Forecasting with DSGE Models in the presence of data ...Forecasting with DSGE Models Medium-scale...

Forecasting with DSGE Modelsin the presence of data revisions.

Ana Beatriz Galvão

Warwick Business School

October 2013

Galvão Release-Based DSGE Forecasting

Forecasting with DSGE Models

• Medium-scale DSGE models provide accurate forecasts ofoutput growth and inflation even if estimated using realtime data, in particularly before 2008 (Edge andGurkaynak, 2011; Woulters, 2012; Del Negro andSchorfheide, 2012).

• Time series employed in the estimation of DSGE models,such as output, consumption, investment and inflation, arenational account data and subject to initial revisions,annual revisions, and benchmark revisions.

• If forecasting in real time, the forecasting target may be

• the "first-final" (three months after end of observationalquarter) (Edge and Gurkaynak, 2011), or

• the "most-recent vintage" (all types of revisions for earlierobservations) (Del Negro and Schorfheide, 2012).





• If forecasting in real time, the forecasting target may be• the "first-final" (three months after end of observational

quarter) (Edge and Gurkaynak, 2011), or

• the "most-recent vintage" (all types of revisions for earlierobservations) (Del Negro and Schorfheide, 2012).





• If forecasting in real time, the forecasting target may be• the "first-final" (three months after end of observational

quarter) (Edge and Gurkaynak, 2011), or• the "most-recent vintage" (all types of revisions for earlier

observations) (Del Negro and Schorfheide, 2012).


Real Time Data and Forecasting

• Conventional approach: estimate the forecasting modelwith the data vintage available at each point in time, thencompute forecasts condition on early estimates.

• Problems:

• mixture of apples (heavily revised data) with oranges(lightly revised data) may deliver forecasts that do notminimise the MSFE (Kishor and Koenig, 2011; Clementsand Galvão, 2012).

• data revisions may be predictable and useful to improveforecasts of revised data.


Real Time Data and Forecasting

• Conventional approach: estimate the forecasting modelwith the data vintage available at each point in time, thencompute forecasts condition on early estimates.

• Problems:• mixture of apples (heavily revised data) with oranges

(lightly revised data) may deliver forecasts that do notminimise the MSFE (Kishor and Koenig, 2011; Clementsand Galvão, 2012).

• data revisions may be predictable and useful to improveforecasts of revised data.


Anticipating Initial US GDP Revisions

• Clements and Galvao (2012).

• Ex: Q3 observation. 1st: October; 2nd: November; 3rd:December.

• Professional forecasters (Bloomberg survey) are able toanticipate the first but not the second revision to US GDP.

• Both first and second revisions are predictable in real timeusing “market moving” economic monthly indicators anddaily financial variables, but they are not predictable basedon past vintages of output growth alone.



• Clements and Galvao (2012).• Ex: Q3 observation. 1st: October; 2nd: November; 3rd:

December.

• Professional forecasters (Bloomberg survey) are able toanticipate the first but not the second revision to US GDP.





December.• Professional forecasters (Bloomberg survey) are able to

anticipate the first but not the second revision to US GDP.





December.• Professional forecasters (Bloomberg survey) are able to

anticipate the first but not the second revision to US GDP.• Both first and second revisions are predictable in real time

using “market moving” economic monthly indicators anddaily financial variables, but they are not predictable basedon past vintages of output growth alone.


The Release-Based approach for real-time forecasting

• Updated measurement equations to include both"first-release" and "first-final" values; modelling the initialrevisions process.

• No change in the structure of the DSGE model.• Agents (and the econometrician) filter the current

first-release values based on past first releases and firstfinals considering that:

1 Initial revisions may be predictable while increasing thevariance of the first release.

2 If the statistical agency filters the data before releasing it(Sargent, 1989), data revisions are caused by newinformation and may be correlated with unexpectedstructural shocks.

• The Release-Based approach provides a measure of theeffect of structural shocks (technology, cost-push) onoutput growth and inflation initial data revisions.


The Release-Based approach

• The approach differs from:

• Neri and Ropele (2011): impact of the use of real-time dataon assessing policy decisions with a DSGE model.

• Casares and Vazquez (2012): agent decisions in real-timemay have an impact on future data revisions (changes inthe structural model).

• Blanchard, L’Huillier and Lorenzoni (2012): noisyproductivity shocks as a cause of business cycles becauseconsumers are not able to distinguish between permanentand temporary productivity shocks.



• The approach differs from:• Neri and Ropele (2011): impact of the use of real-time data

on assessing policy decisions with a DSGE model.

• Casares and Vazquez (2012): agent decisions in real-timemay have an impact on future data revisions (changes inthe structural model).




• The approach differs from:• Neri and Ropele (2011): impact of the use of real-time data

on assessing policy decisions with a DSGE model.• Casares and Vazquez (2012): agent decisions in real-time

may have an impact on future data revisions (changes inthe structural model).



Forecasting with DSGE models: the ConventionalApproach I

• The DSGE model state-space representation:

xt = F(θ)xt−1 +G(θ)vt, vt ∼ N(0, Q)Xt = d(θ) +H(θ)xt.

• If estimating the model with the data vintage available atT+ 1:

XT+1t = d(θ) +H(θ)xt, t = 1, ..., T.

• Heavily revised data: t = 1, ..., T− 14; subject to annualrevisions: t = T− 13, ..., T− 1; subject to initial and annualrevisions: t = T.


Forecasting with DSGE models: the ConventionalApproach II

• The apples-oranges-mixing problems implies that theconventional approach does not deliver forecasts of (V)ARthat minimise the MSFE (Koenig et al, 2003; Kishor andKoenig, 2011; Clements and Galvão, 2012, JAE;)


Forecasting with DSGE models: the Release-BasedApproach I

• The "first-final" value Xt+2t is an efficient estimate of true

value Xt (Garratt et al, 2008; Kishor and Koenig, 2011).

• First releases{

Xt+1t}t=T

t=2 ; first finals{

Xt+1t−1

}t=Tt=2 .

• The updated measurement equations are:

[Xt+1

tXt+1

t−1

]=

[d(θ) +M

d(θ)

]+

[H(θ) 0m Im

0m H(θ) 0m

] xtxt−1revt

where

revt = (Xt+1t −Xt)−M.

• Structural parameters θ are estimated with true values ofthe observables: Xt.


Forecasting with DSGE models: the Release-BasedApproach II

• The updated state equations are:

xtxt−1revt

= F(θ) 0m 0m

Im 0m 0m0m 0m K

xt−1xt−2

revt−1

+ G(θ) 0m

0m 0m0m Im

[ vtηt

]

where ηt ∼ N(0, Z) (Z diagonal).

• Sources for data revisions innovations ηt = εt −Avt :

1 The first-release Xt+1t differs from the true value due to

measurement error εt, and revisions (Xt+1t −Xt) may be

serially correlated. Howrey (1978) model. Noise revisions.


Forecasting with DSGE models: the Release-BasedApproach III

2 The statistical agency filters the data before their initialrelease (efficient forecast), so data revisions are caused bynew information. Sargent (1989) model. News revisions.Unexpected change in the true value = structural shock,−Avt.

• ut =[

vt ηt]′, then

var(ut) = QN =

[Q N′

N Z

].

• A positive structural shock vt > 0 may be correlated with anegative unexpected revision since first release wouldunder-estimate true values.

• But when computing variance decompositions, a Choleskydecomposition of QN is used: data revisions innovationsdo not affect xt!


Forecasting with DSGE models: the Release-BasedApproach IV

• Forecasts are computed with:

XT+h|T = d(θ) +H(θ)xT+h|T


Release-Based approach in the Smets and Wouters(2007) I

• Modelling data revision processes of output growth andinflation.

∆ log(GDPt+1t )

∆ log(ConsT+1t )

∆ log(InvT+1t )

∆ log(WageT+1t )

∆ log(HoursT+1t )

∆ log(Pt+1t )

FFRt∆ log(GDPt+1

t−1)∆ log(Pt+1

t−1)

=

γγγγ

lπrγπ

+

yt − yt−1ct − ct−1it − it−1

wt −wt−1ltπtrt

yt−1 − yt−2πt−1

+

My + revyt0000

Mp + revπt000


Release-Based approach in the Smets and Wouters(2007) II

• Additions to the state vector:

revyt = Kyrevyt−1 + ηyt

revπt = Kπrevπt−1 + ηπt,

where var(ηyt) = Z2y and var(ηπt) = Z2

π;cov(ηyt, ηa

t ) = σaZyPya and cov(ηπt, ηpt ) = σpZπPπp,

∣∣Pya∣∣

and∣∣Pπp

∣∣ are ≤ 1, and σa and σp are standard errors ofproductivity and price-markup innovations.


Estimates

• T+ 1 =2008Q4; observations from 1984Q1-2008Q3.• Posterior means/quantiles of structural parameters with

the release-based approach are very similar to theconventional approach.

• Differences in the parameters of the price-markup shock.


Variance Decomposition

• Data revisions explain 2% of the unexpected variation offirst-release GDP, and 4.5% of the variation of first releaseinflation (GDP deflator) [the remaining variation isexplained by structural shocks].

• Productivity shocks explain 62% of the unexpected changes inGDP data revisions [the remaining variation is explained byvariable-specific data revision innovations]. Data revisionsto output are mainly due to new information, in agreementwith Clements and Galvão (2012).

• Price markup shocks explain 12% of variation in inflation datarevisions. Data revisions to inflation are mainly ameasurement error.


Estimates

• T+ 1 =2008Q4; observations from 1984Q1-2008Q3.• Posterior means/quantiles of structural parameters with

the release-based approach are very similar to theconventional approach.

variance decomposition impact of the shockout rev inf rev out rev inf rev

g 0.04 0.10 0.0219 0.0118b 0.01 0.01 0.0335 0.0158i 0.01 0.11 0.01 0.0136a 0.56 0.06 0.0816 0.0096p 0.03 0.02 0.0511 0.0131w 0.01 0.38 0.0122 0.025r 0.02 0.01 0.0601 0.0168own 0.32 0.30 0.1615 0.0927


Variance Decomposition

Computed at the posterior mean.


Forecasting

• Out-of-sample vintages: 1999Q1-2008Q4.• h = 1, ..., 8.• Forecasting errors computed with "first final" and the

"most-recent vintage" (2012Q2).• RMSFEs computed with rolling windows of 20 forecasts

over the out-of-sample period.


Forecasting Output: Release-Based vs Conventional


Forecasting Inflation: Release-Based vs Conventional


Forecasting Fed rates: Release-Based vs Conventional


Forecasting: Released-Based vs AR(2)


+ Data Revisions to Consumption and Investment

• Measurement equation augmented to include first-finals ofconsumption and investment + first releases. Parametersof the data revision processes of consumption and inflationestimated as before.

• Innovations to consumption data revisions may becorrelated with risk-premium shocks; innovations toinvestment data revisions may be correlated withinvestment-specific shocks.

• The release-based posteriors of the parameters of theinvestment-specific shock process suggest a less persistentand more variable shock if compared with theconventional approach.

• Innovations to investment-specific shocks explain 9% ofthe variation of investment data revisions.


Variation of first releases explained by revisioninnovations


Improvement of Fed Fund Rates Forecasts


Conclusions

• I provide a solution for the apples-oranges-mixingproblem if forecasting with DSGE models in real time.

• Agents/Econometrician filter initial releases based on pastinitial releases and revised data.

• Forecasting improvements from the release-basedapproach are more frequent at short horizons whenfiltering first-release data to remove measurement and/orfiltering errors pays off. RMSFE differences are sizeable:15-20%.

• Data revisions may be correlated with structural shocks (asin Sargent, 1989; news revisions). 62% of the unexpectedvariation of US GDP initial revisions are explained byproductivity shocks.


Smets and Wouters (2007) Model I

Equations for the endogenous variables:

1 Aggregate resource constraint: yt = cyct + iyit + zyzt + εgt

2 From consumption Euler equation: ct =c1ct−1+ (1− c1)Etct+1+ c2(lt−Etlt+1)− c3(rt−Etπt+1+ εb

t )

3 From investment Eulerequation: it = i1it−1 + (1− i1)Etit+1 + i2qt + εi

t

4 Arbitrage equation for the value of capital:qt = q1Etqt+1 + (1− q1)Etrk

t+1 − (rt − Etπt+1 + εbt )

5 Production function yt = φb(αkst + (1− α)lt + εa

t )

6 Capital used: kst = kt−1 + zt

7 Capital utilization costs: zt = z1rkt

8 Dynamics of capital accumulation:kt = k1kt−1 + (1− k1)it + k2εi

t

9 Firms’ markup: µpt = α(ks

t − lt) + εat −wt


Smets and Wouters (2007) Model II10 Phillips Curve: πt = π1πt−1 + π2Etπt+1 − π3µ

pt + ε

pt

11 Solution for rental-rate of capital: rkt = −(kt − lt) +wt

12 Workers’ markup: µwt = wt −

[σllt + 1

1−λ/γ (ct − λ/γct−1)]

13 Wage dynamics: wt = w1wt−1 + (1−w1)(Etwt+1 +Etπt+1)−w2πt +w3πt−1 −w4µw

t + εwt

14 Monetary Policy rule: rt = ρrt−1 + (1− ρ){rππt + rY(yt −yp

t )}+ r∆y[(yt − ypt )− (yt−1 − yp

t−1)] + εrt

Equations for the shocks:

1 exogenous spending: εgt = ρgε

gt−1 + η

gt + ρgaηa

t

2 risk premium: εbt = ρbεb

t−1 + ηbt

3 investment: εit = ρiε

it−1 + ηi

t

4 productivity: εat = ρaεa

t−1 + ηat

5 price markup: εpt = ρpε

pt−1 + η

pt − µpη

pt−1


Smets and Wouters (2007) Model III

6 wage markup: εwt = ρwεw

t−1 + ηwt − µwηw

t−1

7 monetary policy: εrt = ρrε

rt−1 + ηr

t


Forecasting with DSGE Models in the presence of data ...Forecasting with DSGE Models Medium-scale...

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