Working Paper Series
Günter Coenen, Peter Karadi,
Sebastian Schmidt, Anders Warne

The New Area-Wide Model II:
an extended version of
the ECB’s micro-founded model
for forecasting and policy analysis
with a financial sector
Revised December 2019

No 2200 / November 2018

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

Abstract
This paper provides a detailed description of an extended version of the ECB’s New
Area-Wide Model (NAWM) of the euro area (cf. Christoffel, Coenen, and Warne 2008).
The extended model—called NAWM II—incorporates a rich financial sector with thethreefold aim of (i) accounting for a genuine role of financial frictions in the propagationof economic shocks and policies and for the presence of shocks originating in the financial
sector itself, (ii) capturing the prominent role of bank lending rates and the gradualinterest-rate pass-through in the transmission of monetary policy in the euro area, and(iii) providing a structural framework useable for assessing the macroeconomic impact of
the ECB’s large-scale asset purchases conducted in recent years. In addition, NAWM II
includes a number of other extensions of the original model reflecting its practical uses in
the policy process over the past ten years.
JEL Classification System: C11, C52, E30, E37, E58
Keywords: DSGE modelling, Bayesian inference, financial frictions, forecasting, policy
analysis, euro area

ECB Working Paper Series No 2200 / November 20181

Non-technical summary
In recent years, the ECB’s standard monetary policy operations have been complemented
by several non-standard measures (NSMs) which have responded to the challenges posed by
the different phases of the financial crisis that had begun in 2007. Asset price reactions
suggest that these NSMs had expansionary effects but the quantitative impact on othermacroeconomic variables remains uncertain. Hence there is a compelling need to aid theanalysis of the quantitative effects of NSMs by developing coherent structural macroeconomic modelling frameworks. Yet standard DSGE models are silent on the pertinenttransmission channels of NSMs.
Against this background, this paper provides a detailed description of an extended version of the ECB’s New Area-Wide Model (NAWM). In its original version (cf. Christoffel,
Coenen, and Warne 2008), the NAWM features only stylised financial frictions in the formof exogenous risk premium shocks but no endogenous financial propagation mechanisms. In
contrast, the extended version of the NAWM—called NAWM II—includes a rich financial
sector which is centered around two distinct types of financial intermediaries that are exposed to sector-specific shocks: (i) funding-constrained “wholesale banks” à la Gertler andKaradi (2011) which engage in maturity transformation and originate long-term loans, and(ii) “retail banks” à la Gerali, Neri, Sessa, and Signoretti (2010) which distribute these loans
to the non-financial private sector and adjust the interest rates on loans only sluggishly. The
long-term loans are required by the non-financial private sector to finance capital investments as in Carlstrom, Fuerst, and Paustian (2017). Furthermore, building on Gertler andKaradi (2013), NAWM II includes a set of no-arbitrage and optimality conditions whichgovern the holdings of domestic and foreign long-term government bonds by the financial
and the non-financial private sector, respectively. These conditions give rise to an explicit
exchange-rate channel of private and public-sector asset purchases.
The incorporation of these financial extensions into the original model reflects the threefold aim pursued in the development of NAWM II, namely: (i) to account for a genuinerole of financial frictions in the propagation of economic shocks and policies and for thepresence of shocks originating in the financial sector itself, (ii) to capture the prominentrole of bank lending rates and the gradual interest-rate pass-through in the transmission ofmonetary policy in the euro area, and (iii) to provide a structural framework useable forassessing the macroeconomic impact of the ECB’s large-scale asset purchases which havebeen conducted in recent years, along with other NSMs.

ECB Working Paper Series No 2200 / November 20182

In addition, NAWM II features a number of other extensions of the original model
reflecting its practical uses in the policy process at the ECB over the past ten years, including an endogenous mechanism concerning private-sector agents’ perceptions of the central
bank’s inflation objective which permits to capture possible fluctuations in longer-term
private-sector inflation expectations.

ECB Working Paper Series No 2200 / November 20183

1

Introduction

In recent years, the ECB’s standard monetary policy operations have been complemented byseveral non-standard measures (NSMs) which have responded to the challenges posed by thedifferent phases of the financial crisis that had begun in 2007. Asset price reactions suggestthat these NSMs had expansionary effects (see ECB 2017 and the references therein) but
the quantitative impact on other macroeconomic variables remains uncertain. Hence there
is a compelling need to aid the analysis of the quantitative effects of NSMs by developing
coherent structural macroeconomic modelling frameworks. Yet standard DSGE models are
silent on the pertinent transmission channels of NSMs.
A new class of DSGE models has extended the standard framework with financial market imperfections, regularly referred to as financial frictions. In an environment with financial frictions, the balance sheet conditions of borrowers and/or lenders influence theconditions through which credit is granted, and credit conditions affect macroeconomic
outcomes. Furthermore, in a two-way interaction, the macroeconomic outlook feeds backto the balance sheet conditions through its impact on asset prices. Consequently, theintroduction of financial frictions has modified the transmission of standard economic
shocks and policies (Kiyotaki and Moore 1997; Bernanke, Gertler, and Gilchrist 1999;
Iacoviello 2005), enabled the analysis to account for fluctuations of a financial nature(Jermann and Quadrini 2012; Christiano, Motto, and Rostagno 2014), and could explain theeffectiveness of NSMs through distinct mechanisms. NSMs, like the large-scale asset purchase programmes conducted by major central banks, were argued to improve economy-wide
credit conditions by circumventing and relieving the stressed financial intermediary sector(Cúrdia and Woodford 2011; Gertler and Karadi 2011), injecting liquidity to the financial
system (Del Negro, Eggertsson, Ferrero, and Kiyotaki 2017), or creating asset scarcity inrelevant market segments (Chen, Cúrdia, and Ferrero 2012).1 Calibration and estimationof the relevance of financial frictions with pre-NSM data allowed using these frameworks toassess the likely macroeconomic impact of NSM policies.
Against this background, this paper provides a detailed description of an extended
version of the ECB’s New Area-Wide Model (NAWM). In its original version (cf. Christoffel,
Coenen, and Warne 2008), the NAWM features only stylised financial frictions in the formof exogenous risk premium shocks but no endogenous financial propagation mechanisms. In
contrast, the extended version of the NAWM—hereafter called NAWM II—includes a rich
1

Additional research (Bhattarai, Eggertsson, and Gafarov 2015) has argued that asset purchase policies
exerted their influence through signalling the central bank’s commitment to maintain low interest rates in
the future.

ECB Working Paper Series No 2200 / November 2018

4

financial sector which is centered around two distinct types of financial intermediaries thatare exposed to sector-specific shocks: (i) funding-constrained “wholesale banks” à la Gertler
and Karadi (2011) which engage in maturity transformation and originate long-term loans,and (ii) “retail banks” à la Gerali, Neri, Sessa, and Signoretti (2010) which distribute theseloans to the non-financial private sector and adjust the interest rates on loans only sluggishly.
The long-term loans are required by the non-financial private sector to finance capital
investments as in Carlstrom, Fuerst, and Paustian (2017). Furthermore, NAWM II includes
a set of no-arbitrage and optimality conditions which govern the holdings of domestic andforeign long-term government bonds by the financial and the non-financial private sector,
respectively, building on Gertler and Karadi (2013).
The incorporation of these financial extensions into the original model reflects the threefold aim pursued in the development of NAWM II, namely: (i) to account for a genuinerole of financial frictions in the propagation of economic shocks and policies and for thepresence of shocks originating in the financial sector itself, (ii) to capture the prominentrole of bank lending rates and the gradual interest-rate pass-through in the transmission ofmonetary policy in the euro area, and (iii) to provide a structural framework useable forassessing the macroeconomic impact of the ECB’s large-scale asset purchases which havebeen conducted in recent years, along with other NSMs. In addition, NAWM II features anumber of other extensions of the original model reflecting its practical uses for forecastingand policy analysis since its integration into the ECB policy process about ten years ago,
including an endogenous mechanism concerning private-sector agents’ perceptions of thecentral bank’s inflation objective which permits to capture possible fluctuations in longerterm private-sector inflation expectations.
In estimating NAWM II, we follow the standard Bayesian approach outlined in An
and Schorfheide (2007), which was likewise adopted by Christoffel, Coenen, and Warne(2008)—henceforth referred to as CCW—for estimating the original version of the NAWM.
In doing so, we retain the 18 macro variables that were used as observed variables for
estimating the original model, albeit with two important changes: all real variables havebeen transformed into per-capita units, and the estimation sample has been extended until
2014Q4. In addition, six variables have been added to the original set of observables inorder to provide useful measurements for identifying the model’s financial-sector parametersand shocks, to inform the estimation of the perceived inflation objective as well as trend
productivity growth, and, last but not least, to establish a link with traditional measuresof the euro area output gap. To allow for prior distributions with dependencies among
the parameters and, at the same time, to avoid outcomes which assign too much mass to

ECB Working Paper Series No 2200 / November 20185

unrealistically large population standard deviations for the observed variables, we use a socalled system prior, originally proposed by Del Negro and Schorfheide (2008) and further
developed by Andrle and Beneš (2013). Apart from guiding the prior distributions of the
population standard deviations of a subset of observables, our system prior also exerts a
direct influence on the slope coefficient of the domestic price Phillips curve, which is a key
reduced-form parameter of the model.
The properties of NAWM II are inspected along multiple dimensions, including by meansof impulse-response analysis, by conducting historical as well as forecast-error-variance decompositions, and by providing an evaluation of its relative forecasting performance. While
the presence of a financial sector in NAWM II enhances the transmission mechanism underlying the propagation of its structural shocks when compared to the original NAWM, bothmodels feature broadly similar impulse responses to important common shocks, such as astandard monetary policy shock. The newly introduced financial shocks, in turn, provide amore comprehensive picture of how shocks originating in the financial sector are transmitted
to the macro economy through the reaction of various asset prices. These shocks are foundto play a non-trivial role in the evolution of economic fluctuations in the run-up to, during
and in the aftermath of the financial crisis of 2008/09.
NAWM II also expands the range of potential applications for model-based policy analysis, as illustrated by means of two examples. The first application uses the model toconduct counterfactual simulations of the ECB’s large-scale asset purchases, one of the main
objectives for the development of NAWM II. The second application explores the potential
consequences of a de-anchoring of longer-term inflation expectations. With regard to theeffects of asset purchases, we find that the model gives rise to bond-yield reactions thatare contained, but consistent with the empirical findings of several event studies. Also, themacroeconomic effects, as reflected in the responses of real GDP growth and inflation, arebroadly in line with, albeit slightly smaller than, other model-based assessments. A key
insight from the counterfactual simulations is that the novel international dimension of
the financial frictions in NAWM II, which gives rise to an exchange-rate channel of asset
purchases, meaningfully influences the impact of this non-standard instrument.
The remainder of the paper is organised as follows. Section 2 outlines the specificationof NAWM II with a focus on the financial-sector extension, and Section 3 reports on theestimation of the model using the Bayesian approach. Section 4 inspects the model properties, while Section 5 presents illustrative applications. Section 6 concludes and discusses
directions for future research. An appendix provides details on the log-linear version of themodel, including the computation of its steady state.

ECB Working Paper Series No 2200 / November 20186

2

The model

In this section we outline the specification of NAWM II. As the model extends the original
version of the NAWM with a rich financial intermediary sector but otherwise retains its
basic structure, we just provide a non-technical sketch of the original model and present
subsequently the new elements, as well as the new equations, that are most relevant forunderstanding the enhanced role of the financial sector in the extended model. In addition,
we briefly describe some other extensions of the original NAWM which reflect its practicaluses for forecasting and policy analysis over the past years and which have been incorporated
into NAWM II as well.2

2.1

The original model: A bird’s eye view

The original NAWM is an open-economy DSGE model of the euro area designed for use inthe (Broad) Macroeconomic Projection Exercises regularly undertaken by ECB/Eurosystemstaff and for analysis of topical policy issues; see CCW for a detailed description of themodel’s structure. Its development has been guided by the principal consideration of covering a comprehensive set of core projection variables, including a small number of foreign
variables, which, in the form of exogenous assumptions, play an important role in the
preparation of the staff projections.3
The NAWM features four types of economic agents: households, firms, a fiscal authority and the central bank. Households make optimal choices regarding their purchases ofconsumption and investment goods, the latter determining the economy-wide capital stock.
They supply differentiated labour services in monopolistically competitive markets, they
set wages as a mark-up over the marginal rate of substitution between consumption andleisure, and they trade in domestic and foreign (short-term) bonds.
As regards firms, the NAWM distinguishes between domestic producers of tradable
intermediate goods and domestic producers of three types of non-tradable final goods: a
private consumption good, a private investment good, and a public consumption good. Theintermediate-good firms use labour and capital services as inputs to produce differentiatedgoods, which are sold in monopolistically competitive markets domestically and abroad.
2

Another major extension, which is not considered further in this paper, concerns the development ofa rich specification of the NAWM’s fiscal sector. This extension was triggered by the need to analyse thelarge-scale response of fiscal policy to the financial crisis in the euro area. For details, see Coenen, Straub,and Trabandt (2012, 2013).
3
For an overview of the ECB/Eurosystem staff macroeconomic projection exercises and a description of
the techniques, models and tools used therein, see ECB (2016).

ECB Working Paper Series No 2200 / November 20187

In doing so, they set different prices for domestic and foreign markets as a mark-up overtheir marginal costs. The final-good firms combine domestic and foreign intermediate goods
in different proportions, acting as price takers in fully competitive markets. The foreignintermediate goods are imported from producers abroad, who set their prices in euro inmonopolistically competitive markets, allowing for a gradual exchange-rate pass-through.
A foreign retail firm in turn combines the exported domestic intermediate goods, withaggregate export demand depending on total foreign demand.
Both households and firms face a number of nominal and real frictions, which have been
identified as important in generating empirically plausible dynamics. Real frictions are
introduced via external habit formation in consumption, through generalised adjustment
costs in investment, imports and exports, and through fixed costs in intermediate-good production. Nominal frictions arise from staggered price and wage-setting à la Calvo (1983),
in combination with (partial) dynamic indexation of price and wage contracts to past inflation. In addition, there already exist some stylised financial frictions which however enter
the model only in the form of exogenous risk premia.
The fiscal authority purchases the public consumption good, issues domestic bonds, andlevies different types of distortionary taxes, albeit at constant rates. Nevertheless, Ricardianequivalence holds because of the simplifying assumption that the fiscal authority’s budget
is balanced each period by means of lump-sum taxes. The central bank sets the shortterm nominal interest rate according to a Taylor (1993)-type interest-rate rule, stabilising
inflation in line with the ECB’s definition of price stability.
The NAWM is closed by a rest-of-the-world block, which is represented by a structuralvector-autoregressive (SVAR) model determining five foreign variables: foreign demand,
foreign prices, the foreign interest rate, foreign competitors’ export prices and the priceof oil. The SVAR model does not feature spill-overs from the euro area, in line with thetreatment of the foreign variables as exogenous assumptions in the projections.

2.2

The extended model with financial intermediaries

The financial-sector extension of the NAWM modifies the households’ decision problem,
introduces three new types of agents and five new (nominal) assets. The new assets aredeposits, long-term retail and wholesale loans, and domestic and foreign long-term government bonds. The households face a financing constraint for investments in physical capital,
which gives rise to a demand for long-term loans, and they can invest in domestic longterm government bonds subject to portfolio adjustment frictions. The investment loans are

ECB Working Paper Series No 2200 / November 20188

supplied by two out of the three new types of agents, which act as financial intermediaries.
First, wholesale banks use the deposits raised from the households and their net worth toissue wholesale loans and to purchase domestic and foreign long-term bonds. Second, retailbanks purchase the wholesale loans, transform them into retail loans and offer these retailloans to the households. Because of the financing constraint on the part of the households,
the production of new physical capital is now separated from the households’ decision problem and relegated to the third of the three new types of agents, namely capital producers. In
the following, we describe the modified decision problem of the households and the decision
problems of the three new agents one by one. They give rise to a set of modified and newmodel equations which we state below.
In terms of notation, the extended model with financial intermediaries directly builds
on the original model. That is, details on the variables and parameters that are common
to both the extended and the original model can be found in CCW to the extent that they
are not separately provided in this paper.
2.2.1

Households

We first describe the new assets households can invest in, then we set up the households’
modified decision problem and detail their choice of allocations.
AssetsHouseholds can acquire long-term government bonds and obtain retail investment loans.
• Long-term nominal government bonds, BL,t+1 , are modeled as perpetuities withgeometrically decaying coupons as in Woodford (2001).

In particular, the asset

pays 1, ̺L , ̺2L , . . . units of the numéraire in consecutive periods, where ̺L ∈ ( 0, 1 ) is
the rate of decay. We denote their discount price as QL,t . Its (ex post) nominal rateof return can be expressed as
RL,t+1 =

1 + ̺L QL,t+1
.
QL,t

(1)

The assumption of geometric decay facilitates the aggregation of bonds issued indifferent periods: given the time pattern of repayment, loans issued in period t−p havethe same value as ̺pL assets issued in period t. Relatedly, the amount of outstanding
bonds decays with the rate ̺L , and the new issuance equals CFL,t = BL,t+1 − ̺L BL,t .
• We introduce long-term nominal retail investment loans in an analogous way. The

ECB Working Paper Series No 2200 / November 20189

loans, BI,r,t+1 , are raised from a continuum of retail banks r ∈ [ 0, 1 ]. An investment
loan generates an upfront payoff to the household in the amount QI,r,t for each unit of
the loan and requires a geometrically decaying coupon repayment from the householdwith a rate of decay ̺I ∈ ( 0, 1 ). Consequently, these assets represent liabilities of thehouseholds, whereas long-term government bonds are assets. The aggregate amountof new loans issued in period t equals CFI,t = BI,t+1 − ̺I BI,t .
In addition, households hold short-term (one-period) government bonds, Bt+1 , which arepurchased with a discount in period t and repayed at par in period t + 1, as well as interestbearing nominal deposits Dt+1 with the wholesale banks. Short-term government bonds
and deposits are both nominally riskless, and they are perfect substitutes. In equilibriumRPthey earn the same interest, which we denote as RD,t = ǫRPt Rt . As in the original model, ǫt

represents a serially correlated risk premium shock which drives a wedge between the returnon the household’s deposits with the wholesale banks and, in equal measure, between the
short-term government bond yield and the short-term nominal interest rate Rt controlled
by the central bank. In economic terms, this shock can also be interpreted as a liquidity
premium reflecting the distinct liquidity services provided by central bank assets versus
government bonds and wholesale bank deposits.
Decision problem
An individual household h ∈ [ 0, 1 ] maximises its expected discounted lifetime utility
Et

" ∞
X
k=0

βk



1
(Nh,t+k )1+ζln (Ch,t+k − κ Ct+k−1 ) −
1+ζ

#

(2)

subject to three constraints. The first is the period-by-period budget constraint, which ismodified relative to that in the original NAWM:−1(1 + τtC ) PC,t Ch,t + PC,t p̃I,t Ih,t + RD,t
Bh,t+1 + Dh,t+1+ BI,h,t + QL,t (BL,h,t+1 − ̺L BL,h,t + ΓL (BL,h,t+1 )) + Υh,t + Ξt
= (1 − τtN − τtWh ) Wh,t Nh,t + (1 − τtK ) (RK,t uh,t − Γu (uh,t ) PC,t p̃I,t ) Kh,t
+ τtK δ PC,t p̃I,t Kh,t + (1 − τtD ) Dh,t − Tt + Bh,t + RD,t−1 Dh,t
+ QI,t (BI,h,t+1 − ̺I BI,h,t) + BL,h,t.

(3)

We describe the differences of this constraint relative to the original model. First, house-

ECB Working Paper Series No 2200 / November 201810

hold h purchases investment goods in quantity Ih,t at a relative price p̃I,t from the capital
producers. Second, it places deposits in the amount of Dh,t+1 to the wholesale banks andreceives a (gross) return RD,t−1 on previous-period deposits. Third, it purchases new longterm domestic government bonds in quantity BL,h,t+1 − ̺I BL,h,t at the market price QL,tand receives a coupon payment equal to unity on each outstanding unit of government
bonds BL,h,t. As in Gertler and Karadi (2013), we assume that the household faces a costwhen adjusting its portfolio holdings of these bonds. The cost function takes the form
ΓL (BL,h,t+1 ) = 1/2 · γLh (BL,h,t+1 − B L,h )2 /B L,h(4)

so that the household can hold a fixed quantity B L,h of bonds costlessly, but needs to pay
a quadratic cost to raise its holdings above this value. The parameter γLh determines thesensitivity of the cost to the size of the adjustment.
And fourth, the household raises a basket of differentiated investment loans supplied by
the continuum of retail banks r, which operate in monopolistically competitive markets asin Gerali et al. (2010).4 The basket of new loans, CFI,h,t , is a CES aggregate of individual
retail loans:
CFI,h,t = BI,h,t+1 − ̺I BI,h,t =

Z 1
0

1
ϕI
t

CFI,h,r,t dr

!ϕIt

,

(5)

where the possibly time-varying parameter ϕIt < 1 is inversely related to the elasticity of
substitution between the differentiated loans.5
Cost minimisation by households implies a demand function for individual retail bankloans:
CFI,h,r,t =

QI,r,tQI,t ϕIt I
1−ϕt

CFI,h,t ,(6)where QI,r,t is the price of a new loan from retail bank r, while the aggregate loan-priceindex is given by
QI,t =

Z 1
0

1
1−ϕI
t

QI,r,t dr!1−ϕIt.

(7)

As can be seen from the budget constraint (3), household h raises an amount of
R1
QI,t CFI,h,t = 0 QI,r,t CFI,h,r,t dr of investment loans in period t and repays a coupon
4
Our approach extends the sticky-loan-rate assumption of Gerali et al. (2010), who consider one-periodloans, to long-term loans.
5
As detailed in Section 2.2.4, the parameter ϕIt determines the mark-down on loan prices that monopolistically competitive retail banks charge in the process of intermediating wholesale loans to the households.

ECB Working Paper Series No 2200 / November 201811

of unity for its outstanding loans BI,h,t.6
Finally, it should be noted that the short-term foreign bond holdings have disappeared
from the household’s budget constraint because we assume now that the trade balance isfinanced by long-term foreign government bonds, which are intermediated by the wholesalebanks; see Section 2.2.3. Also the term Dh,t in the budget constraint now denotes the totalityof profits from different sources which are assumed to be transferred to the household in a
lump-sum fashion.
The second constraint the household faces is a capital accumulation equation:7
Kh,t+1 = (1 − δ) Kh,t + ǫIt Ih,t ,(8)where ǫIt represents a serially correlated investment-specific technology shock.
The third constraint of the household is a Loan-in-Advance (LIA) constraint on financing
its investment expenditures as in Carlstrom, Fuerst, and Paustian (2017):
PC,t p̃I,t Ih,t ≤ QI,t (BI,h,t+1 − ̺I BI,h,t) .

(9)

According to this constraint, household h needs to finance the costs of purchasing
investment goods, expressed in nominal terms, by raising new retail loans in quantity
CFI,h,t = BI,h,t+1 − ̺I BI,h,t with unit payoffs QI,t . The constraint establishes a specialrole for retail bank loans: they are the only source of funding for new investment projects.
Furthermore, the constraint exposes investment to the evolution of the retail loan price
QI,t , which is determined in general equilibrium.
Choice of allocations
The household maximises its lifetime utility (2) subject to its budget constraint (3), the6
The basket of investment loans BI,h,t+1 requires a periodic repayment B̃I,h,t+1 , which is only equal
to BI,h,t+1 up to a first-order approximation. We abstract from this distinction and, instead, impose theequality of the two quantities, based on the understanding thatR 1 we only conduct first-order analysis. Morespecifically, the repayment evolves as B̃I,h,t+1 = ̺I B̃I,h,t+1 + 0 CFI,h,r,t dr, while the evolution of the basket
of loans is described in equation (5). The two variables are different because the repayment is derived fromthe simple sum of retail-bank-level loans (unit repayment for each unit of loan from each retail bank), while
the measure for the basket of investment loans is derived from the CES aggregate of loans across retail banks.
However, the two variables are equal up to a first-order approximation around a non-stochastic steady state,
which, as in our case, has no dispersion in retail loan prices.
7
The investment adjustment cost, which is part of the household’s problem in the original model, is now
paid by the capital producers; see Section 2.2.2. This modification has no impact on the investment choice,ceteris paribus, but simplifies the investment problem in the presence of financial frictions. For example, theb h,t+1 = (1 − δ)Kb h,t + δ(blog-linearised capital accumulation equation (abstracting from growth), KǫIt + Ibh,t ),is equivalent to the log-linear capital accumulation equation in the original model because the investment
adjustment cost and its first derivative are both zero in steady state.

ECB Working Paper Series No 2200 / November 201812

capital accumulation equation (8), and the LIA constraint (9). As in the original NAWM,
we define Λh,t /PC,t and Λh,t Qh,t to be the Lagrange multipliers associated with the budget
constraint (3) and the capital accumulation equation (8), respectively. Consequently, Λh,t
represents the shadow value of a unit of the consumption good and Qh,t the shadow valueof a unit of the investment good; that is, Tobin’s Q. In addition, let ςh,t Λh,t /PC,t be theLagrange multiplier associated with the LIA constraint (9). This multiplier represents the
shadow value of retail loans and measures the utility costs of financial frictions.
The first-order condition with respect to investment isp̃I,t (1 + ςh,t ) = Qh,t ǫIt .

[Ih,t ] :(10)

As the left-hand side of the equation shows, the marginal cost of investment is now notgiven by the relative price p̃I,t of purchasing investment goods from the capital producers
alone, but it includes the additional cost caused by the extra retail loans the household
needs to raise to finance the purchase.8 The gains from an extra investment unit, indicatedon the right-hand side, are equal to the shadow value of investment Qh,t scaled by theinvestment-specific technology shock ǫIt .
The first-order condition with respect to the basket of retail investment loans is[BI,h,t+1 ] :QI,t (1 + ςh,t ) = EtΛh,t+1 PC,t
(1 + ̺I QI,t+1 (1 + ςh,t+1 )) .
β
Λh,t PC,t+1(11)

According to this equation, the period-t gains from an extra retail loan unit, whichraises QI,t for each unit of the new loan and eases the household’s LIA constraint by thesame amount, must be equal to the discounted present value of the future costs of this loan.
The stochastic nominal discount factor is βΛh,t+1 /Λh,t PC,t /PC,t+1 and the future cost is thesum of the unit coupon the household needs to repay to the retail bank in the next period
and the next-period value of the loan. The loan quantity decays with parameter ̺I , and thenext-period value of the loan is in turn determined by the next-period replacement value ofthe loan QI,t+1 and the tightness of the LIA constraint in the next period, ςh,t+1 .
The household’s demand for long-term government bonds comes from the consolidated
first-order conditions with respect to short and long-term government bond holdings:[Bh,t+1 , BL,h,t+1 ] : BL,h,t+1 =−1
1 + γLh EtΛh,t+1 PC,tβ
(RL,t+1 − RD,t )B L,h . (12)Λh,t PC,t+1

8
Compared to the original model, p̃I,t replaces the relative price pI,t = PI,t /PC,t in the first-orderconditions with respect to capital Kh,t+1 and capital utilisation uh,t , which are not separately stated here.

ECB Working Paper Series No 2200 / November 201813

That is, the demand of household h for long-term government bonds depends on the
expected present value of the excess bond return relative to the short-term government bondyield (which is equal to the deposit rate), RL,t+1 − RD,t . The household would demand afixed amount B L,h of government bonds if this premium were zero, and otherwise, when
the premium increases, it raises its demand with an elasticity equal to the inverse of theportfolio adjustment cost parameter γLh . As this parameter declines towards zero, thedemand elasticity increases and the household responds ever more flexibly to a change inthe premium. Accordingly, the adjustment cost is a crucial determinant of the overalllevel of financial frictions in the model. If the adjustment cost were zero, the households’
behaviour would neutralise the impact of financial frictions. More concretely, when thewholesale banks’ balance sheet constraint tightens, the premium of long-term government
bonds rises, as we show below. If the adjustment cost were zero, the households would react
to this rise in the premium by flexibly purchasing bonds from the wholesale banks. This
would immediately ease the banks’ balance sheet constraint and offset any transmission of
their balance sheet problems to the economy.
2.2.2

Capital producers

The problem of the capital producers is standard. They face investment adjustment costs:
in particular, in order to produce investment goods of a quantity It , they need inputs
in quantity (1 + ΓI (It /It−1 ))It . They purchase their investment inputs at the relative
price PI,t /PC,t , and sell their investment output at the relative price p̃I,t . They discountfuture income using the stochastic discount factor of the households, who are their owners.
Therefore, they maximise
Et

"∞
X

k





β Λh,t+k p̃I,t+k It+k − 1 + ΓI

k=0



It+k
It+k−1PI,t+kIt+kPC,t+k

#

.

(13)

The first-order condition for the capital producers’ maximisation problem with respect
to the investment good is:[It ] :

PI,tp̃I,t =
PC,t



1 + ΓI



It
It−1



+ Γ′I



It
It−1



It
It−1





 2 
Λh,t+1 PI,t+1 ′ It+1 It+1
ΓI
− Et β.
Λh,t PC,t+1
It
It2

(14)

The first-order condition equates the relative selling price of the marginal unit of the

ECB Working Paper Series No 2200 / November 201814

investment good to its marginal cost. The marginal cost depends on the relative price of
the investment inputs and the change in the adjustment costs this period and in the next
brought about by the production of the marginal unit of the investment good. The profits
of the capital producers are redistributed to the households in a lump-sum fashion.
2.2.3

Wholesale banks

We introduce wholesale banks into the model, which face an agency problem as in Gertler
and Karadi (2011). Accordingly, each household h is composed of a measure f of wholesalebankers and a measure (1 − f ) of workers. New wholesale bankers obtain a fixed start-up
fund from the household, which forms the basis of their net worth. They invest their net
worth and deposits, which they collect from other households, into investment loans andgovernment bonds, and build their net worth over time from their retained earnings. An
agency friction limits the wholesale banks’ leverage, and, therefore, the amount of deposits
they can collect. In each period, wholesale bankers become workers with time-varying
probability 1 − θt and return their net worth to the household they are a member of. This
setup ensures finite expected lifetime for wholesale bankers and thereby limits their ability
to free themselves from their binding leverage constraints. To keep the share of the bankers
constant, each period f (1 − θt ) workers become wholesale bankers. Wholesale bankers andworkers enjoy perfect consumption risk sharing.
Assets
The wholesale banks are indexed by b ∈ [ 0, 1 ] and hold three types of long-term nominal
assets: wholesale investment loans and domestic as well as foreign long-term government
bonds.
• The wholesale banks issue nominal long-term investment loans BI,b,t+1 at wholesale
price Q̃I,t . The wholesale investment loans follow the same repayment schedule as
the retail loans, with a repayment of unity in the first period, and a geometricallydecaying coupon with parameter ̺I . The nominal rate of return of the wholesale
investment loan isR̃I,t+1 =1 + ̺I Q̃I,t+1
.
Q̃I,t

(15)

• They purchase domestic and foreign nominal long-term government bonds, BL,t+1 and∗BL,t+1. Analogously to the domestic long-term government bonds that we introducedin the previous section, foreign government bonds (denominated in foreign currency)
have a geometrically decaying coupon with a rate of decay ̺∗L and new issuance equals

ECB Working Paper Series No 2200 / November 201815∗ = B∗∗ ∗CFL,tL,t+1 − ̺L BL,t . The price of the bond in foreign currency is denoted by

Q∗L,t , and the rate of return of the foreign long-term government bond denominatedin foreign currency is∗
RL,t+1=

1 + ̺∗L Q∗L,t+1
Q∗L,t

.

(16)

Decision problem
The nominal balance sheet of a wholesale bank b (at the end of period t) ispp∗,pQ̃I,t BI,b,t+1+ QL,t BL,b,t+1+ St Q∗L,t BL,b,t+1= NWb,t + Db,t+1 ,(17)

where the superscript p indicates privately intermediated assets.9
The balance sheet identity imposes the equality of the value of assets, including investment loans and domestic as well as foreign bonds, with the bank’s liabilities, which are its
nominal net worth NWb,t and the households’ nominal deposits with the bank, Db,t+1 .
The net worth of bank b accumulates through retained earnings:pp
NWb,t+1 = R̃I,t+1 Q̃I,t BI,b,t+1+ RL,t+1 QL,t BL,b,t+1∗,p∗+ St+1 /St RL,t+1
Q∗L,t BL,b,t+1− RD,t Db,t+1="(R̃I,t+1 − RD,t )p
Q̃I,t BI,b,t+1

NWb,t+ (RL,t+1 − RD,t )p
QL,t BL,b,t+1

NWb,t

#
∗ B ∗,pS
Q
t
L,t
L,b,t+1∗+ St+1 /St RL,t+1+ RD,t NWb,t . (18)
− RD,tNWb,tAs can be seen from the first equality in this accumulation equation, the bank obtains
revenue from the returns on its asset holdings, and it pays interest on its deposits. The∗. Combining thisreturn on the foreign currency holdings in local currency is St+1 /St RL,t+1

equation with the balance sheet identity (17), we can express the law of motion for banklevel net worth as a function of excess asset returns over the deposit rate and asset-level
leverage (asset-to-net-worth) ratios, as shown by the second equality. The net worth ofbanks, if uninvested, would earn the deposit rate RD,t (which is equal to the short-term
government bond yield and is shown as the last term on the right-hand side), but they earn
9

The wholesale banks hold foreign currency assets and finance them from domestic currency deposits.
This formulation is different from alternative setups like the one in Aoki, Benigno, and Kiyotaki (2016),
which were developed to describe emerging market economies and in which domestic assets are financed byforeign currency deposits. The difference is motivated by the observation that the euro area maintains a
positive net-foreign-asset position.

ECB Working Paper Series No 2200 / November 201816

leveraged excess returns when invested in risky assets.
The wholesale banker b maximises its discounted net worth upon exiting the wholesalemarket, which happens with probability 1 − θt+1 . As the bank can earn excess returns on
its net worth, it is optimal to continue to invest it and to postpone all net worth payouts
to the household till the bank exits. Accordingly, the value function associated with thebanker’s decision problem isVb,t (NWb,t ) =
=

max
p
p
∗,p
,BL,b,t+1,BL,b,t+1{BI,b,t+1
}
max

p
p
∗,p
,BL,b,t+1,BL,b,t+1{BI,b,t+1}"∞X(1 − θt+k )
Et
h

k=1

k−1
Y
i=1

θt+i

!

Λt,t+k Π−1
C,t+k NWb,t+k#

Et (1 − θt+1 )Λt,t+1 Π−1
C,t+1 NWb,t+1i+ θt+1 Λt,t+1 Π−1
V
(NW
)
b,t+1
b,t+1
C,t+1

(19)

with Λt,t+k = βΛh,t+k /Λh,t and ΠC,t+k = PC,t+k /PC,t .
We assume that each wholesale bank b faces an agency problem: in particular, it can
abscond with a share Ψ of the assets. If this happens, the bank forgoes its franchise value
and its depositors are left with the remaining (1 − Ψ) share of the assets. To guarantee thatsuch event never takes place, the depositors impose an incentive compatibility constraint
on the bank:
p
p
∗,p
∗
Vb,t (NWb,t ) ≥ Ψ(Q̃I,t BI,b,t+1+ ωL QL,t BL,b,t+1+ ωL,t
St Q∗L,t BL,b,t+1
).

(20)

Under this constraint, no bank will ever abscond in equilibrium because the franchisevalue never gets below the gains from absconding. The bank’s value function is maximised
subject to this constraint, as well as the net worth accumulation equation (18).
The incentive compatibility constraint also shows that the absconding rate varies acrossassets: we assume that the bank can abscond with share Ψ of the investment loans, with∗ Ψ of the foreign government bonds, where
share ωL Ψ of the domestic and with share ωL,t
∗ < 1. The idea here is that the domestic and foreign governments have superiorωL , ωL,tability relative to the private sector to recover the assets. The relative absconding rate forforeign government bonds is assumed to depend on the country’s net-foreign-asset position:
the higher the foreign bond holdings, the harder it is to recover a sizeable share of theassets. In particular, the relative absconding rate for the foreign bonds takes the form

ECB Working Paper Series No 2200 / November 201817

∗∗ = ω ω̃ ∗ /(1 − Γ ∗ (s ∗RP )) with
ωL,t
L L
BL BL ,t+1 ; ǫt∗ΓBL∗ (sBL∗ ,t+1 ; ǫRP) = γL∗
t





∗
 1∗
St Q∗L,t BL,t+1
RP ∗ γLexp−1 ,ǫt
PY,t Yt(21)∗
where sBL∗ ,t+1 = St Q∗L,t BL,t+1/PY,t Yt is the share of the country’s aggregate foreign bond∗holdings in domestic output and ǫRP
represents a serially correlated risk premium shock.
t
We estimate both the relative absconding rate parameters ωL , ω̃L∗ , and the parameter γL∗determining the elasticity of the relative absconding rate for foreign bonds with respect tothe country’s net-foreign-asset position.
Portfolio allocation
To solve the banker’s decision problem, we postulate, and later verify, that the banker’s valuefunction is linear in net worth and symmetric across banks; that is, Vb,t (NWb,t ) = vt NWb,t .
The bank’s decision problem leads to three first-order conditions with respect to its
assets, an envelope condition with respect to its net worth and the incentive compatibility
constraint:p[Q̃I,t BI,b,t+1]:
p[QL,t BL,b,t+1]:∗,p[Q∗L,t BL,b,t+1]:[NWb,t ] :[µt ] :

hi
Et Λt,t+1 Ωt+1 Π−1
(
R̃
−
R
)
= µt Ψ,
I,t+1
D,t
C,t+1
h
i
Et Λt,t+1 Ωt+1 Π−1(R−R)= µt ωL Ψ,
L,t+1
D,t
C,t+1
h
i
∗
∗
Et Λt,t+1 Ωt+1 Π−1= µt ωL,tΨ,
C,t+1 St+1 /St RL,t+1 − RD,thi
(1 − µt )vt = Et Λt,t+1 Ωt+1 Π−1
C,t+1 RD,t ,

(22)
(23)
(24)
(25)

p
p
∗,p
∗
vt NWb,t = Ψ(Q̃I,t BI,b,t+1+ ωL QL,t BL,b,t+1+ ωL,t
St Q∗L,t BL,b,t+1). (26)

Here, the bank’s stochastic discount factor is modified with the factor Ωt+1 = (1 − θt+1 ) +θt+1 vt+1 , which measures the value of an extra unit of net worth next period: it is worth avalue of unity in case of exit (with probability 1 − θt+1 ), and it is worth vt+1 otherwise. The
bank’s discount factor Λt,t+1 Ωt+1 Π−1
C,t+1 is different from the households’ discount factor
Λt,t+1 Π−1
C,t+1 , because a payoff for the bank in the presence of a binding leverage constraint
is more valuable than the same payoff for the household; that is, vt+1 > 1.
The first three equations equalise the excess returns of marginal investments into theindividual assets to the marginal costs accruing through their impact on the incentive constraint. The excess returns measure the gains from holding the assets relative to their costs,
which include payouts on the deposits and foregone returns on net worth that were used

ECB Working Paper Series No 2200 / November 201818

to finance them. The marginal costs of extra investments are influenced by the absconding∗ Ψ for the individual assets and the tightness of the incentive conrates Ψ, ωL Ψ and ωL,tstraint. The latter is measured by µt = µ̃t /(1 + µ̃t ), where µ̃t is the Lagrange multiplierof the incentive constraint. We assume that the incentive constraint always binds. Under
the calibration used later in the paper, the constraint binds in the model’s non-stochastic
steady state, so for small enough shocks the assumption is indeed satisfied.
Combining the first-order conditions (22) to (24), we can obtain two no-arbitrage relationships between the expected excess returns of investment loans and domestic government
bonds, and between domestic and foreign government bonds:hiωL Et Λt,t+1 Ωt+1 Π−1
(
R̃
−
R
)
=
I,t+1
D,t
C,t+1
h
i
Et Λt,t+1 Ωt+1 Π−1
(R
−
R
)
,
L,t+1
D,t
C,t+1
h
i
∗
ωL Et Λt,t+1 Ωt+1 Π−1
S
/S
R
−
R
=
t+1
t
D,t
L,t+1
C,t+1
h
i
−1
∗
ωL,t Et Λt,t+1 Ωt+1 ΠC,t+1 (RL,t+1 − RD,t ) .

(27)

(28)

These no-arbitrage conditions imply that the expected excess returns of the bank’s
assets weighted by the inverse of the relative absconding rates must be equal. The relative
absconding rates enter these conditions because they determine the relative impact of theassets on the bank’s incentive constraint. This reflects the fact that the relative absconding
rates influence the market-determined “haircuts” of the assets, i.e. how easy it is to raiseoutside funding to purchase them.
The dynamics of the exchange rate are governed by the second no-arbitrage condition,
instead of the standard uncovered interest parity (UIP) relationship. According to thisno-arbitrage condition, expected exchange-rate revaluations need to equalise expected discounted excess returns of domestic over foreign long-term government bonds.10 This interaction between excess returns and the exchange rate opens the door to a direct exchange-ratechannel of central bank asset purchase policies: to the extent that these policies improvethe balance sheet conditions of banks, they will depreciate the domestic currency. Moreprecisely, because asset purchases ease banks’ balance sheet constraint, the excess return∗on domestic government bonds declines. As the foreign currency return RL,t+1
on foreign

bonds is determined internationally and remains unaffected by domestic developments, theexchange rate needs to depreciate so that its expected appreciation reduces the domestic
10

It is straightforward to show that, without financial frictions, this condition simplifies to the UIP condition.

ECB Working Paper Series No 2200 / November 201819

currency return on foreign bonds.
It remains to determine the value of vt . To this end, we define the bank’s “risk-weighted”
leverage Φt as
Φt =

p
p
∗ S Q∗ B ∗,p
Q̃I,t BI,b,t+1+ ωL QL,t BL,b,t+1+ ωL,tt L,t L,b,t+1

NWb,t

,

(29)

where the relative absconding rates determine the relative risk weights, reflecting the factthat the bank can raise more deposits for a unit of net worth to purchase government
bonds compared to the issuance of investment loans. Therefore, government bonds can be
downweighted in an effective leverage measure.
This definition of leverage is particularly useful since, evoking the incentive constraint (20), bank leverage can be expressed as Φt = vt /Ψ. Substituting this relationshipinto the first-order condition (22), we get:hiµt vt = Et Λt,t+1 Ωt+1 Π−1
(
R̃
−
R
)Φ
I,t+1
D,t
t .
C,t+1

(30)

We can then substitute this equation into the envelope condition (25) to obtain an
expression for vt :hivt = Et Λt,t+1 Ωt+1 Π−1
(
R̃
−
R
)Φ
+
R
.
I,t+1
D,t
t
D,t
C,t+1

(31)

From vt = ΨΦt we finally get:hi
Et Λt,t+1 Ωt+1 Π−1
C,t+1 RD,t
h
i.
Φt =
Ψ − Et Λt,t+1 Ωt+1 Π−1
(
R̃
−
R
)
I,t+1
D,t
C,t+1

(32)

This equation gives a closed-form expression for the bank’s endogenous leverage limit Φt .
Intuitively, the obtainable leverage is smaller, the larger Ψ, i.e. the larger the share of theassets the bank can abscond with. Yet the leverage limit is higher if the bank’s franchisevalue gets higher and the incentives to abscond, therefore, becomes lower, either as a resultof higher expected excess returns or a higher expected deposit rate. The value of vt , furthermore, is independent of bank-level characteristics, including the bank-level net worth,so the bank’s value function is indeed linear in its net worth, as postulated above.
Aggregation
As we have shown above, the banks’ leverage Φt does not depend on bank-level factors, so

ECB Working Paper Series No 2200 / November 201820

we can easily aggregate the bank-level balance sheet conditions into an aggregate balance
sheet condition for the wholesale banking sector:
p
p
∗,p
∗
Q̃I,t BI,t+1+ ωL QL,t BL,t+1+ ωL,t
St Q∗L,t BL,t+1= Φt NWt .

(33)

The aggregate law of motion of the net worth of the wholesale banking sector becomes:
NWt+1 = θt+1

(R̃I,t+1 − RD,t )p
Q̃I,t BI,t+1

NWt+ (RL,t+1 − RD,t )∗,p∗+ St+1 /St RL,t+1− RD,tp
QL,t BL,t+1

NWt!

 St Q∗L,t BL,t+1+ RD,t NWt + Θt+1 , (34)
NWt

where the second term on the right-hand side is the start-up fund Θt+1 which the newwholesale bankers receive from the households. This start-up fund is assumed to evolve inline with actual consumer price inflation ΠC,t+1 and trend productivity growth gz,t+1 . The
first term represents the retained earnings of the existing wholesale bankers, a share θt+1 ofwhich remain bankers in period t + 1.
2.2.4

Retail banks

As discussed in Section 2.2.1, there exists a continuum of monopolistically competitive retailbanks indexed by r. Households raise QI,r,t CFI,r,t new investment loans from an individual
retail bank r, which satisfies the households’ demand for new loans by purchasing new loans
from the wholesale banks in an amount equal to Q̃I,t CFI,r,t . The retail bank differentiates
the new wholesale loans and sells the differentiated loans to the households subject to amark-down. In doing so, the retail bank obtains an upfront profit and then channels thescheduled repayments fully from the households to the wholesale banks. The profits are
redistributed to the households in a lump-sum fashion.
Under the maintained assumption of a loan-price mark-down, which is embodied in thesteady-state calibration of the households’ basket of new investment loans with ϕI < 1(see equation (5) in Section 2.2.1) and holds in the neighbourhood of the steady state,
the retail bank’s amount of loan purchases from the wholesale banks is larger than theloan amount extended to the households; that is Q̃I,t CFI,r,t > QI,r,t CFI,r,t . Moreover, themark-down assumption implies a steady-state mark-up of the retail-loan-rate spread over
the wholesale-loan-rate spread; see Section 3.2.1.
To capture the empirically documented sluggish adjustment of loan rates applied to new

ECB Working Paper Series No 2200 / November 201821

issuance, we further assume that the retail banks face rigidities constraining their ability to
re-set the prices of their loans. In particular, like in Calvo (1983), a retail bank can re-set
the price of a new loan only with probability 1 − ξI . All retail banks r that can re-set theirprices in period t choose the same price Q◦I,t = Q◦I,r,t maximising



ϕI
∞

  Q◦  1−ϕt+k
I
X


I,t
t+k
◦
Et 
ξIk Λt,t+k Π−1
CFI,t+k  .
C,t+k Q̃I,t+k − QI,t
QI,t+k(35)

k=0This expression measures the present discounted value of profits from setting theloan price Q◦I,t . With probability ξIk , the retail bank r will still offer loans at thesame price in period t + k. The households’ demand for its loans in period t + k isI

I

(Q◦I,t /QI,t+k )ϕt+k /(1−ϕt+k ) CFI,t+k , and its profit comes from the difference between theamount of payoff it receives for obtaining a unit loan Q̃I,t+k from the wholesale bank andthe amount Q◦I,t it pays to the household. The retail bank is owned by the households, so
it discounts the future profits with the households’ nominal stochastic discount factor.
After some straightforward simplifications, the first-order condition is

∞
X k
Et 
ξI Λt,t+k Π−1
C,t+k
k=0

1
1 − ϕIt+k



∞
X k
Et 
ξI Λt,t+k Π−1
C,t+k
k=0





I

Q◦I,t
QI,t+k ϕt+k
I

1−ϕ
t+k


CFI,t+k+1  =ϕI ◦  t+k
−1
QI,t
1−ϕI
ϕIt+k
Q̃I,t+kt+kCFI,t+k+1  ,I
QI,t+k1 − ϕt+k QI,t+k(36)

which implicitly determines the optimal loan price Q◦I,t .
A measure ξI of the retail banks keep their previous-period price unchanged, and ameasure (1 − ξI ) set the new optimal price. Hence, the aggregate loan price index is

QI,t =

1
1−ϕIt

ξI QI,t−1 + (1 − ξI )Q◦I,t

1
1−ϕI
t

!1−ϕIt.

(37)

Finally, for future use we define the nominal loan rate as the yield to maturity of theinvestment loans. They can be expressed as the internal rate of return of a loan withimmediate payoff QI,t and a geometrically decaying repayment schedule 1, ̺I , ̺2I , . . . . It is

ECB Working Paper Series No 2200 / November 201822

easy to show that the gross loan rate RI,t is
RI,t =

1+ ̺I ,
QI,t(38)

noting that this rate needs to be distinguished from the investment loans’ ex post return.
2.2.5

Foreign assets and domestic bond supply

Foreign assets
Foreign assets in the form of foreign long-term government bonds are assumed to be intermediated by the wholesale banks. The idea is that foreign trade is conducted throughfinancial intermediaries which invest the trade surplus into foreign currency assets and,in return, provide domestic households with local currency deposits. In this process, thewholesale banks enter an open foreign exchange position. As a result, exchange-rate fluctuations influence the balance sheet condition of wholesale banks (see equation (17)) and,in a two-way interaction, banks’ balance sheet condition will influence the exchange rate.
This is the consequence of the no-arbitrage condition between the spreads of domestic andforeign government bonds (see equation (28)).
The foreign long-term government bond holdings of the wholesale banks evolve according
to:

 TBt
∗
∗
∗
Q∗L,t BL,t+1− ̺∗L BL,t=
+ BL,t.
St(39)

That is, the wholesale banks invest the country’s current account surplus, which encompasses the trade balance TBt /St (expressed in foreign currency) and the coupon pay∗ on the banks’ foreign bond holdings, into long-term foreign bonds. To this end,ments BL,t∗
∗ , which are supplied flexibly
they purchase new foreign bonds in quantity BL,t+1− ̺∗L BL,t

at the foreign currency price Q∗L,t .
Domestic government bonds
We assume an exogenous supply of domestic long-term government bonds BL,t+1 , which isfinanced by lump-sum taxes. We also assume that short-term government bonds Bt+1 arein zero supply.
2.2.6

Central bank asset purchases and market clearing

Central bank asset purchases
The central bank can purchase long-term wholesale investment loans, as well as domestic

ECB Working Paper Series No 2200 / November 201823

and foreign long-term government bonds from the wholesale bank. It issues short-termgexcess reserves Dt+1
to finance these purchases. We assume that wholesale banks holdthese excess reserves and that they cannot divert them. As a result, holding excess reserves
does not tighten the balance sheet constraints of wholesale banks, because they can financethem with extra deposits. Accordingly, the central bank’s balance sheet identity is
g
g
∗,g
g
Q̃I,t BI,t+1+ QL,t BL,t+1+ St Q∗L,t BL,t+1= Dt+1,(40)

where the superscript g indicates central bank assets and liabilities.
Importantly, the central bank can issue excess reserves and purchase loans and bonds
without the agency friction that banks face, as in Gertler and Karadi (2011). The idea isthat the public is confident that the central bank does not abscond with any of the assets. At
the same time, the central bank is arguably less efficient than banks in intermediating assets,
which we model simply by assuming that it faces efficiency costs ϑI , ϑL and ϑ∗L associatedwith its purchases of the respective asset (expressed as a share of domestic output). Theseasset-specific efficiency costs enter the model’s aggregate resource constraint.
Market clearing
Clearing of the loan and bond markets requires that the assets intermediated by the central
bank and the wholesale banks and the assets held by the households (domestic long-term
government bonds only) are equal to their aggregate supply:gpBI,t+1 = BI,t+1+ BI,t+1
,

(41)

g
p
BL,t+1 = BL,t+1+ BL,t+1+ BL,h,t+1 ,

(42)

∗,g
∗,p
∗
BL,t+1= BL,t+1+ BL,t+1.

(43)

The formulation of the market clearing conditions concludes the description of thefinancial-sector extension of the NAWM. An appendix towards the end of the paper provides details on the log-linear version of the extended model, including the derivation of its
steady state, with a focus on the amendments that relate to the model’s financial-sector
extension.

2.3

Other model extensions

Reflecting the practical experience gained with using the NAWM in the policy process at
the ECB over the past ten years, a number of other extensions have been made to its

ECB Working Paper Series No 2200 / November 201824

original specification. In the following, we briefly describe those extensions that have been
incorporated into NAWM II.
2.3.1

Non-zero import content of exports

The extended model allows for a non-zero import content of exports. This is an empiricallyimportant feature of the euro area economy, and the incorporation of this feature into
the model has a noticeable bearing on the propagation of a variety of shocks via tradeflows. Below, we describe the changes to the original model specification implied by the
introduction of a non-zero import content of exports. Further details, including on thecomputation of the model’s steady state and on the derivation of its log-linear equations,are provided in Coenen and Vetlov (2009).
Unlike in the original model, the differentiated intermediate goods Yf,t produced by its
continuum of monopolistically competitive firms f ∈ [ 0, 1 ] can either be directly sold todomestic producers of final goods or be combined with imported foreign intermediate goods,
X , and then be sold abroad. The non-zero import content of the intermediate goods
IMf,tsold abroad is modelled by assuming that the production of the exported good Xf,t features
a CES production technology:

Xf,t


 µX
−1
−1
1
1
µX −1
 µX
 µX
X
X
µX
µX
µX
µX
+ (1 − νX )
=
(νX )
Hf,t
IMf,t
,

(44)

X and IM X are respectively the domestic and the foreign intermediate-good inputs
where Hf,tf,tused in its production. The parameter νX ∈ [ 0, 1 ] determines the share of domestic inputs—that is, the home bias—in the production of the exported good; and the parameter µX > 1
represents the elasticity of substitution between the domestic and the foreign intermediategood inputs.
The foreign intermediate-good input is given by the index
XIMf,tZ 1 
ϕ∗t
1X,f ϕ∗t∗=IMf ∗,t
df
,

(45)

0

where the possibly time-varying parameter ϕ∗t > 0 is inversely related to the elasticity
of substitution between the differentiated goods supplied by foreign intermediate-goodfirms f ∗ ∈ [ 0, 1 ].11
To determine the optimal demand for the domestic and foreign inputs in the production
The parameter ϕ∗t also represents the price mark-up charged by the monopolistically competitive foreignintermediate-good firms selling their goods in domestic markets; see CCW, Section 2.2.2.
11

ECB Working Paper Series No 2200 / November 201825

of exports, an intermediate-good firm f must solve the problem of minimising total input
X +PX
cost MCt Hf,t
IM,t IMf,t subject to the technology constraint (44), taking the prices of

the inputs, MCt and PIM,t , as given. Here, MCt denotes the marginal cost of producing a
X (identical across firms as they face the same
unit of the domestic intermediate good Hf,tinput prices and since they have access to the same production technology), and PIM,t is
the import price index of the foreign intermediate goods.
X the Lagrange multiplier associated with the technology conDefining as MCf,tstraint (44), the first-order conditions of the firm’s cost minimisation problem with respect
to domestic and foreign inputs are given by
X
MCf,t
(νX )

Xf,t
X
Hf,t

! 1

= MCt ,

(46)

Xf,t
X
IMf,t

! 1

= PIM,t .

(47)

1
µX

1

X
MCf,t
(1 − νX ) µX

µX

µX

The above optimality conditions determine the firm’s demand for domestic and imported
intermediate goods:
X
Hf,t

X
IMf,t

= νX

MCt
X
MCf,t

= (1 − νX )

!−µX

PIM,t
X
MCf,t

Xf,t ,!−µX(48)

Xf,t .

(49)

Substituting the demand equations (48) and (49) into the production technology (44),
X , or nominal marginal cost, in terms of thewe can express the Lagrange multiplier MCf,tgiven input prices:
X
MCf,t
=

νX (MCt )1−µX + (1 − νX )(PIM,t )1−µX



1
1−µX

.

(50)

Since all firms f face the same input prices and the same production technology, nominal
X will be identical across firms; that is, MC X = MC X .
marginal cost MCf,ttf,tX represents an index of imported differentiated intermediate
Finally, recalling that IMf,tgoods, the demand by firm f for the imported good IMf ∗,t is given by

IMfX,f∗,t=

ECB Working Paper Series No 2200 / November 2018



P
PIM,t

IM,f ∗,t

 ϕ∗t ∗
1−ϕt

X
IMf,t
,

(51)

26

where PIM,f ∗,t and PIM,t denote the price of the differentiated imported good f ∗ and theaggregate import price index, respectively. Hence, the aggregate demand by domestic producers for the imported good is given by

IMfX∗,t =where IMtX =
2.3.2

Z 1
0

IMfX,f∗,t df=



PIM,f ∗,tPIM,t

 ϕ∗t ∗
1−ϕt

IMtX ,(52)

R1

X
0 IMf,t df .

Generalised price and wage Phillips curves

The specifications of the price and wage Phillips curves in NAWM II have been generalised,in part because of conceptual considerations and partly on empirical grounds. In the following, the nature of the respective generalisation is outlined and the resulting modified
price and wage Phillips curves are stated. Further details are available in Coenen, Levin,and Christoffel (2007) and Coenen (2009), respectively.
Price Phillips curves
Besides the usual nominal rigidity due to the assumption of staggered price contracts on thepart of firms, the generalised price-setting framework of NAWM II incorporates a source ofreal rigidity to better account for the very low cyclical sensitivity of prices at the aggregate
level. In particular, following Kimball (1995), the demand curves for the differentiatedintermediate goods Yf,t , which are produced by a continuum of monopolistically competitive
firms f ∈ [ 0, 1 ] and then sold in both domestic and foreign markets, are assumed to exhibit
a high degree of curvature (approximating a kinked demand curve) as a function of thedeviation of the individual firm’s price from the average price level. Thus, when a firm is
re-optimising its domestic and foreign price contracts, its optimal prices will be relatively
less sensitive to changes in the firm’s marginal cost.
Noting that the intermediate-good firms charge different prices for the goods sold indomestic markets, Hf,t , and for those sold in foreign markets, Xf,t , we will focus by meansof example on the firms’ optimal price-setting decisions for the goods sold domestically,
Hf,t .12 These goods are aggregated by a distinct set of competitive firms into a final good,
12

Besides the pricing decision of the domestic intermediate-good firms f concerning their goods soldabroad, there is yet another pricing decision concerning the imported goods produced by foreign intermediategood firms f ∗ with an analogous treatment.

ECB Working Paper Series No 2200 / November 201827

using the following technology:
Z 1G(Hf,t /Ht ) df

= 1,

(53)

0

where the function G(·) is increasing and strictly concave with G(1) = 1.13 Under thisassumption, the steady state of aggregate output, H, is identical to the steady-state output
of each individual firm, Hf .
Henceforth we use µH to denote the steady-state elasticity of demand; that is,µH = −G ′ (1)/G ′′ (1) > 1. Furthermore, we use ǫH to denote the relative slope of the demand elasticity around its steady-state value; that is, ǫH = µH G ′′′ (1)/G ′′ (1) + µH + 1.
Thus, the special case ǫH = 0 corresponds to the specification of Dixit and Stiglitz (1977)
with a constant demand elasticity, for which G(·) = (·)(µH −1)/µH , with µH representing theelasticity of substitution of the differentiated intermediate goods.
Under these assumptions, each firm f faces the following implicit demand curve for its
output as a function of its price PH,f,t relative to the aggregate price index PH,t :′G (Hf,t /Ht ) =PH,f,tPH,tZ 1(Hz,t /Ht ) G ′ (Hz,t /Ht ) dz.

(54)

0

The concavity of G(·) ensures that the demand curve is downward-sloping; that is,
dHf,t /dPH,f,t < 0. The price index PH,t can be obtained explicitly by multiplying bothsides of equation (54) by the factor Hf,t /Ht and then integrating over the unit interval:
PH,t =

Z 1(Hz,t /Ht ) PH,z,t dz.

(55)

0

As in the original model, there is sluggish price adjustment due to staggered pricecontracts à la Calvo (1983). Accordingly, in a given period t each firm f receives permission
to optimally reset the price of the output sold in the domestic market with probability
1 − ξH . All firms that receive permission to reset their price contracts in a given period t◦ = P◦
choose the same optimal price, PH,t
H,f,t . Those firms which do not receive permission

are allowed to adjust their prices according to the following scheme:
χ

1−χH

H
PH,f,t = ΠH,t−1Π̄t

PH,f,t−1 .

(56)

It is assumed that the competitive final-good firms producing the private consumption good QC
t , theprivate investment good QIt and the public consumption good QG
t have the same implicit demand function
for the domestic intermediate good f . Accordingly, it is sufficient to consider the aggregate demand for thisC
I
G
good from the three final-good firms, Hf,t = Hf,t+ Hf,t+ Hf,t.
13

ECB Working Paper Series No 2200 / November 201828

That is, the price contracts are indexed to a geometric average of past (gross) intermediategood inflation, ΠH,t−1 = PH,t−1 /PH,t−2 , and the central bank’s possibly time-varying (gross)inflation objective, Π̄t , where χH ∈ [0, 1] is an indexation parameter determining the weighton past inflation.
We use πbH,t = log(ΠH,t /Π̄) to denote the logarithmic deviation of the rate of domesticb̄t = log(Π̄t /Π̄)
price inflation from the central bank’s long-run inflation objective, while π
represents the logarithmic deviation of the possibly time-varying inflation objective fromits long-run value. Then, combining the log-linearised first-order condition characterising

the firms’ optimal price-setting decision and the log-linearised aggregate price index yields
the following log-linear domestic price Phillips curve:14b̄t
πbH,t − π

with



=
+



χH
β
b̄t+1 +
Et π
bH,t+1 − π
1 + βχH
1 + βχHβχH
1 + βχHb̄t
πbH,t−1 − π



(57)




(1 − ξH ) (1 − βξH )  H
b̄t+1 − πb̄t + Ψ(µH , ǫH )Et πmc
ct + ϕbHtξH (1 + βχH )Ψ(µH , ǫH )−1 = 1 +ǫH,µH − 1

where mccH
bH
t and ϕt denote, respectively, firms’ real marginal cost (identical across firms

as they face the same input prices and since they have access to the same production
technology) and a time-varying price mark-up. Both variables are expressed as logarithmic

deviations from their respective steady-state values, with the steady-state price mark-up
ϕH being inversely related to the steady-state elasticity of demand µH .
It should be emphasised that the real rigidity coefficient Ψ(µH , ǫH ) depends solely on therelative curvature of the firms’ demand function and has a value of unity in the special casewith constant demand elasticity; that is, for the Dixit-Stiglitz specification with ǫH = 0.
Furthermore, it should be noted that the parameter ǫH is not separately identified fromthe Calvo parameter ξH determining the degree of nominal rigidity in firms’ price-setting
behaviour. Nevertheless, as will be shown in Section 3 below, a reasonable calibration of
the curvature of the demand function will help to account for the strong empirical evidence
on the existence of a very flat price Phillips curve for the euro area, without necessarily
relying on an implausibly large Calvo parameter.
14

Details of the derivation of the log-linear price Phillips curve are available upon request.

ECB Working Paper Series No 2200 / November 201829

Wage Phillips curve
In generalising the wage-setting framework of the original NAWM, we allow for less thanfull indexation of wages to trend labour productivity. Like in the case of price setting byfirms, there is sluggish wage adjustment by a continuum of households h ∈ [ 0, 1 ] due tostaggered wage contracts à la Calvo. Accordingly, in a given period t each household hreceives permission to optimally reset its nominal wage contract Wh,t with probability
1 − ξW . All households that receive permission to reset their wage contracts in a given◦ . Those households which do not
period t choose the same optimal wage rate Wt◦ = Wh,treceive permission are allowed to adjust their wage contracts according to the following
scheme:†Wh,t = gz,tΠ†C,t Wh,t−1 ,
χ̃

1−χ̃W

†
where gz,t
= gz,tW gz

χ

1−χW

W
and Π†C,t = ΠC,t−1
Π̄t

(58)

. That is, the nominal wage contracts areindexed both to a geometric average of the current (gross) rate of productivity growth, gz,t =zt /zt−1 , and the steady-state (gross) rate of productivity growth, gz , and to a geometricaverage of past (gross) consumer price inflation, ΠC,t−1 = PC,t−1 /PC,t−2 , and the central
bank’s possibly time-varying (gross) inflation objective, Π̄t , where χ̃W ∈ [0, 1] and χW ∈[0, 1] are the respective indexation parameters.
In analogy to the derivation of the log-linear price Phillips curve above, we use πbC,t =

log(ΠC,t /Π̄) to denote the logarithmic deviation of the rate of consumer price inflationb̄t = log(Π̄t /Π̄) represents thefrom the central bank’s long-run inflation objective, while πlogarithmic deviation of a possibly time-varying inflation objective from its long-run value.

††
Similarly, we define the logarithmic productivity growth deviation as gbz,t= log(gz,t/gz ) =χ̃χ̃log(gz,tW /gz W ). Then, combining the log-linearised first-order condition characterising thehouseholds’ optimal wage-setting decision and the log-linearised aggregate wage index yields
the following log-linear wage Phillips curve:15w
bt =β(1 − χ̃W )1 − χ̃W1
βEt [wbt+1 ] +w
bt−1 +
Et [bgz,t+1 ] −
gz,t
b
1+β
1+β
1+β
1+β

+

+
15

(59)


1 + βχWχβ(1 − χW ) βb̄C,t+1
Et [bπC,t+1 ] −π
bC,t + W π
bC,t−1 −
Et π
1+β
1+β
1+β
1+β

(1 − ξW ) (1 − βξW )1 − χWb̄C,t − Ψ̃(ϕW, ζ)πwbtτ − mrs
dt − ϕbWt1+β(1 + β) ξW

For details on the derivation of the log-linear wage Phillips curve, see Coenen (2009).

ECB Working Paper Series No 2200 / November 2018

30

with
Ψ̃(ϕW, ζ)−1 = 1 +ϕW
ζ,ϕW − 1

where wbt (wbtτ ) represents the productivity-adjusted (after-tax) real wage deflated by the
consumer price index, while mrs
d t and ϕbWt denote, respectively, the households’ marginal

rate of substitution between consumption and leisure (identical across households as we

assume that there exists a mechanism which provides insurance against household-specificincome risk) and a time-varying wage mark-up. All variables are expressed as logarithmic
deviations from their respective steady-state values. The parameter ζ is the inverse of thehouseholds’ Frisch elasticity of labour supply which can be interpreted as a source of real
rigidity influencing the slope of the wage Phillips curve.
Finally, it should be noted that for the original NAWM with full indexation of wages totrend productivity (that is, with χ̃W = 1) the two separate productivity terms in the above
log-linear wage Phillips curve vanish.
2.3.3

Uncertainty about shifts in trend productivity

In the original NAWM, labour productivity is shifted recurrently, and lastingly, by shocks to
the intermediate-good firms’ production technology. These permanent technology shocks zt
are assumed to evolve according to a serially correlated process,gz,t = (1 − ρgz ) gz + ρgz gz,t−1 + ηtgz ,(60)

where gz,t = zt /zt−1 represents the (gross) growth rate of trend labour productivity. The
parameters gz and ρgz determine, respectively, the unconditional mean (that is, the drift)
and the degree of persistence of the process, and ηtgz is a serially uncorrelated innovation.
While future shocks to trend labour productivity are unknown, a shock occurring in
the current period is perfectly observed by all economic agents, including the central bank.
Following a positive shock, forward-looking households and firms predict a rise in their
future income and profits and, hence, they increase their current level of spending. The
strong wealth effect of the anticipated rise in income and profits eventually boosts aggregate
demand beyond supply in the short run and may give rise to a temporary increase in firms’
costs of production. As a result, inflationary, rather than disinflationary, pressures canemerge following a positive permanent technology shock.
In NAWM II, the strength of the wealth effect associated with a permanent technology

ECB Working Paper Series No 2200 / November 201831

shock is mitigated by introducing uncertainty on the part of economic agents about thedegree of persistence of the shock following the approach in Edge, Laubach, and Williams(2007). In particular, it is assumed that the permanent technology shock gbz,t (expressedas the logarithmic deviation from its deterministic component) is the composite of twoptr . Bothdistinct components: a persistent component, gbz,t, and a transitory component, bgz,tcomponents have a permanent impact on the level of trend labour productivity. They differ,
however, to the extent that they have either a protracted or a one-off impact on overall trend
labour productivity growth:ppp+ ηbtgz ,gbz,t= ρgzp gbz,t−1

(61)

g tr

p

tr
gbz,t
= ηbt z .

g tr

(62)

Here, ηbtgz and ηbt z are serially uncorrelated innovations to the persistent and to the transitory

component of the permanent technology shock with variances σg2p and σg2tr , respectively. Thezzparameter ρgzp determines the degree of persistence of the former component.

The agents in the extended model do not directly observe the two individual components.
Instead, they only observe the composite permanent technology shock,ptrgz,t = gbz,t
b
+b
gz,t
,

(63)

and need to estimate the values of the individual components by recursively solving a signalextraction problem.
As in Edge, Laubach, and Williams (2007) we assume that, to solve the signal-extraction
problem and to update the estimates of the persistent and the transitory component of thepermanent technology shock over time, the agents employ the Kalman filter. The resulting
updating rules for the (steady-state) Kalman filter are as follows:
p
p
p
p
tr
+ Kgzp (bgz,t+ gbz,t− ρgzp bgz,t−1|t−1),
gbz,t|t= ρgzp gbz,t−1|t−1

(64)

p
p
tr
tr
gbz,t|t= Kgztr (bgz,t+ gbz,t− ρgzp bgz,t−1|t−1
),

(65)

where Kgzp and Kgztr are the Kalman gain parameters governing the rate of updating,Kgzp = 1 −

2 − (1 − ρ2gp − σg2p /σg2tr ) +zzz

Kgztr = 1 − Kgzp ,ECB Working Paper Series No 2200 / November 2018q2
(1 − ρ2gp − σg2p /σg2tr )2 + 4 σg2p /σg2tr
z

z

z

z

,

(66)

z

(67)

32

with the ratio of variances σg2p /σg2tr representing the signal-to-noise ratio associated withzz

the signal-extraction problem.
In order to solve the extended model jointly with the signal-extraction problem, weappend the Kalman filter updating equations to the structural equations of the model as aseparate recursive block. To achieve recursiveness, we introduce a change in notation fromp
tr to g̃ p and g̃ tr . Moreover, to ensure that the appended Kalman filter blockgbz,tand gbz,t
z,t
z,t

p
tr ,
is complete, we complement the updating equations with laws of motion for g̃z,tand g̃z,twhich duplicate equations (61) and (62) above.

A suitable model solution algorithm—e.g., the AiM algorithm developed in Andersonand Moore (1985), or the generalised Schur form-based algorithm of Klein (2000)16 —canthen be used in a first step to solve for agents’ forward-looking expectations so as to obtain
the observed structure of the model. This structure respects the information set available
to agents in period t and is not influenced by the Kalman filter updating equations (64)and (65). In particular, it generically depends on agents’ period-t estimates of the individualptr . In the same step, the solution algorithm provides recurshock components, gbz,t|t
and bgz,t|tp
tr , whichsive Kalman filter-based period-t estimates of the shock components, g̃z,t|t
and g̃z,t|treflect the new information about the composite technology shock that has become available

while moving from period t − 1 to period t. In a second step, agents’ estimates of the shockcomponents in the observed structure are set equal to the Kalman filter-based estimates,pp
tr = g̃ tr . This requires appropriately modifying the coefficient matrigbz,t|t= g̃z,t|t
and bgz,t|tz,t|t

ces of the observed structure obtained from the model solution algorithm. The modified
coefficient matrices allow to compute the recursive reduced-form representation of the fullmodel, including the solution of the signal-extraction problem, in a straightforward way.
2.3.4

Time-varying equilibrium real interest rate

In the original NAWM, the central bank is assumed to adjust the logarithmic deviationof the (riskless) short-term nominal interest rate from its long-run level, rbt = log(Rt /R),in response to logarithmic deviations of some key macroeconomic variables—inflation andoutput (growth)—from their respective target or equilibrium levels, i.e. by following a Taylor(1993)-type interest-rate feedback rule. The long-run nominal interest rate R is exogenously
determined as the product of the non-stochastic steady-state rate of inflation Π (equal tothe central bank’s long-run inflation objective Π̄) and the long-run equilibrium real interest
16

Both algorithms are available in YADA, the Matlab programme used for solving, estimating and simulating NAWM II; see Warne (2018).

ECB Working Paper Series No 2200 / November 201833

rate Rr , with the latter being influenced by long-run trend productivity growth, Rr = β −1 gz .
The potential shortcoming of this specification, however, is that, in case there is a slowdown
in economic activity due to lower productivity growth and if this slowdown is expected topersist well into the future, the model tends to prescribe, all else equal, a mistakenly tightmonetary policy stance for current and future periods.
Given the slowing of euro area productivity growth over the past decades, the interestrate rule in NAWM II is now amended by relating the central bank’s estimate of the equilibrium real interest rate to perceived medium-term fluctuations in productivity growth, as
captured by the estimate of the persistent component of the model’s permanent technologypr = β −1 g p . The resulting log-linear interest-rate rule is:shock gz,t|t, with Rt|t
z,t|t



r
b̄t + φΠ (bb̄t ) + φY ybt
rbt = φR rbt−1 + (1 − φR ) rbt|t+π
πC,t − π+ φ∆Π (bπC,t − πbC,t−1 ) + φ∆Y (byt − ybt−1 ) + ηbtR ,

(68)

p
r =g
where rbt|tbz,t|t,πbC,t = log(ΠC,t /Π̄) denotes the logarithmic deviation of (gross) consumer

price inflation ΠC,t = PC,t /PC,t−1 from the central bank’s long-run inflation objective Π̄,b̄t = log(Π̄t /Π̄) represents the logarithmic deviation of the central bank’s possibly timeand π
varying inflation objective from its long-run value. Similarly, ybt = Ydt /zt is the logarithmic

deviation of aggregate output Yt from the trend output level zt , which is determined by thehistory of the composite permanent technology shock {gz,t , gz,t−1 , . . .}. This deviation will
be referred to as output gap hereafter.17 Finally, ηbtR is a serially uncorrelated shock to theshort-term nominal interest rate.

This specification of the model’s interest-rate rule implies that the central bank recog-

nises persistent deviations of the long-run productivity growth rate from its steady-statevalue and alters the short-term nominal interest rate accordingly, namely by lowering (increasing) the interest rate in response to negative (positive) shifts in the perceived value ofthe persistent component of the model’s permanent technology shock.
2.3.5

Time-varying perceived inflation objective

NAWM II also accounts for situations in which persistent fluctuations in inflation outcomes eventually result in a drift of private-sector agents’ longer-term inflation expecta17

We acknowledge that this output gap measure has no strong theoretical basis (see Galı́ and Gertler
2007). Exploring the model with a theory-consistent measure of the output gap—that is, the deviation of
actual output from the output level that can be attained in an environment of full nominal flexibility (seeWoodford 2003)—is left for the future.

ECB Working Paper Series No 2200 / November 201834

tions. Within the model, a possible drift of longer-term inflation expectations is implemented through a gradual shift in private-sector agents’ perception of the central bank’s
inflation objective, Π̄pt , which provides the long-run anchor for their formation of inflation
expectations. At the same time, it is assumed that the actual inflation objective of thecentral bank, which is guiding its policy decisions, remains unchanged, Π̄t = Π̄.18
The perceived inflation objective is determined via a simple adaptive scheme (formulated
in terms of logarithmic deviations from the central banks’s invariant long-run inflation
objective):


p
(4)
b̄pt = πb̄pt−1 + ̟Π̄p πb̄pt−1 + ηbtΠ̄πbC,t−1 − π
(4)

p

p

b̄t−1 + ηbtΠ̄= ̟Π̄p πbC,t−1 + (1 − ̟Π̄p ) π

p

(69)

(4)

b̄t = log(Π̄pt /Π̄) and πwith πbC,t−1 = log((PC,t−1 /PC,t−5 )/Π̄4 )/4. The parameter ̟Π̄p ∈ [0, 1]pmeasures the sensitivity of the perceived inflation objective to past inflation, and ηbtΠ̄ is a
serially uncorrelated shock to the perceived objective.

According to the reformulation of the adaptive scheme in the second equality, the current

value of the perceived inflation objective is determined as a weighted average of past annual
consumer price inflation and the value of the perceived inflation objective in the previous
period.19 If the weight on past inflation ̟Π̄p is zero, and in the absence of shocks both in thepresent and in past periods, the perceived inflation objective is equal to the actual inflationb̄pt = 0. Otherwise, and depending on the magnitude of ̟Π̄p , the perceived
objective, with π
inflation objective is influenced by movements in actual inflation, with possibly adverse

economic consequences. For example, households and firms will respond to a downward

shift in the perceived inflation objective by downwardly adjusting their desired wage andprice contracts.20 Eventually, this will lead to the materialisation of self-reinforcing secondround effects and an ensuing fall in inflation expectations. This in turn will push up thereal interest rate and, as a consequence, curtail aggregate demand. The implied demand
shortfall will exacerbate the downward pressure on wages and prices, over and above the18

Linking the anchoring of longer-term inflation expectations to private-sector agents’ perceptions of thecentral bank’s inflation objective is motivated by the widespread notion that stable inflation expectations
are inherently linked to the central bank’s commitment to achieving, and the ability to achieve, its inflation
objective over the medium term.
19
For further discussion and for details on modelling inflation expectations using the adaptive scheme, seeGürkaynak, Levin, Marder, and Swanson (2007).
20
Within NAWM II, this adjustment is implemented through replacing the time-varying inflation objectiveb̄t with the perceived inflation objective term πb̄ pt in the price and wage Phillips-curve equations (57)
term πand (59) stated in Section 2.3.2 above.

ECB Working Paper Series No 2200 / November 201835

direct effects resulting from the fall in inflation expectations.
Another important consequence that arises from misperceptions of the central bank’s
inflation objective is that the central bank’s actual interest-rate rule differs from the interestrate rule assumed by households and firms in their decision-making:21 when forming expectations of current and future short-term nominal interest rates households and firms
will over-predict the interest rate as the perceived inflation objective falls below the actual
objective, and vice versa. This mismatch between actual and perceived interest rates canhave material effects on aggregate demand on its own.
To solve the augmented model, the adaptive scheme determining the perceived inflation
objective (69) is appended to the model’s structural equations as a separate recursive block,
like in the case of solving NAWM II with the signal-extraction problem concerning the unobserved components of its permanent technology shock (see Section 2.3.3). Accordingly,
in the employed two-step solution procedure, the model’s observed structure is first deterb̄t . The
mined conditional on the central bank’s possibly time-varying inflation objective πpb̄t by means of appropriate adjustments
latter is then set equal to the perceived objective π

to the coefficient matrices of the observed structure, which thereafter allows to compute themodel’s reduced-form representation.

3

Bayesian estimation

As in the case of the NAWM, we adopt the approach outlined in An and Schorfheide (2007)
and Schorfheide (2000) and estimate NAWM II using Bayesian inference methods. This
involves obtaining the posterior distribution of the model’s estimated parameters based on
its log-linear state-space representation.22 For a detailed exposition of these methods, see
Herbst and Schorfheide (2016). The computations are performed with YADA, a Matlab
programme for Bayesian analysis of DSGE models; see Warne (2018).
An extensive discussion of the estimation results for NAWM II is beyond the scope of
this paper. Here we report selectively on the data used in the estimation, on the model’s
structural shocks, on the calibration of its steady-state expenditure shares and of a subset offinancial and non-financial-sector parameters, and, as a last step, on the prior and posterior
21
Specifically, the interest-rate rule of the central bank in equation (68) of Section 2.3.4 above includesb̄ t = 0 in case the actual objective remains unchanged, whereas thethe actual inflation objective, with πinterest-rate rule assumed by households and firms in forming their expectations includes the time-varyingb̄ pt .
perceived inflation objective, π
22For details on the derivation of the model’s log-linear representation around its non-stochastic steadystate, see the appendix towards the end of the paper.

ECB Working Paper Series No 2200 / November 201836

distributions of the financial and non-financial-sector parameters that we chose to estimate.
The main focus of the discussion is on those aspects that help to understand the enhancedrole of the financial intermediary sector in our extended model. Some additional discussion
relates to the novel use of system priors. For details concerning the estimation of the originalmodel, see CCW, Section 3.

3.1
3.1.1

Data and shocks
Data

In estimating the original version of the NAWM, CCW used times series for 18 macroeconomic variables which feature prominently in the ECB/Eurosystem staff projection exercises: real GDP, private consumption, total investment, government consumption, extraeuro area exports and imports, the GDP deflator, the consumption deflator, the extra-euroarea import deflator, total employment, nominal wages (measured as compensation per employee), the short-term nominal interest rate (corresponding to the 3-month EURIBOR), thenominal effective exchange rate of the euro, foreign demand, foreign prices, the foreign shortterm interest rate, competitors’ export prices, and the price of oil. For estimating NAWM II,
we retain the same variables, but with an extended estimation sample ranging from 1985Q1
to 2014Q4 (again using the period 1980Q2–1984Q4 as training sample). The time series ofthe variables are taken from an updated version of the AWM database (see Fagan, Henry,
and Mestre 2001), except for the time series of the extra-euro area trade variables.23 The
last five variables of the above list form part of a structural vector-autoregressive (SVAR)
model of the euro area’s external environment, the estimated parameters of which are kept
fixed throughout the analysis in this paper. Similarly, government consumption is specified
by means of an autoregressive (AR) model with fixed parameters.
The time series of the 18 macro variables are displayed in Figure 1, with real GDP,
private consumption, total investment, exports, imports, the GDP deflator, the consumption deflator, the import deflator, nominal wages, foreign demand, and foreign prices being
all transformed into quarterly growth rates (approximated by the first difference of theirlogarithm). All other variables are measured as logarithmic levels, except for the domestic
and foreign short-term nominal interest rates which are expressed in annualised percentage
terms. In contrast to the estimation of the original version of the NAWM, all real variables
23

Note that the foreign interest rate is proxied by the US Dollar 3-month LIBOR instead of the federal
funds rate used in the estimation of the original NAWM, and that the other foreign variables and the euro
nominal effective exchange rate are constructed as a weighted average for the euro area’s 38 main trading
partners instead of the smaller group of countries covered in earlier vintages of the AWM database.

ECB Working Paper Series No 2200 / November 201837

used in the estimation of NAWM II have beforehand been transformed into per-capita units
by scaling them with a measure of the euro area working age population (aged 15 to 64).
This scaling is motivated by the deceleration in working age population growth observed
over the extended estimation period.
A number of further transformations are made to ensure that variable measurement
is consistent with the properties of the balanced-growth path for NAWM II and that theunderlying modelling assumption of stationarity of all relative prices is satisfied. First,
the sample mean growth rates of extra-euro area exports and imports as well as foreign
demand are matched with the sample mean growth rate of real GDP. Second, we takethe logarithm of government consumption and remove a linear trend consistent with themodel’s steady-state growth rate for aggregate output of 1.5% per annum. Third, for the
logarithm of employment we remove a linear trend consistent with an increase in the labour
force of 0.3% per annum.24 Fourth, we construct a measure of the real effective exchange
rate from the nominal effective exchange rate, the domestic GDP deflator and foreign prices(computed as a weighted average of foreign GDP deflators) and then remove the sample
mean. Finally, competitors’ export prices and oil prices (both expressed in the currency
basket underlying the construction of the nominal effective exchange rate) are deflated withforeign prices before linear trends are removed from the deflated variables.
For the estimation of NAWM II, we use six additional time series, which are displayedin Figure 2. First, the added financial data used in the estimation comprise time series
for 10-year government bond yields for the euro area and for the United States and acomposite euro area long-term lending rate. The euro area 10-year government bond yield
series covers, in changing composition, all sovereign issuers whose rating is AAA. It isavailable from 2004Q3 onwards, while the earlier part of the series concerns the German
10-year government bond yield. The 10-year government bond yield for the United Statescorresponds to the US 10-year treasury yield, covering the full estimation sample. The euroarea long-term lending rate is available from 2003Q1 onwards and comprises (new business)lending with an original maturity of over one year to households for house purchases and tonon-financial corporations. The sources of the financial data are the ECB’s Statistical Data
Warehouse, the Deutsche Bundesbank database, and the FRED database of the Federal
Reserve Bank of St. Louis. All data are expressed as annualised percentages.
24
In other words, the steady-state output growth rate of 1.5% is assumed to have two components: trend
labour productivity growth of 1.2% and trend labour force growth of 0.3%; see Section 3.2.1 for details. The
former component is broadly in line with average labour productivity growth over the estimation period,
whereas the latter one approximates the steady increase in labour force participation which causes an upward
trend in our (per-capita) employment measure.

ECB Working Paper Series No 2200 / November 201838

Second, we use survey data on long-term inflation expectations and long-term growth
expectations from the ECB’s Survey of Professional Forecasters (SPF) as proxy measures
for the unobserved perceived inflation objective and trend productivity growth, respectively.
These measures refer to expectations five (calendar) years ahead and are expressed in termsof annual percentages. They are available in quarterly frequency from 2001 onwards, aswell as for the respective first quarters of the years 1999 and 2000. And third, we use ameasure of the euro area output gap, which is constructed using the European Commission’s
estimate of potential output taken from the Autumn 2014 vintage of its AMECO database(after having interpolated the annual potential output data into quarterly data using a
cubic spline) and our real GDP data. The output gap measure is expressed in percent ofpotential output and covers the period from 1999Q1 onwards.
3.1.2

ShocksCommensurate with the number of time series used in the estimation, NAWM II features 24
distinct structural shocks.25 In particular, we retain the 12 structural shocks incorporated
in the original NAWM (see CCW, Section 3.2.2), including the domestic and external risk
premium shocks, which can be interpreted as (exogenous) liquidity premia driving a wedge
between the interest rate controlled by the central bank and the returns required by privatesector agents, as well as the permanent technology shock, capturing fluctuations in trend
labour productivity growth. The permanent technology shock in NAWM II is however split
into a persistent and a transitory component, giving rise to a signal-extraction problem on
the part of all agents; see Section 2.3.3.
In addition, we distinguish two structural shocks originating in the financial intermediary
sector of NAWM II: a shock to the survival rate of the model’s wholesale banks, and a shockto the mark-down parameter of its retail banks. A shock to the survival rate affects thenet worth of the wholesale banking sector and, because of the prevailing funding constraint,
their ability to originate loans, whereas a shock to the mark-down parameter of retail banks
captures shifts in their market power and drives a wedge between the wholesale lending rate
and the retail lending rate in the model. We also add shocks to the two updating equations
for the private sector’s perceived inflation objective of the central bank and for the perceived
trend growth rate. Finally, we augment the SVAR model of the foreign variables with an
25

Like in the original model, NAWM II also allows for measurement error in extra-euro area trade dataas they are prone to sizeable revisions. It also accounts for small errors in the measurement of real GDP
and the GDP deflator to alleviate discrepancies between the national accounts framework underlying theconstruction of official GDP data and the model’s aggregate resource constraint.

ECB Working Paper Series No 2200 / November 201839

equation for the US 10-year government bond yield and an associated yield shock.26
All shocks are assumed to follow first-order autoregressive processes, except for the shockto the transitory component of the permanent technology shock, the shock to the central
bank’s interest-rate rule, the shocks in the two updating equations, and the shocks in the
SVAR model of the foreign variables and in the AR model of government consumption.
These shocks are assumed to be serially uncorrelated innovations.

3.2
3.2.1

Calibration and prior distributions
Calibration

In NAWM II, all real variables are assumed to evolve along a balanced-growth path with asteady-state growth rate of 1.5% per annum, which roughly matches average per-capita real
GDP growth in the estimation sample. Consistent with the balanced-growth assumption, we
calibrate the steady-state expenditure shares of the model’s aggregate demand components
by broadly matching their empirical counterparts over the sample period; see Table 1 fordetails. Specifically, the shares of private consumption, total investment and government
consumption are set equal to, respectively, 57.5%, 21.0% and 21.5% of nominal GDP, while
the extra-euro area export and import shares are set to 16%, ensuring balanced trade insteady state. Regarding the import content of the individual expenditure components,
we choose values for the quasi-share parameters νC and νI in the model’s aggregators for
final private consumption and final investment-good production that allow the model toreplicate the import content of private consumption and total investment expenditures,
which amount to roughly 8.5% and 4.5% of nominal GDP according to data from inputoutput tables for the euro area. Similarly, we choose the quasi-share parameter νX in theexport aggregator to calibrate the import content of exports at 3%, whereas government
consumption is assumed to relate to domestic goods only (νG = 0).
Information on the calibration of selected non-financial-sector parameters of NAWM II
is presented in Table 2. Concerning preferences, the households’ discount factor β is chosen
to imply a steady-state equilibrium (net) real interest rate of 2.0% per annum, conditionalon the model’s steady-state rate of trend productivity growth. The inverse of the Frischelasticity of labour supply ζ, which is inherently difficult to identify empirically, is assigned
a value of 2 as in CCW and in line with the range of available estimates in the literature.
26

Identification of the shocks in the SVAR model is achieved by a Choleski decomposition of its estimatedvariance-covariance matrix, the ordering of variables being: foreign prices, foreign demand, foreign shortterm interest rate, foreign long-term interest rate, oil prices and competitors’ export prices.

ECB Working Paper Series No 2200 / November 201840

As regards technology parameters, we set the depreciation rate of physical capital δ equal
to 10% per annum. The capital share in the domestic firms’ intermediate-good production
technology α is set to 36%, while the fixed-cost parameter ψ is calibrated such that firms’
profits are zero in steady state. Labour productivity is assumed to rise at a trend rateof 1.2% per annum, which is broadly in line with average productivity growth over the
sample period, while employment is assumed to grow with a trend rate of 0.3% per annum,
approximating an increasing trend in labour force participation.
Our calibration of the steady-state mark-ups influencing households’ and firms’ wage
and price-setting decisions in the model follows the calibration in CCW, while the slopeof the demand elasticity implied by the Kimball aggregator used in the derivation of themodel’s generalised price Phillips curves is set uniformly equal to 10, following Coenen,
Levin, and Christoffel (2007). We also keep the values of the tax rates at the values chosen
in CCW, noting that we now allow for a wedge between the return on capital and the shortterm government bond yield which is chosen in the computation of the model’s steady state
so as to be consistent with a capital income tax rate of 30%.
With regard to monetary policy, the central bank’s long-run (net) inflation objective
is set equal to 1.9% per annum, consistent with the ECB’s quantitative definition of pricestability. The long-run inflation objective determines the model’s steady-state inflation rate,
which, in combination with a steady-state equilibrium real interest rate of 2.0% per annum,
implies a steady-state short-term nominal interest rate of 3.9% per annum.
Details on the calibration of key financial-sector parameters of NAWM II are provided
in Table 3. The behaviour of the wholesale banks in the model are governed by three
central parameters: the absconding rate Ψ, the steady-state value of the normalised start-up
fund, ϑ,27 and the steady-state value of the survival rate, θ. We calibrate these parameters tomatch certain steady-state moments. First, we set the steady-state leverage of the wholesalebanks equal to 6, which corresponds to the average asset-over-equity ratio of monetary andother financial institutions as well as non-financial corporations, with weights equal to theirshare of assets in total assets between 1999Q1 and 2014Q4 according to the euro area
sectoral accounts.28 Second, by making use of the fact that RD = R, we set the annualised
steady-state spread of the retail lending rate over the riskless rate, RI − R, equal to 2.17
27

The need for the normalisation of the start-up fund Θt arises from the fact that the start-up fund isassumed to evolve in line with consumer price inflation and trend productivity growth; see Section 2.2.3.
For details on the normalisation, see the appendix.
28
We include the leverage of non-financial corporations because, in practice, both banks and firms holdleveraged positions. In our model, firms do not hold leveraged positions, so we assign the average composite
leverage to financial intermediaries.

ECB Working Paper Series No 2200 / November 201841

percentage points, which is the average spread between the long-term cost of private-sector
borrowing and the short-term nominal interest rate over the period from 2003Q1 to 2014Q4.
Third, we set the wholesale banks’ planning horizon equal to 5 years, corresponding to asurvival rate of 0.95. The calibrated parameters are in line with those used in the related
literature (see, e.g., Gertler and Karadi 2011). As regards the behaviour of the retail banks,
we target a 10% steady-state mark-up of the retail lending rate spread, RI − R, over thewholesale lending rate spread, R̃I − R. In particular, we set the mark-down parameter ϕI
to a value such that αI (RI − R) = R̃I − R, where 1/αI = 1.1.
The decay parameters ̺I , ̺L and ̺∗L of the long-term assets in the model are calibrated
so that these assets have the same duration as long-term bonds with 10-year maturities. The
evolution of the yields of the model’s domestic and foreign government bonds can therefore
be directly matched with the developments in 10-year yields, which are among the observed
variables used in the estimation. We choose the same benchmark value for the long-term
investment loans because there are no better generally accepted measures for the maturityof long-term loans in the euro area. Our predictions about the impact of asset purchasespresented below are not sensitive to this calibration.
The supply of domestic long-term government bonds BL is calibrated such that thesteady-state bond supply QL BL equals 70% of nominal GDP, whereas the constant B L,hin the portfolio adjustment cost function of the households is chosen such that, in steadystate, 25% of the domestic long-term government bonds are held by wholesale banks. Thisis broadly consistent with the sovereign debt holdings of financial intermediaries according
to the euro area sectoral accounts. Finally, we set the efficiency costs ϑI , ϑL , and ϑ∗L ofasset purchases equal to zero. Our results are not sensitive to these parameter choices.
3.2.2

Marginal priors and system priors

Choice of marginal priors
Concerning the choice of the marginal prior distributions for the estimated parameters thatare common to NAWM II and the original NAWM, we use broadly the same priors as CCW(see Section 3.3 and Table 1).29 So our discussion here focuses on the prior distributions of
the parameters characterising the financial intermediary sector in the extended model, as
detailed in the third column of Table 4.
29

An exception is the prior distribution for the investment adjustment cost parameter, for which wehave chosen a somewhat higher mean so as to contain the heightened role of the interest-rate channel indetermining investment spending relative to consumption spending. In addition, the tightness of several
prior distributions has been moderately increased to better cope with the computational challenges that
result from the model’s high-dimensional parameter space.

ECB Working Paper Series No 2200 / November 2018

42

The means of the priors for some of the financial-sector parameters are informed by longterm averages of the relevant observables used in the estimation of NAWM II. Specifically,
the prior mean of the relative absconding rate of the domestic government bond ωL is set
equal to the ratio of the spread between the euro area 10-year AAA government bond yieldand the short-term nominal interest rate over the period from 2003Q1 to 2014Q4 (being
equal to 1.4 percentage points) and the spread between the long-term cost of borrowing andthe short-term rate without the 10% retail mark-down. The prior mean of the absconding
rate of the foreign government bond relative to the domestic bond ω̃L∗ is calibrated to equal
unity to reflect the broad similarity of the average US and euro area 10-year AAA yields
between 2003Q1 and 2014Q4.
The choice of priors for the other financial-sector parameters is more agnostic. The
prior mean of the Calvo parameter ξI governing the retail banks’ loan re-pricing decisions
is set equal to 0.75, consistent with a rather flexible re-pricing policy, while the means of
the portfolio adjustment cost parameters γLh and γL∗ of households and wholesale banks
are conservatively assigned rather small values, containing the role of financial frictions apriori. Finally, the priors for the parameters of the model’s financial shock processes follow
standard specifications of priors for structural shock processes in the literature.
Choice of system priors
The marginal prior distributions discussed so far are based on the assumption that theparameters are independent, a property which is often at odds with what is a priori envisaged. For example, certain parameters of the central bank’s interest-rate rule (68), such asφΠ and φY , are expected to be related since they are arguably influenced by the weights
given to inflation and output fluctuations in the central bank’s implicit objective function.
While these parameters should perhaps be negatively correlated in a realistic joint priordistribution, there is typically a lack of guidance from economic theory on how to model
dependence between parameters.
Although correlations between parameters can be introduced in many ways, one natural
approach is to consider particular model or system features that one would like to condition
the empirical analysis on. Several papers have introduced ways that such information can be
accounted for in DSGE models, albeit with different terminology. Del Negro and Schorfheide(2008) suggest an approach for introducing beliefs about steady-state relationships andsecond moments of the endogenous variables to avoid priors which, among other things,
assign too much mass to steady-state values and other functions of the parameters that are
eventually unreasonable. In this context, Christiano, Trabandt, and Walentin (2011) refer

ECB Working Paper Series No 2200 / November 201843

to endogenous priors and focus on the population standard deviations of observed variables
used in the estimation. Their choice of a joint Gaussian distribution for these moments ismotivated by asymptotic arguments. Andrle and Beneš (2013), on the other hand, extend
the ideas in Del Negro and Schorfheide (2008) by discussing what they call system priors, a
concept which includes priors about, for instance, conditional and unconditional population
moments, impulse-response functions, or outcomes of hypothetical policy experiments suchas the sacrifice ratio.
In this paper we follow the terminology of Andrle and Beneš (2013) and refer to asystem prior as a set of prior beliefs about certain system characteristics which can bemodelled with a suitable density function conditional on the model parameters θ. Let h(θ)
be a vector-valued function of the system features concerned and hS a vector of fictitious
measurements such thathS = h θ + ωS ,with ωS being a vector of measurement errors. This relation can be expressed as a likelihood
function (conditional density), L(h(θ)|hS ) = p(hS |h(θ)), which, when combined with amarginal prior density p(θ) and Bayes theorem, implies that p θ hS ∝ L h(θ) hS p θ .

(70)Here, the density p(θ|hS ) is the system prior, while the constant of proportionality is givenby the marginal system prior likelihood p(hS ).
To formulate a system prior for NAWM II, we focus on two system features for which
the original prior p(θ) may not be sufficiently flexible. First, the population covariancematrix of the observed variables used in the estimation of the model is a complex functionof its parameters and having reasonable prior distributions for this matrix is difficult inpractice. Second, a particularly important parameter determining the relationship between
real economic developments and inflation is the “slope” coefficient (that is, the reducedform coefficient on firms’ marginal cost) in the model’s domestic price Phillips curve. It isdeemed useful to exert some control over the prior for this parameter, instead of formulating
merely marginal priors for the underlying structural parameters.
A common prior for covariance matrices is the inverted Wishart distribution. However
this distribution is often inadequate because of its restrictive form, implying a common
number of degrees of freedom. Barnard, McCulloch, and Meng (2000) suggest to begin
from the standard decomposition of a covariance matrix into standard deviations σ and

ECB Working Paper Series No 2200 / November 201844

correlations c, and to formulate the joint prior as a marginal density for σ times a density
for c conditional on σ. Specifically, they consider a multivariate log normal prior for the
standard deviations and a joint, or marginal, uniform prior for the correlations.
We follow this approach to formulating a joint prior for the population covariance matrix for the following observed variables: real GDP, private consumption, total investment,
the GDP deflator and the private consumption deflator (with variable measurements asdetailed in Section 3.1.1). In particular, we assume that each standard deviation has a log
normal prior, while each correlation has a uniform prior with lower and upper bounds of−1 and 1, respectively. For the log normal priors we use pre-sample data for the period
1980Q2–1984Q4 to suggest a suitable mean. Specifically, we assume that the population
standard deviation of real GDP has prior mean 0.55 and standard deviation 0.1. For private
consumption we set these hyperparameters equal to 0.45 and 0.1, respectively. For total
investment they are 1.35 and 0.2, while for the GDP and private consumption deflators we
set them to 0.45 and 0.05.
Turning next to the prior distribution for the slope coefficient of the domestic
price Phillips curve (see equation (57) in Section 2.3.2), we consider the transformation
Smc = 100 smc , where
smc =



ǫH
1+
µH − 1−1
1 − ξH 1 − βξH .
ξH 1 + βχH

We assume that Smc has a gamma distribution with mean 1 and standard deviation 0.15.
The selected value of the mean is based on the estimate of the slope coefficient of the price
Phillips curve in Smets and Wouters (2007), computed from the posterior mode estimates of
the underlying parameters reported in Lindé, Smets, and Wouters (2016, Table 7; No ZLB
model) using US data until 2014Q2.
Comparing marginal and system priors
To assess the effects on the parameters from using the system prior information, we compare
the marginal system prior densities to the marginal prior densities. While the marginalpriors p(θ) have analytical expressions and allow for direct sampling, the system priordensities p(θ|hS ) are unknown, but can be estimated via standard Markov-Chain MonteCarlo (MCMC) methods. Specifically, in our application of these methods we use therandom-walk Metropolis sampler with 200,000 draws to enable kernel density estimation of
the marginal densities of the system prior; see Herbst and Schorfheide (2016, Chapter 4.1)
for details about the posterior sampler.

ECB Working Paper Series No 2200 / November 201845

The two sets of densities for the individual parameters of NAWM II are plotted inAppendix Figure A.1. It can be seen that imposing the system prior tightens the density of
the Calvo parameter ξH entering the slope coefficient of the model’s domestic price Phillips
curve. The standard deviation of the marginal system prior is estimated at 0.015, while
the standard deviation from the original marginal prior is equal to 0.0375. Furthermore,
the density of the indexation parameter χH shifts somewhat to the left due to a lower
mean of 0.72 for the system prior, compared with a mean of 0.75 for the original prior. An
explanation for these effects is arguably the fairly tight system prior on the slope coefficientof the domestic price Phillips curve.
As regards the parameters of the interest-rate rule in equation (68), the system priorinformation mainly affects the coefficient φΠ on contemporaneous inflation. For this parameter, the system prior has a higher mean and a lower standard deviation than the originalprior. Finally, and as expected, the system prior tightens the densities for some of thestandard deviations of the shock innovations, in particular for the persistent component of
the permanent technology shock, the investment-specific technology shock, and the priceand wage mark-up shocks. It is also worth pointing out that the marginal prior densities ofthe financial-sector parameters are not visibly affected by the system prior information.

3.3

Posterior distributions

The posterior distributions of NAWM II have been estimated using the random-walkMetropolis sampler, taking into account the system priors. The estimation results are basedon a Markov chain with 1,000,000 draws, with the first 500,000 draws being discarded asburn-in draws. The marginal posterior densities of the individual parameters are plottedagainst their marginal system prior densities in Appendix Figure A.2.
Convergence
A standard approach to monitoring convergence of the posterior sampler is to employ multivariate analysis of variance (MANOVA). Based on the method discussed by Brooks andGelman (1998), we have calculated the so-called multivariate potential scale reduction factor(MPSRF) that summarises the information about within-chain and between-chain variation
for a number of parallel Markov chains. The factor is greater than unity for a finite numberof posterior draws per chain and a finite number of chains. As the sampling algorithm
converges, the factor declines towards 1, with values less than 1.1 being interpreted as signsof convergence. In the upper panel of Figure 3 we have plotted sequential estimates of the
MPSRF based on five Markov chains (including the Markov chain underlying the estima-

ECB Working Paper Series No 2200 / November 201846

tion results presented subsequently in this section) each having 1,000,000 draws with thefirst 500,000 draws being discarded as burn-in draws. The sequential estimates start with
10,000 post burn-in draws and are updated every 10,000 draws. After around 175,000 postburn-in draws we find that the MPSFR has dropped below 1.1.
In addition to monitoring the MPSRF, Brooks and Gelman (1998, p. 447) suggest to
monitor the determinants of the within-chain covariance matrix and the pooled covariancematrix. These matrices are used in the computation of the MPSRF and monitoring theirdeterminants allows also checking if they both stabilise as functions of the number of posterior draws. Since the determinants can assume very small values in models with a large
number of parameters and where some are highly correlated, we have instead plotted thesequential estimates of the trace of these two matrices in the lower panel of Figure 3. If
the posterior sampler has converged, they should have the same trace when the number ofposterior draws has become sufficiently large. As can be seen from this panel, the sequential trace estimates indeed stabilise, with the trace of the pooled covariance matrix beingslightly larger than the trace of the within covariance matrix.
Financial-sector parameters
In Table 4, we first present estimation results for the parameters characterising the financial
sector in NAWM II. The entries in the posterior-mode column refer to the values of theparameters that are obtained by maximising the model’s joint posterior density. The remaining two columns report the 5% and 95% percentiles of the marginal posterior densities(see the plots in Appendix Figure A.2).
Comparing the posterior and prior densities of the financial-sector parameters gives
an indication of how informative the observed data used in the estimation, including theadditional financial data, are about the individual parameters. That is, in the case of
those parameters for which the posterior deviates from the prior, the data are likely to
be informative. Accordingly, our estimation results suggest that the observed data are
generally informative about the financial-sector parameters. The posterior estimate of therelative absconding rate for domestic (foreign) government bonds, ωL (ω̃L∗ ), turns out tobe somewhat higher (lower) than its prior. This finding implies a larger (smaller) relative“riskiness” of domestic (foreign) government bonds, compared to what is implied by the
choice of the prior mean on the basis of historical spreads (see Section 3.2.2). The posteriormode estimate of the households’ portfolio adjustment cost parameter with respect to theholdings of domestic government bonds, γLh , is 0.009, which is lower, but close to the priormean of 0.01. Volume data on (sectoral) government bond holdings or bank lending, which

ECB Working Paper Series No 2200 / November 201847

are currently not used in the estimation, could arguably be informative and help improvethe estimation of this parameter. However, our posterior mode estimate for γLh is very close
to the posterior mode estimate of 0.007 reported in Darracq Pariès and Kühl (2016), eventhough this study uses data on bank loan volumes and, moreover, employs a prior with ahigher mean and a larger standard deviation.30
Non-financial-sector parameters
In Tables 5 and 6, we report the posterior mode estimates of the parameters that arecommon to NAWM II and the original NAWM, or that relate to the other non-financial
extensions of the original model, as outlined in Section 2.3. In particular, columns 3 to 5
in the two tables show the posterior mode estimates of the individual parameters as well as
the 5% and 95% percentiles of the corresponding marginal posterior densities (see Appendix
Figure A.2), whereas columns 6 and 7 show for comparison purposes the posterior mode
estimates of the parameters of the original model as reported in CCW, Table 1, and whenre-estimated using (per-capita) data until 2014Q4.
Overall, the posterior mode estimates of the parameters characterising households’ preferences, wage and price-setting behaviour, final-good production, adjustment costs andinterest-rate setting are found to be broadly similar across the two models. That is, theestimation of the common parameters appears rather robust to the extensions of the original model and to the inclusion of the additional variables in the set of observables usedin the estimation. Nevertheless a number of estimation results are noteworthy. First, on
the real side NAWM II appears to feature, ceteris paribus, a somewhat higher degree of
intrinsic persistence when compared to the original model. The estimated habit formation
parameter κ is noticeably larger, and even more so the investment adjustment cost parameter γI . In the case of κ, the comparison with the re-estimated version of the original model
suggests that this finding may be explained by using an extended sample. Second, the estimate of the Calvo parameter ξH entering the reduced-form slope coefficient of the domestic
price Phillips curve is quite a bit lower. This, however, reflects primarily the presence of
the additional element of real rigidity represented by the calibrated Kimball parameter ǫH ,which, ceteris paribus, lowers the slope coefficient. Taking into account the system prior,
the estimate of the slope coefficient is actually 0.007 and, hence, only slightly higher than30
We have conducted sensitivity analysis using the same prior specification as in Darracq Pariès andKühl (2016), which resulted in a somewhat larger posterior mode estimate of 0.037. The findings of thequantitative analysis in this paper would not be notably different for the model’s non-financial variables if
this posterior mode estimate were to be used, except for the effects of shocks that directly affect the funding
constraint of wholesale banks, such as shocks to the banks’ survival rate or their asset holdings. Yet evenfor these shocks the differences in the effects remain contained.

ECB Working Paper Series No 2200 / November 201848

the implied estimate of 0.005 for the original model. Third, the estimate of the parameterχ̃W , which determines the degree of indexation of wages to the model’s permanent technology shock, is 0.66, compared to the implicitly calibrated value of unity in the originalmodel. This implies a lower sensitivity of wages to shifts in trend productivity growth in
the extended model. Fourth, different from the original model, the data seem to prefer a
specification of NAWM II with variable capital utilisation, with the estimate of the adjustment cost parameter γu,2 being of moderate size. Fifth, all else equal, the estimates of theinterest-rate rule parameters, which now account for a positive albeit small interest-rate
response to the level of the output gap, imply a higher degree of interest-rate smoothing
and a stronger response to inflation. Sixth, the estimates of the sensitivity parametersin the updating equations for the perceived inflation objective and the perceived growthrate of trend output are rather small, with values of 0.06 each. And finally, the estimatedsignal-to-noise ratio of the signal-extraction problem concerning the nature of the permanent technology shocks determining trend output is rather small, thereby attenuating theotherwise much stronger wealth effects on aggregate demand.

4

Model properties

In this section, we inspect the empirical properties of NAWM II by (i) examining the modelimplied sample moments of the observed variables used in its estimation, (ii) discussing
selected impulse-response functions to shed light on the propagation of its structural shocks,
with a focus on the new financial channels, (iii) interpreting the historical and the forecasterror-variance decomposition of per-capita real GDP growth in terms of structural shock
contributions, and (iv) assessing the model’s forecasting performance for a small set of theobserved variables, namely per-capita real GDP growth, GDP deflator inflation and theshort-term nominal interest-rate.

4.1

Sample moments

As the first element of our model inspection, Table 7 reports the sample means and standard
deviations implied by NAWM II for the observed variables used in its estimation, along withthe sample moments based on the observed data for the estimation sample 1985Q5–2014Q4.
The model-based sample moments have been estimated through simulation. Specifically,for each one of the 5,000 draws of parameter values from the posterior distribution that we

ECB Working Paper Series No 2200 / November 201849

use,31 a sample of the observed variables is simulated by drawing shock innovations andmeasurement errors such that the number of simulated observations matches the numberof observed data points. In doing so, the missing observations are taken into account.
For each such sample of simulated data, the sample moments of the observable variables
have thereafter been calculated. The table shows the averages of these moments as well as
their 5% and 95% percentiles. In addition, Figure 4 displays model and data-based sample
autocorrelations between real GDP and other observed variables that are endogenously
determined within NAWM II.32 In particular, the figure shows the averages of the modelbased sample autocorrelations and the 70% and 90% equal-tail credible intervals, along withthe sample autocorrelations based on the observed data.
Regarding the sample means, we conclude from Table 7 that the NAWM II-based means
are broadly in line with the data-based means. In particular, concerning the real variables
the data means are close to the model-based means with the exception of long-term growth
expectations. For the latter, the data mean is substantially higher than the model-based
mean but nevertheless well below the 95% percentile. For the nominal variables the datameans are greater than the model-based means albeit below the corresponding 95% percentiles, with the exception of the import deflator for which the data mean is smaller thanthe corresponding 5% percentile. Finally, the data means for the 10-year government bondyield and, to a lesser extent, for the short-term nominal interest rate are close to the modelbased means, whereas the data mean for the composite long-term lending rate is smaller
than the corresponding 5% percentile.
Turning to the sample standard deviations, we find for the real variables that real GDP,
consumption, investment, exports, imports and the output gap have a data-based volatility
measure that is below the 5% percentile generated by simulating NAWM II. Among thenominal variables, we likewise obtain data-based sample standard deviations less than themodel-based 5% percentiles for GDP deflator, consumption deflator and wage inflation, as
well as for long-term inflation expectations. Among the remaining seven variables only thedata-based sample standard deviation of the 10-year government bond yield is above themodel-based 95% percentile. All in all, the use of the system prior for the population covariance matrix of the observed variables (see Section 3.2.2) has been an important factor in
31

The 5,000 posterior parameter draws are taken from the 500,000 available post-burn-in draws as draw
number 1, 101, 201, etc. Compared to using all 500,000 draws, the selected sub-sample has the advantage ofcombining moderate computational costs with a lower autocorrelation among the draws. At the same time,
the length of the sub-sample retains a sufficiently high estimation accuracy.
32
We have only excluded the SPF-based long-term growth and inflation expectations from the figure forthe sake of limiting its size to one page.

ECB Working Paper Series No 2200 / November 201850

limiting the discrepancies between the model and data-based sample standard deviations,most notably for the observed real variables. Likewise the system prior for the slope coefficient of the model’s domestic price Phillips curved helped containing the implied standard
deviations for the observed nominal variables.
As to the dynamics between real GDP and 15 of the other endogenous observed variables,
as captured by their autocorrelations, Figure 4 shows that the data-based correlations are
generally inside the 90% equal-tail credible intervals of the model-based correlations. At thesame time, it is noteworthy that the data-based autocorrelations with respect to both GDP
and consumption deflator inflation are greater than the 95% percentiles of the model-based
correlations for some leads and lags around zero. Nevertheless, the overall findings suggestthat NAWM II is able to match reasonably well the fluctuations in the observations of theendogenous variables over the sample period. Moreover, these results are broadly consistent
with the findings reported in CCW for the original NAWM.

4.2

Propagation of structural shocks

To portray key features of the propagation mechanisms of NAWM II, Figures 5 to 10 show
the model’s impulse responses to a subset of its structural shocks. This subset comprises a
shock to the short-term nominal interest rate (i.e., a standard monetary policy shock), threefinancial shocks—a shock to the survival rate of the wholesale banks in the model, a shockto the market power of the retail banks, and a domestic risk premium shock—and, finally,a shock to the persistent component of the permanent technology shock (i.e., a shock to thegrowth rate of trend labour productivity). Unless otherwise stated, the figures depict themeans and the 70% and 90% equal-tail credible intervals of the impulse responses to shocks
equal to one standard deviation for the main observed variables that are endogenously
determined within NAWM II and for two unobserved state variables, namely the net worthof the wholesale banks and the Lagrange multiplier for the households’ Loan-in-Advance(LIA) constraint. These state variables play a central role in the model’s propagation
mechanism via financial channels. Like the sample moments, the credible intervals are
based on 5,000 draws from the posterior distribution of the parameters. Where available,
the figures also display the mean of the impulse responses for the original NAWM, aspresented in CCW. All impulse responses are reported as percentage deviations from themodel’s non-stochastic balanced-growth path, except for those of inflation and interest rates
which are reported as annualised percentage-point deviations.

ECB Working Paper Series No 2200 / November 201851

Shock to the short-term nominal interest rate
In Figure 5, we depict impulse responses to a shock to the short-term nominal interest rate.
The temporary increase in the short-term rate leads to a hump-shaped decline in domestic
demand, with investment falling to a considerably larger extent than private consumption.
Reflecting the enhanced transmission mechanism of NAWM II, the increase in the shortterm interest rate is propagated to households’ investment decisions through a rise in thelong-term wholesale lending rate (which is not shown in the figure but closely linked to thegovernment bond yield via a no-arbitrage condition) and its gradual pass-through to thelong-term retail lending rate for investment loans. The demand for domestic goods is further
dampened by an appreciation of the domestic currency which leads, via a deterioration of
the terms of trade, to a switch of domestic and foreign demand towards goods produced
abroad. In response to the broad-based decline in aggregate demand for domestic goods,
firms reduce their demand for labour. In equilibrium, both, employment and wages fall. The
fall in wages contributes to a decline in firms’ marginal cost which, in turn, puts downward
pressure on domestic prices.33 The decrease in domestic prices, together with the drop in
import prices triggered by the appreciation of the domestic currency, leads to a decline
in consumer prices. The trough in economic activity and inflation is reached after about
one year. Interestingly, the real effects are somewhat stronger in NAWM II than in theoriginal NAWM, while the impact on inflation seems marginally weaker once accounting
for the differential exchange-rate effect. This finding is consistent with empirical evidence
that inflation has become less sensitive to fluctuations in economic activity in recent years.
Finally, it is noteworthy that the responsiveness of both exports and imports is markedly
higher in NAWM II because of the non-zero export content of imports.
Figure 6 sheds light on the role of the financial frictions, and the implied “financial
accelerator” mechanism, in the propagation of the interest-rate shock in NAWM II. To
this end, the impulse responses of the standard version of the model are compared to the
responses of a version where the financial frictions are shut off. For computing the two
sets of impulse responses, the posterior mode estimates for the parameters of the standard
model are used.34 As the central bank raises the short-term interest rate, the present value
33

In addition, firms utilise fewer capital services due to both a gradual decline in the physical capital stock
and a downward adjustment in the capital utilisation rate. The ensuing fall in the rental rate of capital
amplifies the negative impact on marginal cost.
34h
To shut off the financial frictions, the households’ portfolio adjustment cost parameter γLand the Calvo
parameter ξI governing the loan pricing of the retail banks are both set to (values close to) zero. Without
portfolio adjustment costs, the expected excess return on long-term bonds over the deposit rate is zero torule out any arbitrage by the households. Similarly, the excess returns on investment bonds and foreign
bonds also stay zero by the no-arbitrage conditions of the wholesale bank. The zero Calvo parameter of the

ECB Working Paper Series No 2200 / November 201852

of the long-term fixed-coupon assets (i.e., investment loans and government bonds) in theportfolio of the wholesale banks in the model declines. This triggers a drop in banks’ net
worth, and the agency friction brings about an accompanying withdrawal of deposits. The
ensuing scarcity of funding forces the wholesale banks to tighten credit supply, which leads
to curtailed wholesale lending and elevated lending rates on wholesale investment loans.
Higher wholesale lending rates pass through sluggishly to retail lending rates, generatinga hump-shaped response of the latter. The evolution of the tightness of credit conditions
for new investment is best represented by the multiplier of the households’ LIA constraint.
Consistent with the sluggish increase of retail lending rates and the declining credit demand
due to the downturn, the multiplier eases initially, but it increases persistently in the medium
term signalling a deterioration in lending conditions. This leads to an amplification of thedecline in investment in the standard version of NAWM II relative to the version without
financial frictions.
Two adjustment channels attenuate the strength of the financial accelerator mechanism
amplifying the propagation of the interest-rate shock. The first is related to the availabilityof long-term government bonds and the households’ ability to invest directly into thesebonds. The expected excess return on government bonds increases in parallel with theexcess return on investment bonds to ensure the absence of arbitrage opportunities for thewholesale banks. This requires an immediate drop in the price of long-term government
bonds, which can further exacerbate the capital losses of wholesale banks. At the sametime, and mirroring the decline in bond prices, yields on long-term government bonds go
up. The higher expected return on government bonds induces households to increase theirlong-term government bond holdings through purchasing bonds from the wholesale banks.
This mitigates the tightening of the wholesale banks’ capacity to issue investment loans
and partially offsets the negative impact of the initial shock. The second effect, which also
dampens the accelerator mechanism, comes from the enhanced future profitability of thewholesale banks due to higher excess returns, which allows them to maintain a higher riskweighted leverage without violating their incentive constraint. The higher leverage eases
their balance sheet constraint ceteris paribus, but it is insufficient to offset the impact ofthe much larger drop in their net worth.
Finally, the financial frictions also bear international ramifications. In order for thewholesale banks’ no-arbitrage conditions to hold, the increase in the expected excess return
retail banks ensures that the changes in wholesale lending rates are passed through to retail lending rates
immediately. These conditions jointly imply that the relevant cost of borrowing is the deposit rate as in anenvironment without financial frictions.

ECB Working Paper Series No 2200 / November 201853

on domestic long-term government bonds has to be accompanied by an increase in the
expected excess return on foreign long-term government bonds. For this to happen, agents
have to expect a future depreciation of the domestic currency. Consequently, the initial
appreciation of the exchange rate gets amplified in the standard version of NAWM II relative
to the version without financial frictions.
Shock to the survival rate of wholesale banks
Figure 7 shows impulse responses to a shock to the survival rate of the wholesale banksin NAWM II. The temporary increase in the survival rate leads to a transitory increase inwholesale banks’ aggregate net worth since fewer existing banks, which have accumulated
retained earnings in the past, leave the financial sector. The shock, therefore, can beinterpreted also as a temporary drop in banks’ propensity to pay dividends. The increasein net worth improves their leverage ratio and allows for an easing of lending conditions.
Both the yield on long-term government bonds and the rate on long-term wholesale loans
decline, the latter being only gradually passed through to the long-term retail lending rate,
which hence displays a hump-shaped pattern. In turn, private investment is stimulated andtriggers an inflationary increase in aggregate demand, despite a temporary crowding out
of private consumption. The central bank, following its interest-rate feedback rule, raises
the short-term nominal interest rate, thereby curtailing private demand and mitigating theincrease in overall economic activity and inflation.
Shock to the mark-down parameter of retail banks
Figure 8 shows impulse responses to a shock to the mark-down parameter of the retail banks.
The temporary fall in the market power of the retail banks leads to a hump-shaped decline
in the long-term retail lending rate. Private investment is stimulated and boosts aggregate
demand, while private consumption is crowded out over the shorter term. The central
bank responds by raising the short-term interest rate, thereby dampening the stimulative
effect from lower retail lending rates. At the same time, and on the back of an equally sized
increase in the rate on deposits placed by households, the implied increase in the refinancing
costs of the wholesale banks triggers a decline in the price of their long-term assets. The
fall in asset prices in turn leads to a decline in their net worth, impairing the scope for
issuing new investment loans. In sum, while the retail price of investment loans increaseson account of the fall in retail banks’ market power, both the wholesale price of loans andthe price of long-term government bonds decrease. Mirroring the decrease in the price ofgovernment bonds, the yield on government bonds rises.

ECB Working Paper Series No 2200 / November 201854

Shock to the domestic risk premium
Figure 9 shows impulse responses to a domestic risk premium shock. The shock drives
a wedge between the interest rate on households’ deposits with wholesale banks and, inequal measure, between the one-period domestic government bond yield and the short-term
nominal interest rate controlled by the central bank. The increase in the wedge leads to aninter-temporal reallocation of private consumption expenditures towards the future, similar
to the effects of a shock to the short-term policy rate (see Figure 5). At the same time,
the present discounted value of future income from renting capital services to firms declines
and consequently the shadow price of a unit of the investment good falls, resulting in a
reduction of investment. Both, the decline in consumption and the drop in investment
causes aggregate output to fall. Accordingly, firms reduce their demand for labour, thereby
putting downward pressure on wages. In equilibrium, both, employment and wages fall.
The decline in wages contributes to a decline in firms’ marginal cost which in turn puts
downward pressure on domestic prices. The no-arbitrage condition between domestic andforeign long-term bonds induces an appreciation of the domestic currency that curtails
exports and leads foreign firms to lower the price of goods sold domestically. The decreaseof domestic prices and import prices, in turn, induces a decline in consumer prices. The
central bank responds to the decline in aggregate output and inflation by lowering the shortterm interest rate, but the implied degree of policy accommodation is insufficient to fully
offset the contractionary effect of the domestic risk premium shock. Like for the interestrate shock, the individual impulse responses across NAWM II and the NAWM are very
similar, with the responses being somewhat stronger and more drawn out for the former,
primarily because of the higher estimated degree of persistence of the shock process.
Shock to the persistent component of the permanent technology shock
Figure 10 shows impulse responses to an increase in the persistent component of the permanent technology shock. Whereas agents observe the realisation and know the persistentnature of the permanent technology shock in the original NAWM, agents in NAWM II
only observe the realisation of the composite of its persistent and transitory components
and need to solve a signal-extraction problem to infer the nature of the particular component driving the observed realisation of the composite shock. In the original model,
forward-looking households anticipate a persistent rise in their future income following thepermanent technology shock and, hence, they already increase the current levels of theirconsumption and investment expenditures. While transitory technology shocks are typically associated with a temporary decline in firms’ labour demand and a muted response

ECB Working Paper Series No 2200 / November 201855

of wages, the strong demand effect triggered by the persistent increase in the permanent
technology shock is sufficiently stimulative to push labour demand and wages up. Firms’
marginal cost of production eventually increases giving rise to upward rather than downward pressure on domestic goods prices. The central bank raises the short-term interest
rate, but the monetary policy tightening is not aggressive enough to offset the expansionary
and inflationary effect of the shock. In NAWM II, the responses are quantitatively much
more muted, reflecting the fact that agents initially do not know whether they are witnessing a persistent or a one-off increase in the permanent technology shock. Hence, expected
future income increases by less than in the original model, resulting in a more attenuatedincrease in households’ expenditures. Moreover, the inflation response is very subdued, also
on account of the merely partial indexation of wages to the permanent technology shock
further moderating the wage response in the shorter term.

4.3

Historical decomposition of real GDP growth

Historical decompositions are widely used to identify the drivers of observed economic developments through the lens of a structural model in terms of the contributions of its
estimated shocks. In accordance with this practice, we examine the contributions of thestructural shocks obtained from NAWM II to the observed fluctuations in per-capita real
GDP growth.35 In order to facilitate the presentation of the shock contributions, we focus on
the historical period from 2000 to 2014 and bundle the structural shocks into seven groups:
technology shocks, demand shocks, mark-up shocks, financial shocks, foreign shocks andperception shocks, plus a monetary policy shock.36 The technology shock group comprises
the persistent and the transitory component of the model’s permanent technology shock(which are not separately observed by the agents in the model and estimated by solving
a signal-extraction problem), the transitory technology shock and the investment-specifictechnology shock. The demand shock group includes the shocks to government consumption, to import demand and to export demand preferences, while the mark-up shock groupconsists of the shocks to the wage mark-up, the domestic price and export price mark-ups,
as well as the import price mark-up. The financial shock group comprises the domestic
and external risk premium shocks, the shock to the survival rate of the wholesale banks
35

The smoothed estimates of the model’s structural shocks and of their standardised innovation components are shown in Appendix Figures A.3 and A.4, respectively.
36
For the sake of convenience, we do not report the small contribution of the measurement errors accounted
for in the estimation of the model and the fading effect of the estimated initial conditions for its unobserved
state variables.

ECB Working Paper Series No 2200 / November 201856

and the shock to the mark-down parameter of the retail banks. The foreign shock groupassembles the innovations in the SVAR model of the foreign variables, while the perception
shocks correspond to the innovations in the updating equations for the perceived inflation
objective of the central bank and the perceived trend growth rate. Finally, the monetary
policy shock represents unanticipated deviations of the short-term nominal interest ratefrom the prescriptions of the central bank’s interest-rate feedback rule.37
The historical decomposition of per-capita real GDP growth depicted in the upper panelof Figure 11 (in terms of annual growth rates and in deviation from the model-impliedmean growth rate of 1.5%) shows that the growth acceleration both in the early years of
the period under consideration and during the run-up to the financial crisis of 2008/09
is explained to a considerable extent by positive contributions of financial shocks. These
positive contributions are expression of the very favourable financing conditions at the time,
fostering domestic demand. In both sub-periods, the financial shocks more than offset thepersistently negative contribution from adverse technology shocks, on the back of a positive
contribution from (wage) mark-up shocks reflecting a protracted period of wage moderation.
According to the decomposition, the episode of subdued growth in the interim period from2002 to 2004 is primarily attributed to the waning of favourable financing conditions, as
captured by a reversal in the previously positive contribution from financial shocks. This
reversal was arguably triggered by the global asset market disruptions around the year
2001. Throughout this interim period, favourable monetary policy shocks (i.e., a looser
stance than suggested by the interest-rate rule) supported domestic demand and prevented
a stronger slowing of real GDP growth.
The sharp and protracted decline in real GDP growth caused by the unfolding of thefinancial crisis in 2008 is attributed primarily, and in roughly equal proportions, to a large
negative contribution of foreign shocks, capturing the dramatic fall in world trade and theimplied contraction in euro area foreign demand, and a large negative contribution fromfinancial shocks. The latter contribution arguably reflects the sudden freezing of financial markets which gave rise to a surge in risk premia. The protracted slump in GDP
growth is accompanied by a lasting weakness in investment and a slowing of trend growth,
being associated with an increasing negative contribution of technology shocks. Amongthe individual technology shocks (not reported), investment-specific technology shocks and37

Note that the grouping of the shocks differs from the shock grouping for the original NAWM in CCW.
Specifically, the domestic and external risk premium shocks have been moved from the demand shock groupand the foreign shock group, respectively, to the group of financial shocks, whereas the export preference
shock has been moved from the foreign shock group to the demand shock group. Similarly, the import pricemark-up shock has been moved from the foreign shock to the mark-up shock group.

ECB Working Paper Series No 2200 / November 201857

permanent technology shocks are particularly important. The subsequent recovery in GDP
growth in late 2009 is explained by a marked turnaround in the beforehand negative contributions of the foreign and financial shocks, reflecting the stabilisation of both the world
economy and financial markets. At the same time, price and wage rigidities hampered therecovery, as reflected in the negative contribution of the mark-up shocks. While the decomposition suggests that monetary policy shocks contributed positively to the recovery, thiscontribution is found to be negative in the immediate aftermath of the crisis despite thefact that the ECB, like other major central banks around the world, rapidly reduced its key
interest rates to historically low levels in order to bolster domestic demand and stabilise
financial markets. Clearly, when interpreting this finding due account should be taken of
the fact that the ECB also swiftly implemented a number of non-standard monetary policy
measures, including the provision of unlimited liquidity to the banking system, in order tosustain financial intermediation and to maintain the availability of credit to the private sector (see ECB 2010). The effects of these non-standard measures are not directly capturedby the model-based contribution analysis, but only indirectly and, arguably, via positive
contributions of the financial shocks.
The setback in the recovery in the course of 2010 and 2011—owing to the reintensification of the financial crisis on account of elevated tensions in euro-area sovereign
debt markets—is explained to a great extent by the waning of the previously positive contribution from financial shocks (tantamount to a fresh surge in risk premia), in conjunction
with a renewed increase in the negative contribution of technology shocks against the backdrop of a further weakening of investment and a resumed slowing of trend growth. Similarly,
insufficient downward adjustment of prices and wages continued to weigh adversely on GDP
growth, as indicated by the protracted negative contribution of the mark-up shocks.
The decomposition of the contribution of the financial shock group in the lower panel of
Figure 11 reveals that, amongst the individual financial shocks, the domestic risk premium
shock explains, by and large, the greater part of the historical fluctuations in real GDP
growth. This feature reflects the fact that, when compared to the other financial shocks,
the domestic risk premium shock is the only shock that generates a degree of co-movement
amongst the different demand components of real GDP which is commensurate with thestrong co-movement in the observed data (see the corresponding impulse-response functionsin Figures 7, 8 and 9). Nevertheless, the shock to the survival rate of the model’s wholesalebanks is a significant factor in explaining the acceleration of GDP growth both in the run-up
to the financial crisis of 2008 and during the recovery following the crisis on the back of a

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declining government bond yield spread (recalling that the long-term government bond yieldin the model is matched to the euro area 10-year AAA bond yield). In contrast, the shockto the mark-down parameter of the model’s retail banks makes a more nuanced contribution
to GDP growth. In particular, its contribution is negative prior to and during the unfoldingof the financial crisis on account of a widening spread between the long-term (euro areawide composite) lending rate and the long-term government bond yield, turns positive inthe recovery (arguably reflecting the positive effects of the ECB’s liquidity measures aimed
at sustaining longer-term bank funding), and is persistently negative during the evolving
sovereign debt crisis owing to the renewed rise in the lending-rate spread.38
All in all, this section demonstrates that the contribution analysis based on the shocks
identified through the lens of NAWM II can guide the development of a compelling narrative for the fluctuations in real GDP growth observed in the past, including the crisis
years. Yet given the particular choice of observables for the government bond yield and thelending rate, and without a proper model mechanism that separates risks emerging in thegovernment bond market from risks in the financial intermediary sector, or that accounts forthe inherently non-linear nexus between these two types of risk,39 the shock contributions
identified for the different phases of the crisis need to be interpreted with due caution.

4.4

Forecast-error-variance decomposition for real GDP growth

Forecast-error-variance decompositions allow to combine, on the one hand, the statistical
approach employed in the comparison of the simulation-based sample moments of NAWM IIwith those based on the observed data and, on the other hand, the structural approach toidentifying the contributions of its estimated shocks to fluctuations in the observed databy means of historical decompositions. In particular, we can exploit the Bayesian settingof NAWM II to construct credible sets for the contributions of its shocks to the implied
forecast error variances of the observed variables at different horizons. As an example,
Table 8 reports posterior mean estimates and 90% equal-tail credible intervals for the shock
contributions to the forecast error variance of per-capita real GDP growth in the short
38

In this context it is noteworthy that a shock to the mark-down parameter of the retail banks in the model,
which brings about a fall in the lending rate, results in a marked increase in the government bond yield (seethe impulse responses in Figure 8 and the accompanying explanations). This negative conditional correlation
between the lending rate and the government bond yield is a critical factor in explaining developments inthe lending-rate spread and hence for the identification of the individual financial shocks.
39
In this respect see, for example, Bocola (2016), who examines the macroeconomic implications of sovereign credit risk in a model where banks are exposed to domestic government debt. The model features
time-variation in risk premia and occasionally binding financial constraints and therefore necessitates theuse of non-linear solution methods which are not yet applicable to large-scale models such as NAWM II.

ECB Working Paper Series No 2200 / November 201859

run (4-quarter horizon) and in the long run, based on 5,000 draws from the posterior
distribution of the model’s structural parameters. For the sake of simplifying the exposition,
the structural shocks have again been bundled into seven groups: technology shocks, demand
shocks, mark-up shocks, foreign shocks, financial shocks and perception shocks, plus amonetary policy shock.
In the short run, the observed fluctuations of real GDP growth are primarily driven
by technology and financial shocks, with shares of 28% and 22%, respectively. Among theindividual financial shocks, the domestic risk premium shock explains most of the forecast error variance (18%), while the shocks to the survival rate of wholesale banks and tothe mark-down parameter of retail banks are less important (3% and 1%, respectively).40
Concerning the individual technology shocks (not reported), the share of the investmentspecific technology shock is particularly large, while the share of the two components ofthe permanent technology shock is smaller. Moreover, the demand and the mark-up shockgroups explain 12% and 14% of the variance, while the shares due to monetary policy andforeign shocks are modest.
In the long run, the forecast error variance of real GDP growth is equal to its variance.
It is interesting to note how small the differences in the shares are when compared with theshort-run shares. The main difference is that the structural shocks account for 99% of thevariance in the long run, with the remaining 1% being due to measurement errors, rather
than 90% as is recorded for the short run. Furthermore, the importance of technology
shocks increases somewhat to roughly one-third of the variance, and investment-specificshocks remain the main contributor at 21%, while the two permanent technology shockcomponents account for approximately 8%.

4.5

Evaluation of real GDP, inflation and interest-rate forecasts

As the last element of our model inspection, we conduct an evaluation of the relative
forecasting performance of NAWM II for a small set of its observed variables over theforecast sample period 2006Q1–2014Q4. To this end, we compute root-mean-squared errors(RMSEs) of one to eight-quarter-ahead point forecasts for annual per-capita real GDP
growth, annual GDP deflator inflation and the annualised short-term nominal interest rate.
The forecasts of NAWM II are compared to forecasts from an updated version of the original
NAWM and two naı̈ve forecast benchmarks. The updated NAWM takes into account the40

Like for the historical decomposition of real GDP growth discussed above, this pattern of relative
importance is rooted in the high degree of co-movement amongst the demand components generated by thedomestic risk premium shock.

ECB Working Paper Series No 2200 / November 201860

use of per-capita data and has been estimated on the same data sample as NAWM II. Thenaı̈ve forecasts are given by the no-change/random-walk assumption (according to which thelast pre-forecast sample observation represents the forecast over the full forecast horizon)
and the pre-forecast sample mean (corresponding to a random walk with drift for the levelof real GDP).
The point forecasts are made out-of-sample with the end of the estimation sample being
gradually extended from 2005Q4 to 2013Q4. For NAWM II and the updated NAWM, thepoint forecasts for computing the RMSEs are given by the mean forecasts conditional on
the parameters being evaluated at the posterior mode. Both models are re-estimated in the
fourth quarter of each calendar year, which is a reasonable representation of how often suchmedium-scale DSGE models are re-estimated at policy institutions.41
The mean forecast paths underlying the computation of the RMSEs, also known asspaghetti plots, are displayed in Figure 12. Concerning the real GDP growth forecasts inPanel A, we find that the paths look broadly similar for NAWM II and the NAWM. Like
most macroeconomic forecasts at the time, both models substantially overpredict real GDP
growth during the unfolding of the financial crisis in 2008/09 and in the wake of its reintensification in 2012. At the same time, the NAWM has a clear tendency to underpredict
GDP growth over the years prior to the crisis and during the short-lived recovery in theinterim period from 2010 to 2012.42 Turning to the forecast paths for GDP deflator inflationin Panel B, the behaviour of the two models is quite different. Overall, the paths for
NAWM II are downward-sloping prior to the crisis and upward-sloping thereafter, while
those for the NAWM are typically hump shaped. In Panel C, we depict the forecast paths
for the short-term interest rate. It appears that the paths from NAWM II lie closer to theactual data than those from the NAWM, especially prior to the period of very low interest
rates starting towards the end of 2012. During the low interest-rate period, both models
strongly overpredict actual interest-rate developments, thereby exposing the limitations of
the simple interest-rate feedback rules assumed in the models.
In Figure 13, we have plotted the RMSEs of the model-based point forecasts relative tothe corresponding pre-forecast sample mean. Hence, values below (above) unity indicate abetter (worse) point forecasting performance than this naı̈ve benchmark. Regarding the real
GDP growth forecasts, we observe that NAWM II has slightly smaller RMSEs for all forecast
41
The recursively computed posterior mode estimates for the parameters of NAWM II are shown inAppendix Figure A.5.
42
It is interesting to observe that the share of the squared mean errors in the overall mean squared errors
for real GDP growth is greater for NAWM II than for the NAWM.

ECB Working Paper Series No 2200 / November 201861

horizons up to six quarters ahead when compared to the NAWM, while the random walk isout-performed at all horizons. Interestingly, at the outer forecast horizons the sample mean
is competitive with both NAWM II and the NAWM, with the corresponding relative RMSEs
being close to unity. As regards the forecasts of GDP deflator inflation, NAWM II performs
again slightly better than the NAWM for the forecasts up to four quarters ahead, while thesituation is reversed for the longer horizons. The random walk-based forecasts, however, aregenerally found to have smaller RMSEs, except for the two-year horizon. Compared to thepre-sample forecast mean, all model-based forecasts do better, with their relative RMSEs
lying markedly below unity.43 For the short-term nominal interest rate, NAWM II yields
somewhat better point forecasts than the NAWM and the random walk, for which we haveobtained broadly similar RMSEs. Like in the case of GDP deflator inflation, the relative
RMSEs of the model-based forecasts are substantially lower than unity.
All in all, on the basis of our limited forecast evaluation exercise, the comparative
evidence suggests that NAWM II fares quite well relative to the updated version of theoriginal NAWM and the two naı̈ve benchmarks.

5

Applications

We finally consider two applications to illustrate the potential contributions that NAWM II
can make to conducting counterfactual policy analysis at the ECB.44 The first applicationshows how the model can be used to assess the macroeconomic impact of large-scale central
bank asset purchases which were implemented by major central banks, including the ECB,
in the aftermath of the financial crisis once policy rates had reached their effective lower
bound. In this context, we highlight the role of two critical modelling assumptions that
influence the overall impact of asset purchases: the central bank’s promise to keep thepolicy rate unchanged over a number of quarters—that is, the use of forward guidance oninterest-rate policy—and the mechanism underlying the determination of the exchange rateand, thus, the strength of the exchange-rate channel of asset purchases. In the second
application we give an example of how the model can be used in a real-time setting toanalyse the adverse impact of a possible de-anchoring of longer-term inflation expectations
43
As pointed out by CCW, the good performance of the random walk-based forecasts can be explained by
the fact that inflation has been relatively stable during the EMU period. By contrast, the bad performanceof the sample mean reflects the protracted period of higher average inflation rates in the pre-EMU period.
44
For an exemplification of the basic need in policy analysis to address questions of a counterfactual
nature and of the comparative advantage of structural models, notably DSGE models, to satisfy this need,
see Coenen, Motto, Rostagno, Schmidt, and Smets (2017).

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on the macro economy in an environment where the lower bound on the short-term interest
rate is binding. From a methodological perspective, this application illustrates how existing
DSGE models can be modified to allow for both small deviations from rational expectations
and non-linear constraints on interest rates.

5.1

Macroeconomic effects of central bank asset purchases

This section illustrates how NAWM II can be used to assess the macroeconomic impactof central bank asset purchases by means of counterfactual simulations. The simulations
are designed to capture some of the key features of the ECB’s expanded asset purchaseprogramme (EAPP) as announced in January 2015. In the simulations, the total amount ofasset purchases equals 11% of nominal GDP. The share of long-term domestic government
bonds in the purchases is assumed to equal 20% and the share of long-term investment
loans is assumed to equal 80%. This composition aims to account for the fact that, inthe estimation of NAWM II, the observed variable corresponding to the long-term domestic
government bond yield only comprises the 10-year government bond yield series of sovereignissuers whose rating is AAA at a given point in time. The share of 20% government bondholdings is broadly consistent with the share of AAA government bond purchases as a shareof all purchases (70% government bond purchases, and a 30% capital key for Germany, theNetherlands and Luxembourg among the euro area countries). We consider sovereign issuerseligible for the EAPP with an investment grade rating below AAA as well as corporate bondpurchases as investment loans in the simulations. We furthermore assume that the stockof purchased assets follows a hump-shaped path, peaking 2 years after the start of the
programme and with a gradual reduction thereafter as the purchased assets mature. Thispattern is approximated with a second-order autoregressive process with parameters set
equal to 1.7 and −0.71.
Figure 14 shows the paths of key model variables for a benchmark variant of the asset
purchase simulation under two alternative assumptions about interest-rate policy. The solid
blue lines depict the variable paths when the short-term nominal interest rate is assumed to
be unconstrained and set according to the model’s interest-rate feedback rule. These paths
are reported in the form of percentage deviations from the model’s non-stochastic balancedgrowth path, except for the paths of the inflation and interest rates which are reported as
annualised percentage-point deviations. All in all, the model-based benchmark simulationsuggests that the EAPP is effective because it improves credit conditions. In particular,
the central bank asset purchases, the evolution of which is shown in the upper-left panel

ECB Working Paper Series No 2200 / November 201863

of the figure, remove assets from the wholesale banks’ balance sheets and create excess
balance sheet capacity that banks can use to extend new credit to the private sector. As aconsequence, lending conditions improve and stimulate private investment on the back of alower lending rate. Concomitantly, the lending rate spread and the expected excess returns
on government bonds fall and asset valuations rise. This generates windfall gains for thewholesale banks, raising their net worth, and allows them to loosen credit conditions further
in a positive feedback loop. The ensuing increase in aggregate demand puts upward pressure
on firms’ marginal cost of production and leads to a rise in domestic prices. The decline in
expected excess returns on domestic long-term government bonds goes hand in hand with adecrease in expected excess returns on foreign long-term government bonds, which is brought
about by an instantaneous depreciation of the domestic currency, boosting exports. Since
the evolution of the short-term nominal interest rate is governed by a standard feedback
rule, the central bank partly counteracts the increase in inflation and economic activity byraising the short-term nominal rate. The monetary policy tightening translates into a risein the short-term real interest rate and dampens private domestic demand, leading to atemporary decline in private consumption.
The blue dashed lines in Figure 14 depict the variable paths for the benchmark variantof the simulation when the central bank promises to keep the short-term nominal interest
rate unchanged for 8 quarters of the simulation. The 8-quarter interest-rate peg coincides
with the period over which net central bank asset purchases are positive. This simulationis thus tantamount to a scenario in which the policy rate is temporarily constrained by its
lower bound and the central bank employs asset purchases and forward guidance on futureinterest-rate policy to stimulate the economy. In principle, this type of simulation is prone
to the so-called forward guidance puzzle (see Del Negro, Giannoni, and Patterson 2012, andCarlstrom, Fuerst, and Paustian 2015). That is, in standard DSGE models credible nonstate-contingent announcements about future interest-rate policy can have unrealisticallylarge macroeconomic effects. To attenuate the forward guidance puzzle in our alternative
benchmark simulation, we assume that only a fraction of households and firms believe inthe central bank’s announcement about unchanged future interest rates.45 In the absence of
the immediate interest-rate hike observed in the simulation with an unconstrained nominalinterest rate, the nominal and real effects of the central bank asset purchases get elevated.
45

This approach of modelling limited credibility of policy announcements follows Coenen and Wieland(2004). To conduct the asset-purchase simulation with the imperfectly credible temporary interest-rate peg,
we make use of the code developed by Montes-Galdón (2018). In the simulation shown, it is assumed that
only 50% of households and firms find the interest-rate announcement credible. The remaining households
and firms do observe the short-term interest rate set in the current period but build expectations on theassumption that in future periods the central bank follows the standard interest-rate rule.

ECB Working Paper Series No 2200 / November 201864

Both real GDP and inflation rates increase more strongly, albeit still moderately, and thecurrency depreciation is larger than in the benchmark simulation without the temporaryinterest-rate peg.
Figure 15 compares the benchmark variant of the asset purchase simulation to an alternative variant where the riskiness of the long-term investment bonds has been increased,reflecting an environment with a more fragile financial intermediary sector.46 To focus on
the role of the riskiness of assets as such, the short-term nominal interest rate is assumed
to be unconstrained in both simulations. In the alternative simulation with heightened
riskiness of investment bonds (red dashed lines), the overall absorption of risk from banks’balance sheets through the asset purchases is significantly higher than in the benchmark
simulation (blue solid lines). The decline in the long-term lending rate therefore gets amplified, boosting the rise in investment and real GDP.
Figure 16 sheds light on the role that the modelling assumptions concerning international financial markets have on the exchange-rate channel of central bank asset purchases.
The simulation of the standard version of NAWM II with an unconstrained short-term
nominal interest rate (blue solid lines) is compared to a version where the foreign long-term
government bonds are replaced by foreign one-period bonds which can be traded directly
by domestic households (red dashed lines). In this alternative model version, the standard
uncovered interest parity condition (UIP) holds. For the counterfactual asset purchase simulation, the path of the exchange rate differs across the two versions of the model. Whereas
the exchange rate depreciates on impact in the standard NAWM II, as discussed above,
there is almost no instantaneous response of the exchange rate in the alternative version of
the model. The lack of an immediate exchange-rate depreciation also translates into a more
muted rise in consumer prices in the alternative model. At the same time, in the absence ofan exchange-rate depreciation net exports initially decline, rather than rise, mitigating theamplification in the response of real GDP all else equal. Reflecting less severe inflationarypressures, the central bank raises the short-term nominal interest rate by less than in thestandard version, thereby attenuating the decline in private consumption and exacerbating
the rise in investment.
The results of the benchmark and variant simulations of the asset purchase counterfactual for real GDP growth and consumer price inflation are summarised in Table 9. In
the benchmark simulation with an 8-quarter interest-rate peg, average annual real GDP
growth increases by 0.34 percentage point at the peak, and average annual inflation by 0.19
46

In this alternative simulation, the annualised steady-state spread of the retail lending rate over thedeposit rate was raised by 64 basis points compared to the benchmark simulation.

ECB Working Paper Series No 2200 / November 201865

percentage point. These results are broadly consistent with other quantitative model-based
assessments of the macroeconomic effects of central bank asset purchases for the euro area,
albeit at the lower end of the range of results. For example, Burlon, Gerali, Notarpietro,and Pisani (2017) use a calibrated open-economy New Keynesian model of the euro areawith preferred habitat motive as in Chen, Cúrdia, and Ferrero (2012) to compare alternative simulations of the EAPP. In their benchmark simulation with an 8-quarter interest-rate
peg, inflation increases by up to 0.8 percentage point in annualised terms and annualised
real GDP growth by about 1 percentage point. The inflation effects are more sizeable thanin the simulations based on NAWM II, most likely because Burlon et al. (2017) assume
that the central bank’s announcement to keep the short-term nominal interest rate constantis perfectly credible. Andrade, Breckenfelder, De Fiore, Karadi, and Tristani (2016) use amodified version of the New Keynesian model developed in Gertler and Karadi (2013) tosimulate the effects of the EAPP in a scenario with an endogenous lower bound constraint.
In their benchmark simulation, the central bank asset purchases increase annualised inflation by up to 0.4 percentage point and the level of real GDP by 1.1%.
Finally, the quantitative impact on the 10-year government bond yield in the modelbased asset purchase simulations is around 10 basis points. This is in the ballpark of
the effects of the EAPP announcement of 22 January 2015 on 10-year government bondyields found in event studies. Altavilla, Brugnolini, Gürkaynak, Motto, and Ragusa (2019),
for example, identify effects between 13 to 15 basis points for the 10-year German, French,
Italian and Spanish government bonds. As the announcement came only partly as a surprise,
the overall yield impact of the programme is likely to be somewhat higher; see the metaanalysis of the literature in Andrade et al. (2016).47 Thus we conclude that our estimates
based on NAWM II are at the low end, but within the range, of the available empiricalfindings concerning bond-yield reactions to large-scale asset purchases.

5.2

Consequences of a de-anchoring of longer-term inflation expectations

Longer-term inflation expectations are generally seen to be an indicator of the credibilityof central banks in achieving their inflation objectives and should, therefore, remain solidly“anchored”. In this section, we employ NAWM II to conduct a counterfactual simulation
with the aim of illustrating the macroeconomic consequences of a decline in longer-term
inflation expectations, over and above the moderate fall in inflation expectations observed on
47
Additional sensitivity analysis, which is not reported in the paper, shows that, all else equal, a higher
pace of asset purchases, commensurate with a less persistent process for the EAPP shock, results in astronger initial bond-yield reaction.

ECB Working Paper Series No 2200 / November 201866

the basis of the ECB’s Survey of Professional Forecasters (SPF) during the year 2014 (see thelower-left panel in Figure 2).48 Such a decline in expectations may reflect a growing privatesector concern that the central bank’s ability commitment to achieving, and the ability toachieve, its inflation objective over the medium term has weakened against the backdropof the prolonged period of low inflation in the aftermath of the financial crisis. The deanchoring of longer-term expectations is modelled within NAWM II through a gradual shift
in the private sector’s perceptions of the central bank’s inflation objective, which provides
the long-run “anchor” for the formation of inflation expectations (see Section 2.3.5). At
the same time, it is assumed that the central bank’s actual inflation objective guiding its
monetary policy decisions remains unchanged.
The counterfactual de-anchoring simulation is conducted relative to a baseline which represents actual economic developments until the end of 2014 (corresponding to the historical
data used in the estimation of NAWM II) and economic predictions for the following years
that arguably incorporate the anticipated macroeconomic effects of the ECB’s EAPP announcement in January 2015 and its subsequent implementation.49 In the baseline, theprivate sector’s inflation anchor is assumed to follow the movements in the observed SPF
measure of longer-term inflation expectations and, hence, it declines by about 0.1 percentage point below the central bank’s maintained inflation objective of 1.9% in the course of
2014. Thereafter, the announcement and implementation of the EAPP is assumed to havere-anchored longer-term inflation expectations. Accordingly, in the baseline, the decline in
the inflation anchor comes to a halt at the turn of the year 2014/15, and it gradually recovers along an increasing path towards 1.9% in subsequent years.50 In the counterfactual,
the evolution of the inflation anchor from the beginning of 2015 onwards is instead determined endogenously. Specifically, the inflation anchor is assumed to evolve in an adaptive
manner and to adjust downwards in response to consumer price inflation outcomes runningpersistently below the perceived inflation objective over the simulation horizon.51
The four panels in Figure 17 portray the adverse consequences of the counterfactual deanchoring of longer-term inflation expectations in comparison with the baseline paths for48

For an interpretation of this counterfactual simulation that attributes a key role to the announcementof the ECB’s asset purchases in actually preventing a de-anchoring of longer-term inflation expectations, see
Coenen and Schmidt (2016).
49
That is, to avoid double counting, the effects of the EAPP purchases, as gauged in the previous section,
are not separately accounted for in the counterfactual simulation.
50
For a description of the developments in both survey and market-based indicators of longer-term inflation
expectations in early 2015, see ECB (2015).
51
In the adaptive scheme for the inflation anchor, the weight on lagged consumer price inflation is set
equal to the posterior mode estimate of 0.058.

ECB Working Paper Series No 2200 / November 201867

annual consumer price inflation (measured in terms of the private consumption deflator),
annual per-capita real GDP growth, the output gap, and the annualised short-term nominalinterest rate (corresponding to the EONIA).52 These baseline paths were extended beyond
the year 2014 using commensurate vintages of Consensus Forecasts surveyed from financial
and economic forecasters, the Commission’s output gap forecast, as well as market-based
interest-rate expectations.53 They are represented by the blue solid lines, while the modelbased outcomes of the counterfactual de-anchoring simulation are depicted by the red dashedlines. The green solid and dash-dotted lines in the upper-left panel indicate the baseline
and the counterfactual path of the inflation anchor, respectively.
In the counterfactual, the persistently low inflation outcomes over the simulation horizon
lead to a sizeable additional downward shift in longer-term inflation expectations. The
forward-looking private-sector agents respond to the decline in expected inflation rates byreducing their price and wage claims, giving rise to self-reinforcing second-round effects. The
resulting moderate but lasting slowing of price and wage inflation towards levels consistent
with the lower inflation anchor is exacerbated by the binding effective lower bound on
nominal interest rates. The latter (marked by the pink shaded area in the lower-rightpanel) prevents the central bank from counteracting the further decline in inflation bylowering its policy rate. As a consequence, the real interest rate rises (and the real effective
exchange rate of the euro appreciates), so aggregate demand is dampened and real GDP
grows more slowly than in the baseline. The emerging slack (as indicated by the widening
output gap) lowers price pressures over and above the direct effects resulting from the fallin expectations and further hampers the inflation adjustment process.
Thus, the counterfactual simulation illustrates the importance of solidly anchoring
private-sector inflation expectations to avoid the prolongation of a period of low inflation
outcomes through expectations-driven second-round effects.

6Conclusion

In this paper, we have outlined the specification of NAWM II, which extends the original
version of the NAWM by adding a rich financial sector. Our specification of the financial
52
For conducting the counterfactual, the 3-month EURIBOR used in the estimation has been mapped
into the EONIA (Euro OverNight Index Average) so as to account more realistically for the existence of aneffective lower bound on the riskless short-term nominal interest rate in the model. In the post-financialcrisis environment of excess liquidity in money markets, the latter is given by the rate on the ECB’s deposit
facility that banks may use to make overnight deposits with the Eurosystem.
53
For details on the methodology for extending the baseline paths with predictions for a restricted set ofobserved variables, see Appendix B in Coenen and Warne (2014).

ECB Working Paper Series No 2200 / November 201868

sector distinguishes between wholesale banks, which face funding constraints inhibiting theirability to originate new loans, and retail banks, which distribute these new loans subject tostaggered loan-rate setting. This specification comes close to meeting our threefold objectiveof accounting for a genuine role of the financial sector in the wider economy, capturing theprominent role of sluggish lending rates in the monetary transmission mechanism of theeuro area, and providing a structural framework for assessing the macroeconomic impact oflarge-scale asset purchases by central banks.
We have presented estimation results for NAWM II, which are obtained by employing
Bayesian methods and using an enhanced data set including financial time-series data. The
properties of the model have been examined on the basis of selected impulse-response functions, by studying the implied historical and forecast-error-variance decompositions for real
GDP growth, by comparing its implied sample moments with those based on the data, andby evaluating its relative forecasting performance. Overall, the estimated model is found tohave economically and empirically plausible properties, including with regard to the natureand strength of the propagation of monetary and financial shocks to the wider economy andconcerning the identification of the main sources of economic fluctuations in the run-up to,during and in the aftermath of the financial crisis of 2008/09. At the same time, the established features and properties of the original NAWM have been largely preserved, including
the quantitative effects of standard monetary policy shocks on key macro variables, eventhough they are propagated through a far richer set of transmission channels in NAWM II.
Furthermore, in terms of forecasting ability, NAWM II fares quite well compared to the
NAWM as well as naı̈ve benchmarks. Finally, illustrative applications demonstrate thatthe new model can make valuable contributions to the conduct of counterfactual policy
analysis, including the quantitative assessment of the macroeconomic impact of the ECB’slarge-scale asset purchases carried out in recent years and the analysis of pertinent risks tothe economic outlook, such as a possible de-anchoring of longer-term inflation expectationsin an environment of persistently low inflation.
In the NAWM II, large-scale asset purchases exert their influence through credit easing
and the exchange-rate channel. While these channels clearly played a prominent role, othernon-modelled channels arguably also influenced the impact of these policy interventions.
For example, asset purchase programmes, which reduce long-term government bond yields,
can generate policy space that a fiscal authority can use to influence the effectiveness ofthe programmes. On the one hand, without violating deficit limits, the fiscal authority canreinforce the stimulative impact of the asset purchases by spending the gains from lower debt

ECB Working Paper Series No 2200 / November 201869

financing costs on additional fiscal expenditures or tax cuts. On the other hand, the fiscal
authority might offset part of the stimulative impact, if it were to use the flatter yield curve
to extend the maturity and, therefore, the duration risk of its outstanding debt. Such a fiscal
reaction would re-elevate the risk in private-sector financial portfolios, mitigating the initialrisk-absorbing impact of the asset purchases.54 Explicit modelling of fiscal policy reactions
can shed light on the relative importance of these mechanisms. Additionally, asset purchaseprogrammes can have a direct impact on interest-rate expectations, so they can reinforce
the strength of accompanying forward guidance announcements (Bhattarai, Eggertsson,
and Gafarov 2015). Furthermore, they can forestall a possible de-anchoring of inflation
expectations through signalling the central bank’s commitment to its medium-term inflation
objective, as illustrated by the de-anchoring counterfactual in this paper. The empiricalassessment of the strength of these channels in the euro area would be an interesting exercise.
We leave this for future research.

54

For an early assessment of this channel in the euro area, see Andrade et al. (2016).

ECB Working Paper Series No 2200 / November 201870

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Lindé, J., F. Smets, and R. Wouters (2016). Challenges for central banks’ macro models. In J. B. Taylor and H. Uhlig (Eds.), Handbook of Macroeconomics, Volume 2B,
Chapter 28, pp. 2185–2262. Amsterdam: North Holland.
Iacoviello, M. (2005). House prices, borrowing constraints, and monetary policy in thebusiness cycle. American Economic Review 95 (3), 739–764.

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Jermann, U. and V. Quadrini (2012). Macroeconomic effects of financial shocks. American
Economic Review 102 (1), 238–271.
Montes-Galdón, C. (2018). Imperfect credibility and the forward-guidance puzzle: An
empirical evaluation. Manuscript, European Central Bank.
Schorfheide, F. (2000). Loss function-based evaluation of DSGE models. Journal of Applied Econometrics 15 (6), 645–670.
Smets, F. and R. Wouters (2007). Shocks and frictions in US business cycles: A Bayesian
DSGE approach. American Economic Review 97 (3), 586–606.
Taylor, J. B. (1993). Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39 (1), 195–214.
Warne, A. (2018). YADA manual – Computational details. Manuscript, European Central
Bank, available at https://www.texlips.net/download/yada.pdf.
Woodford, M. (2001). Fiscal requirements for price stability. Journal of Money, Credit
and Banking 33 (3), 669–728.
Woodford, M. (2003). Interest and Prices: Foundations of a Theory of Monetary Policy.
Princeton: Princeton University Press.

ECB Working Paper Series No 2200 / November 201875

Appendix: The log-linearised model
In this appendix we provide details on the derivation of the log-linear version of NAWM II,
including the computation of its non-stochastic steady state, with a focus on the equations
that relate to the model’s financial-sector extension. The exposition follows closely theordering of the equations in Section 2.2 in the main text, which outlines the financial-sector
extension in non-linear form.
Transformation of variables
We start by casting the model’s structural equations into stationary form. The reason
is twofold: First, because of the assumed unit-root process underlying the evolution oflabour productivity, and consistent with the balanced-growth property of the model, allreal variables, with the exception of hours worked, have a real stochastic trend in common.
And second, as the central bank aims at stabilising inflation, rather than the price level, allnominal variables share a nominal stochastic trend.
To render the model stationary, we therefore scale all variables that share the common
real trend with the level of productivity, zt , while we divide all nominal variables by theprice of the consumption good, PC,t . In order to simplify the notation, we introduce theconvention that all transformed variables are represented by lower-case letters, instead of
the upper-case letters employed for the original variables. For example, we use yt = Yt /zt
to denote the stationary level of aggregate output, while we use pI,t = PI,t /PC,t to represent
the price of the investment good relative to the price of the consumption good.
There are, however, a few exceptions from these conventions that are noteworthy. First,
since the nominal wage rate is assumed to grow in line with productivity, it not only needs
to be transformed with the price of the consumption good, PC,t , but also with the productivity level, zt , in order to become stationary; and accordingly we define wt = Wt /(zt PC,t ).
Second, as the model’s endogenous state variables, such as the capital stock, are predetermined in a given period t, they will be scaled with the lagged value of productivity; thatis, kt = Kt /zt−1 . Third, the marginal utility of consumption needs to be scaled up withthe level of productivity to become stationary; and hence we define λt = zt Λt . And fourth,
we scale the foreign real variables with the productivity trend prevailing abroad, zt∗ , while
maintaining the assumption that zt and zt∗ share the same stochastic trend. Thus, we treatz̃t = zt /zt∗ as a stationary process that captures the degree of asymmetry in productivity
developments in the domestic versus the foreign economy.
Log-linearisation of equations around the non-stochastic steady state
After having made the necessary stationary-inducing transformations, we proceed with thederivation of the new, or modified, non-stochastic steady-state equations for NAWM II andwith the log-linearisation of the re-scaled model equations around the steady state. In sodoing, we indicate the logarithmic deviation of a variable from its steady-state value by ahat (‘c’) and define the latter implicitly by dropping the time subscript t. For example,
the log-deviation from steady state for the scaled output variable is ybt = log(yt /y).
ECB Working Paper Series No 2200 / November 2018

76

A.1

Re-scaled equations

Applying the transformations and conventions outlined above, this section lists the re-scaled
stationary equations of the financial-sector block of NAWM II.
A.1.1

Householdsp̃I,t (1 + ςt ) = Qt ǫIt

(A.1)



−1
p̃I,t it = QI,t bI,t+1 − ̺I bI,t Π−1gC,t z,t ,(A.2)

where bI,t+1 = BI,t+1 /(PC,t zt )EtbL,h,t+1 =1 + ̺I QI,t+1 (1 + ςt+1 )λt+1 −1gΠ−1βλt z,t+1 C,t+1
QI,t (1 + ςt )
1 + γL∗ −1 Et





= 1

(A.3)


λt+1 −1−1βgΠ(RL,t+1 − RD,t ) bL,h ,λt z,t+1 C,t+1(A.4)

where bL,h,t+1 = BL,h,t+1 /(PC,t zt )−1
kt+1 = (1 − δ)gz,t
kt + ǫIt it

A.1.2

(A.5)

Capital producers
p̃I,t = pI,t 1 + ΓI



gz,t

it
it−1



− Et

+ Γ′I





λt+1
β
λt

gz,t


it
it−1



gz,t

pI,t+1 Γ′I



it
it−1



it+1
gz,t+1iti2
gz,t+1 t+1
i2t



,

(A.6)

where pI,t = PI,t /PC,t
A.1.3

Wholesale banks∗
st Q∗L,t b∗,p
Q̃I,t bpI,t+1 + ωL QL,t bpL,t+1 + ωL,t
L,t+1 pY,t z̃t = Φt nwt ,

(A.7)

p
p
∗,p
∗ ∗
where bpI,t+1 = BI,t+1/(PC,t zt ), bpL,t+1 = BL,t+1/(PC,t zt ), b∗,p
L,t+1 = BL,t+1 /(PY,t zt ), st =∗ /P , z̃ = z ∗ /z and p
St PY,tY,tttY,t = PY,t /PC,tt

nwt+1 = θt+1 (R̃I,t+1 − RD,t )+∗st+1 RL,t+1
ΠY,t+1stΠ∗Y,t+1− RD,tQ̃I,t bpI,t+1!

nwt+ (RL,t+1 − RD,t )st Q∗L,t b∗,p
L,t+1 pY,t z̃t

ECB Working Paper Series No 2200 / November 2018

nwt

+ RD,t!

QL,t bpL,t+1
nwt−1nwt Π−1
C,t+1 gz,t+1 + ϑt+1 (A.8)

77where ϑt+1 = Θt+1 /(PC,t+1 zt+1 ) = ϑΦt =ω L Etω L Et

"



h
i
−1
−1
Et β λλt+1
Ω
R
Π
g
t+1
D,t
z,t+1
C,t+1
t
h
i
λt+1 −1−1
Ψt − Et β λt ΠC,t+1 gz,t+1Ωt+1 (R̃I,t+1 − RD,t )
λt+1 −1−1ΠgβΩt+1 (R̃I,t+1 − RD,t ) =λt C,t+1 z,t+1

λt+1 −1−1ΠgΩt+1 (RL,t+1 − RD,t )Et β
λt C,t+1 z,t+1stΠ∗Y,t+1− RD,t!#(A.10)=


λt+1 −1−1ΠgΩt+1 (RL,t+1 − RD,t )β
λt C,t+1 z,t+1(A.11)Ωt = (1 − θt ) + θt Ψt Φt(A.12)−1
cfI,t = bI,t+1 − ̺I Π−1
C,t gz,t bI,t

(A.13)

Retail banks




Et 

A.1.5

∗
st+1 RL,t+1
ΠY,t+1

λt+1 −1Πg −1 Ωt+1
β
λt C,t+1 z,t+1
∗
ωL,t
Et

A.1.4

(A.9)

∞
X
k=0

ξIk β kλt+k1
λt 1 − ϕIt+k






I

Q◦I,t
QI,t+k ϕt+k
I

1−ϕ
t+k


cfI,t+k+1  =

 ◦ 
QI,t
ϕIt+k

k k λt+k
Et 
ξI β
I
λt 1 − ϕt+k QI,t+k
k=0
∞
X

1−ϕI
t+k
−1
ϕI
t+k



Q̃I,t+k
cfI,t+k+1 
QI,t+k

(A.14)

Foreign assets and domestic bond supply


−1 −1
∗
Q∗L,t b∗L,t+1 − ̺∗L Π∗−1
g
z̃
z̃
b
=
t−1 L,tY,t z,t t

tbt −1−1 −1∗z̃ + Π∗−1
Y,t gz,t z̃t z̃t−1 bL,t (A.15)
pY,t st t

bL,t+1 = bL,t+1(A.16)

bt+1 = 0,(A.17)

where bL,t+1 = BL,t+1 /(PC,t zt ) and bt+1 = Bt+1 /(PC,t zt )ECB Working Paper Series No 2200 / November 201878

A.1.6

Central bank asset purchases and market clearinggQ̃I,t bgI,t+1 + QL,t bgL,t+1 + st Q∗L,t b∗,g
L,t+1 pY,t z̃t = dt+1 ,(A.18)gwhere dgt+1 = Dt+1/(PC,t zt )A.2

bI,t+1 = bgI,t+1 + bpI,t+1(A.19)

bL,t+1 = bgL,t+1 + bpL,t+1 + bL,h,t+1(A.20)∗,pb∗L,t+1 = b∗,g
L,t+1 + bL,t+1(A.21)

Non-stochastic steady stateThis section first lists the new, or modified, steady-state equations for the financial-sector
block of NAWM II. Modifications due to the new exchange-rate channel do not have any
influence on the steady state as b∗L = 0 and s = 1. Moreover, central bank holdings offinancial assets are zero in steady state, bgI = bgL = b∗,g
L = 0, so the efficiency costs related
to holding these assets have no influence on the steady state either. Thereafter, the section
explains how the steady state of NAWM II can be calculated without adding any new
equation to the system of non-linear equations that enters the computation of the steadystate of the original NAWM.
A.2.1

Households and capital producersp̃I (1 + ς) = Q p̃I = pI

γu,1 =rK
pI

pI (1 + ς) = Q

K= (1 + ς)(1 − τ K )−1 (β −1 gz + δ − 1 − τ K δ) rspread,(A.22)(A.23)

noting that the latter equation is obtained by combining the households’ first-order condiK
tions with respect to Kh,t+1 and uh,t and substituting in equation (A.22), with rspread
representing a free parameter used in the empirical implementation to calibrate the investmentto-output ratio for a given capital tax rate
bI

=

pI i
QI (1 − ̺I Π̄−1 gz−1 )1QI (β −1 Π̄gz − ̺I )(A.25)


1 + γL∗ −1 β Π̄−1 gz−1 (RL − R) bL,h ,(A.26)i = (1 − (1 − δ)gz−1 )k(A.27)(1 + ς) =bL,h =(A.24)

where we have used the fact that RD = R

ECB Working Paper Series No 2200 / November 201879

A.2.2Wholesale banks
Q̃I bpI + ωL QL bpL = Φnw(A.28)!
Q̃I bpI
QL bpLnw = θ (R̃I − R)
+ (RL − R)
+ R nwΠ̄−1 gz−1 + ϑ
nw
nw(A.29)

ΛΩΠ̄−1 R,Ψ − ΛΩΠ̄−1 (R̃I − R)

(A.30)

ωL (R̃I − R) = (RL − R)

(A.31)∗
ωL∗ (RL − R) = ωL (RL− R)(A.32)Ω = (1 − θ) + θΨΦ(A.33)

Φ =where Λ = βgz−1=

1 + ̺I Q̃I
Q̃I(A.34)RL =1 + ̺L QL
QL(A.35)∗
RL=

1 + ̺∗L Q∗L
Q∗L(A.36)R̃I

A.2.3

Retail banks
cfI= bI − ̺I bI Π̄−1 gz−1

(A.37)QI= ϕI Q̃I(A.38)QI=

1
R I − ̺I

(A.39)The retail loan rate mark-up is a proportion αI of the loan rate spread:
RI − R̃I= (1 − ϕI )(RI − ̺I ) = αI (RI − R)

ECB Working Paper Series No 2200 / November 2018

(A.40)

80

A.2.4

Steady-state calculation

For the calculation of the steady state of NAWM II, we assume that the steady-state loan
rate spread, RI − R, and the wholesale banks’ leverage in steady state, Φ, are given, andthat the absconding rate Ψ and the normalised start-up funds of new wholesale bankers
ϑ are adjusting. In the following, we first state the equations that allow to recursively
compute the state-state values of key financial-sector variables conditional on the solutionof a small system of non-linear steady-state equations. We then briefly explain how thesystem of non-linear equations for the original NAWM needs to be modified to obtain therelevant system of equations for computing the steady state of NAWM II.
First, the risk-less (gross) interest rate equals
R =

gz Π̄
1
= Π̄.
β
Λ

(A.41)

From equations (A.24) and (A.27) we get the steady-state amount of investment loans,bI=pI (1 − (1 − δ)gz−1 )k,QI (1 − ̺I Π̄−1 gz−1 )(A.42)

where the steady-state capital stock k is one of the variables which needs to be solved fornumerically.
The amount of privately intermediated government bonds are
bpL = bL − bL,h ,(A.43)

where bL,h is given by equation (A.26).
The wholesale banks’ net worth is given by equation (A.28),
nw = Φ−1 Q̃I bpI + ωL QL bpL .

(A.44)The start-up funds of new wholesale bankers are obtained from equation (A.29),
ϑ =1 − θ Π̄−1 gz−1

Q̃I bpI
QL bpL(R̃I − R)+ (RL − R)
+R
nw
nw

!!

nw.

(A.45)

From equations (A.30) and (A.33), and after some algebra, we get the absconding rate:Ψ =(1 − θ)(1 + ΦΛΠ̄−1 (R̃I − R)).
Φ(1 − θ(1 + ΦΛΠ̄−1 (R̃I − R)))

(A.46)

From equation (A.40), the steady-state mark-down of the retail banks is
ϕI

= 1−

αI (RI − R).
R I − ̺I

(A.47)

From the definitions of RI and R̃I and from equation (A.38) we can get that:R̃I= ϕI (RI − R) + (1 − ϕI )̺I + ϕI R

ECB Working Paper Series No 2200 / November 2018

(A.48)81

RL = ωL (R̃I − R) + R(A.49)∗RL= ω̃L∗ (RL − R) + R,

(A.50)

where we have made use of the fact that net-foreign-asset holdings are zero in steady stateand hence ω̃L∗ = ωL∗ /ωL .
Finally, concerning interdependencies amongst the above steady-state equations, we notethat the relationship between the input price of investment pI and the price of capital Q isgiven by equation (A.22). It depends on the Lagrange multiplier ς on the households’ LIA
constraint, which can be obtained from equation (A.25). The Lagrange multiplier enters
the combined first-order conditions for households’ physical capital holdings and the capitalutilisation rate, resulting in equation (A.23).
The combined first-order conditions for households’ capital holdings and the capitalutilisation rate are also part of the system of non-linear steady-state equations of the original
NAWM that needs to be solved using numerical methods. Hence, taking into account thedependency on the Lagrange multiplier (as well as the introduction of the free spread
K
parameter rspread) the otherwise unchanged system of non-linear steady-state equations of
the original NAWM allows to numerically determine the steady state of NAWM II.55

A.3

Log-linearised equations

Finally, this section lists the log-linearised equations of the financial-sector block of
NAWM II, which are derived as first-order approximations around the model’s nonstochastic steady state.
A.3.1

Households and capital producers

where Σt = (1 + ςt )bt = Qbt + bb̃
pI,t + ΣǫIt ,(A.51)


 h
i


b̃
pI,t = pbI,t + γI gz2 (bit − bit−1 ) − β Et bit+1 − bit − (βEt [bgz,t+1 ] − gbz,t ) (A.52)
bI,t +b̃
pI,t + bit = QΠ̄gz
Π̄gz − ̺IbbI,t+1 − ̺I bbI,t − Π
b C,t − gbz,t
Π̄gz



β̺I  bbbbbbb
QI,t + Σt = Et λt+1 − λt − ΠC,t+1 − gbz,t+1 +QI,t+1 + Σt+1
Π̄gz

(A.53)(A.54)

55
For necessary modifications of the steady-state computations that are due to the incorporation of anon-zero import content of exports, see Coenen and Vetlov (2009).

ECB Working Paper Series No 2200 / November 201882

bL,hbbL,h,t+1 = bL,hbbL,h,t+1

h
bt+1 − λbt − Π
b C,t+1 − gbz,t+1+ bL,h γL∗ −1 β Π̄−1 gz−1 Et (RL − R) λibL,t+1 − R bbǫRP+ RL R+
R, (A.55)tt

bD,t = bbwhere we have used the fact that RǫRPt + Rt and RD = R

A.3.2

b
kt+1 =

Wholesale banks
1 − δ b1−δ b
(kt − bgz,t ) + 1 −it + bǫItgz
gz(A.56)

Q̃I bpI  b̃
QI,t + bbpI,t+1
Φnw
QL bpL  bsQ∗L pY y z̃ b∗,p
+ ωL
bL,t + ωL∗
bL,t+1 , (A.57)
QL,t + bbpL,t+1 + ω
Φnw
Φnw− bp )/y, bbp= (bp− bp )/y and bb∗,p = (b∗,p − b∗,p )/y are

bt =
nw
ct +Φ

where bbpI,t+1 = (bpI,t+1
I
I,t+1
L,t+1
L
L,t+1
L,t+1
L
the wholesale banks’ asset holdings expressed as a share of steady-state output in deviationfrom the steady-state sharenw
c t+1 =

θ
Π̄gz

+

Rnw
ct +




Q̃I bpI b̃b̃ + bbp+
R̃
R(R̃I − R) Q
I I,t
I,t
I,t+1
nw




QL bpL 
bL,t+1bL,t + bbp+
RR(RL − R) Q
L
L,t+1
nw
sQ∗ pY y z̃ ∗+ L
(RL − R)bb∗,p
L,t+1
nw
!
!


Q̃I bpI
QL bpLRP
bt + b
−+−1 R R
ǫt
nw
nw
+




θ 
b C,t+1 − b
R̃I − R Φ + R θbt+1 − Π
gz,t+1 ,Π̄gz(A.58)

where we have used the fact that ϑbt+1 = 0
bt =
Φ

!
h
i
R̃I − R
bt+1 − λbt − Π
b C,t+1 − bb t+1 − Ψbt
1+
Φ Et λgz,t+1 + Ω
R
+


i 

Φ h b̃RPbtbt (A.59)
Et R̃I RI,t+1 − R b
ǫRP
+
R
+
b
ǫ
+
R
t
t
R

ECB Working Paper Series No 2200 / November 2018

83


h
i


h
i


b̃
RP
RP
b
b
b
ωL R̃I Et R
−
R
b
ǫ
+
R
=
R
E
R
−
R
b
ǫ
+
R
I,t+1
t
L t
L,t+1
t
t
t

(A.60)hi∗∗bL,t+1b Y,t+1 − Πb ∗Y,t+1 − R bb
RL
Et sbt+1 + R− sbt + Π
ǫRP
+
R
=
t
t



h
i


∗
∗
RP
b
b
ω̃L∗ (RL − R) γL∗ sb∗L,t+1 + b
ǫRP
+
ω̃
R
E
R
−
R
b
ǫ
+
R
, (A.61)
L
t
L,t+1
t
t
L
t
∗

∗
where we have used the fact that ωbL,t= γL∗ sb∗L,t+1 + bǫRP, ω̃L∗ = ωL∗ /ωL and s∗L,t+1 =t∗St Q∗t BL,t+1/PY,t Yt .

bt =
Ω

A.3.3

Retail banks
cI,t =
cf



1−

1
Ω






1 − θ bbt
θbt + 1 −
Ψt + Φ
Ω

b̃
R
I,t =

̺I Q̃I b̃b̃
QI,t − Q
I,t−1
1 + ̺I Q̃I

bL,t =R

̺L QL bbL,t−1
QL,t − Q
1 + ̺L QL

b∗
R
L,t =

̺∗L Q∗L b∗
b∗
Q −Q
L,t−1
1 + ̺∗L Q∗L L,t(A.63)(A.64)(A.65)


1
bbI,t+1 − ̺I Π̄−1 g −1 bbI,t − Π
b
−
g
b
C,t
z,t
z
1 − ̺I Π̄−1 gz−1

b◦
Q
I,t

= (1 − βξI )Et

"∞
X
k=0

h

(A.62)(A.66)#b̃ξIk β k (QbIt+k )
I,t+k + ϕib̃ + ϕb◦I,t+1 + (1 − βξI )(Q= ξI βEt Q
bIt ),
I,t(A.67)

where we have used the fact that Q◦I = ϕI Q̃I

bI,t = ξI Q
bI,t−1 + (1 − ξI )Qb◦I,t
Q
bI,t = − RI − ̺I Q
bI,t
R
RI

ECB Working Paper Series No 2200 / November 2018

(A.68)(A.69)

84

A.3.4Foreign assets and domestic bond supply
−1b∗
Q∗L bb∗L,t+1 − ̺∗L Π̄∗−1
g
b
=
z
L,t
Y

1 b
tbt + Π̄Y∗−1 gz−1bb∗L,t ,pY s(A.70)

b t = (tbt − tb) /y are expressed as a share of steadywhere both bb∗L,t+1 = (b∗L,t+1 −b∗L )/y and tb
state output in deviation from the steady-state share, and we assume that b∗L = tb = 0
bbL,t+1 = bbL,t+1
A.3.5(A.71)

bbt+1 = 0

(A.72)bg
Q̃I bbgI,t+1 + QLbbgL,t+1 + sQ∗L pY z̃bb∗,g
L,t+1 = dt+1 ,(A.73)

Central bank asset purchases and market clearing∗,g∗,gwhere bbgI,t+1 = (bgI,t+1 − bgI )/y, bbgL,t+1 = (bgL,t+1 − bgL )/y, bb∗,g
L,t+1 = (bL,t+1 − bL )/y anddbg = (dg − dg )/y are expressed as a share of steady-state output in deviation from the
t+1

t+1

g
steady-state share, and we furthermore assume that bgI = bgL = b∗,g
L =d =0bI bbI,t+1 = ybbgI,t+1 + bpIbbpI,t+1(A.74)

bb∗
b∗,g
b∗,p
L,t+1 = bL,t+1 + bL,t+1(A.76)

bLbbL,t+1 = ybbgL,t+1 + bpLbbpL,t+1 + bL,hbbL,h,t+1

ECB Working Paper Series No 2200 / November 2018

(A.75)

85

Table 1: Calibrated expenditure shares
Share

Description

Value

sC
sI
sG
sX
sIM

Private consumption
Investment
Government consumption
Exports
Imports

57.5
21.0
21.5
16.0
16.0

of which:
sIM C
sIM I
sIM G
sIM X

Import share of pr. consumption
Import share of investment
Import share of gov. consumption
Import share of exports

8.5
4.5
0.0
3.0

Note: This table provides information on the calibration of the steady-state ratios forthe different expenditure categories in NAWM II, expressed as a share of GDP. The
expenditure shares are computed using national accounts data and data from inputoutput tables, with the import shares being obtained by appropriately adjusting thequasi-share parameters ν C , ν I , ν G , and ν X in the respective final and intermediate-good
aggregators of the model.

ECB Working Paper Series No 2200 / November 201886

Table 2: Calibrated non-financial-sector parameters
Parameter

Description

Value

A. Preferencesβ†ζDiscount factor
Inverse Frisch elasticity

0.998
2.0

Depreciation rate
Capital share
Fixed cost in production
Gross labour productivity growth

0.025
0.36
0.738
1.003

Gross labour force growth

1.00075

B. Technology
δ
α
ψ‡
gz
C. Employment
gE

D. Wage and price setting
ϕW
ϕH , ϕX , ϕ∗
ηH , ηX , η ∗Wage mark-up
Price mark-up
Slope of demand elasticity

1.30
1.35
10.0

Consumption tax
Labour income tax
Employees’ social security contr.
Employers’ social security contr.
Capital income tax
Profit income tax

0.183
0.122
0.118
0.219
0.30
0.0

Gross inflation objective
Gross short-term nom. interest rate

1.00475
1.00975

E. Tax rates
τC
τN
τ Wh
τ Wf
τK
τD
F. Monetary policyΠ̄R

Note: This table provides information on the calibrated non-financial-sector parametersof NAWM II. The superscript ‘† ’ indicates that the discount factor is calibrated so that
it is consistent with a steady-state net real interest rate of 2% per annum and withsteady-state net labour productivity growth of 1.2% per annum, while the superscript ‘‡ ’indicates that the fixed cost in production is calibrated such that the intermediate-goodfirms’ profits are zero in steady state.

ECB Working Paper Series No 2200 / November 201887

Table 3: Calibrated financial-sector parameters
Parameter

Description

Value

A. Wholesale banksΨ†ϑ†θ

Absconding rate
Start-up funds
Survival rate

0.380
0.049
0.950

Mark-down parameter

0.987

B. Retail banks
ϕI ‡C. Duration of assets (= 1/(4(1 − ̺/R))
̺I ♯
̺L ♯
̺∗L ♯

Decay parameter: inv. loans
Decay parameter: dom. gov. bonds
Decay parameter: foreign gov. bonds

0.974
0.976
0.976

D. Long-term government bonds
QL sBL
B L,h /BL

Supply of bonds over GDP
Share of household bond holdings

0.7
0.75

E. Cost of asset purchases
ϑI , ϑL , ϑ∗L

Cost of asset purchases

0.0

Note: This table provides information on the calibrated financial-sector parameters of
NAWM II. The superscript ‘† ’ indicates that the absconding rate and the start-up funds
are calibrated so that the steady-state leverage ratio Φ equals 6, and the retail lending
rate spread over the deposit rate, RI − R, equals 2.17 percentage points on an annualised basis. The superscript ‘‡ ’ indicates that the retail banks’ mark-down parameteris calibrated to generate a 10% mark-up in the excess return in the retail lending rate
relative to the excess return in the wholesale lending rate. The superscript ‘♯ ’ indicatesthat the decay parameters of the loans and bonds are calibrated to reflect assets with
10-year maturity.

ECB Working Paper Series No 2200 / November 201888

Table 4: Prior and posterior distributions of estimated financial-sector parameters

Parameter

Description

Prior distribution

Posterior distribution
mode

5%

95%

gamma(0.72,0.05)
gamma(1.00,0.05)

0.83
0.96

0.78
0.90

0.91
1.03

beta(0.75,0.0375)

0.74

0.69

0.78

gamma(0.01,0.0025)
gamma(0.01,0.0025)

0.009
0.004

0.006
0.003

0.013
0.006

beta(0.75,0.05)
beta(0.75,0.05)

0.81
0.72

0.71
0.64

0.87
0.79

invgamma(0.1,2)
invgamma(0.1,2)

5.12
1.22

3.75
0.98

6.93
1.64

A. Wholesale banks
ωLω̃L∗

Absconding of dom. bonds
Absconding of foreign bonds

B. Retail banks
ξI

Calvo: price of inv. loans

C. Portfolio adjustment costs
γLh
γL∗Households
Wholesale banks

D. Autoregressive parameters of shock processesρθρϕISurvival rateMark-down parameter

E. Scaling parameters of shock processesσθσ ϕISurvival rateMark-down parameter

Note: This table provides information on the marginal prior and posterior distributions of the estimated parameters
for the financial sector of NAWM II. The prior distributions are characterised by the parameters determining theirrespective means and variances, except for the inverse gamma prior distributions for which the mode and the degrees
of freedom are reported. The posterior distributions, which also take into account the system prior, are based on a
Markov chain with 1,000,000 draws, with 500,000 draws being discarded as burn-in draws. See Appendix Figure A.2
for graphs of the marginal system prior and posterior densities of the parameters.

ECB Working Paper Series No 2200 / November 201889

Table 5: Posterior distributions of estimated non-financial-sector parameters: Model structure
Posterior distributionof NAWM II

Posterior modeof NAWM

mode

5%

95%

CCW updated

A. Preferencesκ
Habit formation

0.62

0.56

0.66

0.56

0.65

B. Wage and price setting
ξW
Calvo scheme: wages
χW
Indexation to inflation: wages
χ̃W
Indexation to productivity: wages
ξH
Calvo scheme: domestic prices
χH
Indexation: domestic prices
ξX
Calvo scheme: export prices
χX
Indexation: export prices
ξ∗
Calvo scheme: import prices
χ∗Indexation: import prices∗o
Oil import share

0.78
0.37
0.66
0.82
0.23
0.75
0.31
0.58
0.38
0.29

0.73
0.24
0.46
0.80
0.15
0.69
0.21
0.51
0.26
0.23

0.82
0.52
0.83
0.84
0.32
0.80
0.44
0.65
0.54
0.36

0.76
0.63
[1.00]
0.92
0.42
0.77
0.49
0.53
0.48
0.16

0.72
0.41
[1.00]
0.89
0.48
0.73
0.52
0.49
0.35
0.20

C. Final and intermediate-good productionµC
Subst. elasticity: consumptionµI
Subst. elasticity: investmentµX
Subst. elasticity: exportsµ∗Price elasticity: exports

2.78
1.38
0.82
1.12

2.33
1.03
0.64
0.82

3.34
1.92
1.09
1.50

1.94
1.60
—
1.03

2.54
1.94
—
1.08

D. Adjustment costs
γI
Investment
γu,2Capital utilisationγIM C
Import content: consumptionγIM I
Import content: investmentγ∗
Export market share

10.78
0.91
6.27
0.74
2.03

8.63
0.67
4.71
0.39
1.24

13.62
1.36
8.61
2.09
4.76

5.17
[Inf]
5.60
0.40
2.42

5.77
[Inf]
4.61
1.38
2.23

E. Interest-rate ruleφR
Interest-rate smoothingφΠ
Response to inflationφ∆Π
Response to change in inflation
φY
Response to output gap
φ∆Y
Response to change in output gap

0.93
2.74
0.04
0.03
0.10

0.91
2.38
0.02
0.02
0.09

0.94
3.30
0.07
0.05
0.12

0.86
1.90
0.18
[0.00]
0.15

0.86
1.86
0.22
[0.00]
0.09

F. Perception updating equations
̟Π̄pSens. of perc. inflation objective̟gp
Sens. of perc. trend growth rate

0.06
0.06

0.04
0.05

0.07
0.08

—
—

—
—

G. Employment (bridge) equation
ξE
Calvo-style weighing scheme

0.86

0.84

0.87

0.85

0.82

Parameter

Description

Y

Note: This table provides information on the marginal posterior distributions of the estimated parameters for the nonfinancial-sector model structure of NAWM II, along with posterior mode estimates of the corresponding parameters of
the original NAWM as reported in CCW and when re-estimated using (per-capita) data until 2014Q4. The posterior
distributions for NAWM II, which take into account the marginal prior distributions of the parameters and the system
prior, are based on a Markov chain with 1,000,000 draws, with 500,000 draws being discarded as burn-in draws. See
Appendix Figure A.2 for graphs of the marginal system prior and posterior densities of the parameters. For the NAWM,
entries in brackets denote calibrated values.

ECB Working Paper Series No 2200 / November 201890

Table 6: Posterior distributions of estimated non-financial-sector parameters: Shock processes
Posterior distributionof NAWM II

Posterior modeof NAWM

mode

5%

95%

CCW updated

A. Autoregressive parameters
ρRP
Domestic risk premium shockρRP ∗External risk premium shockρg z
Permanent technology shockpρg z[. . .]: persistent component
ρεTransitory technology shock
ρI
Investment-specific techn. shock
ρϕ W
Wage mark-up shock
Domestic price mark-up shockρϕ H
Export price mark-up shock
ρϕ X
ρϕ ∗
Import price mark-up shock
ρIM
Import demand shockρν ∗Export preference shock

0.97
0.99
—
0.94
0.92
0.91
0.68
0.59
0.41
0.50
0.85
0.88

0.96
0.97
—
0.92
0.87
0.86
0.61
0.51
0.33
0.42
0.73
0.74

0.97
1.00
—
0.96
0.95
0.95
0.73
0.65
0.48
0.58
0.89
0.92

0.92
0.88
0.80
—
0.90
0.71
0.67
0.40
0.38
0.55
0.86
0.81

0.97
0.99
0.70
—
0.98
0.44
0.68
0.58
0.34
0.82
0.82
0.87

B. Scaling parameters
σRP
Domestic risk premium shockσRP ∗External risk premium shock
σg zPermanent technology shock
σgzp[. . .]: persistent component
σεTransitory technology shock
σI
Investment-specific techn. shock
σ ϕW
Wage mark-up shockσ ϕH
Domestic price mark-up shock
σ ϕX
Export price mark-up shock∗σϕ
Import price mark-up shock
σIM
Import demand shockσν ∗Export preference shock
σR
Interest rate shockσΠ̄pPerc. inflation objective shock
σg pPerc. trend growth rate shock

0.14
0.13
—
0.07
1.00
0.25
0.10
0.13
0.90
1.10
6.49
7.97
0.11
0.03
0.03

0.12
0.11
—
0.06
0.81
0.22
0.08
0.11
0.78
0.94
5.26
5.40
0.10
0.02
0.02

0.17
0.19
—
0.09
1.37
0.29
0.13
0.15
1.06
1.28
9.47
14.82
0.12
0.03
0.03

0.16
0.43
0.12
—
1.13
0.41
0.11
0.12
1.06
0.97
4.60
8.07
0.12
—
—

0.12
0.19
0.50
—
0.81
0.53
0.14
0.16
1.35
1.27
6.46
8.67
0.11
—
—

C. Signal-to-noise ratio
σg2p /σg2tr Permanent technology shock

0.06

0.05

0.06

—

—

Parameter

Description

Y

z

z

Note: This table provides information on the marginal posterior distributions of the estimated parameters of the nonfinancial-sector shock processes of NAWM II, along with posterior mode estimates of the corresponding parameters of
the original NAWM as reported in CCW and when re-estimated using (per-capita) data until 2014Q4. The posterior
distributions for NAWM II, which take into account the marginal prior distributions of the parameters and the system
prior, are based on a Markov chain with 1,000,000 draws, with 500,000 draws being discarded as burn-in draws. See
Appendix Figure A.2 for graphs of the marginal system prior and posterior densities of the parameters.

ECB Working Paper Series No 2200 / November 201891

Table 7: Sample means and standard deviations of observed variables
Sample mean
Variable

Real GDP
Consumption
Investment
Exports
Imports
GDP defl. inflation
Consumption defl. inflation
Import defl. inflation
Employment
Wage inflation
Short-term nom. interest rate
Real effective exchange rate
10-year gov’t bond yieldComp. long-term lending rateLong-term inflation expect’s
Long-term growth expect’s
Output gap

NAWM II

Sample standard deviation
NAWM II

Data

Mean

5%

95%

0.38
0.38
0.37
0.38
0.37
0.47
0.47
0.47
−0.01
0.77
3.89
0.12
5.54
6.06
1.88
1.50
0.09

0.14
0.13
−0.12
−0.02
−0.05
0.16
0.16
0.09
−2.00
0.40
0.91
−11.13
4.33
4.38
0.42
0.76
−10.75

0.60
0.62
0.86
0.78
0.79
0.78
0.77
0.86
2.00
1.13
6.82
11.39
6.76
7.71
3.36
2.25
10.71

0.37
0.35
0.36
0.37
0.37
0.58
0.56
0.05
0.00
0.82
5.01
0.00
5.21
4.09
1.91
2.10
−0.01

Data

Mean

5%

95%

0.88
0.92
3.12
3.92
2.99
0.61
0.55
2.92
2.08
0.77
2.52
13.15
0.97
0.74
0.69
0.34
4.94

0.72
0.75
2.39
3.32
2.43
0.50
0.44
2.40
1.23
0.62
1.53
8.45
0.61
0.37
0.33
0.17
2.29

1.05
1.10
3.97
4.62
3.64
0.74
0.68
3.51
3.16
0.94
3.83
19.31
1.45
1.24
1.23
0.60
8.75

0.59
0.50
1.49
2.49
2.05
0.33
0.37
2.48
2.43
0.52
3.43
8.59
1.90
0.67
0.06
0.29
2.05

Note: This table reports posterior mean estimates as well as the 5% and 95% percentiles for the sample means andstandard deviations implied by NAWM II for the observed variables used in its Bayesian estimation, along with the corresponding sample moments based on the data. The model-based sample means and standard deviations are computedby simulating data with the model using 5,000 draws from the posterior distribution of its estimated parameters with
one sample path per parameter draw.

ECB Working Paper Series No 2200 / November 201892

Table 8: Forecast-error-variance decomposition for real GDP growth4-quarter horizon

Shock groupLong run

Mean

5%

95%

Mean

5%

95%

Technology
DemandMark-ups
PolicyForeign
Financialof which:dom. risk prem. shock
ext. risk prem. shock
shock to survival rate
mark-down shock
Perceptions

28
12
14
7
7
22

23
9
11
5
6
18

33
16
17
9
8
26

34
13
15
7
7
23

28
9
12
5
6
19

40
16
18
9
9
27

18
0
3
1
0

14
0
2
0
0

22
0
4
1
0

17
1
4
1
0

13
0
3
1
0

21
1
6
2
0

All

90

88

91

99

99

99

Note: This table reports posterior mean estimates as well as the 5% and 95% percentiles for the contributions of the structural shocks of NAWM II to the forecast error variance of per-capita real GDP growth at
the 4-quarter horizon and in the long run. The shock contributions are reported only for the share of theforecast errors attributable to the structural shocks (expressed in percent), while the shares of the forecast
errors due to measurement errors and unobserved state variables are skipped. The shock contributions
are computed using 5,000 draws from the posterior distribution of the model’s estimated parameters. The
structural shocks are bundled into seven groups: technology, demand, mark-up, foreign, financial andperception shocks, plus a monetary policy shock. For the financial shock group, the contributions of theindividual financial shocks are reported as well.

ECB Working Paper Series No 2200 / November 201893

Table 9: Effects of central bank asset purchases

Simulation

Benchmark w/o interest-rate peg
Benchmark w interest-rate peg

Real GDP growth (pp)Consumption
deflator inflation (pp)Year 1

Year 2

Year 3

Year 1

Year 2

Year 3

0.06
0.34

0.09
0.21

0.02
−0.04

0.03
0.19

0.03
0.18

0.01
0.12

0.07
0.04

0.12
0.08

0.05
0.05

0.03
0.01

0.03
−0.00

0.01
−0.01

Variants w/o interest-rate peg:
Higher riskiness of inv. bonds
No exchange-rate channel

Note: This table reports the NAWM II-based responses of real GDP growth and consumption deflator inflation to acentral bank asset purchase shock with a total size of 11% of GDP. The responses are expressed as average annual
percentage-point (pp) deviations from the model’s balanced-growth path. They are computed using the posteriormode estimates of the parameters of the standard model.

ECB Working Paper Series No 2200 / November 2018

94

ECB Working Paper Series No 2200 / November 2018

95

1990

2000

2010

Government consumption

-15
1980

-10

-5

0

5

10

1990

1990

2000

Exports

2000

Private consumption

2010

2010

-10
1980

-5

0

5

1980

-6

-4

-2

0

2

4

6

1990

1990

2000

Imports

2000

Total investment

2010

2010

Note: This figure shows the updated and extended time series of the observed variables used in the estimation of the original version of the NAWM. Details on
the variable transformations are provided in Section 3.1.1. Inflation and interest rates are reported in annualised percentage terms.

-5
1980

0

5

-4
1980

-4
1980
2010

-2

-2

2000

0

0

1990

2

2

Real GDP

Figure 1: Data for original model

ECB Working Paper Series No 2200 / November 201896

Note: See above.

-5
1980

0

5

1990

2000

Employment

2010

-1
1980

0

1

2

3

4

-5
1980

2010

-5
1980
2000

0

0

1990

5

5

15

10

GDP deflator

10

15

2000

1990

2000

Nominal wages

1990

Consumption deflator

2010

2010

Figure 1: Data for original model (continued)

0
1980

5

10

15

20

-40
1980

-20

0

20

40

2000

2010

1990

2000

2010

Short-term nominal interest rate

1990

Import deflator

ECB Working Paper Series No 2200 / November 2018

97

2000

2010

Note: See above.

1990

2000

2010

-100
1980

-50

0

100

150

1980

0

-20
1980

2010

2010

-5

0

5

10

50

0
1980
2000

2000

Competitors' export prices

1990

Foreign demand

10

20

30

-10
1980

-5

0

5

-10

1990

Foreign short-term interest rate

1990

Real effective exchange rate

5

10

15

20

-20
1980

-10

0

10

20

30

Figure 1: Data for original model (continued)

1990

1990

2000

Oil prices

2000

Foreign prices

2010

2010

ECB Working Paper Series No 2200 / November 2018

98

2000

2010

1990

2000

2010

Long-term growth expectations

1990

Composite long-term lending rate

-5
1980

0

5

1990

1990

2000

Output gap

2000

2010

2010

Foreign 10-year government bond yield

0
1980

5

10

15

Note: This figure shows the time series of the additional observed variables used in the estimation of NAWM II. The euro area 10-year government bond yield
series (AAA) is available from 2004Q3 onwards, while the earlier observations concern the German 10-year government bond yield. The euro area long-term
lending rate is available from 2003Q1 onwards and covers (new business) lending with an original maturity of over 1 year to households for house purchases andto non-financial corporations.

2010

1.5
1980

2000

1.5
1980

1990

2

2

3

2.5

Long-term inflation expectations

2.5

3

2010

0
1980

2000

0
1980

1990

5

5

15

10

10-year government bond yield

10

15

Figure 2: Additional financial, survey and output gap data

Figure 3: Convergence of the posterior sampling algorithm

Sequential estimates of the multivariate potential scale reduction factor (MPSRF)

2.2
2
1.8
1.6
1.4
1.2
1
4

5

6
7
8
RWM draw number (with 500,000 burn-in draws)

9

10
×10 5

Pooled and within variation in the 5 parallel MCMC chains
3.5
3
2.5
2
1.5
1
Trace: within variance
Trace: pooled variance

0.5
0
4

5

6
7
8
RWM draw number (with 500,000 burn-in draws)

9

10
×10 5

Note: The upper panel in this figure displays sequential estimates of the multivariate potential scale
reduction factor (MPSRF) for NAWM II based on five Markov chains. Each chain has 1,000,000 posteriordraws, with the first 500,000 being discarded as burn-in draws. The lower panel shows sequential estimatesof the trace of the within covariance matrix used in the computation of the MPSRF and of the trace ofthe pooled covariance matrix.

ECB Working Paper Series No 2200 / November 201899

Figure 4: Sample correlations with respect to real GDP growth

Real GDP

1

Consumption

1

0

0

-1

0

-1
-10

0
Quarters

10

Exports

1

-1
-10

0
Quarters

10

Imports1

0

0Quarters

10

1

0

0

-1

0
Quarters

10

Import defl. inflation

0
Quarters

10

Wage inflation

1
0

0Quarters

Nominal interest rate0
Quarters

10

1

0

0

0
Quarters

10Long-term lending rate0
Quarters

100Quarters

10

Real effective exchange rate
1

-10

0
Quarters

10Output gap

1
0

-1
-10

-10

-1
-10

Long-term gov. bond yield
1

-1

10

0

-1
-10

0
Quarters
Employment

1

10

0

-1

-10

-1
-10

1

GDP defl. inflation

0

-1
-10

10

-1
-10

Consumption defl. inflation
1

0
Quarters

0

-1
-10

-10

1

0

-1

Investment

1

-1
-10

0
Quarters

10

-10

0
Quarters

10

Note: This figure shows the mean (blue solid lines) and the 70% and 90% equal-tail credible intervals(grey-shaded areas) of the model-based sample correlations between real GDP growth and other observed
variables for NAWM II, along with the sample correlations based on the data (red solid lines with plus
markers). The model-based correlations are computed using 5,000 draws from the posterior distributionof the model’s estimated parameters using one simulated sample path per parameter draw.

ECB Working Paper Series No 2200 / November 2018100

Figure 5: Propagation of an interest-rate shock

Real GDP

Consumption

Investment

0.00

0.00

0.00
-0.20

-0.20

-0.20

Exports
0.00
-0.20

-0.40

-0.40

-0.40

-0.60

-0.40

-0.80
0

10 20 30
Quarters

40

0Imports

10 20 30
Quarters

40

0

GDP defl. inflation

10 20 30
Quarters

40

Consump. defl. inflation

-0.40
0

10 20 30
Quarters

0.00

0.00

-0.05

-0.05

-0.20

-0.10

-0.10

-0.40

-0.15

-0.15

Employment

10 20 30
Quarters

40

Wage inflation

0.00

0.00

-0.05

-0.10

-0.10

-0.20

-0.15

-0.30

40

-0.60
-0.80

0

40

10 20 30
Quarters

Import defl. inflation

0.00
0.00
-0.20

0

0

0.40

10 20 30
Quarters

400Nominal interest rate

10 20 30
Quarters

40

Real exchange rate
0.00
-0.20

0

10 20 30
Quarters

0.20

-0.60

10-year gov. bond yield
0.08

-0.80

0.00
0

40

-0.40

10 20 30
Quarters

400Long-term lending rate

10 20 30
Quarters

40

Net worth

0.00

-1.00
0.01

0.02
0.00
0

10 20 30
Quarters

40

-0.10

-2.00

0.00

-0.20

-3.00
0

10 20 30
Quarters

40

40Multiplier LIA constr.

0.02

0.04

10 20 30
Quarters

0.10

0.00
0.06

0

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the mean (blue solid lines) and the 70% and 90% equal-tail credible intervals(grey-shaded areas) of the impulse responses to an interest-rate shock equal to one standard deviation for
key variables of NAWM II, along with the mean (red dashed lines) of the corresponding impulse responses
to a shock of equal size for the original NAWM. For each model, the impulse responses are reported aspercentage deviations from its non-stochastic balanced-growth path, except for the impulse responses of
the inflation and interest rates which are reported as annualised percentage-point deviations. The mean
and the uncertainty bands of the impulse responses are computed for each model using 5,000 draws fromthe posterior distribution of its estimated parameters.

ECB Working Paper Series No 2200 / November 2018

101

Figure 6: Propagation of an interest-rate shock: The role of financial frictions

Real GDP

GDP defl. inflation

Investment

0.00

0.00

0.00

-0.10
-0.20

-0.05

-0.40

-0.10

0.30
0.20

-0.20

0.10

-0.30

0.00

-0.60
0

10 20 30
Quarters

040

Nominal interest rate

Price invest. bonds

10 20 30
Quarters40

0

10 20 30
Quarters

40

0

Net worthPrice gov. bonds

0.00

0.00

0.00

-0.20

-0.20

-1.00

10 20 30
Quarters

40

Exc. ret. invest. bonds
0.15
0.10
0.05

-2.00

-0.40

-0.40
0

10 20 30
Quarters

0.00
0

40

10 20 30
Quarters

40

010-year gov. bond yield Long-term lending rate
0.06

10 20 30
Quarters

40

0Multiplier LIA constr.

0.04

10 20 30
Quarters

40

Exc. ret. gov. bonds
0.10

0.00

0.04
0.02
0.02

0.05

-0.10

0.00

0.00
0

10 20 30
Quarters

40

0.00

-0.20
0

10 20 30
Quarters

40

0

HH gov. bond holdings Risk-weighted leverage

10 20 30
Quarters

40

0Exc. ret. foreign bonds

1.50

10 20 30
Quarters

40

Real exchange rate

0.00

4.00

0.10
-0.20

1.00
2.00

-0.40

0.05

0.50

-0.60
0.00

0.00
0

10 20 30
Quarters

40

0.00
0

10 20 30
Quarters

40

-0.80
0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the impulse responses to an interest-rate shock equal to one standard deviation for
key variables of the standard version of NAWM II with financial frictions (blue solid lines) and for a versionof the model without financial frictions (red dashed lines). The two sets of impulse responses are reported
as percentage deviations from the model’s non-stochastic balanced-growth path, except for the impulse
responses of the inflation and interest rates which are reported as annualised percentage-point deviations.
They are computed using the posterior mode estimates of the parameters of the standard model.

ECB Working Paper Series No 2200 / November 2018102

Figure 7: Propagation of a shock to the survival rate of wholesale banks

Real GDP

Consumption

0.60

Investment

0.50

0.40

Exports

3.00

1.50

2.00

1.00

1.00

0.50

0.00

0.00

0.00
0.20
-0.50

0.00
0

10 20 30
Quarters

40

0Imports

10 20 30
Quarters

40

0

GDP defl. inflation

0.20

0.10

0.00

0.05

10 20 30
Quarters

400Consump. defl. inflation

10 20 30
Quarters

40

Import defl. inflation
1.50

0.10

0.00

0.00

-0.05

-0.05

-0.20

0

10 20 30
Quarters

1.00
0.05

0

40

Employment

10 20 30
Quarters

40

0.00
-0.50
0

Wage inflation

10 20 30
Quarters40

10 20 30
Quarters

40

Real exchange rate
2.00

0.30

0.20

0.20

0.10

1.00

0.10
0.00

0

Nominal interest rate

0.20

0.10

0.50

0.00

0.00
0.00

-0.10
0

10 20 30
Quarters

40

010-year gov. bond yield
0.00

10 20 30
Quarters

400Long-term lending rate

10 20 30
Quarters

40

0

Net worth

10 20 30
Quarters

40

Multiplier LIA constr.
0.00

0.00
20.00

-0.10

-0.10

-1.00

10.00
-0.20

-0.20

-2.00

0.00
0

10 20 30
Quarters40

0

10 20 30
Quarters40

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the mean (blue solid lines) and the 70% and 90% equal-tail credible intervals(grey-shaded areas) of the impulse responses to a shock to the survival rate of wholesale banks equal to
one standard deviation for key variables of NAWM II. The impulse responses are reported as percentage
deviations from the model’s non-stochastic balanced-growth path, except for the impulse responses of
the inflation and interest rates which are reported as annualised percentage-point deviations. The mean
and the uncertainty bands of the impulse responses are computed using 5,000 draws from the posterior
distribution of the model’s estimated parameters.

ECB Working Paper Series No 2200 / November 2018103

Figure 8: Propagation of a shock to the mark-down parameter of retail banks

Real GDP

Consumption

0.30

0.20

0.20

0.10

0.10

0.00

Investment

Exports

2.00
0.20
1.00

0.00
0.00

-0.10

0.00
0

10 20 30
Quarters

40

-0.10
0

Imports

10 20 30
Quarters

40

0

GDP defl. inflation

0.40

0.10

10 20 30
Quarters

40

0

0.02

Consump. defl. inflation
0.02

0.00

0.00

10 20 30
Quarters

40

Import defl. inflation
0.05

0.20

0.00

0.00

-0.02

-0.02

-0.20
0

10 20 30
Quarters

040

Employment

10 20 30
Quarters

40

0Wage inflation

0.00

10 20 30
Quarters

400Nominal interest rate

10 20 30
Quarters

40

Real exchange rate
0.30

0.10

0.08
0.06
0.04
0.02
0.00
-0.02

0.05

-0.05

0.20
0.05

0.10
0.00

0.00

-0.10

-0.05
0

10 20 30
Quarters

040

10 20 30
Quarters

40

010-year gov. bond yield
Long-term lending rate
0.04
0.00

10 20 30
Quarters

40

0

Net worth

10 20 30
Quarters

40

Multiplier LIA constr.
0.00

0.00
0.02
-0.10
0.00

0

10 20 30
Quarters

40

-0.50

-1.00

-1.00

-1.50

-0.20

-0.02

-0.50

0

10 20 30
Quarters40

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the mean (blue solid lines) and the 70% and 90% equal-tail credible intervals(grey-shaded areas) of the impulse responses to a shock to the mark-down parameter of retail banks equal
to one standard deviation for key variables of NAWM II. The impulse responses are reported as percentage
deviations from the model’s non-stochastic balanced-growth path, except for the impulse responses of theinflation and interest rates which are reported as annualised percentage-point deviations. The mean and theuncertainty bands of the impulse responses are computed using 5,000 draws from the posterior distributionof the model’s estimated parameters.

ECB Working Paper Series No 2200 / November 2018104

Figure 9: Propagation of a domestic risk premium shock

Real GDP

Consumption

0.00

0.00

-0.20

-0.20

Investment
0.00

-0.20
-0.50

-0.40

-0.40

-0.40

-1.00

-0.60

-0.60

Exports
0.00

-0.60
-0.80

-0.80
0

10 20 30
Quarters

40

0Imports
0.00
-0.20
-0.40
-0.60
10 20 30
Quarters

40

GDP defl. inflation

0.20

0

10 20 30
Quarters

0

0.00

-0.10

-0.10

-0.20

-0.20

-0.30

-0.30
0

Employment

10 20 30
Quarters

40

-0.10
-0.20

0

10 20 30
Quarters

40

Import defl. inflation
0.00

-0.50

-1.00
0

Wage inflation

0.00

40

Consump. defl. inflation

0.00

40

10 20 30
Quarters

10 20 30
Quarters

400Nominal interest rate

10 20 30
Quarters

40

Real exchange rate

0.00

0.00

0.00

-0.20

-0.20

-0.50

-0.40

-0.40
-1.00

-0.60

-0.30
0

10 20 30
Quarters

40

-0.60
0

10 20 30
Quarters

40

010-year gov. bond yield
Long-term lending rate
0.04
2.00
0.00
0.02
1.00
0.00
-0.02
-0.02
-0.04
0.00
-0.04
-0.06
-0.06
-1.00
-0.08
-0.08
0

10 20 30
Quarters40

0

10 20 30
Quarters40

10 20 30
Quarters

40

0

Net worth

10 20 30
Quarters

40

Multiplier LIA constr.
0.10

0.00

-0.10
0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the mean (blue solid lines) and the 70% and 90% equal-tail credible intervals(grey-shaded areas) of the impulse responses to a domestic risk premium shock equal to one standard
deviation for key variables of NAWM II, along with the mean (red dashed lines) of the corresponding
impulse responses to a shock of equal size for the original NAWM. For each model, the impulse responses
are reported as percentage deviations from its non-stochastic balanced-growth path, except for the impulse
responses of the inflation and interest rates which are reported as annualised percentage-point deviations.
The mean and the uncertainty bands of the impulse responses are computed for each model using 5,000
draws from the posterior distribution of its estimated parameters.

ECB Working Paper Series No 2200 / November 2018105

Figure 10: Propagation of a permanent technology shock: Persistent component

Real GDP

Consumption

Investment

1.00

1.00

Exports

2.00
1.00
1.00

0.50

0.50
0.00

0.50

0.00
0

10 20 30
Quarters

40

0.00

0.00
0

Imports

10 20 30
Quarters

40

GDP defl. inflation

1.50

0

10 20 30
Quarters

40

Consump. defl. inflation
0.20

10 20 30
Quarters
Employment

10 20 30
Quarters

40

Wage inflation

0.15

-0.20

0.00
0

40

Import defl. inflation

-0.10

0.00
0

40

0.00

0.10

0.10

0.00

10 20 30
Quarters

0.10

0.20
1.00
0.50

0

0

0.15

1.00

10 20 30
Quarters

400Nominal interest rate

10 20 30
Quarters

40

Real exchange rate
0.00

0.10

0.10

-0.20
0.50

0.05

0.05
0.00
0

10 20 30
Quarters

40

-0.40

0.00

0.00
0

10 20 30
Quarters

40

010-year gov. bond yield
Long-term lending rate
0.08
0.08
0.00
0.06

0.06

0.04

0.04

0.02

0.02

0.00

0.00
0

10 20 30
Quarters40

10 20 30
Quarters

40

Net worth

40

40

0.02
0.00
-0.02
-0.04
-0.06
-0.08

-2.00
10 20 30
Quarters

10 20 30
Quarters

Multiplier LIA constr.

-1.00

0

0

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the mean (blue solid lines) and the 70% and 90% equal-tail credible intervals(grey-shaded areas) of the impulse responses to an increase in the persistent component of the permanent
technology shock equal to one standard deviation for key variables of NAWM II, along with the mean
(red dashed lines) of the corresponding impulse responses to a shock of equal long-run impact for theoriginal NAWM. For each model, the impulse responses are reported as percentage deviations from its
non-stochastic balanced-growth path, except for the impulse responses of the inflation and interest rates
which are reported as annualised percentage-point deviations. The mean and the uncertainty bands of theimpulse responses are computed for each model using 5,000 draws from the posterior distribution of its
estimated parameters.

ECB Working Paper Series No 2200 / November 2018106

Figure 11: Historical decomposition of real GDP growth

Annual per-capita real GDP growth in deviation from mean

6

4

2

0

-2

-4

-6

-8

-10
2000

Technology
DemandMark-ups
PolicyForeign
Financial
Perceptions
Real GDP growth
2002

2004

2006

2008

2010

2012

2014

Contribution of financial shocks to annual per-capita real GDP growth

4

2

0

-2

-4
2000

Dom. risk premium
Ext. risk premiumMark-down parameter
Survival rate
Financial shocks
2002

2004

2006

2008

2010

2012

2014

Note: The upper panel in this figure depicts the decomposition of annual per-capita real GDP growth
into the contributions of the structural shocks of NAWM II over the period 2000 to 2014. The shocks arebundled into seven groups: technology, demand, mark-up, foreign, financial and perception shocks, plus
a monetary policy shock. The decomposition is computed in deviation from the model-implied mean real
GDP growth rate using the posterior mode estimates of the model’s estimated parameters. The lower panel
shows the contributions of the individual financial sector shocks in the real GDP growth decomposition.

ECB Working Paper Series No 2200 / November 2018107

Figure 12: Mean paths of real GDP, inflation and interest-rate forecasts

A. Real GDP growth5

NAWM II

NAWM

5

0

0

-5

-5

-10
2004 2006 2008 2010 2012 2014-102004 2006 2008 2010 2012 2014

5

No change

5

Sample mean

0

0

-5

-5

-10
2004 2006 2008 2010 2012 2014-102004 2006 2008 2010 2012 2014

B. GDP deflator inflation
4

NAWM II

4

NAWM

2

2

0

0

-2
2004 2006 2008 2010 2012 2014-2
2004 2006 2008 2010 2012 2014

4

No change

4

Sample mean

2

2

0

0

-2
2004 2006 2008 2010 2012 2014-2
2004 2006 2008 2010 2012 2014

Note: For NAWM II, the original NAWM, and two naı̈ve benchmarks (the no change/random walk andthe sample mean), this figures shows the mean paths of unconditional one to eight quarter-ahead forecasts
for annual per-capita real GDP growth, annual GDP deflator inflation and the annualised short-term
nominal interest rate. The forecasts are computed out-of-sample over the period 2006Q1 to 2014Q4. For
NAWM II and the NAWM, the forecasts are given by the means of the predictive densities conditional on
the posterior mode estimates of the model’s parameters.

ECB Working Paper Series No 2200 / November 2018108

Figure 12: Mean paths of real GDP, inflation and interest-rate forecasts (continued)

C. Short-term nominal interest rate
8

NAWM II

8

NAWM

6

6

4

4

2

2

0
2004 2006 2008 2010 2012 201402004 2006 2008 2010 2012 20148

No change

8

Sample mean

6

6

4

4

2

2

0
2004 2006 2008 2010 2012 201402004 2006 2008 2010 2012 2014

Note: See above.

ECB Working Paper Series No 2200 / November 2018109

Figure 13: Root-mean-squared errors of real GDP, inflation and interest-rate forecasts

Real GDP growth

2

0.4

1

0.5

0.3

0.2

0
4

6

8

0.2
NAWM II
NAWM
No change

0.1

0.1
2

Short-term nominal interest rate

0.3

RMSE

0.4

RMSE

1.5

RMSE

GDP deflator inflation

0.5

0
2

Prediction horizon

4

6

Prediction horizon

8

2

4

6

8

Prediction horizon

Note: For NAWM II, the original NAWM, and a naı̈ve benchmark (the no change/random walk), this figure
shows the root-mean-squared errors (RMSEs) of one to eight-quarter-ahead forecasts for annual per-capita
real GDP growth, annual GDP deflator inflation and the annualised short-term nominal interest rate,
relative to the RMSEs of their sample mean forecasts. RMSEs below (above) unity reflect a better (worse)
point forecasting performance than the sample mean. The forecasts are computed out-of-sample over theperiod 2006Q1 to 2014Q4. For NAWM II and the NAWM, the forecasts are given by the means of thepredictive densities conditional on the posterior mode estimates of the model’s parameters.

ECB Working Paper Series No 2200 / November 2018110

Figure 14: Effects of central bank asset purchases

Asset purchase shock

Real GDP

Investment

Consumption

0.60

0.30

10.00

1.50

0.20

0.40

1.00

0.10

5.00

0.20
0.00

0.00
0

10 20 30
Quarters

040

10 20 30
Quarters

Exports

0.00

0.50

-0.10

0.00

40

0

10 20 30
Quarters

40

GDP defl. inflation

Imports
0.30

0.60

0.20

0.40

10 20 30
Quarters

40

Consump. defl. inflation

0.20
0.80

0

0.20

0.10

0.10

0.00

0.00

0.10

0.20

0.00

0.00
0

10 20 30
Quarters40

0

10 20 30
Quarters

Employment40

0

10 20 30
Quarters

40

Nominal interest rate

Wage inflation

0.10

10 20 30
Quarters

40

Real exchange rate
1.00

0.30

0.20

0

0.05

0.20
0.10

0.50
0.10

0.00

0.00

0.00
0

10 20 30
Quarters

40

010-year gov. bond yield
0.00

0.00
10 20 30
Quarters

40

Long-term lending rate

-0.02

2.00

-0.04

0.00

-0.06

-2.00

-0.08

-0.10
0

10 20 30
Quarters40

10 20 30
Quarters40

0

10 20 30
Quarters

40

Multiplier LIA constr.

Net worth

4.00

0.00

-0.05

0

0.00
-0.20
-0.40
-0.60

-4.00
0

10 20 30
Quarters40

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the impulse responses to a central bank asset purchase shock with a total size of 11%
of GDP for key variables of NAWM II when using the benchmark simulation set-up with an endogenous
short-term nominal interest rate reaction (blue solid lines) and when using the benchmark set-up with
the nominal interest rate being kept unchanged for eight quarters and with imperfect credibility of thecentral bank’s announcement thereof (blue dashed lines). The two sets of impulse responses are reported
as percentage deviations from the model’s non-stochastic balanced-growth path, except for the impulse
responses of the inflation and interest rates which are reported as annualised percentage-point deviations.
They are computed using the posterior mode estimates of the model’s parameters.

ECB Working Paper Series No 2200 / November 2018111

Figure 15: Effects of asset purchases: The role of the riskiness of assets

Asset purchase shock
10.00

Real GDP
0.20

0.20

1.00

5.00

0.10

0.00

0.00

0.00

-0.20

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

0.00
0

10 20 30
Quarters

00Consump. defl. inflation

10 20 30
Quarters

0.00

0.00

-0.02

-0.02

40

0

Wage inflation

10 20 30
Quarters

40

0.10

0.00
0.00

-0.02
0

10-year gov. bond yield
0.00

10 20 30
Quarters40

0

10 20 30
Quarters

40

0.00
-0.20

0.00
-0.05

-0.40

-2.00

-0.06

-0.60

-4.00

-0.80

-0.10
10 20 30
Quarters

40

40Multiplier LIA constr.

2.00

0

10 20 30
Quarters

4.00

-0.02

-0.08

0

Net worthLong-term lending rate

0.00

-0.04

Real exchange rate

0.20

0.00

40

40

0.05

0.02

10 20 30
Quarters

10 20 30
Quarters

0.40

0.04

0

0

Nominal interest rate

0.06

-0.05

40

0.02

Employment

0.00

10 20 30
Quarters

0.02

0.10
0.05

40

0.04

0

40

10 20 30
Quarters

GDP defl. inflation

Imports
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04

0.20

0.50
0.00

Exports
0.40

Investment

Consumption

0

10 20 30
Quarters40

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the impulse responses to a central bank asset purchase shock with a total sizeof 11% of GDP for key variables of NAWM II when using the benchmark simulation set-up (blue solidlines) and when using an alternative simulation set-up with a higher riskiness of the long-term investment
bonds (red dashed lines). The two sets of impulse responses are reported as percentage deviations fromthe model’s non-stochastic balanced-growth path, except for the impulse responses of the inflation andinterest rates which are reported as annualised percentage-point deviations. They are computed using theposterior mode estimates of the model’s parameters.

ECB Working Paper Series No 2200 / November 2018112

Figure 16: Effects of asset purchases: The role of the exchange-rate channel

Real GDP

Asset purchase shock

Consumption

Investment

0.20
10.00

1.00

0.10
0.10

5.00
0.00

0.00

0.50

-0.10

0.00

0.00
0

10 20 30
Quarters40

0

10 20 30
Quarters

Exports40

0

10 20 30
Quarters

40

Consump. defl. inflation

0.02

0.20

0.00

0.00

0.00

0.00

-0.02

-0.20
40

40

0.02

0.20

10 20 30
Quarters

10 20 30
Quarters

GDP defl. inflation

Imports

0.40

0

0

0

10 20 30
Quarters

40

-0.02
0

40

0

0.06

10 20 30
Quarters

40

Real exchange rate

Nominal interest rate

Wage inflation

Employment

10 20 30
Quarters

0.10

0.06
0.04

0.04
0.02

0.02

0.00

0.00

0.40
0.05
0.20
0.00

-0.02

0.00

-0.02

-0.04
0

10 20 30
Quarters

40

010-year gov. bond yield
0.00

-0.05

10 20 30
Quarters

40

4.00

-0.02

2.00

-0.04

0.00

-0.06

-2.00

0

10 20 30
Quarters40

10 20 30
Quarters

40

0

Net worthLong-term lending rate

0.00

10 20 30
Quarters

40

Multiplier LIA constr.
0.00

-0.08

-0.10

0

-0.20
-0.40
-0.60

-4.00
0

10 20 30
Quarters40

0

10 20 30
Quarters40

0

10 20 30
Quarters

40

Note: This figure shows the impulse responses to a central bank asset purchase shock with a total size of
11% of GDP for key variables of the standard version of the NAWM II with a no-arbitrage condition for
long-term government bonds determining the exchange-rate response (blue solid lines) and for a versionof the model in which this no-arbitrage condition is replaced by the standard UIP condition (red dashedlines). The two sets of impulse responses are reported as percentage deviations from the model’s nonstochastic balanced-growth path, except for the impulse responses of the inflation and interest rates which
are reported as annualised percentage-point deviations. They are computed using the posterior mode
estimates of the parameters of the standard model.

ECB Working Paper Series No 2200 / November 2018113

Figure 17: Consequences of a de-anchoring of longer-term inflation expectations

Consumer price inflation

3.0

Percentages

2.0

Percentages

Real GDP growth

4.0

1.0
Baseline (BL)

2.0

0.0

Counterfactual (CF)

0.0

2011

Inflation anchor: BL
Inflation anchor: CF

2012

2013

2014

2015

2016

-2.0
2011

2017

2012

2013

Years

Output gap

1.5

2015

2016

2017

Short-term nominal interest rate

1.0

0.0

Percentages

Percentages

2.0

2014

Years

-2.0

0.5

0.0
-4.0
2011

2012

2013

2014

2015

2016

2017

Years

2011

2012

2013

2014

2015

2016

2017

Years

Note: This figure shows the results of the counterfactual simulation of a de-anchoring of longer-term inflation expectations within NAWM II. In the baseline (BL) simulation, it is assumed that the private sector’s
inflation anchor follows the movements in the SPF measure of longer-term inflation expectations until theend of 2014 and, hence, it falls by about 0.1 percentage point below the central bank’s maintained inflation
objective of 1.9% in the course of 2014. Thereafter, the inflation anchor is assumed to gradually recover,along a gently increasing path. In the counterfactual (CF) simulation, the inflation anchor is obtained
endogenously from an adaptive expectations scheme, with the weight on lagged consumer price inflation
set equal to the estimated value of 0.058. Consumer price inflation (measured in terms of the private
consumption deflator) and per-capita real GDP growth are expressed as annual percentages, the output
gap is measured in percent of potential output and the short-term nominal interest rate (corresponding
to the EONIA) is expressed in annualised percentage terms. The effective lower bound on the short-term
nominal interest rate is imposed at an interest-rate level of -14 basis points (set equal to the minimumof the EONIA forward curve over the extended baseline horizon). For conducting the simulations, theposterior mode estimates of the model’s parameters are used.

ECB Working Paper Series No 2200 / November 2018

114

115

0

0.4

χ̃W

0
0.2

2

4

0.6

0.8

1

0

10

20

30

0
2

0
1

2

4

6

2

4

6

σ ϕI

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0

4
2

0.005 0.01 0.015 0.02

0.8

1.1

0.9

1.2

0

0.4

0.7

0.5

0.6

0.75

ξH

0.6

κ

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0.8

0.8

0

1

2

3

0

5

10

0

2

4

6

ρθ

1

6

0.9

5

10

8

0.8

ω̃L∗

8

50

100

150

0
1

0
0.9

2

2
0.8
∗
γL

4

4

0.7

6

6

0.6

8

8

ωL

0.6

0.4

0.6

0.6

0.6

χH

0.7

ξW

0.7

ρϕ I

0.7

ξI

0.8

0.8

0.8

0.8

1

0.9

0.9

0

5

10

0

2

4

0

2

4

6

0

50

100

150

0.2

0

γLh

0.6

0.4

1

0.7

ξX

0.6

χW

2

σθ

0.8

0.8

3

1

0.9

0.005 0.01 0.015 0.02 0.025

Figure A.1: Marginal prior densities of estimated parameters with and without system priorNote: This figure compares the marginal prior densities of the estimated parameters of NAWM II using the system prior information (blue solid lines) andtheir marginal prior densities without the system prior (red dashed lines). The parameter densities are ordered according to the order of the parametersin Tables 4 to 6.

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2

2.5

1

0

6

8

0
4

0

2

5

10

0.2

0.4

γ∗

0
10 12 14

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1.5

0

0.5

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γI

1.5

0.5

0.1

4

1

1

2

0.9

2

3

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0

0.7

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φR

0.8

1

γu,2

1.5

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0.5

1

0

0.2

0.4

0

0.5

1

µI

0.8

1

0.7

2

4

1.5

0.6

ξ∗

1.5

1

2

0.5

µC

0.2

0.3

0

1

2

0
0.8

0
0.2
0.6

5

2

0.4

10

χX

0

1

2

1

0.2

2

µX

4

3

φΠ

6

2

0.6

γIM C

1.5

0.4

χ∗

4

8

2.5

0.8

5

1

0

2

4

0

0.2

0.4

0

0.5

1

1.5

0

2

4

6

8

0

0

0

2

1

0.1

0.5

φ∆Π

4

6

2

0.3

γIM I

1.5

µ∗

0.2

o∗

Figure A.1: Marginal prior densities of estimated parameters with and without system prior (continued)

4Note: See above.

φ∆Y

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117

0.3

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0

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4

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0.5

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0.4

8

8

ρϕ X

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0.05

0.1

0.15

0.2

0.3

0.4

0.4

0.4

0.5

ρϕ ∗

0.6

ρI

0.6

ρRP

0.6

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0.8

1

0.7

1

0

2

4

0

2

4

6

8

0

2

4

0

5

5
0

10

10

0
0.6

ρǫ

0.5

ξE

0.2

15

0

0.4

0.1

φ∆Y
15

2

0

0

φY

0.3

0.4

0.4

0.4

0.6

ρIM

0.5

ρϕ W

0.6

ρRP ∗

0.8

0.6

0.8

0.7

0.05 0.1 0.15 0.2 0.25

̟Π̄p

1

1

0

2

4

0

5

10

0.4

0.6

ρgzp

0.15

0.6

ρ

ν∗

0.5

ρϕ H

0.1

0.4

0.4

0.05

0.3

0
0.2

2

4

0

5

10

15

̟gYp

0.2

0.8

0.6

0.8

Figure A.1: Marginal prior densities of estimated parameters with and without system prior (continued)

2

4

0

1

2

0

5

10

Note: See above.

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ECB Working Paper Series No 2200 / November 2018
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0.7

1

0.25

1

5

10

1

0.5

1

118

Note: See above.

0

4

6

0

0

σΠ̄p

0.5

2

4

0

2

0

0

σ ϕ∗

0.4

5

10

2

4

6

8

0

2

4

6

8

0.2

σI

0
0.5

0

4

6

2

0

σRP

0

0

0

0

1

2

0.2

1

2

Y

σg p

4

σIM

0.4

σ ϕW

2

σRP ∗

3

6

0.6

3

0

20

40

60

80

0

2

4

0

10

20

0

5

10

0

2

0.04

0.05

0.1

0.06

σg2p /σg2tr
z
z

4

σν ∗

0.1

σ ϕH

0.2

σgzp

6

0.15

0.3

0.08

0

5

10

0

2

4

6

8

0

2

4

6

0

0

0

0.4

σR

0.4

σ ϕX

1

Marg Prior
System Prior
Marginal Mode
Joint Mode

0.2

0.2

0.5

σǫ

0.6

0.6

1.5

Figure A.1: Marginal prior densities of estimated parameters with and without system prior (continued)

2

4

6

8

PSfrag replacements0ρν ∗ 0ECB Working Paper Series No 2200 / November 2018
0.8

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1

2

8
-3

0.2

2.5

×10

10

15

0

0

2

4

0.4

0.6

χ̃W

0.8

1

0.5

0.7

0.9

ξH

0.6

κ

0.8

ρθ

1

0.7

0.9

1.1

0

2

0

4

6

8

0

5

10

15

0

5

10

0.6

ξW

0.7

ρϕ I

0.7

ξI

0.8

0.8

0.1

0.2

0.3

χH

0.4

0.9

0.5

0.65 0.7 0.75 0.8 0.85

0.5

0
0.6

5

10

15

10
0.78 0.8 0.82 0.84 0.86 0.88

0.6

0.8

ω̃L∗

20

30

0
1.5

σ ϕI

6

0

4

5

2

2

4

6

8

1

2

0

200

400

γL∗

1

0
0.9

0

0.8

5

5

0.7

10

10

ωL

0

5

10

0

2

4

0

0.2

0.4

0

100

200

0

0.2

0.6

2

Figure A.2: Marginal system prior and posterior densities of estimated parameters

4

6

σθ

0.7

ξX

0.4

χW

0.01

γLh

0.8

0.6

8

0.02

0.9

0.8

10

Note: This figure plots the marginal posterior densities of the estimated parameters of NAWM II based on a Markov chain with 1,000,000 draws (blue solidlines) against their marginal system prior densities (red dashed lines), with 500,000 draws being discarded as burn-in draws. The parameter densities are orderedaccording to the order of the parameters in Tables 4 to 6.

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0

6

4

0.6

1

1.5

0

120
10

0
5

0

Note: See above.

φ∆Y

20

0

0.2

γ∗

10 12 14 16 18

0.4

8

1

2

40

0

0.1

0.2

0.3

γI

0
3

µC

0.4

0

2

0.2

5

10

0.5

1

1.5

0

2

4

6

χX

0.5

0.4

0.9

1

1

0.5

0.92

φR

1.5

γu,2

2

µI

0.6

ξ∗

0.94

2

0.7

3

0

0.5

1

1.5

0

0.2

0.4

0

1

2

3

0

2

4

2

2

4

0.5

0.2

6

3

φΠ

8

γIM C

1

µX

0.4

χ∗

10

4

0.6

12

1.5

14

0.8

0

10

20

30

0

0.5

1

0

1

2

0

5

10

0

0

0.5

0.1

1

µ

φ∆Π

4

1.5

0.3
∗

γIM I

0.05

2

0.2

o∗

Figure A.2: Marginal system prior and posterior densities of estimated parameters (continued)

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0.1

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0.2

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0
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ρI

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0

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̟Π̄p

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ρIM

ρϕ W

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0.02 0.04 0.06 0.08 0.1 0.12

0
0.92

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0

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0

60

0.94 0.95 0.96 0.97 0.98

0.15

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ρRP

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φ∆Y

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0
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10

ρǫ

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10

0.8

0.06

0.85

ξE

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20

40

15

0.8

0.02

φY

0

5

10

0

5

10

0

10

20

30

0.4

0.4

ρ

0.6

0.5

ν∗

0.8

0.6

ρϕ H

0.7

0.860.88 0.9 0.920.940.960.98

ρgzp

1

0
0.02 0.04 0.06 0.08 0.1 0.12

20

40

̟gYp

Figure A.2: Marginal system prior and posterior densities of estimated parameters (continued)

15

0

20

40

0

20

40

60

Note: See above.

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0.05

10

50
0

50

0

0.02 0.025 0.03 0.035 0.04

100

100

σΠ̄p

1.2

150

1

150

0.8

5

σIM

0.15

15

0.2

0
0.04

0.02 0.025 0.03 0.035 0.04

Y

σg p

10

0

20

40

60

80

0

0.1

0.2

0

10

20

0.1

0.25

20

0
1.6

0.4

0.2

σ ϕW

0.15

20

40

30

0
1.4

0.35

0.1

σRP ∗

30

0

2

σ ϕ∗

0.3

0.2

0.2

0.25

σI

0.15

10

20

0.4

0.2

0.1

σRP

15

20

0.1

σg2p /σg2tr
z
z

10

σν ∗

0.15

σ ϕH

0.08

25

0.2

0.12

0.04 0.05 0.06 0.07 0.08

5

0.1

0.06

σgzp

0

20

40

60

0

2

4

0

1

2

3

0.1

0.8

1

2.5

1.4

0.14

2

1.2

0.12

σR

1

σ ϕX

1.5

System Prior
PosteriorMarginal Mode
Joint Mode

0.08

0.6

0.5

σǫ

Figure A.2: Marginal system prior and posterior densities of estimated parameters (continued)

4

0

10

20

0

10

20

30

Note: See above.

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ECB Working Paper Series No 2200 / November 2018

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2000

2010

1990

2000

2010

-5

0

5

2000

2010

1990

2000

2010

Transitory technology shock

1990

External risk premium shock

-2

-1

0

1

2

-1

-0.5

0

0.5

1

2000

2010

1990

2000

2010

Inv.-spec. technology shock

1990

Permanent tech. shock, persistentNote: This figure shows the smoothed estimates of the structural shocks of NAWM II conditional on the posterior mode estimates of the its parameters.

-0.6

-0.4

-0.2

0

0.2

0.4

Permanent tech. shock, transitory

-2

-1

-1

1990

0

0

-2

1

2

1

2

Domestic risk premium shock

Figure A.3: Smoothed estimates of shocks

ECB Working Paper Series No 2200 / November 2018

124

1990

Note: See above.

-4

-2

0

2

2000

2010

-50

0

50

-0.6

-0.6

Price markup shock: imports

-0.4

-0.4

4

-0.2

-0.2

2010

0

0

2000

0.2

0.2

1990

0.4

0.4

Wage markup shock

1990

1990

2000

Import demand shock

2000

2010

2010

Price markup shock: domestic

0

2

4

-60

-40

-20

0

20

40

60

-4

-2

Figure A.3: Smoothed estimates of shocks (continued)

2000

1990

2000

Export preference shock

1990

2010

2010

Price markup shock: exports

ECB Working Paper Series No 2200 / November 2018

125

2000

2010

1990

2000

2010

Retail banks' mark-down shock

1990

Government consumption shock

Note: See above.

-5

0

5

-5

0

5

-0.06

-0.04

-0.02

0

0.02

0.04

-0.4
2000

2010

1990

2000

2010

Perceived inflation target shock

-0.05

0

0.05

-40

-20

-0.2

20

40

0

1990

Interest rate shock

0

0.2

0.4

Figure A.3: Smoothed estimates of shocks (continued)

2000

2010

1990

2000

2010

Perceived trend growth rate shock

1990

Bankers' survival rate shockECB Working Paper Series No 2200 / November 2018

126

1990

2000

2010

1990

2000

2010

Foreign long-term interest rate shock

Note: See above.

-3

-2

-1

0

1

2

3

-5

-4

-2

0

2

4

-5
1990

2010

1990

2000

2010

Competitors' export price shock

2000

-5

0

5

-5

0

0

0

Foreign price shock5

5

5

Foreign demand shock

Figure A.3: Smoothed estimates of shocks (continued)

1990

1990

2000

Oil price shock

2000

2010

2010

Foreign interest rate shockECB Working Paper Series No 2200 / November 2018

127

2010

2000

2010

1990

2000

2010

Transitory technology shock

1990

External risk premium shock

-5

0

5

-5

0

5

2000

2010

1990

2000

2010

Inv.-spec. technology shock

1990

Permanent tech shock, persistentNote: This figure shows the smoothed estimates of the standardised innovation component of the structural shocks of NAWM II conditional on the posteriormode estimates of its parameters.

2000

-5

1990

-5

5

0

Permanent tech shock, transitory

2010

0

5

2000

-5

1990

-5

5

0

Domestic risk premium shock

0

5

Figure A.4: Smoothed estimates of innovation component of shocks

ECB Working Paper Series No 2200 / November 2018

128

2010

Note: See above.

2000

2010

-5

1990

-5

5

0

Price markup shock: imports

0

5

2000

-5

1990

-5

5

0

Wage markup shock

0

5

1990

1990

2000

Import demand shock

2000

2010

2010

Price markup shock: domestic

-5

0

5

-5

0

5

2000

1990

2000

Export preference shock

1990

2010

2010

Price markup shock: exports

Figure A.4: Smoothed estimates of innovation component of shocks (continued)

ECB Working Paper Series No 2200 / November 2018129

Note: See above.

2000

2010

-5

1990

-5

5

0

Retail banks' mark-down shock

2010

0

5

2000

-5

1990

-5

5

0

Government consumption shock

0

5

2000

2010

1990

2000

2010

Perceived inflation target shock

1990

Interest rate shock

-5

0

5

-5

0

5

2000

2010

1990

2000

2010

Perceived trend growth rate shock

1990

Bankers' survival rate shock

Figure A.4: Smoothed estimates of innovation component of shocks (continued)

ECB Working Paper Series No 2200 / November 2018

130

2000

2010

Note: See above.

2000

2010

-5

1990

-5

5

-5

0

5

0

Foreign long-term interest rate shock1990

Foreign demand shock

0

5

-6

-4

-2

0

2

4

6

2000

2010

1990

2000

2010

Competitors' export price shock1990

Foreign price shock

-5

0

5

-5

0

5

1990

1990

2000

Oil price shock

2000

2010

2010

Foreign interest rate shock

Figure A.4: Smoothed estimates of innovation component of shocks (continued)

131

0.4

0.6

0.8

1.2

1.4

1.6

1.8

-0.1

0

0.1

0.2

2006 2008 2010 2012 2014

χ̃W

2006 2008 2010 2012 2014

σ ϕI

2006 2008 2010 2012 2014

γL∗

0.7
2006 2008 2010 2012 2014

0.1

0.2

0.8

0.4

0.6

0.8

1

0.6

0.7

0.8

0.9

0.6

0.8

1

0.3

ξH

2006 2008 2010 2012 2014

κ

2006 2008 2010 2012 2014ρθ

2006 2008 2010 2012 2014

ω̃L∗

0.9

1

0.4

0.6

0.8

0.6

0.8

1

0.8

0.7

2006 2008 2010 2012 2014

0.9

0.8

1.1
1

ωL

0.9

1

2006 2008 2010 2012 2014

χH

2006 2008 2010 2012 2014

ξW

2006 2008 2010 2012 2014

ρϕ I

2006 2008 2010 2012 2014

ξI

Figure A.5: Recursive posterior mode estimates of parameters

0.6

0.7

0.8

0.9

0.2

0.3

0.4

0.5

5

5.2

5.4

5.6

-0.1

0

0.1

0.2

2006 2008 2010 2012 2014

ξX

2006 2008 2010 2012 2014

χW

2006 2008 2010 2012 2014σθ

2006 2008 2010 2012 2014

γLh

Note: This figure graphs the recursively estimated posterior mode of the parameters of NAWM II, with the estimation sample being gradually extended by afull year from 2005Q4 to 2014Q4. The graphs of the recursive posterior mode estimates are ordered according to the order of the parameters in Tables 4 to 6.

PSfrag replacements

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132

2.7

2.8

2.9

0.8

2.2

1

1.1

0.8

1

1.2

1.2

1.4

1.6

0.9

2006 2008 2010 2012 2014γ∗2006 2008 2010 2012 2014

γI

2006 2008 2010 2012 2014

µC

2.4

2.6

9.5

10

10.5

11

2.5

Note: See above.

φ∆Y

2006 2008 2010 2012 2014

2006 2008 2010 2012 2014

φR

2006 2008 2010 2012 2014

γu,2

2006 2008 2010 2012 2014

µI

2

2.2

2.4

2.6

2.8

6.6
6.4
6.2
6
5.8

0.7

0.8

0.9

1

0.2

0.4

0.6

2006 2008 2010 2012 2014

χ∗

0.3

0.4

2006 2008 2010 2012 2014φΠ

2006 2008 2010 2012 2014

γIM C

2006 2008 2010 2012 2014

µX

-0.1

0

0.1

0.2

0.8

1

1.2

1

1.1

1.2

1.3

0.1

0.4

ξ∗

0.2

0.6

0.8

0.2

2006 2008 2010 2012 2014

χXo∗2006 2008 2010 2012 2014φ∆Π

2006 2008 2010 2012 2014

γIM I

2006 2008 2010 2012 2014µ∗

2006 2008 2010 2012 2014

Figure A.5: Recursive posterior mode estimates of parameters (continued)

0.3

0.4

0.5

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133

0.3

0.3

2006 2008 2010 2012 2014

0.4

0.5

0.6

0.4

0.5

0.6

0.4

0.7

ρϕ X

0.6

0.8

2006 2008 2010 2012 2014

0.8

1

0.8

0.9

1

1.1

ρǫ

2006 2008 2010 2012 2014

0.9

0.8

0.7

1

1.1

0.9

1

ξE

0

-0.1

2006 2008 2010 2012 2014

0.1

0

0.3
0.2

φY

2006 2008 2010 2012 2014

ρϕ∗2006 2008 2010 2012 2014

ρI

2006 2008 2010 2012 2014

ρRP

2006 2008 2010 2012 2014

φ∆Y

0.6

0.8

1

0.4

0.6

0.8

0.8

0.9

1

1.1

-0.1

0

0.1

0.2

2006 2008 2010 2012 2014

ρIM

2006 2008 2010 2012 2014

ρϕ W

2006 2008 2010 2012 2014

ρRP ∗2006 2008 2010 2012 2014

̟Π̄p

0.7

0.8

0.9

1

0.4

0.5

0.6

0.7

0.7

0.8

0.9

1

1.1

-0.1

0

0.1

0.2

̟gYp

2006 2008 2010 2012 2014ρν ∗2006 2008 2010 2012 2014

ρϕ H

2006 2008 2010 2012 2014

ρgzp

2006 2008 2010 2012 2014

Figure A.5: Recursive posterior mode estimates of parameters (continued)

0.1

0.2

Note: See above.

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134

-0.1

-0.1

2006 2008 2010 2012 2014

0

0

0.2
0.1

σΠ̄p

0.1

0.2

6.5

0.9

7.5

8

0

7

2006 2008 2010 2012 2014

σ ϕ∗2006 2008 2010 2012 2014

2006 2008 2010 2012 2014

σgYp

2006 2008 2010 2012 2014

σIM

2006 2008 2010 2012 2014

-0.1

0

0.1

0.2

8.5

9

9.5

10

0

0.1

0.1

0.3

-0.1

0

0.1

0.2

0.2

σ ϕW

2006 2008 2010 2012 2014

σRP ∗

0.2

0.3

1

1.1

1.2

0.2

0.4

0.6

σI

0

0

2006 2008 2010 2012 2014

0.1

0.1

0.3
0.2

σRP

2006 2008 2010 2012 2014

σg2p /σg2trzz

2006 2008 2010 2012 2014σν ∗2006 2008 2010 2012 2014

σ ϕH

2006 2008 2010 2012 2014

σgzp

0

0.1

0.2

0.3

0.7

0.8

0.9

1

1.1

0.8

1

1.2

σǫ

2006 2008 2010 2012 2014

σR

2006 2008 2010 2012 2014

σ ϕX

2006 2008 2010 2012 2014

Figure A.5: Recursive posterior mode estimates of parameters (continued)

0.2

0.3

Note: See above.

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Acknowledgements
We would like to thank Kai Christoffel, Fiorella De Fiore, Jordi Galí, Andrea Gerali, Philipp Hartmann, Luc Laeven, Johannes Pfeifer,
Giorgio Primiceri, Ricardo Reis, Chris Sims, Frank Smets, Mathias Trabandt and Oreste Tristani for helpful discussions and suggestions
at the various stages of the model-development project. We are particularly grateful to Marco Onofri, who provided excellent research
assistance, to José-Emilio Gumiel, who offered meticulous data support, and to Carlos Montes-Galdón, who provided us with the codefor simulating the effects of interest-rate forward guidance under imperfect credibility. We have benefited from presentations of earlier
drafts and of related material at the ECB, to the Monetary Policy Committee of the European System of Central Banks and to its
Working Group on Econometric Modelling, at the 2016 GSE Summer Forum in Barcelona, at the 1st Research Conference of the CEPR
Network on Macroeconomic Modelling and Model Comparison in Frankfurt, at the 7th BIS Research Network Meeting on “Pushing thefrontier of central banks’ macro-modelling” in Basle, at the 20th Central Bank Macroeconomic Modelling Workshop in Paris, and at the24th International Conference on Computing in Economics and Finance in Milan. The views expressed in this paper are those of theauthors and do not necessarily reflect the views of the ECB.
Günter Coenen (corresponding author)
European Central Bank, Frankfurt am Main, Germany; email: gunter.coenen@ecb.europa.eu
Peter Karadi
European Central Bank, Frankfurt am Main, Germany; email: peter.karadi@ecb.europa.eu
Sebastian Schmidt
European Central Bank, Frankfurt am Main, Germany; email: sebastian.schmidt@ecb.europa.eu
Anders Warne
European Central Bank, Frankfurt am Main, Germany; email: anders.warne@ecb.europa.eu© European Central Bank, 2019
Postal address 60640 Frankfurt am Main, Germany
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This paper can be downloaded without charge from www.ecb.europa.eu, from the Social Science Research Network electronic library orfrom RePEc: Research Papers in Economics. Information on all of the papers published in the ECB Working Paper Series can be foundon the ECB’s website.
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