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Intro ducti on

The m odel

Resul ts

Conc lusion

Money and risk in a DSGE framework: A

Bayesian application to the Eurozone

IFABS, 4th International Conference,

Valencia, Spain, June 18-20, 2012.

Jonathan Benchimol1and André Fourçans2

June 2012

1ESSEC Business School and Université Paris 1 Panthéon Sorbonne

2ESSEC Business School

Jonat han Be nchim ol ESSE C Busin ess Sch ool an d Unive rsité Paris 1

Intro ducti on

The m odel

Resul ts

Conc lusion

Mone y or no mon ey ?

New Ke ynesia n mod els

Litera ture rev iew

The question of money

IIn the current New Keynesian literature, the role of monetary

aggregates is generally neglected.

IThe main economic variables of this kind of models are: the

output gap, in‡ation and the interest rate.

IYet it’s hard to imagine money completely “passive” to the

rest of the system !

3 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Mone y or no mon ey ?

New Ke ynesia n mod els

Litera ture rev iew

Brunner and Meltzer

IAs individuals re-allocate their portfolio of assets, the behavior

of real money balances induces relative price adjustments on

…nancial and real assets.

IIn the process, aggregate demand changes, and thus output.

IBy a¤ecting aggregate demand, real money balances become

part of the transmission mechanism.

IThe interest rate alone is thus not su¢ cient to explain the

impact of monetary policy and the role played by credit and

…nancial markets.

IThis monetarist transmission process may also imply a speci…c

role to real money balances when dealing with risk aversion.

4 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Mone y or no mon ey ?

New Ke ynesia n mod els

Litera ture rev iew

Money and new Keynesian models

IMost of studies about New Keynesian models ignore money

because of separable utilities, such as following:

Et

∞

∑

i=0

βi"C1σ

t+i

1σ+γ

1bMt+i

Pt+i1b

χN1+η

t+i

1+η#

ISolving this problem makes money completely recursive to the

rest of the system of equations.

IYet, real money holdings could a¤ect household’s

consumption.

IIn other words, real money balances are supposed to a¤ect the

marginal utility of consumption, i.e. we have to assume

non-separable utility between consumption and real money

balances.

5 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Mone y or no mon ey ?

New Ke ynesia n mod els

Litera ture rev iew

Selected papers

IAndrés, López-Salido and Vallés, 2006, Money in an

Estimated Business Cycle Model of the Euro Area,

Economic Journal.

IBarthélemy, Clerc, and Marx, 2011, A two-pillar DSGE

monetary policy model for the euro area,Economic

Modelling.

IIreland, 2004, Money’s Role in the Monetary Business

Cycle,Journal of Money, Credit and Banking.

ISmets and Wouters, 2003, An Estimated Dynamic

Stochastic General Equilibrium Model for the Euro Area,

Journal of the European Economic Association.

6 / 33

Intro ducti on

The m odel

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Conc lusion

The m odel

Solvin g the mo del

Micro f unded m acro m odel

New Keynesian framework

Economic agents of 3 types :

IHouseholds

Purchase goods for consumption, hold money and bonds,

supply labor, and maximize the expected present value of

utility.

IFirms

Hire labor, produce and sell di¤erentiated products in

monopolistically competitive goods markets, and maximize

pro…ts.

ICentral bank

Controls the nominal rate of interest.

7 / 33

Intro ducti on

The m odel

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Conc lusion

The m odel

Solvin g the mo del

Micro f unded m acro m odel

Non-separable money in the utility

IPreferences of the representative household are de…ned over a

composite consumption good Ct, real money balances Mt

Pt,

and leisure 1 Nt, where Ntis the time devoted to market

employment.

ICES utility function:

Ut=1

1σ(1b)C1ν

t+beεm

tMt

Pt1ν1σ

1νχN1+η

t

1+η

IBudget constraint:

PtCt+QtBt+MtBt1+Mt1+WtNt

IProduction function:

Yt=AtNt1α

8 / 33

Intro ducti on

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Conc lusion

The m odel

Solvin g the mo del

Micro f unded m acro m odel

Solving the model

IBy using Lagrangian method in order to optimize the utility

function with respect to the budget constraint and the

solvency condition, we obtain three …rst-order optimal

conditions.

IWe log-linearize around the steady state these conditions.

IWe add an ad-hoc Taylor type rule equation to close our

model.

IFinally, we have 6 equations of 6 unknown variables for our

economy: output gap ( ˆyt) and its ‡exible-price counterpart

(ˆyf

t), in‡ation rate ( ˆ

πt), real money balances ( cmpt) and its

‡exible-price counterpart ( cmpf

t) and nominal interest rate (ˆ

ıt).

IStructural shocks are assumed to follow a …rst-order

autoregressive process with an i.i.d.-normal error term such as

εk

t=ρkεk

t1+ωk,twhere εk,tN(0;σk)for

k=fp,m,i,ag.

9 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

The m odel

Solvin g the mo del

Micro f unded m acro m odel

ˆyf

t=υy

aεa

t+υy

mcmpf

tυy

c+υy

sm εm

t(1)

cmpf

t=υm

y+1Ethˆyf

t+1i+υm

yˆyf

t+1

νεm

t(2)

ˆ

πt=βEt[ˆ

πt+1]+κx,tˆytˆyf

t+κm,tcmptcmpf

t(3)

ˆyt=Et[ˆyt+1]κr(ˆ

ıtEt[ˆ

πt+1]) (4)

+κmp Et[∆cmpt+1]+κs m Et[∆εm

t+1]

cmpt=ˆytκiˆ

ıt+1

νεm

t(5)

ˆ

ıt=(1λi)λπ(ˆ

πtπc)+λxˆytˆyf

t+λm˜

Mt,k(6)

+λiˆ

ıt1+εi

t

10 / 33

Intro ducti on

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The m odel

Solvin g the mo del

Micro f unded m acro m odel

Micro-funded model

υy

a=1+η

(ν(νσ)a1)(1α)+η+ακr=1

νa1(νσ)

υy

m=(1α)(νσ)(1a1)

(ν(νσ)a1)(1α)+η+ακmp =(σν)(1a1)

νa1(νσ)

υy

c=(1α)

(ν(νσ)a1)(1α)+η+αlog ε

ε1κi=a2/ν

υy

sm =(νσ)(1a1)(1α)

((ν(νσ)a1)(1α)+η+α)(1ν)κsm =(1a1)(νσ)

(νa1(νσ))(1ν)

υm

y+1=a2

ν(ν(νσ)a1)a1=1

1+(b/(1b))1/ν(1β)(ν1)/ν

υm

y=1+a2

ν(ν(νσ)a1)a2=1

exp(1/β)1

κm,t=(σν) (1a1)(1α)(1

θβ)(1θ)(1+(ε1)εp

t)

1+(α+εp

t)(ε1)

κx,t=ν(νσ)a1+η+α

1α(1α)(1

θβ)(1θ)(1+(ε1)εp

t)

1+(α+εp

t)(ε1)

11 / 33

Intro ducti on

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Conc lusion

The m odel

Solvin g the mo del

Micro f unded m acro m odel

Money in the Taylor rule ?

˜

Mis a money variable: when k=0, money does not enter the

Taylor rule; k=1 to 3 corresponds respectively to the real money

gap (di¤erence between real money balances and its ‡exible-price

counterpart), the nominal money growth and the real money

growth.

12 / 33

Intro ducti on

The m odel

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Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Methodology

IAs in Smets and Wouters (2003), and An and Schorfheide

(2007), we apply Bayesian techniques to estimate our DSGE

model.

IWe use Eurozone data like Andrès et al. (2006) and

Barthélemy, Clerc and Marx (2011) from the Euro Area Wide

Model database (AWM) of Fagan, Henry and Mestre (2001).

IWe use the M3 monetary aggregate from the Eurostat

database.

ITo make output and real money balances stationary, we use

…rst detrended data, as in Ireland (2004), Andrés,

López-Salido and Vallés (2006), and Barthélemy, Clerc and

Marx (2011).

13 / 33

Intro ducti on

The m odel

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Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Data

Iˆ

πtis the log-linearized detrended in‡ation rate measured as

the yearly log di¤erence of detrended GDP De‡ator from one

quarter to the same quarter of the previous year;

Iˆytis the log-linearized detrended output per capita measured

as the di¤erence between the log of the real GDP per capita

and its trend;

Iˆ

ıtis the short-term (3-month) detrended nominal interest

rate.

Icmptis the log-linearized detrended real money balances per

capita measured as the di¤erence between the real money per

capita (log di¤erence between the money stock per capita and

the GDP De‡ator) and its trend.

Iˆyf

t, the ‡exible-price output, and cmpf

t, the ‡exible-price

real money balances, are completely determined by

structural shocks.

14 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Calibration

IFollowing standard conventions, we calibrate beta

distributions for parameters that fall between zero and one,

inverted gamma distributions for parameters that need to be

constrained to be greater than zero, and normal distributions

in other cases.

IThe calibration of σis inspired by Rabanal and Rubio-Ramírez

(2007) and by Casares (2007), respectively of 2.5 and 1.5.

Iσ=2 corresponds to a standard risk aversion.

Iσ=4, twice the standard value, represents a high level of risk

aversion, around twice the estimated value.

IAs our goal is to analyze two di¤erent con…gurations of risk,

we adopt the same priors in the two models with di¤erent risk

aversion calibration.

IA detailed calibration description is provided in the paper.

15 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Methodology

ISample: 117 observations from 1980 (Q4) to 2009 (Q4) in

order to avoid high volatility periods before 1980.

IAlgorithm: Metropolis-Hastings of 10 distinct chains, each of

100000 draws (Smets and Wouters, 2007; Adolfson et al.,

2007).

IAverage acceptation rate per chain for the benchmark model

(σestimated) are included in the interval [0.2601;0.2661]and

for (σ=4) in the interval [0.2587;0.2658].

16 / 33

Intro ducti on

The m odel

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Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Bayesian estimation of structural parameters (1)

Priors Posteriors

σestimated σ=4

Law Mean Std. Mean Mean

αbeta 0.33 0.05 0.378 0.484

θbeta 0.66 0.05 0.710 0.726

vnormal 1.25 0.05 1.447 1.528

σnormal 2.00 0.50 2.157

bbeta 0.25 0.10 0.252 0.246

ηnormal 1.00 0.10 1.053 1.120

εnormal 6.00 0.10 5.978 5.979

λibeta 0.50 0.10 0.573 0.614

λπnormal 3.00 0.50 3.494 3.491

λxnormal 1.50 0.50 1.872 1.923

λmnormal 1.50 0.50 1.011 0.964

πcnormal 2.00 0.10 1.903 1.908

17 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Bayesian estimation of structural parameters (2)

Priors Posteriors

σestimated σ=4

ρabeta 0.75 0.10 0.992 0.994

ρpbeta 0.75 0.10 0.973 0.972

ρibeta 0.50 0.10 0.460 0.560

ρmbeta 0.75 0.10 0.971 0.984

σainvgamma 0.02 2.00 0.013 0.019

σiinvgamma 0.02 2.00 0.018 0.012

σpinvgamma 0.02 2.00 0.004 0.004

σminvgamma 0.02 2.00 0.026 0.027

18 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

First period variance decomposition (percent)

estimated σ σ =4

εp

tεi

tεm

tεa

tεp

tεi

tεm

tεa

t

ˆyt2.16 31.17 7.50 59.16 2.23 11.19 22.38 64.20

ˆ

πt77.72 22.16 0.08 0.03 83.73 16.08 0.13 0.06

ˆ

ıt16.35 83.44 0.14 0.07 16.66 82.99 0.23 0.13

cmpt1.28 13.76 69.46 15.49 1.09 5.46 77.25 16.20

ˆyf

t0.00 0.00 10.56 89.44 0.00 0.00 24.89 75.11

cmpf

t0.00 0.00 81.72 18.28 0.00 0.00 82.62 17.38

19 / 33

Intro ducti on

The m odel

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Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Unconditional variance decomposition (percent)

estimated σ σ =4

εp

tεi

tεm

tεa

tεp

tεi

tεm

tεa

t

ˆyt1.65 1.09 3.07 94.18 0.83 0.28 10.38 88.51

ˆ

πt97.66 2.14 0.09 0.12 97.64 1.79 0.24 0.33

ˆ

ıt78.53 19.64 0.64 1.19 74.41 20.67 1.86 3.07

cmpt1.85 0.91 52.49 44.75 0.83 0.26 60.87 38.04

ˆyf

t0.00 0.00 3.06 96.94 0.00 0.00 10.23 89.77

cmpf

t0.00 0.00 54.42 45.58 0.00 0.00 62.04 37.96

20 / 33

Intro ducti on

The m odel

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Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Alternative ECB’s Taylor rules (1)

estimated σ

˜

Mt,0˜

Mt,1˜

Mt,2˜

Mt,3

λi0.527 0.573 0.561 0.547

(1λi)λπ1.594 1.491 1.463 1.537

(1λi)λx1.066 0.799 1.018 1.042

(1λi)λm0.431 0.1360.084

ST y

m(%)7.05 7.50 2.23 3.66

LT y

m(%)2.75 3.07 2.24 2.36

LMD -629.8 -618.2 -634.9 -635.3

estimations are not signi…cant in terms of student tests (t<1.645)

22 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Meth odolo gy

Calibra tion

Estim ation

Simu lation

Alternative ECB’s Taylor rules (2)

σ=4

˜

Mt,0˜

Mt,1˜

Mt,2˜

Mt,3

λi0.545 0.614 0.546 0.547

(1λi)λπ1.579 1.345 1.585 1.575

(1λi)λx1.034 0.741 1.038 1.039

(1λi)λm0.371 -0.012-0.018

ST y

m(%)22.61 22.38 23.20 23.28

LT y

m(%)9.56 10.38 9.29 9.15

LMD -639.8 -626.5 -646.1 -646.1

estimations are not signi…cant in terms of student tests (t<1.645)

23 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Comments

IWhatever the formulation of the Taylor rule, the estimated

parameters of the whole model are quite similar. This is true

with both levels of risk aversion.

IThe impact of a money shock on output, as shown through

the short term (ST y

m, in the …rst period) and the long term

(LT y

m) variance decomposition of output with respect to a

money shock, are also rather similar whatever the Taylor rule

24 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Interpretation

IThe weight of the money shock on output dynamics, κsm , and

on ‡exible-price output, υy

sm , increases with risk aversion.

IThe higher the risk aversion, the higher the role of

money on output.

IThe central bank strives for …nancial stability in crisis periods.

The smoothing parameter in the Taylor rule equation, λi,

increases with risk aversion.

IThe higher the risk aversion, the stronger the smoothing

of the interest rate. This re‡ects probably the central

bankers’objective not to agitate markets.

IThe introduction, or not, of a money variable in the ECB

monetary policy reaction function does not really appear to

change signi…cantly the impact of money on output and

in‡ation dynamics.

25 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Policy implications

IMoney is an important variable, at least during high

uncertainty periods.

IA real money gap variable appears to be justi…ed in the Taylor

rule.

IDuring crisis, monetary authorities should pay attention on

this variable.

26 / 33

Intro ducti on

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Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Conclusion

IUnder a standard risk aversion: money plays a minor role in

explaining output variability, as in the literature.

IUnder a higher risk aversion: money plays a

non-negligible role in explaining output and ‡exible-price

output ‡uctuations.

IThe explicit money variable does not appear to have a notable

direct role in explaining in‡ation variability.

IOur results suggest that a nominal or real money growth

variable does not improve the estimated ECB monetary policy

rule. Yet, a real money gap variable signi…cantly improves

the estimated Taylor rule.

IOne may infer that by changing economic agents’

perception of risks, the last …nancial crisis may have

increased the role of money in the transmission mechanisms

and in output changes.

27 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Further research

ICompare the baseline model (Gali 2008) versus our model.

IUse di¤erent data sets (demeaned, detrended).

IEnhance the model (capital, investment, central bank

preferences...).

IMoving window estimations with small sample.

IForecasting performances.

28 / 33

Intro ducti on

The m odel

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Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Productivity shock model (thesis)

Out-of-sample forecasting errors (DSGE Forecast)

06Q2 06Q3 06Q4 07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Comparison of output and inf lati on DSGE forecas t errors

Posi ti ve bar: Non-S eparable model i s better

Negati ve bar: Bas eli ne model is bet ter

Inflation

Output

Figure:

29 / 33

Intro ducti on

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Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Comparison between the role of money on output and the spreads

between the Bubill/BTF and the Euribor

06Q1 06Q3 07Q1 07Q3 08Q1 08Q3 09Q2 09Q4

-10

0

10

20

30

40

50

%

Role of Money on Output

10x(EURIBOR-BTF)

10x(EURIBOR-Bubill)

30 / 33

Intro ducti on

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Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Markup shock model (JMacro)

Comparison of output and in‡ation DSGE forecast errors. Our

model is better when the bar is positive, the baseline is better

otherwise.

07Q1 07Q2 07Q3 07Q4 08Q1 08Q 2 08Q3 08Q4 09Q1 09Q2 09Q 3 09Q4 10Q1 10Q2 10Q3 11Q1

-1

-0.5

0

0.5

1

Sample s ize: 24 observations

Output

Inflation

07Q1 07Q2 07Q3 07Q4 08Q1 08Q 2 08Q3 08Q4 09Q1 09Q2 09Q 3 09Q4 10Q1 10Q2 10Q3 11Q1

-1

-0.5

0

0.5

1

Sample s ize: 48 observations

Output

Inflation

31 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Comparison between the role of money on output (short run

variance decomposition) and the spreads

07Q1 07Q2 07Q3 07Q4 08Q1 08Q 2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q 1

-2

0

2

4

6

8

10

12

%

Sample s ize: 24 observations

Role of Money on O utput (ST)

5x(EURIBOR-Bubill)

5x(EURIBOR-BTF)

07Q1 07Q2 07Q3 07Q4 08Q1 08Q 2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q 1

-2

0

2

4

6

8

10

12

%

Sample s ize: 48 observations

Role of Money on O utput (ST)

5x(EURIBOR-Bubill)

5x(EURIBOR-BTF)

32 / 33

Intro ducti on

The m odel

Resul ts

Conc lusion

Comm ents

Conc lusion

Furthe r researc h

Comparison between the role of monetary policy on output (short

run variance decomposition) and the spreads

07Q1 07Q2 07Q3 07Q4 08Q1 08Q 2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q 1

0

5

10

15

20

25

%

Sample s ize: 24 observations

Role of Monetary P olicy on Output (ST)

10x(EU RIB OR-B ubill)

10x(EURIBOR-BTF)

07Q1 07Q2 07Q3 07Q4 08Q1 08Q 2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q 1

0

5

10

15

20

25

%

Sample s ize: 48 observations

Role of Monetary P olicy on Output (ST)

10x(EU RIB OR-B ubill)

10x(EURIBOR-BTF)

33 / 33