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Money and monetary policy in the

Eurozone: an empirical analysis

during crises

Jonathan Benchimolyand André Fourçansz

April 21,2017

Abstract

This paper analyses the role of money and monetary policy as well

as the forecasting performance of New Keynesian dynamic stochas-

tic general equilibrium (DSGE) models with and without separability

between consumption and money. The study is conducted over three

crisis periods in the Eurozone, namely, the ERM crisis, the Dot-com

crisis and the Global Financial Crisis (GFC). The results of succes-

sive Bayesian estimations demonstrate that during these crises, the

non-separable model generally provides better out of sample output

forecasts than the baseline model. We also demonstrate that money

shocks have some impact on output variations during crises, espe-

cially in the case of the GFC. Furthermore, the response of output

to a money shock is more persistent during the GFC than during

the other crises. The impact of monetary policy also changes during

crises. Insofar as the GFC is concerned, such an impact increases at

the beginning of the crisis, but decreases sharply thereafter.

Keywords: Eurozone, Money, Monetary Policy, DSGE, Crises.

JEL Classi…cation: E31, E32, E51, E58.

This paper does not necessarily re‡ect the views of the Bank of Israel. We thank two

anonymous referees for their helpful and constructive comments.

yBank of Israel, POB 780, 91007 Jerusalem, Israel. Phone: +972-2-6552641. Fax:

+972-2-6669407. Corresponding author. Email: jonathan.benchimol@boi.org.il.

zESSEC Business School and THEMA, Economics Department, Avenue Bernard

Hirsch, 95021 Cergy-Pontoise Cedex 2, France. Phone: +33-1-34433017. Fax: +33-1-

34433689. Email: fourcans@essec.edu

1

Please cite this paper as:

Benchimol, J., and Fourçans, A., 2017. Money and monetary pol-

icy in the Eurozone: an empirical analysis during crises. Macroeco-

nomic Dynamics, 21(3), 677–707.

2

1 Introduction

Since the seminal paper of Smets and Wouters (2003), and even as far back

as the development of the New Keynesian paradigm in the mid-1990s, tradi-

tional New Keynesian dynamic stochastic general equilibrium (DSGE) mod-

els have not given an explicit role to money, neither in the Eurozone, nor

in the US. When money is explicitly taken into consideration, its impact

is generally found to be negligible (Ireland,2003;Andrés et al.,2006,2009;

Barthélemy et al.,2011). Yet, Benchimol and Fourçans (2012) …nd that when

risk aversion is su¢ ciently high, money has an impact on output dynamics.

Furthermore, Canova and Menz (2011) use a small-scale structural mone-

tary business cycle model to …nd that output and in‡ation ‡uctuations are

in‡uenced by money.

Whatever the structures of these models, monetary policy is a central

tenet and its impact on output and in‡ation— through interest rate adjustments—

is well-documented, for example, in Smets and Wouters (2007).

The roles of money and monetary policy may also change during crises.

The Global Financial Crisis (GFC) hints at these possible changes. The pol-

icy arena surrounding these questions is ripe with endless debates, notably

with respect to monetary policy and its possible in‡uence on output and in-

‡ation. Chadha et al. (2014) …nd that money conveys signi…cant information

to the central bank when there are shocks to credit supply, as may be the case

during crises. Also, El-Shagi and Giesen (2013) analyze the consequences of

the Federal Reserve’s response to the …nancial crisis and …nd evidence of the

substantial impact of money on US prices. The role of money in the US

business cycle is also highlighted in El-Shagi et al. (2015).

Analyses conducted via New Keynesian DSGE models may be useful for

clarifying these questions. In order to conduct this type of analysis, it is useful

to assume non-separable preferences between consumption and real money

holdings into such a model, compare this model with one where consumption

and real money holdings are assumed to be time-separable, and conduct

empirical analyses that focus on crisis periods. This approach enables us to

study the role of money and monetary policy, in order to determine explicitly

whether their impact on output and in‡ation is a¤ected during crises.

The impact of money and monetary policy may change for various rea-

sons: for instance, changes in the transmission mechanism due to variations

in banks’behavior; changes in money holding and consumption/investment

behaviors; changes in portfolio allocation between money and other assets;

changes in expectations or risk evaluation, and more generally, increase in

uncertainty, and so forth.

This paper seeks to understand the impact of money and monetary policy

3

on the dynamics of the economy during crises, and the forecasting perfor-

mances and abilities of two types of models.

In terms of meaningful statistical observations, crisis periods do not, in

general, last very long. Hence, in order to capture the impact of short-run

changes in the dynamics of the economy, there is a need to use as short

sample periods as possible. Yet, one also needs to obtain a su¢ cient number

of observations in order to achieve statistically signi…cant sample sizes.

To deal with these two types of questions— namely, bringing forth the

role of money and monetary policy and taking into consideration the short

sample constraint— our research strategy consists of comparing two types

of micro-founded New Keynesian models in a DSGE framework and testing

them over periods short enough to capture the crisis e¤ects, but long enough

to be statistically meaningful.

The …rst model is a standard one, the baseline model, where money is

omitted from the utility function–that is, where it is assumed time-separable

preferences between households’ consumption and real money holdings; in

this model, money is also excluded from the monetary policy rule, as in the

baseline model of Galí (2008). The second model incorporates money in

two di¤erent ways. First, by assuming non-separability between real money

balances and consumption, money is explicitly included in the utility func-

tion.1This non-separability between consumption and real balances could

be signi…cant in the Eurozone, especially during crisis periods (Jones and

Stracca,2006). Second, as the central bank minimizes its loss function at

least with respect to in‡ation, its optimization program implies that money

enters automatically the monetary policy rule (Woodford,2003).

We apply Bayesian techniques to estimate these two models. We use

Eurozone data over periods that include three di¤erent crises, namely, the

beginning of the 1990s when there were speculative currency attacks on the

European exchange rate mechanism (ERM); the growth and bust of the Dot-

com bubble in the beginning of the 2000s; and the Global Financial Crisis

(GFC) from 2007 through 2011.

We analyze the dynamics of both models by studying the variance de-

composition of the variables with respect to structural shocks (our focus is

money and monetary policy shocks, but markup and technology shocks are

also taken into consideration) over the three periods. We compare the fore-

casting performances of the models in each period, as well as the responses of

output, ‡exible-price output, output gap and in‡ation to the shocks (IRF).

Focusing on each of these periods sheds light on the speci…c role of money

1Here, the term separability must be di¤erentiated from the terminology used in mon-

etary aggregation literature (Barnett,1980).

4

and monetary policy in crisis situations. It also provides informative results

regarding output and in‡ation dynamics during periods of uncertainty.

The analysis shows that, during crises, the impact of money on output and

‡exible-price output variances is stronger than usually found in the literature

(Ireland,2004;Andrés et al.,2006,2009). The response of output to a money

shock also increases, especially during peaks of the ERM crisis and the GFC.

The persistence of the response of output and ‡exible-price output to a money

shock is higher during the GFC than during the other crises. The impact

of conventional monetary policy on output and in‡ation also changes during

crises. More speci…cally, as far as the GFC is concerned, the impact of

monetary policy on output and in‡ation constantly increases until the peak

of the crisis (2008 Q3). It then decreases sharply over the next two quarters,

and remains at a lower and stable level through 2011.

The response of ‡exible-price output to a money shock during the GFC is

about as strong as the response of output itself, and in addition is signi…cantly

stronger and longer lasting than during the other crises. Yet, a monetary

policy shock appears to have no e¤ect on ‡exible-price output for either of

the crises.

Finally, our analysis demonstrates that during crises, a New Keynesian

model with non-separable preferences between consumption and money, and

with money in the Taylor (1993) rule, leads to better out-of-sample output

forecasts than a standard New Keynesian model–assuming separable prefer-

ences between consumption and money. This information can be a valuable

input for the central bank in its decision-making process.

In Section 2, we discuss the data and empirical methodology. We analyze

the ERM crisis in Section 3, the Dot-com crisis in Section 4and focus on

the GFC in Section 5. We compare the three crises in Section 6and o¤er a

conclusion in Section 7.

2 Data and empirical methodology

The two New Keynesian DSGE models used in this paper are presented in

the online appendix. The baseline model is the well known Galí (2008) model

(Model 1). The non-separable model (Model 2) is presented in Benchimol

and Fourçans (2012).

2.1 Data

We use the same data set for both models of the Eurozone. ^ytis the output

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

5

capita and its linear trend; ^tis the in‡ation rate, measured as the yearly

log di¤erence of the GDP de‡ator from one quarter to the same quarter of

the subsequent year; and ^{tis the short-term (three-month) nominal interest

rate. The latter two are linearly detrended. This data set is extracted from

the (Euro) Area Wide Model database (AWM) of Fagan et al. (2001). cmpt

is the real money balances per capita, measured as the di¤erence between

the real money per capita and its linear trend, where real money per capita

is measured as the log di¤erence between the money stock per capita and

the GDP de‡ator. We choose the M3monetary aggregate from the Eurostat

database. As in Andrés et al. (2006), Barthélemy et al. (2011), Benchimol

and Fourçans (2012), and De Santis et al. (2013), M3is used because it

serves as the institutional de…nition of money in the Eurozone and plays a

prominent role in the de…nition of monetary policy.2

^yf

t, the ‡exible-price output, and cmpf

t, the ‡exible-price real money bal-

ances, are entirely determined by structural shocks.

2.2 Methodology

Theoretically, only very short sample sizes (from one to a few years) are able

to capture the changes in the values of parameters owing to short-run crises.

Yet, to be reliable, statistical analyses necessitate a su¢ cient amount of ob-

servations. As far as we know, there is no speci…c statistical rule establishing

the minimum number of observations necessary for reliable Bayesian tests.

To deal with this issue, we follow Fernández-Villaverde and Rubio-Ramírez

(2004) by choosing a sample size of 48 observations (quarterly data over 12

years). Indeed, Fernández-Villaverde and Rubio-Ramírez (2004) demonstrate

that such a sample size is su¢ cient to obtain valid Bayesian estimations. The

con…dence in such small sample size tests is reinforced by the fact that several

studies have shown that the small sample performances of Bayesian estimates

tend to outperform classical ones, even when evaluated by frequentist criteria

(Geweke et al.,1997;Jacquier et al.,2002).

The periods of interest are presumed to contain higher uncertainty than

standard periods. We choose to study three crises, as indicated earlier, in the

2Kelly et al. (2011) suggest that o¢ cial monetary aggregates, at least in the US, use an

aggregation methodology that is increasingly incorrect as the aggregate becomes broader.

Belongia and Ireland (2014) show that a Divisia aggregate of monetary services tracks the

true monetary aggregate almost perfectly whereas a simple-sum measure often behaves

quite di¤erently in the US (the so-called Barnett (1980) critique, see also Hendrickson

(2014)). As they are not published by the European Central Bank, these types of mon-

etary aggregates cannot be used in our paper. Benchimol (2016) uses Divisia monetary

aggregates leading to similar conclusions for Israel.

6

years between 1990 Q1 and 2011 Q1. For every quarter of each crisis period,

we run a Bayesian estimation by using the 48 observations before each re-

spective quarter. This re-estimation through rolling windows of data is fairly

typical in forecasting studies, since it generates a panel of forecasts at various

horizons that allow the assessment of the average forecasting performance of

a given model.

We calibrate both models (see Appendix Afor parameters’description

and Appendix Bfor detailed calibration) and estimate them by using Bayesian

techniques for every quarter (see Appendix Cfor posteriors). We also run

simulations and DSGE forecasts for both models, for every quarter in each

crisis period.

Our purpose in this paper is not to present all the results, a very cum-

bersome task indeed. Instead, from the estimates, we intend to draw the

evolution of the variance decomposition of variables with respect to di¤er-

ent shocks in the short and the long runs. We also intend to compare the

forecasting performance of both models, and compare the main IRFs over

crises.

The estimates provide values of micro and macro parameters through time

that a¤ect the dynamics of the variables. Fig. 17 through Fig. 19 (Appendix

C) suggest that our results are stable over the various periods. These …gures

also suggest that structural deep parameters (,,,) change without dis-

playing any drift (see Appendix Afor parameters description). During crisis

periods, these changes appear to result from structural economic changes

rather than statistical artifacts (Hurtado,2014). Furthermore, the online

appendix shows that the standard deviations of the structural parameter

posterior means over our crisis periods are signi…cantly lower than those of

the non-structural and macro parameters.

For both models, the diagnosis concerning the numerical maximization

of the posterior kernel indicates that the optimization procedure leads to a

robust maximum for the posterior kernel. The convergence of the proposed

distribution to the target distribution is thus satis…ed for all estimations and

all moments.3

Furthermore, well identi…ed structural parameters are key for valid infer-

ence. For both models, after each estimation, we use the Global Sensitivity

Analysis (GSA) techniques to test identi…cation for all parameters (Ratto,

2008). Following Iskrev (2010), all parameters, structural and non-structural,

are well identi…ed.4

3For both models, and for each estimation, a diagnosis of the overall convergence for

the Metropolis–Hastings sampling algorithm can be provided upon request.

4We use the sensitivity analysis toolbox provided in Dynare 4.4.3 for both models and

for each estimation. All parameters are identi…ed in the model (rank of H) and by J

7

The role of each shock can be analyzed via the successive estimations and

simulations, leading to variance decompositions of variables with respect to

the shocks (the markup shock ("p

t), the technology shock ("a

t), the monetary

policy shock ("i

t), and the money shock ("m

t) for Model 2). For reasons already

explained, we center this analysis on money and monetary policy shocks.

After each estimation, we perform out-of-sample DSGE forecasts (each

over four periods, that is, one year) to compare the forecasting performance

of both models.5To conduct these forecasting exercises, we simulate our

estimated models starting with a given state and analyze the trajectories of

the forecasted endogenous variables.

Finally, we analyze the responses of output, ‡exible-price output, output

gap and in‡ation to money and monetary policy shocks. In order to avoid an

over-cumbersome paper, we do not present all the IRFs for each crisis. We

select two key points for each crisis, and for both models when appropriate,

and compare the IRFs at di¤erent key points.

This analysis is done by using Metropolis-Hastings iterations on the basis

of the posterior means of each estimated variable. Then, we evaluate the

forecasts with respect to the actual data. Finally we compare the forecasts

of both models by calculating their respective root mean-squared deviations

(RMSD). After calculating the sum of the absolute values of the correspond-

ing RMSD over four out-of-sample forecasts, we compare these values be-

tween the two models. We also use the Giacomini and White (2006) test to

compare the predictive abilities of both models.

The performance of our models is assessed via their forecasting abilities.

We do not compare the models through their respective log marginal data

density or posterior odds ratio for several reasons. First, the di¤erence be-

tween two log marginal data densities of two di¤erent models does not mean

that we must disregard the model with the lowest log marginal data den-

sity. For instance, the latter model can still be used to perform forecasting

under changing environments. Second, whatever the log marginal data den-

moments (rank of J). These results can be provided upon request.

5DSGE models are increasingly being utilized by central banks and other policy-making

institutions to assist with policy decisions and forecasting, as pointed by Edge and Gürkay-

nak (2010). Sims and Zha (1998) introduced Bayesian methods to vector autoregressive

(VAR) models to improve the accuracy of out-of-sample forecasts in a dynamic multi-

variate framework. More recently, researchers have started to examine the forecasting

performance of these models. In one such investigation, Smets and Wouters (2007) show

that a DSGE model can generate forecasts that have a lower root mean-squared devia-

tion (RMSD) than a Bayesian Vector Autoregression (BVAR). On the other hand, Edge

et al. (2010) show that the out-of-sample forecasting performance of the Federal Reserve

Board’s new DSGE model for the US economy (EDO) is in many cases better than their

large-scale macro-econometric model (FRB/US).

8

sity function, it may be argued that the model is designed to capture only

certain characteristics of the data.6Whether or not the marginal likelihood

is a good measure to evaluate how well the model accounts for particular

aspects of the data is an open question. Third, Model 1 and Model 2 do not

have the same dimensions. Model 2 has more parameters (structural as well

as non-structural) and variables, and the Bayes factor discriminates against

these. The Bayes factor penalizes the di¤erence in the dimensionality of the

parameter space, incarnating a strong preference for stingy modeling (Koop,

2003;Fernández-Villaverde and Rubio-Ramírez,2004;Del Negro et al.,2007).

It can be argued that adding frictions to models may improve the in-

sample …t (Bekiros and Paccagnini,2015;Villa,2016). However, when com-

paring two di¤erent models that share neither the same historical variables

(time series used for estimation) nor the same household’s preferences, such

view is not applicable. Model 1 contains three historical variables (output,

in‡ation and interest rate) whereas Model 2 contains four historical variables

(output, in‡ation, interest rate and money) and a di¤erent household’s util-

ity function. Hence, a comparison of the two models through their in-sample

…ts is not relevant in our case.

3 European exchange rate mechanism crisis

The …rst period under scrutiny includes the European exchange rate mecha-

nism (ERM) crisis of 1992. The peak of the crisis is characterized by the so

called Black Wednesday. This refers to the events of Wednesday, September

16, 1992, when the British government withdrew the pound sterling from the

European ERM.

The period of analysis is from 1990 Q1 through 1994 Q1. Other crises

also occurred during this period, such as the oil crisis following the …rst

Gulf war7from 1990 Q2 through 1991 Q2; the Russian crisis8from 1992 Q2

through 1992 Q4; and the French real estate crisis9from 1992 through 1996.

In addition to the ERM crisis, these episodes also a¤ected the Eurozone.

6As a matter of fact, this comment is also valid as far as the forecasting performances

of the models are concerned.

7The 1990 oil price spike occurred in response to the Iraqi invasion of Kuwait on August

2, 1990. The war lasted until February 28, 1991.

8The constitutional crisis of 1993 was a political stand-o¤ between the Russian president

and the Russian parliament that was resolved by using military force.

9From 1992 through 1996, real estate prices declined up to 40%.

9

3.1 Variance decomposition

For each Bayesian estimation of each model, we compute the short-run (con-

ditional to the …rst period) and long-run (unconditional) variance decompo-

sition of the variables with respect to the shocks.

The impact of money (Model 2) on output in the short run is relatively

small (between 3% and 6% depending on the quarter). The impact in the

long run is even smaller (between 0.5% and 1.1%), and follows the same

pattern through time.

90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3 91Q4 92Q1 92Q2 92Q3 92Q4 93Q1 93Q2 93Q3 94Q1

24

26

28

30

32

34

S hort run

90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3 91Q4 92Q1 92Q2 92Q3 92Q4 93Q1 93Q2 93Q3 94Q1

1.5

2

2.5

3

Long run

Model 1 Model 2

Figure 1: Variance decompositions of output with respect to the monetary

policy shock (in percent) in Model 1 (solid lines) and Model 2 (dashed lines)

The monetary policy shock plays a signi…cant role in output ‡uctuations

in the short run (Fig. 1). It explains just below 30% of the output variance

before 1992 Q3 for Model 2, and the percentage increases quickly from this

period. The long-run impact is much smaller (between 2% and 3%).

All in all, output variability is mainly explained by the monetary policy

shock (around 30%) and the technology shock (around 60%) in the short run

for both models. The technology shock explains most of the variance in the

long run (around 87%) for both models. The markup shock has a negligible

role on output in both the short and long runs.

Money also plays a small role in explaining ‡exible-price output variations

in the short run. The dynamics of these impacts follow a path similar to that

10

90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3 91Q4 92Q1 92Q2 92Q3 92Q4 93Q1 93Q2 93Q3 94Q1

10

15

20

25

30

35 S hort run

90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3 91Q4 92Q1 92Q2 92Q3 92Q4 93Q1 93Q2 93Q3 94Q1

1.5

2

2.5

3

3.5

4

4.5 Long run

Model 1 Model 2

Figure 2: Variance decompositions of in‡ation with respect to the monetary

policy shock (in percent) in Model 1 (solid lines) and Model 2 (dashed lines)

of current output. The long-run impact of money on ‡exible-price output

remains small.

Regardless of the model, the monetary policy shock has no impact on

‡exible-price output dynamics in either the short or long run. Flexible-price

output is essentially explained by the technology shock in both runs (around

90%) for both models.

The variance decomposition of in‡ation shows that the money shock has

a very small role to play, be it in the short or long run (less than 2%). As

Fig. 2demonstrates, the monetary policy shock has a signi…cant impact on

in‡ation dynamics in the short run, but a very small one in the long run.

The markup shock is important as well (around 80%) in the short run and

dominates the process in the long run (around 96%) for both models.

Fig. 1and Fig. 2indicate that the short-run impact of monetary policy on

output remains relatively constant, whereas its impact on in‡ation increases

from the beginning of the period until the peak of 1992 Q3. It increases in

both cases after 1992 Q3 and the ERM crisis, whatever the model used.

However, the role of monetary policy appears to be greater in Model 2,

with stronger impacts in the short than in the long run.10

10 We do not present the decomposition of output, ‡exible-price output, and in‡ation

with respect to the markup and technology shocks. As they are negligible, we present nei-

11

3.2 Forecasting performances

As mentioned previously, from each Bayesian estimation, we simulate the

out-of-sample forecasts of output and in‡ation over the next four periods

(one year) and compare these values to the historical values. This enables

us to compute the RMSD of each period for each model. A negative number

(negative bar) implies that the RMSD of the non-separable model is higher

than that of the baseline model. In such cases, the forecasting performance

of Model 1 is better than that of Model 2. To further compare the forecasting

performances of output, we also use the Giacomini and White (2006) tests

of equal predictive ability.

90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3 91Q4 92Q1 92Q2 92Q3 92Q4 93Q1 93Q2 93Q3 94Q1

-2%

-1.5%

-1%

-0.5%

0%

0.5%

1%

1.5%

2%

Output

Inflation

Figure 3: Comparison of output and in‡ation DSGE forecast errors— Model

2 is better when the bar is positive; Model 1 is better otherwise.

Fig. 3shows that Model 2 has better predictive power for output dynam-

ics than Model 1 when speculative attacks on currencies occurred between

1991 Q4 and 1992 Q4. It is also the case in 1990, when other crisis events im-

pacted the Eurozone (essentially, the oil crisis following the Gulf War). This

result is con…rmed by pairwise Giacomini and White (2006) tests of equal

conditional and unconditional predictive ability of output over the period.

ther the decomposition of in‡ation with respect to the money shock nor the decomposition

of the ‡exible-price output with respect to the monetary policy shock. Finally, we do not

present the decomposition of output and ‡exible-price output with respect to the money

shock. This applies to all crises when appropriate. Yet, all these variance decompositions

are available upon request.

12

Equal predictive ability of Model 1 and Model 2 is rejected and Model 2 out-

performs Model 1 with a p-value of 0.001 (for conditional and unconditional

predictive ability tests).

In terms of in‡ation, Fig. 3shows that the predictive power of both

models is quite similar, except after the ERM crisis where Model 2 dominates

Model 1. Also, Giacomini and White (2006) tests of equal predictive ability

of in‡ation are not rejected (at least at 10%).

3.3 Interpretation

The previous analysis suggests that money has a small impact on output,

even though this impact appears to be stronger than what Ireland (2004)

and Andrés et al. (2006) found.

The transmission mechanism of shocks follows a complex process in our

models. Such complexity is manageable when studying the impact of the

money shock; an analysis of the macro-parameters is, in this case, su¢ cient

to interpret changes in the transmission process.11 It is more complicated

to interpret changes in the transmission mechanism of a monetary policy

shock. An analysis of the values of the macro-parameters alone is not su¢ -

cient. The monetary policy shock ("i

t) enters the model through the Taylor

rule; furthermore, there is no macro-coe¢ cient enabling a direct study of its

impact. Therefore, it is hard to analyze the changes in the impact of such a

shock, other than through the variance decomposition results.

Fig. 1indicates that in 1992 Q3, at the peak of the ERM crisis, the impact

of monetary policy on output reaches its lowest level. This may be due to

the conduct of monetary policy, which in that period, was more focused on

limiting exchange rate variations than on stabilizing output.

The RMSD errors comparison (Fig. 3) highlights two di¤erent periods,

namely, from 1990 Q2 through 1991 Q1 and from 1991 Q4 through 1992 Q4,

whereby Model 2 has better predictive abilities than Model 1.

4 Dot-com crisis

The bursting of the Dot-com bubble in the Eurozone occurred approximately

one quarter later (2000 Q3) than in the United States (2000 Q2). Our period

of study is from 1999 Q1 through 2003 Q1. This enables us to analyze the

peak of the bubble in the Eurozone (2000 Q2–Q3) and the period following

the burst of the bubble.

11 See the online appendix for a detailed description of the macro-parameters.

13

4.1 Variance decomposition

The impact of the money shock on output variance when the bubble was in

process (between 2000 Q1 and Q4) is small, in the short run (between 2%

and 6%) as well as in the long run (between 0.2 % and 1.5%).

Monetary policy has a signi…cant impact on output in the short run

(around 27–28% for Model 2, Fig. 4), but this impact diminishes follow-

ing the burst of the bubble. The impact in the long run is very small and

negligible.

99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 01Q1 01Q2 01Q3 01Q4 02Q1 02Q2 02Q3 03Q1

22

23

24

25

26

27

28 S hort run

99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 01Q1 01Q2 01Q3 01Q4 02Q1 02Q2 02Q3 03Q1

1.2

1.4

1.6

1.8

2

2.2

2.4

Long run

Model 1 Model 2

Figure 4: Variance decompositions of output with respect to the monetary

policy shock (in percent) in Model 1 (solid lines) and Model 2 (dashed lines)

As in the previous crisis period, output is mainly explained by the mone-

tary policy and technology shocks (respectively around 27–28% and 65% for

Model 2) in the short run, but mainly by the technology shock in the long run

(around 86%). The markup shock should also be taken into consideration in

both runs, even though its role is less important than that of the above two

shocks (11% and 14% in the short and long runs, respectively).

As far as ‡exible-price output is concerned, our results show that the

impact of the money shock is also small in the short run (between 2% and

6%) and in the long run (0.2% and 1.5%). These results are applicable to the

monetary policy shock as well. Flexible-price output is essentially explained

by the technology shock in the short as well as long run (around 90% for

both models).

14

99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 01Q1 01Q2 01Q3 01Q4 02Q1 02Q2 02Q3 03Q1

15

20

25

30

S hort run

99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 01Q1 01Q2 01Q3 01Q4 02Q1 02Q2 02Q3 03Q1

1.5

2

2.5

3

Long run

Model 1 Model 2

Figure 5: Variance decompositions of in‡ation with respect to the monetary

policy shock (in percent) in Model 1 (solid lines) and Model 2 (dashed lines)

The money shock has a very small impact (less than 2%) on the variance

of in‡ation. Monetary policy, on the other hand, has a signi…cant role to

play in in‡ation variability, at least in the short run (Fig. 5). This impact

increases a bit after the peak of the bubble.

All in all, the variance of in‡ation is primarily explained by the monetary

policy and markup shocks in the short run (around 30% and 80% for Model

2, respectively), and by the markup shock (around 97% for Model 2) in the

long run. The other shocks (money and technology) have a negligible impact

in both models.

4.2 Forecasting performances

According to Fig. 6, between 1999 Q4 and 2000 Q4 when the bubble was

building up, Model 2 does not demonstrate signi…cantly better predictive

power of output dynamics than the baseline model. The results change in

the two quarters following the burst of the bubble, until the events of Sep-

tember 11, 2001 (2001 Q3). Pairwise Giacomini and White (2006) tests of

equal predictive ability (conditional and unconditional) over the period can-

not statistically assess which model is better than the other (p-value of 0.83

for the unconditional test and of 0.69 for the conditional test).

15

99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 01Q1 01Q2 01Q3 01Q4 02Q1 02Q2 02Q3 03Q1

-1%

-0.8%

-0.6%

-0.4%

-0.2%

0%

0.2%

0.4%

0.6%

Output

Inflation

Figure 6: Comparison of output and in‡ation DSGE forecast errors— Model

2 is better when the bar is positive; Model 1 is better otherwise.

In terms of in‡ation forecasts outside crisis periods, Model 1 is generally

a better predictor than Model 2; whereas during crisis periods, the former

model prevails. The Giacomini and White (2006) tests of equal predictive

ability of in‡ation are not rejected.

4.3 Interpretation

Even if the impact of money on output and ‡exible-price output before 2000

Q3 (the peak of the …nancial bubble) is small, it is close to the value found by

Ireland (2004) and Andrés et al. (2006). This may be due to the fact that the

Dot-com crisis ultimately had a rather small impact on European economies.

The low impact on output is explained in Model 2 by the very low value of the

expected money growth parameter (mp =()(1a1)

a1()) and of the expected

money shock growth parameter on output (sm =(1a1)()

(a1())(1)).

The Dot-com crisis appears to have reinforced the impact of monetary

policy on in‡ation. This impact has increased since the beginning of the

period (Fig. 5) in the long and short runs to reach a maximum level at the

end of the period.

As explained in Section 3.3, the transmission of the monetary policy shock

is not linked to an estimated parameter (the value multiplying the monetary

policy shock is equal to one). The values of the parameters alone are, there-

16

fore, not su¢ cient to explain the behavior of the impact of monetary policy

on output and in‡ation dynamics.

5 The Global Financial Crisis

The rise in subprime mortgage delinquencies and foreclosures in the United

States and the resulting decline of securities backed by these mortgages

around the world started in 2007 Q3. After the subprime crisis, the debt

crisis started around 2010 Q2 in the Eurozone. In order to capture the im-

pact of these events, our period of analysis ranges from 2007 Q1 through

2011 Q1.

5.1 Variance decomposition

Fig. 7shows that the impact of the money shock on output variance in

the short run increases from 2007 Q2 and peaks in 2007 Q3 and 2008 Q3,

explaining about 10% of the variance between these two peaks. The rapid

decrease of the value of this impact between 2008 Q3 and 2009 Q1 is notable,

after which it stabilizes. The value in the long run remains very small through

the period and follows a similar pattern as in the short run. After 2009 Q1,

the impact manifests a decreasing trend, to reach about 6.5% in 2011 Q1.

The monetary policy shock has a signi…cant impact on output variation

in the short run (Fig. 8) with a peak in 2008 Q3. At this point, it explains

more than 30% and 25% of the output variance in Model 1 and Model 2,

respectively. The impact of monetary policy on output increases over the

…rst quarters of the GFC and reaches its highest level at the peak of the

GFC (2008 Q3). Following this peak, the impact decreases fairly sharply, to

reach its lowest level in the beginning of 2009.

As shown, the impact of monetary policy on output is lower for Model 2

than Model 1. By construction, money shocks have no impact on output in

the baseline model (Model 1), whereas it has such an impact in Model 2; and

this impact of the money shock is fairly strong during this period. Therefore,

the impact of the money shock on output lowers the impact of the monetary

policy shock on output in Model 2, in the short as well as long runs.

As in the previous crises, output variability in the short run is primarily

explained by the monetary policy shock (between 20% and more than 30%)

and the technology shock (around 64%). The technology shock dominates

the process in the long run (around 85%). The markup shock also has a

non-negligible role to play, since it accounts for 12% of the output variance

in the short run and about 14% in the long run in Model 1. The result is

17

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

4

5

6

7

8

9

10

11 S hort run

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

1

1.5

2

2.5

3

3.5

4

Long run

Figure 7: Variance decompositions of output with respect to the money shock

(in percent) in Model 2

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

15

20

25

30

S hort run

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

1

1.5

2

Long run

Model 1 Model 2

Figure 8: Variance decompositions of output with respect to the monetary

policy shock (in percent) in Model 1 (solid lines) and Model 2 (dashed lines)

18

somewhat di¤erent in the case of Model 2, because the role of the markup

shock is limited to around 5%.

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

25

30

35

40

45

50 S hort run

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

2

2.5

3

3.5

4

4.5

5

Long run

Model 1 Model 2

Figure 9: Variance decompositions of in‡ation with respect to the monetary

policy shock (in percent) in Model 1 (solid lines) and Model 2 (dashed lines)

The impact of the money shock on ‡exible-price output follows the same

pattern as the one on current output but with somewhat higher values in

the short run (between 7% and 13%), and comparable values in the long run

(between 1% and 4.5%). However, the impact of the monetary policy and

markup shocks on this variable become insigni…cant in both models, in the

short and long runs.

On the whole, ‡exible-price output is essentially explained in both models

by the technology shock, in the short and long runs (with a value around

80%).

As during the other crises, the impact of the money shock on in‡ation is

insigni…cant. In‡ation variations in the short run are driven mainly by the

monetary policy shock (as Fig. 9shows, it explains between 20% and 50%

of the variance) and the markup shock (around 79%), and by the markup

shock (around 97%) in the long run, in both models. The signi…cant change

in the importance of these impacts from 2008 Q3 to 2011 Q1 is noticeable.

19

5.2 Forecasting performances

Fig. 10 indicates that at the core of the GFC (2007 Q4 through 2009 Q4),

Model 2 provides better forecasts of output than Model 1 in terms of RMSE.

This outcome is reversed following 2010 Q1, when the debt crisis starts. Pair-

wise Giacomini and White (2006) tests of equal predictive ability (conditional

and unconditional) con…rm that Model 2 provides better forecasts of output

than Model 1. Equal predictive ability of Model 1 and Model 2 is rejected

and Model 2 outperforms Model 1 with a p-value of 0.001 (for conditional

and unconditional predictive ability tests).

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

-1%

-0.5%

0%

0.5%

1%

Output

Inflation

Figure 10: Comparison of output and in‡ation DSGE forecast errors— Model

2 is better when the bar is positive; Model 1 is better otherwise.

Even though Model 1 is in general better than Model 2 in terms of in-

‡ation forecasts, the di¤erence is insigni…cant, a result con…rmed by the

Giacomini and White (2006) tests of equal predictive ability.

5.3 Interpretation

As far as the US is concerned, Cecchetti (2009) and Mishkin (2010) consider

that the crisis began in 2007 Q1, when several large subprime mortgage

lenders started to report losses. The real trigger for the crisis was in 2007

Q3, when the French bank BNP Paribas temporarily suspended redemptions

from three of its fund holdings that had invested in assets backed by the

US subprime mortgage debt. As a result, credit spreads began widening,

20

overnight interest rates in Europe shot up, and the European Central Bank

(ECB) immediately responded with the largest short-term liquidity injection

in its nine-year history.

The Euro Group heads of states and governments and the ECB held

an extraordinary summit in October 2008 to determine joint action for the

Eurozone. They agreed on a bank rescue plan that would entail hundreds of

billions of euros— governments would inject banks with capital and guarantee

interbank lending. Financial uncertainty decreased as a consequence of this

action. This decrease may explain the diminishing impact of money and

monetary policy on output variations after October 2008 (Fig. 7and Fig.

8), as well as the decreasing impact of monetary policy on in‡ation (Fig. 9).

The change in the impact of money on output is explained in the model

(cf. the online appendix) by the variations in the expected money growth

parameter (mp) and the expected money growth shock parameter on output

(sm).

The impact of money on ‡exible-price output partly results from the

variation of the money shock parameter (y

sm =(1)()(1a1)

((a1())(1)++)(1)).

Similar to the previous crisis periods, the values of the parameters alone

are not su¢ cient to describe the behavior of monetary policy impacts on

output and in‡ation dynamics.

As explained in Section 3.3, the transmission mechanism or at least its

consequences are better understood by analyzing the variance decomposition

with respect to structural shocks, than by going through the changes in the

values of parameters. The exceptions to this are parameters that directly

multiply a shock in the macro-equation of a core variable (as is the case with

mp,sm, and y

sm).

Our monetary policy shock describes only conventional monetary policy

shocks. The decreasing role of conventional monetary policies after 2008 Q3

is probably due to the emergence of unconventional monetary policy around

the same period. This change in the policy regime may have in‡uenced

money related parameters in the ‡exible-price output equation (y

sm,y

m=

(1)()(1a1)

(a1())(1)++and y

c=(1) ln("=("1))

(a1())(1)++).

The output RMSD comparison (Fig. 10) is not a¤ected by the change

in policy that occurred during the last quarter of 2008. 2008 Q3 is not the

end of the crisis, even if the impact of money and monetary policy on output

declines. Uncertainty and risk aversion are ever-present in the economy. This

probably explains why Model 2 has a better predictive power for output than

Model 1 during the GFC.

Contrary to other studies, such as Ireland (2004), Andrés et al. (2006),

and Andrés et al. (2009), our analysis indicates that money did have a sig-

21

ni…cant role to play in the GFC. This may con…rm the predictive abilities of

Model 2 during crisis periods.

To better understand the relationship between the role of money and

monetary policy during the …nancial crisis, it may be useful to introduce the

evolution of the interest rate spread over the period as an indication of the

uncertainty level. This spread12 provides an assessment of counterparty risk

from interbank lending, re‡ecting both liquidity and credit risk concerns.

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

6

7

8

9

10

11

Short run rol e of money on output (%)

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

-0.5

0

0.5

1

1.5

2

Spread EUR IBOR-Bubil l (%)

Role of money on output (ST)

Spread E uribor-Bubi ll

Figure 11: Comparison between the role of money on output (short-run

variance decomposition, Model 2) and the Euribor–Bubill spread

Fig. 11 indicates that the dynamics of the short-run impact of money on

output during the GFC and the interest rate spread are positively related

(except in 2009 Q1 and after 2009 Q4). This relationship underscores the

link between …nancial risk and the role of money on output.

In the same vein, Fig. 12 and Fig. 13 show that the impact of monetary

policy on output and in‡ation follows the same direction as the spread. These

impacts are signi…cant and increase with the crisis, from 2007 Q1 up to the

peak of the GFC (2008 Q3). They diminish rapidly and signi…cantly after

2008 Q3, remaining at a lower but still meaningful level until the end of

the period (2011 Q1). This sharp decline coincides with the introduction of

unconventional monetary policies.

12 The spread is measured as the di¤erence between the three-month Euribor and a

short maturity bond. As a European bond does not exist, we choose the one-year Bubill

(Germany) as short-term Treasury bills.

22

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

10

20

30

S hort run role of monetary polic y on output (% )

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

-2

0

2

S pread Euri bor-Bubil l (% )

Role of monetary policy on output (ST)

S pread Euri bor-Bubil l

Figure 12: Comparison between the role of monetary policy on output (short-

run variance decomposition, Model 2) and the Euribor–Bubill spread

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

20

30

40

50

S hort run role of monetary pol icy on infla tion (% )

07Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 10Q1 10Q2 10Q3 11Q1

-1

0

1

2

S pread E uribo r-Bubi ll (% )

Role of monetary policy on inflation (S T)

S pread Euri bor-Bubil l

Figure 13: Comparison between the role of monetary policy on in‡ation

(short-run variance decomposition, Model 2) and the Euribor–Bubill spread

23

When Lehman Brothers and other major …nancial institutions failed in

2008 Q3, the credit freeze in the money market brought the global …nancial

system to the brink of collapse. The Federal Reserve, the ECB, and other

central banks purchased almost 3 trillions dollars of government debt and

troubled private assets from banks over the last quarter of 2008. That was

the largest liquidity injection into the credit market and the largest uncon-

ventional monetary policy action in world history. These measures explain

the fall of the spread and the sharp decline in the impact of monetary policy

on output and in‡ation after this period (Fig. 12 and Fig. 13).

Uncertainty started to decrease in the aftermath of these policy actions,

decreasing the short-run impact of money on output following the peak of

the spread in 2008 Q3 (Fig. 11).

6 A comparison of the three crises

In order to compare the three crises, we analyze the impulse responses of

output, output gap and in‡ation to money and monetary policy shocks over

key periods. The comparison is for both models as far as the monetary

policy shock is concerned. A comparison of variance decompositions over the

di¤erent crises is also useful to better understand the respective roles of the

shocks.

6.1 Impulse response functions

Besides indicating the impact of di¤erent shocks, the IRF give the opportu-

nity to quantify the persistence of the shocks over each period.

The impulse response functions of in‡ation are reported in percentage

points, whereas the other impulse responses are reported in percentage devi-

ations from each variable’s period-speci…c linear trend (see Section 2). The

selected dates correspond to the two most relevant peaks of each crisis.13

Fig. 14 shows the impulse response functions of output, ‡exible-price

output, output gap and in‡ation following a 1% increase in the money shock’s

standard deviation (Model 2). Interestingly, a positive money shock implies

almost the same response of output for the ERM crisis and the GFC (0.3%),

at least on impact, whereas the on-impact response of output for the Dot-com

crisis is lower (0.15%–0.2%). Yet, the impact on the ‡exible-price output is

stronger for the GFC than for the other crises.

13 We do not present all the impulse response functions over the three crises, for each

period, and for both models; because that would be too heavy a task. However, all these

results are available upon request.

24

020 40

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035 Inflation

020 40

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35 Output

020 40

0

0.01

0.02

0.03

0.04

0.05

0.06 Output gap

1990Q4 1992Q3 2000Q3 2002Q2 2007Q3 2008Q3

Figure 14: Comparison of impulse response functions following a 1% standard

deviation money shock (Model 2) over the three crises

The persistence of this shock is higher for the GFC than for the other

crises. It is a re‡ection of the fact that it takes more time for output and

‡exible-price output to reach their steady-state values over the GFC than

over the other two crises.

The impact of the money shock on the output gap di¤ers between crises.

It is more signi…cant in the …rst few quarters following the peaks of the ERM

crisis (almost 0.06%) than in the …rst few quarters following the peaks of the

Dot-com crisis (0.03%) and the GFC (0.015%).

The response of in‡ation to a 1% money shock is higher during the ERM

crisis than during the two other crisis periods. These di¤erences may be at

least partly explained by the fact that during the ERM crisis, the uncertainty

about the exchange rate was higher than for other crisis periods.

As for output and ‡exible-price output, the responses of in‡ation to a

money shock are more persistent over the GFC than over other crises.

1 2 3

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0Infl ation

1 2 3

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0Output

1 2 3

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0Output gap

1990Q4 1992Q3 2000Q3 2002Q2 2007Q3 2008Q3

Figure 15: Comparison of impulse response functions following a 1% standard

deviation monetary policy shock (Model 2) over the three crises

25

Fig. 15 shows an enlargement of the impulse response functions to a

1% increase in the monetary policy shock’s standard deviation in the non-

separable framework (Model 2).

The responses of ‡exible-price output to a monetary policy shock are not

shown since they are about nil (of the order of 1016) for all key periods.

The response of output to a monetary policy shock di¤ers between time

periods. There is a decrease on impact from about 0.4% in 2007 Q3 to 0.65%

in 1990 Q4. The impact of monetary policy on output was, therefore, stronger

over the ERM crisis period than the Dot-com crisis, and stronger over the

Dot-com crisis than the GFC period. Similar implications are true for the

output gap. It is also true for the in‡ation rate, but to a lesser extent. The

exchange rate channel may have had a more signi…cant impact on monetary

policy, and on transmission channels, during the ERM crisis than during the

more recent periods.

After a positive technology shock, output and ‡exible-price output in-

crease, the output gap slightly decreases, and in‡ation decreases (…gures not

shown). Interestingly, the sensitivity of output to a technology shock is sig-

ni…cantly higher during the GFC (in 2008 Q4 and 2010 Q2) than during the

two other crises.

The impact of a price-markup shock on output and in‡ation decreases

from 1990 to 2010. Regardless of the period, a positive price-markup shock

leads to an increase in in‡ation, but to a decrease in output and the output

gap. The impact of a price-markup shock to ‡exible-price output is nil (of

the order of 1016).

1 2 3

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0Infl ation

1 2 3

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0Output

1 2 3

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0Output gap

1992Q3 (1) 1992Q3 (2) 2002Q2 (1) 2002Q2 (2) 2008Q3 (1) 2008Q3 (2)

Figure 16: Comparison of impulse response functions following a 1% standard

deviation monetary policy shock over the three crises (Model 1: solid lines;

Model 2: dashed lines)

Fig. 16 shows an enlargement of the impulse response functions to a

monetary policy shock in the separable and non-separable frameworks, that

26

is, a comparison of the responses of output, output gap and in‡ation between

Model 1 and Model 2. These impulse response functions are focused only on

the peak-point in each crisis that appears to be more critical.

The impact of a monetary policy shock on output, output gap and in‡a-

tion in the baseline model is typically smaller than in the model including

money. However, the persistence of the monetary policy shock does not

appear to be signi…cantly a¤ected by the inclusion of money in the model.14

6.2 Variance decompositions

During the GFC, money has a relatively signi…cant impact on output and

‡exible-price output whereas it is smaller during the ERM and Dot-com

crises, especially in the short-term. These impacts are signi…cantly stronger,

especially during the GFC (between 6.5% and 11%), than those of Ireland

(2004), Andrés et al. (2006), and Andrés et al. (2009), who found a negligible

e¤ect of money on output (between 0–2%). However, the impact of money

on in‡ation variability is very small.

Over all the three crises analyzed in this paper, the short-run impact

of monetary policy on output remains high (around 15–30%), but its value

‡uctuates more during the GFC, indicating the higher disruptive e¤ect of

this crisis as compared with the others.

The short-run impact of monetary policy shocks on in‡ation variability

also remains high over the three crises (15–50%), again with higher ‡uctua-

tions during the GFC (about 25–50%).

A focus on the GFC (Section 5.3) con…rms the link between the spreads

that measure uncertainty in the …nancial market and the impact of the money

and monetary policy shocks on the dynamics of the economy.

Finally, in terms of output forecasting, Model 2 generally performs better

than Model 1 over crisis periods, especially during periods of high uncertainty.

The results concerning the …nancial crisis are striking in that respect (Fig.

10).

7 Conclusion

This paper studied the role of money and monetary policy during crisis peri-

ods in the Eurozone, as well as the forecasting performances and abilities of

two models. We use two DSGE models - one baseline separable model, as in

Galí (2008), and one with non-separable preferences between consumption

14 The responses of ‡exible-price output to a monetary policy shock are not shown since

they are not signi…cant (of the order of 1016 ) for both models.

27

and real money balances, and with a money augmented Taylor rule. The

study is conducted over three crisis periods running from 1990 through 2011,

including the European ERM crisis (1992), the Dot-com crisis (2001) and

the GFC (2007).

We tested both models by using successive Bayesian estimations so as

to obtain empirical estimates of the variations of the micro-parameters. We

ran simulations to obtain variance decompositions from both models over

the three crises and capture short- and long-run dynamics that are generally

hidden in longer sample sizes. We also ran DSGE forecasts to compare the

out-of-sample forecasting performances of both models over the crises, and

analyze the responses of output, output gap and in‡ation to shocks.

Our analysis indicates that the impact of money shocks on output varia-

tions seems to increase during crises, especially during the GFC. This impact

was higher during the GFC than the ERM and Dot-com crises. The impact

of conventional monetary policy is also a¤ected during crises. As far as the

GFC is concerned, the impact appears to increase in the beginning of the

crisis, but decreases sharply afterwards.

In addition, our results demonstrate that during these periods, the non-

separable model generally provides better out-of-sample forecasts of output

(and sometimes in‡ation) than the baseline model, in terms of RMSE. Gi-

acomini and White (2006) tests demonstrate that the non-separable model

outperforms the baseline model during the ERM and GFC crises.

The results also underscore the fact that the impact of money and mone-

tary policy on output variability diminishes signi…cantly following what ap-

pears to be the peak of the GFC (2008 Q3). In‡ation variability does not

seem to be a¤ected directly by money variables. It is mainly explained by

the monetary policy and markup shocks in the short run, and essentially by

the markup shock in the long run, as found in the literature.

The response of output to a money shock is stronger at the peak of the

GFC than at the peak of the ERM and Dot-com crises. And the persistence

of the output response to a money shock is higher over the GFC than over

the other crises.

Lastly, it is interesting to note that the response of ‡exible-price output to

a money shock during the GFC is about as strong as the response of output

itself. In addition, it is signi…cantly stronger and longer lasting than it does

during other crises. Yet, a monetary policy shock appears to have no e¤ect

on ‡exible-price output for all crises (in both models).

The …ndings of our paper can be a valuable input for a central bank in its

decision-making process as far as macroeconomic forecasting is concerned, at

least during crisis periods.

Finally, our results also provide some clues regarding the dynamics of the

28

economy that may help inform central banks, markets, and policy regulators.

For example, the more signi…cant than generally expected role of real money

balances during crises, as well as the changing role of monetary policy, are

important indicators.

8 Appendix

A Parameters description

See the online appendix for a detailed description of the models.

Intertemporal deterministic discount factor.

Share of worked hours in the production process.

Probability of …rms that keep their prices unchanged (Calvo,1983).

Inverse elasticity of substitution between consumption

and real money balances.*

Inverse intertemporal elasticity of substitution, which is also, in our

framework, the coe¢ cient of relative risk aversion.

bRelative weight of real money balances in utility.*

Inverse Frisch elasticity of labor supply.

"Elasticity of substitution between individual goods.

iInterest rate smoothing.

In‡ation coe¢ cient in the monetary policy rule.

xOutput gap coe¢ cient in the monetary policy rule.

In‡ation target.

aPersistence of the technology shock.

pPersistence of the preference shock.

iPersistence of the interest-rate shock.

mPersistence of the money shock.*

aStandard error of the technology shock.

pStandard error of the preference shock.

iStandard error of the monetary policy shock.

mStandard error of the money shock.*

* Parameter equal to zero in Model 1.

Table 1: Description of the parameters

29

B Calibration and priors

Both models’parameters are calibrated identically (Table 2). The monetary

policy rule is an ad hoc reaction function and completely dependent on the

monetary authority.

Following standard conventions, we calibrate beta distributions for pa-

rameters 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.

Priors Priors

Law Mean Std. Law Mean Std.

B0.33 0.05 aB0.75 0.10

B0.66 0.05 pB0.75 0.10

N2.00 0.05 iB0.50 0.10

N1.25 0.25 mB0.75 0.10

N2.00 0.10 aI0.04 2.00

iB0.50 0.10 pI0.04 2.00

N3.00 0.25 iI0.04 2.00

xN1.50 0.25 mI0.04 2.00

mp N1.50 0.25

Note: Nstands for Normal distribution, Bfor Beta

distribution, and Ifor Inverted-Gamma distribution.

Table 2: Priors summary

The calibration of is inspired by Rabanal and Rubio-Ramírez (2005)

and by Casares (2007). They choose risk aversion parameters of 2.5 and 1.5,

respectively. In line with these values, we consider that = 2 corresponds

to a standard risk aversion, as in Benchimol and Fourçans (2012). We adopt

the same priors in both models with the same risk aversion calibration.

As in Smets and Wouters (2003), the standard errors of the innovations

are assumed to follow inverse gamma distributions. Furthermore, we choose

a beta distribution for shock persistence parameters (as well as for the back-

ward component of the Taylor rule) that should be less than one.

The calibration of ,,,, and "comes from Galí (2008) and Casares

(2007). The relative weight of real money balances in the utility function

30

(b) is calibrated to 0.25, as in Benchimol and Fourçans (2012), and the in-

‡ation target parameter is calibrated to an annual target of 2%. The

smoothed Taylor-type rule (i,,x, and mp) is calibrated following An-

drés et al. (2009), Barthélemy et al. (2011), and Benchimol (2014,2015);

analogue priors as those used by Smets and Wouters (2003) for the monetary

policy parameters. In order to take into consideration possible changes in

the behavior of the central bank, we assign a higher standard error for the

coe¢ cients of the Taylor rule. v(the non-separability parameter) must be

greater than one. imust be greater than one, insofar as this parameter

depends on the elasticity of substitution of money with respect to the cost

of holding money balances, as explained in Söderström (2005); while still

informative, this prior distribution is dispersed enough to allow for a wide

range of possible and realistic values to be considered (that is, > > 1).

The calibration of the shock persistence parameters and the standard

errors of the innovations follows Smets and Wouters (2003), where a much

lower mean is adopted for i. All the standard errors of shocks are assumed to

be distributed according to inverted gamma distributions, with prior means

of 0.04. The latter law ensures that these parameters have a positive support.

The autoregressive parameters are all assumed to follow beta distributions.

Except for monetary policy shocks, all these distributions are centered around

0.75. We take a common standard error of 0.1 for the shock persistence

parameters, as in Smets and Wouters (2003).

31

C Posteriors

Fig. 17, Fig. 18, and Fig. 19 present the Bayesian estimations15 of both

models. The solid and dashed lines represent the results for Model 1 and

Model 2, respectively.

The estimation of the implied posterior distribution of the parameters

for each sample size and each model is done using the Metropolis-Hastings

algorithm (three distinct chains, each of 5000 draws; see Smets and Wouters

(2007), and Adolfson et al. (2007)). Average acceptation rates per chain are

around 0.25, as settled by the literature; priors and posteriors distributions

are not presented, but are available upon request.

0.35

0.4

0.45

1.6

1.8

2

0.5

1

1.5

0.4

0.6

0.8

1.8

1.9

2

1.6

1.8

2

1

2

3

1.36

1.38

1.4

0.65

0.7

0.25

0.3

0.35

0.96

0.98

1

0.9

0.95

1

90Q1 90Q3 91Q2 92Q1 92Q3 93Q2 94Q1

0.35

0.4

0.45

90Q1 90Q3 91Q2 92Q1 92Q3 93Q2 94Q1

0.7

0.75

0.8

Mo d el 1 Mo de l 2

Figure 17: Parameter values for both models during the ERM crisis

15 The results of parameter estimations and validation and robustness tests can be pro-

vided upon request. All Student tests are above 1:96 and parameter estimations are stable

over time.

32

0.4

0.45

0.5

1.6

1.8

2

0

1

2

0.65

0.7

1.8

1.9

2

1.6

1.8

2

1

2

3

1.36

1.38

1.4

0.65

0.7

0.3

0.32

0.95

1

0.96

0.97

0.98

99Q1 99Q3 00Q2 00Q4 01Q3 02Q2 03Q1

0.35

0.4

99Q1 99Q3 00Q2 00Q4 01Q3 02Q2 03Q1

0.7

0.8

0.9

Mo d el 1 Mo de l 2

Figure 18: Parameter values for both models during the Dot-com crisis

0.4

0.45

0.5

1.6

1.8

2

0.5

1

1.5

0.5

0.6

0.7

1.8

1.9

2

2

2.5

3

1

2

3

1.3

1.35

1.4

0.65

0.7

0.25

0.3

0.35

0.96

0.98

1

0.96

0.98

1

07Q1 07Q3 08Q2 08Q4 09Q3 10Q2 11Q1

0.35

0.4

0.45

07Q1 07Q3 08Q2 08Q4 09Q3 10Q2 11Q1

0.85

0.9

0.95

Mo d el 1 Mo de l 2

Figure 19: Parameter values for both models during the GFC

33

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