dsge model-based forecasting...dsge model-based forecasting marco del negro federal reserve bank of...

DSGE Model-Based Forecasting

Marco Del NegroFederal Reserve Bank of New York

Frank SchorfheideUniversity of Pennsylvania, CEPR, NBER

Conference in Honor of Thomas Sargent and Christopher Sims, FRBMinneapolis; May, 2012

Disclaimer: The views expressed are mine and do not necessarily reflect those of the FederalReserve Bank of New York or the Federal Reserve System

Why bother with forecasting with DSGE models?

• DSGE models have been trashed, bashed, and abused during theGreat Recession and after. One of the many reasons for the bashingwas their alleged inability to forecast.

• In this paper we show that DSGE models forecasts’ accuracy iscomparable to, if not better than, that of Blue Chip forecasters (andGreenbook).

• What’s new? (relative to Edge & Gurkaynak, BPEA 2010)

• Sample is 1992-2011

• Incorporate external information (long term surveys, nowcast)

• .. and financial variables (spreads). In particular, documentforecasting performance of a SW+BGG DSGE model during theGreat Recession.

• Talk is based on a chapter for Handbook of Economic Forecasting

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 2 / 31

Why bother with forecasting with DSGE models?

• DSGE models have been trashed, bashed, and abused during theGreat Recession and after. One of the many reasons for the bashingwas their alleged inability to forecast.

• In this paper we show that DSGE models forecasts’ accuracy iscomparable to, if not better than, that of Blue Chip forecasters (andGreenbook).

• What’s new? (relative to Edge & Gurkaynak, BPEA 2010)

• Sample is 1992-2011

• Incorporate external information (long term surveys, nowcast)

• .. and financial variables (spreads). In particular, documentforecasting performance of a SW+BGG DSGE model during theGreat Recession.

• Talk is based on a chapter for Handbook of Economic Forecasting

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 2 / 31

Why bother with forecasting with DSGE models?

• DSGE models have been trashed, bashed, and abused during theGreat Recession and after. One of the many reasons for the bashingwas their alleged inability to forecast.

• In this paper we show that DSGE models forecasts’ accuracy iscomparable to, if not better than, that of Blue Chip forecasters (andGreenbook).

• What’s new? (relative to Edge & Gurkaynak, BPEA 2010)

• Sample is 1992-2011

• Incorporate external information (long term surveys, nowcast)

• .. and financial variables (spreads). In particular, documentforecasting performance of a SW+BGG DSGE model during theGreat Recession.

• Talk is based on a chapter for Handbook of Economic Forecasting

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 2 / 31

Poverty of the econometrician’s information set

• Quality of forecasts is constrained by quality of model, and theobservables used by the econometrician. The “usual” set ofobservables (mostly NIPA based) falls short in two dimensions:

1 Timeliness: NIPA data are available with a lag. Professionalforecasters have current information that the DSGEeconometrician is not using.

2 Breadth: The “usual” set of observables may not conveyenough information about the state of the economy.

• Augment the set of observables: Use nowcasts from professionalforecasters, spreads, surveys ... → variables that may conveyinformation about the state of the economy not contained in“usual” data set.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 3 / 31

Poverty of the econometrician’s information set

• Quality of forecasts is constrained by quality of model, and theobservables used by the econometrician. The “usual” set ofobservables (mostly NIPA based) falls short in two dimensions:

1 Timeliness: NIPA data are available with a lag. Professionalforecasters have current information that the DSGEeconometrician is not using.

2 Breadth: The “usual” set of observables may not conveyenough information about the state of the economy.

• Augment the set of observables: Use nowcasts from professionalforecasters, spreads, surveys ... → variables that may conveyinformation about the state of the economy not contained in“usual” data set.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 3 / 31

Real time data sets

• Particularly important if DSGE model forecasts are compared toprofessional forecasts (Blue Chip)/Greenbook

• ... as opposed to basing forecast evaluations on the latest availabledata vintage at the time the study was conducted.

• Level the playing field: don’t give the DSGE econometricianinformation that private forecasters do not possess at the time of theforecasts.

• Reference: Croushore and Stark (2001), Edge and Gurkaynak (2010)

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 4 / 31

Real time data sets

Quarter Greenbook End of Estimation Initial ForecastDate Sample T Period T + 1

Q1 Jan 21 2003:Q3 (F) 2003:Q4Mar 10 2003:Q4 (P) 2004:Q1

Q2 Apr 28 2003:Q4 (F) 2004:Q1June 23 2004:Q1 (P) 2004:Q2

Q3 Aug 4 2004:Q2 (A) 2004:Q3Sep 15 2004:Q2 (P) 2004:Q3

Q4 Nov 3 2004:Q3 (A) 2004:Q4Dec 8 2004:Q3 (P) 2004:Q4

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 4 / 31

Real time data sets

Quarter Greenbook End of Estimation Initial ForecastDate Sample T Period T + 1

Q1 Jan 21 2003:Q3 (F) 2003:Q4Mar 10 2003:Q4 (P) 2004:Q1

Q2 Apr 28 2003:Q4 (F) 2004:Q1June 23 2004:Q1 (P) 2004:Q2

Q3 Aug 4 2004:Q2 (A) 2004:Q3Sep 15 2004:Q2 (P) 2004:Q3

Q4 Nov 3 2004:Q3 (A) 2004:Q4Dec 8 2004:Q3 (P) 2004:Q4

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 4 / 31

Generating forecasts with a DSGE model

• Linearized DSGE = state space model

• Measurement equation:

yt = Ψ0(θ) + Ψ1(θ)t + Ψ2(θ)st

• Transition equation:

st = Φ1(θ)st−1 + Φε(θ)εt

where yt and st are the vectors of observables and states,respectively.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 5 / 31

• Use MCMC methods to generate draws from predictive distribution

p(yT+1:T+H |y1:T ) =∫(sT ,θ)

p(yT+1:T+H |sT , θ, y1:T ) p(sT |θ, y1:T )︸ ︷︷ ︸posterior of sT |θ

p(θ|y1:T )︸ ︷︷ ︸posterior of θ

d(sT , θ)

where p(θ|y1:T ) = p(y1:T |θ)p(θ)p(y1:T )

, p(sT |θ, y1:T ) obtains from the

Kalman filter, and

p(yT+1:T+H |sT , θ, y1:T ) =

∫sT+1:T+H

p(yT+1:T+H |sT+1:T+H)

p(sT+1:T+H |sT , θ, y1:T )dsT+1:T+H

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 6 / 31

Baseline DSGE Model: SW (2007)

• Measurement equation:

Output growth = LN((GDPC )/LNSINDEX ) ∗ 100Consumption growth = LN((PCEC/GDPDEF )/LNSINDEX ) ∗ 100Investment growth = LN((FPI/GDPDEF )/LNSINDEX ) ∗ 100Real Wage growth = LN(PRS85006103/GDPDEF ) ∗ 100Hours = LN((PRS85006023 ∗ CE 16OV /100)/LNSINDEX )

∗100Inflation = LN(GDPDEF/GDPDEF (−1)) ∗ 100FFR = FEDERAL FUNDS RATE/4

Sample starts in 1964:Q1

• Same prior on θ as SW.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 7 / 31

SW vs Greenbook (March 1992-Sept 2004)

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

1 2 3 4 5 6 7 80.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 80

0.15

0.3

0.45

0.6

0.75

SWGB

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 8 / 31

SW vs Blue Chip (Jan 1992-Apr 2011)

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

1 2 3 4 5 6 7 80.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 80

0.15

0.3

0.45

0.6

0.75

SWBC

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 9 / 31

Incorporating 10-yrs inflation expectations from surveys

• SW forecasts inflation relatively well but ... somewhat tight prior onπ∗:∼ Gamma(.62, .10).

• No need of such a prior: Use a loose prior (π∗ ∼ Gamma(.75, .40))and survey data as an observable:

πO,40t = π∗ + IE t

[1

40

40∑k=1

πt+k

]

= π∗ +1

40Ψ2(θ)(π,.)(I − Φ1(θ))−1

(Φ1(θ)− Φ1(θ)41

)st ,

• ... and change the model to be able to explain it:

Rt = ρRRt−1 + (1− ρR)(ψ1(πt − π∗t ) + ψ2(yt − y f

t ))

+ψ3

((yt − y f

t )− (yt−1 − y ft−1)

)+ rmt ,

where π∗t = ρπ∗π∗t−1 + σπ∗επ∗,t .

• Similar to Wright’s “democratic prior” – but survey not used to forma prior.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 10 / 31

Incorporating 10-yrs inflation expectations from surveys

• SW forecasts inflation relatively well but ... somewhat tight prior onπ∗:∼ Gamma(.62, .10).

• No need of such a prior: Use a loose prior (π∗ ∼ Gamma(.75, .40))and survey data as an observable:

πO,40t = π∗ + IE t

[1

40

40∑k=1

πt+k

]

= π∗ +1

40Ψ2(θ)(π,.)(I − Φ1(θ))−1

(Φ1(θ)− Φ1(θ)41

)st ,

• ... and change the model to be able to explain it:

Rt = ρRRt−1 + (1− ρR)(ψ1(πt − π∗t ) + ψ2(yt − y f

t ))

+ψ3

((yt − y f

t )− (yt−1 − y ft−1)

)+ rmt ,

where π∗t = ρπ∗π∗t−1 + σπ∗επ∗,t .

• Similar to Wright’s “democratic prior” – but survey not used to forma prior.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 10 / 31

Incorporating 10-yrs inflation expectations from surveys

• SW forecasts inflation relatively well but ... somewhat tight prior onπ∗:∼ Gamma(.62, .10).

• No need of such a prior: Use a loose prior (π∗ ∼ Gamma(.75, .40))and survey data as an observable:

πO,40t = π∗ + IE t

[1

40

40∑k=1

πt+k

]

= π∗ +1

40Ψ2(θ)(π,.)(I − Φ1(θ))−1

(Φ1(θ)− Φ1(θ)41

)st ,

• ... and change the model to be able to explain it:

Rt = ρRRt−1 + (1− ρR)(ψ1(πt − π∗t ) + ψ2(yt − y f

t ))

+ψ3

((yt − y f

t )− (yt−1 − y ft−1)

)+ rmt ,

where π∗t = ρπ∗π∗t−1 + σπ∗επ∗,t .

• Similar to Wright’s “democratic prior” – but survey not used to forma prior.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 10 / 31

SW vs SW-Loose vs SWπ

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

1 2 3 4 5 6 7 80.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 80

0.15

0.3

0.45

0.6

0.75

SWSW−LooseSWπ

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 11 / 31

Timeliness of information: Incorporating nowcasts

• Factor model literature (for DSGEs, Boivin and Giannoni (2007))addresses the issue by using the current indicators observed byprofessional forecasters (confidence indexes, ISM, durable goodsorders, . . . ) as data.

• As a shortcut, we use those data as digested by professionalforecasters → incorporate Blue Chip consensus nowcasts as (possiblynoisy) observations on GDP, inflation, ...

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 12 / 31

Incorporating nowcasts

Forecast End of Est. External ForecastOrigin Sample T Nowcast T + 1 h = 1 h = 2

Apr 92 91:Q4 92:Q1 based on Apr 92 BC 92:Q1 92:Q2

Jul 92 92:Q1 92:Q2 based on Jul 92 BC 92:Q2 92:Q3

Oct 92 92:Q2 92:Q3 based on Oct 92 BC 92:Q3 92:Q4

Jan 93 92:Q3 92:Q4 based on Jan 93 BC 92:Q4 93:Q1

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 13 / 31

Incorporating nowcasts

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

1 2 3 4 5 6 7 80.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 80

0.15

0.3

0.45

0.6

0.75

SWπSWπ−nowBC

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 13 / 31

Incorporating interest rate expectations

• Add interest rate expectations ReT+1+k|T+1 (from

Blue Chip Financial Survey, markets, ...) as observables:

ReT+1+k|T+1 = R∗ + IET+1 [RT+1+k ]

• ... and add anticipated policy shocks (Laseen and Svensson (2008),but also Evans et al. (2012) ) to give the model a chance to explainit:

rmt = ρrm rmt−1 + σrmεmt +

K∑k=1

σrm,kεmk,t−k

where rmt is the exogenous component in the policy rule

Rt = ρRRt−1 + (1− ρR)(ψ1(πt − π∗t ) + ψ2(yt − y f

t ))

+ψ3

((yt − y f

t )− (yt−1 − y ft−1)

)+ rmt ,

and the εmk,t−k capture announcements about future monetary policy(“measured pace”, “considerable period”,...) .

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 14 / 31

Incorporating interest rate expectations

• Add interest rate expectations ReT+1+k|T+1 (from

Blue Chip Financial Survey, markets, ...) as observables:

ReT+1+k|T+1 = R∗ + IET+1 [RT+1+k ]

• ... and add anticipated policy shocks (Laseen and Svensson (2008),but also Evans et al. (2012) ) to give the model a chance to explainit:

rmt = ρrm rmt−1 + σrmεmt +

K∑k=1

σrm,kεmk,t−k

where rmt is the exogenous component in the policy rule

Rt = ρRRt−1 + (1− ρR)(ψ1(πt − π∗t ) + ψ2(yt − y f

t ))

+ψ3

((yt − y f

t )− (yt−1 − y ft−1)

)+ rmt ,

and the εmk,t−k capture announcements about future monetary policy(“measured pace”, “considerable period”,...) .

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 14 / 31

A detour: the effects of policy anticipation

Unanticipated policy shocksInterest Rates Output Growth Inflation

0 4 8 12−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Per

cent

0 4 8 12−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Per

cent

0 4 8 12−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

0

Per

cent

Six-periods ahead anticipated policy shocksInterest Rates Output Growth Inflation

0 4 8 12−0.2

−0.15

−0.1

−0.05

0

0.05

Per

cent

0 4 8 12−0.15

−0.1

−0.05

0

0.05

0.1

Per

cent

0 4 8 12−0.1

−0.09

−0.08

−0.07

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

0

Per

cent

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 15 / 31

... forecasts conditional on an FFR path

Interest Rates Output Growth Inflation

2007 2008 2009 2010 2011 2012 2013 2014 20150

0.2

0.4

0.6

0.8

1

1.2

1.4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2007 2008 2009 2010 2011 2012 2013 2014 2015−2

−1.5

−1

−0.5

0

0.5

1

1.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2007 2008 2009 2010 2011 2012 2013 2014 2015−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 16 / 31

Forecasting using interest rate expectations

Forecast End of Est. External Interest Rate Exp Forecast

Origin Sample T Nowcast T + 1 ReT+2|T+1, . . . ,R

eT+5|T+1 h = 1 h = 2

Apr 92 91:Q4 92:Q1 based on Apr 92 BC 92:Q2 - 93:Q1 92:Q1 92:Q2

Jul 92 92:Q1 92:Q2 based on Jul 92 BC 92:Q3 - 93:Q2 92:Q2 92:Q3

Oct 92 92:Q2 92:Q3 based on Oct 92 BC 92:Q4 - 93:Q3 92:Q3 92:Q4

Jan 93 92:Q3 92:Q4 based on Jan 93 BC 93:Q1 - 93:Q4 92:Q4 93:Q1

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 17 / 31

Forecasting using interest rate expectations

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

1 2 3 4 5 6 7 80.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 80

0.15

0.3

0.45

0.6

0.75

SWπ−nowSWπ−R−now

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 17 / 31

Forecasting the Great Recession: Oct 10, 2007 (2007Q2data)

SWπ SWπ-FF SWπ+Current FFR,Spr

2003 2004 2005 2006 2007 2008 2009 2010 2011−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2003 2004 2005 2006 2007 2008 2009 2010 2011−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2003 2004 2005 2006 2007 2008 2009 2010 2011−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 18 / 31

July 10, 2008 (2008Q1 data)

SWπ SWπ-FF SWπ+Current FFR,Spr

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 19 / 31

Jan 10, 2009 (2008Q3 data)

SWπ SWπ-FF SWπ+Current FFR,Spr

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 20 / 31

Forecasting the Great Recession: Inflation

SWπ SWπ-FF SWπ+Current FFR,Spr

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−1

−0.5

0

0.5

1

1.5

−1

−0.5

0

0.5

1

1.5

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 21 / 31

Can the model explain the comovement of output andinflation in the aftermath of the Great Recession?

• Hall (AER 2011):

The dominant model of inflation embedded in practicalmacro models today . . . cannot explain the stabilization ofinflation at positive rates in the presence of long-lastingslack.

• Ball and Mazumder (BPEA 2011):

A puzzle emerges when Phillips curves estimated over1960-2007 are used to predict inflation over 2008-10:inflation should have fallen by more than it did . . . theGreat Recession provides fresh evidence against the NewKeynesian Phillips curve with rational expectations.

• Del Negro, Giannoni, Schorfheide (yet to be written): maybe not

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 22 / 31

Output, inflation, and interest rates in the aftermath ofthe Great Recession

Output Inflation FFR

2004 2005 2006 2007 2008 2009 2010 2011 2012−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

2004 2005 2006 2007 2008 2009 2010 2011 2012−1

−0.5

0

0.5

1

1.5

−1

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−1

−0.5

0

0.5

1

1.5

2

−1

−0.5

0

0.5

1

1.5

2

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 23 / 31

Relative forecasting accuracy over time: SW vs SW+BGG

Difference in 4-quarter-ahead Rolling RMSEsOutput Inflation

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 24 / 31

Conclusions

Congressman Brad Miller, Committee on Science and Technology,Subcommittee on Investigations and Oversight, U.S. House ofRepresentatives:

Greenspan’s fallen model of the market shares manyassumptions with the model that’s favored today, from academeto the world’s central banks. The macroeconomic model iscalled the Dynamic Stochastic General Equilibrium modelmercifully called DSGE for short. According to the model’smost devoted acolytes, the model’s insights rival the perfectknowledge Paul described in the First Letter to the Corinthians;but unlike the knowledge Paul described, DSGE’s insights areavailable in the here and now.

• That’s right

• Seriously, there is a long way to go... but when given enoughinformation, these model’s forecasting performance may not be sobad, especially relative to the competition.

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 25 / 31

RSMEs: SW vs Blue ChipAverages

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

1 2 3 4 5 6 7 80.18

0.19

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.27

1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

SWBC

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 26 / 31

Incorporating Long-Run Output Growth Expectations(SWπY)

• Add one more observable:

GrowthO,40t = γ + IE t

[1

40

40∑k=1

(yt+k − yt+k−1 + zt+k)

],

• ... and change the model to be able to explain it: growth rate of thestochastic trend Zt in deviations from γ, follows the process:

zt = log(Zt/Zt−1)− γ =1

1− α(ρz − 1)zt−1 +

1

1− ασzεz,t + zp

t

wherezpt = ρzpzp

t−1 + σzpεzp,t .

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 27 / 31

SWπ vs SWπY

Output Growth Inflation Interest Rates

1 2 3 4 5 6 7 80.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 80.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 80

0.15

0.3

0.45

0.6

0.75

SWπSWπY

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 28 / 31

Forecasting the Great Recession: Inflation

October 10, 2007 July 10, 2008 January 10, 2009

SWπ Model

2003 2004 2005 2006 2007 2008 2009 2010 2011−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

SWπ-FF Model

2003 2004 2005 2006 2007 2008 2009 2010 2011−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

SWπ-FF Model + Current Informaton on FFR and Spreads

2003 2004 2005 2006 2007 2008 2009 2010 2011−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−0.5

0

0.5

1

1.5

−0.5

0

0.5

1

1.5

2004 2005 2006 2007 2008 2009 2010 2011 2012−1

−0.5

0

0.5

1

1.5

−1

−0.5

0

0.5

1

1.5

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 29 / 31

Evaluation

• Question: are predictive densities are well calibrated?

• Roughly: in a sequential forecasting setting events that are predictedto have 20% probability, should roughly occur 20% of the time.

• Probability Integral Transforms:• If Y is cdf F (y), then

P{F (Y ) ≤ z} = P{Y ≤ F−1(z)} = F(F−1(z)

)= z

• PITs

zi,t,h =

∫ yi,t+h

−∞p(yi,t+h|Y1:T )dyi,t+h.

References for PITs: Rosenblatt (1952), Dawid (1984), Kling and Bessler (1989),

Diebold, Gunther, and Tay (1998), Diebold, Hahn, and Tay (1999), . . ., Geweke and

Amisano (2010), Herbst and Schorfheide (2011).Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 30 / 31

PITs

2 Quarters-AheadOutput Growth Inflation Interest Rates

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

4 Quarters-AheadOutput Growth Inflation Interest Rates

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

8 Quarters-AheadOutput Growth Inflation Interest Rates

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

50

Del Negro, Schorfheide DSGE Model-Based Forecasting Sargent/Sims Conference 31 / 31