034
1.039

1.250
1.078
1.043
1.055

1.257
1.101
1.068
1.064

0.195
0.284
0.425
0.540

M1

M2

M3

K1

K2

1
2
3
4

1.005
0.975
0.969
0.968

1.001
0.977
0.968
0.966

1.002
0.969
0.965
0.965

1.008
0.970
0.964
0.966

1.008
0.972
0.967
0.968

1
2
3
4

0.991
0.975
0.970
0.982

0.996
0.974
0.962
0.979

0.994
0.978
0.963
0.980

0.997
0.982
0.966
0.981

0.988
0.972
0.968
0.980

CPI inflation
1.132
0.973
0.902
0.867

1
2
3
4

1.051
1.041
1.025
1.009

0.986
0.989
0.996
0.989

1.014
1.005
1.006
0.995

1.023
1.016
1.012
1.000

1.028
1.018
1.013
1.003

T-Bill
0.427
0.769
1.112
1.440

1
2
3
4

1.303
1.083
1.044
1.047

1.181
1.055
1.028
1.029

1.241
1.070
1.032
1.024

1.224
1.069
1.029
1.024

1.206
1.072
1.026
1.023

M1

Real GDP growth
2.027
0.999
1.630
0.998
1.524
0.963
1.433
0.939

NOTE: The table reports in- and pseudo-out-of-sample root mean square error of predictions of SPF forecasts using changes in three-month and ten-year Treasury yields, evaluated as
forecasts of actual data. The entries are ratios relative to Survey Forecast RMSE.

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Journal of Business & Economic Statistics, October 2009

For real GDP growth and CPI inflation, some of the entries
are less than one, meaning that our forecasts of the survey is
doing a slightly better job than the survey itself. In other cases,
the relative RMSPEs are slightly above one, but this is perhaps
not too surprising. Only for the unemployment rate at the shortest horizons do our θ = 1 forecasts markedly less well than the
actual surveys. Overall, these results indicate that our model
predictions have similar informational content to the surveys
themselves, but of course have the advantage that they can be
constructed at a much higher frequency.

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4. MEASURING THE EFFECT OF NEWS
ANNOUNCEMENTS ON AGENTS’ EXPECTATIONS
Applying the Kalman smoother to models, K1 and K2, we
can estimate what forecasters’ expectations were on a day-today basis conditional on the whole sample. Hence, we can,
in principle, measure agents’ expectations immediately before
and after a specific event (e.g., macroeconomic news announcements, Federal Reserve policy shifts, or major financial crises)
and so measure the impact of such events on their expectations.
The impacts of some events such as September 11 and Hurricane Katrina can indeed be seen in Figure 1.
As an illustration, we show how our method can be used to
estimate the average effect of a nonfarm payrolls data release
(one of the most important macroeconomic news announcements) coming in 100,000 stronger than expected on the expectations of respondents to the SPF. Nonfarm payrolls data
are released by the Bureau of Labor Statistics once a month,
at 8:30 a.m. sharp. We measure ex ante expectations for nonfarm payrolls releases from the median forecast from Money
Market Services (MMS) taken the previous Friday. The surprise component of the nonfarm payrolls release is then the
released value less the MMS survey expectation.