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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
Resul ts
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
Resul ts
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
The m odel
Resul ts
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
The m odel
Resul ts
Conc lusion
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
The m odel
Resul ts
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
Resul ts
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
Resul ts
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
Resul ts
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
Resul ts
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
Resul ts
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
The m odel
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
Resul ts
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
The m odel
Resul ts
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
The m odel
Resul ts
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