Risk Aversion in the Eurozone

Abstract

We propose a New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model where a risk aversion shock enters a separable utility function. We analyze five periods from 1971 through 2011, each lasting for twenty years, to follow over time the dynamics of several parameters such as the risk aversion parameter; the Taylor rule coefficients; and the role of the risk aversion shock in output, inflation, interest rate, and real money balances in the Eurozone. Our analysis suggests that risk aversion was a more important component of output and real money balance dynamics between 2006 and 2011 than it was between 1971 and 2006, at least in the short run.

Full text

Risk Aversion in the Eurozone
Jonathan Benchimol
March 2014
Abstract
We propose a New Keynesian Dynamic Stochastic General Equilibrium
(DSGE) model where a risk aversion shock enters a separable utility func-
tion. We analyze five periods from 1971 through 2011, each lasting for twenty
years, to follow over time the dynamics of several parameters such as the
risk aversion parameter; the Taylor rule coefficients; and the role of the risk
aversion shock in output, inflation, interest rate, and real money balances in
the Eurozone. Our analysis suggests that risk aversion was a more important
component of output and real money balance dynamics between 2006 and
2011 than it was between 1971 and 2006, at least in the short run.
Keywords: Risk aversion, Output, Money, Eurozone, New Keynesian DSGE
models, Bayesian estimation.
JEL Codes: E23, E31, E51.
Bank of Israel, Research Department, POB 780, 91007 Jerusalem, Israel. Phone: +972-2-6552641.
Fax: +972-2-6669407. Email: jonathan.benchimol@boi.org.il. This paper does not necessarily reflect
the views of the Bank of Israel. I would like to thank André Fourçans, Christian Bordes, Laurent
Clerc, Marc-Alexandre Sénégas, and the two anonymous referees for their useful comments.
1

Please cite this paper as:
Benchimol, J., 2014. Risk aversion in the Eurozone. Research in Economics 68
(1), 39–56
2

1 Introduction
The New Keynesian model, as developed by Galí (2008) and Walsh (2017), brings
together three equations to characterize the dynamic behavior of three key macro-
economic variables: output, inflation, and the nominal interest rate. The out-
put equation corresponds to the log-linearization of an optimizing household’s
Euler equation, linking consumption and output growth to inflation-adjusted re-
turn on nominal bonds—that is, to the real interest rate. The inflation equation
describes the optimizing behavior of monopolistically competitive firms that ei-
ther set prices in a randomly staggered fashion (Calvo, 1983), or face explicit costs
of nominal price adjustment (Rotemberg, 1982). The nominal interest rate equa-
tion, a monetary policy rule of the kind proposed by Taylor (1993), dictates that
the central bank should adjust the short-term nominal interest rate in response to a
trade-off between changes in inflation and output, and changes in the past interest
rate.
Following optimization of household preferences, relative risk aversion explic-
itly enters the first two equations. It has often been calibrated, estimated, and
analyzed as a simple and constant parameter in the literature (Christiano et al.,
2014). Although they deal with issues largely related to risk aversion by consid-
ering log-utilities, some studies are not able to analyze constant relative risk aver-
sion (Iacoviello, 2005). Yet, its role in the economic dynamics of the Eurozone has
not been analyzed further, at least not including a relative risk aversion shock in
a microfounded new Keynesian Dynamic Stochastic General Equilibrium (DSGE)
model.
Alpanda (2013) highlights the important role played by risk aversion shocks in
the US between 2006 and 2011. However, few studies quantify this link, or even
consider risk aversion as a shock in a New Keynesian DSGE framework applied
to the Eurozone. No studies use Bayesian techniques—as Fernández-Villaverde
(2010) does—to analyze the role of the risk aversion shock in output, inflation,
interest rate, and money dynamics in the Eurozone.
Constant relative risk aversion may change across different time periods. Ev-
idence of time-varying risk aversion can be found in simple applied analysis car-
ried out by Donadelli and Prosperi (2012). For instance, risk aversion varies in
response to news about inflation (Brandt and Wang, 2003). However, what is the
contribution of a risk aversion shock to the dynamics of output, inflation, and
money, over time? Building a simple New Keynesian DSGE model including a
time-varying relative risk aversion variable should be able to answer this ques-
tion.
As relative risk aversion measures the willingness to substitute consumption
over different periods, lower the level of risk aversion, more willing the house-
holds are to substitute consumption over time. Results on the relationship be-
3

tween relative risk aversion and equity risk premium can be found in Bansal and
Yaron (2004). Additionally, Wachter (2006) and Bekaert et al. (2010) show that
an increase in risk aversion involves an increase in equity and bond premiums,
and may either increase or decrease the real interest rate through a consumption
smoothing effect or a precautionary savings effect, respectively. Bommier et al.
(2012) further show that risk aversion enhances precautionary savings. These
studies confirm the potential link between money holdings, output, and risk aver-
sion.
However, most new Keynesian DSGE models do not include money in agents’
utility (MIU). Ireland (2004), Andrés et al. (2006), and Barthélemy et al. (2011) do
not analyze the link between relative risk aversion of households and the dynam-
ics of key macroeconomic variables.
However, Benchimol and Fourçans (2012) establish a significant link between
money, output, and risk aversion. They show that real money has a significant role
with regard to output if the relative risk aversion level is sufficiently high. Even
though they study the role of the level of risk aversion in a non-standard MIU
function (CES), they do not include a study of the microfounded risk aversion
shock for the Eurozone, without non-separabilities.
As in other studies, we consider a new Keynesian DSGE model including stan-
dard shocks: a price-markup shock, a monetary policy shock, and a technology
shock. To analyze the role of risk aversion in the dynamics of other variables, we
consider a time-varying relative risk aversion including a risk aversion shock.
Additionally, we consider a money equation to take account of the behaviors
of national central banks (before 1999) and the European Central Bank (after 1999),
and to close the model with as many historical variables as exogenous shocks.
This article contributes to the literature in several ways. First, we analyze the
role of a microfounded risk aversion shock in the dynamics of a New Keynesian
DSGE model. Second, a completely microfounded model with a risk aversion
shock is an original development, both in terms of findings as well as an estima-
tion technique.
Mainly inspired by Smets and Wouters (2007) and Galí (2008), our model ex-
plores the role of risk aversion in inflation, output, interest rates, real money bal-
ances, as well as in flexible-price output.
Specific emphasis will be placed on how the risk aversion shock impacts the
dynamics of these key variables over time. We use Bayesian techniques, as in
An and Schorfheide (2007), to estimate five subsamples of the Eurozone between
1971 and 2011, each for a period of twenty years. This framework allows us to
successively analyze the informational content of the last two crises (subprime
and sovereign debt crises) in comparison with other crises that occurred between
1971 and 2006 in the Eurozone.
4

Bayesian estimations and dynamic analyses of the model, with impulse re-
sponse functions and short- and long-run variance decomposition following struc-
tural shocks, yield different relationships between risk aversion and other vari-
ables. This approach sheds light on the importance of risk aversion, and its impact
on output and real money balances during the last five years (2006 to 2011).
This original focus on the last forty years highlights that the effect of risk aver-
sion shocks on output and real money balances are stronger in recent years than
in the distant past. It also shows that the role of monetary policy with regard to
output in the short run has decreased in recent years.
Finally, using modern theoretical and empirical tools, this study explores a fun-
damental question about the role of the perception of economic risks—the ability
of households to consume now or later—in the dynamics of the main economic
variables for the Eurozone.
The remainder of the paper is organized as follows. Section 2 describes the the-
oretical setup. In Section 3, the model is calibrated and estimated using Eurozone
data. Impulse response functions and variance decompositions are analyzed in
Section 4. Section 5 concludes, and the Appendix presents additional theoretical
and empirical results.
2 The model
The model consists of households that supply labor, purchase goods for consump-
tion, and hold money and bonds; and firms that hire labor, and produce and sell
differentiated products in monopolistically competitive goods markets. Each firm
sets the price of the good it produces, but not all firms reset their price during
each period. Households and firms behave optimally: households maximize the
expected present value of utility, and firms maximize profits. Additionally, there
is a central bank that controls the nominal rate of interest.
2.1 Households
We assume a representative infinitely lived household, seeking to maximize
Et"∞
∑
k=0
βkUt+k#(1)
where Utis the period utility function and β<1 is the discount factor. The house-
hold decides allocation of its consumption expenditure among different goods.
This requires that the consumption index Ctbe maximized for any given level of
expenditure (Galí, 2008). Furthermore, conditional on such optimal behavior, the
5

period budget constraint takes the form
PtCt+Mt+QtBtBt1+WtNt+Mt1(2)
where t=0, 1, 2..., Ptis an aggregate price index; Mtis the quantity of money
holdings at time t;Btis the quantity of one-period nominally riskless discount
bonds purchased in period tand maturing in period t+1 (each bond pays one
unit of money at maturity and is priced at Qt, where it=ln Qtis the short-
term nominal rate); Wtis the nominal wage; and Ntdenotes hours of work (or the
measure of household members employed). The above sequence of period budget
constraints is supplemented with a solvency condition.1
Preferences are measured with a common time-separable utility function (MIU).
Under the assumption of a period utility given by
Ut=C1σt
t
1σt
+γ
1νMt
Pt1ν
χN1+η
t
1+η(3)
consumption, money demand, labor supply, and bond holdings are chosen to
maximize Eq. 1, subject to Eq. 2 and the solvency condition. This MIU utility
function depends positively on the consumption of goods, Ct, and real money
balances, Mt
Pt; and negatively on labor, Nt.σt>0 is the time-varying coefficient of
the relative risk aversion of households (or the inverse of the intertemporal elas-
ticity of substitution), defined as σt=σ+εr
t, where εr
tis a risk aversion shock
(detailed in Section 3.1). νis the inverse of the elasticity of money holdings with
respect to the interest rate, and ηis the inverse of the elasticity of work effort with
respect to the real wage. γand χare positive scale parameters.
This setting leads to the following conditions2, which must hold in equilib-
rium, in addition to the budget constraint. The resulting log-linear version of the
first-order condition corresponding to the demand for contingent bonds implies
that
ct=Et[ct+1]1
σt
(itEt[πt+1]ρc)(4)
where ct=ln (Ct)is the logarithm of aggregate consumption, itis the nominal
interest rate, Et[πt+1]is the expected inflation rate in period t+1 with knowledge
of the information in period t, and ρc=ln (β).
The demand for cash that follows from the household’s optimization problem
is given by
σtctνmptρm=a2it(5)
where mpt=mtptare the log linearized real money balances, ρm=ln (γ)+
1Such as 8tlim
n!∞Et[Bn]0, in order to avoid Ponzi-type schemes.
2See Appendix 6.A
6

a1, and a1and a2are resulting terms of the first-order Taylor approximation of
ln (1Qt)=a1+a2it.
Real cash holdings depend positively on consumption with an elasticity equal
to σt
νand negatively on the nominal interest rate.3We consider nominal interest
rate as the policy instrument of the central bank.
The resulting log-linear version of the first-order condition corresponding to
the optimal consumption-leisure arbitrage implies that
wtpt=σtct+ηntρn(6)
where wtptcorresponds to the log of the real wage, ntdenotes the log of hours
of work, and ρn=ln (χ).
Finally, these equations represent the Euler condition for the optimal intratem-
poral allocation of consumption (Eq. 4), the intertemporal optimality condition
setting the marginal rate of substitution between money and consumption equal
to the opportunity cost of holding money (Eq. 5), and the intratemporal optimality
condition setting the marginal rate of substitution between leisure and consump-
tion equal to the real wage (Eq. 6).
2.2 Firms
Backus et al. (1992) have shown that capital appears to play a rather minor role in
the business cycle. To simplify the analysis and focus on the role of risk, we do not
include the capital accumulation process in this model, as in Galí (2008).
We assume a continuum of firms indexed by i2[0, 1]. Although each firm
produces a differentiated good, they all use identical technology, represented by
the following production function
Yt(i)=AtNt(i)1α(7)
where At=exp (εa
t)represents the level of technology, assumed to be common to
all firms, and which evolves exogenously over time, and εa
tis a technology shock.
All firms face an identical isoelastic demand schedule and take the aggre-
gate price level Ptand aggregate consumption index Ctas given. As in the stan-
dard Calvo (1983) model, our generalization features monopolistic competition
and staggered price setting. At any time, t, only a fraction of firms, 1 θ, with
0<θ<1, can reset their prices optimally, while the remaining firms index their
prices to lagged inflation.
3Since 1
β>1, a2>0.
7

2.3 Central bank
The central bank is assumed to set its nominal interest rate according to an aug-
mented smoothed Taylor (1993) rule such as:
it=(1λi)λπ(πtπc)+λxytyf
t+λm(mptmpc)+λiit1+εi
t(8)
where λπ,λx, and λmare policy coefficients reflecting the weight assigned to the
inflation gap, the output gap, and the real money gap, respectively; the parameter
0<λi<1 captures the degree of interest rate smoothing; and εi
tis an exoge-
nous ad hoc shock accounting for fluctuations of the nominal interest rate. πcis
an inflation target and mpcis a money target, essentially included to account for
changes in policies targeting inflation (Svensson, 1999) and monetary aggregates
(Fourçans, 2007). Other studies introduce a relevant money variable in the Euro-
zone Taylor rule (Andrés et al., 2006, 2009; Barthélemy et al., 2011; Benchimol and
Fourçans, 2012).
Additionally, λmtakes into account the potential money targeting of the na-
tional central bank before the creation of the European Central Bank (ECB, 1999).
After 1999, the ECB followed an explicit money targeting policy until 2004, called
the Two Pillars policy (Barthélemy et al., 2011), and might have even followed an
implicit money targeting policy after that (Kahn and Benolkin, 2007).
3 Empirical results
3.1 DSGE model
Our macro model consists of five equations and five dependent variables: infla-
tion, nominal interest rate, output, real money balances, and flexible-price output.
Flexible-price output is completely determined by shocks.
yf
t=1+η
σt(1α)+η+αεa
t+(1α)ln (1α)+ρnln ε
ε1
σt(1α)+η+α(9)
πt=βEt[πt+1]+(1θ) (1βθ) (σt(1α)+η+α)
θ(1α+αΛt)ytyf
t(10)
yt=Et[yt+1]σ1
t(itEt[πt+1]ρc)(11)
mpt=σt
νyta2
νitρm
ν(12)
it=(1λi)λπ(πtπc)+λxytyf
t+λm(mptmpc)+λiit1+εi
t(13)
where a1=ln 1e1
β
1
β
e
1
β1
and a2=1
e
1
β1
.
8

All structural shocks are assumed to follow a first-order autoregressive process
with an i.i.d. (independent and identically distributed) normal error term, such as
εk
t=µkεk
t1+ωk,t, where εk,tN(0; σk)for k=fp,i,a,rg.
3.2 Calibration
Following standard conventions, we calibrate beta distributions for parameters
that fall between zero and one, inverted gamma distributions for parameters that
need to be constrained at greater than zero, and normal distributions in other
cases.
The parameters of the utility function are assumed to be distributed as follows.
Only the discount factor is fixed at 0.98 in the estimation procedure. The intertem-
poral elasticity of substitution (i.e., the level of relative risk aversion) is set at 2, a
mean between the calibrations of Rabanal and Rubio-Ramírez (2005) and Casares
(2007), and consistent with the calibrated value used by Kollmann (2001) and the
value estimated by Lindé et al. (2009). The inverse of the Frisch elasticity of labor
supply is assumed to be approximately 1, as in Galí (2008), and the scale parame-
ters on money and labor are assumed to be approximately 0.2, as in Benchimol
and Fourçans (2012).
The calibration of α,θ, and εcomes from Smets and Wouters (2007), Casares
(2007), and Galí (2008). The smoothed Taylor rule (λi,λπ,λx, and λm) priors are
calibrated following Smets and Wouters (2003), Andrés et al. (2009), and Barthélemy
et al. (2011). To observe both the behavior of the central bank and risk aversion,
we assign a higher standard error (0.2) and a Normal prior law for the relative risk
aversion level and for the Taylor rule coefficients (including inflation and money
targets), except for the smoothing parameter, which is restricted to be positive and
less than one (Beta distribution). The inflation target, πc, is calibrated to 2 percent,
and the money target, mpc, is assumed to be approximately 4 percent.
The calibration of the shock persistence parameters and the standard errors of
the innovations follow Smets and Wouters (2007). All the standard errors of shocks
are assumed to be distributed according to inverted Gamma distributions, with
prior means of 0.01. The latter ensures that these parameters have positive sup-
port. The autoregressive parameters are all assumed to follow Beta distributions.
All of these distributions are centered around 0.75, except for the autoregressive
parameter of the monetary policy shock and the risk aversion shock, which are
centered around 0.50, as in Smets and Wouters (2007). We take a common stan-
dard error of 0.15 for the shock persistence parameters, which is a mean between
that of Benchimol and Fourçans (2012) and Smets and Wouters (2007).
9

Law Mean Std. Law Mean Std.
αbeta 0.33 0.10 λmnormal 1.00 0.20
θbeta 0.66 0.10 πcnormal 2.00 0.20
σnormal 2.00 0.20 m pcnormal 4.00 0.20
vnormal 1.50 0.10 ρabeta 0.75 0.15
εnormal 6.00 0.10 ρpbeta 0.75 0.15
ηnormal 1.00 0.10 ρibeta 0.50 0.15
γbeta 0.20 0.05 ρrbeta 0.50 0.15
χbeta 0.20 0.05 σainvgamma 0.01 2.00
λibeta 0.50 0.10 σpinvgamma 0.01 2.00
λπnormal 3.00 0.20 σiinvgamma 0.01 2.00
λxnormal 1.50 0.20 σrinvgamma 0.01 2.00
Table 1: Calibration summary
3.3 Eurozone data
In our Eurozone model, πtis the detrended inflation rate measured as the yearly
log difference of the detrended GDP deflator from one quarter to the same quar-
ter of the previous year; ytis the detrended output per capita measured as the
difference between the log of real GDP per capita and its trend; and itis the short-
term (3-month) detrended nominal interest rate. These data are extracted from
the AWM (Area Wide Model) database (Fagan et al., 2005). m ptis the detrended
real money balance per capita measured as the difference between real money per
capita and its trend, where real money per capita is measured as the log difference
between money stock per capita and the GDP deflator. We use the M3 monetary
aggregate from the Eurostat database.
3.4 Results
The model is estimated with 160 observations from the first quarter of 1971 to the
first quarter of 2011, with Bayesian techniques, as in Smets and Wouters (2007).
However, to capture different policies and risk perceptions in the Eurozone be-
tween 1971 and 2011, and more specifically between 2006 and 2011, we divide this
large sample into five subsamples, each consisting of 80 observations (20 years).
This procedure allows us to analyze five different periods with a sufficiently
large sample, as specified in Fernández-Villaverde and Rubio-Ramírez (2004). Ac-
cordingly, we estimate our model over five different periods: from 1971 Q1 to 1991
Q1 (P1); from 1976 Q1 to 1996 Q1 (P2); from 1981 Q1 to 2001 Q1 (P3); from 1986
Q1 to 2006 Q1 (P4); and from 1991 Q1 to 2011 Q1 (P5).
The estimation of the implied posterior distribution of the parameters across
the five periods (Fig. 1) is performed using the Metropolis-Hastings algorithm (10
distinct chains, each of 100, 000 draws). The average acceptance rates per chain
10

0.5
0.6
0.7
1.2
1.4
0.7
0.8
0.9
0
0.2
0.4
1.9
2
2.1
3.98
4
4.02
2.6
2.8
0.92
0.94
0.96
0.4
0.45
0.5
0.99
1
1.01
6
6.005
6.01
1.9
2
2.1
0.198
0.2
0.202
0.2
0.21
0.22
0.98
1
P1 P2 P3 P4 P5
0.6
0.8
1
P1 P2 P3 P4 P5
0.35
0.4
0.45
P1 P2 P3 P4 P5
0.9
0.95
1
Figure 1: Bayesian estimation of parameters over the selected periods
are included in the interval [0.19; 0.22], and the Student’s t-tests are all above 1.96
in absolute terms.
To assess the model validation, we ensure convergence of the proposed dis-
tribution to the target distribution for each period. Appendix 6.B shows that the
estimation results are valid and that convergence is obtained for all estimations
and all moments.
Distribution of priors and posteriors are presented in Appendix 6.C. It shows
that the maximum posterior distribution reaches the posterior mean of each esti-
mated parameter. The estimation is relatively well identified, and the data is quite
informative for most of the estimated microparameters.
4 Interpretation
We analyze the forecast error variance decomposition of each variable following
exogenous structural shocks.
The analysis is conducted via an unconditional variance decomposition to an-
alyze long-term variance decomposition (the gray bar in Fig. 2), and conditional
variance decomposition, conditionally to the first period, to analyze short-run
variance decomposition (the black bar in Fig. 2).
Fig. 2 shows that output is mainly explained by the technology shock in the
long run (approximately 90%), and by the monetary policy shock (approximately
35%) and the technology shock (approximately 50%) in the short run. Rest of the
11

0
10
20
Output
Risk aversion
0
2
4
6Price-markup
0
20
40
60 Monetar y policy
0
50
100 Technology
0
0.05
0.1
Inflation
0
50
100
0
0.05
0.1
0
5
10
15
0
5
10
Interest rate
0
50
100
0
50
100
0
5
10
15
P1 P2 P3 P4 P5
0
20
40
60
Real money
P1 P2 P3 P4 P5
0
5
10
P1 P2 P3 P4 P5
0
10
20
30
P1 P2 P3 P4 P5
0
50
100
Short r un var iance Long run variance
Figure 2: Variance decomposition over the selected periods
variance in output is explained by the risk aversion shock (approximately 5% from
P1 to P4, and more than 15% for P5) in the short term, whereas risk aversion shock
has a limited role in output variance in the long run.
Fig. 2 also shows that, in accordance with the literature, inflation is mainly
explained by the price-markup shock, and interest rate variance is mainly driven
by monetary policy in the short run and monetary policy and price-markup in the
long run. Furthermore, most of the variance in real money balances is induced
by the risk aversion shock (approximately 40%) and the monetary policy shock
(approximately 25%) in the short run, whereas in the long run, real money balance
variance is mainly driven by the technology shock. All these results are in line
with the literature.
Sections 4.1 to 4.4 present the role of each shock in the fluctuations of the
macroeconomic variables, and the response of these key variables to structural
shocks over the study period.
4.1 Price-markup shock
Fig. 2 shows that the price-markup shock explains almost all of the variability in
the inflation rate, at least in the short run. Its role in the long run on real money
balance fluctuations is halved across the study period.
Fig. 3 shows that from P1 to P5, the impact of the price-markup shock on out-
12

put, inflation, nominal interest rate, and real money balances is at least halved.
While transitioning from one period to another, the impact of the price-markup
shock on the overall economy reduces. Regardless of the period under study, af-
ter a positive price-markup shock, inflation rate increases, thus, nominal interest
rate increases, decreasing real interest rate, output, output gap, and real money
balances.
4.2 Technology shock
Fig. 2 indicates that technology plays an increasingly important role in the short
term for the inflation rate and, thus, for the interest rate in the selected period.
Fig. 4 highlights that in response to a positive technology shock, output in-
creases but inflation decreases, resulting in an increase in real money holding, and
a slight decrease in nominal interest rate and output gap. The improvement in
technology is partly accommodated by the central bank, which lowers the nomi-
nal and real interest rate, while increasing the quantity of money in circulation.
Interestingly, note that maximum sensitivity of output to a technology shock
was observed in P1 and P2.
4.3 Monetary policy shock
Fig. 2 shows that compared to the previous periods (P1 to P4), monetary policy
has a smaller role in the short run output variability over the last period (P5)–
from around 37% to 22%, respectively. This highlights a switch from the role of
the monetary policy to the role of risk aversion during recent years. This confirms
the declining influence of European monetary policy relative to the influence of
risk aversion shocks in recent years.
Fig. 5 indicates that in response to an interest rate shock, inflation rate, output,
output gap, and real money balances fall. The nominal and real interest rates rise.
A positive monetary policy shock could also induce a fall in interest rates due to a
low enough degree of intertemporal substitution (i.e., the risk aversion parameter
is high enough), which generates a large impact response of current consumption
relative to future consumption (Jeanne, 1994; Christiano et al., 1997). Note that
in P5, nominal and real interest rates are the least sensitive of all other periods,
suggesting the largest relative risk aversion compared to all other periods.
4.4 Risk aversion shock
Fig. 2 shows that output and real money balance variances have an important
risk aversion shock component. This finding shows the leading role of relative
13

020 40
0
0.2
0.4
0.6
0.8 Inflation
020 40
-0.4
-0.3
-0.2
-0.1
0Output
020 40
-0.4
-0.3
-0.2
-0.1
0Output g ap
020 40
0
0.2
0.4
0.6
0.8 Nominal interest rate
020 40
-0.2
-0.15
-0.1
-0.05
0
0.05 Real inter est rate
020 40
-0.8
-0.6
-0.4
-0.2
0Real money bal ances
P5 P4 P3 P2 P1
Figure 3: Impulse response function with respect to a price-markup shock
020 40
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02 Inflation
020 40
0.4
0.6
0.8
1
1.2 Output
020 40
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1 Output g ap
020 40
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02 N ominal i nterest r ate
020 40
-0.04
-0.03
-0.02
-0.01
0
0.01 Real interes t rate
020 40
0.7
0.8
0.9
1
1.1
1.2
1.3
Real money balances
P5 P4 P3 P2 P1
Figure 4: Impulse response function with respect to a technology shock
14

risk aversion in the dynamics of output (Black and Dowd, 2011) and real money
balances (Benchimol, 2011).
Although inflation rate, nominal interest rate, and flexible-price output are
strong components of output, risk aversion has a minor role to play in the vari-
ance of inflation and interest rate, and it does not play a role with regard to the
flexible-price output (less than 0.2% in the short- and long-run), which is com-
pletely determined by the technology shock. It also shows that inflation and in-
terest rate variances are quasi-unaffected by the introduction of the risk aversion
shock, allowing these variables to be mainly explained by the price-markup shock
and the monetary policy shock, respectively.
Additionally, Fig. 2 shows that risk aversion plays a more significant role in
output dynamics in the last period (P5) than in other periods (P1 to P4) in the
short run. This finding reflects the increasing role played by risk aversion in more
recent years (between 2006 and 2011) as compared to the past (between 1971 and
2006).
This case is very interesting because Fig. 6 shows that a risk aversion shock
leads to a decrease in output and an increase in inflation. This implies a tighten-
ing of monetary policy (because of the strong weight that the central bank places
on inflation) and its strength depends on the period (strong monetary policy tight-
ening in P1 and low monetary policy tightening in P5). The risk aversion shock
also implies an increase in real money balances and real money growth, and a de-
crease in the output gap. Our risk aversion shock also suggests that uncertainty is
counter cyclical (Baker and Bloom, 2013).
Household consumption reduces (decreasing output), and companies increase
their price (to face high risk aversion and possibly, low consumption), which im-
plies an increase in the inflation rate, constrained by a tightening of monetary
policy.
Fig. 6 exhibits that the risk aversion shock has a longer impact in P5 than it does
in the other periods. This is due to the increase of the autoregressive parameter
of the risk aversion shock, ρr, over the periods, as shown in Fig. 1. Although
the sensitivity of monetary policy with respect to risk aversion shock is lower in
P5 than during other periods, it is more persistent in P5 than in the other periods.
This highlights that the central bank reacts less strongly after a risk aversion shock,
but the persistence of the impact of this risk aversion shock on nominal interest
rate is stronger over time.
Bloom (2009) simulates a macro uncertainty shock, which produces a rapid
drop in aggregate output, mainly because higher uncertainty causes firms to tem-
porarily pause their investment and hiring. Our results suggest that the impact
of the risk aversion shock—a micro uncertainty shock—on output and output gap
is very important during the last period, P5, as compared to the other periods.
15

020 40
-0.01
-0.008
-0.006
-0.004
-0.002
0Inflation
020 40
-1
-0.8
-0.6
-0.4
-0.2
0Output
020 40
-1
-0.8
-0.6
-0.4
-0.2
0Output g ap
020 40
0
0.2
0.4
0.6
0.8
1Nomi nal interest r ate
020 40
0
0.2
0.4
0.6
0.8
1Real interest r ate
020 40
-1.5
-1
-0.5
0Real money balances
P5 P4 P3 P2 P1
Figure 5: Impulse response function with respect to a monetary policy shock
020 40
0
0.002
0.004
0.006
0.008
0.01
0.012 Inflation
020 40
-0.5
-0.4
-0.3
-0.2
-0.1
0Output
020 40
-0.4
-0.3
-0.2
-0.1
0Output g ap
020 40
0
0.1
0.2
0.3
0.4 Nomi nal inter est rate
020 40
0
0.1
0.2
0.3
0.4 Real interes t rate
020 40
0
0.5
1
1.5
2Real money balances
P5 P4 P3 P2 P1
Figure 6: Impulse response function with respect to a risk aversion shock
16

As a matter of fact, an important part of the variation in output is dependent,
through the risk aversion shock, on major shocks such as crises, news, and disas-
ters (Bloom, 2009; Baker and Bloom, 2013). Controlling these media-parameters—
for instance, by communication–could attenuate their impact on growth.
The leading role of the risk aversion shock in the dynamics of real money bal-
ance in the short run is another important finding. Fig. 2 indicates that real money
balances are mainly explained by the technology shock (approximately 80%) in
the long run, whereas in the short run, real money balances are mainly explained
by the risk aversion shock and the monetary policy shock. Last but not the least,
in line with Benchimol and Fourçans (2012), a risk aversion shock drastically in-
creases real money balances response, despite increasing inflation and nominal
interest rate responses (Fig. 6).
5 Conclusion
Risk aversion as a concept in economics and finance is based on the behavior of
consumers and investors who are exposed to uncertainty. It is the reluctance of a
person to accept a bargain with an uncertain payoff, rather than one that offers a
more certain, but possibly lower, expected payoff.
This paper presents a standard New Keynesian DSGE model that includes a
risk aversion shock. It shows the involvement of this risk aversion shock in the
dynamics of the economy: it increases inflation, decreases output (Fig. 6), and
diminishes the impact of the action by the central bank on output variance, at
least in the short run (Fig. 2).
Additionally, risk aversion plays an important role in output and real money
balance dynamics. It is clearly identified that risk aversion plays a negative role
in determining output, whereas it increases real money balances and real money
growth in the initial period (Fig. 6).
Moreover, while estimations are quite robust (Fig. 7 to Fig. 12), they show
that risk aversion shock has a stronger impact on output dynamics during the last
twenty years (P5) as compared to other analyzed periods (P1 to P4). This result is
explained by the inclusion of the subprime and sovereign debt crises in P5 from
2007 to 2011.
This enhanced baseline model shows the importance of such a parameter to
the economy, especially its impact on output, money, and monetary policy. It also
serves to show the importance of controlling shocks to the agents’ risk aversion,
for instance, by communication.
17

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6 Appendix
A Solving the model
Price dynamics
Let us assume a set of firms not reoptimizing their posted prices in period t.
Using the definition of the aggregate price level and the fact that all firms resetting
prices choose an identical price P
t, leads to
Pt=hθP1Λt
t1+(1θ) (P
t)1Λti1
1Λt(14)
where Λt=1+1
1
ε1+εp
t
is the elasticity of substitution between consumption goods
in period t, and Λt
Λt1is the markup of prices over marginal costs (time varying).
Dividing both sides by Pt1and log-linearizing around P
t=Pt1yields
πt=(1θ) (p
tpt1). (15)
In this setup, we do not assume inertial dynamics of prices. Inflation results
from firms reoptimizing their price plans in any given period, and choosing a price
that differs from the economy’s average price in the previous period.
Price setting
A firm reoptimizing in period tchooses price P
tthat maximizes the current
market value of the profits generated, while the price remains effective. This prob-
lem resolves and leads to a first-order Taylor expansion around the zero inflation
steady state:
p
tpt1=(1βθ)
∞
∑
k=0
(βθ)kEthc
mct+kjt+(pt+kpt1)i(16)
where c
mct+kjt=mct+kjtmc denotes the log deviation of marginal cost from its
steady state value mc =µ, and µ=ln ε
ε1is the log of the desired gross
markup.
Equilibrium
Market clearing in the goods market requires Yt(i)=Ct(i)for all i2[0, 1]and
all t. Aggregate output is defined as Yt=R1
0Yt(i)11
ΛtdiΛt
Λt1; it follows that
Yt=Ctmust hold for all t. One can combine the above goods market clearing
21

condition with the consumer’s Euler equation (4) to yield the equilibrium condi-
tion
yt=Et[yt+1]σ1
t(itEt[πt+1]ρc)(17)
Market clearing in the labor market requires Nt=R1
0Nt(i)di. With the pro-
duction function (7) and taking logs, one can express the following approximate
relationship between aggregate output, employment, and technology as
yt=εa
t+(1α)nt(18)
An expression is derived for the marginal cost of an individual firm in terms
of the economy’s average real marginal cost:
mct=(wtpt)m pnt(19)
=wtpt1
1α(εa
tαyt)ln (1α)
for all t, where mpntdefines the economy’s average marginal product of labor. As
mct+kjt=(wt+kpt+k)m pnt+kjt, we have
mct+kjt=mct+kαΛt
1α(p
tpt+k)(20)
where the second equality follows from the demand schedule combined with the
market clearing condition ct=yt. Substituting (20) into (16) yields
p
tpt1=(1βθ)
∞
∑
k=0
Θt+k(βθ)kEt[c
mct+k]+
∞
∑
k=0
(βθ)kEt[πt+k](21)
where Θt=1α
1α+αΛt1 is time varying to take into account the markup shock.
Finally, (15) and (21) yield the inflation equation
πt=βEt[πt+1]+λmctc
mct(22)
where β,λmct=(1θ)(1βθ )
θΘt.λmctis strictly decreasing in the index of price
stickiness θ, in the measure of decreasing returns α, and in the demand elasticity
Λt.
Next, a relationship is derived between the economy’s real marginal cost and
a measure of aggregate economic activity. From (6) and (18), the average real
marginal cost can be expressed as
mct=σt+η+α
1αyt1+η
1αεa
tlog (1α)ρn(23)
Under flexible prices, the real marginal cost is constant and equal to mc =µ.
22

Defining the natural level of output, denoted by yf
t, as the equilibrium level of
output under flexible prices leads to
mc =σt+η+α
1αyf
t1+η
1αεa
tlog (1α)ρn(24)
thus, implying
yf
t=υaεa
t+υc(25)
where υa=1+η
σt(1α)+η+αand υc=(1α)(ln(1α)+ρnln(ε
ε1))
σt(1α)+η+α. Subtracting (26) from
(25) yields
c
mct=σt+η+α
1αytyf
t(26)
where c
mct=mctmc is the real marginal cost gap and ytyf
tis the output gap.
Combining the above equation with (24), we obtain
πt=βEt[πt+1]+ψtytyf
t(27)
where ψt=(1θ)(1βθ)(σt(1α)+η+α)
θ(1α+αΛt), and ytyf
tis the output gap.
The second key equation describing the equilibrium of the model is obtained
by rewriting (20) to determine output
yt=Et[yt+1]σ1
t(itEt[πt+1]ρc)(28)
Equation (28) is thus, a dynamic IS equation including real money balances.
The third key equation describes the behavior of real money balances. From (5),
we obtain
mpt=σt
νyta2
νitρm
ν(29)
B Model validation
The red and blue lines in Fig. 7 represent an aggregate measure based on the
eigenvalues of the variance-covariance matrix of each parameter both within and
between chains. Each graph represents specific convergence measures and has
two distinct lines that represent the results within and between chains. These mea-
sures are related to the analysis of the parameter’s mean (first moment), variance
(second moment), and third moment of the model for the relevant period. Con-
vergence requires both lines for each of the three measures to become relatively
constant and converge to each other.
Diagnoses of the numerical maximization of the posterior kernel indicate that
the optimization procedure was able to obtain a robust maximum for the poste-
23

7
8
9
10
P1
First moment
8
10
12
14 Second moment
40
60
80
100 Third moment
6
8
10
12
P2
5
10
15
40
60
80
100
7
8
9
10
P3
5
10
15
0
50
100
7
8
9
10
P4
8
10
12
14
40
60
80
0 5 10
x 10 4
7
8
9
Iterati ons
P5
0 5 10
x 10 4
5
10
15
Iterati ons 0 5 10
x 10 4
0
50
100
Iterati ons
Within variance Between and within vari ance
Figure 7: Multivariate Metropolis-Hastings convergence diagnosis
24

rior kernel. A diagnosis of the overall convergence for the Metropolis-Hastings
sampling algorithm is provided in Fig. 7.
Diagnoses for each individual parameter were also obtained, following the
same structure used for overall convergence. Most of the parameters do not seem
to exhibit convergence problems, notwithstanding that this evidence is stronger
for some parameters than it is for others.
C Priors and posteriors
The following figures present the priors and posteriors of the estimated structural
parameters over the study period.
00.45 0.9
0
2
00.94
0
10
20
02.5
0
1
2
0 2
0
2
4
00.99
0
2
06.01
0
2
00.2 0.4 0.6
0
5
00.2 0.4 0.6
0
5
0 2
0
1
0 4
0
1
00.54
0
2
4
02.8
0
1
2
01.76
0
1
2
00.73 1.46
0
1
2
00.99
0
50
00.39 0.78
0
5
00.96
0
10
20
00.52 1.04
0
2
4
00.05
0
50
100
00.05
0
50
100
00.05
0
50
100
00.05
0
100
Poster ior dis tribution Prior distribution Posterior mode
Figure 8: Priors and posteriors of the estimated parameters (P1)
25

00.46 0.92
0
2
00.93
0
10
20
02.6
0
1
2
0 2
0
2
0 1
0
2
06.01
0
2
4
00.2 0.4
0
5
00.21 0.42
0
5
0 2
0
1
2
0 4
0
1
00.52
0
2
4
02.82
0
1
2
01.78
0
1
2
00.43 0.86 1.29 1.72
0
1
2
00.99
0
50
00.42 0.84
0
5
00.95
0
10
00.77
0
5
00.05
0
50
100
00.05
0
50
100
00.05
0
50
100
00.05
0
100
Poster ior dis tribution Prior distribution Poster ior mode
Figure 9: Priors and posteriors of the estimated parameters (P2)
26

00.43 0.86
0
2
00.94
0
10
20
02.54
0
1
2
02.04
0
2
4
00.99
0
2
4
0 6
0
2
4
00.2 0.4
0
5
00.2 0.4 0.6
0
5
01.97
0
1
0 4
0
1
00.57
0
5
02.91
0
1
2
01.69
0
1
2
00.64 1.28 1.92
0
1
2
00.99
0
50
00.42 0.84
0
5
00.94
0
10
00.66
0
5
00.05
0
100
00.05
0
100
00.05
0
100
00.05
0
100
200
Poster ior dis tribution Prior distribution Poster ior mode
Figure 10: Priors and posteriors of the estimated parameters (P3)
27

00.43 0.86
0
2
00.93
0
10
20
02.5
0
1
2
02.06
0
2
4
00.99
0
2
0 6
0
2
4
00.2 0.4
0
5
00.21 0.42
0
5
01.95
0
1
03.99
0
1
00.62
0
5
02.95
0
1
2
01.66
0
1
2
00.45 0.9 1.35 1.8
0
1
2
00.99
0
50
100
00.46
0
5
00.94
0
10
20
00.81
0
5
00.05
0
100
00.05
0
100
200
00.05
0
100
200
00.05
0
100
Posterior distribution Prior di stribution Pos teri or mode
Figure 11: Priors and posteriors of the estimated parameters (P4)
28

00.43 0.86
0
2
00.95
0
20
02.51
0
1
2
02.05
0
2
4
00.99
0
2
0 6
0
2
00.2 0.4 0.6
0
5
00.2 0.4
0
5
01.98
0
1
0 4
0
1
00.56
0
5
02.95
0
1
2
01.66
0
1
2
00.73 1.46
0
1
2
00.99
0
50
00.42 0.84
0
5
00.95
0
10
20
00.9
0
10
00.05
0
100
00.05
0
100
200
00.05
0
100
00.05
0
100
200
Poster ior dis tribution Prior distribution Poster ior mode
Figure 12: Priors and posteriors of the estimated parameters (P5)
29