Forecasting with Judgment and

Models

This version: January 19, 2008.

Francesca Monti∗

ECARES, Universite Libre de Bruxelles

CP 114 Av.F.D. Roosevelt, 50.

B-1050 Bruxelles

fmonti@ulb.ac.be

Abstract

This paper proposes a parsimonious and model-consistent method for com-bining forecasts generated by structural micro-founded models and judgmen-tal forecasts. The method also allows interpreting the judgmental forecaststhrough the lens of the model. We illustrate the proposed methodology witha real-time forecasting exercise, using a simple version of an RBC model andthe Survey of Professional Forecasters.

JEL Classification: C32, C53Keywords: Forecasting, Judgment, Kalman filter, Real time

∗I am greatly indebted to Domenico Giannone, Lucrezia Reichlin and Philippe Weilfor invaluable guidance and advice. I also thank Marco Del Negro for for very helpfulcomments. Finally, I am grateful to Gunter Coenen, David De Antonio Liedo, AndreaFerrero, Mark Gertler, Simon Potter, Paulo Santos Monteiro, Argia Sbordone, FrankSchorfheide, Andrea Tambalotti, Dan Waggoner, Tao Zha and all seminar participants atthe ECB, University of Pennsylvania, Federal Reserve Bank of NY, Federal Reserve Bankof Atlanta and Federal Reserve Bank of Philadelphia for comments and useful discussions.

1 Introduction

Much of the macroeconometric literature of the last decade has focused onmaking micro-founded dynamic stochastic general equilibrium (DSGE) mod-els a viable option for policy analysis and forecasting. Since Smets andWouters (2004) have shown that DSGE models estimated with Bayesiantechniques seem to perform quite well in forecasting relative to standardbenchmark models such as VARs, DSGE models are playing a more relevantrole in practice and have indeed become an increasingly important tool forpolicy analysis and forecasting at central banks.

Despite their growing employment in practice, model-based forecasts stillseem to be outperformed at short horizons -and particularly in the nowcast1-by forecasts produced by institutional and professional forecasters, such asthe Federal Reserve’s Greenbook (e.g. Sims, 2003) or the Survey of Profes-sional Forecasters. Where does advantage of the judgmental forecasters comefrom?

Judgmental forecasters, as I will define the institutional and professionalforecasters from now on, monitor and analyze literally hundreds of data se-ries, using informal methods to distill information from the available data.Not only they access what is generally called hard data (data series that arereleased by the statistical agencies, as for example, GDP, industrial produc-tion, etc), they also gather so-called soft information, such as the quantityof goods transported by railway in each month (Bruno and Lupi, 2004) orthe electricity consumed each month (Marchetti and Parigi, 1998). Moreover,judgmental forecasters are able to incorporate new data and new informationas it becomes available throughout the month or the quarter and thereforecan take advantage of the timeliness of this information. Indeed, as Gian-none, Reichlin and Small (2005) point out, timely information seems to playa very important role in improving the quality of the forecasts, and of thenowcasts in particular. Finally, in their forecasts, judgmental forecasters ac-count also for all sheerly judgmental information. A typical example is theadjustments of the forecasts made in 1999 in order to account for the fear ofthe Y2K bug. Indeed this seemed at the time a very important event, butsince it had never happened no model could be expected to encompass it,while the judgmental forecasters could.

Hence, judgment - i.e. information, knowledge and views outside thescope of a particular model 2 - strongly informs the judgmental forecasts.The empirical evidence at hand suggests that the ability to account for more,

1Nowcasts are estimates of the current value of variables, such as GDP, that are un-known in the current period due to information lags

2This definition appears in Svensson (2005)

2

more timely and ”softer” information is what makes the judgmental forecastsbetter at nowcasting and forecasting short horizons.

The introduction of DSGE models in a policy and projection environmenthas given rise to a literature on how the model’s outcomes should be combinedwith judgmental input and off-model information. The aim of this paper isto propose a method for combining judgmental forecasts and model-basedforecasts, in order to make predictions that are more accurate but neverthe-less disciplined by rigorous economic theory. In particular, we propose tointerpret the judgmental forecasts as an estimate - made with a different,possibly richer, information set - of the real signal, estimate which can be fil-tered in order to extract the information it contains. We then use the modelto generate another forecast that can now also account for judgmental infor-mation and hence make more accurate predictions. The new forecast thatwe generate is a combination of the model-based forecast and the judgmentalforecast: the Kalman filter will automatically associate weights to the twoforecasts depending on the information content of the judgmental forecasts.Moreover, with the methodology we propose, we will be able to look at thejudgmental forecasts through the lens of the model. Storytelling is difficultwhen it comes to judgmental forecasts; in our set-up we will be able to inter-pret the forecasts in light of the model and therefore somehow structuralizethe forecasts. The approach we propose is similar in spirit to the one used byCoenen, Levin and Wieland (2005) and Koenig (2005) to deal with revisions.One of the key factors that distinguishes our approach from theirs is that weconsider the judgmental forecasts as optimal forecasts made with a differentinformation set, not a noisy signal of the actual variables.

Recently, other authors have addressed the issue of how to use soft dataand judgment in models. Svensson (2005), Svensson and Tetlow (2005) andSvensson and Williams (2005) develop different frameworks that allow ac-counting for central bank judgment when constructing optimal policy pro-jections of the target variables and the instrument rate. They show that suchmonetary policy may perform substantially better than monetary policy thatdisregards judgment and follows a given instrument rule. Our approach dif-fers quite substantially from theirs: our goal is solely to produce model-basedforecasts that can account for judgmental and off-model information. Ourapproach leaves the structure of the DSGE model unchanged while combiningthe model-based forecasts with the judgmental forecasts.

In a Bayesian framework, Robertson, Tallman and Whiteman (2005) sug-gest a minimum relative entropy procedure for imposing moment restrictionson simulated forecasts distributions from a variety of models. This techniqueinvolves changing the initial predictive distribution to a new one that sat-isfies specific moment conditions that come from outside of the models, i.e.

3

that are judgmental. Therefore, minimum-entropy methods allow adjustingthe full posterior distribution of the DSGE models to match a given experts’assessment.

Another approach that can be used to incorporate judgmental and off-model information is that of Boivin and Giannoni (2005). They build on thefactor model literature, started by Stock and Watson (1999, 2002) and Forni,Hallin, Lippi and Reichlin (2000), and propose an empirical framework forthe estimation of DSGE models that exploits the relevant information from adata-rich environment. Their methodology allows using as much informationas possible to estimate the structural model and to update the estimates ofthe state variables featuring in the model. In this way, soft information canbe used systematically to update the current assessment of the state variablesas well as of the short-term forecast.

The paper is structured as follows. In Section 2 we outline the frameworkand describe the proposed methodology; we illustrate how to extract theweights given to the model-based and the judgmental forecast; and describehow to structuralize the professional forecasts. In Section 3 we apply theproposed methodology on a simple version of an RBC model using the Sur-vey of Professional Forecasters’ forecasts to extract judgmental information.Section 4 presents the results of the empirical application described in theprevious section. In Section 5 we give some conclusions and outline futureextensions of this paper.

2 The Econometric Methodology

2.1 The Framework

Linear or linearized rational expectations models, solved with methods sug-gested by Blanchard and Kahn (1980), Klein (1997) and Sims (2000) amongothers, allow a representation for zt in the state space form

st+1 = A(θ)st + B(θ)εt+1 (1)

zt = C(θ)st + νt

where st is an n×1 vector of possibly unobserved state variables, zt is a k×1vector of variables observed by an econometrician, and εt is an m× 1 vectorof economic shocks impinging on the states, such as shocks to preferences,technologies, agents’ information sets, and νt is an l×1 vector of measurementerrors (0 6 l 6 k, hence measurement error can be absent or affect some orall of the variables). A(θ), B(θ) and C(θ) are functions of the underlyingstructural parameters of the DSGE model. The εt’s are Gaussian vector

4

white noise satisfying E(εt) = 0, E(εtε′t) = I, E(εtε

′t+j) = 0, for j > 0.

The νt’s are Gaussian vector white noise satisfying E(νt) = 0, E(νtν′t) = R,

E(νtν′t+j) = 0, for j > 0. The assumption of normality is for convenience

and allows us to associate linear least squares predictions with conditionalexpectations. For notational simplicity we will drop the indication that thematrices A, B, etc... are function of the structural parameters θ.

Associated with the state space representation (1) is the innovations rep-resentation3

st|t = Ast−1|t−1 + Ktut (2)

zt = CAst−1|t−1 + ut

where st|t = E[st|zt, zt−1, ..., z0] is the estimate of the state vector st based onthe observations of zτ up to date t, ut = zt − zt|t−1 = zt − E[zt|zt−1, ..., z0] isthe forecast error made when forecasting zt given the observations of zτ upto date t-1,

Kt = Ωt|t−1C′(CΩt|t−1C

′ + R)−1,

and Ωt|t−1 = E(st − st|t−1)(st − st|t−1)′ converges to Ω, the unique positive

semidefinite solution that satisfies the algebraic Riccati equation

Ω = BB′ + AΩA′ − AΩC ′(CΩC ′)−1CΩA′. (3)

2.2 Model of the Judgmental Forecasts

The goal of this section is to show how to incorporate judgmental forecastsinto models of the form (1) or, equivalently, (2). In order to do so, weneed to somehow formalize these forecasts. More specifically, we need tomake assumptions on the model and the information set that the judgmentalforecasters use to generate their forecasters.

The assumptions about the information available in each period t areoutlined in Table 1. Shocks hit the economy at the beginning of period t.There are two types of forecasters. The first type generates his forecastssolely on the basis of the model of the economy (1) and the data released bythe statistical agency. The statistical agency releases data about the currentperiod at the end of the period, so in period t there is data available only up

3The conditions for the existence of this representation are stated carefully, among otherplaces, in Anderson, Hansen, McGrattan, and Sargent (1996). The conditions are thatthat (A,B,C) be such that iterations on the Riccati equation for Ωt|t−1 = E(st−st|t−1)(st−st|t−1)

′ converge, which makes the associated Kalman gain converge. Sufficient conditionsare that (A, C′) is stabilizable and that (A′, B′) is detectable. See Anderson, Hansen,McGrattan, and Sargent (1996, page 175) for definitions of stabilizable and detectable.

5

Table 1: Information structure

t t + 1

shocks hit the economyagents observe them

JF collect informationand release their forecast

stat. agency releasesdata on period t

to t-1. Therefore the information set available to the first type of forecaster intime t comprises exclusively information up to time t-1 : his information set isMt = Spzt−1, zt−2, ...z0, i.e. the space spanned by zt−1, zt−2, ...z0. Fromnow on I will call the first type of forecaster ’purely’ model-based forecaster.

The second type of forecaster uses a reduced form version of the model ofthe economy - i.e. he or she knows A, B, C, but not θ - to make its forecastsand accesses the information set IJ

t , which comprises Mt but is possibly moreinformative. This type represents the judgmental forecasters (JF from nowon). As highlighted in the Introduction, their information set is plausiblyricher than Mt: they collect soft, intra-period extra-model information, suchas monthly electricity consumption or quantity of goods transported by rail-way in each month. This allows them to make a better estimate of the currentand (possibly) future value of the variables of interest. In what follows, weassume that judgmental forecasters have extra-model information only onthe current period. In appendix we illustrate the case in which they havesome extra-model information that allows them to have a better estimate ofthe future value of the variables of interest. Considering the way the judg-mental forecasts are made and the type of extra-information they use - i.e.,information about this month electricity consumption, but also informationon future tax raises or on the possible effects of extraordinary events like theY2K bug or the World Cup- , both cases are credible. However, the pos-sible theorectical inconsistency arising from assuming that the judgmentalforecasters know more about the future that the agents, but that the agentsdon’t incorporate them in their solution, persuaded me to relegate this partto the appendix. Finally, in what follows, we also assume that IJ

t ⊆ Mt+1.This means that, once the observable variables are actually observed, theinformational content of the judgmental forecasts is nihil. Hence, the infor-mation the JF can observe does not improve their estimate of past values ofthe state variable.

Let us formalize rigorously the judgmental forecasters. At any given timet their information set IJ

t comprises Mt but is such that, for h > 0

E[

utIJt

′]

6= 0, (4)

ut+h ⊥ IJt

6

We assume that the judgmental forecasters use the reduced form versionof model (1) and their richer information set IJ

t to generate the forecasts, butwe also allow for the presence of an error, e.g. a typo made in communicatingthe forecasts. At time t, both purely model-based forecasters and JF aregoing to construct the innovations representation (2) for τ = 1, 2, ..., t − 1.4

For τ > t, judgmental forecasters will report the following: for h=0,

zJt|t = E[zt|I

Jt ] + ηt (5)

where E[zt|IJt ] = CAst−1|t−1 + E[ut|I

Jt ] is the least squares forecast made by

the PF with their information set IJt and ηt is the measurement error - the

typo - possibly made by the professional forecasters in t while reporting theirforecast. This can be cast in state-space form as follows. For h=0,

st|t = Ast−1|t−1 + Ktut (6)

zJt|t = CAst−1|t−1 + E[ut|I

Jt ] + ηt|t

︸ ︷︷ ︸

wt

,

where [Ktut

wt

]

∼ N(

0 , Σ0

)

with

Σ0 =

[KE(utu

′t)K

′ KE[utE(ut|IJt )′]

E(E[ut|IJt ]u′

t)K′ E[E(ut|I

Jt )E(ut|I

Jt )]′ + Ση

]

.

For h > 0 we have

st+h|t+h = Ast+h−1|t+h−1 + Kut+h (7)

zJt+h|t = CAst+h−1|t+h−1 + CAhKE[ut|I

Jt ] − C

h∑

j=1

AjKut+h−j + ηt+h

︸ ︷︷ ︸

wt+h

,

where [Kut+h

wt+h

]

∼ N(

0 , Σh

)

and

Σh =

[KE(ut+hu

′t+h)K

′ 00 E[wt+hw

′t+h]

]

.

As above, ηt+h is the measurement error (the typo) made by the judgmentalforecasters in t while reporting their forecast for period t + h. We assume

4This comes from the assumption that IJt⊆ Mt+1

7

that ηs ⊥ uτ , for any s and τ , and that ηt+h ⊥ E(ut|IJt ) for h > 0. Clearly,

the form of the matrices Σh depends crucially on the assumptions we madeabout the information set of the JF. Here Σh will be block diagonal for allh > 0, since we have assumed that the JFs’ have some information only onthe current period’s innovation. In appendix we present the case in whichthe JF can have extra-information up to h periods ahead. In that case, theΣh will not necessarily be block diagonal: the value of the off-diagonal termswill depend on the information about the future actually contained in thejudgmental forecasts.

We now need to recover the exact form of the covariance matrices Σ0 andΣh for h > 0. Let us start with Σ0. First of all, the variance E(utu

′t) can be

obtained by the Kalman filter on the system of equations (1) simply as

E(utu′t) = CΩt|t−1C

′ + R

where Ωt|t−1 = E(st − st|t−1)(st − st|t−1)′. Hence the upper left block of Σ0 is

readily pinned down. Moreover, notice that

E[utzJ ′t|t] = E[utE(ut|I

Jt )′].

This equality derives from the fact that ut ⊥ CAst−1|t−1 by constructionand that ηt ⊥ ut by assumption. The ut’s are readily available via theKalman filter, so we are able to recover empirically the value of E[utz

J ′t ], and

therefore of E[utE(ut|IJt )′]. That is, we use an estimate of the covariance

E[utzJ ′t ], multiplied by Kt, to recover the off-diagonal block of Σ0.

Notice also that E(ut|IJt ) is a linear projection of ut on the space spanned

by IJt , i.e.

ut = E(ut|IJt ) + µt

where µt is orthogonal to the space spanned by IJt . Therefore,

E[utE(ut|IJt )′] = E[E(ut|I

Jt )E(ut|I

Jt )′], (8)

i.e. the variance of the expected value of the current period innovationgiven the information set IJ

t , E(ut|IJt ) is equal to the covariance among the

innovation and its expected value.In order to recover the lower right block of Σ0

Ewtw′t = E[E(ut|I

Jt )E(ut|I

Jt )′] + E[ηtη

′t], (9)

(remember that ηt ⊥ E(ut|IJt ) by assumption), we will first define the fore-

casters’ forecast error as

et = zt − zJt|t

= ut − E(ut|IJt ) − ηt.

8

Its variance - whose value can be recovered from sample data - is:

E(ete′t) = E(utu

′t) − E[utE(ut|I

Jt )′] − E[utE(ut|I

Jt )′]′ + (10)

+ E[E(ut|IJt )E(ut|I

Jt )′] + E[ηtη

′t]

We recover the value of the variance of the typo E[ηtη′t] from the following

equation:

E(ete′t) = E(utu

′t) − E[E(ut|I

Jt )E(ut|I

Jt )′] + Eηtη

′t. (11)

We therefore have pinned down all the values of the matrix Σ0 in equation(7). Analogously we recover Σh for h > 0.

Finally, we extract the optimal linear projection of zt+h given IJt , i.e

E[zt+h|IJt ], from zJ

t+h|t, by filtering model the new model(6)-(7). Using aKalman smoother we can obtain optimal estimates of the state variabless+

t+h|t that incorporate the extra-information contained in the professional

forecasts and employ it optimally within the model.5 Having s+

t+h|t for we

can finally construct the augmented forecasts z+

t+h|t

z+

t+h|t = Cs+

t+h|t (12)

that incorporate optimally in the model-based framework the judgementalinformation coming from the conjunctural forecasters.

In fact, these new augmented forecasts are nothing but linear combina-tions of the ’purely’ model-based and the judgmental forecasts. The weightsgiven to the two forecasts depend on the past performance of the two fore-casts. The more information the judgmental forecasters had about the stateof the economy, the more the Kalman filter will use their forecasts when com-bining the two. On the other hand, it will down-weigh them if the varianceof their forecast errors is too large. To see this, consider the new innovationsrepresentation, obtained filtering (6)

s+

t|t = As+

t−1|t + K+

h at (13)

zJt|t = CAs+

t−1|t + at,

initialized with s+

t−1|t = st−1|t−1 and where

s+

t|t = E(st|t|zJt|t, zt−1, ....),

at = zJt|t − E

[zJ

t|t|zt−1, ....z1

].

5The notation s+

t+h|t means the estimate of the state st+h made in t give the augmented

information set IJt.

9

The Kalman gain K+

h is time-varying and takes the form: for h=0,

K+

0 = Σ0

12Σ0

22

−1

and

K+

h = (AΩh|h−1A′C ′ + Σh

12)(CAΩh|h−1A′C ′ + Σh

22)−1 (14)

otherwise. Manipulating (13) we can rewrite the augmented nowcast for zt

asz+

t|t = (I − CK+

0 )CAst−1|t−1 + CK+

0 zJt|t

where CAs+

t−1|t is the purely model-based nowcast. Since K+

0 has the form

described in equation (14), the weight given to the judgmental forecast zJt|t is

directly proportional to Σ012, i.e. to the correlation among ut and E[ut|I

Jt ],

and inversely proportional to the variance of the judgmental forecasts Σ022.

The assumption that the professional forecasters have information onlyon the current period shocks is crucial in determining the negligible weightsassigned to the professional forecasts for h 6= 0. In appendix we presentsome results for the case in which the JF are assumed to have some off-modelinformation on current and future innovations up to four periods ahead. Inthat case, the weight associated to the judgmental forecast will be sizeable -depending on the informational content, of course - at all horizons considered.

2.3 Using the model to interpret judgemental forecasts

Another interesting aspect of this procedure is that it also allows to inter-pret the judgmental forecasts through the lens of the model. Storytellingis difficult when it comes to judgmental forecasts; in our set-up we will beable to interpret the forecasts in light of the model and therefore somehowstructuralize the forecasts.

Let us have another look at model (13). The element K+

0 at, with

at = zJt|t − E

[zJ

t|t|zt−1, zt−2, ...],

is the estimate of the current period’s structural shocks made by the judg-mental forecasters with their information set IJ

t . That is, these are theinnovations the professional forecasters perceive given their information set;they do not necessarily coincide with the ”real” structural shocks. We wantto recover the expected value of Bεt in model (1), given all obervation up tot-1 and the judgmental forecasts. I.e., we are looking for

E[Bεt|z

Jt|t, zt−1, ...

]= E

[st|z

Jt|t, zt−1, ...

]− E

[Ast−1|z

Jt|t, zt−1, ...

]. (15)

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We assumed that the information the JF can observe does not improve theirestimate of past values of the state variable. This means that, in fact,

E[st−1|z

Jt|t, zt−1, ...

]= st−1|t−1,

as already pointed out above. Now, applying the law of iterated expectationsfor nested information set, we have that

E[st|t|z

Jt|t, zt−1, ...

]= E

[st|z

Jt|t, zt−1, ...

]

and hence we obtain:

K+

0 at = E[Bεt|z

Jt|t, zt−1, ...

].

Hence we can extract the SPFs estimate of the structural shock and tryto understand if some shocks count more that others in determining theirforecast. We can also construct different scenarios - e.g. assume that theprofessional forecasters have extra information only on certain types of shocksbut not on others - and compare them among each other. As we will showin Section 4, this can be very informative.

3 An application

In order to illustrate the methodology proposed in the previous section, I willapply it to a prototypical real business cycle model, in the spirit of Christianoand Eichenbaum (1992). The model consists of a representative household, arepresentative firm and the fiscal policy authority. The representative house-hold derives disutility from hours worked H and utility from consumption Crelative to a habit stock. We assume that the habit stock is given by the levelof technology A.6 The representative household maximizes expected utility

Et

[∞∑

s=t

βs−t

((Ct+s/At+s)

1−τ − 1

1 − τ− χHt+s

)]

(16)

where β is the discount factor, τ the risk aversion parameter and χ is a scalefactor.

The household supplies perfectly elastic labor supply services to the firmperiod by period and receives in return real wage Wt. Moreover it owns assetsKt that pay a gross real interest of Rt. The household can spend its income

6This assumption ensures that the economy evolves along a balanced growth path.

11

on consumption or investment, and has to pay lump-sum taxes Tt. Hence,its budget constraint is:

Ct + It + Tt = WtHt + RtKt (17)

The transversality condition on asset accumulation rules out Ponzi schemes.The capital stock evolves following:

Kt+1 = (1 − δ)Kt + It. (18)

The government consumes a fraction ζt of output and levies a lump-sum tax(or subsidy) Tt to finance any shortfall in government revenues (or to rebateany surplus), so its budget constraint is:

ζtYt = Tt. (19)

Hence, if we define gt = 1/(1 − ζt) and assume that gt = ln(gt/g∗) follows a

stationary AR(1) process

gt = ρg gt−1 + εg,t (20)

where εg,t can be broadly interpreted as a government spending shock, wecan rewrite the household’s budget constraint (17) as:

Ct + Kt+1 =WtHt

gt

+

[

(1 − δ) +Rt

gt

]

Kt (21)

The household hence maximizes it utility (16) subject to the constraint (21).The representative firm produces good Yt using a Cobb-Douglas produc-

tion function that has labor Ht and capital Kt as inputs. Hence, in eachperiod, it chooses Ht and Kt to maximize profits

Πt = Yt − WtHt − RtKt

subject toYt = (AtHt)

1−αKαt , (22)

where At is a labor-augmenting technology process that follows a unit rootprocess of the form:

ln At = ln γ + ln At−1 + at, (23)

whereat = ρaat−1 + εa,t. (24)

Hence, there will be a stochastic trend in the model. εa,t can be broadlyinterpreted as a technology shocks that affects all firms in the same way.

12

To solve the model, we derive the optimality conditions from the house-hold’s and the firm’s maximization problems. Consumption, output, wagesand the marginal utility of consumption are detrended by total factor pro-ductivity At, in order to obtain a model that has a deterministic steady-statein terms of the detrended variables. The loglinearized system can be reducedto the following equations:

yt = kt − at −1 − α

α(gt + τ ct)

kt+1 = (1 − δ)e−γ(kt − at) +Y ∗

g∗K∗(yt − gt) −

C∗

K∗ct (25)

0 = Et

[

−τ(ct+1 − ct) − e−γβ(1 − δ)at+1 + (1 − e−γβ(1 − δ))(yt+1 − kt+1 − gt+1)]

gt = ρggt−1 + εg,t

at = ρaat−1 + εa,t

The relation between logdeviations from steady state and observable out-put growth and consumption growth is given by the following measurementequation:

∆ ln Yt = ln γ + yt − yt−1 + at (26)

∆ ln Ct = ln γ + ct − ct−1 + at

The model given by equations (25) and (26) can then solved with standardtechniques, such as those proposed by Blanchard and Kahn (1980), Uhlig(1999), Klein (2000), Sims (2002), among others, and hence cast in a standardstate-space model (1).

For the estimation and the forecasting exercise we use real-time quarterlydata for real GDP and real consumption for the US from the PhiladelphiaFed real-time dataset. The dataset covers the period 1947 through 2005 andthe first available vintage is 1965:Q4. Due to the unavailability of real-timedata on population, we have made the somewhat heroic assumption thatthe population has been constant throughout the period considered. In whatfollows, we will perform an out-of-sample real-time forecasting exercise, usingas evaluation sample the period 1987-2004. We estimate the parametersof the model only once, at the beginning of the evaluation sample, usingbayesian methods and data from 1947Q2 to 1987Q1. All parameters arereported in Table 2. The covariance matrices Σh are instead estimated usinga rolling window.

We use the Survey of Professional Forecasters (SPF) as example of judg-mental forecast. The Survey of Professional Forecasters, conducted by theFederal Reserve Bank of Philadelphia, is based on many individual commer-cial forecasts, which are then grouped in mean or median forecasts. The

13

Parameter value

β 0.9900 calibratedα 0.3466 estimatedδ 0.0130 calibratedγ 0.3113 estimatedχ 0.5000 estimatedg∗ 2.0552 estimatedρa 0.6236 estimated

rhog 0.9855 estimatedτ 1.1461 estimatedσa 0.6336 estimatedσg 0.6946 estimated

Table 2: Parameter values for the model with the autocorrelated but notcross-correlated residual.

Survey is conducted near the end of the second month of each quarter andpublishes forecasts for the current quarter and the next 4 quarters in thefuture. We consider a sample period going from the second quarter of 1987to the fourth quarter of 2004.

An important data-related issue regards the appropriate ”actual” seriesto use when comparing the various forecasts. Because macroeconomic data iscontinuously revised, we need to make a choice about which revision to use.Following Romer and Romer (2000), we choose to use the second revision,i.e. the one done at the end of the subsequent quarter. The second revisionseems to be the appropriate series to use because it is based on relativelycomplete data, but it is still roughly contemporaneous with the forecasts weare analyzing. This series does not include rebenchmarking and definitionalchanges that occur in the annual and quinquennial revisions and should,therefore, be conceptually similar to the series being forecast.

Let us now present some forecasting results that will highlight the motiva-tion of this paper. We will use the constant growth model, i.e. random walkin levels, as a benchmark with which to compare the forecasts. Tables 3 and4 report the performance in out-of-sample forecasting of the forecasts gener-ated with the RBC model and of the SPF relative to the naive benchmark,for GDP growth and consumption growth respectively. Each table is dividedin two subtables which consider the full sample period 1987:Q2-2004:Q4 andthe subsample 1996:Q2-2004:Q4. In the first column of each table is reportedthe ratio of the mean square error of the purely model-based forecast (RBC)against the mean square error of the naive benchmark, while the second

14

relative to constant growthEVALUATION SAMPLE: 1987:2 - 2004:4

Forecast horizon RBC SPFQ0 0.87 0.68 ∗∗Q1 0.95 0.77Q2 0.93 0.88Q3 0.95 0.94Q4 1.05 0.95

EVALUATION SAMPLE: 1996:2 - 2004:4

Forecast horizon RBC SPFQ0 0.87 0.80∗Q1 0.96 0.94Q2 0.93 1.01Q3 0.92 1.01Q4 1.04 1.01

Table 3: Relative MSFE of forecasts of GDP growth with respect to naive bench-mark. Asterisks denote forecasts that are statistically more accurate than thenaive benchmark at 1% (∗ ∗ ∗), 5%(∗∗) and 10%(∗)

relative to constant growthEVALUATION SAMPLE: 1987:2 - 2004:4

Forecast horizon RBC SPFQ0 1.09 0.70 ∗Q1 0.93 0.89Q2 1.01 0.94Q3 1.18 0.99Q4 1.22 1.00

EVALUATION SAMPLE: 1996:2 - 2004:4

Forecast horizon RBC SPFQ0 0.99 0.96Q1 0.93 1.06Q2 1.11 1.03Q3 1.22 1.03Q4 1.34 1.08

Table 4: Relative MSFE of forecasts of Consumption growth with respect to naivebenchmark. Asterisks denote forecasts that are statistically more accurate thanthe naive benchmark at 1% (∗ ∗ ∗), 5%(∗∗) and 10%(∗)

15

column reports the ratio of the mean square error of the SPF against themean square error of the naive benchmark. Asterisks indicate a rejectionof the test of equal predictive accuracy between each forecast and the naivebenchmark.7

This simple RBC model has little forecasting power, but it still allowsus to tell a consistent economic story around the forecasts. The professionalforecasters fare better that the model, in that their forecasts, at least for thenowcast, are better than the naive benchmark in a statistical sense. Andthis hold both for GDP growth and for consumption growth, though to alesser extent. It will hence be interesting to understand if the methodologywe propose will allow for generating new ”augmented” model-based forecaststhat are more accurate than the original ”purely model-based” ones. Figure1 reports the smoothed forecast errors for the nowcast of GDP (centeredmoving average 4 quarters on each side) over the full sample period. Modeland judgement seem to contain information that is useful in different pointsin time: in few periods the model does even better than the SPF. However,particularly during recessions, judgement seems to fare better than the model(a similar result can be found in Giannone, Reichlin and Sala, 2005).

In the following section we present the results obtained when applyingthe methodology proposed in Section 2 to the model presented above andusing the SPF forecasts.

4 Results of the Forecasting Exercise

The main goal of this section is to present model-based forecasts for realGDP and real consumption that can account for the judgmental informationcontained in the SPF forecasts. We will compare their performance on thebasis of their mean square forecast error, i.e. deeming better a forecast with asmaller MSE. We will perform out-of-sample forecasting exercises on the fullevaluation sample 1987:Q2-2004:Q4 and on the subsample 1996:Q2-2004:Q4.

7Following Romer and Romer (2000), our inference is based on the regression: (zht −zm

ht)2 − (zht − znaive

ht)2 = c + uht where z is the variable to be forecasted at horizon h

using model -m . The estimate of c is simply the difference between forecast-m and aNaive model MSFEs, and the standard error is corrected for heteroskedasticity and serialcorrelation over h-1 months. This testing procedure falls in the Diebold-Mariano-Westframework, and Giacomini and White (2006, Section 3.2, see in particular Comment 4)show that by using rolling window estimators, as we do here, the limiting behavior ofthis type of tests is standard, and therefore standard asymptotic theory can be used forinference on the difference in predictive accuracy.

16

Q1−90 Q3−92 Q1−95 Q3−97 Q1−00 Q3−02

0.5

1

1.5

2

2.5

NOWCAST: Smoothed Square Forecast errors (relative to constant growth)

SPFRBC

Figure 1: NOWCASTS: Smoothed Square forecast errors

We construct the augmented forecasts following the procedure describedin the previous section, that is assuming that the professional forecasters haveextra-information on the current period. In appendix we present some resultsfor the case in which we assume that the professional forecasters have someinformation also that can help them predict future values of the variables ofinterest.

Figure 2 reports the smoothed forecast errors for the nowcast of GDP(centered moving average 4 quarters on each side) over the full sample period.The line identified by the diamond-shaped marker is the SPF nowcast, theline with the cross-shaped marker is the ’purely’ model-based nowcast and theline with the circle marker is the ’augmented’ nowcast. Interestingly, wherethe SPF perform worse than the model, the augmented nowcast is closer tothe ’purely’ model-based forecast and viceversa. Hence the augmented modelperforms reasonably well, thanks to its ability to combine the two forecastsin an information-efficient and model-consistent manner.

Table 5 reports the mean square forecast error (MSE) of the purely model-based forecasts, the SPF and the augmented forecasts relative to the naivemodel (random walk in levels), when forecasting GDP growth. Figure 3reports the nowcasts of the model, the SPF and the augmented forecasts

17

relative to constant growthEVALUATION SAMPLE: 1987:2 - 2004:4

Forecast horizon RBC SPF AUGQ0 0.87 0.68 ∗∗ 0.69 ∗∗Q1 0.95 0.77 0.90Q2 0.93 0.88 0.90Q3 0.95 0.94 0.95Q4 1.05 0.95 1.02

relative to constant growthEVALUATION SAMPLE: 1996:2 - 2004:4

Forecast horizon RBC SPF AUGQ0 0.87 0.80∗ 0.72 ∗Q1 0.96 0.94 0.91Q2 0.93 1.01 0.90Q3 0.92 1.01 0.92Q4 1.04 1.01 1.01

Table 5: Relative MSFE of forecasts of GDP growth with respect to naivebenchmark. Asterisks denote forecasts that are statistically more accuratethan the naive benchmark at 1% (∗ ∗ ∗), 5%(∗∗) and 10%(∗)

compared with actual data for GDP over the full evaluation sample.In all samples considered, the augmented forecasts outperform quite con-

sistently the model-based forecasts. The greatest gain is achieved in thenowcast, since that is where the judgmental forecasts help. For higher hori-zons, the weight associated to the judgmental forecast is very small, andtherefore the augmented forecast is very similar to the purely model-basedone. This result crucially depends on the assumptions made on the informa-tion set of the professional forecasters. The results for the case in which theJFs are assumed to have information also on future innovations are reportedin appendix.

Table 7 reports the weights that the filter gives to the judgmental fore-casts of real GDP growth and real consumption growth when constructingthe augmented forecasts. In particular, the first column gives the weightsassociated to the SPF forecasts of real GDP growth when constructing theaugmented forecast of real GDP growth; the second column instead gives theweights associated to the SPF forecasts of real consumption growth whenconstructing the augmented forecast of real consumption growth.

Clearly, since we assume that the SPF have more information on the

18

Q1−90 Q3−92 Q1−95 Q3−97 Q1−00 Q3−02

0.5

1

1.5

2

2.5

NOWCAST: Smoothed Square Forecast errors (relative to constant growth)

SPFRBCAUG

Figure 2: NOWCASTS: Smoothed Square forecast errors

current period but not on future periods, the judgmental forecast receives asignificant weight in the construction of the augmented forecasts only in thenowcast. The reason is that the weights given by the Kalman filter to the SPFtend to zero as their information content goes to zero. Finally, notice thatthe weight associated to the SPF forecast of consumption growth is smallerthan those associated to the SPF forecast of GDP growth. This indicatesthat the extra-model information accessed by the professional forecasters ismore informative on GDP than on consumption. Table 8 reports the meansquare forecast error (MSE) of the purely model-based forecasts, the SPFand the augmented forecasts relative to the naive model (random walk inlevels), when forecasting consumption growth.

Finally, we report few illustrative results on the ”structural” analysis ofthe SPF forecasts. We can infer the type of shocks the Professional Forecast-ers saw when performing their forecasts. Figure 4 reports actual GDP growthand perceived technology and government spending shocks. This graph pro-vides our answer - that is, the answer of the method and the simple RBCmodel - to the widely discussed question: why did the most professionalforecasters miss out on the technology boom of the 90’s? Well, is seems thatthey attributed the growth to demand side factors rather than to technology

19

Table 6: Relative MSFE of forecasts of Consumption growth with respectto naive benchmark. Asterisks denote forecasts that are statistically moreaccurate than he naive benchmark at 1% (∗ ∗ ∗), 5%(∗∗) and 10%(∗)

relative to constant growthEVALUATION SAMPLE: 1987:2 - 2004:4

Forecast horizon RBC SPF AUGQ0 1.09 0.70 ∗ 0.93Q1 0.93 0.89 0.96Q2 1.01 0.94 1.01Q3 1.18 0.99 1.20Q4 1.22 1.00 1.22

relative to constant growthEVALUATION SAMPLE: 1996:2 - 2004:4

Forecast horizon RBC SPF AUGQ0 0.99 0.96 0.95Q1 0.93 1.06 0.96Q2 1.11 1.03 1.11Q3 1.22 1.03 1.23Q4 1.34 1.08 1.34

∆GDP ∆CONS

nowcast 0.4033 0.2233

1 step ahead -0.0574 -0.0094

2 step ahead -0.0072 -0.0047

3 step ahead 0.0198 -0.0032

4 step ahead 0.0310 -0.0017

Table 7: Weight given to the SPF forecast of ∆GDP and ∆CONS in theaugmented forecast . 2004:4

20

Q1−90 Q1−95 Q1−00

−0.5

0

0.5

1

1.5

Figure 3: Nowcast for GDP - EVALUATION SAMPLE 1987:2-

2004:4. The grey solid line represents the actual data; the magenta solid linewith diamonds is the series of the SPF forecasts, the blue solid line with x-markersportrays the fully model-based forecasts; the green solid line with circles corre-sponds to the the augmented forecasts

shock. In this paper, we apply the method to a very simple RBC model,where only a technology shock and a government spending shock impingeon the economy. However the proposed procedure would, when applied to amore elaborate DSGE model, allow for understanding the perception of thedifferent shock - monetary, fiscal, etc.. - that the SPF have.

We can also perform counterfactual exercises to analyze the importanceof the two shocks in determining the SPFs forecasts. The top panel of Fig-ure 5 reports real GDP growth over the full sample, the SPF nowcast andthe nowcast that the SPF would have produced if they had, respectively,no information on the current period, information only on the governmentspending shock and information only on the technology shock. The bottompanel of Figure 5 reports the same for consumption growth. The SPF now-cast of GDP growth and the one they would have produced if they only hadinformation on the technology shock are very close. This means that theextra-information the SPF collect regarding the government spending shock

21

Q1−90 Q1−95 Q1−00

−0.5

0

0.5

1

1.5

actual GDP growthperceived tech shockperceived govt spending shock

Figure 4: Current structural shocks perceived by the SPF when

nowcasting 1987:2-2004:4. The dotted line is actual GDP growth, the redline is the technology shock as perceived by the SPF, the green line is the perceivedgovernment spending shock.

22

Q1−90 Q1−95 Q1−00

−0.5

0

0.5

1

1.5

GDP growth

GDPSPFSPF no−infoSPF info on govt shockSPF info on tech shock

Q1−90 Q1−95 Q1−00

−0.5

0

0.5

1

1.5

consumption growth

CONSSPFSPF no−infoSPF info on govt shockSPF info on tech shock

Figure 5: Counterfactual exercise -nowcast- 1987:2-1994:4. The blackdotted line represents actual real GDP or consumption growth; the black solid lineis the actual SPF nowcast. The red dotted line is the nowcast the SPF would havemade if the would have had no information on any of the shocks, the red solid linethe nowcast they would have made if they had extra-information only on the govtspending shock, while the red line with the diamond marker is the nowcast theywould have made if they had extra-information only on the technology shock.

23

does not play a big role in the formation of their forecasts of GDP growth.On the other hand the consumption growth forecasts seem do per informedby both types of information.

5 Conclusions and Extensions

In this paper I propose a model-consistent and parsimonious method of com-bining judgmental and model-based forecasts. I suggest modeling the judg-mental forecasts as optimal estimates of the variables of interest, made witha different, possibly more informative, information set; I then show howthey can be accounted for in the framework of a linearized and solved DSGEmodel. The methodology I propose allows generating forecasts that are moreaccurate than the purely model-based ones, but that are still disciplined bythe economic rigor of the model.

I have also highlighted how to infer the information content of the judg-mental forecasts from the weights that the Kalman filter assigns to them. Inparticular, the weights given by the Kalman filter to the SPF go to zero astheir information content goes to zero. More precisely, the more the profes-sional forecasters are able to gather information on the shocks, the more theKalman filter will use the professional forecasts when combining them withthe predictions from the model, but it will down-weigh them if the varianceof their forecast errors is too large.

Finally I have described how to interpret the forecasts through the lensof the model, by extracting the structural shocks as they are perceived bythe professional forecasters and making several counterfactual exercises onthe forecasts the professional forecasters would have done if they saw onlysome of the shocks.

I am working on several extensions to this paper. First, in a joint pa-per with Domenico Giannone and Lucrezia Reichlin, we allow for the timelyinformation to enter the model directly, not pre-processed by the judgmen-tal forecasters. In particular, we show how to combine reduced form esti-mates of current quarter macroeconomic variables based on a large panel ofmonthly information with structural micro-founded models which focus onfew key macroeconomic variables (such as GDP, consumption, investment,inflation). The paper differentiates itself from the emergent literature onDSGE in data-rich environments (Boivin and Giannoni, 2005), in that itcaptures the importance of timely information, allowing for the use of datawith different frequencies and with non-synchronous releases.

I am also working on reformulating the problem so to be able to account

24

for the possibility that the forecasts feedback into the model. If for examplewe wanted to include a policymaker that targeted current inflation and cur-rent output gap, the estimate of inflation and output made using judgmentalinformation should feedback into the model via the policy rule. This exten-sion can be implemented using the extension of the Kalman filter proposedby Svensson and Woodford (2003) that allows to do signal-extraction withforward-looking obsverables8.

Once I have reformulated the problem, I will be able to apply the method-ology we propose to richer DSGE models, with more shocks. This can bevery interesting from a storytelling perspective, because, as I have sketchedin the simple application we consider in this paper, it will allows us to un-derstand which types of shocks the professional forecasters perceived. Moreimportantly, we will be able to understand, in the cases in which the pro-fessional forecasters forecasts where very close to the actual data, the extentto which the perception of certain shocks helped them forecasting so welland infer if the movements in the data were due to, say, a technology or amonetary shock.

8Since the forecasts feedback into the model, we cannot solve the model first, as wedid in our simple RBC case, and then forecast. For this reason we will need to deal withforwarding-looking observables.

25

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[9] Giacomini, R. and H. White (2006), ”Tests of Conditional PredictiveAbility”, Econometrica, vol. 74(6=, 1545-1578

[10] Giannone, D., Reichlin, L. and Sala, L., (2005). ”Monetary Policy inReal Time,” CEPR Discussion Papers 4981, C.E.P.R. Discussion Papers.

[11] Giannone, D., Reichlin, L. and Small, D., (2005). ”Nowcasting GDP andInflation: The Real Time Informational Content of Macroeconomic DataReleases,” CEPR Discussion Papers 5178, C.E.P.R. Discussion Papers.

[12] Ingram,B.F.,Kocherlakota,N.R.,Savin,N.E. (1994), ”Explaining busi-ness cycles:a multiple-shock approach. Journal of Monetary Economics”34,415 –428.

26

[13] Ireland, P.N., (2004), ”A method for taking models to the data,” Journalof Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1205-1226

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[17] Marchetti, D.J. and G. Parigi (1998), ”Energy Cconsumption, SurveyData and the Prediction of Industrial Production in Italy”, Temi diDiscussione del Servizio Studi della Banca d’ Italia, No 342

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27

[25] Stock, J.H., and M. W. Watson (2002), ”Macroeconomic ForecastingUsing Many Predictors”.

[26] Svensson, L.E.O (2005), ”Monetary Policy with Judgement: ForecastTargeting”, NBER Working Paper 11167

[27] Svensson, L.E.O and R.J. Tetlow (2005), ”Optimal Policy Projections”,NBER Working Paper 11392

[28] Svensson, L.E.O. and N. Williams (2005), ”Monetary Policy with ModelUncertainty: Distribution Forecast Targeting”, NBER Working Paper11733

[29] Svensson, L.E.O. and M. Woodford (2003), ”Indicator Variables for Op-timal Policy”, Journal of Monetary Economics 50, 691-720

[30] Tinsley, P. A., Spindt, P. A. and Friar, M. E., 1980. ”Indicator and filterattributes of monetary aggregates : A nit-picking case for disaggrega-tion,” Journal of Econometrics, Elsevier, vol. 14(1), 61-91

28

6 Appendix: alternative modeling of the pro-

fessional forecasters

Here I show how to construct an augmented forecast that extracts and ac-counts for the information contained in professional forecasts under the as-sumption that the professional forecasters have extra-model information oncurrent and future shocks.9 Their information set IJ

t ⊇ Mt and is such that,for h = 0, 1, 2, 3, 4

E[ut+hIJ ′t+h] 6= 0. (27)

In this case, the forecasters will report the following state-space form. Forh=0,

st|t = Ast−1|t−1 + Kut (28)

zJt = E[zt|I

Jt ] + ηt|t = CAst−1|t−1 + wt|t,

wherewt|t = E[ut|I

Jt ] + ηt|t

and [Kut

wt|t

]

∼ N(

0 , Σ0

)

where

Σ0 =

[KE(utu

′t)K

′ KE(utw′t|t)

E(wt|tu′t)K

′ Ewt|tw′t|t

]

,

ηt|t is, as before, the measurement error (the typo) made by the forecastersin t while reporting their forecast for period t. The professional nowcastcoincides with the one generated under the assumption that the forecastershave information only on the current period; the forecasts will instead bedifferent. For h = 1, 2, 3, 4 we have

st+h|t+h = Ast+h−1|t+h−1 + Kut+h

E[zt+h|IJt ] = CAst+h−1|t+h−1 + wt+h|t

where

wt+h|t = Ch∑

i=1

GiK[E(ut+h−i|I

Jt ) − ut+h−i

]+ E[ut+h|I

Jt ] + ηt+h|t (29)

9We acknowledge, but for now ignore the potential inconsistency arising from the factof assuming that professional forecasters have information on future shocks, while agentsdo not and fail to look at the professional forecasters to have more information.

29

[Kut+h

wt+h|t

]

∼ N(

0 , Σh

)

and

Σh =

[KE(ut+hu

′t+h)K

′ KE(ut+hw′t+h|t)

(wt+h|tu′t+h)K

′ Ewt+h|tw′t+h|t

]

.

As above, ηt+h|t is, as before, the measurement error (the typo) made by theforecasters in t while reporting their forecast for period t + h. We assumethat ηs|t ⊥ uτ , for any s and τ , and that ηt+h|t ⊥ E(ut+i|I

Jt ) for any i, h.

Moreover we will make the following assumptions:

uτ ⊥ E(uτ |IJt ) ∀τ 6= t

E(uτ |IJt ) ⊥ E(us|I

Jt ) ∀τ 6= s (30)

uτ ⊥ E(us|IJt ) ∀τ 6= s

which will allow us to recover Σ0 and Σh for h=1,2,3,4.Once we have recovered the exact form of the covariance matrices Σ0

and Σh we can then smooth (28) and (??) with a time-varying Kalmansmoother, in order to obtain optimal estimates s+

t+h|ISPFt

,for h=0,1,2,3,4,

that comprise the extra-information contained in the forecasts and employsit optimally within the model. Therefore, using s+

t+h|ISPFt

we can create a

forecast z+

t+h|ISPFt

,

z+

t+h|ISPFt

= Λs+

t+h|ISPFt

, (31)

that incorporates optimally in the model-based framework the judgementalinformation coming from the conjunctural forecasters.

Since the nowcasts coincides with the ones of the previous subsection, Σ0

can be recovered exactly in the same way. To recover all the elements of Σh,we proceed as follows. Given the assumptions we made in (30), it is easy toshow that

E(ut+hw′t+h|t) = E[ut+hE(ut+h|I

Jt )′].

On the basis of assumptions (30), the following equality holds

E[ut+hE(zt+h|IJt )′] = E[ut+hE(ut+h|I

Jt )′],

As the series for the ut+h are readily available via the Kalman filter, weare able to recover empirically the value of E[ut+hE(zt+h|I

Jt )′], and therefore

of E[ut+hE(ut+h|IJt )′]. Moreover, notice that, since E(ut+h|I

Jt ) is a linear

projection of ut+h on the space spanned by IJt , Sp(IJ

t ), then

ut+h = E(ut+h|IJt ) + µt

30

where µt is orthogonal to the space spanned by IJt . Therefore,

E[ut+hE(ut+h|IJt )′] = E[E(ut+h|I

Jt )E(ut+h|I

Jt )′], (32)

i.e. we have determined also the variance of the expected value of the currentshock given the information set IJ

t , E(ut+h|IJt ), and we showed it is equal to

the covariance among the shock and its expected value.In order to recover Ewt+h|t+hw

′t+h|t+h we will first define the forecasters’

forecast error as

et+h = yt+h − E(yt+h|IJt )

= ut+h − wt+h|t.

The variance of et+h, whose value can be recovered from sample data, is:

E(et+he′t+h) = E(ut+hu

′t+h) − E[ut+hw

′t+h|t] +

− E[ut+hwt+h|t]′ + E[wt+h|tw

′t+h|t]

E(ut+hu′t+h) can be obtained by the Kalman filter as follows

E(ut+hu′t+h) = CΩt+h|t+h−1C

′ + R (33)

Where Ωt+h|t+h−1 is the solution of the Riccati equation. Using the aboveequations, we can finally recover E[wt+h|tw

′t+h|t] and we therefore have pinned

down all the values of the matrix Σh.We have shown how to construct model-based forecasts that incorporate

extra-model information coming from the professional forecasts under twopossible modelizations of the professional forecasters’ information set. Sim-ilar results would hold however under all intermediate assumptions, as, forexample, the assumption that the professional forecasters have extra-modelinformation on the current and 1-step ahead shock. The only difference wouldbe in the definition of wt + h|t, which depends on the assumptions made.

31

Table 8: Relative MSFE of forecasts of GDP growth with respect to naivebenchmark. Asterisks denote forecasts that are statistically more accuratethan he naive benchmark at 1% (∗ ∗ ∗), 5%(∗∗) and 10%(∗)

relative to constant growthEVALUATION SAMPLE: 1987:2 - 2004:4

Forecast horizon RBC SPF AUGQ0 0.87 0.68 ∗∗ 0.69 ∗∗Q1 0.95 0.77 0.80Q2 0.93 0.88 0.84Q3 0.95 0.94 0.93Q4 1.05 0.95 0.98

Table 9: Weight given to the SPF forecast of ∆GDP and ∆CONS in theaugmented forecast . 2004:4

∆GDP ∆CONS

nowcast 0.4033 0.2233

1 step ahead 0.3851 0.0916

2 step ahead 0.3761 0.0517

3 step ahead 0.3839 0.0423

4 step ahead 0.3819 0.0419

32