d11.4 – robust monetary and fiscal policies under model ... · robust monetary and fiscal...
TRANSCRIPT
MACFINROBODS – 612796 – FP7-SSH-2013-2
D11.4 – Robust Monetary and Fiscal Policies under Model Uncertainty
Project acronym: MACFINROBODS
Project full title: Integrated Macro-Financial Modelling for Robust Policy Design
Grant agreement no.: 612796
Due-Date: 31 October 2016 Delivery: 31 October 2016 Lead Beneficiary: GU Dissemination Level: PU Status: submitted Total number of pages: 80
This project has received funding from the European Union’s Seventh Framework Programme (FP7) for research, technological development and demonstration under grant agreement number 612796
Robust Monetary and Fiscal Policies under Model
Uncertainty∗
Elena Afanasyeva† Michael Binder‡ Jorge Quintana§ Volker Wieland¶
October 31, 2016
Abstract
Policy robustness is defined as a search for monetary and fiscal rules that perform well across
a wide range of policy-focused macro models. This paper draws on multiple models from the
Macroeconomic Model Database to study the impact of new models with rich financial sector
frictions on the form of robust monetary and fiscal rules for the Euro Area – in particular, relative
to earlier generation macroeconomic models. We document that for the models with financial
frictions studied in this paper, robust monetary policies feature a weaker response to inflation
and the output gap than for their standard New Keynesian counterparts. We also document
that for this class of models a systematic and direct response of the monetary policy rate to
financial sector variables, i.e., a leaning-against-the-wind-type monetary policy, does not appear
advisable. Lastly, we consider an active rules-based role for fiscal policy in macroeconomic and
debt stabilization.
∗The research leading to the results in this paper has received funding from the European Community’s SeventhFramework Programme (FP7/2007-2013) under grant agreement “Integrated Macro-Financial Modeling for RobustPolicy Design” (MACFINROBODS, grant no. 612796).†Goethe University Frankfurt, [email protected]‡Goethe University Frankfurt, [email protected]§Goethe University Frankfurt, [email protected]¶Goethe University Frankfurt, [email protected]
1
Contents
1 Introduction 3
2 Model Set and Policy Experiment Description 42.1 Model Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Estimating Carlstrom, Fuerst, Ortiz and Paustian (2014) for the Euro Area . . 82.2 Robust Policy Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Comparing Robust Monetary Policy Rules Between Financial Frictions Modelsand Standard-NK Models 183.1 Model-Specific Optimal Simple Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Bayesian Policy Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Robustness of Leaning-Against-the-Wind-Type Policies 32
5 Fiscal Rules Exercises 39
6 Conclusion 57
A Data Description and Sources 65
B Model Estimation Posterior Marginal Densities 66
C Robustness Checks 69C.1 Loss Outlier Exclusion Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69C.2 Different Weights for V arm (∆it) in the Central Bank’s Loss Function . . . . . . . . . 69
D Definition of Common Financial Variables 70D.1 EA CFOP14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70D.2 EA GNSS10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71D.3 EA QR14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72D.4 EA GE10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
E Estimation of Justiniano et al. (2011) for the Euro Area 75
F Fiscal Rules Additional Optimizations 78
2
1 Introduction
Policy robustness is defined as a search for monetary and fiscal rules that perform well across a wide
range of policy-focused macro models. This paper draws on multiple models from the Macroeconomic
Model Database (MMB)1 to study the impact of new models with rich financial sector frictions on the
form of robust monetary and fiscal rules – in particular, relative to earlier generation macroeconomic
models. The motivation for our study is twofold. Firstly, the great financial crisis has brought the
relevance of financial sector frictions to the forefront of policy debates in most developed economies.
It is thus important that we understand the implications of these frictions on rules-based policies,
especially in contrast to any previously held consensus about the appropriate formulation of monetary
and fiscal policy. And secondly, over the last decade there have been important developments in the
design of models for policy analysis, towards explicitly integrating a role for financial markets in
defining the dynamic properties of macroeconomic variables. However, no consensus has yet been
reached on either the correct way to model financial sector frictions or on the implications they carry
for rules-based monetary and fiscal policy. In sum, uncertainty surrounding the economic modelling
and policy-making disciplines has increased further.
In such circumstances, the concept of robustness under model uncertainty becomes yet more
relevant for policy design. This paper thus aims to study the optimal design of simple rules-based
policies under full commitment in the presence of model uncertainty. Given the policy relevance of
this analysis, we delimit our study to a specific empirical context by focusing on the Euro Area.
Essentially, we start off from the analysis of Orphanides and Wieland (2013), and then take a
fresh look at their findings by accounting for the developments in macro modelling which have
taken place since the great financial crisis. Specifically, we are interested in gauging the level of
robustness of policy rules from the traditional New Keynesian (NK) framework with respect to the
financial frictions (FF) framework and vice versa. Further, we exploit the FF models considered in
our analysis by looking at the potential for improving the central bank’s performance by adopting
leaning-against-the-wind-type policies. And lastly, we consider an active rules-based role for fiscal
policy in macroeconomic and debt stabilization. Thus, this study falls within the large body of
1The MMB is an archive of macroeconomic models based on a common computational platform that providesvarious tools for systematic model comparison. Both MMB documentation and the software can be found athttp://www.macromodelbase.com/
3
literature drawing out the implications of FF for policy prescriptions.
The rest of the paper is structured as follows. Section 2 presents the set of policy-focused Euro
Area models considered in our analysis. Section 3 presents the main results from the standard-NK
vs FF comparison exercise. Section 4 focuses on whether leaning-against-the-wind-type policies are
beneficial in the Euro Area. Section 5 looks at the robustness implications for fiscal rules and Section
6 concludes.
2 Model Set and Policy Experiment Description
In this section, we describe the set of models employed in our analysis and the corresponding policy
exercises which deliver our results.
2.1 Model Set
Since optimal policy rules depend on the dynamic properties of the model from which they are
derived, we place the following restrictions on the set of models considered here: (i) all models
must be estimated on Euro Area data; (ii) all models must be designed for policy analysis; and
(iii) the set of FF models considered should represent well the rich variety of modelling approaches
present in the literature. The intuition behind these restrictions has to do with policymakers’ need to
form quantitative expectations about the consequences of their policies. Thus, it seems appropriate
to consider models which aim to describe the complete data generating process of the underlying
economy, rather than models which match only a small number of stylized facts. Additionally, the
optimal monetary policy rule for any given model will depend crucially on the structure of the
variance-covariance matrix of shocks, so it is important that this object be accurately identified.
Finally, restriction (iii) is motivated by the lack of consensus within the literature on how FF are
best modeled. In such circumstances, prudence calls for a wide array of FF modelling specifications
to be considered.
4
Table 1. Set of Euro Area Models# Label Reference
New Keynesian Models1 EA AWM05 Dieppe et al. (2005)2 EA CW05fm Coenen and Wieland (2005),
Fuhrer-Moore-staggered contracts3 EA CW05ta Coenen and Wieland (2005),
Taylor-staggered contracts4 G3 CW03 Coenen and Wieland (2003)5 EA SW03 Smets and Wouters (2003)6 EA QUEST3 Ratto et al. (2009)
Financial Frictions Models7 EA GE10 Gelain (2010)8 EA GNSS10 Gerali et al. (2010)9 EA QR14 Quint and Rabanal (2014)10 EA CFOP14poc Carlstrom et al. (2014),
privately optimal contract11 EA CFOP14bgg Carlstrom et al. (2014),
Bernanke et al. (1999) contract12 EA CFOP14cd Carlstrom et al. (2014),
Christensen and Dib (2008) contract
The set of models we consider in our analysis builds on and overlaps with the models employed in
the analysis of Orphanides and Wieland (2013). Our set of models, listed in Table 1, is divided into
two broad categories: New Keynesian models and financial frictions models. We label each model as
per the nomenclature of the MMB, from where the models are drawn.2
The NK models we include in our analysis cover a wide range of specifications for the Euro
Area economy and include different ingredients in terms of policies, frictions, parameters and shocks.
The European Central Bank’s (ECB) Area-Wide model (labeled EA AWM05) developed in Dieppe
et al. (2005) represents the oldest vintage of macroeconomic models used for policy analysis in
the sample.3 This is an open-economy large-scale model which features detailed specifications for
both the demand and supply sides of the economy, e.g., there is a rich characterization of the
2As yet, the model of Carlstrom et al. (2014) has not been included in the MMB, but will in a forthcoming release.We acknowledge and thank the authors for graciously sharing their estimation code with us. For detailed discussionson the framework for policy comparison of the MMB and the models therein, see Wieland et al. (2012), Schmidt andWieland (2013) and, especially, Wieland et al. (2016).
3This is the only model in our sample which might be considered of the traditional Keynesian variety, rather thanfrom the “New Keynesian” generation.
5
government sector and of the labor market. In contrast to the other models included in our sample,
the EA AWM05 model predominantly features backward-looking elements. The models of Coenen
and Wieland (2005), i.e., EA CW05fm and EA CW05ta, are small-scale macroeconomic models
which differ in the type of wage contracts they assume. While EA CW05fm assumes Fuhrer-Moore-
style contracts, the EA CW05ta model is characterized by Taylor-style staggered wage contracting.
The G3 CW03 model, developed in Coenen and Wieland (2003), is an extended open-economy
version of the Taylor-style staggered wage contracts model of Coenen and Wieland (2005) and includes
estimated blocks for the U.S., Euro Area and Japanese economies. Labeled EA SW03 is the model of
Smets and Wouters (2003), which is a medium-scale dynamic stochastic general equilibrium (DSGE)
model. Because of its microfounded structure and rational expectations assumption, it can be thought
of as being representative of the current generation of DSGEs for monetary analysis. Finally, the
European Commission’s EA QUEST3 model (presented in detail in Ratto et al. (2009)) completes
our list of NK models. This is an open-economy large-scale DSGE which features, in addition to a rich
set of frictions and shocks, a detailed specification of fiscal policy and the presence of rule-of-thumb
households.4
The set of FF models we look at includes several specifications for financial markets, which include
frictions on part of entrepreneurs, financial intermediaries and households that give way to diverse
financial contracts. The model of Gelain (2010) (labeled EA GE10) is the Smets and Wouters (2003)
model appended with the financial accelerator mechanism developed by Bernanke et al. (1999),
which assumes a costly-state verification framework as in Townsend (1979) that leads to a risky-
debt contract between lenders and entrepreneurs (borrowers). The EA GNSS10 is the medium-scale
DSGE model developed by Gerali et al. (2010), which features borrowing constraints a la Iacoviello
(2005) on both entrepreneurs and households, and a monopolistic banking sector – modeled through
the Dixit–Stiglitz framework – subject to capital adjustment costs and rate stickiness. Quint and
Rabanal (2014) construct in EA QR14 a medium-scale two-sector, two-economy DSGE with common
monetary and macroprudential policies; hence, the authors are able to estimate the model with Euro
Area data treating one economy as the “core” Euro Area countries and the other as the “peripheral”
countries of the currency bloc. The model features financial intermediaries and a non-tradable
4In the paper, the authors refer to such agents as standing in for FF, based on the assumption that they live hand-to-mouth due to liquidity constraints. We interpret this modelling strategy of FF as outside the current generation ofFF models and so see EA QUEST3 as much closer to NK models.
6
housing goods sector in each economy, with households funding such investments through loans
subject to financial contracts as in Bernanke et al. (1999). Lastly, we consider three versions of
the model developed in Carlstrom et al. (2014). This paper, where different versions of the model
are estimated for the U.S. economy, develops a financial contract similar to that of Bernanke et al.
(1999), but which allows for the loan rate between lenders and entrepreneurs to be indexed to the
aggregate return on capital; this contract is referred to as the privately optimal contract. The FF
block is then appended to the medium-scale NK-DSGE model developed in Justiniano et al. (2011).
For our analysis, we estimate three different versions of this model on Euro Area data, allowing for
different specifications of the financial contract. Each of these is described in some detail in the
section that follows, where we report our estimation.
Figure 1. IRFs of a Monetary Policy Shock under the GR Rule
0 5 10 15 20-0.5
-0.25
0
0.1Output Gap
EA_CW05ta
EA_CW05fm
EA_AWM05
EA_SW03
EA_QUEST3
EA_GE10
G3_CW03
EA_GNSS10
EA_QR14
EA_CFOP14poc
EA_CFOP14bgg
EA_CFOP14cd0 5 10 15 20
-0.2
-0.1
0
0.05Inflation
0 5 10 15 20-0.25
0
0.5
1Interest Rate
In order to give a better idea of the different dynamics captured by our set of models, Figure 1
shows the impulse-response functions (IRFs) of the output gap, inflation and the nominal interest rate
7
to a one-percent exogenous increase in the interest rate, under the policy rule found in Gerdesmeier
et al. (2004) (the GR rule from hereon) to describe the systematic component of the ECB’s policy.
As is clear from the graph, the models considered in our analysis cover a wide range of dynamics.
In response to a one-percent contractionary monetary policy shock, the estimated trough of the
output gap varies from about -0.5% almost immediately after the shock in the EA GNSS10 model5
to around -0.1% for EA CW05fm, which occurs seven quarters after the shock. Further, the number
of periods in which the output gap closes after the initial drop can take from about seven quarters
in the EA QUEST3 model to well over twenty in both the traditional Keynesian EA AWM05 model
and the FF-DSGE model of EA GE10. With regard to inflation dynamics, the contrast between
models is even more striking. In this case, the estimated trough ranges from -0.21% three quarters
after the shock in EA QR14 to as little as -0.02 in EA CFOP14cd, and as far out as 21 quarters after
the shock for the EA AWM05 model. Thus, we see that model uncertainty poses serious challenges
for both the practical conduct of monetary policy and the theoretical design of policy rules.
2.1.1 Estimating Carlstrom, Fuerst, Ortiz and Paustian (2014) for the Euro Area
In order to expand the set of FF considered in this study, an estimation of the model developed in
Carlstrom et al. (2014) was carried out employing Euro Area data. This model is well-suited to our
analysis because it allows for different financial contracts within the richly-specified microfounded
structure of the core model. Specifically, the paper develops a mechanism for modelling FF which
builds on Bernanke et al. (1999) by allowing for contract indexation. This mechanism is imbedded into
the medium-scale NK-DSGE model developed by Justiniano et al. (2011) and estimated by Bayesian
techniques using U.S. data on real, nominal and financial variables. We estimate three versions of
the model, allowing for different types of financial contracts between financial intermediaries and
entrepreneurs: (i) a “privately optimal contract” (POC), that is, a risky-debt contract allowing for
indexation of the promised real interest rate to the aggregate return on capital; (ii) a risky-debt
contract a la Bernanke et al. (1999) (BGG), where the promised real rate of interest is not state-
dependent; and (iii) a contract as in Christensen and Dib (2008) (CD), where the risky-debt contract
5In this paper, we follow Orphanides and Wieland (2013) in employing the production function definition of output.Specifically, we use the last equation of p.114 in Gerali et al. (2010). As regards the IRFs presented on p.129 of theoriginal paper, they are constructed by defining output as consumption plus new capital; that is, an auxiliary variableis introduced which feeds back into the model exclusively through the central bank’s reaction function.
8
is written in nominal terms.
For our estimation, we start from Carlstrom et al. (2014) and substitute their priors with those
of Christiano et al. (2010) and Gelain (2010), when applicable, and make them more diffuse when
reasonable.6 Our sample runs from 1999Q1 to 2015Q47 and has ten observables: employment,
inflation, the nominal interest rate, entrepreneurial net worth, the external finance premium, real
GDP, consumption, investment, wage and the relative price of investment. The construction of
the dataset closely follows Justiniano et al. (2011) for the real and nominal variables, the external
finance premium is taken from Gilchrist and Mojon (2014), and the construction of a measure of
entrepreneurial net worth follows Christiano et al. (2010). A detailed description of the data is
presented in Appendix A. Measurement error, modeled as an AR(1) process, is included for the
external finance premium and net worth. The original estimation of Carlstrom et al. (2014) does not
employ net worth in estimation but rather takes the series of Gomme et al. (2011) as an observable
for the aggregate return on capital. As no comparable and reliable or widely-accepted series exists
for the Euro Area, we substitute this series with that of net worth in order to maintain the original
set of shocks.8
The specifications and priors governing the shocks and measurement errors follow Carlstrom
et al. (2014). This differs from Christiano et al. (2010), who use tight prior distributions on the
measurement errors of financial variables to limit the amount of variation in the observable that is
attributed to the measurement error. We deviate from this approach because we are particularly
6This last modification responds to the work of Herbst and Schorfheide (2015), which illustrates the benefits ofworking with diffuse priors. Their analysis is applicable to our work in so far as the values of many of the parameterswe estimate are not well-documented in the literature and the sample we use is smaller than comparable estimationsfound in the literature.
7This time period contains only five observations where the policy rate could be considered to be at its lower bound.8The model has ten shocks: intermediate firms’ neutral technology factor and capital agencies’ investment-specific
productivity factor are unit root processes, wages and intermediate goods’ prices are subject to ARMA(1,1) mark-upshocks, an intertemporal preference shock affects households, capital agencies’ marginal efficiency of investment issubject to an exogenous disturbance, entrepreneurs are subject to net worth and idiosyncratic risk shocks, and bothgovernment spending and the monetary policy rate are subject to shocks. If not stated otherwise, shocks are modeledas AR(1) processes.
The series we employ for entrepreneurial net worth is constructed as in Christiano et al. (2010), however,we also tested the series “Net Worth” reported in the ECB’s Euro Area Accounts – defined as financialnet worth of non-financial corporations (series QSA.Q.N.I8.W0.S11.S1.N.N.BF90.F. Z. Z.XDC. T.S.V.N. Tof the ECB’s Statistical Data Warehouse) plus fixed assets of non-financial corporations (seriesQSA.Q.N.I8.W0.S11.S1. Z.D.LE.N11N. Z. Z.EUR. Z.S.V.N. T) – but found it to be less informative, in thesense that the standard deviation of its measurement error is proportionally larger than that of the series employedby Christiano et al. (2010).
9
interested in correctly identifying the variance-covariance matrix of shocks, while recognizing that
financial variables’ empirical measures are imperfect.9 That is, we prefer to avoid inaccurate variances
on the shocks over unwarrantedly small standard deviations on the measurement errors.
An area where our estimation differs from that of Carlstrom et al. (2014) is in choosing which
parameters to calibrate. Specifically, while the original paper estimated the discount factor and
the steady state markups for prices and wages, we calibrate these parameters to the values used by
Christiano et al. (2010). This responds to the fact that the Calvo parameter on wages and the steady
state wage markup cannot be separately identified due to collinearity,10 and that the discount factor
is very close to the upper bound of unity. Further, instead of calibrating the elasticity of the external
finance premium with respect to entrepreneurial leverage, we estimate this parameter directly due
to its importance for the dynamics of the model. We set the number of Metropolis-Hastings draws
at 2,000,000 (with two chains), with a burn-in of 50% and retain one of every five subsequent draws.
This procedure follows Carlstrom et al. (2014) closely but with a much higher number of simulations
(the original paper uses 100,000 draws); which responds in part to the smaller size of our sample.
The acceptance rates are around 23% in all cases.
For greater clarity, the estimation equations related to the FF under the POC are as follows:11
Et(rkt+1
)− rdt = ν
(qt + kt − nt
)+ σt (1)
rlt = rdt−1 + [1 + θg (χk − 1)][rkt − Et−1
(rkt)]
(2)
where rkt is the real return on holding capital, rdt is the real rate on deposits, qt is the price of capital,
kt is the capital stock, nt is entrepreneurial net worth, σt is the variance of the idiosyncratic risk shock,
and rlt is the real rate on lending – that is, the real return on the financial intermediaries’ portfolio
of loans, not the promised repayment rate agreed between the intermediary and the individual
entrepreneur. All variables are expressed as log-deviations from their value at the non-stochastic
steady state.
9Christiano et al. (2010) allow for white noise measurement errors in the observation of financial variables (includingthe external finance premium and the stock market index) “as a way to capture the degree of model misspecificationalong those dimensions – financial frictions – that are still unconventional in equilibrium modeling” (p.34).
10The identification analysis proposed by Iskrev and Ratto (2011) reveals that all parameters of the model areidentified except for those relating to wage stickiness.
11Equations (1) and (2) are, respectively, equations (57) and (A20) of Carlstrom et al. (2014).
10
Equation (1) is the conventional equation linking the external finance premium to the repre-
sentative entrepreneur’s balance sheet (summarized here by the leverage ratio) and including a
shock. The parameter ν ≥ 0 measures the elasticity of the external finance premium with re-
spect to entrepreneurial leverage and captures the fact that the cost of external finance increases
as entrepreneurs’ net worth decreases relative to the size of the investment project, implying a de-
terioration in the state of their balance sheets. The added shock is the variance on the unit-mean
lognormal return from holding capital between periods, which is time-varying. This captures the fact
that in a risky-debt contract a higher variance in entrepreneurs’ return on holdings of capital implies
a cross-sectional distribution which is more skewed to the right12 and, consequently, a greater mass
of projects below the default threshold. Thus, an increase in the variance on idiosyncratic risk leads
to an increase in the external finance premium.
Equation (2) is the contract indexation equation and relates the return on lending to the deposit
rate and the expectational error in the aggregate return to capital. Contract indexation means
that the promised repayment rate of entrepreneurs to the financial intermediary is linked to the
realized return on aggregate capital, which is costlessly observed by all. Thus, the costs/benefits
from surprises in the return on capital are shared by the entrepreneur and the financial intermediary.
This shows up in equation (2) in the second term, [1 + θg (χk − 1)] ≥ 0; that is, the return on lending
increases (decreases) with positive (negative) surprises on the return to aggregate capital. Carlstrom
et al. (2014) show that the amplification effect of the FF built into the model is diminished as the
level of contract indexation increases. For a full description of the model we refer the reader to the
original paper.
In all estimations, θg is set to 0.95. For the BGG and CD versions of the model, χk is set to -0.05
so that there is no contract indexation and equation (2) becomes:
rlt = rdt−1 under BGG
rlt = rt−1 − πt under CD
where rt is the nominal short-term rate and πt is the inflation rate.
12Note that in the assumed lognormal distribution, the mean is always unity. That is, changes in the variance arealways assumed to be mean-preserving.
11
Our parameter calibration is presented in Table 2 and the estimation results for all parameters
are presented in Tables 3a and 3b.
Table 2: Model Estimation – Calibrated ParametersParameter Value Source
Discount Factor (β) 0.999 CMR10
Depreciation Rate (δ) 0.02 CMR10
Steady State Price Markup (λπ ) 20% CMR10
Steady State Wage Markup (λw ) 5% CMR10
Steady State External Finance Premium 400bp CMR10
Steady State Leverage Ratio 1.87 Sample mean
Steady State Government Consumption 20% of GDP Sample mean
Entrepreneurial Survival Rate 0.978 CMR10
Contract Indexation Parameter θg 0.95 Normalization
*CMR10 denotes Christiano et al. (2010)
The results presented in Table 3a show that our estimates are in line with those found in the
literature. Regarding standard parameters’ values, three things from Table 3a are worth pointing
out. Firstly, the level of wage inflation indexation to past levels of inflation is somewhat lower than
that estimated by Christiano et al. (2010) and Gelain (2010).13 This may be due to the different
definition of real wages that we used – we exclude the farming business sector, whereas it appears
that the cited papers do not – and/or the sample period employed. Secondly, our estimates of the
elasticity of capital utilization costs are also somewhat lower; they are closer, albeit higher, to the
values found by Carlstrom et al. (2014) for the U.S. However, the variance of the estimates found in
the literature for this parameter is quite high and our estimates fall well within that range. Lastly, it
is important to note that the parameter of the Taylor rule’s response to the output gap collapses into
a mass point at the lower bound of its prior, which is equal to zero. This fact, along with interest rate
smoothing parameter being close to unity suggests that the ECB has followed a 1st-difference rule
– where changes in the interest rate respond to inflation target-deviations and output gap growth
– throughout the sample period. This finding is in line with Orphanides and Wieland (2013) and
Smets (2008), and our estimates for the policy rule parameters are also very similar to those of
Christiano et al. (2010), who exclude the output gap from their estimated policy rule and include
some leaning-against-the-wind elements.
13Recall that Christiano et al. (2010) report – in contrast to Gelain (2010) – estimates of the level of indexation tothe target inflation rate. Thus, the comparable figure becomes one minus the values they report in Table 4, p. 94.
12
Table 3a: Model Estimation − Estimated ParametersPOC Model BGG Model CD Model
Log data density -580.74 -574.49 -572.25
Param Description Prior Posterior Posterior Posterior
density mean s.d. mean 5% 95% mean 5% 95% mean 5% 95%
α Cap share N 0.30 0.10 0.16 0.13 0.19 0.16 0.13 0.19 0.16 0.13 0.19
ιp Price index B 0.50 0.15 0.27 0.10 0.43 0.26 0.10 0.41 0.27 0.10 0.43
ιw Wage index B 0.50 0.15 0.10 0.03 0.17 0.10 0.04 0.16 0.10 0.04 0.17
γz SS tech N 0.50 0.06 0.40 0.31 0.49 0.39 0.30 0.48 0.38 0.29 0.74
growth
γν SS IST growth N 0.50 0.06 0.49 0.39 0.59 0.48 0.38 0.58 0.48 0.38 0.58
h Cons habit B 0.70 0.10 0.72 0.64 0.81 0.72 0.63 0.80 0.71 0.62 0.80
log Lss SS hours N 0.00 0.50 0.10 -0.70 0.91 0.13 -0.68 0.93 0.12 -0.66 0.93
100(π−1) SS Inflation N 0.45 0.10 0.37 0.24 0.51 0.38 0.25 0.51 0.38 0.25 0.51
ψ Inv Frisch G 2.00 0.75 2.03 1.03 2.99 1.86 0.93 2.76 1.86 0.93 2.74
elasticity
ξp Calvo prices B 0.75 0.10 0.70 0.61 0.79 0.70 0.61 0.79 0.70 0.61 0.79
ξw Calvo wages B 0.75 0.10 0.82 0.73 0.91 0.83 0.75 0.91 0.84 0.76 0.92
ϑ Elas cap G 6.00 5.00 9.39 1.76 17.75 8.98 1.51 16.42 9.49 1.87 17.26
util costs
S Inv adj N 10.00 5.00 14.39 9.50 19.17 13.84 8.96 18.68 13.88 9.26 18.60
costs
φπ Taylor infl N 1.75 0.10 1.70 1.54 1.86 1.69 1.53 1.86 1.70 1.53 1.87
φx Taylor gap N 0.125 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
φdx Taylor gap N 0.25 0.10 0.27 0.19 0.34 0.27 0.20 0.35 0.27 0.20 0.35
growth
ρR Taylor B 0.80 0.05 0.89 0.86 0.92 0.89 0.86 0.92 0.89 0.86 0.92
smoothing
ν Elas risk I 0.05 ∞ 0.10 0.06 0.14 0.09 0.06 0.12 0.09 0.06 0.12
premium
χk Index to Rk G 2.00 1.00 0.41 0.10 0.70 - - - - - -
*Note: The distributions of the parameters φπ and φx were bounded from below at zero in the estimation.
As regards the two key parameters of the FF block of the Carlstrom et al. (2014) model, the
results for ν are relatively high but in line with the literature and the estimate for χk is much lower
than that found for the U.S. For the Euro Area, Gelain (2010) estimates the elasticity of the external
finance premium to entrepreneurial leverage at 0.0267, Villa (2013) estimates it at 0.07, Villa (2016)
at 0.04 and Queijo (2006) at 0.05. The value for χk, in contrast, is much lower than the U.S. estimate
of Carlstrom et al. (2014) at 2.43. However, it must be stressed that they do not estimate ν but
13
rather calibrate it at 0.19, which is much higher than conventional values found in the literature.14
For instance, Christensen and Dib (2008) using data for Canada estimate it (without employing
financial sector data) at 0.042 and De Graeve (2008) obtains a posterior mode of 0.1 for the U.S. At
present there is no figure of χk with which to compare in the literature for the Euro Area. Finally,
one should remark on the fact that, according to our estimation, the data for the Euro Area reject
the presence of contract indexation of the form of Carlstrom et al. (2014) (see row for “Log data
density” in Table 3a). Rather, our results indicate that the data favor the CD version of the model
over the BGG and POC specifications. In fact, the POC version of the model achieves the worst fit
of the three.
Table 3b contains the estimation results for the exogenous components of the model. In this case,
it is important to remark on the fact that the relative ordering of the estimated standard deviations
of shocks is consistent with that of Carlstrom et al. (2014). As regards the estimated values, only the
marginal efficiency of investment shock’s variance is substantially larger than in the original paper.
However, this comparison is somewhat misleading since this shock can have significantly different
implications for the effect on macroeconomic variables depending on the overall parameterization
of the model. In particular, the impact of the marginal efficiency of investment shock on output
depends not only on the size of the shock but also on its level of persistence; since the model assumes
that agents have rational expectations, a higher level of persistence increases the present value of the
shock, holding all else equal. Thus, we find that the lower estimated level of persistence (relative to
the U.S. estimates) more than compensates for the larger variance such that the impact on output
of a one-standard-deviation innovation to the marginal efficiency of investment shock is slightly less
in the Euro Area (reaching a peak of around 0.3%) than in the U.S. (with a peak impact of about
0.5%).15
14In the model of Carlstrom et al. (2014) a high value for χk leads to a weak financial accelerator mechanism (i.e.,there is little amplification of shocks due to FF). The authors’ estimates indicate that their dataset does not favora strong financial accelerator mechanism. So, if the strength of the model’s financial accelerator mechanism wereweakened through a lower value of ν, possibly the estimate of χk would be lower too.
15Specifically, we are referring to the POC versions of the model. For the BGG versions, the analogous measure isslightly larger in the euro area than in the U.S.
14
Table 3b: Model Estimation – Shock ProcessesPOC Model BGG Model CD Model
Param Description Prior Posterior Posterior Posterior
density mean s.d. mean 5% 95% mean 5% 95% mean 5% 95%
ρmp Mon pol B 0.60 0.20 0.50 0.38 0.62 0.48 0.36 0.59 0.47 0.35 0.59
ρz Tech growth B 0.60 0.20 0.50 0.36 0.63 0.49 0.35 0.62 0.47 0.33 0.61
ρg Gov spend B 0.60 0.20 0.99 0.97 1.00 0.99 0.97 1.00 0.99 0.97 1.00
ρν IST growth B 0.60 0.20 0.74 0.59 0.89 0.70 0.56 0.84 0.70 0.57 0.84
ρp Price mark-up B 0.60 0.20 0.86 0.75 0.97 0.87 0.76 0.97 0.86 0.76 0.97
ρw Wage mark-up B 0.60 0.20 0.56 0.32 0.81 0.55 0.29 0.80 0.54 0.30 0.79
ρb Intertem pref B 0.60 0.20 0.34 0.09 0.60 0.30 0.05 0.54 0.31 0.06 0.56
θp Price mark-up MA B 0.50 0.20 0.30 0.07 0.52 0.30 0.07 0.52 0.30 0.07 0.51
θw Wage mark-up MA B 0.50 0.20 0.49 0.23 0.75 0.48 0.20 0.75 0.48 0.21 0.74
ρσ Idiosyn var B 0.60 0.20 0.97 0.96 1.00 0.98 0.96 1.00 0.98 0.97 1.00
ρnw Net worth B 0.60 0.20 0.59 0.27 0.90 0.64 0.36 0.91 0.63 0.35 0.91
ρµ Marg effic B 0.60 0.20 0.38 0.15 0.61 0.39 0.15 0.61 0.38 0.16 0.59
of inv
ρrpme Risk prem B 0.60 0.20 0.66 0.40 0.93 0.64 0.36 0.91 0.65 0.39 0.93
measur error
ρrpme Net Worth B 0.60 0.20 0.51 0.33 0.69 0.52 0.34 0.69 0.52 0.34 0.70
measur error
σmp Mon pol I 0.2 1.0 0.11 0.08 0.14 0.11 0.08 0.13 0.11 0.08 0.13
σz Tech growth I 0.5 1.0 0.82 0.70 0.94 0.82 0.69 0.94 0.81 0.69 0.94
σg Gov spend I 0.5 1.0 0.28 0.24 0.32 0.28 0.24 0.32 0.28 0.24 0.32
σν IST growth I 0.5 1.0 0.66 0.56 0.75 0.66 0.56 0.75 0.66 0.56 0.75
σp Price mark-up I 0.1 1.0 0.16 0.11 0.20 0.16 0.11 0.20 0.16 0.11 0.20
σw Wage mark-up I 0.1 1.0 0.21 0.16 0.26 0.21 0.16 0.27 0.21 0.16 0.26
σb Intertem pref I 0.1 1.0 0.07 0.03 0.10 0.08 0.04 0.11 0.07 0.04 0.11
σσ Idiosyn var I 0.5 1.0 0.19 0.13 0.25 0.16 0.12 0.20 0.16 0.12 0.19
σnw Net worth I 0.5 1.0 0.81 0.15 1.60 0.48 0.15 0.85 0.47 0.15 0.81
σµ Marg eff I 0.5 1.0 11.95 6.85 17.07 11.71 6.44 16.80 11.85 6.76 16.87
of inv
σrpme Risk prem I 0.5 1.0 0.18 0.13 0.24 0.17 0.12 0.22 0.17 0.12 0.22
measur error
σrpme Net Worth I 0.5 1.0 6.22 5.04 7.37 5.98 4.91 7.01 5.98 4.89 7.05
measur error
Finally, we turn to the measurement errors. The standard deviations reported in the table are
equivalent to roughly 30% and 70% of the standard deviation of the observables for the external
finance premium and entrepreneurial net worth, respectively. Both these figures represent a notice-
ably larger proportion of the observables’ variation that is attributed to the measurement error, as
15
compared to the estimation of Christiano et al. (2010), where the comparable figures are 10% and
15%. However, as stated above, the latter’s results can be accounted for by their choice of tight priors
for these parameters. In contrast, Carlstrom et al. (2014) (from whom we take our priors) find that
the measurement errors on the external finance premium and the aggregate return on capital account
for 50-55% of the variation in their observables. In general, these results provide a rough measure of
the appropriateness of the proxies of financial variables used in the macro models considered here.16
This notwithstanding, we are able to identify all parameters and their posteriors converge to their
ergodic distributions; graphs of the prior and posterior distributions are presented in Appendix B. In
the exercises that follow, the three estimated models are labeled EA CFOP14poc, EA CFOP14bgg
and EA CFOP14cd.
2.2 Robust Policy Exercises
In gauging the effect of FF on optimal policy rules, there are two broad avenues a researcher could
choose to take. One is to take a model with FF and identify the net contribution of the friction by
exogenously muting that particular financial mechanism, given that specific model, or comparing the
estimated FF version with its estimated frictionless counterpart. Alternatively, one can compare the
average effect across models with and without FF. Here, we opt for the latter as we view it to be
naturally in line with the policy concerns that lie at the heart of our analysis. Thus, if we say that FF
imply a weaker response to inflation, we mean this in the sense that if the policymaker thought them
to be relevant, she would, in designing her policy rule, ascribe positive weight to the macro models
for policy analysis which feature a detailed specification for their interplay with the macroeconomy.
The theoretical framework for the exercises we carry out in order to gauge policy rules’ degree
of robustness is formally developed in Kuester and Wieland (2010). Here, we provide an intuitive
presentation of these exercises, which can be best understood through the following thought experi-
ment. A risk-averse and benevolent policymaker must fully commit to a simple rule for the term of
his tenure. For this he seeks out the aid of the central bank’s staff, which promptly draws on the set
of models it has developed for policy analysis. There is model uncertainty in the sense that only one
16For instance, it is not surprising that our measure of the external finance premium, i.e., the proxy developed byGilchrist and Mojon (2014), is less susceptible to measurement error than the somewhat crude measure employedby Carlstrom et al. (2014), i.e., the BAA-Treasury spread. Finding the best empirical counterpart to macro models’financial variables is an important area of research in its own right, but outside the scope of this paper.
16
of the models at the central bank is the “true model” of the economy, but there is no way of knowing
ex ante which one.17 There can be no backtracking on the choice of the rule. The question then is
how can the policymaker make use of the staff’s expertise to set in place a simple rule to maximize
his loss function in the presence of model uncertainty?
The answer to this question, of course, must account for the policymaker’s beliefs regarding the
economy. For instance, if he were to hold complete conviction about a specific model being the true
model,18 then he would simply find the optimal policy prescribed by that model and dismiss that
rule’s implications for the staff’s other models as irrelevant. However, if the policymaker believes that
there is a positive probability that some other model is the true model, then he will want to take into
account the implications of different model-specific optimal rules on other possible models as they
represent potential costs from mistakenly choosing the wrong model. Kuester and Wieland (2010)
show that robust policies – in the sense that they perform well across a wide range of policy-focused
macro models – can be obtained by minimizing a weighted average19 of models’ ad hoc loss functions.
This is the approach we adopt here; we refer to such policies as “Bayesian policy rules.”
While this approach is well-suited for deriving robust policies for different types of models, it
should be noted that our analysis is silent on the net contribution of the FF to the form of the
optimal policy rule in each model. Whether the difference between FF and Standard-NK policy
rules is due in greater measure to the FF per se or to broader differences in model specifications and
parameterizations remains an open question. Although this issue is interesting both theoretically
and in terms of policy implications, it is not clear how one could address it in a way that is both
conceptually clean and practically feasible without doing harm to the concept of model uncertainty
we employ.
In setting the models as restrictions to the policymaker, including a large number of models in
our set and taking only those designed for policy analysis, we seek to account for the widest range
of policy-oriented modelling approaches which are empirically reasonable. This implies respecting
the original modellers’ preferred specification, choice of sample, observables and metaparameters.
Thus, the seemingly natural option of either restricting the FF models or extending the Standard-
NK models would imply a relaxation of the policymaker’s constraints which could result in a loss
17For a detailed discussion on the concept of model uncertainty, see Orphanides and Wieland (2013).18Alternatively, one could simply think of the “true model” as the best approximation to the underlying economy.19The weights employed in this optimization problem allow for incorporating prior beliefs held by the policymaker.
17
of robustness. Alternatively, one could also argue for keeping with modellers’ preferences regarding
model specification and metaparameters while updating each model’s estimation. However, it is not
obvious that the resulting model would be any modeller’s first choice, for if they had had access to
the dataset to which we do, perhaps the general specification, selection of priors, observables, etc.
would have been different. Further, given the diversity of our model set, such a strategy is likely
to prove prohibitively costly to implement in a reasonable timeframe by any researcher. Thus, we
defer this issue to future work and concentrate here on the case where the macroeconomic models
the policymaker considers are assumed to be a strict constraint in drawing out the implications of
FF for policy robustness.
3 Comparing Robust Monetary Policy Rules Between Fi-
nancial Frictions Models and Standard-NK Models
In this section we compare the optimal policies, both model-specific and Bayesian, of models with
FF and those of Standard-NK models and characterize robust policies in this context.
3.1 Model-Specific Optimal Simple Rules
Here we look at the optimal model-specific rules of the class considered in Orphanides and Wieland
(2013) and compare their performance to three popular policy rules, two of which have been shown
to describe the ECB’s actions well. We also ask how robust the model-specific rules are and if there
are differences in the rules of the two types of models considered here.
An optimal policy for model m is defined as the set of coefficients{ρ, α, β, β, h
}that solves the
central bank’s following problem:20
min{ρ,α,β,β,h}
£m = V arm (π) + V arm (y) + V arm (∆i) (3)
s.t. it = ρit−1 + αEt (pt+h − pt+h−4) + βEt (yt+h) + βEt (yt+h − yt+h−4)
0 = Et[fm(zt, x
mt , x
mt+1, x
mt−1, θ
m)]
20In carrying out the exercise, we use Dynare to solve each model and Matlab’s Global Optimization Toolbox tofind the global minimum of the constrained loss function, with parameter bounds set as follows: ρ ∈ [0, 1.5], α ∈ [0, 3]and β, β ∈ [−3, 3]. These constraints turn out to be slack in all cases.
18
where it is the annualized nominal interest rate, pt is the log of the price level, yt is the output gap
and h = {0, 2, 4} is the central bank’s forecast horizon. The last line denotes the structure of model
m, which is a function of the model’s parameters, model-specific variables and common variables,
zt.21 Note that the central bank must take the models as given, such that they serve as a constraint
on the policymaker. This specification considers policies under commitment to a simple rule, which
have been found to be more robust than alternatives that respond to a greater number of variables
(see Levin et al. (1999) and Taylor (1999)).22 Regarding the performance criterion used, we adopt
an ad hoc loss function which places equal weight on the variance of annual inflation, the output gap
and changes in the interest rate. Following Kuester and Wieland (2010), the last term is incorporated
into the loss function in order to rule out policies which would imply frequently reaching the lower
bound on the interest rate. The weight on the output gap equal to the weight on inflation follows
from the analysis presented in Debortoli et al. (2014), which shows that for a standard-NK model23
this loss function accurately approximates the representative household’s loss function as long as the
central bank behaves optimally. The results of this exercise are presented in Table 4 and crosschecks
with alternative weights are presented in Appendix C.
The main results of Table 4 are as follows. No model presents a corner solution for the optimal
policy parameters. Almost all models put positive weight on all the variables to which the central
bank is allowed to respond. The exceptions are G3 CW03, which optimally does not respond to
the growth rate of the output gap, and the three versions of EA CFOP14, which prescribe that the
central bank not react to the output gap, but rather respond exclusively to output gap growth. It is
noteworthy that optimal coefficients of EA CFOP14 on interest rate smoothing and on the output
gap are surprisingly similar to the estimated parameters reported in Table 3a. With regard to the
forecast horizon, no FF model admits a forward-looking policy rule as optimal while two of the
standard-NK models prescribe forward-looking policy rules.24 These are EA AWM05, which is from
the oldest vintage of models treated here and is extensively discussed in Kuester and Wieland (2010)
and Orphanides and Wieland (2013), and EA CW05ta, which in contrast to EA AWM05 features
21Note that we include the annualized nominal interest rate, the log of the price level, and the output gap in thecommon variables.
22Limiting the analysis to this class of policy rules is also useful due to computational constraints.23Specifically, the model used in their analysis is the Smets and Wouters (2007) model.24Although we refer here to two-period-ahead forecasts as “forward-looking,” one should keep in mind that in
practice central banks are only able to observe output measures from one or two periods prior, at the latest.
19
Table
4:
Model-
Sp
eci
fic
Opti
mal
Poli
cyR
ule
sR
ule
Inte
rest
lag
Infl
atio
nO
utp
ut
gap
Ou
tpu
tga
pgr
owth
hM
inL
oss
Tay
lor
Los
sG
RL
oss
1st
-Diff
Los
s
EA
AW
M05
0.8
370.4
911.
236
0.24
24
3.08
5.79
7.93
∞E
AC
W05f
m0.
850
0.52
00.
581
0.06
90
5.71
10.3
49.
528.
75
EA
CW
05ta
0.85
70.
143
0.84
1-0
.213
22.
634.
704.
803.
76
G3
CW
03
0.87
10.
129
0.53
50.
009
01.
953.
443.
282.
59
EA
SW
03
0.97
50.
100
1.09
4-0
.276
01.
464.
905.
062.
57
EA
QU
ES
T3
1.0
450.7
490.
145
0.42
00
3.03
18.0
17.
963.
18
EA
GE
10
1.04
20.
120
0.01
80.
706
034
.18
60.6
551
.59
40.7
4
EA
GN
SS
101.2
130.7
600.
555
-0.1
780
13.6
6∞
23.0
821
.00
EA
QR
14
1.08
61.
392
1.04
3-0
.506
00.
171.
220.
610.
24
EA
CF
OP
14p
oc
1.0
160.0
470.
006
1.30
40
7.88
11.6
618
.15
25.2
9
EA
CF
OP
14b
gg1.0
160.0
400.
006
1.29
30
8.04
12.1
519
.62
27.3
7
EA
CF
OP
14c
d1.
016
0.03
70.
007
1.33
30
8.15
12.2
719
.72
28.1
0
*N
ote:
1st
-Diff
eren
ceru
lesp
ecifi
cati
on
isw
ithh
=0.
20
forward-looking behavior. For the CFOP14 models, the rules are very similar between them.
Another result to remark on is that FF models, in general, warrant a higher level of interest
rate smoothing than standard-NK models, almost in all cases prescribing near-unity coefficients,
suggesting 1st-difference type rules. Indeed, it is noteworthy that the financial accelerator models –
i.e., EA GE10 and the three versions of EA CFOP14 – contrast with EA GNSS10 and EA QR14 in
that they prescribe a very modest response to inflation and place relatively more weight on responding
to output gap growth, rather than the level of the output gap. This follows from the relatively weaker
response of inflation and stronger response of the output gap to variations in the policy rate in the
financial accelerator models considered in the sample. This is shown in Figure 2, which presents the
IRFs of inflation and the output gap to a contractionary monetary policy shock of one percent under
the GR rule and the 1st-difference rule. Since the central bank has less influence over inflation in the
financial accelerator models, it must adjust the policy rate by a greater degree to keep inflation in
check than if it were acting in either EA GNSS10 or EA QR14. But doing this would directly increase
the central bank’s losses since the variance of both the output gap and the changes in the interest
rate would be higher. And since the output gap is more sensitive to interest rate movements in the
financial accelerator models, these models prescribe more moderate responses to inflation. Thus, for
an ECB concerned with stabilizing the output gap, financial accelerator models prescribe reacting
strongly to output gap growth and weakly to inflation. Unfortunately, the policy prescription of the
remaining two FF models (EA GNSS10 and EA QR14) appear to go in the opposite direction as
both imply it is optimal to respond aggressively to inflation and negatively to output gap growth.
This shows some of the policy dilemmas that can arise in the presence of model uncertainty.
21
Figure 2: IRFs to a Contractionary Monetary Policy Shock of 1%
GR Rule 1st-Diff Rule (h = 0)
0 5 10 15 20
Periods
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05Inflation
0 5 10 15 20
Periods
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1Output Gap
0 5 10 15 20
Periods
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1Inflation
0 5 10 15 20
Periods
-0.8
-0.6
-0.4
-0.2
0
0.2Output Gap
Zero LineEA GE10EA GNSS10EA QR14EA CFOP14pocEA CFOP14bggEA CFOP14cd
As regards the “conventional” policy rules, these are the Taylor rule (ρ = 0, α = 1.5, β = 0.5,
β = 0, h = 0), the GR rule (ρ = 0.66, α = 0.66, β = 0.1, β = 0, h = 0) and the 1st-difference rule of
Orphanides and Wieland (2013) (ρ = 1, α = 0.5, β = 0, β = 0.5, h = 0). We note that only the GR
rule does not generate explosive dynamics in any model. However, the two explosive cases occur for
reasons that are precisely identified: while EA AWM05 does not typically admit ρ = 1, EA GNSS10
does not admit ρ = 0.25 Excluding explosive behavior, the best performing policy rule appears
to be the 1st-difference rule, which – except for the EA CFOP14 models – achieves the minimum
conventional rule loss for all non-explosive cases.
25Both models are discussed in Orphanides and Wieland (2013)
22
Table 5: Lack of Robustness of Model Specific Policy RulesStandard-NK Models’ Loss (% increase relative to minimum loss [IIP])
Rule EA AWM05 EA CW05fm EA CW05ta G3 CW03 EA SW03 EA QUEST3
EA AWM05 0 51 [1.71] 7 [0.43] 13 [0.49] 75 [1.05] 483 [3.82]
EA CW05fm 120 [1.92] 0 11 [0.54] 10 [0.45] 24 [0.59] 93 [1.68]
EA CW05ta 41 [1.12] 219 [3.53] 0 1 [0.11] 23 [0.59] ∞G3 CW03 101 [1.76] 105 [2.44] ∞ 0 18 [0.51] ∞EA SW03 896 [5.25] 153 [2.95] 35 [0.95] 26 [0.71] 0 1624 [7.01]
EA QUEST3 ∞ 58 [1.82] 67 [1.32] 54 [1.03] 68 [1.00] 0
EA GE10 118 [1.90] 69 [1.98] 17 [0.67] 14 [0.53] 27 [0.63] 70 [1.46]
EA GNSS10 ∞ 831 [6.89] 1331 [5.91] 326 [2.52] 115 [1.30] 17 [0.72]
EA QR14 ∞ 244 [3.73] 414 [3.30] 293 [2.39] 116 [1.30] 27 [0.90]
EA CFOP14poc 121 [1.92] 178 [3.19] 65 [1.30] 56 [1.05] 41 [0.77] 442 [3.66]
EA CFOP14bgg 119 [1.91] 197 [3.35] 64 [1.30] 56 [1.04] 41 [0.77] 513 [3.94]
EA CFOP14cd 125 [1.95] 209 [3.46] 70 [1.35] 60 [1.09] 43 [0.79] 559 [4.11]
Financial Frictions Models’ Loss (% increase relative to minimum loss [IIP])
Rule EA GE10 EA GNSS10 EA QR14 EA CFOP14poc EA CFOP14bgg EA CFOP14cd
EA AWM05 328 [10.59] ∞ 1585 [1.63] 26 [1.43] 29 [1.52] 30 [1.57]
EA CW05fm 115 [6.28] 47 [2.54] 44 [0.27] 35 [1.65] 37 [1.73] 37 [1.75]
EA CW05ta 888 [17.42] ∞ 189 [0.56] 31 [1.56] 35 [1.68] 38 [1.75]
G3 CW03 791 [16.45] ∞ 82 [0.37] 29 [1.50] 33 [1.62] 35 [1.70]
EA SW03 665 [15.07] ∞ 55 [0.30] 29 [1.50] 32 [1.61] 34 [1.68]
EA QUEST3 21 [2.66] 35 [2.19] 15 [0.16] 231 [4.27] 248 [4.46] 249 [4.50]
EA GE10 0 84 [3.38] 57 [0.31] 25 [1.40] 31 [1.57] 35 [1.68]
EA GNSS10 45 [3.91] 0 18 [0.17] 201 [3.98] 209 [4.10] 204 [4.08]
EA QR14 61 [4.55] 16 [1.48] 0 196 [3.93] 205 [4.06] 199 [4.02]
EA CFOP14poc 49 [4.10] 220 [5.48] 76 [0.36] 0 0 [0.10] 0 [0.17]
EA CFOP14bgg 60 [4.54] 218 [5.45] 78 [0.36] 0 [0.09] 0 0 [0.06]
EA CFOP14cd 68 [4.81] 228 [5.58] 80 [0.37] 0 [0.15] 0 [0.06] 0
Turning now to the question of how robust model-specific optimal policies are, we present in Table
5 for each model (column) the percent increase in its loss function (with respect to the level achieved
at the optimum) caused by implementing the optimal policy implied by another model (row) in the
set. Following Kuester and Wieland (2010), in addition to the percent increase in the central bank’s
loss relative to the model optimum, we present in brackets the implied inflation premium (IIP) which
is “the increase in the standard deviation of inflation relative to the outcome under the best simple
rule that is necessary to match the loss under the alternative policy” (p.882). The table reveals a
striking lack of robustness exhibited by the model-specific policy rules.26
26Some of the numbers comparable to those reported in Orphanides and Wieland (2013) differ due to numerical
23
Some additional results from the table are worth stressing. Firstly, the FF models appear to be
more fault-tolerant than the standard-NK models.27 Three out of six standard-NK models exhibit
explosive dynamics when subjected to other models’ optimal policy rules. In contrast, only one
out of six FF models exhibits explosive dynamics as a consequence of non-optimal policies; this is
EA GNSS10, which exhibits a worryingly high level of intolerance to the policy rules prescribed
by standard-NK models. Secondly, there is no clear asymmetry between different model types’
performance on the other group. However, there is a marked contrast between the “within group”
performance of models’ rules. Note that no FF models exhibit explosive behavior as a result of
implementing rules derived from other FF models. The same is not true of standard-NK models,
where we see that half of the standard-NK models become explosive when implementing some other
standard-NK model’s optimal policy rule. Finally, we refer to models’ policy rules. Note that with
the exception of EA CW05fm, every policy rule derived from a standard-NK model causes explosive
dynamics in at least one model in the sample. In contrast, the rules of the four financial accelerator
models do not generate explosive dynamics in any of the models in the sample.
3.2 Bayesian Policy Rules
As we have shown in the previous section, for the Euro Area there are very high estimated potential
costs associated with ignoring model uncertainty in the design of simple policy rules. This represents
a strong argument for searching for robust policies in the Euro Area. In this section, we pursue just
that objective by looking at the Bayesian policy rules implied by our set of models. Further, we
are particularly interested in understanding the implications of newer FF models on robust policy
rules. Specifically, we compare the Bayesian policy rules for models with FF to those of standard-
NK models. Our chief question can then be posed as follows: how does a robust simple monetary
policy rule look like for the Euro Area if the policymaker believes FF to be a relevant factor affect-
ing macroeconomic dynamics vis a vis the case where she does not consider them to be of prime
importance?
Following Orphanides and Wieland (2013), we define Bayesian simple rules as the set of coefficients
error. The only case where the difference is significant is in the reported loss for EA GNSS10 when subjected to theoptimal rule of EA AWM05; we find ∞ vs 126 reported in the original paper. This is probably a typo mistake.
27Recall that “a model is deemed fault tolerant if deviations from the best rule for that specific model do not triggera steep increase in losses in that model” (Kuester and Wieland (2010), p.887).
24
{ρ, α, β, β, h
}that solves the following problem faced by the policymaker:
min{ρ,α,β,β,h}
£ =M∑m=1
ωm£m (4)
s.t. it = ρit−1 + αEt (pt+h − pt+h−4) + βEt (yt+h) + βEt (yt+h − yt+h−4)
0 = Et[fm(zt, x
mt , x
mt+1, x
mt−1, θ
m)]
∀m
where ωm ≥ 0 is the weight associated with model m and the variables and constraints are as in
(3). Bayesian policy rules have been shown by Kuester and Wieland (2010) to be robust to model
uncertainty and they allow for including into the analysis subjective beliefs held by the policymaker;
namely by interpreting the model weights as the subjective probabilities that each model is the true
model.28
First, we set equal weights on all models, i.e., ωm = ω > 0 ∀m, and look at the Bayesian policies
implied by all models in the sample, the rule particular to the standard-NK models and the rule of
the FF models. We refer to these policies as “flat priors Bayesian rules.” The rules’ coefficients and
model losses are reported in Tables 6 and 7, respectively.
Table 6: Flat Priors Bayesian RulesRule Interest lag Inflation Output gap Output gap growth h
All models 0.975 0.392 0.238 0.534 0
Standard-NK 0.914 1.628 0.813 0.300 4
Financial Frictions 1.040 0.032 0.013 0.388 0
As can be seen from Table 6, our main result is that FF models prescribe a Bayesian policy that is
much less aggressive in its response to inflation and the output gap than that implied by standard-NK
models. This remains the case also between the flat priors Bayesian rule obtained from all models
in the set and the one particular to the standard-NK models. The response to output gap growth is
similar between the two types of models. The FF rule is outcome-based since no model in that class
prescribes a forward-looking rule, whereas the standard-NK rule is forward-looking, although only
28Alternatively, one can devise an algorithm which recasts the model weights as objective probabilities, using forinstance model posteriors derived from observed data. This approach, while promising, is beyond the scope of thispaper. See Kuester and Wieland (2010) for such an algorithm.
25
two of the six standard-NK models feature forward-looking rules at the optimum. Given that the
optimal standard-NK horizon is set to four, this is likely due to the significant lack of fault-tolerance
of the EA AWM05 model, as discussed in Kuester and Wieland (2010).
Thus, if FF are thought to play an important role in the Euro Area economy, a robustness
approach to monetary policy design along the lines developed here calls for a weaker response to
inflation and the output gap than would otherwise be the case. This result follows mainly from
the financial accelerator models’ influence on the flat priors Bayesian rule, along with FF models’
relatively high level of fault tolerance. Figure 3 shows the average impulse-response functions of
inflation and the output gap to a one-percent increase in the policy rate for both the standard-NK
and FF models. We set the policy rule to be the same for all models in the impulse-response functions
and look at the GR rule and the outcome-based 1st-difference rule.29 As can be seen in the graphs,
FF models on average in the Euro Area imply a much stronger effect on inflation and the output
gap from monetary policy shocks than do standard-NK models. In most cases, the response of the
variable is at least twice as large for FF models than for standard-NK models. Therefore, under model
uncertainty, the conventional “amplification effect” of FF found in the literature implies for robust
simple rules a more moderate response to variations in inflation and the output gap; as stronger
reactions by the central bank risk destabilizing the economy to the extent that FF are relevant to
the macroeconomy.
29In computing the average impulse-response function for the 1st-difference rule we exclude the EA AWM05 modelas it presents explosive dynamics when subjected to this rule.
26
Figure 3: IRFs to a Contractionary Monetary Policy Shock of 1%
GR Rule 1st-Diff Rule (h = 0)
0 5 10 15 20
Periods
-0.08
-0.06
-0.04
-0.02
0
0.02Inflation
0 5 10 15 20
Periods
-0.2
-0.15
-0.1
-0.05
0Output Gap
0 5 10 15 20
Periods
-0.25
-0.2
-0.15
-0.1
-0.05
0Inflation
0 5 10 15 20
Periods
-0.4
-0.3
-0.2
-0.1
0
0.1Output Gap
Zero LineNK models meanFF models mean
In Table 7 we see that group-specific policy rules are less robust than the rule optimized over all
models, as would be expected. The average loss increase for the Bayesian rule is 41%, while it is 112%
for the standard-NK rule and 86% for the FF rule. As regards the group-specific rules’ performance
on other groups, the Bayesian rule of models with FF seems to perform somewhat better than that of
standard-NK models, with an average loss increase of 133% vs 193% from the standard-NK models’
rule. This is supported by the IIP, which show a more marked contrast in terms of performance,
with FF models averaging 3.3% higher inflation variance against a 1.9% increase for standard-NK
models.
27
Table 7: Flat Bayesian Optimization LossesStandard-NK Models’ Losses (% increase relative to minimum loss [IIP])
Rule EA AWM05 EA CW05fm EA CW05ta G3 CW03 EA SW03 EA QUEST3
All models 116 [1.88] 11 [0.80] 16 [0.65] 15 [0.53] 25 [0.61] 23 [0.83]
Standard-NK 24 [0.86] 12 [0.83] 14 [0.61] 19 [0.60] 84 [1.11] 26 [0.89]
Financial Frictions 122 [1.93] 402 [4.79] 29 [0.87] 21 [0.64] 54 [0.89] 168 [2.26]
Financial Frictions Models Losses (% increase relative to minimum loss [IIP])
Rule EA GE10 EA GNSS10 EA QR14 EA CFOP14poc EA CFOP14bgg EA CFOP14cd
All models 26 [2.97] 73 [3.16] 35 [0.24] 48 [1.94] 52 [2.04] 53 [2.09]
Standard-NK 42 [3.78] 287 [6.26] 521 [0.94] 99 [2.80] 105 [2.91] 105 [2.93]
Financial Frictions 4 [1.13] 50 [2.61] 127 [0.46] 15 [1.08] 19 [1.23] 22 [1.34]
Now, we alter the central bank’s problem slightly to control for possible “loss outliers” in the set
of models considered. By loss outlier, we mean a model whose loss function, for reasonable values
of the policy rule coefficients, is significantly above that of all other models. The presence of loss
outliers, as commented by Kuester and Wieland (2010) and Adalid et al. (2005), causes the flat priors
Bayesian rule to set coefficients that may closely follow those of the model with the highest absolute
loss. In our application, this issue is particularly relevant for the FF group, where the minimal loss of
EA GE10 is orders above those of the other models. This is not in itself worrisome if the policymaker
is concerned with finding robust policy rules for a given set of models. As discussed in the literature,
a strictly positive choice of priors will suffice to insure against explosive dynamics in the models
considered in the optimization. However, if the policymaker is concerned about maintaining some
level of robustness with respect to models outside the sample (e.g., models of a different class), the
issue becomes more sensitive. Thus, we now ask if optimizing with respect to models’ normalized
loss function allows for a better performance in “out-of-sample” robustness, as compared to the flat
priors Bayesian rule, and look at the corresponding prescribed policy. In this way we also seek to
curb any possibly over-sized influence of loss outliers on the Bayesian policy rules.
In this case, we set the model weights such that the central bank’s problem (4) is equivalent to
minimizing the average percent-increase in models’ loss functions (with respect to their minimum loss
level), instead of minimizing the absolute average loss level. This is achieved by setting ωm = 1/£minm
∀m, where £minm denotes the loss function of model m evaluated at the optimum.30 We refer to the
30Note that this normalization still allows for the inclusion of subjective beliefs into the analysis; one can simplyadd a second set of model weights to be interpreted as the probabilities that each model is the true model.
28
resulting policies as “normalized loss Bayesian rules.” The rules’ coefficients and model losses are
presented in Tables 8 and 9, respectively.
Table 8: Normalized Loss Bayesian RulesRule Interest lag Inflation Output gap Output gap growth h
All models 0.983 0.255 0.138 0.524 0
Standard-NK 0.984 1.158 0.986 0.041 4
Financial Frictions 1.030 0.062 0.032 0.625 0
In Table 8, we see that the normalized loss Bayesian rule optimized over all models is quite similar
to the equivalent flat priors rule. Relative to the flat priors Bayesian rule, it prescribes a slightly
weaker response to inflation, the output gap and output gap growth and a slightly higher degree
of interest rate smoothing. The group-specific rules, however, present some noticeable differences.
For the standard-NK rules, we observe a drop in the response to inflation and output gap growth,
while the autoregressive coefficient and the response to the output gap increase by a small amount.
For the FF rule, only the autoregressive coefficient falls slightly, while all other parameters increase
substantially (in percentage terms). As before, the policy rule optimized over FF models prescribes
a much more moderate response to inflation and the output gap than the standard-NK policy rule
does, but now the response to output gap growth is much stronger in the FF rule. This is also the
case when comparing the normalized loss Bayesian rule obtained from all the models with that of
the standard-NK models. As before, both the all-models and FF normalized loss Bayesian rules are
outcome-based, while the standard-NK rule optimally reacts to four-quarter-ahead forecasts. Thus,
the main qualitative result that FF models imply weaker responses to variations in inflation and the
output gap continues to hold, albeit with a bit less quantitative clarity.
29
Table 9: Normalized Loss Bayesian Optimization LossesStandard-NK Models’ Losses (% increase relative to minimum loss [IIP])
Rule EA AWM05 EA CW05fm EA CW05ta G3 CW03 EA SW03 EA QUEST3
All models 89 [1.66] 22 [1.13] 10 [0.51] 8 [0.40] 28 [0.64] 33 [1.00]
Standard-NK 31 [0.98] 5 [0.52] 5 [0.36] 7 [0.37] 46 [0.82] 39 [1.09]
Financial Frictions 80 [1.56] 117 [2.58] 15 [0.63] 12 [0.48] 29 [0.65] 148 [2.12]
Financial Frictions Models’ Losses (% increase relative to minimum loss [IIP])
Rule EA GE10 EA GNSS10 EA QR14 EA CFOP14poc EA CFOP14bgg EA CFOP14cd
All models 17 [2.41] 70 [3.09] 53 [0.30] 38 [1.73] 42 [1.84] 44 [1.89]
Standard-NK 63 [4.65] 173 [4.87] 468 [0.89] 55 [2.08] 59 [2.18] 59 [2.20]
Financial Frictions 7 [1.57] 77 [3.24] 78 [0.36] 9 [0.85] 12 [0.98] 14 [1.07]
We now look at the robustness and out-of-sample performance of the normalized loss Bayesian
rule as compared to that of the flat priors Bayesian rule. Table 9 shows the level of robustness of the
normalized loss Bayesian rules by presenting the percent increase in models’ loss function and IIP
for the different rules, while Table 10 reports three statistics which serve to gauge in-sample and out-
of-sample performance: the minimum, mean and maximum percent loss increases and corresponding
IIP. In comparing the relative performance of flat priors Bayesian policy rules, it was noted that while
they are robust to “in-sample model uncertainty,” their performance significantly deteriorates when
such rules are applied to other groups of models. In this sense, the policymaker might be concerned
not only with avoiding large losses among a set of baseline models, but also with limiting the large
potential losses induced in models outside the baseline sample.
Table 10 shows that in terms of the average loss increase, there is relatively little difference in
the performance of the flat priors and normalized loss Bayesian rules; for the full set of models the
average loss increase is 41% and 38%, respectively, and IIPs are also similar. In fact, the dominance of
the normalized loss Bayesian rule is by construction, as it is exactly the average percent loss increase
which is minimized. What is more surprising is that the normalized loss Bayesian rule is able to
effectively limit the maximum percent loss increase, while at the same time maintaining a good
performance in the loss outliers. The result is a flatter distribution of loss increases across models;
something that would seem desirable from the perspective of a risk-averse policymaker. In our sample
Euro Area of models, this mechanism is clearly identified. While the flat priors optimization looks
to push the loss of the loss outliers to their minimum level, thus minimizing the average, this comes
30
at the cost of a steep increase (in percentage terms) in the loss of models that are not fault-tolerant,
evident in the 116% loss increase of EA AWM05 in the flat priors Bayesian rule. The normalized
loss Bayesian rule, on the other hand, lowers this number to 89% at virtually no cost to the loss
outliers.31 This result is supported by the corresponding IIP.
Table 10: Flat vs Normalized Loss Bayesian Rules
Flat Priors: Models’ Losses
(% increase relative to minimum loss [IIP])
Minimum Average Maximum
Rule All NK FF All NK FF All NK FF
All Models 11 [0.24] 11 [0.53] 26 [0.24] 41 [1.48] 34 [0.88] 48 [2.07] 116 [3.16] 116 [1.88] 73 [3.16]
NK Models 12 [0.60] 12 [0.60] 42 [0.94] 112 [2.04] 30 [0.82] 193 [3.27] 521 [6.26] 84 [1.11] 521 [6.26]
FF Models 4 [0.46] 21 [0.64] 4 [0.46] 86 [1.60] 133 [1.90] 39 [1.31] 402 [4.79] 402 [4.79] 127 [2.61]
Normalized Loss: Models’ Losses
(% increase relative to minimum loss)
Minimum Average Maximum
Rule All NK FF All NK FF All NK FF
All Models 8 [0.30] 8 [0.40] 17 [0.30] 38 [1.38] 32 [0.89] 44 [1.88] 89 [3.09] 89 [1.66] 70 [3.09]
NK Models 5 [0.36] 5 [0.36] 56 [0.89] 84 [1.75] 22 [0.69] 146 [2.81] 468 [4.87] 46 [1.09] 468 [4.87]
FF Models 7 [0.36] 12 [0.48] 7 [0.36] 50 [1.34] 67 [1.34] 33 [1.34] 148 [3.24] 148 [2.58] 78 [3.24]
To some extent, the previous result is expected.32 More noteworthy (and corroborated by the IIP
as well) is the fact that the normalized loss Bayesian rule achieves a strikingly better performance
in terms of out-of-sample robustness. In comparing the reported statistics for the standard-NK and
FF rules between flat priors and normalized loss optimizations, note that the normalized loss rules
dominate the flat priors rules (both in percent loss increase and IIP terms) in practically all cases and
where they do not, it is by a small amount. It is also noteworthy that the values for the maximum
average loss increase under the normalized loss rules are lower than under the flat priors rules. As
regards group-specific rules, the FF Bayesian rule performs better on standard-NK models than does
31Note, however, that there is always a cost in terms of some risk. Namely, that the “true model” is actually oneof the cases whose loss increase is larger under the normalized loss Bayesian rule than under the flat priors Bayesianrule.
32Kuester and Wieland (2010) obtain a similar result for a policy rule optimized with ambiguity-averse preferences.However, we are here more interested in comparing the policy implications of standard-NK vs FF models. In thissense, we have preferred to ignore minimax policies (which are imbedded in the ambiguity-averse framework) andfocus on the relatively more risk-tolerant Bayesian framework.
31
the standard-NK models’ rule on FF models, regardless of whether the flat priors or normalized loss
weights are used in the optimization.
In conclusion, the explicit consideration of FF in the Euro Area economy leads to important policy
implications. Both the flat priors and normalized loss Bayesian optimizations imply different policy
rules between standard-NK and FF models, and the Bayesian rule optimized over all models differs
markedly from that of the standard-NK models. By taking into account models which explicitly deal
with FF present in the Euro Area, a risk-averse policymaker preferring to implement policy rules
that are robust to model uncertainty should respond less strongly to inflation and the output gap and
more strongly to output gap growth than would otherwise be the case. Further, she is also advised
to place more weight on the past realizations of macroeconomic aggregates than on her expectation
of future output and inflation. Finally, if she places a higher probability weight on either of the two
types of models considered here, she should take into account that better results are obtained from
the normalized loss Bayesian policy than the flat priors policy, noting that there is a greater risk in
mistakenly favoring standard-NK models than mistakenly favoring FF models.
4 Robustness of Leaning-Against-the-Wind-Type Policies
In the previous section, employing a representative set of Euro Area macro models for policy analysis,
we drew out the implications of model uncertainty for the design of robust simple rules in the presence
of FF affecting the economy. In this section, we employ our set of FF models to ask whether leaning-
against-the-wind-type (LAW) policies are advisable for the Euro Area. The debate on whether or not
the central bank should directly respond to financial sector variables in setting its policy stance has
a long history, garnering special attention in the late-90s in the context of the dot-com bubble. In
this respect, Bernanke and Gertler (2001) can be viewed as representative of the pre-crisis consensus
which rejected a direct response by the central bank to financial sector variables by means of the
policy rate and overwhelmingly favored inflation-targeting regimes as the appropriate framework to
guarantee macroeconomic stability. After the recent financial crises in several developed economies
this consensus has been called into question both on theoretical and legal grounds.33 Mishkin (2011)
33Some of the regulatory reforms enacted since the crisis have expanded and/or strengthened the central bank’soversight responsibilities with respect to the financial sector. In this context, a related question – which we do notaddress here – is if such a change of mandate should lead us to modify the central bank’s loss function.
32
provides a discussion on the consequences of the great financial crisis on the consensus surrounding
the use of the monetary policy rate to respond to developments in the financial sector.
Therefore, the LAW debate’s salience is again on the rise and is now the subject of various
studies that make use of the modelling developments which have taken place over the last decade.
For instance, Lambertini et al. (2013) study monetary policies which lean against house price and
credit cycles. They find it is optimal for the interest rate to respond to credit growth. Christiano
et al. (2010) also argue in favor of leaning against credit growth based on simulations done with
a medium-scale estimated DSGE, appended with frictions a la Bernanke et al. (1999), but their
analysis focuses almost exclusively on signal shocks.34 Gilchrist and Leahy (2002) also carry out a
shock-specific analysis using calibrated models and focus on asset prices, but based on their results
they do not favor including this variable in monetary policy rules. Gambacorta and Signoretti (2014),
using a simplified and calibrated version of the EA GNSS10 model, find that the central bank should
optimally respond to variations in credit or asset prices. Curdia and Woodford (2015) use a calibrated
model to argue in favor of a rule which responds to changes in current and expected future interest
rate spreads. And, Laseen et al. (2015), using a calibrated model, find that a rule responding to
leverage could improve macroeconomic outcomes, but note that the results are sensitive to parameter
values.
From this very brief survey, we may surmise that the literature has focused mainly on calibrated
models and has not addressed model-uncertainty concerns. It thus seems timely and important to
approach the question from a robustness perspective and in specific relation to the Euro Area. Thus,
we seek to bring to bear to the debate the framework employed so far such that our results are
applicable to the actual conduct of monetary policy in the Euro Area. Specifically, we investigate
to what extent the central bank can obtain lower losses by adopting LAW policies – defined as the
direct and systematic reaction to variations in financial variables by the central bank through its
main policy rate – and to what extent such policies are robust to model uncertainty. We do so
by constructing six common financial variables for our set of models, since the literature on LAW
policies of the type treated here has not yet converged towards a single financial variable to which
the central bank would optimally respond, as should be clear from the review above. These variables
34In this regard, the authors recognize that “[a] full evaluation of the policy of including credit in the interest ratetargeting rule would evaluate the performance of this change when other shocks are present as well” (p. 23).
33
are real credit, real credit growth, the credit to GDP ratio, the external finance premium or spread,
the leverage ratio and a measure of asset prices.35
The central bank then solves the following problem:
min{ρ,α,β,β,h,gj}
£ =M∑m=1
ωm£m (5)
s.t. it = ρit−1 + αEt (pt+h − pt+h−4) + βEt (yt+h) + βEt(gjt+h
)0 = Et
[fm(zt, gt, x
mt , x
mt+1, x
mt−1, θ
m)]
∀m
where the variables and constraints are as in (3) and (4), the LAW parameter is bounded such that
β ∈ [−3, 3] and gjt is the jth element of the vector of common financial variables, gt:
g =
real credit
real credit growthreal credit / GDP
external finance premiumleverage
asset prices
As above, we begin by looking at the model-specific optimal policies; that is, all weights in
problem (5) are set to zero except for the model in question. Note, however, that we have dropped
output gap growth from the set of variables the central bank can respond to. This simplifies both
the analysis and computational burden without affecting our results (as is discussed below). The
results of this optimization problem (shown in the rows with the model label) are presented in Table
11 along with the no-LAW optimal policy rule (i.e., row “without LAW” where we exogenously set
β = 0 in the optimization problem). The table also presents the gains achieved by the central bank
by adopting the optimal LAW rule; recall that the four-coefficient rule (i.e., the rule with LAW) will
always perform better than the three-coefficient rule (i.e., no LAW in this case) since the latter is
nested in the former.
35See Appendix D for a full model-specific description of each common financial variable.
34
Table 11: Model-Specific LAW Optimal PoliciesModels Gain (%) Interest lag Inflation Output gap LAW coefficient h
[IPP] (Variable)
EA GE10 with LAW 0.1 1.0836 0.0034 0.0092 -0.0003 2
without LAW [0.16] 1.0829 0.0029 0.0092 (Real Credit) 2
EA GNSS10 with LAW 0.8 1.3251 0.9218 0.4035 0.0442 0
without LAW [0.33] 1.2216 0.8205 0.3678 (Real Credit) 0
EA QR14 with LAW 0.1 1.1275 1.1977 0.6135 -0.0007 0
without LAW [0.01] 1.1211 1.1933 0.6123 (Leverage) 0
EA CFOP14poc with LAW 0.5 0.8130 0.2416 0.0965 0.1477 4
without LAW [0.21] 0.8659 0.2269 0.1885 (Credit Growth) 4
EA CFOP14bgg with LAW 0.6 0.8087 0.2384 0.0819 0.1567 4
without LAW [0.24] 0.8644 0.2307 0.1837 (Credit Growth) 4
EA CFOP14cd with LAW 0.7 0.8042 0.2415 0.0798 0.1630 4
without LAW [0.25] 0.8609 0.2358 0.1845 (Credit Growth) 4
The results from our exercise reveal that, conditional on the central bank following the optimal
policy rule, adopting a LAW policy does not generate gains in terms of macroeconomic stabilization.
Two models, namely EA GE10 and EA QR14, place virtually no weight on variations in financial
variables, while the rest do not imply significant gains for the loss function. In fact, the highest loss
gain occurs in EA GNSS10 and represents a mere 0.8% reduction in the loss level. And since no model
implies significant gains from LAW, we can safely assume that the same is true for Bayesian policies.
Further, this result would continue to hold if we compared the four-coefficient rule in (4) to its five-
coefficient LAW counterpart. Hence, we find that the FF models considered here do not provide a
strong argument for leaning against the wind. Apart from this general picture, it is interesting to
notice that for financial accelerator models the reduction of the policy parameters available (recall
that now the central bank is not allowed to respond to output gap growth) makes it optimal for
policy to be forward-looking. Now recall that financial accelerator models in the four-parameter case
find it optimal to place a relatively higher weight on output gap growth than on the level of the
output gap. Thus, this result could be explained by the fact that the growth of the output gap serves
as an indicator for future developments in inflation and/or the output gap. Finally, we would note
35
that the models in our set suggest (by majority) that credit is the most relevant financial variable
for the central bank to pay attention to.
The message that emerges from Table 11 is that allowing for LAW policies cannot significantly
improve on the simpler policy rule which reacts exclusively to inflation and the output gap. However,
as we saw in the previous section, under model uncertainty the policymaker would do well to abstain
from placing all his conviction in any single model and instead incorporate that uncertainty into his
design of a robust policy. Thus, we now check whether or not LAW policies lead to a performance
improvement on robust policy rules; specifically, we allow for the Bayesian rules we derived earlier
to react to the common financial variables and find the corresponding optimal LAW coefficient for
each model. For completeness we also include the three conventional rules of Table 4 in the analysis.
Table 12 presents the results obtained from minimizing the central bank’s loss function (5) for each
model taking as given the parameters of the policy rule (listed in each column).36
The results from Table 12 again argue against LAW policies.37 In general, the improvement in the
performance of the policy rules varies widely across the rules and no single financial variable stands
out as a better indicator of business cycle volatility. While conventional policies are able to access
sizable gains in some cases, the gains from LAW policies in Bayesian rules are much more modest,
as would be expected given their higher degree of robustness. However, notice that the coefficients
found for financial variables in the Bayesian rules are in almost all the cases of the “wrong” sign.
That is, if the central bank has adopted one of the robust policy rules derived above or one of
the conventional policy rules considered here, it would be counterproductive or destabilizing to lean
against the wind, under most models. Recall that we have constructed Table 12 with the restriction
that β ∈ [−3, 3]. Therefore, if we further limited the set of available policies to include only those
where the central bank actually “leans against the wind,” the results would overwhelmingly lie at
the lower bound of β = 0, delivering no gains from the baseline rule. Read in this way, the instances
where LAW is actually advised by these models is limited to EA GNSS10 under the normalized loss
36That is, we solve problem (5) while imposing the restrictions ωm = 1, ω−m = 0, ρ = ρl, α = αl, β = βl, β = βl, h =hl for l = {FF Flat Pr iors, FF Norm Loss, Taylor, GR, 1st-Diff} for each m ∈M . Note that the rules labeled“Norm Loss” and “Flat Priors” in Table 10 refer to the normalized loss and flat priors Bayesian rules optimized overthe FF models, not those obtained by averaging over all models.
37Note that the values reported are not the deterioration of the loss function as before, but instead the improvementachieved by the central bank. This follows from the fact the extra degree of freedom which the LAW parameter grantsthe central bank implies that it cannot do worse than the benchmark case. Consequently, all the IIP reported arenegative.
36
Table
12:
Lean-A
gain
st-t
he-W
ind
Poli
cies
Mod
elC
on
cep
tR
ule
Nor
mL
oss
Fla
tP
rior
sT
aylo
rG
R1st
Diff
(h=
0)C
BG
ain
(%)
[IIP
]4.
44[-
1.28
]2.
06[-
0.85
]2.
92[-
1.33
]3.
20[-
1.29
]4.
12[-
1.30
]
EA
GE
10
Coeffi
cien
t0.
0138
0.00
61-0
.432
5-0
.044
4-0
.102
0
Vari
able
Cre
dit
Cre
dit
Ass
etP
rice
sR
eal
Cre
dit
Ass
etP
rice
s
CB
Gai
n(%
)[I
IP]
0.90
[-0.
46]
1.62
[-0.
58]
-10
.84
[-1.
58]
3.04
[-0.
80]
EA
GN
SS
10
Coeffi
cien
t-0
.162
9-0
.111
2-
-0.1
000
-0.9
805
Vari
able
EF
PC
red
itG
row
th-
Rea
lC
red
itE
FP
CB
Gai
n(%
)[I
IP]
0.24
[-0.
03]
0.50
[-0.
04]
3.86
[-0.
22]
8.59
[-0.
23]
1.77
[-0.
06]
EA
QR
14C
oeffi
cien
t-0
.000
1-0
.000
1-0
.433
7-0
.234
1-0
.051
3
Vari
able
Cre
dit
toG
DP
Cre
dit
toG
DP
EF
PE
FP
EF
P
CB
Gai
n(%
)[I
IP]
1.68
[-0.
38]
3.46
[-0.
56]
4.47
[-0.
72]
18.4
7[-
1.83
]18
.73
[-2.
18]
EA
CF
OP
14p
oc
Coeffi
cien
t-0
.005
5-0
.005
0-0
.042
3-0
.034
7-0
.051
0
Vari
able
Lev
erag
eL
ever
age
Cre
dit
toG
DP
Cre
dit
toG
DP
Cre
dit
toG
DP
CB
Gai
n(%
)[I
IP]
2.38
[-0.
46]
4.44
[-0.
65]
5.55
[-0.
82]
23.4
5[-
2.15
]19
.87
[-2.
33]
EA
CF
OP
14b
ggC
oeffi
cien
t-0
.002
9-0
.002
5-0
.046
8-0
.038
8-0
.052
3
Vari
able
Cre
dit
Cre
dit
Cre
dit
toG
DP
Cre
dit
toG
DP
Cre
dit
toG
DP
CB
Gai
n(%
)[I
IP]
2.97
[-0.
53]
5.49
[-0.
74]
5.11
[-0.
79]
22.6
2[-
2.11
]17
.60
[-2.
22]
EA
CF
OP
14cd
Coeffi
cien
t-0
.003
2-0
.002
8-0
.044
7-0
.037
6-0
.049
4
Vari
able
Cre
dit
Cre
dit
Cre
dit
toG
DP
Cre
dit
toG
DP
Cre
dit
toG
DP
37
Bayesian rule and the 1st-difference rule, and EA QR14 under the conventional rules. Otherwise, the
exercise seems to clearly advise against LAW policies in for the Euro Area.
This result is confirmed in Table 13, which presents the flat priors Bayesian coefficients. Again,
we observe that in all cases the optimal coefficients, although very close to zero, require the central
bank to adjust the policy rate “in the direction of the wind” instead of leaning against it. In general,
we conclude from this exercise that the downside risks from model uncertainty become much more
pronounced in trying to implement LAW policies, while the potential gains from such policies over
simple rules are negligible. In sum, in the presence of model uncertainty a risk-averse policymaker
is better off keeping it simple.
Table 13: Robust Conventional Rules with LAWRule LAW Variable LAW Coefficient
Norm Loss Credit Growth -0.0260
Flat Priors Credit -0.0010
Taylor Credit Growth -0.0145
GR Credit Growth -0.0288
1st-Diff (h = 0) Credit Growth -0.0397
Lastly, we should stress that in the aforefound non-LAW robust policies, the central bank still
takes into account financial variables in setting its policy stance as their interaction with the macroe-
conomy is explicitly modeled. But since the models are interpreted as constraints on the central
bank – in as much as they capture the actual workings of the underlying economy – when designing
its policy rule, a direct and systematic response to financial variables seems to be ill-advised in the
Euro Area. As mentioned before, some studies have addressed circumstances in which it would be
advisable to use the policy rate to curb excesses in financial markets in order to avoid or limit a
potential macroeconomic disruption,38 but we regard these as falling within the discretionary and/or
macroprudential operation of central banks, and as such lying outside the space of policies we ana-
lyze here. Our analysis has focused exclusively on policies of full commitment to simple rules. It is
also worth stressing that we do not dispute the fact that there may be areas of the parameter space
for each model where LAW would be optimal, but our subject concerns these models as they best
38This, of course, requires that the central bank be able to accurately identify bubbles in real time – a recurrentargument against LAW. Alternatively, the policy rate has frequently been seen as “too blunt” an instrument withwhich to address financial sector imbalances. More recently, Stein (2013) has argued that there are benefits to usingthe interest rate in the context of a sophisticated financial sector where product innovation and regulatory arbitrageare prevalent: “namely that it gets in all of the cracks” (p. 17).
38
approximate the Euro Area economy. In this sense, we interpret our results as directly applicable to
the actual conduct of monetary policy in the currency union.
5 Fiscal Rules Exercises
In this section, we extend the previous analysis to fiscal policy in the Euro Area. As is the case with
monetary policy, the global financial crisis of 2007-2009 and the ensuing policy responses implemented
by the governments of several major advanced economies around the world sparked an important
development in research on the effects and transmission channels of fiscal policies. Indeed, there
has been a particularly noteworthy renewed interest in accurately gauging the quantitative effects
of discretionary fiscal stimulus on output. Less focus, however, has been placed on the impact of
fiscal rules. While the work done on fiscal multipliers is important in enhancing our understanding
of the transmission mechanism of discretionary fiscal policy (see Christiano et al. (2011), Fernandez-
Villaverde (2010) and Eggertsson and Krugman (2012), among others), here we focus on fiscal policy
rules along the lines of Leeper et al. (2010), where these are understood as the “systematic portion
of fiscal policy” (Reicher (2014)) or “the rules in law that make fiscal revenues and outlays relative
to total income change with the business cycle” (McKay and Reis (2016)). That is, fiscal policy is
modeled as following a set of fixed rules which determine the endogenous response of the government’s
instruments – such as labor income taxes and purchases – while being constrained by a target rule
that determines the speed with which the budget converges in the absence of shocks towards its
long-run level.39 Thus, we are not concerned with measuring the size of fiscal multipliers (which are
linked to the discretionary components of fiscal policy), but rather on finding robust fiscal rules for
the Euro Area and characterizing them.
In order to do this, we proceed as follows. First, we define a new set of models for robust analysis,
including three standard-NK models and three FF models. A common fiscal block is then appended
to each of the models, including a set of simple fiscal rules. We specify a Bayesian loss-function
minimization problem for the fiscal authority similar to that of the central bank above. Robust
policies are defined as those which solve the fiscal authority’s optimization problem.
39In this framework, there have been a variety of specifications proposed, used and estimated for different countries;for a comparison of some models see Coenen et al. (2012).
39
The following caveats and observations are in order. Firstly, in contrast to the monetary policy
exercises above, we cannot interpret our results as estimates, since only one of the models in our
sample has been estimated with a detailed fiscal sector and using relevant data. Secondly, our
analysis assumes a common fiscal policy for the Euro Area, which is not in actuality the case and so
is less applicable than that concerning monetary policy. Thirdly, we do not incorporate a direct link
between the government’s debt level and the interest rate on government bonds, but rather include
an ad hoc term in the fiscal authority’s loss function to account for the potentially adverse effects of
volatile debt dynamics. Fourthly, for each model we set the central bank’s reaction function equal
to that model’s estimated policy rule and allow for monetary policy shocks. Finally, it is important
to note that carrying out an analysis analogous to the one realized above would require estimating
all of the treated models after implementing the fiscal extension, preferably with fiscal data as well.
However, we think that the strategy we employ here provides a first approximation to the likely
results that would be obtained if we proceeded as in Section 3.
The set of models we consider overlaps with that employed in the sections above and is reported
in Table 14. From the previous sections we include EA SW03 and EA QUEST3 in the standard-
NK models, and EA GE10 and EA CFOP14poc in the FF subset. These models are described in
Section 2.1. Further, we include in the subset of standard-NK models EA JPT11 (described in
detail in Justiniano et al. (2011)), which is the “core model” of the EA CFOP14poc model.40 Note
that EA GE10 and EA CFOP14poc can be interpreted as direct FF-extensions of EA SW03 and
EA JPT11, respectively, since each of the latter models is nested in the former. Finally, in the FF
subset, we include a version of the model developed by Gertler and Karadi (2011) that is estimated
for the Euro Area in Villa (2016), which we label EA GK16. Essentially, the estimated version of
this model appends the financial sector block of Gertler and Karadi (2011) to the model of Smets and
Wouters (2003), with some modifications.41 As regards the financial block, the model is characterized
by the presence of financial intermediaries which collect deposits from the household sector to issue
contingent claims to firms. An agency problem between intermediaries (i.e., banks) and households
40Specifically, the EA JPT11 model’s specification is obtained by setting ν = 0, χk = −0.05 and ρmp = 0 in theEA CFOP14poc model. The estimation for the Euro Area of this model is presented in Appendix E.
41The reader is referred to Villa (2016) for a full treatment of this model and the estimation. In our application, wealso decrease by a common factor the persistence parameters of the exogenous components of the model to limit thevariance of debt implied after appending the common fiscal block.
40
leads to an endogenous constraint on the amount of leverage intermediaries can take on, creating a
feedback between the state of banks’ balance sheets and the macroeconomy.
Table 14. Set of Euro Area Models# Label Reference
New Keynesian Models1 EA SW03 Smets and Wouters (2003)2 EA JPT11 Justiniano et al. (2011)3 EA QUEST3 Ratto et al. (2009)
Financial Frictions Models4 EA GE10 Gelain (2010)5 EA CFOP14poc Carlstrom et al. (2014),
privately optimal contract6 EA GK16 Villa (2016),
after Gertler and Karadi (2011)
Analogously to the central bank’s problem defined above, the fiscal authority’s loss function is
defined as the sum of the variance of inflation and the output gap.42 Additionally, we add the
(weighted) variance of government debt to account in an ad hoc manner for the need to keep fiscal
accounts in order:
£m = V arm (π) + V arm (y) + θbV arm (b)
The common fiscal block which is appended to the models follows Binder et al. (2016) and includes
government spending, taxes on labor and consumption goods, and transfers. The budget constraint
is given by:
Gt +Bt−1 = τCCt + τNt WtNt + Tt +Bt
Rt
where Gt is government consumption, Bt denotes one-period bonds, τC and τNt are respectively
taxes on consumption, Ct, and real labor income, WtNt, Tt are lump-sum taxes (or transfers from
households to the government) and Rt is the gross interest rate paid on government bonds.
Finally, lump-sum taxation guarantees that the government’s budget constraint always holds and
42See Blanchard et al. (2016) for arguments in favor of employing the ad hoc loss function to evaluate fiscal policies.Most relevant to our analysis, is their observation that the assumptions of models similar to Smets and Wouters (2007)(that households perfectly share consumption risk and that all variations in labor take place at the intensive margin)are likely to underestimate the costs of large output gaps.
41
follows a rule similar to that of Cogan et al. (2010):
T
GDPtt = φB
B
GDPbt + φG
G
GDPgt
where the steady state annual debt-to-GDP ratio is set to 0.6, government spending-to-GDP is
model-specific but around 0.2, and φB = 0.043 and φG = 0.124.
As shown in Binder et al. (2016), in this setting, fiscal policy affects the economy through dis-
tortions introduced via households’ intratemporal labor-consumption optimality condition and the
economy’s resource constraint:
Wt
(1− τNt
)=uN,tuC,t
(6)
GDPt = Ct + It +Gt +MSmt (7)
where uN,t is the marginal utility of labor, uC,t is the marginal utility of consumption, GDPt is the
gross domestic product, It is aggregate investment and MSmt denotes other terms particular to model
m ∈ M .
Our specification for the government’s fiscal rules is close to that of Leeper et al. (2010), who
estimate an RBC-style model with a detailed specification of fiscal rules on U.S. data, and allows
us to consider an explicit role for the fiscal authority in macroeconomic stabilization.43 In log-linear
form (letting xt ≡ log(Xt)− log(X) and X denote the value of Xt at the non-stochastic steady state),
fiscal policy rules are defined as follows:
gt = −ϕgyt − γgbt−1 (8)
τNt = ϕτyt + γτbt−1 (9)
where yt is the output gap; with the steady state values of the taxes on labor income and consumption
set according to Cogan et al. (2013): τN = 0.122 and τC = 0.183. Leeper et al. (2010) estimate these
43Alternative formulations in the literature follow Bohn (1998), which relates the government’s primary surplus toGDP ratio to debt and other controls. This specification has been mostly employed to study fiscal policy as it relatesto debt sustainability. For an empirical assessment of this type of “fiscal reaction functions” in the Euro Area, seeBerti et al. (2016) and for the econometric challenges inherent in accurately estimating these rules, see Leeper and Li(2016). Since we are mainly interested in stabilization objectives, we consider the specification of Leeper et al. (2010)to be more appropriate. An empirical study on the use of this type of policies across a large sample of countries isReicher (2014)
42
rules within a more detailed fiscal sector and set output as the relevant macroeconomic variable for
the fiscal authority. We include the output gap in the fiscal authority’s reaction function instead since
we are interested in deriving the government’s optimal rule. As the output gap is the more relevant
measure of household welfare in this enviroment, it seems natural to allow the fiscal authority to
react directly to it. Further, there is no reason to assume that the fiscal authority cannot observe
this variable given that we have supposed throughout that the central bank can.44 That is, both the
government spending rule (8) and the labor income tax rule (9) are composed of a macro-stabilizing
component and a debt-stabilization component.
Thus, the fiscal authority’s optimization problem is given by:
min{ϕg ,γg ,ϕτ ,γτ}
£ =M∑m=1
ωm [V arm (π) + V arm (y) + θbV arm (b)] (10)
s.t. gt = −ϕgyt − γgbt−1
τNt = ϕτyt + γτbt−1
0 = Et[fm(zt, x
mt , x
mt+1, x
mt−1, θ
m)]
∀m
This specification raises the question of where we should set the bounds on parameters ϕg, γg, ϕτ
and γτ in defining the rules available to the fiscal authority. As regards the debt-stabilizing compo-
nents of fiscal policy, we can set γg, γτ ≥ 0 and unambiguously rule out destabilizing policies since in
all models debt is decreased by either reducing government spending or increasing the labor income
tax. In the case of the macro-stabilizing parameters (ϕg and ϕτ ), however, we need to be more
careful. The reason is that equations (6) and (7) hold for both the sticky-price economy and the
flexible-price economy, the difference of which defines the output gap in most of the models in our
set. Thus, each instrument’s effect on the output gap depends crucially on the magnitude of the
response of potential output relative to that of output.
In Figures 4 and 5 we show for each model the IRFs of output, potential output and the output
gap to a positive government spending shock and a positive labor income tax shock, respectively.45 In
44Although this is certainly a valid concern for both sectors of government, addressing it in a detailed manner isbeyond the scope of this paper.
45For the government spending shock the magnitude of the innovation is model-specific and set equal to the estimatedstandard deviation. In the case of the labor income tax, this shock has been added as an AR(1) process, withpersistence parameter equal to 0.95, to all models in the set and the graphs correspond to a one-percent innovation.
43
the case of the EA QUEST3 model, we only present the output gap since this model does not have a
measure of output comparable to the other models in the set. The output gap is defined as a weighted
average of the deviation of labor and capital utilization from their steady state levels. Although this
implies that the measure of the output gap in this model is slightly different, it is useful to keep this
model in the set as it is estimated employing fiscal data. The responses of both output and potential
output are conventional in all cases. As seen in Figure 4, increased government spending raises
both variables by inducing households to increase their labor supply due to a negative wealth effect.
Meanwhile, the output gap increases in all models since the response of output in the sticky-price
economy is greater than that of the flexible-price economy. This is intuitive because government
spending is an instrument which affects quantities; its impact will be greater in an environment
where prices cannot adjust perfectly. The implication for the macro-stabilizing component of the
government spending rule is that the restriction ϕg ≥ 0 is sufficient to rule out procyclical policies.
Figure 4. IRFs of a Government Spending Shock
0 5 10 15 20Periods
0
0.1
0.2
0.3 EA SW03
0 5 10 15 20Periods
-0.5
0
0.5
1
1.5 EA GE10
0 5 10 15 20Periods
0
0.1
0.2
0.3 EA JPT11
0 5 10 15 20Periods
0
0.1
0.2
0.3EA CFOP14poc
0 5 10 15 20Periods
-0.2
0
0.2
0.4 EA QUEST3
0 5 10 15 20Periods
-0.5
0
0.5
1
1.5 EA GK16
Zero Line Output Gap Output Potential Output
Figure 5 shows that the dynamic response of output and potential output is also standard in all
For the EA QUEST3 model, we present the IRFs of the original specification, with only the labor income tax modifiedas mentioned before; the relevant qualitative properties of the fully-modified version remain the same.
44
models for the case of a positive labor income tax shock. A higher tax rate reduces household labor
and consumption by cutting disposable labor income and, in turn, leads to a fall in output. However,
the response of the output gap is model-specific. For the models in our set where it is defined as the
difference between the sticky-price economy and the flexible-price economy, the response is positive.
Recall that the labor income tax is an instrument that works on prices, thus its impact is greater
when all other prices immediately reflect the change. So, if the fiscal authority is to respond to the
output gap directly, it must adjust this policy instrument in the opposite direction of the movement
in the output gap in order to stabilize it. In contrast, in the case of the EA QUEST3 model, the
fall in labor directly affects the output gap and is reinforced by a fall in the utilization rate. This
leads to a fall in the output gap in response to the increase in the labor income tax; suggesting that
if the fiscal authority is to use this instrument according to a rule, it should respond in the same
direction in order to stabilize it. Thus, we do not impose a bound at zero for the macro-stabilizing
parameter of the labor income tax rule in the exercises that follow. Instead, we restrict policies such
that ϕτ ∈ [−5, 5]; and similarly for the other parameters: 0 ≤ ϕg, γg, γτ ≤ 5.46
Figure 5. IRFs of a Labor Income Tax Shock
0 5 10 15 20Periods
-0.4
-0.2
0
0.2 EA SW03
0 5 10 15 20Periods
-0.4
-0.2
0
0.2 EA GE10
0 5 10 15 20Periods
-0.4
-0.2
0
0.2 EA JPT11
0 5 10 15 20Periods
-0.4
-0.2
0
0.2EA CFOP14poc
0 5 10 15 20Periods
-0.1
-0.05
0
0.05 EA QUEST3
0 5 10 15 20Periods
-0.2
-0.1
0
0.1
0.2 EA GK16
Zero Line Output Gap Output Potential Output
46The selection of five as the relevant bound is arbitrary, but does not affect our results.
45
We begin by asking which of the two fiscal instruments treated here is more effective for macroe-
conomic stabilization and which for debt stabilization in each model. In order to do this, we look
at the percent gain (i.e., decrease) in the loss function under θb = 0 associated with a one-percent
variation in the unconditional standard deviation of government debt which results from using each
instrument exclusively for the purpose of either macroeconomic or debt stabilization. The results
are reported in Table 15. Column Macro-Stabilization, Government Spending registers the percent
gain resulting from implementing the government spending rule (8) with γg = 0 and setting ϕg such
that the standard deviation of government debt is one percent higher than under passive fiscal policy
(i.e., ϕg, γg, ϕτ , γτ = 0); similarly for the column Macro-Stabilization, Labor Tax. This measure is
intuitive because it takes as numeraire the funds households must provide to implement such policies,
so that loss gains can be approximately read as per unit of additional debt.47 Naturally, the impact
of government spending and the labor income tax on both output and debt is model-specific, hence
the need to impose a common benchmark between models and instruments.48 The analogous discre-
tionary expansionary fiscal policy exercise would ask which countercyclical measure – either increased
government spending or reduced taxes – can increase output more, while holding constant the funds
elicited from the public to finance such policies. As regards the Debt-Stabilization columns, these
report the percent gain in the loss function associated with a one-percent decrease in the standard
deviation of government debt. That is, each instrument is used solely to decrease the volatility of
debt, so that the relevant object of comparison is the associated gain (or cost, if negative) in terms
of macroeconomic stability – as measured through the loss function under θb = 0.
47Recall that, with the exception of EA QUEST3, our approach does not model the negative macroeconomic effectsof increased debt volatility. Thus, in most cases the achievable gains from debt-financed macro-stabilization policiesare not endogenously limited.
48In this sense, given the semi-calibrated nature of our approach, the policy parameters are not strictly comparablebetween models as the fiscal rules (and other variables’ response to them) have not been estimated. Only if the modelswere estimated with a common fully-specified fiscal sector could the rules themselves be employed as a benchmark.As this is not the case, it is more appropriate to employ variations in public debt as the policy benchmark.
46
Table 15: Fiscal Instrument Effectiveness(Gain from 1% change in σ(b) wrt passive fiscal policy (%))
Macro-Stabilization Debt-Stabilization
Model Government Spending Labor Tax Government Spending Labor Tax
EA SW03 10.42 12.01 -0.17 0.13
EA JPT11 0.85 2.76 1.17 -0.69
EA QUEST3 - 12.76 -0.09 -0.22
EA GE10 40.30 2.40 2.06 -1.70
EA CFOP14poc 0.85 2.03 0.61 -0.39
EA GK16 5.60 7.00 0.00 -0.53
The figures shown in Table 15 show that the labor income tax tends to be more effective in
stabilizing the output gap and inflation and government spending is a more effective instrument
for debt stabilization. In the case of macroeconomic stabilization, four out of the six models in our
sample achieve a higher gain in the loss function by means of the labor income tax than by government
spending. The two exceptions are EA QUEST3 and EA GE10. The former is peculiar because it was
estimated using fiscal data and incorporating a detailed government sector. It turns out that in this
model, after imposing the same fiscal policy specification as in the other models, government spending
is self-financing, so that countercyclical policies also reduce the volatility of government debt. As
regards EA GE10, this model seems to be an outlier in terms of the effectiveness of the government
spending rule in stabilizing the output gap and inflation. In the case of debt stabilization, government
spending is identified as the more efficient instrument. Only for EA SW03 does the labor income
tax perform better in terms of debt stabilization; indeed, it is the only model where stabilizing debt
through this instrument also stabilizes the macroeconomy. In all other cases, government spending
is able to stabilize debt dynamics at a lower cost to the loss function than the labor income tax.
Next, we let the government employ each instrument both for macro- and debt-stabilization
purposes. Table 16 reports the optimal parameter values for each model for both the government
spending rule (8) and the labor tax rule (9), as well as the percent gain in the loss function obtained
from implementing such rules with respect to the passive fiscal policy case. The reported exercises
refer to the case where the fiscal authority uses each instrument exclusively. That is, the parameters
reported under “Government Spending” solve problem (10) under the restrictions ϕτ = 0 and γτ = 0
and where the model weights are zero for all models other than that specified in the row. Similarly,
47
the results reported under “Labor Tax” are obtained under the restrictions that ϕg = 0 and γg = 0.
We show the results attributing two different weights to the fiscal authority’s preference for debt
stabilization: θb = 0 (in which case no importance is given to debt stabilization) and θb = 1.49 The
first case is useful for gauging the potential welfare gains to be had from implementing rules-based
fiscal policy in this environment, but the cases where θb = 1 may be interpreted as yielding more
realistic results since in reality a high volatility of government debt tends to be associated with high
macroeconomic instability. Note that the assumption that the fiscal authority only has access to a
single instrument implies that countercyclical policies must be financed by debt.
Table 16: Model-Specific Rules - Single Instrument Case
θb=0
Gain wrt Passive Government Spending Gain wrt Passive Labor Tax
Model Fiscal Policy (%) Output Gap (ϕg ) Debt (γg ) Fiscal Policy (%) Output Gap (ϕb ) Debt (γτ )
EA SW03 71.47 5.00 0.00 15.93 -5.00 0.61
EA JPT11 54.94 5.00 0.10 5.21 -5.00 0.73
EA QUEST3 10.08 5.00 0.00 12.80 3.85 0.32
EA GE10 63.42 5.00 0.00 28.26 -5.00 0.00
EA CFOP14poc 47.84 5.00 0.04 4.72 -5.00 0.67
EA GK16 23.12 5.00 1.58 12.88 -5.00 0.00
θb=1
Gain wrt Passive Government Spending Gain wrt Passive Labor Tax
Model Fiscal Policy (%) Output Gap (ϕg ) Debt (γg ) Fiscal Policy (%) Output Gap (ϕb ) Debt (γτ )
EA SW03 79.30 0.60 4.43 72.63 -0.73 5.00
EA JPT11 68.36 0.29 4.31 60.74 -1.56 5.00
EA QUEST3 89.93 5.00 5.00 85.71 5.00 5.00
EA GE10 88.65 1.07 5.00 78.06 1.31 5.00
EA CFOP14poc 78.34 0.21 4.83 72.73 -1.36 5.00
EA GK16 90.64 1.05 5.00 86.66 0.96 5.00
The first thing to note from Table 16 is that there seems to be quite a lot of room for fiscal
policy to contribute towards more stable inflation and output gap fluctuations. This is clear from
the top panel, which shows the results of the case where debt stabilization is not an issue, i.e.,
the case of θb = 0. The percent gains in the loss function are economically significant under both
the government spending and labor tax rules in all models; even the most conservative estimates
49In Appendix F we present comparable tables for θb = 0.5, where the results shown here continue to hold.
48
of EA QUEST3 are above 10%.50 As regards optimal policies, in practically all models the macro-
stabilizing parameters are at the bound, with only little weight placed on debt stabilization. As
Figure 5 suggested previously, the sign of the macro-stabilizing component of the labor income tax is
positive for the EA QUEST3 (as a higher tax rate reduces the output gap) and negative for the other
models in the sample. Note, however, that this does not necessarily imply that the labor income tax
is procyclical with respect to output. Since, in each model, some shocks move output and the output
gap in the same direction and others in opposite directions, the average co-movement of the labor
income tax and output will depend on which shocks are estimated to be more predominant and,
thus, on the correlation between output and the output gap. These issues pertain to the concerns
regarding model uncertainty and support the case for designing and employing robust policies.
The fact that nearly all macro-stabilizing parameters are at their bounds in the case of θb = 0
follows because, as stated above, in this setting there is no link between the level of debt that the
government owes and other real variables in the economy. We incorporate the issue of potentially
adverse debt dynamics into our analysis by explicitly including a debt-stabilization term into the loss
function. It turns out that macroeconomic stabilization comes at an extremely high cost in terms
of debt volatility. This is clear from the θb = 1 case, where the macro-stabilization parameters are
greatly reduced in all models except EA QUEST3 (which reaches the upper bound on all parameters),
relative to the θb = 0 case. Indeed, both instruments are now heavily geared towards reducing the
volatility of government debt, as indicated by the relatively larger debt-stabilization parameters.
Thus, if a preference for debt stability is assumed, optimal fiscal policy becomes much more focused
on debt-stabilization than on macroeconomic objectives, at least in single-instrument case.
50It may be argued that the potential gains from active fiscal policy are unrealistically high. This owes to thesemi-calibrated nature of our procedure. They cannot be read as estimated potential gains. An empirically moremeaningful comparison would be to compare the loss function of the model estimated with fiscal rules to the lossfunction at the optimum under the estimated parameterization. This is, however, beyond the scope of this paper.
49
Table 17: Model-Specific Rules - Two Instrument Caseθb = 0
Gain wrt Passive Government Spending Labor Tax
Model Fiscal Policy (%) Output Gap (ϕg) Debt (γg) Output Gap (ϕb) Debt (γτ )
EA SW03 77.62 5.00 0.00 -5.00 5.00
EA JPT11 55.45 5.00 0.10 -5.00 0.00
EA QUEST3 25.31 5.00 0.00 5.00 0.22
EA GE10 71.36 5.00 0.00 -5.00 5.00
EA CFOP14poc 53.75 5.00 0.00 -5.00 5.00
EA GK16 27.97 5.00 1.45 -5.00 5.00
θb = 1Gain wrt Passive Government Spending Labor Tax
Model Fiscal Policy (%) Output Gap (ϕg) Debt (γg) Output Gap (ϕb) Debt (γτ )
EA SW03 85.53 1.56 4.19 -5.00 5.00
EA JPT11 71.92 0.67 4.58 -5.00 0.00
EA QUEST3 93.86 5.00 3.16 4.99 5.00
EA GE10 94.41 5.00 5.00 -5.00 5.00
EA CFOP14poc 80.68 0.95 4.61 -5.00 5.00
EA GK16 92.28 3.20 5.00 -5.00 5.00
In Table 17, we present analogous results allowing for the fiscal authority to use both instruments
simultaneously. This table shows that a key factor driving the results of Table 16 is that limiting to
a single instrument the policies available to the fiscal authority forces macro-stabilizing policies to
be financed by debt. If the fiscal authority has two instruments at its disposal, this need not be the
case. Indeed, if the government has access to both fiscal rules and cares about debt volatility, we find
that government spending is optimally employed to stabilize debt dynamics – although it also has a
relevant macroeconomic stabilization component – while the labor income tax takes on a strong role
in both macroeconomic and debt stabilization. As was noted above, our set of Euro Area models
suggests that government spending is relatively more effective in stabilizing fluctuations in debt than
in the output gap. And this is the principal role this instrument takes on in the two-instrument case,
where in almost all models the debt-stabilization parameter on the government spending rule is at
or near its bound for the case where debt dynamics are of concern to the fiscal authority. In contrast
to the single instrument exercises presented above, the labor income tax rule’s macro-stabilization
parameter is now also at or near its bound. Thus, when the fiscal authority is able to implement
50
rules using two instruments and has a preference for stable debt dynamics, it should employ both
instruments such that government spending ensures a sound level of volatility in debt and the labor
income tax responds strongly to output gap and debt fluctuations. Finally, we stress once again the
high level of loss gains (with respect to the passive fiscal policy case) that the fiscal authority can
achieve in the case of θb = 0, where debt dynamics are not a concern.
Table 18: Robustness – Model-Specific Fiscal Policy Rulesθb = 0Models’ Loss Increase (%)
Rule EA SW03 EA JPT11 EA QUEST3 EA GE10 EA CFOP14poc EA GK16
EA SW03 0 2 99 0 0 1
EA JPT11 30 0 117 6 12 7
EA QUEST3 33 21 0 51 19 33
EA GE10 0 2 99 0 0 1
EA CFOP14poc 0 2 99 0 0 1
EA GK16 70 38 115 6 43 0
θb = 1Models’ Loss Increase (%)
Rule EA SW03 EA JPT11 EA QUEST3 EA GE10 EA CFOP14poc EA GK16
EA SW03 0 2 ∞ 28 1 6
EA JPT11 5 0 ∞ 29 1 14
EA QUEST3 168 154 0 235 157 106
EA GE10 20 33 ∞ 0 34 4
EA CFOP14poc 2 0 ∞ 36 0 8
EA GK16 5 11 ∞ 7 11 0
Table 18 shows the level of robustness of the model-specific fiscal rules for the two-instrument
scenario. Specifically, for the two weights of the variance of debt we consider, the row denotes model
from which the optimal rule was derived. These rules are implemented in the models listed in the
columns and the percent increase in their loss function with respect to its optimum is reported in the
tables. While the fiscal rules of most models in our sample are fairly robust, as would be expected
given than that many parameters are at their bound, they all generate explosive dynamics in the
EA QUEST3 model in the case where debt dynamics are a concern to the fiscal authority. Thus, it
makes sense to ask if a robust fiscal rule is available and, if so, how can we characterize it.
51
Tables 19 and 20 address this question by presenting the relevant normalized loss Bayesian two-
instrument fiscal rules and their level of robustness, respectively. The results of Table 19 confirm
what we noted from the model-specific rules. For θb = 0, debt stabilization is not an issue and the
countercyclical components of both rules are at or near their bounds; the EA QUEST3 model appears
to dictate the labor income tax macro-stabilization parameter. In the case of θb = 1, debt stabilization
becomes an explicit policy objective that is optimally tackled by means of the government spending
rule (although this rule also plays a role in macro-stabilization), while the labor income tax rule is
geared towards macroeconomic stabilization. In comparing the Bayesian rules of standard-NK and
FF models, we note that the former imply a stronger response of government spending to output gap
fluctuations, as well as a more modest response from the labor income tax. The latter, in contrast,
prescribe a strong response to debt fluctuations from the labor income tax, while standard-NK models
set this parameter close to zero. The all-models Bayesian rule gives no weight to the debt-stabilizing
role of the labor income tax.
Table 19: Normalized Loss Bayesian Rules - Two Instrument Caseθb = 0
Gov Spending Labor Tax
Rule Output Gap (ϕg) Debt (γg) Output Gap (ϕτ ) Debt (γτ )
All models 5.00 0.00 5.00 5.00
Standard-NK 5.00 0.00 5.00 5.00
Financial Frictions 5.00 0.00 -5.00 5.00
θb = 1Gov Spending Labor Tax
Rule Output Gap (ϕg) Debt (γg) Output Gap (ϕτ ) Debt (γτ )
All models 3.70 4.35 -4.97 0.00
Standard-NK 4.25 5.00 -3.44 0.16
Financial Frictions 2.92 5.00 -5.00 5.00
52
Table 20: Robustness – Bayesian Fiscal Policy Rulesθb = 0
Models’ Loss Increase (%)
Rule EA SW03 EA JPT11 EA QUEST3 EA GE10 EA CFOP14poc EA GK16
All Models 5 6 26 11 2 7
NK 5 6 26 11 2 7
FF 0 2 99 0 0 1
θb = 1Models’ Loss Increase (%)
Rule EA SW03 EA JPT11 EA QUEST3 EA GE10 EA CFOP14poc EA GK16
All Models 35 34 105 18 36 13
NK 49 41 67 41 43 19
FF 3 8 ∞ 9 8 0
Table 20 shows the level of robustness of the two-instrument normalized loss Bayesian rules of the
standard-NK models, the FF models and the complete set of models. We see that the rule optimized
over all models is able to ensure stable dynamics in all models, as in the case of monetary policy.
This is also the case for the in-sample robustness of group-specific Bayesian rules and the out-of-
sample robustness of standard-NK models’ Bayesian rule. In contrast, FF models’ Bayesian rules
produce unstable dynamics in EA QUEST3. In general, the all-models Bayesian rule proves to be
the more robust fiscal policy, averaging a loss increase of 40%; lower than the 43% average increase
of the standard-NK Bayesian rule. Thus, our analysis suggests a robust fiscal rule in the Euro Area
should employ both government spending and the labor tax as instruments, but utilize the labor tax
exclusively towards macroeconomic stabilization objectives, while government spending should have
a strong debt-stabilizing – as well as a more modest countercyclical – component.
At this point it is useful to draw on previous work done in the area of fiscal policy to interpret our
results, given the semi-calibrated nature of our methodology – in contrast to the exercises presented in
Sections 3 and 4 – and the fact that our optimization results are frequently at the bound. Specifically,
we point to the fact that our results echo those of Cogan et al. (2013), which deals with debt-
consolidation strategies in a model with a much richer fiscal specification. Similarly to our results,
but in a different context, they find that it is optimal to employ government spending to reduce
excess debt, while taxes should be employed to support macroeconomic activity. This follows for two
main reasons: (i) lower levels of government spending allow for tax reductions which boost household
53
wealth, and (ii) reducing taxes eliminates distortions and spurs economic activity in a more efficient
way than government spending can. It turns out that this logic largely carries over to the case of fiscal
rules of the class we have defined here. To see this, we present two sets of IRFs for the well-known
EA SW03 model, which can be considered as representative of what occurs on average in our model
set.
Figure 6. IRFs of a Productivity Shock – EA SW03 Macro-Stabilization Case
0 10 20Periods
-0.4
-0.2
0
Output Gap
0 10 20Periods
0
0.5
1
Output
0 10 20Periods
0
0.5
1
Potential Output
0 10 20Periods
-0.6-0.4-0.2
0
Labor
0 10 20Periods
0
0.1
0.2 Consumption
0 10 20Periods
0
0.5
Investment
0 10 20Periods
-0.4
-0.2
0
Policy Rate
0 10 20Periods
-0.1
-0.05
0
0.05 Inflation
0 10 20Periods
0
0.05
0.1 Wages
0 10 20Periods
0
0.5
1Government Spending
0 10 20Periods
00.10.2
Labor Tax
0 10 20Periods
-0.50
0.51
Debt
Zero Line No Fiscal Policy Both Instruments Gov Spending Labor Tax
The first set of graphs, presented in Figure 6, shows the IRFs of a one-standard-deviation pro-
ductivity shock under four cases: (i) fiscal policy is completely passive (dotted line), (ii) the fiscal
54
authority exclusively employs government spending to stabilize the macroeconomy (red line), (iii)
the fiscal authority exclusively employs the labor tax as a macro-stabilizer (blue line), and (iv) the
fiscal authority uses both instruments along the lines specified above (green line).51 As can be seen
from the figure, the positive productivity shock increases both output and potential output (i.e.,
output in the flexible-price economy). The passive fiscal policy case serves as a useful reference
point but, more importantly, we also plot the dynamics of the flexible-price economy because it is
also affected by fiscal policy and it represents the actually optimal response of the economy to the
productivity shock (i.e., dotted line, top-right graph). In all cases, because prices cannot fully adjust
in the sticky-price economy, the output gap turns negative. Deflationary pressures ensue and the
central bank responds by lowering the interest rate. If the fiscal authority only increases government
spending to stabilize the macroeconomy (red line), it is able to dampen the drop in the output gap.
However, this policy causes output to be significantly above its optimal response, consumption and
investment are strongly crowded out and debt increases by a significant degree. If, on the other
hand, the fiscal authority increases the labor income tax to stabilize the macroeconomy following
the shock (blue line), it does not manage to achieve a significant moderation in the output gap drop,
relative to the passive fiscal policy case. The negative wealth effect on households exacerbates the
drop in labor, further depressing output relative to its optimal level, while government debt falls by a
larger amount than in the passive fiscal policy case. In contrast, when the government employs both
instruments to stabilize the macroeconomy in response to the shock (green line) it can moderate the
decrease of the output gap by achieving a level of output which is more in line with the economy’s
optimal response, while keeping the debt level practically unchanged. Increased taxes serve both
to fund additional government spending, which induces households to work more, and to limit the
resulting increase in output above its potential. This support is achieved, as seen above, by closely
linking government spending to variations in debt and the labor income tax to fluctuation in the
output gap.
Figure 7 presents the analogous exercise for debt stabilization. That is, the passive fiscal policy
(dotted line) and two-instrument case (green line) are the same as those presented above, but now the
government spending case (red line) and the labor income tax case (blue line) are geared exclusively
51Specifically, we set the debt-stabilization parameters to 5 in the single-instrument cases and the policy parametersequal to their optimal for the two-instrument case. All fiscal policy parameters are set to zero in the passive fiscalpolicy case.
55
towards debt-stabilization. In this case, we see that only the two-instrument case is able to stabilize
government debt while simultaneously moderating the fall in the output gap. As would be expected
given our modification of the model, in neither the single-instrument government spending or la-
bor income tax cases is there a positive macroeconomic spill-over from pursuing debt-stabilization
policies.
Figure 7. IRFs of a Productivity Shock – EA SW03 Debt-Stabilization Case
0 10 20Periods
-0.4
-0.2
0
Output Gap
0 10 20Periods
0
0.5
Output
0 10 20Periods
0
0.5
Potential Output
0 10 20Periods
-0.6-0.4-0.2
0
Labor
0 10 20Periods
0
0.1
0.2
Consumption
0 10 20Periods
0
0.5
1 Investment
0 10 20Periods
-0.3-0.2-0.1
0
Policy Rate
0 10 20Periods
-0.1
0
0.1 Inflation
0 10 20Periods
0
0.05
0.1 Wages
0 10 20Periods
0
0.5Government Spending
0 10 20Periods
-0.2
0
0.2
Labor Tax
0 10 20Periods
-0.4
-0.2
0
Debt
Zero Line No Fiscal Policy Both Instruments Gov Spending Labor Tax
In conclusion, these examples serve to illustrate the main findings of the robustness exercise: a
risk-averse fiscal authority concerned not only with macroeconomic stability by also worried about
56
the level of debt volatility will favor a set of fiscal rules which employ two instruments in a specialized
manner. Specifically, the government spending rule will be primarily geared towards debt stabiliza-
tion and the labor income tax will be linked to macroeconomic fluctuations. Although a numerically
precise description of this type of fiscal rule would require a prior estimation step where each of the
models employed in the analysis is appended with a fully specified fiscal sector, our results suggest
that there are economically significant potential gains to be had from implementing an active fiscal
policy regime along the lines described here.
6 Conclusion
In this paper we have explored the implications of recent modelling developments in policy-focused
macroeconomic models, which aim to explicitly account for the interaction between financial markets
and the macroeconomy, on the design of robust monetary and fiscal policies for the Euro Area,
where policy robustness is defined as achieving a good performance across a wide range of models.
Specifically, we have drawn on multiple models from the MMB in order to study the impact of
new models with rich financial sector frictions on the form of robust monetary rules – in particular,
relative to earlier generation macroeconomic models. In doing so we estimated three different versions
of the model developed by Carlstrom et al. (2014) for the Euro Area, thus providing an additional
estimation of key structural parameters for the currency union and the first estimation of a policy-
focused macroeconomic model featuring risky-debt contract indexation. Our main estimation result
is that the data do not support the presence of contract indexation, favoring instead the more
commonly used financial contracts of Christensen and Dib (2008) and Bernanke et al. (1999).
With regard to the search for robust monetary policies, we have built on the contributions of
Kuester and Wieland (2010) and Orphanides and Wieland (2013) and employed their Bayesian
framework to identify robust policy rules. Our results indicate that the explicit consideration of
FF in the Euro Area has important policy implications. In particular, we document that for the
models with FF studied in this paper, a risk-averse policymaker who would like to implement policy
rules that are robust to model uncertainty would want to respond less strongly to inflation and
the output gap, and more strongly to growth of the output gap than would otherwise be the case.
The policymaker would also want to place more weight on the past realizations of macroeconomic
57
aggregates than on her expectation of future output and inflation.
Particular to the class of FF models considered in this paper, we investigated to what extent the
central bank can materialize lower loss function realization by adopting LAW policies – defined as
the direct and systematic reaction to variations in financial variables by the central bank through
its main policy rate – and to what extent such policies are robust to model uncertainty. For the
FF models studied in this paper, LAW policies in the Euro Area do not improve on a Taylor-type
policy rule. Indeed, our results suggest that the downside risks from model uncertainty become more
pronounced when trying to implement LAW policies, while the potential gains from such policies
relative to simple rules for the models considered are negligible.
Finally, we considered an active rules-based role for fiscal policy in macroeconomic and debt
stabilization. For the models considered in this paper, the results suggest that a robust fiscal rule
in the Euro Area would want to employ both government spending and the labor income tax as
instruments, but utilize the labor tax mainly towards macroeconomic stabilization objectives, while
government spending should have a strong debt-stabilizing – as well as countercyclical – component.
This follows from the relative effectiveness of each of the instruments we consider – namely, gov-
ernment spending and the labor income tax – in stabilizing the output gap and government debt in
the models we analyze. If the fiscal authority cares about maintaining a stable level of debt, then
government spending in these models is the more effective debt stabilizer as it does not generate
large distortions in households’ consumption-labor decisions, whereas the labor income tax proves
more effective in stabilizing output. By using both instruments simultaneously, the government is
able to take on a constructive role in macroeconomic stabilization without destabilizing debt.
58
References
Adalid, R., G. Coenen, P. McAdam, and S. Siviero (2005). The performance and robustness of
interest-rate rules in models of the euro area. International Journal of Central Banking 1 (1).
Bernanke, B. S. and M. Gertler (2001). Should central banks respond to movements in asset prices?
The American Economic Review 91 (2), 253–257.
Bernanke, B. S., M. Gertler, and S. Gilchrist (1999). The financial accelerator in a quantitative
business cycle framework. Handbook of macroeconomics 1, 1341–1393.
Berti, K., E. Colesnic, C. Desponts, S. Pamies, and E. Sail (2016, April). Fiscal Reaction Functions
for European Union Countries. European Economy - Discussion Papers 2015 - 028, Directorate
General Economic and Financial Affairs (DG ECFIN), European Commission.
Binder, M., P. Lieberknecht, and V. Wieland (2016). Fiscal multipliers, fiscal sustainability and
financial frictions. Technical report, Mimeo, Goethe University, Frankfurt.
Blanchard, O., C. Erceg, and J. Linde (2016). Jump-starting the euro area recovery: would a rise
in core fiscal spending help the periphery? In NBER Macroeconomics Annual 2016, Volume 31.
University of Chicago Press.
Bohn, H. (1998). The behavior of us public debt and deficits. Quarterly journal of economics ,
949–963.
Carlstrom, C. T., T. S. Fuerst, A. Ortiz, and M. Paustian (2014). Estimating contract indexation in
a financial accelerator model. Journal of Economic Dynamics and control 46, 130–149.
Christensen, I. and A. Dib (2008). The financial accelerator in an estimated new keynesian model.
Review of Economic Dynamics 11 (1), 155–178.
Christiano, L., M. Eichenbaum, and S. Rebelo (2011). When is the government spending multiplier
large? Journal of Political Economy 119 (1).
Christiano, L., C. L. Ilut, R. Motto, and M. Rostagno (2010). Monetary policy and stock market
booms. Technical report, National Bureau of Economic Research.
59
Christiano, L., M. Rostagno, and R. Motto (2010, May). Financial factors in economic fluctuations.
Working Paper Series 1192, European Central Bank.
Coenen, G., C. J. Erceg, C. Freedman, D. Furceri, M. Kumhof, R. Lalonde, D. Laxton, J. Linde,
A. Mourougane, D. Muir, S. Mursula, C. De Resende, J. Roberts, W. Roeger, S. Snudden, M. Tra-
bandt, and J. in’t Veld (2012). Effects of fiscal stimulus in structural. American Economic Journal:
Macroeconomics 4 (1), 22–68.
Coenen, G. and V. Wieland (2003). The zero-interest-rate bound and the role of the exchange rate
for monetary policy in japan. Journal of Monetary Economics 50 (5), 1071–1101.
Coenen, G. and V. Wieland (2005). A small estimated euro area model with rational expectations
and nominal rigidities. European Economic Review 49 (5), 1081–1104.
Cogan, J. F., T. Cwik, J. B. Taylor, and V. Wieland (2010). New keynesian versus old keynesian
government spending multipliers. Journal of Economic dynamics and control 34 (3), 281–295.
Cogan, J. F., J. B. Taylor, V. Wieland, and M. H. Wolters (2013). Fiscal consolidation strategy.
Journal of Economic Dynamics and Control 37 (2), 404–421.
Curdia, V. and M. Woodford (2015). Credit frictions and optimal monetary policy. Technical report,
National Bureau of Economic Research.
De Graeve, F. (2008). The external finance premium and the macroeconomy: Us post-wwii evidence.
Journal of Economic Dynamics and Control 32 (11), 3415–3440.
Debortoli, D., J. Kim, J. Linde, and R. Nunes (2014). Designing a simple loss function for the fed:
Does the dual mandate make sense? Discussion Paper No. DP10409, Centre for Economic Policy
Research, London.
Dieppe, A., K. Kuster, and P. McAdam (2005). Optimal monetary policy rules for the euro area: An
analysis using the area wide model*. JCMS: Journal of Common Market Studies 43 (3), 507–537.
Eggertsson, G. B. and P. Krugman (2012). Debt, deleveraging, and the liquidity trap: A fisher-
minsky-koo approach*. The Quarterly Journal of Economics 127 (3), 1469–1513.
60
Fernandez-Villaverde, J. (2010). Fiscal policy in a model with financial frictions. The American
Economic Review 100 (2), 35–40.
Gambacorta, L. and F. M. Signoretti (2014). Should monetary policy lean against the wind?: An
analysis based on a dsge model with banking. Journal of Economic Dynamics and Control 43,
146–174.
Gelain, P. (2010). The external finance premium in the euro area: A dynamic stochastic general
equilibrium analysis. The North American Journal of Economics and Finance 21 (1), 49–71.
Gerali, A., S. Neri, L. Sessa, and F. M. Signoretti (2010). Credit and banking in a dsge model of the
euro area. Journal of Money, Credit and Banking 42 (s1), 107–141.
Gerdesmeier, D., B. Roffia, et al. (2004). Empirical estimates of reaction functions for the euro area.
Swiss Journal of Economics and Statistics (SJES) 140 (I), 37–66.
Gertler, M. and P. Karadi (2011). A model of unconventional monetary policy. Journal of monetary
Economics 58 (1), 17–34.
Gilchrist, S. and J. V. Leahy (2002). Monetary policy and asset prices. Journal of monetary Eco-
nomics 49 (1), 75–97.
Gilchrist, S. and B. Mojon (2014). Credit risk in the euro area. Technical report, National Bureau
of Economic Research.
Gomme, P., B. Ravikumar, and P. Rupert (2011). The return to capital and the business cycle.
Review of Economic Dynamics 14 (2), 262–278.
Herbst, E. P. and F. Schorfheide (2015). Bayesian Estimation of DSGE Models. Princeton University
Press.
Iacoviello, M. (2005). House prices, borrowing constraints, and monetary policy in the business cycle.
The American economic review 95 (3), 739–764.
Iskrev, N. and M. Ratto (2011). Algorithms for identification analysis under the dynare environment:
final version of the software. Joint Research Center European Commission.
61
Justiniano, A., G. E. Primiceri, and A. Tambalotti (2011). Investment shocks and the relative price
of investment. Review of Economic Dynamics 14 (1), 102–121.
Kuester, K. and V. Wieland (2010). Insurance policies for monetary policy in the euro area. Journal
of the European Economic Association 8 (4), 872–912.
Lambertini, L., C. Mendicino, and M. T. Punzi (2013). Leaning against boom–bust cycles in credit
and housing prices. Journal of Economic Dynamics and Control 37 (8), 1500–1522.
Laseen, S., A. Pescatori, and M. J. Turunen (2015). Systemic Risk: A New Trade-off for Monetary
Policy? International Monetary Fund.
Leeper, E. M. and B. Li (2016). Surplus-debt regressions. Technical report, National Bureau of
Economic Research.
Leeper, E. M., M. Plante, and N. Traum (2010). Dynamics of fiscal financing in the united states.
Journal of Econometrics 156 (2), 304–321.
Levin, A. T., V. Wieland, and J. Williams (1999). Robustness of simple monetary policy rules under
model uncertainty. In Monetary policy rules, pp. 263–318. University of Chicago Press.
McKay, A. and R. Reis (2016). The role of automatic stabilizers in the u.s. business cycle. Econo-
metrica 84 (1), 141–194.
Mishkin, F. S. (2011). Monetary policy strategy: lessons from the crisis. Technical report, National
Bureau of Economic Research.
Orphanides, A. and V. Wieland (2013). Complexity and monetary policy. International Journal of
Central Banking .
Queijo, V. (2006). How important are financial frictions in the us and euro area? seminar paper 738.
Institute for International Economic Studies .
Quint, D. and P. Rabanal (2014). Monetary and macroprudential policy in an estimated dsge model
of the euro area. International Journal of Central Banking 10 (2), 169–236.
62
Ratto, M., W. Roeger, and J. in’t Veld (2009). Quest iii: An estimated open-economy dsge model
of the euro area with fiscal and monetary policy. economic Modelling 26 (1), 222–233.
Reicher, C. (2014). A set of estimated fiscal rules for a cross-section of countries: Stabilization and
consolidation through which instruments? Journal of Macroeconomics 42, 184–198.
Schmidt, S. and V. Wieland (2013). Chapter 22 - the new keynesian approach to dynamic general
equilibrium modeling: Models, methods and macroeconomic policy evaluation. In P. B. Dixon
and D. W. Jorgenson (Eds.), Handbook of Computable General Equilibrium Modeling SET, Vols.
1A and 1B, Volume 1 of Handbook of Computable General Equilibrium Modeling, pp. 1439 – 1512.
Elsevier.
Smets, F. (2008). Monetary policy in the euro area: A comment on geraats and neumann.
Smets, F. and R. Wouters (2003). An estimated dynamic stochastic general equilibrium model of
the euro area. Journal of the European economic association 1 (5), 1123–1175.
Smets, F. and R. Wouters (2007). Shocks and frictions in us business cycles: A bayesian dsge
approach. The American Economic Review 97 (3), 586–606.
Stein, J. C. (2013). Overheating in credit markets: Origins, measurement, and policy responses,
speech at the restoring household financial stability after the great recession: Why household
balance sheets matter research symposium sponsored by the federal reserve bank of st. Louis, St.
Louis, Missouri .
Taylor, J. B. (1999). A historical analysis of monetary policy rules. In Monetary policy rules, pp.
319–348. University of Chicago Press.
Townsend, R. M. (1979). Optimal contracts and competitive markets with costly state verification.
Journal of Economic theory 21 (2), 265–293.
Villa, S. (2013). Financial frictions in the euro area: a bayesian assessment. Working Paper Series
1521, European Central Bank.
Villa, S. (2016). Financial frictions in the euro area and the united states: A bayesian assessment.
Macroeconomic Dynamics 20 (5), 1313–1340.
63
Wieland, V., E. Afanasyeva, M. Kuete, and J. Yoo (2016). New methods for macro-financial model
comparison and analysis. In J. B. Taylor and H. Uhlig (Eds.), Handbook of Macroeconomics, Vol.
2A. Elsevier.
Wieland, V., T. Cwik, G. J. Muller, S. Schmidt, and M. Wolters (2012). A new comparative
approach to macroeconomic modeling and policy analysis. Journal of Economic Behavior & Or-
ganization 83 (3), 523–541.
64
A Data Description and Sources
All the data is from the ECB’s Statistical Data Warehouse except for population, which is taken
from Eurostat,52 and the external finance premium, which is from Gilchrist and Mojon (2014). We
follow Justiniano et al. (2011) closely in the construction of the estimation dataset since this is core
model of Carlstrom et al. (2014).53 Thus, the observables are defined as follows:
• Employment: log of hours of all persons in the non-farm business sector divided by population.
• Inflation: quarterly log difference in the consumption deflator.
• The nominal interest rate: the ECB´s main refinancing rate.
• Real GDP: first difference of log of real GDP, where the latter is constructed by diving the
nominal series by population and the deflator for consumption of non-durables and services
(which, in line with the model, is the numeraire).
• Consumption: first difference of log of real consumption, where real consumption is personal
consumption expenditures on non-durables and services (with the same treatment as real GDP).
• Investment: first difference of log of real investment, where real investment is the sum of
personal consumption expenditures on durables and gross private domestic investment (with
same treatment as real GDP).
• Real wage: first difference of log of real wages, where real wages correspond to nominal com-
pensation per hour in the non-farm business sector, divided by the consumption deflator.
• Relative price of investment: first difference of the log of the relative price of investment, where
the relative price of investment corresponds to the ratio of the deflators for consumption and
investment as defined above.
• The external finance premium: see Gilchrist and Mojon (2014).
• Net worth: the Dow Jones EUROSTOXX, deflated by the GDP price deflator.
52As this series is reported in annual terms, we use cubic splines to approximate missing quarterly observations.53In fact, the non-financial data employed by Carlstrom et al. (2014) seems to be the dataset constructed by
Justiniano et al. (2011).
65
B Model Estimation Posterior Marginal Densities
Posterior Marginal Densities: POC Model
0.2 0.4 0.6 0.8 10
10
20
SE_Rs
0.5 1 1.5 2 2.50
5
SE_zs
0.5 1 1.5 2 2.50
10
SE_gs
0.5 1 1.5 2 2.50
5
SE_mius
0 0.2 0.40
10
SE_lambdaps
0.1 0.2 0.3 0.4 0.50
10
SE_lambdaws
0 0.2 0.40
10
SE_bs
0 1 20
5
10
SE_efps
0 2 4 60
2
SE_nws
0 10 20 300
2
SE_upsilons
0 1 20
5
10
SE_mes
0 5 100
2
SE_menws
0 0.2 0.4 0.60
10
20alpha
0 0.5 10
2
4iotap
0 0.2 0.4 0.6 0.80
5
10iotaw
0.2 0.4 0.60
5
gamma100
0.2 0.4 0.6 0.80
5
gammamiu100
0.5 10
5
h
-2 0 20
0.5
Lss
0 0.2 0.4 0.6 0.80
5pss100
0 2 4 60
0.5
niu
0.5 10
5
xip
0.5 10
5
xiw
0 20 400
0.05
0.1
chi
0 10 20 300
0.05
0.1
Sadj
1 1.5 20
2
4
fp
0 0.1 0.20
5
fy
0 0.2 0.4 0.60
5
fdy
0.7 0.8 0.90
10
20
rhoR
0 0.2 0.4 0.6 0.80
5
rhomp
0 0.5 10
5rhoz
0.5 10
50
rhog
0 0.5 10
5rhomiu
0.2 0.4 0.6 0.8 10
5
rholambdap
0 0.5 10
1
2
rholambdaw
0 0.5 10
1
2
rhob
0 0.5 10
1
2
rhoARMAlambdap
0 0.5 10
1
2
rhoARMAlambdaw
0 0.5 10
20
40rhoefp
0 0.5 10
1
2rhonw
0 0.5 10
1
2
rhoupsilon
0 0.5 10
1
2
rhomespr
0 0.5 10
2
rhomenw
0 0.1 0.20
20
cnu
0 2 4 60
1
2
cchi
66
Posterior Marginal Densities: BGG Model
0.2 0.4 0.6 0.8 10
10
20
SE_Rs
0.5 1 1.5 2 2.50
5
SE_zs
0.5 1 1.5 2 2.50
10
SE_gs
0.5 1 1.5 2 2.50
5
SE_mius
0 0.2 0.40
10
SE_lambdaps
0.1 0.2 0.3 0.4 0.50
10
SE_lambdaws
0 0.2 0.40
10
SE_bs
0.5 1 1.5 2 2.50
10
SE_efps
0 1 2 30
2
SE_nws
0 10 20 300
2
SE_upsilons
0 1 20
5
10
SE_mes
2 4 6 8 100
2
SE_menws
0 0.2 0.4 0.60
10
20
alpha
0 0.5 10
2
4
iotap
0 0.2 0.4 0.6 0.80
5
10
iotaw
0.2 0.4 0.6 0.80
5
gamma100
0.2 0.4 0.6 0.80
5
gammamiu100
0.5 10
5
h
-2 0 20
0.5
Lss
0 0.2 0.4 0.6 0.80
5pss100
0 2 40
0.5
niu
0.5 10
5
xip
0.5 10
5
xiw
0 20 40 600
0.05
0.1
chi
0 10 20 300
0.05
0.1
Sadj
1.2 1.6 2 2.40
2
4
fp
0 0.1 0.20
5
fy
0 0.2 0.4 0.60
5
fdy
0.8 10
10
20
rhoR
0 0.2 0.4 0.6 0.80
5
rhomp
0 0.2 0.4 0.6 0.80
5rhoz
0.5 10
50rhog
0.2 0.4 0.6 0.8 10
5rhomiu
0.2 0.4 0.6 0.8 10
5
rholambdap
0 0.5 10
1
2
rholambdaw
0 0.5 10
1
2
rhob
0 0.5 10
1
2
rhoARMAlambdap
0 0.5 10
1
2
rhoARMAlambdaw
0 0.5 10
20
40
rhoefp
0 0.5 10
1
2
rhonw
0 0.5 10
2
rhoupsilon
0 0.5 10
1
2
rhomespr
0 0.5 10
2
4rhomenw
0 0.1 0.20
20
cnu
67
Posterior Marginal Densities: CD Model
0.2 0.4 0.6 0.8 10
10
20
SE_Rs
0.5 1 1.5 2 2.50
5
SE_zs
0.5 1 1.5 2 2.50
10
SE_gs
0.5 1 1.5 2 2.50
5
SE_mius
0 0.2 0.40
10
SE_lambdaps
0.1 0.2 0.3 0.4 0.50
10
SE_lambdaws
0 0.2 0.40
10
SE_bs
0.5 1 1.5 2 2.50
10
SE_efps
0 1 20
2
SE_nws
0 10 20 300
2
SE_upsilons
0.5 1 1.5 2 2.50
5
10
SE_mes
2 4 6 8 100
2
SE_menws
0 0.2 0.4 0.60
10
20
alpha
0 0.5 10
2
4iotap
0 0.2 0.4 0.6 0.80
5
10
iotaw
0 0.2 0.4 0.60
5
gamma100
0.2 0.4 0.6 0.80
5
gammamiu100
0.5 10
5
h
-2 0 20
0.5
Lss
0 0.5 10
5pss100
0 2 4 60
0.5
niu
0.5 10
5
xip
0.5 10
5
xiw
0 20 40 600
0.05
0.1
chi
0 10 20 300
0.1
Sadj
1.2 1.6 20
2
4
fp
0 0.1 0.20
5
fy
0 0.2 0.40
5
fdy
0.8 10
10
20
rhoR
0 0.2 0.4 0.6 0.80
5
rhomp
0 0.5 10
5rhoz
0.5 10
50
rhog
0.2 0.4 0.6 0.8 10
5rhomiu
0.2 0.4 0.6 0.8 10
5
rholambdap
0 0.5 10
1
2
rholambdaw
0 0.5 10
1
2
rhob
0 0.5 10
2
rhoARMAlambdap
0 0.5 10
1
2
rhoARMAlambdaw
0.20.40.60.8 1 1.20
50rhoefp
0 0.5 10
1
2
rhonw
0 0.5 10
2
rhoupsilon
0 0.5 10
1
2
rhomespr
0 0.5 10
2
rhomenw
0 0.1 0.20
20
cnu
68
C Robustness Checks
In this section we provide the flat priors and normalized loss Bayesian rules for two crosschecks: i)
we drop the loss outlier models from each subset of models and ii) we alter the weight associated
with the variance of the changes in the interest rate that is in the central bank’s loss function.
C.1 Loss Outlier Exclusion Check
Tables C.1 and C.2 show the flat priors and normalized loss Bayesian rules for the set and subsets of
models reported in Table 1, excluding models EA CW05fm and EA GE10, which exhibit the highest
minimum value in their loss function as compared to the other models in their group. As can be
seen, the results from Section 3 continue to hold.
Table C.1: Flat Priors Bayesian RulesRule Interest lag Inflation Output gap Output gap growth h
All models 0.929 0.365 0.358 0.344 0
Standard-NK 0.827 2.642 1.378 0.242 4
Financial Frictions 1.140 0.099 0.672 -0.168 0
Table C.2: Normalized Loss Bayesian RulesRule Interest lag Inflation Output gap Output gap growth h
All models 0.982 0.246 0.139 0.519 0
Standard-NK 0.939 1.003 0.841 -0.090 4
Financial Frictions 0.975 0.306 0.789 -0.146 0
C.2 Different Weights for V arm (∆it) in the Central Bank’s Loss Function
Tables C.3 and C.4 report the flat priors and normalized Bayesian rules for different weights in the
loss function of (4) on the variance of changes in the policy rate. Specifically, we verify that the main
results of Section 3 continue to hold for a weight of one half and when dropping this term altogether.
69
Table C.3: Flat Priors Bayesian Rules£m = V arm (π) + V arm (y) + 0.5V arm (∆i)
Rule Interest lag Inflation Output gap Output gap growth h
All models 0.931 0.429 0.230 0.514 0
Standard-NK 0.909 0.886 0.649 0.341 2
Financial Frictions 1.041 0.050 0.016 0.562 0
£m = V arm (π) + V arm (y)Rule Interest lag Inflation Output gap Output gap growth h
All models 1.151 0.999 0.830 1.845 0
Standard-NK 0.841 2.534 1.878 3.000 0
Financial Frictions 1.025 0.233 0.048 2.000 0
Table C.4: Normalized Loss Bayesian Rules£m = V arm (π) + V arm (y) + 0.5V arm (∆i)
Rule Interest lag Inflation Output gap Output gap growth h
All models 0.811 0.462 0.417 0.541 0
Standard-NK 0.819 1.563 1.230 -0.525 4
Financial Frictions 1.027 0.100 0.042 0.944 0
£m = V arm (π) + V arm (y)Rule Interest lag Inflation Output gap Output gap growth h
All models 1.021 2.573 2.989 2.645 0
Standard-NK 1.018 2.869 3.000 3.000 2
Financial Frictions 1.007 0.401 0.151 3.000 0
D Definition of Common Financial Variables
In this section we provide the precise model-specific definition for each of the common financial
variables. In defining the variables, we follow the authors’ notation when available.
D.1 EA CFOP14
1. Real Credit
CRt = QtKt −NWt
where CRt is real credit, Qt is the relative price of capital, Kt is the capital stock and NWt is
entrepreneurial net worth.
70
2. Real Credit Growth
CRgt =
CRt
CRt−1
where CRgt is real credit growth.
3. Real Credit over GDP
CRtoGDPt =CRt
Yt
where CRtoGDPt is real credit to GDP and Yt is GDP.
4. External Finance Premium
EFPt = EtRkt+1 −Rd
t
where EFPt is the external finance premium, EtRkt+1 is the expected aggregate return on
holding capital and Rdt is the deposit rate. The definition of this variable is the authors’.
5. Leverage Ratio
LV Rt =QtKt
NWt
where LV Rt is leverage.
6. Asset Prices
APt = Qt
where APt denotes asset prices.
D.2 EA GNSS10
1. Real Credit
CRt = Bt
where Bt is total real bank loans.
2. Real Credit Growth is as above.
3. Real Credit over GDP is as above.
71
4. External Finance Premium
EFPt =(rbHt − rt
) bItBt
+(rbEt − rt
) bEtBt
where rt is the monetary policy rate, rbHt is the real rate charged on loans to households,
bIt is the amount of loans to households outstanding, rbEt is the real rate charged on loans
to entrepreneurs, and bEt is the amount of loans to entrepreneurs outstanding. That is, the
external finance premium in Gerali et al. (2010) is here taken to be the weighted average (by
outstanding debt) of net borrowers’ interest rate mark up over the policy rate.
5. Leverage Ratio
LV Rt =1
2
qht hIt
qht hIt − bIt
+1
2
qkt kEt
qkt kEt − bEt
where qht is the relative price of housing, hIt is the amount of housing held by households that
are net borrowers, qkt is the relative price of capital, and kEt is the amount of capital held by
entrepreneurs. That is, the leverage ratio is a simple average of the leverage ratio of each net
borrowing sector; alternatively, the weights can be interpreted as population size since both
impatient households and entrepreneurs are of unit mass.
6. Asset Prices
APt = qht
(ht
ht + kt
)+ qkt
(kt
ht + kt
)where ht is the fixed stock of housing and kt is the capital stock. That is, the asset prices index
is constructed as a weighted average of net borrowers’ asset holdings.
D.3 EA QR14
1. Real Credit
CRt = SBt + SB∗
t
where SBt is total outstanding loans of the home country and SB∗
t is total outstanding loans of
the foreign country; recall that in Quint and Rabanal (2014) for expositional purposes there
is a home and a foreign country, but in estimation and dynamic and policy analysis the two
countries are treated as the core and periphery of a currency union.
72
2. Real Credit Growth is as above.
3. Real Credit over GDP is as above.
4. External Finance Premium
EFPt = n(RLt −Rt
)+ (1− n)
(RL
∗
t −Rt
)where n is the size of the home country, RL
t is the real rate charged on loans in the home
country, (1− n) is the size of the foreign country, RL∗
t is the real rate charged on loans in the
foreign country, and Rt is the monetary policy rate common to both countries.
5. Leverage Ratio
LV Rt = n
(PDt D
Bt
PDt D
Bt − SBt
)+ (1− n)
(PD∗t DB∗
t
PD∗t DB∗
t − SB∗
t
)
where PDt is the relative price of housing in the home country, DB
t is the amount of housing
held by the borrowers in the home country and PD∗t and DB∗
t are analogously defined for the
foreign country.
6. Asset Prices
APt = nPDt + (1− n)PD∗
t
D.4 EA GE10
1. Real Credit
CRt = qtkt+1 − nwt
where qt is the relative price of capital, kt+1 is the capital stock and nwt is entrepreneurial net
worth.
2. Real Credit Growth is as above.
3. Real Credit over GDP is as above.
73
4. External Finance Premium
EFPt = Etrkt+1 − rt
where Etrkt+1 is the expected aggregate return on capital and rt is the real short term interest
rate.
5. Leverage Ratio
LV Rt =qtkt+1
nwt
6. Asset Prices
APt = qt
74
E Estimation of Justiniano et al. (2011) for the Euro Area
The estimation’s metaparameters and calibrated parameters are set as described in section 2.1.1.
The observables employed in the estimation are the first eight series reported in appendix A, that
is, no financial variables are employed in the estimation. Following Justiniano et al. (2011), the
monetary policy shock is modeled as a white noise process, rather than an AR(1)process. Tables
E.1 and E.2 report the estimated parameters and the Figure bellow presents the prior and posterior
distributions.
Table E.1: JPT Model Estimation – Estimated ParametersParam Description Prior Posterior
density mean s.d. mean 5% 95%
α Cap share N 0.30 0.10 0.17 0.13 0.20
ιp Price index B 0.50 0.15 0.30 0.11 0.47
ιw Wage index B 0.50 0.15 0.09 0.03 0.15
γz SS tech N 0.50 0.06 0.30 0.22 0.39
growth
γν SS IST growth N 0.50 0.06 0.49 0.39 0.59
h Cons habit B 0.70 0.10 0.65 0.52 0.78
log Lss SS hours N 0.00 0.50 0.33 -0.45 1.11
100(π−1) SS Inflation N 0.45 0.10 0.41 0.29 0.53
ψ Inv Frisch G 2.00 0.75 2.55 1.30 3.73
elasticity
ξp Calvo prices B 0.75 0.10 0.66 0.54 0.79
ξw Calvo wages B 0.75 0.10 0.81 0.72 0.90
ϑ Elas cap G 6.00 5.00 10.15 2.20 18.08
util costs
S Inv adj N 10.00 5.00 7.13 2.59 11.72
costs
φπ Taylor infl N 1.75 0.10 1.67 1.50 1.84
φx Taylor gap N 0.125 0.05 0.00 0.00 0.00
φdx Taylor gap N 0.25 0.10 0.17 0.13 0.20
growth
ρR Taylor B 0.80 0.05 0.91 0.89 0.93
smoothing
75
Table E.2: Model Estimation – Shock ProcessesParam Description Prior Posterior
density mean s.d. mean 5% 95%
ρz Tech growth B 0.60 0.20 0.38 0.22 0.54
ρg Gov spend B 0.60 0.20 0.99 0.98 1.00
ρν IST growth B 0.60 0.20 0.70 0.57 0.83
ρp Price mark-up B 0.60 0.20 0.83 0.69 0.98
ρw Wage mark-up B 0.60 0.20 0.62 0.37 0.86
ρb Intertem pref B 0.60 0.20 0.70 0.58 0.83
θp Price mark-up MA B 0.50 0.20 0.30 0.06 0.52
θw Wage mark-up MA B 0.50 0.20 0.53 0.27 0.80
ρµ Marg effic B 0.60 0.20 0.69 0.55 0.83
of inv
σmp Mon pol I 0.2 1.0 0.08 0.07 0.10
σz Tech growth I 0.5 1.0 0.77 0.65 0.89
σg Gov spend I 0.5 1.0 0.28 0.24 0.32
σν IST growth I 0.5 1.0 0.65 0.56 0.74
σp Price mark-up I 0.1 1.0 0.20 0.15 0.26
σw Wage mark-up I 0.1 1.0 0.20 0.15 0.25
σb Intertem pref I 0.1 1.0 0.04 0.02 0.05
σµ Marg eff I 0.5 1.0 4.24 1.55 6.92
of inv
76
Posterior Marginal Densities: JPT Model
0.2 0.4 0.6 0.8 10
50SE_Rs
0.5 1 1.5 2 2.50
5
SE_zs
0.5 1 1.5 2 2.50
10
SE_gs
0.5 1 1.5 2 2.50
5
SE_mius
0 0.2 0.4 0.60
10
SE_lambdaps
0 0.2 0.40
10
SE_lambdaws
0 0.2 0.40
50SE_bs
0 10 200
2
SE_upsilons
0 0.2 0.4 0.60
10
alpha
0 0.5 10
2
iotap
0 0.2 0.4 0.6 0.80
5
10
iotaw
0 0.2 0.4 0.60
5
gamma100
0.2 0.4 0.6 0.80
5
gammamiu100
0.5 10
5
h
-2 0 20
0.5
Lss
0 0.2 0.4 0.6 0.80
5
pss100
-2 0 2 4 6 80
0.5
niu
0.2 0.4 0.6 0.8 10
5
xip
0.5 10
5
xiw
0 20 40 600
0.05
0.1
chi
0 10 20 300
0.1
Sadj
1 1.5 20
2
4
fp
0 0.1 0.20
10
×104 fy
0 0.2 0.40
10
fdy
0.8 10
20
rhoR
0 0.5 10
2
4
rhoz
0.5 10
50
rhog
0 0.5 10
5
rhomiu
0 0.5 10
5rholambdap
0 0.5 10
1
2
rholambdaw
0 0.5 10
5
rhob
0 0.5 10
1
2
rhoARMAlambdap
0 0.5 10
1
2
rhoARMAlambdaw
0.20.40.60.8 10
5rhoupsilon
77
F Fiscal Rules Additional Optimizations
In this section we present tables comparable to Tables 16-20 for the case of θb = 0.5.
Table F.1: Model-Specific Rules - Single Instrument Case
θb=0.5
Gain wrt Passive Government Spending Gain wrt Passive Labor Tax
Model Fiscal Policy (%) Output Gap (ϕg ) Debt (γg ) Fiscal Policy (%) Output Gap (ϕb ) Debt (γτ )
EA SW03 66.43 1.00 3.62 60.67 -1.71 5.00
EA JPT11 53.26 0.55 3.24 44.71 -1.90 5.00
EA QUEST3 89.64 5.00 5.00 85.45 5.00 5.00
EA GE10 80.89 1.64 5.00 64.83 0.83 5.00
EA CFOP14poc 64.68 0.48 4.15 59.43 -1.64 5.00
EA GK16 83.85 1.74 5.00 78.98 0.57 5.00
Table F.2: Model-Specific Rules - Two Instrument Caseθb = 0.5
Gain wrt Passive Government Spending Labor Tax
Model Fiscal Policy (%) Output Gap (ϕg) Debt (γg) Output Gap (ϕb) Debt (γτ )
EA SW03 77.23 2.51 3.92 -5.00 5.00
EA JPT11 58.65 1.78 5.00 -5.00 5.00
EA QUEST3 93.51 5.00 3.12 4.94 5.00
EA GE10 90.91 5.00 5.00 -5.00 5.00
EA CFOP14poc 68.69 1.57 4.79 -5.00 5.00
EA GK16 86.61 4.27 5.00 -5.00 5.00
Table F.3: Robustness – Model-Specific Fiscal Policy Rulesθb = 0.5Models’ Loss Increase (%)
Rule EA SW03 EA JPT11 EA QUEST3 EA GE10 EA CFOP14poc EA GK16
EA SW03 0 2 ∞ 20 2 4
EA JPT11 2 0 ∞ 25 0 4
EA QUEST3 93 77 0 166 79 61
EA GE10 4 11 ∞ 0 12 0
EA CFOP14poc 3 0 ∞ 29 0 6
EA GK16 2 7 ∞ 4 8 0
78
Table F.4: Normalized Loss Bayesian Rules - Two Instrument Caseθb = 0.5
Gov Spending Labor Tax
Rule Output Gap (ϕg) Debt (γg) Output Gap (ϕτ ) Debt (γτ )
All models 5.00 5.00 -5.00 0.26
Standard-NK 5.00 4.95 -3.21 0.85
Financial Frictions 4.30 5.00 -5.00 5.00
Table F.5: Robustness – Bayesian Fiscal Policy Rulesθb = 0.5
Models’ Loss Increase (%)
Rule EA SW03 EA JPT11 EA QUEST3 EA GE10 EA CFOP14poc EA GK16
All Models 26 21 65 16 24 7
NK 36 26 44 38 29 14
FF 2 7 ∞ 4 8 0
79