Monetary asmmetries without (and with) price stickiness.
Date: 2024-04-19
Institutions: European Central Bank
Subjects: economic fluctuation, economic model, fixing of prices, macroeconomics, monetary policy, price fluctuation

Working Paper Series 

Ivan Jaccard 

Monetary asmmetries without 
(and with) price stickiness 

No 2928 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank 
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

 
 
 
Abstract

The evidence suggests that monetary policy transmission is asymmetric over the
business cycle. Interacting ﬁnancing frictions with a preference for liquidity provides
an explanation for this fact. Our mechanism generates monetary asymmetries in a
model that jointly reproduces a set of asset market and business cycle facts. Account-
ing for the joint dynamics of asset prices and business cycle ﬂuctuations is key; in a
variant of the model that is unable to produce realistic macro-ﬁnance implications,
monetary asymmetries disappear. Our results suggest that asymmetries in the trans-
mission mechanism critically depend on the macro-ﬁnance implications of monetary
policy models, and that resorting to nonlinear techniques is not suﬃcient to detect
monetary asymmetries.

Keywords: Money Demand; Nonlinear Solution Methods; Asset Pricing in
DSGE Models; Term Premium; Stochastic Discount Factor.

JEL: E31, E44, E58.

•

•

ECB Working Paper Series No 29281Non-technical Summary

Asymmetries in the monetary transmission mechanism is a classical topic in macro-
economics that dates back to the Great Depression. In recent years, a renewed interest
in this question has emerged, as a large body of novel empirical work has conﬁrmed that
the eﬀects of monetary policy are not constant over time but vary over the business cycle.
Understanding the root cause of this state dependence is an issue of central importance for
policymakers. Indeed, the risk is that asymmetries in the transmission mechanism could
reduce or amplify the eﬀectiveness of monetary policy, thereby impairing the ability of
central banks to stabilize the economy.

Given the major inﬂuence of aggregate supply in recent years, this article studies the
transmission of monetary policy when supply shocks are the main source of business cycle
In our artiﬁcial economy, the type of negative supply shocks observed in
ﬂuctuations.
recent years gives rise to a large increase in lending rates as well as a contraction in credit.
Our main conclusion is that monetary policy is particularly powerful during these periods
of tight credit conditions and elevated lending rates, which are also times of subdued
economic growth. Therefore, a main implication of our work is that monetary policy has
been a powerful tool in the post-COVID-19 era. We also provide a formal empirical test of
our model’s main theoretical prediction.

We study the transmission mechanism of the type of liquidity operations that have
been used by central banks since the global ﬁnancial crisis. These measures, which are
transmitted via the bank lending channel, rely on the impact of the aggregate liquidity
conditions on the quantity of loanable funds available in the economy. According to this
transmission channel, a reduction in aggregate liquidity implemented by the central bank
reduces the supply of loanable funds in the banking sector. A reduction in the supply of
funds then raises bank lending rates. The resulting tightening of credit conditions, in turn,
forces ﬁrms to reduce employment and investment, leading to a reduction in both economic
activity and inﬂation.

Monetary asymmetries stem from a preference for liquidity, which gives rise to a lower
bound on bank interest rates. Since agents have the option to hold money in the form of
cash, the deposit rate oﬀered by banks is bounded below. The nonlinearity induced by this
lower bound reduces the eﬀectiveness of liquidity injections during periods of high credit
availability because banking rates are close to the lower bound in those states of the world.
In contrast, a tightening of monetary policy has larger eﬀects on the real economy during
periods of credit stress and high bank lending rates when the economy is away from the

ECB Working Paper Series No 29282lower bound. We also study the case in which the central bank issues a digital currency
and show that monetary asymmetries remain signiﬁcant.

Our main takeaway is that the size of this asymmetry critically depends on the model’s
ability to generate interest rate risk. In a model that reproduces a term premium of the
magnitude observed in recent years, the volatility of inﬂation, as well as the volatility and
the level of nominal bank lending rates, this asymmetry signiﬁcantly alters the conduct of
monetary policy. The exact same monetary policy shock has an eﬀect on output that is
much greater in times of credit shortage and subdued economic growth than during periods
of ample credit availability when the economy is booming.

Interestingly, this asymmetry disappears in the version of the model that fails to gen-
erate realistic amounts of interest rate risk. Without realistic ﬂuctuations in real interest
rates, the term premium falls to zero and the eﬀects of monetary policy are symmetric over
the cycle. Indeed, without real interest rate risk, lending rates become too smooth relative
to the data. In this case, the nonlinearity induced by the lower bound on interest rates
becomes irrelevant, and asymmetries in the transmission mechanism disappear.

Finally, for monetary asymmetries to play a signiﬁcant role, we show that it is suﬃcient
to consider a model in which the welfare cost of business cycle ﬂuctuations remains relatively
small, yet much larger than Professor Lucas’ original estimate.

ECB Working Paper Series No 292831 Introduction

Asymmetries in the monetary transmission mechanism is a classical topic in macroeco-
nomics that dates back to the Great Depression. In recent years, a renewed interest in
this question has emerged, as a large body of novel empirical work has conﬁrmed that
the eﬀects of monetary policy are not constant over time but vary over the business cycle.
Understanding the root cause of this state dependence is an issue of central importance for
policymakers. Indeed, the risk is that asymmetries in the transmission mechanism could
reduce or amplify the eﬀectiveness of monetary policy, thereby impairing central banks’
ability to stabilize the economy (e.g. Mishkin (2009)).

This article revisits this classical question in light of more recent developments. Indeed,
the 2007-2009 Global Financial Crisis (GFC) has considerably impacted the conduct of
monetary policy. First, in response to the Subprime and Sovereign Debt Crises in Europe,
the major central banks implemented measures aimed at addressing impairments in credit
markets with the objective to stimulate lending to the real economy (e.g. Bernanke (2009);
Trichet (2009)). Second, the GFC was followed by an unusual period of very low interest
rates, as monetary policy on both sides of the Atlantic was constrained by the eﬀective
lower bound. Although interest rate policies only played a limited role in the post-GFC
era, monetary policy was still the main game in town as central banks resorted to liquidity
injections of an unprecedented magnitude to stimulate the economy.

This article studies monetary asymmetries by analyzing the eﬀect of liquidity injections
to households on bank lending rates, credit and economic activity. Relative to the pre-GFC
benchmark model (e.g. Smets and Wouters (2007)), the ﬁrst main diﬀerence is that we
model liquidity injections in a representative agent model in which shocks to money supply
aﬀect the quantity of loanable funds available in the economy. The second key diﬀerence is
that we introduce an endogenous choice between bank deposits and cash holdings. Owing
to a preference for liquidity, agents ﬁnd it optimal to hold a small fraction of their wealth
in the form of cash. This demand for liquidity in turn depends on the opportunity cost
of holding cash instead of bank deposits. Under standard assumptions, this preference for
liquidity gives rise to a nonlinear money demand. We then show that this nonlinearity
produces an eﬀective lower bound on bank lending rates, as the possibility to hoard money
in the form of cash prevents banks from charging negative rates.

The third main diﬀerence is that we study monetary policy in an environment in which
ﬁnancing constraints per se are a source of monetary non-neutrality. As ﬁrms need to pay
workers in advance of production, the key is that ﬁnancing frictions introduce a distortion

ECB Working Paper Series No 29284or wedge in the labor market. This "labor wedge" is in turn the main channel via which
monetary policy is transmitted to the real economy. Given that our transmission mechanism
works through this labor wedge, money is close to neutral in the absence of ﬁnancing
frictions.
Indeed, our model reduces to a real business cycle model with money in the
utility function in this limiting case.

How does monetary policy aﬀect the real economy? An increase in money supply raises
the quantity of loanable funds available in the economy. Equilibrium in the credit market
in turns implies a reduction in bank lending rates, as the supply of funds increases. In
a model in which ﬁrms need to ﬁnance inputs in advance of production, the key is that
the size of the labor wedge is determined by the level of bank lending rates. Variations
in lending rates therefore aﬀect aggregate supply via this labor wedge stemming from the
presence of ﬁnancing frictions.

Why is monetary policy transmission asymmetric? Our main ﬁnding is that liquidity
injections that are transmitted via this channel are particularly eﬀective during credit
crunches. Periods of credit crunches, or credit stress, are times in which credit conditions
are tighter than usual. Monetary policy is particularly powerful in those states of the world
because the scarcity of credit leads to elevated lending rates. High lending rates in turn
imply a high opportunity cost of holding money in the form of cash. Consequently, in
response to a monetary injection, agents ﬁnd it optimal to channel a larger fraction of this
increase in money supply into the banking sector, as they are reluctant to hold cash. In
those states of the world, the shock therefore has a particularly strong eﬀect on the supply
of loanable funds. The key is that a larger increase in the supply of loanable funds in
turn leads to a more pronounced decline in lending rates than in normal times. Since a
decline in lending rates reduces the labor wedge, the stimulative eﬀect on production is
more pronounced during periods of credit scarcity.

Monetary policy is less eﬀective during periods of ample credit availability because the
opportunity cost of holding cash is low. In those states, credit supply is higher than usual,
which in turn implies low lending rates. Since the opportunity cost of holding cash is
low, and owing to their preference for liquidity, agents have little incentive to lend funds
to entrepreneurs. Consequently, monetary policy becomes ineﬀective because liquidity
injections do not reach the real economy, as agents prefer to hoard liquidity instead. In
those states of the world, liquidity injections only have a muted impact on credit supply.
Consequently, the decline in lending rates is smaller than during periods of credit stress. A
smaller decline in lending rates in turn imply a more muted eﬀect on the labor wedge and
hence production.

ECB Working Paper Series No 29285We ﬁnd that the size of this asymmetry critically depends on the model’s ability to
generate interest rate risk. In a model that reproduces a term premium of the magnitude
observed in recent years, the volatility of inﬂation, as well as the volatility and the level of
nominal bank lending rates, this asymmetry signiﬁcantly alters the conduct of monetary
policy. The exact same monetary policy shock has an eﬀect on output that is much greater
in times of credit shortage than during periods of ample credit availability.

Interestingly, this asymmetry disappears in the version of the model that fails to gen-
erate realistic amounts of interest rate risk. Without realistic ﬂuctuations in real interest
rates, the term premium falls to zero and the eﬀects of monetary policy are symmetric over
the cycle. Indeed, without real interest risk, lending rates become too smooth relative to
the data. In this case, the nonlinearity induced by agents’ preference for liquidity becomes
irrelevant and asymmetries in the transmission mechanism disappear.

For asymmetries to play a signiﬁcant role, we also ﬁnd that it is suﬃcient to consider
a model in which the welfare cost of business cycle ﬂuctuations remains relatively small,
yet much larger than Lucas’ original estimate. To illustrate this point, we calculate the
additional income that agents would demand as compensation for having to live in a world
subject to business cycle ﬂuctuations. We ﬁnd that this "business cycle ﬂuctuation pre-
mium" amounts to about 1.88% of total income per quarter in the model that matches the
data. This premium falls to 0.023% in the variant of the model that is unable to produce
realistic macro-ﬁnance implications and in which monetary transmission is symmetric over
the cycle.1

The asymmetry documented in our study continues to play a major role if we introduce
Calvo staggered contracts (Calvo, 1983), which is a widely used speciﬁcation of nominal
rigidities in the New Keynesian literature. The introduction of price stickiness also con-
siderably ampliﬁes the average eﬀectiveness of liquidity injections. In addition, we discuss
the case of a more general preference speciﬁcation, provide an empirical test of the main
model mechanism, and consider the case of demand shocks.

Finally, we study the case in which the central bank is able to remunerate cash. This
latter experiment can be motivated by the ongoing discussions with regards to central
bank digital currencies (CBDCs). Indeed, if CBDCs were introduced, central banks could
remunerate cash by paying an interest rate on virtual money.

This paper is structured as follows. A literature review is provided in Section 2. The
model economy is described in Section 3, whereas the calibration and results are discussed

1While the methodologies are not directly comparable, in Lucas (2003) the welfare cost measure amounts

to 0.05% of consumption per year.

ECB Working Paper Series No 29286in Sections 4 and 5, respectively. The monetary policy transmission mechanism is de-
constructed in Section 6. The main result of the paper, namely the state dependence of
monetary policy transmission is discussed in Section 7. The robustness analysis as well
as the version of the model with price stickiness are presented in Section 8. Section 9
concludes.

2 Literature Review

As regards evidence on asymmetries in the transmission of monetary policy, two main
conclusions emerge from the literature: (i) there is ample evidence showing that the eﬀects
of monetary policy are not symmetric over the business cycle, and (ii) whether monetary
policy is more or less eﬀective during recessions is still a widely debated question. Given
this lack of consensus, Section 8.3 provides empirical support to our key model mechanism.
The work of Peersman and Smets (2005) studies asymmetries in the transmission mech-
anism of monetary policy in the euro area using data from 74 manufacturing industries for
the period from 1980 to 1998. These authors ﬁnd that monetary policy has stronger eﬀects
on output in a cyclical downturn than in a boom and attribute this asymmetry to factors
related to the ﬁnancial structures of ﬁrms, such as size for instance.

Lo and Piger (2005) investigate the response of output to monetary policy in the
United States using a regime switching model. These authors ﬁnd strong evidence that
monetary policy has larger eﬀects on output during recessions than during expansions.
Garcia and Schaller (2002) also resort to regime switching techniques and show that in-
terest rate changes have a stronger eﬀect on output growth during recessions than during
expansions. A classic explanation for the ﬁndings documented by this strand of literature
is that asymmetries are due to credit market frictions (e.g. Gertler and Gilchrist (1994)).
Santoro, Petrella, Pfajfar and Gaﬀeo (2014) focus on the period from 1982 to 2008 and
ﬁnd that monetary policy has larger eﬀects on output during recessions than during booms.
At the same time, they do not ﬁnd evidence of asymmetries in the response of inﬂation to
monetary policy shocks. These authors formalize their empirical results by developing a
general equilibrium model with price stickiness and loss averse consumers.

In contrast to the above-mentioned strand of literature, Tenreyro and Thwaites (2016)
ﬁnd evidence that monetary policy shocks have more powerful eﬀects on output and in-
ﬂation in an expansion than in a recession. These authors also ﬁnd that contractionary
shocks are more powerful than expansionary ones. Relative to Santoro et al. (2014), one
important diﬀerence is that these authors analyze the eﬀects of shocks occurring in the

ECB Working Paper Series No 29287period from 1969 to 2002, and study the response of variables up to 5 years later.

The results documented by Alpanda, Granziera and Zubairy (2021) using a sample
of 18 advanced economies and data until 2018 are consistent with those reported by
Tenreyro and Thwaites (2016). These authors also develop a parsimonious partial equi-
librium model to analyze the channels that could rationalize the empirical facts that they
uncover.

Bruns and Piﬀer (2023) argue that estimating rather than calibrating key parameters
in Smooth Transition models is crucial to study monetary asymmetries. Applying their
methodologies using data from 1979 to 2020, they ﬁnd that monetary policy is more eﬀective
during expansions than during recessions.2

the eﬀectiveness of
Our work is also related to a literature that
monetary policy during periods of very low interest
In particular,
Ahmed, Borio, Disyatat and Hofmann (2021) ﬁnd that the eﬀectiveness of monetary pol-
icy declined after the GFC, which corresponds to a period of very low interest rates. One
possible explanation for their ﬁndings is that the eﬀects of interest rates on consumption
and investment could be nonlinear.

studies

rates.

Harding, Lindé and Trabandt (2022) resolve the missing deﬂation puzzle by considering
the eﬀects of discount factor shocks in a model in which nominal rigidities are combined
with Kimball aggregators (Kimball (1995)). The disconnect between inﬂation and out-
put observed in the aftermath of the GFC suggests that nonlinearities play a key role in
macroeconomics. Indeed, during the 2007-2009 ﬁnancial crisis, the fall in activity was ac-
In contrast, during the recovery
companied by a relatively modest decline in inﬂation.
phase, inﬂation dynamics remained subdued (e.g. Hall (2011)).

In a related study, Andreasen, Caggiano, Castelnuovo and Pellegrino (2021) show that
uncertainty shocks generate a larger contraction during periods of recessions. As in Harding
et al. (2021) and Santoro et al. (2014), this strand of literature highlights the importance
of price rigidities. In contrast, our main result is derived in a ﬂexible price model in which
ﬁnancing constraints are the only source of non-neutrality.

Another literature focuses on the eﬀects of the ﬁnancial cycle on the monetary policy
transmission mechanism. Aikman, Lehnert, Liang and Modugno (2020) study the inﬂu-
ence of the credit cycle on the eﬀectiveness of monetary policy. These authors ﬁnd that
a contractionary monetary policy shock has the usual eﬀect on GDP and inﬂation during
periods of low credit-to-GDP gaps. In contrast, monetary policy becomes ineﬀective when

2A previous version of their paper was circulated under the title: "US monetary policy is more powerful

in recessions: A new approach to Smooth Transition Vector Autoregressions".

ECB Working Paper Series No 29288credit is above trend. Alpanda and Zubairy (2019) focus on the impact of household debt
on the transmission mechanism using data from 1951 to 2015 and ﬁnd that monetary policy
is less powerful during periods of high household debt.

One main lesson from the evidence accumulated over the last 30 years is that ﬁnanc-
ing frictions, in particular frictions aﬀecting access to credit, inﬂuence the transmission of
monetary policy (e.g. Kashyap, Lamont and Stein (1994); Gertler and Gilchrist (1994)).
Following the seminal contribution of Bernanke and Gertler (1989), a vast strand of litera-
ture has interpreted this line of evidence by developing models in which lending is subject to
a "costly state veriﬁcation" problem (Townsend (1979)). Relative to this approach, we in-
troduce ﬁnancing constraints by assuming that ﬁrms need to pay workers and rental costs in
advance of production. By producing a labor wedge (e.g. Jermann and Quadrini (2012)),
ﬁnancing frictions create a channel of monetary policy transmission that is independent of
nominal rigidities.

Since ﬁrms need to pay workers in advance, our approach also builds on the cost chan-
nel of monetary policy literature initiated by the work of Barth and Ramey (2002). Rel-
ative to the cost channel literature, a key diﬀerence is that in our environment prices
increase in response to an accommodative monetary policy shock.
In the ﬂexible price
version, the dynamics of prices is entirely determined by the demand for real money
In the New Keynesian version, as in
balances, and not by the marginal cost of ﬁrms.
Christiano, Eichenbaum and Evans (2005) and Ravenna and Walsh (2006), the dynamics
of prices depends on the marginal cost, which is in turn aﬀected by borrowing costs.

Relative to the ﬁnancial accelerator literature, another key diﬀerence is that ﬁnanc-
ing constraints create a wedge that not only aﬀects investment but also labor demand.
This departure from the standard approach can be motivated by a growing litera-
ture that has uncovered a link between credit market frictions and employment (e.g.
Chodorow-Reich (2014)).
In particular, the evidence available for Europe strongly sug-
gests that credit market frictions aﬀect the real economy through their impact on the labor
market (e.g. Bentolila, Jansen and Jiménez (2018); Popov and Rocholl (2018)).

Whereas credit frictions are the only source of monetary non-neutrality in the ﬂexible
price benchmark, the asymmetry that we obtain critically depends on the lower bound on
interest rates. The evidence documented by Heider, Saidi and Schepens (2019) conﬁrms
that the lower bound plays an important role in the euro area economy. Indeed, banks are
reluctant to pass on negative rates to depositors. As a result, bank lending rates remained in
positive territory, even when monetary policy rates turned negative. The positive skewness
in the distribution of lending rates is also consistent with the view that bank lending rates

ECB Working Paper Series No 29289are bounded below. As shown by Ordoñez (2013), while stronger in economies with less
developed ﬁnancial systems, this positive skewness is observed in many countries.

Relative to the macroeconomic literature on monetary policy, one objective of this paper
is to reproduce some empirical facts about interest rates. The work of Den Haan (1995)
is probably one of the ﬁrst attempts to study the term structure of interest rates in a
model with production and a role for monetary policy. The model developed by the author
replicates the high persistence of interest rates observed in the data. Matching the behavior
of bond prices is however a challenge.

A more recent literature aims to explain the term structure of interest rates, the
term premium as well as the behavior of bond prices within New Keynesian models.
Hördahl, Tristani and Vestin (2008) ﬁnd that a model with nominal rigidities à la Calvo
and habit formation can reproduce a sizeable term premium, as well as volatile long-term
yields. Rudebusch and Swanson (2008) argue that the success of models with habits comes
at the cost of generating predictions for macroeconomic variables which are at variance
with the facts.

In a subsequent study, Rudebusch and Swanson (2012) combine Epstein-Zin-Weil pref-
erences (e.g. Epstein and Zin (1989); Weil (1989); Weil (1990)) with long-run risk (e.g.
Bansal and Yaron (2004)) into a New Keynesian model. These authors are able to gener-
ate a large and variable term premium without compromising the model’s ability to ﬁt the
main macroeconomic aggregates.

Relative to Rudebusch and Swanson (2012), Andreasen, Fernández-Villaverde and
Rubio-Ramírez (2018), henceforth AFVRR (2018), match the level and variability of the
10-year term premium with Epstein-Zin-Weil preferences using a low coeﬃcient of relative
risk aversion. This improvement is obtained by introducing a wedge akin to ﬁnancial fric-
tions into the analysis. Introducing this feedback eﬀect allows the authors to break the
macro-ﬁnance separation result typically obtained with Epstein-Zin-Weil preferences (e.g.
Tallarini (2000)).

Gourio and Ngo (2020) study the eﬀects of the zero lower bound on risk premiums in
a New Keynesian model augmented with Epstein-Zin-Weil preferences. Relative to their
approach, a main diﬀerence is that we study a model in which the lower bound on interest
rates arises because of the presence of cash.

Relative to these studies, another key diﬀerence is that in our case interest rate risk
is generated by combining habits with adjustment costs. Relative to Jermann (1998), or
Campanale, Castro and Clementi (2010) who rely on Chew-Dekel preferences, this mecha-
nism is studied in a model with composite habits (e.g. Jaccard (2014); Dimitriev (2017))

ECB Working Paper Series No 292810in which labor supply is endogenously determined.

As Constantinides (1990) and Boldrin, Christiano and Fisher (2001), we use a speciﬁca-
tion of internal habits, which ensures that the traditional measure of relative risk aversion
is determined by the curvature parameter, which we set to 1. At the same time, and
as emphasized by Campanale, Castro and Clementi (2010) and Swanson (2012), in models
with diﬀerent adjustment margins, the relationship between risk premiums and standard
measures of local risk aversion is imperfect. As in Jermann (1998), our model with habits
loses much of its ability to reproduce realistic risk premiums if we remove adjustment costs
from the analysis. This conﬁrms that increasing the curvature of the utility function is
not suﬃcient to resolve asset pricing puzzles in models with production. The investment
margin also plays a key role and this eﬀect is independent of preferences.

Many studies have already documented real eﬀects of a sizeable magnitude in models
without nominal rigidities. In Fuerst (1992) and Christiano and Eichenbaum (1992), sig-
niﬁcant non-neutralities are obtained in a model with production in which cash-in-advance
constraints are combined with limited participation. At the same time, one limitation of
these models is that the non-neutralities that they generate are not suﬃciently persistent
(e.g. Christiano and Eichenbaum (1995)).

Relative to these studies, Cooley and Quadrini (1999) obtain more persistent real eﬀects
of monetary policy in a model with search and matching frictions in the labor market. In
Khan and Thomas (2015), persistent real eﬀects are obtained in a model in which market
segmentation is endogenously determined. In De Fiore, Teles and Tristani (2011), mone-
tary policy has real eﬀects because debt is predetermined and issued in nominal terms.
In Gomes, Jermann and Schmid (2016), the large non-neutralities that are obtained stem
from the eﬀect of inﬂation on long-term nominal debt contracts that are issued by ﬁrms.
Bullard and DiCecio (2019) derive the optimal monetary policy in a heterogeneous agent
model, without sticky prices, in which non-state contingent contracts are the source of
nominal frictions.

Our approach is also related to a recent strand of literature in which the preference for
liquid assets is explicitly introduced. In Piazzesi, Rogers and Schneider (2019), this pref-
erence for deposit creates a convenience yield on the policy instrument that signiﬁcantly
In
alters the transmission mechanism of an otherwise standard New Keynesian model.
Van den Heuvel (2008), agents’ preference for liquidity introduces a wedge between the
return on equity and the return on bank deposits. In Begenau (2020), the general equi-
librium eﬀects implied by this preference for liquidity can lead to an increase in bank
lending in response to higher capital requirements. The micro-foundations that lead

ECB Working Paper Series No 292811agents to hold money are derived and discussed in the new monetarist literature (e.g.
Williamson and Wright (2010)).

The mechanism studied in this paper should play a relevant role in economies where
ﬁrms are dependent on banks. We therefore choose to calibrate the model using Eu-
In the euro area, small and medium-sized enterprises (SMEs) represent
rozone data.
about 99% of all ﬁrms and account for around two-thirds of the jurisdiction’s work-
force (e.g. Öztürk and Mrkaic (2014); European Central Bank (2014)). This large share
of SMEs makes the Eurozone particularly reliant on the bank lending channel, as these
ﬁrms only have a limited access to market-based ﬁnancing (European Commission (2011),
European Commission (2015)).

3 The Environment

The model is composed of a non-ﬁnancial or corporate sector, a commercial banking sector,
a central bank, a representative household, and a government. A role for external ﬁnancing
is introduced by assuming that ﬁrms in the non-ﬁnancial sector need to pay workers and
capital owners in advance of production.

3.1 Households

The representative agent owns the economy’s stock of capital and derives utility from con-
suming a consumption good, enjoying leisure and holding cash. All variables are detrended
and the deterministic growth rate along which the economy is growing is denoted by 
(e.g. King and Rebelo (1999)) The period  budget constraint of the representative agent
is given as follows:

  +  +  +  + 




+




+




=  +  + 

+1


+

1
1 + 



+1


(1)

The left-hand side of equation (1) reports the various sources of income received by agents.
Since they own all the sectors of the economy, households receive a dividend income paid by
the ﬁnancial and non-ﬁnancial sectors denoted by  . Each period a lump sum transfer,
which is denoted by  is received from the government. Households own the economy’s
capital stock and rent it to the non-ﬁnancial corporate sector. The capital stock is denoted
by  and  is the rental rate of capital. Labor supply being endogenously determined,

ECB Working Paper Series No 292812households divide their total time endowment, which we normalize to 1, between hours
worked in the corporate sector and leisure:

 +  = 1

(2)

where leisure and hours worked are denoted by  and , respectively. The total labor
income received in period  is therefore , where  denotes the wage rate. Relative to
a real business cycle model, the diﬀerence is that households also accumulate real money
balances. The nominal stock of money balances carried from the previous period is denoted
by  whereas money balances available during period  is denoted by +1 Since money
is a nominal asset, the real value of money holdings is obtained by dividing the nominal
stock by the price level, which is denoted by  Relative to the textbook money-in-the-
utility function model, the diﬀerence is that households can either keep money in the form
of cash or deposit part of it in the banking sector. This portfolio decision is captured by
introducing the following constraint:

+1 =  + 

(3)

where  denotes money holdings available during the period. The fraction that is de-
posited in the banking sector is denoted by  and earns a within period interest rate .

  The remaining
In real terms, the net income received from bankers is thus given by 
fraction that households keep in cash is represented by . Following the money-in-the
utility view, a demand for cash is introduced by assuming that the amount of real money
holdings available during the period, which is denoted by  yields utility.

Following the timing adopted in models with money-in-the-utility, it is the amount
available at the end of the period that yields utility (e.g. Walsh (2017)). Whereas 
represents the fraction of money balances that is liquid and that households can access
at any time, the amount deposited in the banking sector is illiquid in the sense that it
cannot be converted into cash within the period. The interest rate on deposit therefore
represents the opportunity cost of keeping liquid money balances in the form of cash instead
of depositing them in the banking sector. Finally, households invest in a short-term risk-
free bond issued by the government. The real payoﬀ received by households depends on
inﬂation and is given by the coupon payment  deﬂated by the price level  .

The right-hand side of equation (1) represents the diﬀerent expenditures faced by agents
in period  Households ﬁrstly choose how to allocate their total income between consump-
tion and investment, which are denoted by  and  respectively. Real money balances
available during period  are denoted by  +1
is the stock of government


, whereas  +1


ECB Working Paper Series No 292813bonds purchased by households during the period. The price at which this one period
1
risk-free bond is purchased is denoted by
1+


Capital accumulation is subject to adjustment costs, and following Jermann (1998) and

Baxter and Crucini (1993) among others, I use the following speciﬁcation:

+1 = (1

) +

−

1

Ã

1

−

1


−


 ¶



µ

+ 2



!

(4)

where  measures the degree of adjustment costs and can be interpreted as the elasticity
of Tobin’s Q with respect to changes in the investment to capital ratio. The parameters 1
and 2 are chosen to ensure that the models with and without adjustment costs have the
same deterministic steady state.

Habits are formed over the composite good consisting of the diﬀerent components of
utility (e.g. Jaccard (2014)). The composite good not only depends on consumption and
leisure but also on the fraction of real money balances  that agents hold in the form of
cash. This implies the following law of motion for the habit stock, which is denoted by  :

+1 =   + (1

 )


−

1



−


 ¶

µ

( + 
 )

(5)

where  is a memory parameter that aﬀects the rate at which the habit stock depreciates
over time. The weight of consumption in the utility function is denoted by the utility
parameter .  and  are two labor supply parameters that control the Frisch elasticity, as
well as the steady state allocation of time between hours worked and leisure, respectively.
The objective of the representative agent is to maximize lifetime utility, which is given as
follows:

max
+1+1+1+1

0

µ

³

´

1







1



−

( + 
 )

1



−



−

¶



−

∞





=0
X

In an inﬁnite horizon model, the subjective discount
subject to constraints (1) to (5).
b
factor is aﬀected by the growth rate of the economy along the balance growth path

1
(Kocherlakota (1990)) and we denote the modiﬁed discount factor by
−

 where

 =

3.2 The non-ﬁnancial or corporate sector

b

b

e

Firms in the non-ﬁnancial sector produce a composite output good using labor  and capital
 as production inputs. The ﬁnal output good produced by the corporate sector is denoted
by  and the production function takes a standard Cobb-Douglas form:

ECB Working Paper Series No 292814 = 

 1
−




(6)

where  is the capital share parameter. The random technology shock  follows an autore-
gressive process of order one,

log  =  log 
−

1 + 

where the random disturbance  is normally distributed with mean zero and standard
deviation . The autoregressive parameter is denoted by , where 0
Proﬁts at time  which are denoted by   are given as follows:

 ≤

≤

1

  = 


 1
−
 −







−

−




(7)

Relative to the neoclassical growth model, a cost channel of monetary policy is introduced
by assuming that ﬁrms need to obtain credit in order to operate. The lending decision
is intratemporal, in the sense that the loan is received at the beginning of the period and
needs to be reimbursed with an interest payment before the end of period  In other words,
the ﬁrm receives  at the beginning of the period and needs to repay (1 + ) before
the period ends.

The amount of externalﬁ nancing needed at the beginning of period  is determined by

the following loan-in-advance constraint:


 ≥

 ( + )

(8)

where the parameter  represents the fraction of total labor and capital costs, i.e. +,
that needs to be paid in advance and which therefore requires ﬁnancing. The objective of
managers in the corporate sector is to maximize the value of the ﬁrm, which is given by
the inﬁnite discounted sum of future proﬁts:

max


0

∞

=0
X

b



 
0

 



0 is the stochastic discount factor of the representative agent who owns ﬁrms

where
in the non-ﬁnancial sector, subject to constraints (6) to (8).



b

ECB Working Paper Series No 2928153.3 The central bank

The central bank provides money to the private sector and any proﬁt or loss made by the
monetary authorities, which is denoted by  is directly transferred to the government.
In period  this implies the following budget constraint:

 = 

+1

 −




(9)

Since money is explicitly modelled, and given that central banks use quantities to inﬂuence
interest rates, the quantity of money  is the policy tool. The deposit rate  is therefore
treated as an endogenous variable. This choice can also be motivated by the environment
in which monetary policy was conducted in the post-GFC era. Indeed, until the energy
price shock triggered by the war in Ukraine, interest rate policies only played a minor role.
However, monetary policy remained very active as central banks around the world have
used balanced sheet policies to stimulate the economy. Moreover, in a model in which
the quantity of money is explicitly introduced, the extent to which monetary policy is
constrained by the zero lower bound is a priori not clear. The empirical results documented
in Belongia and Ireland (2018) for instance suggest that this constraint could be alleviated
by using money supply rather than interest rate rules.

Monetary policy is determined by the following money supply rule:

+1 =  + 





(

 ) + 

−
where  denotes the quantity of money when the economy reaches its steady state. The
monetary policy shock is denoted by the random disturbance   which is normally dis-
tributed with mean zero and standard deviation  .

−

−

¡

¢

(10)

Relative to steady state, the quantity of money set by the central bank ﬁrstly depends
on the quantity available in the previous period, where  is a monetary policy smoothing
parameter. The objective of monetary policy is to stabilize inﬂation and the central bank
adjusts its monetary policy stance each time the price level  deviates from its steady state
value, which is denoted by   Monetary policy therefore becomes more restrictive when 
rises above   and more accommodative when the price level falls below its steady state
value. The sensitivity of monetary policy to deviations of the price level from its target is
captured by the parameter .

ECB Working Paper Series No 2928163.4 The commercial banking sector

As in Van den Heuvel (2008), the commercial banking sector intermediates funds between
households and the non-ﬁnancial sector. Banks collect deposits at the beginning of the
period, which are then lent to the corporate sector.

We simplify the analysis by assuming that the lending and deposit decisions occur
within the period. The timing is as follows. At the beginning of the period, bankers receive
a quantity of deposit  from households. They are then able to extend the quantity of
loan  to ﬁrms.

Before the period ends, bankers receive (1 + ) from ﬁrms. Banks are then able
to return the sum that households deposited along with an interest rate payment, which
amounts to (1 + )

As in Goodfriend and McCallum (2007), we assume that banks are endowed with a
technology that can be used to produce credit using deposits as an input. The production
function is given by a linear technology that links the quantity of loans extended to the
non-ﬁnancial sector to the quantity of deposits raised at the beginning of the period:

 = 

(11)

where  is a technology parameter measuring the eﬃciency of the intermediation technology
operated by banks. Each period, bankers optimally choose the amount of deposits to collect
from households  and the quantity of credit to extend to ﬁrms  to maximize proﬁts,
which are given as follows:

max


 = 


 −






subject to constraint (11).

3.5 The government

Government only plays a passive role in this environment. The lump sum transfer made
to the representative agent is ﬁnanced by issuing a short-term risk-free bond and by the
In period  this implies the following budget
receipts received from the central bank.
constraint:3

3The assumption of lump-sum transfers ensures that money does not have any eﬀect via the government

budget constraint.

ECB Working Paper Series No 292817 =  +

1
1 + 



+1
 −




(12)

3.6 Market clearing condition

The aggregate budget constraint can be derived by combining the budget constraints of
the diﬀerent sectors. Since the representative agent owns the non-ﬁnancial and banking
sectors, the total dividend income received is given by   =   + . Any
loss or proﬁt made by the central bank is transferred to the government, and since the
government in turns makes a lump sum transfer to the representative agent, the economy’s
consolidated budget constraint is given as follows:

 =  + 

(13)

3.7 Equilibrium deﬁnition

A competitive equilibrium in the economy is a sequence of prices:

         

where  denotes the Lagrange multipliers associated with the loan-in-advance constraint,
 is Tobin’s Q,  is marginal utility,  is the Lagrange multiplier associated with the law
of motion of the habit stock, and quantities:

         

that satisfy agents’ eﬃciency conditions, as well as the resource constraint (13) for all states,
for t=1...

 and given initial values for the two endogenous state variables  and 

∞

3.8 The transmission of monetary policy to the real economy

The household optimality conditions can be analyzed to gain intuition into how a monetary
policy shock is transmitted to the real economy. The optimality conditions with respect
to  and  can ﬁrstly be combined to derive the following relationship between the deposit
rate  consumption  the price level  and the amount of cash held by agents :4

 =

1






−


(14)

4See technical appendix in Section 13.

ECB Working Paper Series No 292818The deposit rate represents the opportunity cost foregone by the agent when cash balances
are held liquid instead of being deposited on a bank account. This creates a downward
demand schedule that implies a negative relationship between interest rates and cash hold-
ings. Given the choice to use the quantity of money as the policy instrument, equilibrium
in the money market can be represented by a vertical money supply curve. An exogenous
increase in money supply, which shifts this supply curve to the right, therefore has a di-
rect impact on this opportunity cost by creating a surplus of liquidity, which in turn puts
downward pressure on the deposit rate .

A change in the deposit rate is then passed through to ﬁrms via the banking sector.
Proﬁt maximization in the banking sector implies the following relationship between deposit
and bank lending rates:

 =



(15)

1


where the degree of pass-through depends on the eﬃciency of the ﬁnancial intermediation
technology. A change in lending rates then impacts ﬁrms in the non-ﬁnancial corporate
sector by modifying the cost of obtaining funds from the banking sector. The eﬀects of a
change in the cost of funds on the behavior of ﬁrms can be illustrated by deriving their
optimal demand for inputs:

 = (1

)




1
1 + 

−

(16)

 = 

1
1 + 



A change in funding costs  therefore ﬁrstly aﬀects the real economy through a labor
wedge by moving ﬁrms’ demand for labor. Secondly, since lending rates aﬀect the marginal
productivity of capital, credit frictions also distort the investment decision through an
investment wedge. This latter eﬀect can be illustrated by deriving the Euler condition
associated with capital accumulation which, with adjustment costs, is given by the following
equation:

(17)

 = +1+1

(1

Ã
++1+1

) +

−

1

−

1



µ

1


−

+1
+1 ¶

+ 2

1

−

µ

1


−

+1
+1 ¶

!

A change in borrowing costs therefore modiﬁes the marginal productivity of capital, which
in turn aﬀects Tobin’s Q and thus investment.5

5where, for the sake of notation, we deﬁne  =


−

e

ECB Working Paper Series No 2928193.9 Money and the lower bound on interest rates

For realistic calibrations, the components of utility and the price level are always strictly
positive in this model. Since in equilibrium the deposit rate is equal to the marginal utility
of holding cash (see equation 14), this ensures that the deposit rate  will take values that
are always strictly positive. Introducing an endogenous choice between  and  therefore
captures the restriction on interest rates created by the existence of cash. If the return
on bank deposits is too low, agents can always choose to hold money in cash. As will be
discussed in Section 7, this lower bound on  is a signiﬁcant source of asymmetry in the
transmission mechanism of monetary policy. It is however necessary to solve the model
using a nonlinear solution method to capture this eﬀect.

Since the deposit rate always stays in positive territory, the bank lending rate  also
takes values that are strictly positive (see equation 15). Consequently, the second advantage
of introducing a bound on deposit rates is that strictly positive values for bank lending rates
also rule out the case of occasionally binding constraints. Indeed, the optimality condition
in the non-ﬁnancial sector with respect to  implies that the Lagrange multiplier associated
with constraint (8), which is denoted by  is proportional to the bank lending rate :

 =




(18)

Since marginal utility  is always strictly positive and given the lower bound on the deposit
rate implied by equation (14),  and thus  are always strictly positive. If present, the
loan-in-advance constraint is therefore always satisﬁed with strict equality.

3.10 Equilibrium in the market for loanable funds

Combining the demand for production factors with the liquidity constraint faced by ﬁrms,
and since this constraint is always binding, the following credit demand condition can be
derived:

 = 


1 + 

(19)

which implies a negative relationship between the amount of credit needed by ﬁrms  and
the lending rate  The supply of loanable funds can be derived by ﬁrstly combining the
portfolio allocation constraint,  +1 =  +  with the demand for cash given by
equation (14). Next, using the ﬁnancial intermediation technology in the banking sector

ECB Working Paper Series No 292820given by equation (11), the following supply curve implying a positive relationship between
credit and lending rates can be derived:

 = +1

1






−


−

(20)

3.11 The dynamics of prices

The link between prices and monetary policy can be illustrated by deriving the optimality
condition with respect to the demand for money  :




= +1

1
+1

+






(21)

where  is marginal utility. Optimality in the accumulation of real money balances implies
that the cost of sacriﬁcing one unit of consumption today has to equate the current and
expected marginal beneﬁt of doing so. Since agents can choose to deposit money in the
banking sector, the marginal beneﬁt from holding money also includes the interest rate paid
on deposit . To illustrate how ﬂuctuations in the money market rate aﬀect inﬂation, let
us rewrite equation (21) as follows:

 =





1
−
 +1


1
+1

(22)

³

´

On the denominator, the ﬁrst term denotes the stochastic discount factor,  +1
 that agents

use to evaluate future payoﬀs. The negative relationship between current prices and the
stochastic discount factor illustrates that attitudes towards risk have an impact on inﬂation,
a channel that is typically overlooked in the literature (e.g. Jaccard (2018b)). Everything
else equal, an increase in stochastic discounting, which implies a stronger willingness to
postpone current consumption in favor of future consumption, reduces the price level.
In other words, when agents become more willing to save, they reduce consumption and
accumulate assets, such as real money balances, that they can use to transfer wealth across
time. Since  is the price of consumption, an increase in the degree of patience puts
downward pressure on prices.

Keeping all other variables constant, this condition also shows that an increase in the
short-term rate  reduces the price level. This eﬀect illustrates that an increase in the
deposit rate increases the beneﬁt of holding money. As the accumulation of real money
balances comes at the expense of other components of aggregate demand, such as con-
sumption expenditures, the price level declines when  goes up. Finally the price level is

ECB Working Paper Series No 292821a forward-looking variable in this model and current prices also depend on future expected
values.

3.12 The term premium

The term premium can be derived by pricing a zero-coupon risk-free nominal bond that pays
1 in a given period Following Rudebusch and Swanson (2012), this price can be expressed
recursively as follows:

()
 = 

+1



+1

(
1)
−
+1

(23)


+1

where  +1
is the stochastic discount factors for a nominal asset. Given that the term

premium is typically computed for a bond with a 10-year maturity, we set  to 40. The
price of a bond that pays 1 in the current period is denoted by (0)
 . The short-term risk-free
nominal rate, represented by  is inversely related to the price of a bond that oﬀers a
certain payment of 1 next period:

(1)
 =

1
1 + 

To derive the term premium, we also need to determine the price that a risk-neutral
Following the notation used in
investor would agree to pay to hold this asset.
()
Rudebusch and Swanson (2012), the risk-neutral price is denoted
 and can be obtained
as follows:

where

(0)
 = 1

b

()
 =

1
1 + 

(
1)
−
+1

b

b

For a bond with a 10-year maturity, the yield corresponding to the risk averse and risk

neutral investors, respectively, are given as follows:

b

40
 =

1
40


and

40
 =

1
40


()
Up to a ﬁrst-order approximation or in the deterministic version of the model,
 and
()
 are equivalent since certainty equivalence holds in these two particular cases. However,
once the model is solved using higher-order approximations, the eﬀect of uncertainty on the
valuation drives a wedge between these two concepts, since risk averse investors will require
a compensation for holding an asset whose price declines during recessions, when marginal

b

b

b

ECB Working Paper Series No 292822utility is high. In a model in which risk and stochastic discounting both matter, the price
of a zero-coupon bond computed under the assumption of risk neutrality is therefore higher
than the price obtained using the stochastic discount factor of a risk averse agent. Since
risk adjustments reduce asset prices, risk aversion increases the yield of a long-term bond.
The mean term premium, which needs to be expressed in percent per annum, is then
the diﬀerence between the yield to maturity of the bond and that obtained under the
assumption of risk neutrality:

and provides a measure of the eﬀect of risk adjustments on bond yields.

¢

¡

¢

³¡

() = 

1
40

40


400

·

(24)

1
40

40


−

´

b

4 Parameter selection

The data used to calibrate the model are described in Annex D. Whereas data availability
for the eurozone economy can be an issue, in most cases it is possible to ﬁnd series that
start in the late 1990s. For the sake of parsimony, we only introduce two exogenous shocks
and technology shocks are the only real source of business cycle ﬂuctuations.

4.1 Deterministic growth rate, capital share and labor supply

The deterministic growth rate of the economy is calibrated using data on population growth,
which are available on an annual basis since 1960. Between 1960 and 2018, the average
rate of population growth for the country group that is currently forming the eurozone
is 0.45% per year, which implies a value for the quarterly growth rate  of 1.00112. The
capital share parameter in the production function of the ﬁnal output good  is set to
1/3, which implies a labor share of 2/3. With internal habits, long-term risk aversion
increases with the curvature coeﬃcient  but is independent from the habit parameter
(e.g. Constantinides (1990); Boldrin, Christiano and Fisher (2001)). We therefore set the
curvature parameter  to 1. As shown in Jaccard (2018), increasing this parameter does
not help to resolve asset pricing puzzles in a production economy with endogenous labor
supply.

ECB Working Paper Series No 2928234.2 Frisch elasticity of labor supply and steady state time allo-

cation

The ﬁrst labor supply parameter  is calibrated to ensure that in the steady state, agents
spend about 20 percent of their time on work-related activities, which corresponds to a value
for  of 0.2. The curvature parameter  is chosen to imply a value for the Frisch elasticity
of labor supply of about 0.7 (e.g. Hall (2009); Chetty, Guren, Manoli and Weber (2011)).

4.3 Steady state money supply

The steady state quantity of money available in the economy, which is denoted by 
aﬀects the steady state price level   If the steady state money supply is doubled, the
steady state price level and the quantity of cash holding  double as well, but a change in
money supply has no eﬀect on the real side of the economy. Given this invariance of the
real economy to the value of  we set the steady state money supply to 1.

4.4 Matching moment procedure

The remaining 12 parameters are calibrated to match a set of 12 moments that characterize
the eurozone business cycle. Since with uncertainty higher-order terms in the Taylor ex-
pansion drive a wedge between the deterministic and the stochastic versions of the model,
it is necessary to simulate the model and ﬁnd the combination of parameter values that
minimizes the distance between the estimated and simulated moments. Table 1 below re-
ports the combination that minimizes this distance, and the comparison between the model
and the data is shown in Table 2.





Table 1: Moment matching procedure, parameter values











0.991

0.999

0.97

0.92

0.52

1.6

0.011

0.0069


2.1


0.978



0.0228


0.6

In Table 2,       and  denote the growth rate of output, consumption,
investment, money, deposits and prices expressed in year-over-year growth rates, respec-
tively, where for output the growth rate is computed as (log()
100. () is
the standard deviation of the nominal short-term money market rate, () is the mean
) the mean intermediation
short-term rate, () is the mean term premium and (
spread. Finally, () and () denote the average loan to output and investment to
output ratios, respectively.

log(

4))

−

−

−

·

ECB Working Paper Series No 2928244.5 Solution method

The results reported in Table 2 are generated using Dynare (Adjemian et al. (2014)). We
use a third-order approximation to the policy function as well as the pruning algorithm
developed by AFVRR (2018) to simulate a sample of 200,000 observations.

4.6 Relation between structural parameters and model-implied

ﬁrst and second-order moments

It is diﬃcult to associate each structural parameter with only one moment as most para-
meters have a signiﬁcant impact on the entire system through general equilibrium eﬀects.
Some parameters do however have larger eﬀects on a subset of model implications.
In
this ﬂexible price version of the model, technology shocks are the main drivers of business
cycle aggregates, and account for nearly all the variation in output. The technology shock
standard deviation parameter  can therefore be associated with the volatility of output.
The capital adjustment cost parameter  controls the supply elasticity of capital and has
a ﬁrst-order impact on the volatility of investment. Since capital is the main asset available
to transfer wealth across time, this parameter also aﬀects the ease at which the economy’s
storage technology can be used to achieve consumption smoothing. When combined with
habit persistence, the degree of which is captured by the parameter   the capital adjust-
ment cost parameter also impacts the volatility of marginal utility which in turn aﬀects how
agents discount future payoﬀs. The model’s ability to match the average term premium
therefore critically depends on these two parameters.

Agents’ propensity to save also depends on whether technology shocks, which are the
main source of business cycle ﬂuctuations, are perceived as temporary or permanent.
The mean term premium and the volatility of consumption and investment, denoted by
() () and (), can thus be associated with the capital adjustment costs, habit,
and shock persistence parameters    and  respectively

Fluctuations in the monetary aggregate  are mostly driven by the monetary policy
shock, which illustrates that this moment helps to identify the monetary policy shock
standard deviation  . The preference parameter  determines the weight of real cash
balances in the utility function. The volatility of deposits () is therefore particularly
sensitive to this parameter value. In a model in which supply shocks are the main drivers
of business cycle ﬂuctuations, inﬂation can be a main source of risk for bondholders. As a
result, whereas the inﬂation coeﬃcient in the monetary rule  has a ﬁrst-order impact on
the volatility of prices   this parameter also aﬀects the model’s asset pricing implications.

ECB Working Paper Series No 292825The steady state value for the subjective discount factor  determines agents’ intertem-
poral choices, and has a signiﬁcant eﬀect on the mean term premium and the volatility
of consumption and investment. Since this parameter also has a direct impact on interest
rates, it can be used to pin down the mean short-term rate ()

Table 2: Model vs. data

Data

95% conﬁdence Estimated empirical

()
()
()
( )
()
( )
()
()
()
(−
()
()

)

interval

[1.6, 2.1]

[0.9, 1.2]

[5.0, 6.6]

[2.8, 3.8]

[1.8, 2.4]

[0.8, 1.1]

[1.8, 2.4]

[2.1, 2.6]

[0.5, 0.9]

[2.2, 2.4]

[0.88, 0.95]

[0.21, 0.22]

moments

1.8

1.0

5.7

3.3

2.0

0.9

2.0

2.4

0.7

2.3

0.91

0.22

Model

Simulated moments
(3rd order)

1.8

0.9

5.6

3.3

2.0

0.9

2.5

2.4

0.6

2.3

0.91

0.21

Combining labor or investment frictions with habit formation also has a strong impact
on the volatility of short-term rates (Jermann 1998; Boldrin et al., 2001). This moment
can thus be associated with the habit formation and capital adjustment cost parameters.
)
As illustrated by equation (15), the magnitude of the intermediation spread (
is pinned down by the technology parameter in the production function of loans  The
parameter  measures the fraction of total costs that ﬁrms need to pay in advance. This
parameter therefore determines the quantity of credit needed to operate ﬁrms, and mainly
aﬀects the steady state importance of bank-based ﬁnancing in the economy. This parameter
can thus be associated with the loan-to-output ratio (). The amount of output that
is invested critically depends on the rate at which capital depreciates, and  is therefore
identiﬁed by including the mean investment to output ratio in the loss function ()

−

The last remaining parameter, the monetary policy smoothing parameter   is poorly
identiﬁed. In particular, it is diﬃcult to distinguish its eﬀect on the model dynamics from
that of the shock standard deviation   This parameter however aﬀects the volatility of
inﬂation, interest rates, and monetary aggregates.

ECB Working Paper Series No 2928265 Results

As will be shown in the next sections, the model’s ability to generate asymmetries critically
depends on the eﬀective lower bound on interest rates. To provide a realistic quantitative
assessment, it is thus important to pay particular attention to the dynamics of nominal
variables.

As illustrated in Table 2, the mean as well as the volatility of the short-term nominal rate
can be broadly reproduced. It should be noted that, for the period under consideration, the
volatility of the short-term nominal rate is 2%. Including a longer sample, and in particular
the 70s and 80s would increase the estimated value for the volatility of the nominal rate
. The facts documented by Jordà, Knoll, Kuvshinov, Schularick and Taylor (2019) also
suggest that risk-free rates could be more volatile than typically assumed.

At the same time, a higher risk-free volatility would amplify the asymmetry stemming
from the lower bound. The rather conservative value that is targeted in Table 2 therefore
ensures that the importance of our mechanism is not overstated.

Since this version of the model abstracts from nominal rigidities, it is also important to
ensure that the volatility of prices is in line with the data. In this respect, the fact that
the volatility of monetary aggregates ( ), inﬂation ( ) and deposits () can
be matched is reassuring.

The moment matching procedure described in Section 4 only assigns a very small value
 = 0001 This small value implies that agents hold

to the utility share of money, i.e. 1
on average 2% of their total liquid wealth in cash and 98% in the form of bank deposit.

−

The model generates a term premium of around 0.6%. This value is close to that esti-
mated by Hördhal and Tristani (2012, 2014) using euro area data for the period from 1999
to 2018.6 It is however lower than the value targeted in Rudebusch and Swanson (2012) or
AFVRR (2018) for the United States.

Using data from 2005 to 2017, Wu and Xia (2017) ﬁnd an average value for the term
premium of 1%. Since the risk premium has been declining over time, the diﬀerence with
Hördhal and Tristani can be explained by the diﬀerent samples used in the two studies.

One of the key model parameters that determines the eﬀectiveness of monetary policy
is denoted by  Given that this parameter measures the economy’s credit dependence,
it can be identiﬁed using data on credit to GDP ratios made available by the Bank for
International Settlements. In line with the decentralized equilibrium described in Section
3, the empirical value for the loan-to-output ratio () only includes credit to non-

6I thank the authors for having provided an updated estimate of their results.

ECB Working Paper Series No 292827ﬁnancial corporations obtained by banks, and excludes credit to households or other forms
of non-bank source of funding.

−

It is also possible to match the average spread between bank lending rates and the money
) Due to a lack of data availability, it is only possible to compute this
market rate (
spread for a sample period that starts from the ﬁrst quarter of 2000 onwards. The lending
rate data used to compute this spread is the cost paid by non-ﬁnancial corporations to
obtain a new loan corresponding to amounts smaller than 1 million euros and for a period
of less than a year. Since the representative ﬁrm is a SME, using a measure of interest rate
on loans smaller than 1 mio is a better proxy of the cost of funding than the rate paid on
larger loans. Finally, the fact that the investment share of output () can be matched,
also ensures that the high volatility of investment that we obtain is not due to a steady
state eﬀect.

Whereas the model is able to match the stylized facts reported in Table 2, it is impor-
tant to keep in mind that it fails on some other dimensions. For instance, although the
volatility of deposits can be reproduced, it is not possible to simultaneously account for
the large ﬂuctuations in credit observed in the data. Moreover, the model understates the
volatility of hours worked, a limitation which suggests that incorporating both an extensive
and an intensive margin of labor supply would be necessary to match the data. Since the
model abstracts from unemployment, it also cannot be used to study the link between
diﬀerent measures of slack and inﬂation (e.g. Den Haan, Rendahl and Riegler (2015);
Stock and Watson (2018)).

5.1 What determines the term premium?

In order to isolate the contribution of inﬂation risk to the term premium, let us start
by deriving the pricing equation that corresponds to an inﬂation-indexed long-term bond,
the price of which is denoted by ()
 . Relative to the formula shown in equation (23),
expected inﬂation no longer aﬀects the valuation of an inﬂation indexed long-term bonds.
Consequently, we have the following pricing condition:

()
 = 

+1


(
1)
−
+1

where (0)
 = 1 Following the deﬁnition of term premium given by equation (24), a risk
neutral measure can be obtained by ﬁrstly deriving a formula for the real risk-free rate,
which we denote by :

ECB Working Paper Series No 292828

1
1 + 

= +1

The term premium on the inﬂation-indexed bond, which is denoted by  is then deter-
mined by the diﬀerence between the yield computed using the stochastic discount factor
of the risk averse agent minus the risk-neutral measure. Since  abstracts from inﬂation
risk, the inﬂation risk premium  can be deﬁned as the diﬀerence between the term
premium on a nominal and an inﬂation-indexed long-term bond:

( ) = ()

()

−

This measure therefore captures the impact of expected inﬂation on the compensation
required by investors for holding a nominal asset subject to inﬂation risk.

Table 3: Inﬂation expectations and inﬂation risk premium

( (+3))
 ((+3))
( )

Data

0.19

0.30

-

Model (3rd order)

0.22

0.21

-0.07

Since the inﬂation risk premium critically depends on the cyclical properties of expected
inﬂation, it is important to ﬁrst understand how this measure varies over the business
cycle. Table 3 uses the measure of expected inﬂation from the ECB survey of Professional
Forecasters and reports its correlation with output growth. Since the measure reported
in this survey corresponds to inﬂation expectations three quarters ahead, the model-based
measure of inﬂation expectation is computed as follows: (+3) = ((+3+2
400).
Both in the model and in the data, the correlation between output growth and inﬂation
expectations is shown in the ﬁrst row of Table 3, whereas the second row reports the
standard deviation of inﬂation expectations, i.e. ((+3))

1)

−

·

Although this moment was not targeted, the ﬁrst main result that stands out is that the
model is able to match the correlation between inﬂation expectations and output growth
observed in the data. Moreover, as illustrated by the second row of Table 3, it is possible
to generate ﬂuctuations in the three quarters ahead expected inﬂation rate of a magnitude
that is broadly in line with the one observed in the data.

The average inﬂation risk premium predicted by the model is shown in the last row
of Table 3. Interestingly, the co-movement between expected inﬂation and output growth
observed in the data, and reproduced by the model gives rise to a negative inﬂation risk

ECB Working Paper Series No 292829premium of 7 basis points. In other words, inﬂation contributes to reduce, rather than
increase, the risk associated with an investment in long-term bonds.

Seen through the lens of this model, the fact that euro area inﬂation expectations are
slightly procyclical is therefore a source of risk reduction. To gain intuition into this result,
consider the case of a recession, a period in which marginal utility is higher than usual.
This positive correlation lowers the risk of investing in long-term bonds because it implies
a decline in expected inﬂation during periods of recession. Since a decline in expected inﬂa-
tion increases the value of a nominal bond, this negative co-movement implies that expected
inﬂation acts as a hedge against consumption risk. As pointed out by some recent studies
(e.g. Campbell, Sunderam and Viceira (2016); Camba-Méndez and Werner (2017)), nom-
inal bonds can thus act as “deﬂation hedges”.

If inﬂation is a source of risk reduction, what explains the model’s ability to reproduce
a sizable term premium? The answer is real interest risk. In contrast to expected inﬂation,
real interest rates are countercyclical. For the calibration summarized in Table 1, the
model-generated correlation between output growth and the real interest rate  is -0.3.

Since bond prices and real interest rates move in opposite directions, this correlation
implies that bond prices fall during recessions. Long-term bonds are therefore a bad hedge
against consumption risk. Indeed, in this economy, holders of long-term bonds suﬀer capital
losses during periods of recession, precisely when marginal utility to consume is high. In
spite of the negative inﬂation risk premium implied by expected inﬂation, real interest rates
risk therefore explains why long-term bonds are risky in this model.

6 The real eﬀects of monetary policy

A positive monetary policy shock takes the form of an exogenous increase in the innovation
 to the policy rule in equation (10). A positive shock increases the quantity of money
in circulation and, although a fraction is absorbed by households who derive utility from
holding money in cash, the supply of funds deposited in the banking sector increases. This
increase in deposits is then channeled to ﬁrms in the non-ﬁnancial sector in the form of
short-term credit. The resulting increase in the supply of loanable funds in turn reduces
the rate at which ﬁrms borrow from the banking sector. Finally, a decline in the cost of
funding stimulates the demand for labor and capital through its eﬀects on equations (16)
and (17).

Since the model’s state space is nonlinear, the response to shocks can be inﬂuenced by
the particular point from which the impulse response is computed. To capture this potential

ECB Working Paper Series No 292830state dependence, the impulse responses shown in this section are computed using a third-
order approximation to the policy function. The results reported in Figure A.1 to Figure
A.4 represent the average eﬀect of a monetary policy shock. In each case, it is obtained
by calculating an impulse response starting from many diﬀerent points in the state space
and by computing the average response following Adjemian et al. (2014). These responses
correspond to the case in which monetary policy shocks are the only source of ﬂuctuations.
As illustrated by the top left panel of Figure A.1, a positive innovation to the money
supply rule increases  relative to steady state by around 1.5% on impact. Since it shifts
the money supply curve to the right, equilibrium in the money market implies a reduction
in the money market rate  which in annualized terms declines by around one percentage
point relative to its steady state value. As illustrated by the negative relationship between
prices and the short-term deposit rate shown in equation (21), a decline in the nominal
short-term rate has a positive impact on the price level  , which increases by around 0.4%
on impact. The increase in credit , which is shown in the bottom right panel, is less than
proportional than the increase in money supply, which reﬂects that part of the eﬀect of the
shock is absorbed by households who increase their cash holdings . Since the response
of credit also depends on the eﬃciency of the ﬁnancial intermediation technology, banks
are only able to channel a fraction of the funds they receive to ﬁrms. This explains why
a positive shock that raises money supply by 1.5% on impact only leads to an average
increase in credit by about 1%.

The real eﬀects of monetary policy are illustrated in Figure A.2, which shows the re-
sponse of output  investment  hours worked  and consumption  in percentage devia-
tion from steady state. As can be seen in the top left panel, a monetary policy shock that
increases money supply by 1.5% and reduces the nominal short-term interest rate relative
to steady state by one percentage point raises output on impact by around 0.15%. The
shock has a stronger eﬀect on hours worked, the increase of which exceeds 0.2% on impact.
This stronger eﬀect on hours worked contrasts with the considerably more muted increase
in investment.

The expansionary monetary policy shock stimulates aggregate consumption, the in-
crease of which reaches about 0.2% on impact. The positive impact on consumption can
ﬁrstly be explained by the substitution eﬀect induced by the decline in the short-term real
rate depicted in the upper right panel of Figure A.4. Moreover, since wages and the income
from renting capital to ﬁrms also increase, this substitution eﬀect is reinforced by a positive
income eﬀect that contributes to stimulate consumption on impact.

The two upper panels of Figure A.3 show the response of the real wage and marginal

ECB Working Paper Series No 292831productivity of capital. The increase in the price of inputs conﬁrms that a positive monetary
policy shock stimulates the demand for factors, as quantities and prices both rise.
The response of the real quantity of credit  and the lending spread 

 is shown
on the two lower panels of Figure A.3. As shown on the lower left panel, the main eﬀect
of monetary policy is to stimulate the production of real credit. On impact, the increase
in credit reaches around 0.6%. A higher quantity of credit relaxes the ﬁnancing constraint
(8), which in turn reduces the cost of borrowing for ﬁrms through equation (18).

−

Monetary policy shocks generate a negative co-movement between lending spreads and
real credit. A main eﬀect of monetary policy is therefore to reduce lending spreads. This
eﬀect of lending spreads is particularly relevant for the euro area. Indeed, in the eurozone,
the intermediation spread is strongly negatively correlated with real credit growth. Peri-
ods of high credit growth are associated with low levels of the intermediation spread. In
contrast, these spreads increased during the Subprime and Sovereign Debt Crises.

The response of the term premium to a positive monetary shock is shown in the upper
left panel of Figure A.4. It is necessary to resort to a third-order approximation, at least, in
order to generate time-variation in the term premium. This reﬂects that the term premium
is determined by the covariance between the stochastic discount factor and the return on
a long-term bond.

The very small eﬀect of monetary policy on the term premium illustrates that it is
generally diﬃcult to generate large variations in conditional second moments within this
class of models. At the same time, the decline in the term premium obtained in response to
an expansionary monetary policy shock is consistent with the view that positive monetary
policy shocks reduce risk premiums.

As already mentioned, the short-term real rate declines in response to a pos-
is therefore
itive shock (see the upper right panel of Figure A.4).
able to reproduce the liquidity eﬀect documented by many empirical studies (e.g.
Christiano and Eichenbaum (1995)). Since nominal rigidities are typically needed to re-
produce this eﬀect, the fact that the model passes this important test is reassuring.

The model

As shown by the lower left panel of Figure A.4, the price of a zero-coupon nominal
bond with a 10 year maturity is also sensitive to monetary policy. Relative to its steady
state value, the shock increases bond prices by around 0.5% in response to an expansionary
shock. Finally, the yield on a corresponding nominal long-term bond declines by around 5
basis points on impact.

ECB Working Paper Series No 2928326.1 Credit frictions as a source of non-neutralities

In this environment, the loan-in-advance constraint given by equation (8) is the only source
of monetary policy non-neutrality. Whether a change in  has real eﬀects therefore criti-
cally depends on the credit friction parameter  If  is set to zero, the demand for loanable
funds given by equation (19) falls to zero and a monetary policy shock has no eﬀect on
the real quantity of credit demanded by ﬁrms. To illustrate this point, Figure A.6 ﬁrstly
shows how the level of  aﬀects the steady state of the economy. The sensitivity analysis
performed in this chart shows how the loan-to-output and cash holding ratios, i.e. ()
and () respectively vary with the ﬁnancing frictions parameter 

As  approaches zero, the loan-to-output ratio, which is depicted by the blue diamonded
line, tends towards zero, the model reducing to a creditless economy in this limiting case.
Since the demand for credit becomes negligible as  approaches zero, the degree of credit
frictions also aﬀects the allocation of money between cash  and deposits  In Figure
A.5, this is illustrated by the red crossed line, which shows how a change in  aﬀects the
average share of liquid wealth that households choose to hold in the form of cash. A lower
dependence on credit implies a lower share of bank deposit. In the limit, the ratios 
and  tend towards 0 and 1, respectively, as  approaches zero, since all the money
available in the economy is held in cash. As a result, in the limit, ﬁnancial intermediation
completely disappears and the model reduces to a version of the neoclassical growth model
with money in the utility function.

To illustrate that the value of  also has a crucial impact on the model’s dynamics,
Figure A.6 shows the response to a positive monetary policy shock in the case in which the
ﬁnancial friction parameter  is set to 0.001. As shown by the two upper panels, in this
limiting case, the change in cash holding  is almost exactly proportional to the change
in . In terms of the portfolio allocation constraint (3), this implies that the shock has
a negligible impact on the quantity deposited in the banking sector and thus on credit
creation. As shown by the response of output in the lower right panel, the monetary policy
shock is almost neutral in this case, which reﬂects that a change in lending conditions has
essentially no real eﬀects without ﬁnancing frictions under ﬂexible prices.

6.2 The labor wedge

Whereas a variation in the cost of lending directly aﬀects the demand for both capital
and labor, the transmission mechanism operates primarily through the labor market. The
importance of the labor market can be illustrated by considering the case in which the

ECB Working Paper Series No 292833constraint only depends on capital. If wages do not need to be paid in advance, the loan-
in-advance constraint takes the following form:


 ≥



and a monetary policy shock no longer aﬀects the labor demand equation.

In Figure A.7, the red dotted line shows the response of output to a monetary policy
shock in the model without a labor wedge. This comparison demonstrates that, without a
labor wedge, the model loses most of its ability to generate non-neutralities.

7 The state dependence of monetary policy transmis-

sion

Since monetary policy is transmitted to the real economy by aﬀecting ﬁrms’ borrowing
costs, the transmission mechanism critically depends on the central bank’s ability to control
lending rates. By varying the quantity of liquidity it supplies, the central bank has a direct
impact of the deposit rate, which in turn aﬀects banks’ lending rates. This ability to
control market rates however depends on how agents react to a change in the monetary
policy stance. In particular, the fact that households can choose between depositing money
in the banking sector or keeping money in cash interferes with the conduct of monetary
policy.

The impact of this preference for liquidity on the transmission mechanism can be illus-
trated by analyzing the equilibrium condition in the money market implied by equation
(14). Keeping  and  constant at their steady state value, and using the calibration sum-
marized in Table 1, this relationship is plotted in Figure A.8, which shows  on the vertical
axis as a function of cash balances . For the calibration that reproduces the moments
shown in Table 2, the average short-term nominal money market rate  in annualized
terms, stands at 2.4%. An average interest rate of 2.4% implies a quantity of money held
in cash of about 0.02. In terms of the portfolio allocation, households therefore hold on
average around 2% percent of their liquid wealth in cash and the remaining 98% in the
banking sector in the form of bank deposits.

An interesting consequence of this inverse relationship between cash holdings and the
deposit rate is the potential asymmetry that it entails. Indeed, for very low levels of interest
rates, the demand for cash ﬂattens and converges towards one. What this means is that
households can always choose to withdraw money from their deposit account and keep

ECB Working Paper Series No 292834money in cash if the remuneration on their deposit account is too low. In the limit, the
share of money invested in cash reaches 100%, as the deposit rate  approaches zero.

This nonlinear relationship formalizes the idea that the existence of cash creates a
lower bound on deposit rates that constrains the transmission of monetary policy. To gain
intuition into this result recall that equation (3) implies that, for a given quantity of liquidity
in the system, an increase in cash holdings reduces the quantity of funds deposited in the
banking sector . In other words, the possibility to hold cash instead of bank deposits
limits the room for manoeuvre of the central bank by preventing deposit rates from turning
negative. Indeed, households will always strictly prefer to hold cash rather than incur a
cost for depositing their money in the banking sector.

Consider for instance the case of a very aggressive injection of liquidity occurring during
a period of low interest rates. Clearly, as illustrated by the nonlinear relationship between
 and  depicted in Figure A.8, once the ﬂatter portion of the cash demand curve is
reached, any further increase in liquidity only has a small eﬀect on deposit rates. In terms
of portfolio allocation, this reﬂects that the supply of deposits  and hence  becomes
insensitive to changes in the policy instrument  when the ﬂat portion of the demand for
cash schedule is reached. Since in this case the quantity of deposits remains unaﬀected by
the shock, a change in monetary policy only has a muted eﬀect on the supply of credit.
Indeed, when the opportunity cost of holding cash is so low, agents have no incentives to
channel any further increase in  to the real economy. Consequently, at the eﬀective lower
bound, an increase in the quantity of money in circulation is absorbed by a proportional
increase in cash holdings and has negligible real eﬀects.

7.1 Deconstructing the mechanism

To better understand how the demand for cash aﬀects the transmission mechanism of mon-
etary policy, it is useful to illustrate how initial credit conditions impact the eﬀectiveness
of a monetary policy shock. The equilibrium in the credit market is represented in Figure 1
where the credit supply and credit demand curves given by equations (20) and (19) are de-
picted. In both panels, the red dotted lines represent the demand curves corresponding to
equation (19). These two demand curves are obtained by using the value for the parameter
 taken from Table 1 and by ﬁxing   and  at their steady state values.

In the left panel, the blue continuous line shows the initial credit supply curve in the
case in which the quantity of money available in the economy  stands below its average
value. When monetary conditions are tighter than usual, the credit supply curve is also
steeper. This in turn implies a higher lending rate and a lower equilibrium quantity of

ECB Working Paper Series No 292835credit. The blue dashed line shows how a 1% increase in money supply shifts the credit
supply curve when the economy is in this state of below average equilibrium quantity of
credit.

In the right panel, the blue continuous line represents an initial credit supply curve that
corresponds to a case in which the quantity of money available in the economy is higher
than average. The initial state of the economy is therefore one in which the equilibrium
quantity of credit is above average, which in turn implies lending rates that are lower than
usual. The blue dashed line illustrates how a 1% increase in the money stock shifts the
credit supply curve in this case.

As can be seen by comparing the blue continuous lines across the two panels of Figure 1,
the ﬁrst diﬀerence is that the initial supply curve is ﬂatter in the high credit state. Second,
a 1% shock to money supply, which in each panel is determined by the distance between the
blue continuous and blue dashed lines, has a much smaller eﬀect on equilibrium quantities
and prices in the high money, high credit state. The much lower eﬀect obtained in the
high credit state illustrates the limits of monetary policy in a world in which agents can
choose to hold cash. When the ﬂat portion of the cash demand curve shown in Figure A.8
is reached, any further increase in money supply is hoarded in the form of cash instead of
being deposited in the banking sector.

8

6

4

2

e
t
a
r

i

g
n
d
n
e

l

k
n
a
B

0
0.52

Low credit state

New supply curve
Initial supply curve
Demand curve

High credit state

New supply curve
Initial supply curve
Demand curve

12

10

8

6

4

2

e
t
a
r

i

g
n
d
n
e

l

k
n
a
B

0.525

0.53

0.535

Quantity of credit

0
0.51

0.515

0.52

0.525
Quantity of credit

0.53

0.535

0.54

Figure 1. Equilibrium in the credit market in response to a 1% increase in money supply in

the high and low credit states. x axis: Credit  y axis: Deposit rate 

400

·

The small eﬀect of monetary policy on amounts deposited in the banking sector can
be explained by the low opportunity cost of holding cash when the deposit rate paid to

ECB Working Paper Series No 292836 
 
 
 
households becomes suﬃciently low. Without additional funding, the banking sector is
unable to increase lending to the productive sector. Therefore, the credit supply curve
becomes insensitive to changes in monetary policy. As a result, and as can be seen by
comparing the blue continuous and blue dashed lines shown in the right panel, a 1% change
in money supply only has a negligible eﬀect on the credit supply curve in this case.

The low eﬀectiveness of monetary policy obtained in the high credit state contrasts
with the much stronger eﬀect depicted in the left panel, which corresponds to the low
credit state. In terms of the cash demand curve depicted in Figure A.8, the diﬀerence is
that the demand for cash schedule becomes steeper when monetary conditions are tighter
than average. This nonlinearity reﬂects the notion that the demand for cash  becomes
less sensitive to variations in interest rates when the opportunity cost of hoarding cash is
high. In other words, any change in money supply  has a stronger eﬀect on deposits 
in this case because the demand for cash becomes less sensitive to monetary policy. Since a
change in the quantity of deposits available in the economy in turn shifts the credit supply
curve, the eﬀectiveness of monetary policy increases when agents have a reduced incentive
to hoard cash.

7.2 State dependent impulse response analysis

The next step is to provide a quantitative evaluation of the nonlinearity implied by this
mechanism. In this section, we study the response of output and prices to a one standard
deviation monetary policy shock by diﬀerentiating between periods of low and high credit
availability. This is achieved by ﬁrstly generating 100,000 diﬀerent trajectories for all the
variables, including real credit  by simulating the model with the two exogenous shocks
using a third-order approximation as well as the pruning algorithm of AFVRR (2018). Since
each trajectory depends on a sequence of random shocks, the result of this simulation can
be used to generate a distribution of realized values for real credit in a given period, say
period 100. This allows us to identify states of the economy in which credit is higher or
lower than average. The next step is to compute an impulse response for the other variables
of interest, in our case output, that corresponds to states of the economy in which credit
is higher or lower than average.

Following Adjemian et al. (2014), an impulse response for any variable is computed as
the diﬀerence between the initial simulated series and the same series that is subject to a
one standard deviation shock. The impulse response is then computed as the diﬀerence,
from period 100 onwards, between the initial simulated series, for say output, and the same
series that was hit by a positive monetary policy shock. Periods of low and high credit

ECB Working Paper Series No 292837availability can then be identiﬁed by selecting the set of impulse responses for output to a
monetary policy shock that corresponds to states of the economy in which credit is below
are above average.7

In Figure 2, the blue continuous line shows the impulse response of output to a positive
money supply shock in the credit stress state. The credit stress state corresponds to impulse
responses that were computed in states of the economy in which credit lies within the lower
tercile of the distribution. In other words, the blue continuous line represents the average
impulse response of output that is obtained in states of the economy in which the quantity
of credit in the economy is less than or equal to 33% of all realized observations.

e
t
a
t
s

y
d
a
e
t
s
m
o
r
f

n
o
i
t
a
v
e
d

i

e
g
a
t
n
e
c
r
e
P

0.2

0.15

0.1

0.05

0

1

2

Output

Low credit state
High credit state

4

3
6
Quarters after the shock

5

7

8

Figure 2. Response of output to a positive money supply shock in the low and high credit

states.

Similarly, we deﬁne the high credit state as the case in which the realized value for credit
is included in the upper tercile of the distribution. The red dotted line therefore depicts
the average response of output to a positive monetary policy shock that corresponds to the
ample credit state. The ample credit state corresponds to states of the economy for which
credit takes values greater than or equal to 66% of all realizations.

When looking at Figure 2, what immediately stands out is the asymmetry in the re-
sponse of output to a monetary policy shock between the high and low credit states. On

7The impulse response analysis shown in this section has greatly beneﬁted from comments and sugges-
tions from M. Juillard whose invaluable help is gratefully acknowledged. Any remaining error is our own
responsibility.

ECB Working Paper Series No 292838 
 
 
 
impact, the exact same monetary policy shock generates an increase in output of around
0.05% in the high credit state, as compared to an increase that is more than 3 times greater
in the credit stress regime.

We also ﬁnd that the magnitude of this asymmetry is less pronounced for the price
level than for output. The reason is that the dynamics of prices is directly aﬀected by the
stochastic discount factor. As we discuss in Jaccard (2018b), the presence of habits gives
rise to state dependence in the stochastic discount factor that attenuates the response of
prices during periods of recession.

7.3 Monetary asymmetries in the absence of risk

To illustrate the importance of risk, we now study this asymmetry in a version of the
model that cannot match the term premium observed in the data.
It is well-known
that standard models cannot generate term premiums of a realistic magnitude (e.g.
Rudebusch and Swanson (2008)). In our case, we overcome this challenge by combining
a speciﬁcation of habit formation in the composite of consumption, money and leisure with
capital adjustment costs.

Without habits, a case which can be obtained by setting the habit parameter to 1, the
term premium falls to essentially zero. Interest rate risk disappears because nominal interest
rates and inﬂation become too smooth relative to the data. Matching the volatility of
interest rates and inﬂation is essential because the eﬀective lower bound becomes irrelevant
if the average interest rate produced by the model is too high or if interest rates are not
suﬃciently volatile. At the same time, the impact of the eﬀective lower bound on the
transmission mechanism can be overstated if interest rates are on average too low or too
volatile relative to the data.

To illustrate this point, the exercise illustrated in Figure 2 is repeated using the version
of the model without habits that generates a zero term premium. As shown in Figure A.9,
without realistic amounts of interest rate risk, the asymmetry essentially disappears as the
two lines become indistinguishable.

One main takeaway is therefore that the model’s ability to generate asymmetries is
tightly linked to its asset pricing predictions. Consequently, resorting to nonlinear tech-
niques is not suﬃcient to detect asymmetries.
Indeed, a well-documented limitation of
standard models is their tendency to generate mean interest rates that are too high (e.g.
Weil (1989)) and not suﬃciently volatile. The risk, therefore, is to understate the impor-
tance of asymmetries in the transmission mechanism by overlooking some key macro-ﬁnance
implications of monetary policy models. Our results suggest that the question of asym-

ECB Working Paper Series No 292839metries should be addressed in models capable of matching some basic facts that not only
include the mean and standard deviation of interest rates, but also a measure of risk such
as the term premium.

8 Robustness analysis

For the sake of parsimony and to keep the analysis as transparent as possible, the main
result of the paper, which is illustrated in Figure 2, is derived in the simplest possible
framework. In this section we assess the extent to which our results are robust to more
general assumptions. In particular, following most of the literature on monetary economics,
we ask whether asymmetries are still present in a version of the model augmented with price
stickiness. We then discuss the case of a more general utility speciﬁcation with constant
elasticity of substitution, provide empirical evidence in support of our mechanism, study
additional demand shocks, and provide a measure of the welfare cost of business cycle
ﬂuctuations.

8.1 Introducing price stickiness

In contrast to the vast majority of models used to study monetary policy, the analysis
developed so far abstracts from any source of nominal rigidities. A natural question to ask
as this stage is whether our mechanism still plays a role once embedded into the workhorse
New Keynesian model. Given that we introduce price stickiness using a completely standard
textbook approach (i.e. Galì (2015); Walsh (2017)), the New Keynesian version of the
model is shown in the online appendix.

Parameter selection
Relative to the model analyzed in the previous section, we have two new parameters to
calibrate. Since these two parameters are standard, we use values that are widely accepted
in the New Keynesian literature. First, for the price elasticity of demand parameter  we
follow Galì (2015) and set it to 9. This implies a steady state markup of 12.5%. Second, the
nominal rigidity parameter  determines the average price duration. Following Galì (2015),
we set this parameter to 0.75, which implies an average price duration of four quarters.

The set of calibrated parameters are kept at the values discussed in Section 4. Following
the approach described in Section 3.4, the remaining parameter values are selected to
maximize the model’s ability to reproduce the set of macroeconomic and ﬁnancial variables
shown in Table 2.

ECB Working Paper Series No 292840In the version with Calvo price stickiness, we ﬁnd that the model is still broadly able
to reproduce these moments. In this case, the loss function is minimized for the following
set of parameter values:

Table 4: Moment Matching Procedure, Model with Nominal Rigidities
















0.99

0.999

0.97

0.98

0.49

1.4

0.015

0.0073

0.018


0.977


0.6


1.2

The comparison between the model implied simulated moments and the data is reported
in Table B.1 in the appendix. Overall, it is fair to say that the introduction of price stickiness
does not signiﬁcantly impair the model’s ability to reproduce these moments. Relative to
the benchmark model, the ﬁrst main diﬀerence is that in a model with price rigidities a lower
coeﬃcient in the monetary policy rule  is needed to match the volatility of inﬂation. Since
price stickiness dampens the response of inﬂation, a less aggressive reaction to variations in
prices is needed to match this moment. The second main diﬀerence is that the monetary
policy shock standard deviation  is about 25 percent lower than in the ﬂexible price
model. Since nominal rigidities are a source of monetary policy non-neutrality, the eﬀect
of monetary policy shocks are ampliﬁed and shocks of a smaller magnitude are needed to
reproduce these facts.

The state dependence of monetary policy transmission with price stickiness
The response of output to a one standard deviation monetary policy shock in the low
and high credit states is shown in Figure B.1. The takeaway is that the asymmetry implied
by our mechanism is robust to the introduction of Calvo staggered contracts, which is a
very widely used speciﬁcation of nominal rigidities in the New Keynesian literature. Indeed,
as illustrated in in Figure B.1, the response of output to a monetary policy shock remains
considerably stronger in the low credit state. Relative to the response obtained in the
benchmark model shown in the left panel of Figure 2, the main diﬀerence is that monetary
policy has a stronger eﬀect on output. Although the monetary policy shocks standard
deviation is about 25% smaller in the New Keynesian version, the increase in output in the
low credit state reaches 0.3%. In contrast, in the ﬂexible price model the maximum impact
on output stands below 0.2%.

The persistence of real and nominal variables
A limitation of the ﬂexible price model is that it fails to reproduce the high autocorrela-
tion of inﬂation observed in the data. Indeed, the growth rate of both inﬂation and output,
as measured by the 4-quarter change in logs, exhibits a high degree of persistence. As can

ECB Working Paper Series No 292841be seen in Table 5 below, whereas the ﬂexible price benchmark generates persistence in
output growth, the high autocorrelation of inﬂation cannot be reproduced.

Introducing Calvo staggered contracts considerably improves the model’s ability to re-
produce this high autocorrelation coeﬃcient. Since a fraction of ﬁrms cannot adjust prices
each period, nominal rigidities considerably increase the persistence of inﬂation, the auto-
correlation coeﬃcient of which increases from 0.48 in the ﬂexible price benchmark to 0.86
in the New Keynesian version.

Table 5: The persistence of real and nominal variables

Data

Flexible Price Model

Sticky Price Model

( 
1)
−
(   
1)
−

0.88

0.90

0.75

0.48

0.84

0.86

Table 5. ( 

1) and (   

1) denote the autocorrelation coeﬃcients of output

growth and inﬂation, respectively.

−

−

8.2 CES utility function

Another potential limitation of the baseline model is that we assume a Cobb-Douglas
speciﬁcation for the utility function. This particular utility function in turn implies a
speciﬁc relationship between the deposit rate  and cash  (see equation (14)). In this
section, we assess whether our mechanism is robust to a more general utility function with
constant elasticity of substitution (CES) by considering the following speciﬁcation:

1


1

 + (1
−

 Ã∙

∞



0

=0
X

−

1


1

−

1

1

−

1

 ( + 
 )

)




³

´
1

¸


−

1



−



−

!

This speciﬁcation in turn implies the following money demand function:

b

 =

)

(1

−


1



 ¶

µ

(25)

ECB Working Paper Series No 292842The parameter  denotes the constant price elasticity of demand8 and the Cobb-Douglas
case is obtained when  is set to 1. It is important to acknowledge that the elasticity pa-
rameter  has a major impact on the model’s ability to generate asymmetries. Indeed, if
 is set to 10, the cash demand schedule shown in Figure A.8 becomes ﬂat. Consequently,
without the curvature implied by the Cobb-Douglas speciﬁcation, the model could poten-
tially lose its ability to generate asymmetries. In contrast, for values of  lower than 1, the
nonlinearity of the cash demand schedule is preserved.

Using external evidence to calibrate 
Given the importance of this parameter for our results, we use available evidence to
assess whether the assumption of a unit elasticity can be supported by the data. Starting
from equation (25), we estimate the following equation:

log  = 0 + 1 log


 ¶

µ

For the deposit rate, we use data on new deposits by households with a maturity less than
a year, which is the closest empirical counterpart for . Nominal consumption  is
proxied by ﬁnal consumption expenditures. Data on currency in circulation can be used as
an empirical counterpart for  which denotes cash held by households. We ﬁrst estimate
this equation using monthly data for the period from 2002 to 2018 and then add the
COVID-19 period.9

Table 6: Estimated money demand elasticity

2002q1-2018q1

2002q1-2022q3

1.38

2.5

[0.87; 1.89]

[1.99; 3.0]

Sample
1
95% CI
b

As shown in the ﬁrst column of Table 6, our results suggest that, in the pre-COVID
period, the Cobb-Douglas speciﬁcation cannot be rejected by the data. Indeed, the esti-
 = 1 If we add the
mated value for
1 of 2.5, which therefore implies a value for  of
COVID-19 period, we obtain a value for
0.4.

1 is 1.38 and we cannot reject the hypothesis that 1

b

8With this speciﬁcation, we have that:

b







−

= 

9In the euro area banknotes were introduced physically in January 2002.

ECB Working Paper Series No 292843The main takeaway is that a value for  lower than one, as suggested by the estimated
value obtained for the full sample, does not impair the model’s ability to generate asymme-
tries. To illustrate this point, the impulse response in Figure B.2 is simulated using a value
for  of 0.4 in the version of the model with monopolistic competition and price stickiness.
Clearly, the state dependence of monetary policy transmission is robust to the introduction
of nominal rigidities as well as a more general utility function.10

8.3 Supportive empirical evidence

Having established that the model mechanism under study is robust to the introduction
of nominal rigidities as well as a more general utility speciﬁcation, the objective of this
section is to assess whether some empirical support can be provided. This is achieved by
exploiting the model structure to derive a testable implication. First, given the policy rule
that we have speciﬁed in equation (10), we can construct an empirical counterpart for the
monetary policy shock by estimating the following regression:

1

−

 1 = 0 + 1

1

1

−

−

 1

+ 2(



 ) +



−

³

´

c

c

c

1 denotes the money supply, as proxied by the monetary aggregate 1 and where
where
 is the consumer price index in level.  1 and  denote the sample mean of the money
supply and the price level. Data on money supply and the price level are available on a
b

monthly basis. In this regression, the monetary policy shock therefore corresponds to
and is estimated using monthly data by correcting for heteroskedasticity and autocorrela-
2 has the expected negative sign, as postulated by the
tion. We ﬁnd that the parameter
monetary rule speciﬁed in equation (10).11

b

b

b

b

The next step is to estimate the eﬀect of the monetary policy shock implied by our
theory on ﬁnancing conditions. Indeed, the asymmetry at the core of our mechanism relies
on the eﬀect of monetary policy on bank lending rates. Therefore, one possible way to
formally test our hypothesis is to check whether the eﬀect of the monetary policy shock on
bank lending rates depends on the state of the economy.

Since monetary policy typically works with a delay, we estimate the cumulated eﬀect of
a monetary policy shock over a 12-month period. Indeed, as prices typically adjust after 4

10Relative to the benchmark model, combining price stickiness with a value for  of 0.4 also allows us to
increase the persistence of prices, a dynamics in closer conformity with the available evidence documented
in the literature on structural VARs (e.g. Christiano et al. (2005)).

11The hypothesis that the shock has a unit root can be rejected by performing an augmented Dickey-

Fueller test on the estimated residual.

ECB Working Paper Series No 292844quarters on average, monetary policy should have its largest impact on the economy within
this time frame. We then test for state dependence by introducing an interaction term that
takes the form of a dummy variables. This dummy variable, which is denoted by 10
takes a value of one during months in which a recession was observed in the euro area and
zero otherwise. We then estimate the following condition, where bank lending rates are
denoted by

 :

b

12

12

−



Ã



 = 0 + 1

+ 2 ·
and where  denotes the error term. Our theory ﬁrstly implies a negative value for 1, as
expansionary monetary policy shocks should reduce bank lending rates. If the transmission
mechanism is indeed state-dependent and monetary policy more powerful during recessions,
we should observe a signiﬁcant and negative value for 2

=1
X

=1
X

10

+ 

· Ã



!

!

b

b

b



−

Since in the euro area, SMEs represent about 99% of all ﬁrms, and since SMEs typically
contract small loans, we use data on interest rates that correspond to loans smaller than 1
million euros. Interest rates on loans with short-term maturities are also the best empirical
counterparts for , which captures short-term ﬁnancing conditions.

Bank lending rates for the euro area as a whole are only available since January 2000
on a monthly basis. This sample period nevertheless includes 3 recessions, as deﬁned by
the Centre for Economic Policy Research (CEPR): (i) the Great Recession from the ﬁrst
quarter of 2008 to the second quarter of 2009; (ii) the Sovereign Debt crisis, from the third
quarter of 2011 to the last quarter of 2012; and (iii) the COVID-19 crisis from the ﬁrst to
the second quarter of 2020.

The result of this regression is reported on the ﬁrst line of Table 7 below, where the
interest rate on bank lending rates is the dependent variable. It is reassuring to see that
1 not only has the expected sign but is also signiﬁcant at the 5% level. Importantly, and
2 has the expected
as illustrated by the second column of Table 7, the interaction term
b
sign and is signiﬁcant at the 5% level.12

b

12In this regression, the estimated shock

 is standardized and has mean zero and a standard deviation

of 1.

b

ECB Working Paper Series No 292845Table 7: State-dependent monetary transmission
2
Estimated value
b

95% CI

Estimated value
b

1

-0.098

[-0.158, -0.039]

-0.16

-0.098

[-0.15, -0.04]

-0.18

95% CI

[-0.30, -0.02]

[-0.32, -0.05]

2

0.22

0.30

Dependent

variable



b
b

As illustrated by the second line of Table 7, a very similar conclusion emerges if we

use the deposit rate instead of the bank lending rate. In the data, the deposit rate
refers to the short-term deposit rate received by households and non-proﬁt institutions
serving households, a series which is also available on a monthly basis from January 2000.
Furthermore, we checked that the results are robust if we exclude the COVID-19 period.

b

While imperfect, this test nevertheless provides some tentative empirical support to our
1 conﬁrms that expansionary monetary policy
mechanism. The negative value obtained for
shocks propagate to the economy by reducing bank lending as well as deposit rates. As
b
2, this eﬀect of monetary policy on both lending
shown by the larger coeﬃcient obtained for
and deposit rates is stronger during periods of recession, which in our model corresponds
to periods of credit crunch.

b

8.4 Demand shocks

As illustrated by the results reported for the New Keynesian version in Table B.1, the
model with technology shocks as the only source of real ﬂuctuations is capable of matching
several business cycle and ﬁnancial market facts. This is also the approach followed in the
classic paper of Jermann (1998). For the euro area, the other main motivation to focus on
supply shocks is that the correlation between output and inﬂation, as measured by the core
inﬂation index which excludes energy and processed food, is negative.13

At the same time, and as shown in Table 8 below, although the New Keynesian version
with technology shocks can broadly reproduce the facts reported in Table B.1, it generates a
correlation between output growth and inﬂation of -0.9, whereas in the data this correlation
only reaches -0.2. A natural question to ask is whether asymmetries can still arise in a model
capable of generating a correlation between output growth and inﬂation that matches the
evidence.

13In sticky price models, core inﬂation is the most suited indicator as this index excludes volatile compo-
nents such as the price of energy and unprocessed food, which are not subject to the kind of price rigidities
envisioned in the New Keynesian literature.

ECB Working Paper Series No 292846Recent ﬁndings in the literature have also highlighted the importance of demand shocks
In particular, Albuquerque, Eichenbaum, Luo and Rebelo (2016) have
for asset pricing.
shown that introducing discount factor shocks into consumption-based models provides a
potential resolution to several well-known asset pricing puzzles. In the context of a produc-
tion economy, Miao, Wang and Zha (2020) ﬁnd that discount factor shocks help explain
the disconnect between house prices and rents, a well-established empirical regularity that
models with standard demand shocks cannot reproduce.

In our New Keynesian model, introducing these demand shocks can be achieved by as-
suming that the modiﬁed subjective discount factor  is subject to exogenous disturbances.
With discount shocks, the eﬀective discount rate used by agents to evaluate future ﬂows is
now a time-varying object denoted by :

where the preference shock © is an autoregressive process of order one:

 = ©

© = ©
−

1 + 

and where  is a persistence parameter. In this process, the exogenous disturbance  is
normally distributed with mean zero and standard deviation .

As shown in Table 8 below, we ﬁnd that discount shocks not only enhance the model’s
ability to reproduce a sizeable term premium, these shocks also considerably reduce the
correlation between output and inﬂation.

Table 8: NK model with demand shocks vs. NK model with supply shocks

Technology shocks
= 00073

Demand shocks
 = 0004

Data

Estimated 95% CI

()
()
( 

 )

0.7

1.8

-0.9

0.7

1.6

-0.2

0.7

1.8

-0.2

[0.5, 0.9]

[1.6, 2.1]

[-0.4, 0]



Since discount factor shocks are typically estimated to be persistent (e.g. Miao et al. 2020),
we set the persistence parameter to 0.99. Replacing technology by demand shocks and
setting the shock standard deviation  to 0004 allows the extended model to perfectly
match the term premium () as well as the correlation coeﬃcient between inﬂation and
output, which in Table 8 is denoted by ( 
 ). The standard deviation of output
generated by the model also lies within the estimated conﬁdence interval.



ECB Working Paper Series No 292847Are monetary asymmetries still present? The state dependent impulse response analysis
for the demand shock model is shown in Figure B.3. It is reassuring to see that signiﬁcant
asymmetries can still be obtained if discount shocks are the only source of real ﬂuctuations.

Interest on money
Since the welfare cost of inﬂation stems from the opportunity cost of holding money,
we next consider the case in which the central bank oﬀers a remuneration on cash. Of
course, in practice, paying interest on cash is subject to obvious technical diﬃculties. At
the same time, this is a classic extension in models in which money is explicitly introduced
(e.g. Walsh (2017)). Moreover, at present, such an experiment could be motivated by the
ongoing discussions with regards to central bank digital currencies (CBDCs). Indeed, if
CBDCs were introduced, central banks could remunerate cash directly.

When cash  is remunerated, and given the assumption of a representative agent, the
only diﬀerence relative to the extended model discussed in Section 8.1 is that the policy
rate, which we denote by , aﬀects the money demand equation (14):

where we introduce the following process for the policy rate :

 =  +

(1

)




−


 =  +  (

) + 

−

(26)

(27)

In equation (27),  is a random disturbance that is normally distributed with mean zero
and standard deviation  .  is the interest rate smoothing parameter and  denotes
the steady state value of the policy rate.

To gain intuition into how a change in the interest rate on cash holdings is transmitted
to the economy, Figure B.4 plots the demand curve in equation (26) when the policy rate
 increases from 0 to 0.5%. In contrast to a change in the quantity of money , the key
diﬀerence is that an increase in  shifts the demand for cash to the right.

As pointed out by Piazzesi, Rogers and Schneider (2019), the presence of a convenience
yield dampens the eﬀect of changes in interest rates in New Keynesian models.
In our
analysis, this eﬀect can be explained by the response of  to a change in the policy rate
 Indeed, as can be seen from equation (26), everything else equal, an increase in cash
holdings  in response to a higher remuneration rate attenuates the eﬀect of the monetary
policy shock on the deposit rate  This illustrates that a concave preference for liquidity
implies that banks can aﬀord to pay a lower rate on bank deposit  when agents in the
economy hold large amounts of cash.

ECB Working Paper Series No 292848The pass-through of a change in the policy rate  to the bank deposit rate  therefore
depends on the response of . What does it imply for monetary policy transmission? As
illustrated on Figure B.4, for a given level of  a 0.5% increase in the policy rate  which
makes holding cash more attractive, has a stronger impact on the equilibrium level of the
bank deposit rate  when agents already hold large amounts of cash. The reason is that the
demand for cash is less sensitive to changes in the remuneration rate in those states of the
world. Given the decreasing marginal utility of money, agents’ appetite to hold even larger
quantity of cash declines during periods of low bank rates and abundant cash holdings.
Consequently, an increase in  only leads to a small increase in cash holding  in those
states of the world. Therefore, the dampening eﬀect stemming from the convenience yield
discussed in Piazzesi, Rogers and Schneider (2019) is more muted when agents already hold
large amounts of cash. Indeed, everything else equal, a smaller response of  in reaction
to an increase in  leads to a larger increase in the deposit rate .

In contrast, when households only hold small amounts of cash, an increase in  has
a larger eﬀect on the demand for  The dampening eﬀect is therefore particularly strong
during periods of high interest rates and low cash holdings.

As can be seen on Figure B.5, the impact of the convenience yield on the pass-through
from the interest rate on cash to bank rates is also a source of asymmetries. Indeed, a 0.5%
increase in the rate at which the central bank remunerates cash holdings has a stronger
eﬀect on output during periods of low bank lending rates. The main takeaway, therefore,
is that asymmetries could continue to play an important role if central banks were to issue
CBDCs that are remunerated, a possibility that is currently under discussion.

8.5 Using the welfare cost of business cycle ﬂuctuations to eval-

uate risk aversion

Since the seminal paper of Mehra and Prescott (1985), models are not only evaluated in
terms of their ability to jointly reproduce asset pricing and business cycle facts. The level
of risk aversion necessary to match these facts is also an important criteria.

However, evaluating risk aversion in dynamic general equilibrium models with produc-
tion is a complex task. In contrast to endowment economies, the process for consumption
is endogenously determined within a general equilibrium system. As a result, the ease
with which agents can insure against shocks, and hence the extent to which they care
about uncertainty cannot be summarized by one single measure of curvature of the utility
function.

ECB Working Paper Series No 292849Local measures of risk aversion and the term premium
To illustrate this point, Figure B.6 reports a sensitivity analysis showing how the term
premium varies with the adjustment cost parameter , while all other parameter values are
kept at the values reported in Table 1. Clearly, even in the presence of habits, the model
loses much of its ability to generate a realistic term premium if we reduce adjustment costs.
This illustrates the challenge at hands. In a production economy, local measures of risk
aversion that solely focus on preferences do not tell the full story.
In equilibrium, the
amount of risk agents are exposed to critically depends on general equilibrium eﬀects.

To provide a measure of risk exposure, we indirectly evaluate attitudes towards risk
by exploiting the tight connection between risk aversion and the measure of welfare cost
proposed by Lucas (2003) (e.g. Tallarini (2000)). One possible way to measure risk aversion
is to ask how much agents would be willing to pay to completely eliminate business cycle
ﬂuctuations. This measure is therefore akin to a risk premium that agents would be ready
to pay to be able to live in a certain world. While it cannot be demonstrated analytically,
such a measure is necessarily linked to the curvature of the value function, and hence risk
aversion. Indeed, a risk neutral agent would require a very small compensation, whereas very
risk averse agents would be ready to abandon a large share of their income to completely
eliminate uncertainty.

The cost of business cycle ﬂuctuations as a fraction of GDP
To perform this calculation, the ﬁrst step is to compute lifetime utility, which is given

by the value function of our representative agent, denoted by :

1



−







 = µ

³

´

( + 
 )



−

1



−

1



−

¶

+

+1

Since risk averse agents dislike ﬂuctuations, welfare in the stochastic economy that
reproduces the moments shown on Table 2 is lower than what would be obtained in the
same economy where the standard deviation of all shocks is set to zero, a case which can
be thought of as the certainty equivalent. Denoting by () welfare in the stochastic
economy that generates a 0.6% term premium, and  welfare in the deterministic economy
without shocks, and hence zero risk premiums, we therefore have that ()  

b

But how to convert the distance between () and  into a measure that can be in-
terpretable? We ask how much additional revenue agents would need to receive to be
indiﬀerent between the stochastic and the deterministic economies. Starting from the allo-
cation that matches the facts on Table 2, we therefore need to determine the compensation

ECB Working Paper Series No 292850required to make the agent indiﬀerent between the two allocations. Expressing this com-
pensation as a fraction of output, the compensation received by the agent living in the
risky economy is denoted κ where κ is the compensation parameter.14 The goal of the
exercise is then to ﬁnd a value of κ such that () =  In other words, starting from the
benchmark economy that reproduces a realistic term premium, by how much should we
increase κ to make agents indiﬀerent between the risky and the deterministic allocations?
We obtain a value for κ of 0.0188. This implies a cost of business cycle ﬂuctuations
In comparison, this measure, which is
amounting to 1.88% of total GDP per quarter.
reminiscent to a risk premium, falls from 1.88% to 0.023% if we remove habits from the
analysis.

Without habits, a welfare cost of 0.023% implies that an agent with a total disposable
income of 20,000 EUR would only ask to receive 4.6 EUR per year or about 40 cents per
month to completely eliminate business cycle ﬂuctuations. In this case, the risk premium
demanded by agents for having to live in a world subject to business cycles is thus negligible.
In equilibrium, agents are therefore close to risk neutral. Of course, the model without
habits is also unable to generate a realistic term premium since uncertainty is irrelevant.

In contrast, in the benchmark model that matches both asset pricing and business cycle
facts, for that same household, the cost of business cycle ﬂuctuations represents around
378 EUR per year, or 31.5 EUR per month.

Is the magnitude of this business cycle ﬂuctuation premium plausible? Whereas the
cost of business cycle ﬂuctuations is much larger in the model that matches the data and
produces asymmetries in the transmission mechanism, we argue that the value we obtain is
plausible. Indeed, many European economies do allocate a non-negligible fraction of their
resources to alleviate the eﬀects of business cycle ﬂuctuations. For example, according to
OECD data on public unemployment spending, as an average over the period from 1999
to 2019, Spain spent around 2.17% of GDP on unemployment insurance. In France and
Germany, this measure reaches 1.6% and 1.26% of GDP, respectively.15

9 Conclusion

Interacting ﬁnancing frictions with a preference for liquidity provides a potential expla-
nation for the time-varying eﬀectiveness of monetary policy documented in many studies.

14The compensation parameter therefore aﬀects the entire system.

It can also be interpreted as an

exogenous increase in productivity.

15Spending on unemployment insurance increased dramatically during the COVID-19 crisis.

ECB Working Paper Series No 292851This asymmetry is quantitatively important, as monetary policy is considerably more ef-
fective during periods of credit stress. The main policy implication is that this asymmetry
could reduce the eﬀectiveness of monetary policy, or amplify its impact, thereby impairing
central banks’ ability to achieve their price stability mandate.

With regards to model development, one main takeaway is that the magnitude of this
asymmetry crucially depends on the size of the term premium. Our results therefore suggest
that monetary asymmetries are more likely to play a role in models able to produce realistic
amounts of interest rate risk.

A ﬁrst main limitation is that this study does not consider the issue of ﬁrm heterogeneity.
Since SMEs are typically more likely to be credit constrained than large corporations, the
eﬀect of monetary policy could potentially vary across ﬁrms. This heterogeneity could in
turn generate a reallocation of inputs across ﬁrms in response to monetary policy shocks.
Whether this reallocation channel attenuates or ampliﬁes the asymmetric eﬀect of monetary
policy would be an interesting question for future work.

A second main limitation is that the model cannot reproduce the humped-shaped re-
sponse of inﬂation to monetary policy shocks documented in the literature that uses struc-
tural VARs.16 Jointly reproducing this fact in a framework also able to reproduce realistic
asset pricing implications remains a formidable challenge.

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ECB Working Paper Series No 292857King, R., Rebelo, S. (1999). "Resuscitating Real Business Cycles." Handbook of Macro-
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ECB Working Paper Series No 29286010 Annex A

2

1

0

0

-0.5

-1

Money

Prices

2

4

6

8

Short-term rate

0.4

0.2

0

1

0.5

0

2

4

6

8

Credit

2

4

6

8

2

4

6

8

Figure A.1. Response of the monetary aggregate the price level the short-term deposit rate,

and nominal credit to a one standard deviation monetary policy shock. x axis: quarters after the

shock. y axis: percentage deviation from steady state and annualized percent for short-term rate.

0.2

0.1

0

0.3

0.2

0.1

0

Output

Investment

0.06

0.04

0.02

0

2

4

6

8

0.2

0.4

0.6

0.8

Consumption

Hours

0.2

0.1

0

2

4

6

8

2

4

6

8

Figure A.2. Response of output investment hours and consumption. x axis: quarters after

the shock. y axis: percentage deviation from steady state.

ECB Working Paper Series No 292861Real wage

Marg. prod. capital

0.4

0.2

0

0.6

0.4

0.2

0

2

4

6

8

Real credit

0.6

0.4

0.2

0

0

-0.5

-1

2

4

6

8

Lending spread

2

4

6

8

2

4

6

8

Figure A.3. Response of the real wage, marginal productivity of capital, real credit, and the

lending spread to a one standard deviation monetary policy shock. x axis: quarters after the

shock. y axis: percentage deviation from steady state and annualized percent for lending spread.

Term premium

2

4

6
Bond prices

Real short-term rate

0

-0.05

-0.1

-0.15

6

8

4
Yield

8

2

0

-0.02

-0.04

-0.06

2

4

6

8

2

4

6

8

-0.001

-0.002

-0.003

0.6

0.4

0.2

0

Figure A.4. Response of the term premium, the short-term real rate, nominal bond prices, and

the nominal yield to a one standard deviation monetary policy shock. x axis: quarters after the

shock. y axis: annualized percent and percentage deviation from steady state for bonds prices.

ECB Working Paper Series No 2928621

0.8

0.6

0.4

0.2

0

0

Loan to output ratio
Cash holding ratio

0.2

0.4

0.6

0.8

1

Loan-in-advance parameter

Figure A.5. Sensitivity to credit friction parameter 

1

0.5

0

1.5

1

0.5

0

Money

Cash

1

0.5

0

2

4

6

8

2

4

6

8

Credit

Output

0.4

0.2

0

2

4

6

8

2

4

6

8

Figure A.6. Response of money, cash holdings, credit, and output to a one standard monetary

policy shock when  is set to 0.0001.

ECB Working Paper Series No 2928630.2

0.15

0.1

0.05

0

1

Output

No labor wedge
Benchmark

2

3

4

5

6

7

8

Figure A.7. Response of output to a positive shock in the model with and without a labor

wedge.

e
t
a
r

t
s
e
r
e

t

n

i

m
r
e

t
-
t
r
o
h
S

6

5

4

3

2

1

0

Cash demand schedule
Mean interest rate

0

0.1

0.2
Cash holdings

0.3

0.4

0.5

Figure A.8. Cash demand curve.

ECB Working Paper Series No 292864 
 
e
t
a
t
s

y
d
a
e
t
s
m
o
r
f

n
o
i
t
a
v
e
d

i

e
g
a
t
n
e
c
r
e
P

0.25

0.2

0.15

0.1

0.05

0

1

2

Output

Low credit state
High credit state

4

3
6
Quarters after the shock

5

7

8

Figure A.9. Response of output in the low and high credit states in the model with low interest

rate risk x axis: Quarters after the shock. y axis: Percentage deviation from steady state.

ECB Working Paper Series No 292865 
 
 
 
11 Annex B: Robustness

Table B.1: Model vs. Data

Data

95% conﬁdence Estimated empirical

()
()
()
( )
()
( )
()
()
()
(−
()
()

)

interval

[1.6, 2.1]

[0.9, 1.2]

[5.0, 6.6]

[2.8, 3.8]

[1.8, 2.4]

[0.8, 1.1]

[1.8, 2.4]

[2.1, 2.6]

[0.5, 0.9]

[2.2, 2.4]

[0.88, 0.95]

[0.21, 0.22]

moments

1.8

1.0

5.7

3.3

2.0

0.9

2.0

2.4

0.7

2.3

0.91

0.22

Model

Simulated moments
(3rd order)

1.7

0.9

5.8

3.3

2.1

1.0

2.6

2.2

0.7

2.3

0.86

0.21

Output

Low credit state
High credit state

0.3

0.2

0.1

0

-0.1

1

2

3

4

5

6

7

8

Figure B.1. Response of output in the low and high credit states. Model with price stickiness.

x axis: Quarters after the shock. y axis: Percentage deviation from steady state.

ECB Working Paper Series No 2928660.3

0.25

0.2

0.15

0.1

0.05

0

-0.05

Output

Low credit state
High credit state

1

2

3

4

5

6

7

8

Figure B.2. Response of output in the low and high credit states. Model with price stickiness

and CES utility function. x axis: Quarters after the shock. y axis: Percentage deviation from

steady state.

0.4

0.3

0.2

0.1

0

-0.1

1

Output

Low credit state
High credit state

2

3

4

5

6

7

8

Figure B.3. Demand shock model when () = 07 = 0004 ( 

 ) =

sponse of output in the low and high credit states. x axis: Quarters after the shock. y axis:

Percentage deviation from steady state.

02 Re-

−



ECB Working Paper Series No 292867e
t
a
r

t
s
e
r
e
t
n

i

m
r
e
t
-
t
r
o
h
S

6

5

4

3

2

1

0

Initial demand curve
0.5% increase

0

0.02

0.04
0.06
Cash holdings

0.08

0.1

Figure B.4. Equilibrium in the money market before and after an increase in the interest rate

on cash of 0.5 percentage point.

0.05

0

-0.05

-0.1

-0.15

-0.2

-0.25

Output

Low rate environment
High rate environment

2

4

6

8

10

12

Figure B.5. Response output in the low and high interest rate environment to a 0.5 percentage
point increase in the interest rate on cash . Model with Calvo price stickiness. x axis: Quarters
after the shock. y axis: Percentage deviation from steady state.

ECB Working Paper Series No 292868 
 
3

2.5

2

1.5

1

0.5

0

)

%

.
n
n
a
(

i

m
u
m
e
r
p
m
r
e
T

-0.5

0

1

2
Adjustment cost parameter

3

4

Figure B.6. Sensitivity of the term premium () to the capital adjustment cost parameter



ECB Working Paper Series No 292869 
 
 
12 Annex C: Data Appendix

Variables

Output, 

Description

Real GDP

Source

Stat. Oﬃce of the EC

EA 19, mio of chained 2010 Euros

1995q1-2018q4

Consumption, 

Final consumption expenditures

Stat. Oﬃce of the EC

EA 19, mio of chained 2010 Euros

1995q1-2018q4

Investment, 

Gross capital formation

Stat. Oﬃce of the EC

EA 19, mio of chained 2010 Euros

1995q1-2011q4

Money supply, 

M1 Money supply adjusted for

ECB

reclassiﬁcations, EA 11-19

1997q3-2018q4

Deposit, 

Total deposits of euro area households ECB

amount outstanding

1997q3-2018q4

Price level, 

Harmonized index of consumer prices

ECB

2015=100, EA 11-19

1997q1-2018q4

Monetary policy rate, 

3-month deposit (EURIBOR)

ECB

EA 11-19

1995q1-2018q4

Long-term rate, 10

10-year government benchmark

ECB

bond yield, EA 11-19

1995q1-2018q4

Term premium, ()

Term structure model for the

Hördahl and Tristani

euro area and the U.S.

1999q1m7-2018q4

Intermediation spread, 

−

 Rate on new loans to non-ﬁnancial
corporations (less than 1 mio, less

ECB

2000q1-2018q4

Loan-to-output ratio, 

Credit to non-ﬁnancial corporations

BIS

than a year) minus 3-month deposit

% of GDP, market value

1997q3-2018q4

ECB Working Paper Series No 29287013 Online Technical Appendix (not for publication)

13.1 The competitive equilibrium

Households

max
+1+1+1+1

0

1



−







µ

³

´

1



−



−

¶

( + 
 )



1

−

∞





=0
X

b

where:

such that:

 =

1
−



b

e



+1


=




+




1 =  + 

 +   +  + 




+  +




=  +  + 

+1

 −




+

1
1 + 



+1


+1 = (1

) +

−

1

−



1

Ã

+1 =   + (1

 )


−

µ

The Lagrangian:


 ¶
µ

 ¶

1



−

1


−

+ 2



!

( + 
 )

1



−

( + 
 )

´



1

−

1



−



−

¶







∞





³

µ

 = 0 ⎧
⎪⎪⎪⎨
=0
X
⎪⎪⎪⎩
 +   +  + 
 +1

b

+

∞







=0
X

b

⎡

⎣

 +1

 −



−

´




´
1
1+

+  + 
 +1


 −





−

⎤

⎦

³
 −

−

³

ECB Working Paper Series No 292871+

∞







) +

(1

"

−

1

−



µ

1

Ã

1


−


 ¶

+ 2



−

!

+1

#







  + (1

"

 )


−

µ

1



−


 ¶

( + 
 )

+1

−

#)

=0
X

b
∞

+

=0
X

Banks
Banks maximize proﬁts, which are given by:

b

such that:

Firms

such that:

 = 


 −






 = 

max


  = 


 1
−
 −



−





−





 ≥

 ( + )

The Lagrangian:

= 0

L



 
0 (

∞

=0
X




 1
−
 −

+ 
 −





 ( + )

−

−




)

i

Market clearing condition

b

h



 1
 =  + 
−



13.2 The dynamic system




("

µ

1



−


 ¶

( + 
 )



−



#

−

+ (1

 )

−

)




1

−

µ

1



−


 ¶

( + 

 ) = 




("

µ

1



−


 ¶

( + 
 )



−



#

−

+ (1

 )

−




)

µ

1



−


 ¶



 = 
−

1

ECB Working Paper Series No 292872




1

=





−


 = +1+1

) +

(1

"

−

1

−

1



µ

1


−

+1
+1 ¶

+ 2

1

−

µ

1


−

+1
+1 ¶

+ +1+1

17

#

1 = 1




= +1


−

µ


 ¶
1
+1

+




1
1 + 

= +1






1
+1

+1 =  + 

 =  +1 −




+1

Ã

µ

1



−

+1
+1 ¶

( + 

+1)



−

+1

−

!

(1

−

) +

1

−



µ

1

Ã

1


−


 ¶

+ 2



−

!

+1 = 0

  + (1

 )


−

µ

1



−


 ¶

( + 
 )

−

+1 = 0

 = 

 =

1




 = 

 1
−




17where for the sake of notation, I deﬁne:

 =


−

e

ECB Working Paper Series No 292873


= 


1 +  


 = (1

)

−




1
1 +  


 = 




1
1 +  


 =




 =  + 

+1 =  + 





−

−

(

−

 ) + 

¡
¢
log  =  log 
−

1 + 

13.3 Introducing Price Stickiness

This section describes how the introduction of price stickiness aﬀects the production side
of the economy.

13.3.1 Imperfect competition

Price rigidities imply that ﬁrms are able to set prices and therefore enjoy some degree of
market power. Following Galì (2015), among others, this is achieved by ﬁrstly introducing a
ﬁnal goods sector that produces the ﬁnal output good  The ﬁnal output good is obtained
by combining the inputs produced by each intermediate good producer. Each intermediate
good producer  produces a variety of the intermediate good, which is denoted by 

Every period, the ﬁnal goods producer chooses the quantity of inputs that minimizes

costs:

1

min


Z0



where  represents the price of variety  subject to a Dixit-Stiglitz aggregator that con-
verts intermediate goods into the ﬁnal good  :

ECB Working Paper Series No 2928741

⎛

Z0



1

−



 





1

−

⎞



≥

where we assume the existence of a continuum of goods. The quantity of goods is ﬁxed
and normalized to 1. The outcome of this optimization problem is a demand schedule for
the variety  :

⎝

⎠

 =



(28)




 ¶

µ

The Dixit-Stiglitz parameter  can be interpreted as the price elasticity of demand. The
higher this parameter, the more elastic the demand for variety  and the lower the market
power of intermediate good producer  Optimality in turn implies that the aggregate price
level  is determined as follows:

1

1



−

 =

1

⎛

Z0

⎝


 1
 
−

⎞

⎠

(29)

13.3.2 Intermediate goods producers

In the New Keynesian version, the loan-in-advance constraint appears in the problem of
each intermediate good producer  Each period, intermediate good producer  chooses the
optimal combination of inputs that minimizes costs:



where   and  denote the number of hours worked to hire, the quantity of capital
to rent, and the amount of credit obtained from banks, respectively.18

 + 







 +

min

Firms minimize costs subject to the production function:

 = 

1
−




where  is total factor productivity, which is common across all intermediate good pro-
ducers, and the loan-in-advance constraint:

18Since labor, capital and credit are perfectly mobile across intermediate good producers, wages , the
rental rate of capital  and the bank lending rate  are identical across ﬁrms and we drop the index 
to denote these variables.

ECB Working Paper Series No 292875
 ≥






 +






µ

¶

As in the baseline model, the optimization condition with respect to credit gives rise to the
following condition:

 =




where  is the Lagrange multiplier associated with the loan-in-advance constraint and 
marginal utility.19

Relative to the baseline case, the diﬀerence is that the presence of monopolistic com-
petition introduces a time-varying markup, which is denoted by  and which is identical
across intermediate goods producers.20 Therefore, the labor and capital demand schedules
are given as follows:




1 +

µ

1 +

µ



¶






= (1

)




−






¶

= 




13.3.3 Optimal pricing

After having determined the optimal quantity of inputs, and since they are monopolistic
competitors, intermediate good producers choose the optimal price. Following Galì (2015),
we focus the analysis on the case of Calvo pricing (e.g. Calvo, 1983), which is commonly
used in the New Keynesian literature. The Calvo friction implies that each period only a
 of intermediate good producers are able to adjust prices. When setting its
fraction 1
price, an intermediate good producer  thus needs to take into account that with probability
, it will not be able to reoptimize its price for several periods. When able to adjust its
price, the ﬁrm therefore needs to anticipate that it may be unable to reoptimize for several
periods. Consequently, the optimization problem takes the following form:

−

19As the banking sector charges the same lending rate to each ﬁrm, the tightness of the loan-in-advance
constraint is the same for all intermediate good producers. We therefore drop the index  for the Lagrange
multiplier.

20Marginal costs depend on wages, the rental rate of capital, bank lending rates and total factor pro-
ductivity, which are all common across ﬁrms. We can therefore drop the index  to denote marginal
costs.

ECB Working Paper Series No 292876

max
 ∗

∞

=0
X





 +



+ µ

 ∗
+

+

−

++

¶

b

 +



+

is the stochastic discount factor.  ∗ is the optimal price chosen by a
where
ﬁrm that is able to adjust its price in the current period. The assumption of monopolistic
competition in turn implies that ﬁrms take the demand for their variety  given by equation
(28), as an additional constraint.

b

After a few manipulations, we obtain the following condition for the optimal price chosen
by ﬁrm  . Since ﬁrms that are able to adjust in the current period choose the same price,
we have that (e.g. Walsh (2017)):

 ∗


=





−

1



∞=0  +




+

+

P



∞=0  +




+

³
+


1
´
−

+



+

+



(30)

13.3.4 Aggregate dynamics and price dispersion term in nonlinear models

P

³

´

Using the deﬁnition of the aggregate price level in equation (29), and given that all ﬁrms
resetting prices will choose  ∗  the Calvo pricing assumption in turn implies the following
dynamics for the aggregate price level:



 1
 = (1
−

−

1
) ∗


−




+  1
−

1
−

(31)

When  = 0 equations (31) and (30) therefore imply a constant markup given by the
following expression:

 =



1

−


(32)

Since the model is solved using a nonlinear solution methods, we also need to analyze how
the price dispersion term, which is the source of ineﬃciency in sticky price models, aﬀects
aggregate variables. Starting from the production function of intermediate good producer
 :

 = 

1
−




and given the demand for variety  in equation (28), the economy’s aggregate production
function is given as follows:

where:

 =





 1
−

∆

ECB Working Paper Series No 2928771

∆ =

0 µ
Z



−


 ¶



(33)

and where ∆ denotes the price dispersion term, which can be expressed recursively as
follows21:

∆ = (1

)

−

µ



−

 ∗
 ¶



−

1

−


 ¶

+

µ

∆

1

−

13.4 The New Keynesian version with CES utility

Households

1


1

 + (1
−

)

−

µ

1

−


 ¶

1


1

1

−

1


#

( + 
 )



−

)

−

µ

1

−


 ¶

1


1

1

−

1
1
 −

#

( + 

 )−


1


⎧
⎪⎨

⎡

"

⎣

1


⎪⎩
1

 + (1
−
"
= 

1


1
 + (1
−
"

)

−

µ

1

−


 ¶

1


1

1

−

1


#

( + 
 )



−

⎧
⎪⎨

⎡

⎣

1


⎪⎩
1

 + (1
−
"

)

−


1 + 

)

(1

−





 ¶
µ
∆

=

1

−

1


1

1

−

1


#




1

−



−

⎤

⎦



−

⎤

⎦

+ (1

−

 )⎫
⎪⎬

⎪⎭

+ (1

−

 )⎫
⎪⎬

⎪⎭

(34)

(35)

21To obtain this expression, we ﬁrst need to express equation (33) as follows:

1



−

∆ =

0
Z

 ∗
 ¶

µ



−

1

 +



−



1

−


 ¶

1
Z

 µ

−

Then since the distribution of prices among ﬁrms not adjusting corresponds to the distribution of prices
in period 

1 (e.g. Gali, 2015) we obtain:

−

∆ = (1

)

−

µ



−

 ∗
 ¶

1

−


 ¶

1



−



0 µ
Z

+

µ




1

−
1 ¶
−



−



ECB Working Paper Series No 292878 =



1

−





= +1


 ¶
µ

1

+1

+

1







1
1 + 

= +1

1
+1

 =  +1 −



1


1
+1 + (1
−
"

⎛

)

−

µ

1

−

+1
+1 ¶

1


1

1

−

1


#

( + 

+1)



−

⎝

+1 =   + (1

 )

−

1


1

 + (1
−

"

)

−

µ

1 =  + 

1

−


 ¶

1


1

1

−

1


#

( + 
 )



−

⎞

⎠

 = +1+1

(1

) +

++1

−

Ã
+1
1 + +1





µ
−
∆+1

1
+1
+1

1

1


−

+1
+1 ¶

+ 2

1

−

µ

1


−

+1
+1 ¶

!

1 = 1


−


 ¶

µ

(1

−

) +

1

−



µ

1

Ã

1


−


 ¶

+ 2



−

!

+1 = 0

Optimal Pricing:

 =  + 

 ∗


=






1



−



 1
 = (1
−

−

1
) ∗


−




+  1
−

1
−

(36)

(37)

(38)

(39)

(40)

(41)

(42)

(43)

(44)

(45)

(46)

(47)

(48)

ECB Working Paper Series No 292879∆ = (1

)

−

µ



−

 ∗
 ¶

+



−

∆

1

−

1

−


 ¶

+1

µ
+1


  =  

  + 

 +1

 =  
−


1

 + 

+1



+1

+1

Financial frictions:




= 


1 + 



 = 

 =

 =




1




Production function:

Market clearing:

Monetary policy rule:

 =





 1
−

∆

 =  + 

 =  +  (
−

1

−

) + (

−

 ) + 

TFP shock:

log  =  log 
−

1 + 

(49)

(50)

(51)

(52)

(53)

(54)

(55)

(56)

(57)

(58)

(59)

ECB Working Paper Series No 29288013.5 Replication ﬁles

The main results of the paper can be replicated by using Dynare. Dynare is a free software
that can be downloaded online:

https://www.dynare.org/download/

Replication ﬁles are available on my webpage:

https://sites.google.com/site/ivanjaccard/replication-ﬁles

ECB Working Paper Series No 292881Acknowledgements 

The views expressed in this article are my own and do not represent the views of the ECB or the Eurosystem. This draft as well as 
previous versions of this project have benefited from comments and suggestions from D. Krueger, 4 anonymous referees, O. Tristani, V. 
Quadrini, W. den Haan, G. Rousselet, and from participants at the 7th Asset Pricing Workshop of the University of York, the Workshop in 
Empirical and Theoretical Macroeconomics of King’s College, the T2M conference and the Conference Computing in Economics and 
Finance. The impulse response analysis performed in Section 7 has benefited from comments and suggestions from M. Juillard. Any 
remaining errors are my own responsibility. 

Ivan Jaccard 
European Central Bank, Frankfurt am Main, Germany; email: Ivan.Jaccard@ecb.europa.eu 

© European Central Bank, 2024 

Postal address  60640 Frankfurt am Main, Germany 
Telephone 
Website 

+49 69 1344 0 
www.ecb.europa.eu 

All rights reserved. Any reproduction, publication and reprint in the form of a different publication, whether printed or produced 
electronically, in whole or in part, is permitted only with the explicit written authorisation of the ECB or the authors.  

This paper can be downloaded without charge from www.ecb.europa.eu, from the Social Science Research Network electronic library or 
from RePEc: Research Papers in Economics. Information on all of the papers published in the ECB Working Paper Series can be found 
on the ECB’s website. 

PDF 

ISBN 978-92-899-6676-4 

ISSN 1725-2806 

doi:10.2866/040155 

QB-AR-24-045-EN-N