DSGE Modelling at Central Banks: Country Practices and How it is Used in Policy Making Haris...
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DSGE Modelling at Central Banks: Country Practices and How it is Used in Policy Making
Haris MunandarBank Indonesia
SEACEN-CCBS/BOE-BSP Workshop on DSGE Modelling and Econometric TechniquesManila, 27 November 2009
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2BISMA: Bank Indonesia Structural MAcro model
• Implementation of a full-fledged Inflation Targeting Framework (ITF) on July 2005 necessitates support by a model with the following features: capturing supply and demand side very well more resistant to Lucas critique incorporating rational expectation explicitly through
optimization behaviour of economic agents incorporating forward-looking endogenous interest
rate reaction ability to be utilized in policy simulation and
forecasting
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Role of economic models in Bank Indonesia
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Outline
• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results
4
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Micro-founded Macroeconomic model (DSGE).• New Keynesian – Neoclassical Synthesis:
Long run neoclassical steady state (neutrality of money) Short-run Keynesian dynamics Rational expectation
• Nominal rigidities : price and wage staggered contract ala Rotemberg
• Real rigidities : habit formation in consumption, and adjustment cost in capital
• Interest rate reaction function (Taylor Rule) secara endogen dan forward looking sejalan dengan penerapan ITF
• Two core economic agents (households and firms) and 3 auxiliary economic agents (central bank, government and foreign/rest of the world),
Specification
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6Model structure
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Outline
• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results
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8Household
Own assets (domestic and foreign bond); purchase finished goods and investment goods; receive wages as return for labor supplied to firms; receive rental capital from firms; and receive profits from firm
Objective Function:
Budget Constraints:
, , t t s h ss t
Max E U
1
,
, , 1
11 log
11
h tC Ch t h t tC
LU C C
* * * *, , , , 1 , 1 1 1 , 1
2
,, , 1 , ,
, 1
1 (1 ) (1 )(1 )
1(1 ) (1 ) 1
2
C IC t h t t h t h t t h t t h t t t t h t
h tK S I Iw t h t t h t h t h t t
h t
P C P I B e B i B i e B
IW L P K I P
I
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9Household
• Investment increase the capital stock over time according to Capital Accumulation eq :
• Wage Setting The labor aggregator solve:
where is the flexible-price optimal nominal wage and are in logs
, , 1 ,1S Sh t h t h tK K I
,h tWf
, ,, ,h t h t tW Wf W
,
2 2
, , , 1 h t
s t Wt h s h s h s s
Ws t
Min E W Wf W W
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10Household: log-linear solution
• Consumption
• Flexible Wage
• Investment
where
• Shadow Price of Capital
1 1 1 1 1
11ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ1 1 1
CCC C C
t t t t t t t t tC C Cc c A A c A A i
1 1 1 1ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ1I I R I
t t t t t t t t tIv v A A v A A p
1 1
ˆ ˆt t t twf wf L i
1 1 1 1ˆ ˆˆ ˆ ˆ1R R I K
t t t t t tA i p i
1
2
i
i
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11Household: log-linear solution
• Capital Supply
• Uncovered Interest Parity
• Wage Inflation
where
* * *1 11 1 1
ˆ ˆX O
t tt t t t t t ts s i i A A
1, , 1 ,(1 )( ) ( )
IS S
th t h t h tk k v A
1 1
1 11log
1 1 1t
W W
W W W tt t W
t
wf
w
1 1W W
WW
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12
• Assumption :Monopolistically competitive firms with Cobb-Douglas
• Production Function :
• Profits
• Price SettingThe price aggregator solve:
where is the flexible-price and are in logarithmic
• Flexible price
Domestic Intermediate Firm
,i tPf, ,, ,i t i t tP Pf P
,
2 2
, , , 1 i t
s t Pt i s i s i s s
Ps t
Min E P Pf P P
Dt tPf
1
, , ,
L LD L Di t t i t i tY A L K
2
,, , , , ,
, 1
11
2
i tD D K D Li t t i t t i t t i t t i t
i t
LPY W L P K W L
L
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13Domestic intermediate firm: log-linear solution
• Output
• Labor demand
• Capital demand
• PPI inflation
where
ˆˆˆ (1 )D Dt L t L ty L k
ˆ ˆ ˆD D Kt t t tk y p pf
1 1
1 11log
1 1 1t t t tpf
1 1
1ˆ ˆ ˆ ˆˆLL
Dt t t t t tL L L
L L L y w pf
1 1
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• Consumption goods producer
• Profit
• Price settingThe price aggregator solve:
where is the flexible-price and are in log
• Flexible - consumption goods producer’s price:
Consumption goods producer
, , , ,C C C M Ci t t i t t i t t i tP C PY P M
,
2 2
, , , 1 Ci t
s t C C C C Ct i s i s i s s
P s t
Min E P Pf P P
,Ci tPf , ,, ,C C C
i t i t tP Pf P
C C Ct tPf
1
,, ,
C
C
Ci tC C
i t t i t X Ot t
MC A Y
A A
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15Cons. goods producer: log-linear solution
• Consumption goods
• Domestic consumption intermediate demand
• Imported consumption intermediate demand
• CPI inflation
where
ˆ ˆ ˆ(1 )C Ct C t C tc y m
ˆ ˆC
Ct tty pf c
ˆ ˆ ˆC
C Mt t t tm c p pf
1 1
1 11log
1 1 1t
C C CC C C t
t t C Ct
pf
p
1 1C C
CC
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16
• AssumptionProducing investment goods from imported materials
• Investment Goods Producer
• Profit
Investment goods producer
,,
Ii tI
i t t X Ot t
MI A
A A
, , ,I I M Ii t t i t t i tP I P M
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17Invest. goods producer: log-linear solution
• Investment goods
• Investment goods price
ˆ ˆ It tv m
ˆ ˆM It tp p
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18
• AssumptionProducing government goods from domestic materials
• Government goods producer
• Profit
Government goods producer
, ,G G
i t t i tG A Y
, , ,G G Gi t t i t t i tP G PY
Government goods producer: log-linear solution• Government goods
ˆ ˆ gt tg y
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• Export goods producer
• Profit
• Price SettingThe price aggregator solve:
where is the flexible-price and are in log
• Flexible - export goods producer’s price:
Export goods producer
,
2 2
, , , 1 Xi t
s t X X X X Xt i s i s i s s
P s t
Min E P Pf P P
,X
i tPf , ,, ,X X Xi t i t tP Pf P
X X Xt tPf
1
, , ,
X XX O X Xi t t t i t i tX A A Y M
, , , ,X X X M Xi t t i t t i t t i tP X PY P M
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20Export goods producer: log-linear solution
• Export goods
• Domestic export intermediate demand
• Imported export intermediate demand
• Export price inflation
where
ˆ ˆ ˆ(1 )X Xt X t X tx y m
ˆ ˆX
Xt t ty x pf
ˆ ˆ ˆX
X Mt t t tm x p pf
1 1
1 11log
1 1 1t
X X XX X X t
t t X Xt
pf
p
1 1X X
XX
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21Importers
Importers• Provide imported materials as intermediate inputs to final good
production• Only act like merchants – no production function• The price aggregator solve:
where is the flexible-importer’s price and are in log
• Flexible - import’s price:
,Mi tPf , ,, ,M M M
i t i t tP Pf P
,
2 2
, , , 1 Mi t
s t M M M M Mt i s i s i s s
P s t
Min E P Pf P P
M M Mt tPf
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22Importer: log-linear solution
• Imported Inflation
where
1 1
1 11log
1 1 1t
M M MM M M t
t t M Mt
s
p
1 1M M
MM
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23Central bank
Central bank• Central bank objective function is to set the nominal short term
interest rate it in response to deviations of inflation from the target as well as output gap
1 41 T D Dt CB t CB CB t CB ti i i y y
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24Government
• Government fiscal authority For simplification: government chooses the current government
expenditure by smoothing previous government expenditure
However, it has to consider the source of financing from taxes, and bond issuance
1log log 1 log Gt G t GG G G e
1 11t t t
G G G G Ct t t c t t w t t tB B P G i B P C W L
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25Balance of payment
• Balance of Payment
• Balance of payment equation is the result of interactions among all agents, which has connection with foreign sectors
* * * * *, 1 1 , 1(1 )(1 ) X F
t H t t t t H t t t t t te B i e B P X e P M
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Outline
• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results
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27
• Export:
• Import:
• Dom. Intermediate Goods :
• Nominal GDP :
Market clearing conditions and identities
* *1*
1
1 log logX
Xt t t ttO O O
t t t t t
X X X PY
A A A e P
C I Xt t t tM M M M
D C G Xt t t tY Y Y Y
C I G X Mt t t t t t t t t t tGDPN P C P I P G P X P M
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28Market clearing conditions and identities
• Risk Premium :
• Foreign Economy :
• Technology Growth *
* *
* * *1 1 i
t ti ii i i e
** t tt
t
e Bb
GDPN
*
* *
* * *1log log 1 log y
t ty yy y y e
*
* *
* * *1 1t t e
1log log 1 log At A t AA A A e
(*)
(*) (*)
(*) (*) (*)1
where (*) : C, I, G, X, O
log log 1 log At tA A
A A A e
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Outline
• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results
29
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30Data and methodologi
• Data Kuartalan : 2000 Q1 – 2009 Q2
• Solving Rational Expectation Generalized Schur Decomposition (Klein, 2000)
• Estimation Bayesian
• Robustness Check Impulse Response Function (IRF)
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Outline
• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results
31
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Parameter estimation 32
1 theta_xThe probability that a given Exp. Prod is selected to not re-optimize its price 0.5 BETA_PDF 0.1 0.4951
2 theta_mThe probability that a given Importer is selected to not re-optimize its price 0.5 BETA_PDF 0.1 0.516
3 theta_wThe probability that a given labor is selected to not re-optimize its wage 0.75 BETA_PDF 0.1 0.6462
4 alphacb Coeffi cient of inflation gap 1.5 NORMAL_PDF 0.1 1.3507
5 betacb Coeffi cient of output gap 0.3 BETA_PDF 0.1 0.268
6 rhocb Coeffi cient of interest rate smoothing 0.6 BETA_PDF 0.05 0.8644
7 rhopstar Coeffi cient AR(1) of foreign inflation 0.8 BETA_PDF 0.1 0.4603
8 rhoystar Coeffi cient AR(1) of foreign output 0.8 BETA_PDF 0.1 0.8462
9 rhoistar Coeffi cient AR(1) of foreign interest rate 0.8 BETA_PDF 0.1 0.8846
Standar Deviation
Mean Posterior
DescriptionNo Parameter Mean Prior
Distibution
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Parameter calibration 33
1 thetaThe probability that a given Domestic Prod is selected to not re-optimize its price 0.62
2 theta_cThe probability that a given Cons. prod is selected to not re-optimize its price 0.5
3 rhog Coefficient of Govt expenditure smoothing 0.9
4 chi_l Coeffient of Labour adjustment cost 5
5 rhoa Coefficient AR(1) of Domestic Technology 0.4
6 rhoacCoefficient AR(1) of Consumption-specific Technology 0.85
7 rhoaiCoefficient AR(1) of Investment-specific Technology 0.3
8 rhoag Coefficient AR(1) of Govt-specific Technology 0.3
9 rhoax Coefficient AR(1) of Export-specific Technology 0.85
10 rhoao Coefficient AR(1) of Trade opennes Technology 0.4
No Parameter Description Value
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0 10 20 30 40-2
0
2
4Inflation
Inflation
CPI inflation
0 10 20 30 40-0.5
0
0.5
1Other inflation
Imported inflation
Export inflation
Wage Inflation
0 10 20 30 40-0.2
0
0.2
0.4
0.6Policy rate
Policy Rate
0 10 20 30 40-2
-1
0
1Exchange rate
Real exchange rate
Nom. Dep rate
0 10 20 30 40-0.1
0
0.1
0.2
0.3Import
Import
0 10 20 30 40-0.5
0
0.5
1Consumption Production
Non-Imp Cons.
Imp Cons
Total Cons
0 10 20 30 40-0.5
0
0.5Export Production
Non-Imp Export
Imp Export
Total Export
0 10 20 30 40-0.4
-0.2
0
0.2
0.4Dom. Int Production
Capital
Labor
0 10 20 30 40-0.3
-0.2
-0.1
0
0.1Output
Output
IRF – unfavorable inflation shock 34
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0 10 20 30 40-1
0
1
2Nominal exchange rate depreciation
Real exchange rate
Nom. Dep rate
0 10 20 30 40-0.2
0
0.2Export Production
Non-Imp Export
Imp ExportTotal Export
0 10 20 30 40-0.2
0
0.2Import
Import
0 10 20 30 40-0.5
0
0.5
1Other inflation
Imported inflation
Export inflation
Wage Inflation
0 10 20 30 40-0.5
0
0.5Inflation
Inflation
CPI inflation
0 10 20 30 400
0.02
0.04
0.06Policy rate
Policy Rate
0 10 20 30 40-0.4
-0.2
0Consumption Production
Non-Imp Cons.
Imp Cons
Total Cons
0 10 20 30 40-0.5
0
0.5Investment Production
Investment
0 10 20 30 40-0.1
0
0.1Dom. Int Production
Capital
Labor
0 10 20 30 40-0.05
0
0.05Output
Output
IRF – exchange rate depreciation shock 35
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0 10 20 30 400
0.5
1Foreign
Foreign Output
0 10 20 30 400
0.5
1
1.5Export Good Production
Non-Imp Export
Imp Export
Total Export
0 10 20 30 40-1
-0.5
0
0.5Nominal exchange rate depreciation
Real exchange rate
Nom. Dep rate
0 10 20 30 40-0.5
0
0.5
1Import
Import
0 10 20 30 40-0.5
0
0.5Dom. Int Production
Kapital
Labor
0 10 20 30 40-0.1
0
0.1Output
Output
0 10 20 30 40-0.5
0
0.5
1Investment Production
Investment
0 10 20 30 40-0.5
0
0.5Other inflation
Imported inflation
Export inflation
Wage Inflation
0 10 20 30 40-1
0
1
2Inflation
Inflation
CPI inflation
0 10 20 30 40-0.5
0
0.5Policy rate
Policy Rate
0 10 20 30 40-0.5
0
0.5Consumption Production
Non-Imp Cons.
Imp ConsTotal Cons
IRF – favorable foreign demand shock 36
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0 10 20 30 400
0.5
1
1.5
2Policy rate
Policy Rate
0 10 20 30 40-10
-5
0
5Inflation
Inflation
CPI inflation
0 10 20 30 40-6
-4
-2
0
2Other inflation
Imported inflation
Export inflation
Wage Inflation
0 10 20 30 40-6
-4
-2
0
2Consumption Production
Non-Imp Cons.
Imp Cons
Total Cons
0 10 20 30 40-1
-0.5
0
0.5
1Investment Production
Investment
0 10 20 30 40-4
-2
0
2Exchange rate
Real exchange rate
Nom. Dep rate
0 10 20 30 40-1
-0.5
0
0.5Export Production
Non-Imp Export
Imp ExportTotal Export
0 10 20 30 40-3
-2
-1
0
1Dom. Int Production
Capital
Labor
0 10 20 30 40-2
-1.5
-1
-0.5
0Output
Output
IRF – tight policy 37
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Outline
• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results
38
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Simulation result: loose policy vs. baseline
39
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Simulation result: loose policy vs. baseline
40
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Simulation result: tight policy vs. baseline
41
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Simulation result: tight policy vs. baseline
42
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43
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