D11.4 – Robust Monetary and Fiscal Policies under Model ... · Robust Monetary and Fiscal Policies under Model Uncertainty Elena Afanasyevay Michael Binderz Jorge Quintanax Volker

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]

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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

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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/

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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.

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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.

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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.

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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

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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.

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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).

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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).

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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.

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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.

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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])


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])


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]


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


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])


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 Models’ Losses (% increase relative to minimum loss [IIP])


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]


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


EA CFOP14cd with LAW 0.7 0.8042 0.2415 0.0798 0.1630 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



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


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 (%)


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


All models 3.70 4.35 -4.97 0.00

Standard-NK 4.25 5.00 -3.44 0.16


52

Table 20: Robustness – Bayesian Fiscal Policy Rulesθb = 0

Models’ Loss Increase (%)


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 (%)


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

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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


£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


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


£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


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


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




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.



73


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



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


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 (%)


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


All models 5.00 5.00 -5.00 0.26

Standard-NK 5.00 4.95 -3.21 0.85


Table F.5: Robustness – Bayesian Fiscal Policy Rulesθb = 0.5

Models’ Loss Increase (%)


All Models 26 21 65 16 24 7

NK 36 26 44 38 29 14

FF 2 7 ∞ 4 8 0

79

Documents

D11.4 – Robust Monetary and Fiscal Policies under Model ... · Robust Monetary and Fiscal Policies under Model Uncertainty Elena Afanasyevay Michael Binderz Jorge Quintanax Volker