dsge modelling at central banks: country practices and how it is used in policy making haris...

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

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

Role of economic models in Bank Indonesia

3

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

5

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

6Model structure

Outline

• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results

7

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

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

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

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

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

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

14

• 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

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

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

17Invest. goods producer: log-linear solution

• Investment goods

• Investment goods price

ˆ ˆ It tv m

ˆ ˆM It tp p

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

19

• 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

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

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

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

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

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

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

Outline

• Specification and model structure• Behaviour of agents• Market clearing conditions and identities• Data and methodology• Estimation, calibration and IRF• Forecasting and simulation results

26

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

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

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

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)

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

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

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

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

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

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

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

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

Simulation result: loose policy vs. baseline

39

Simulation result: loose policy vs. baseline

40

Simulation result: tight policy vs. baseline

41

Simulation result: tight policy vs. baseline

42

43

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