Domestic versus foreign drivers of trade (im)balances : how robust is evidence from estimated DSGE models.
Date: 2020-06-24
Institutions: Joint Research Centre
Subjects: Germany, Spain, economic model, foreign exchange market, international trade, regional disparity, research report, trade balance, trade policy

Domestic versus foreign drivers of 
trade (im)balances: 

How robust is evidence from estimated DSGE 

models 

Cardani, Roberta 

Hohberger, Stefan  

Pfeiffer, Philipp 

Vogel, Lukas 

2020 

JRC Working Papers in Economics and Finance, 2020/5 

 
 
 
 
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How to cite this report: Cardani, R., Hohberger, S., Pfeiffer, P. and Vogel, L., Domestic versus foreign drivers of 
trade (im)balances: How robust is evidence from estimated DSGE  models, Publications Office of the European 
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Domestic versus foreign drivers of trade (im)balances: 

How robust is evidence from estimated DSGE models1 

Roberta Cardania, Stefan Hohbergera, Philipp Pfeifferb, Lukas Vogelb 

a European Commission, Joint Research Centre (JRC), Ispra, Italy 

b European Commission, Directorate General for Economic and Financial Affairs, Brussels, Belgium 

2 March 2020 

Abstract: 

Estimated DSGE models tend to ascribe a significant and often predominant part of a country's 

trade balance (TB) dynamics to domestic drivers ("shocks"), suggesting foreign factors to be 

only of secondary importance. This paper revisits the result based on more agnostic approaches 

to shock transmission and using "agnostic structural disturbances". We estimate multi-region 

models for Germany and Spain as countries with very distinct TB patterns since 1999. Results 

suggest  that  domestic  drivers  remain  dominant  when  theory-based  restrictions  on  shock 

transmission are relaxed, although the transmission of foreign shocks is strengthened. 

JEL classification: F30, F32, F41, F45 

Keywords:  Agnostic  structural  disturbances,  open  economy  DSGE  model,  trade  balance, 
Germany, Spain  

1 The views expressed in this document are solely those of the authors and should not be attributed to the European Commission. We are 
grateful to Timo Baas (discussant), Joscha Beckmann, Ansgar Belke, Daniel Gros, Wouter den Haan, Marco Ratto, Werner Roeger, as well as 
participants of the Jean Monnet Workshop "Current Account (Im-)Balances Determinants and Policy Implications" in Brussels for very helpful 
comments and suggestions. We thank Lorenzo Frattarolo for valuable research support. Corresponding author: stefan.hohberger@ec.europa.eu. 

1 

 
 
 
 
 
 
 
 
 
 
                                           
1. Introduction 

The sign and size of a country's trade balance (TB) are affected by domestic and foreign factors 

alike (e.g., Obstfeld and Rogoff, 1996). The relative importance of each group is an empirical 

question, which we revisit through the lens of dynamic stochastic general equilibrium (DSGE) 

models, with a focus on Germany (DE) and Spain (ES) as two large Euro Area (EA) Member 

States that have witnessed strikingly distinct TB dynamics since the start of EMU in 1999. In 

particular,  we  estimate  multi-region  DSGE  models  (EA  Member  State,  the  rest  of  the  EA 

(REA), and the rest of the world (RoW)) for DE and ES, respectively.  

Estimated DSGE models have been a popular tool for decomposing macroeconomic dynamics 

into fundamental drivers since the early 2000s. Their appeal lies, on the theoretical side, in the 

explicit modelling of market interactions in the macroeconomy and, on the empirical side, in 

the extensive use of available information to identify model parameters (transmission channels) 

and  exogenous  shocks  (drivers).  Estimated  open-economy  DSGE  models  tend  to  attribute 

fluctuations in economic activity and net trade in advanced economies primarily to domestic 

factors, however, despite the inclusion of foreign regions and shocks. A classic reference for 

low spillover is Justiniano and Preston (2010), who show that US shocks account for only 1-

3% of output and real effective exchange rate (REER) volatility in an estimated open-economy 

DSGE model of the Canadian economy (1982-2007). Results in Kollmann et al. (2016) and 

Giovannini et al. (2019) with more complex estimated multi-region models are more balanced, 

with  non-negligible  contributions  of  RoW  shocks  to  EA  and  US  GDP  and  trade  balance 

dynamics  since  1999.  Turning  to  individual  EA  countries,  Kollmann  et  al.  (2015)  find  the 

persistence  of  DE's  TB  surplus  to  be  driven  mainly  by  domestic  factors,  although  external 

factors matter quantitatively in the build-up phase. Looking at Spain, in 't Veld et al. (2014, 

2015) find a quantitatively significant contribution of narrowing intra-EA risk premia to the 

country's TB deficit before the financial crisis, but little contribution of (other) foreign factors 

to  GDP  growth  and  net  export  dynamics.  Albonico  et  al.  (2019)  provide  a  comparative 

perspective in which domestic shocks are essential to explain the persistent TB surplus of DE 

and the pre-crisis TB deficit build-up in ES and Italy (IT), whereas foreign shocks account for 

a more substantial part in France, particularly in recent years. 

The finding of a limited role for external  factors is  linked to  the ambivalent  role of various 

shocks  in  terms  of  spillover  and  TB  dynamics.  Positive  foreign  supply  shocks,  e.g.,  tend  to 

generate positive income effects and, at the same time, improve the competitiveness of foreign 

producers, where the first effect strengthens and the second effect weakens net exports of the 

2 

 
domestic  economy.  Spillover  of  positive  foreign  demand  shocks  inside  a  monetary  union  is 

rather weak in normal times, as stronger demand is met by a tightening of monetary policy that 

dampens domestic demand in the domestic economy and appreciates the common currency, 

reducing  net  exports  to  the  RoW.  In  addition,  it  should  be  underlined  that  distinguishing 

between domestic and foreign shocks and between demand and supply shocks is less clear-cut 

in reality. Domestic demand shocks, e.g., can be the result of changes in the credit supply by 

foreign or domestic financial intermediaries, and domestic financial conditions may be subject 

to  contagion  effects  (e.g.,  Dornbusch  et  al.,  2000)  in  excess  of  "real"  trade  and  financial 

linkages. 

The  benchmark  estimates  in  this  paper  are  in  line  with  previous  findings  and  suggest  TB 

dynamics in DE and ES to be driven mainly by domestic (demand) factors. In a counterfactual 

simulation without domestic demand shocks, Spain's TB (in % of nominal GDP) is more than 

5 percentage points (pp) higher in 2008, and the subsequent TB reversal 4 pp less pronounced. 

Domestic  demand  conditions  also  explain  a  large  part  of  the  DE  TB  variation,  but  external 

factors  are  more  important  than  for  ES.  The  REA  pre-crisis  boom  raised  DE  net  exports, 

whereas falling REA demand has weighted negatively on the  DE TB during the subsequent 

recession.  We  find  little  role  for  spillover  of  foreign  supply  shocks  (“competitiveness 

gains/losses”) within the EA, however. Intra-EA relative price dynamics reflect to a large extent 

diverging demand conditions in the benchmark model.  

We then extend the model in two directions to assess the robustness of the benchmark results. 

We first investigate the hypothesis that price and wage pressure from abroad affect net trade 

beyond  the  ambivalent  role  of  supply  shocks  in  the  standard  model  and  the  (realised) 

transmission to export and import prices. We test the idea by including price and wage shocks 

directly in the trade equations and re-estimating the models with wide agnostic priors. The data 

reject the inclusion of supply shocks in trade equations for Spain, supporting the results of the 

baseline  model.  Interestingly,  however,  we  find  some  evidence  for  a  stronger  role  of  price 

pressure  and  spillover  in  the  case  of  DE,  with  a  larger  role  for  foreign  price  shocks.  The 

inclusion of foreign price shocks in trade equations does, however, not overturn the benchmark 

result that domestic demand factors dominate the decomposition of TB dynamics in DE and 

ES. 

Second, we follow recent methodological advances in empirical business  cycle analysis and 

adopt a more agnostic perspective on shock transmission by applying the agnostic structural 

disturbances (ASDs) methodology of Den Haan and Drechsel (2020). ASDs enter the model 

3 

 
like structural shocks, but their impact is a priori unrestricted. Our main results remain robust 

with  different  ASD  specifications,  i.e.  domestic  developments  still  explain  most  of  the  TB 

variance.  One  of  the  ASDs  that  we  investigate  shares  essential  similarities  with  the  key 

domestic demand shock, but also implies stronger international co-movement in the spirit of 

global  risk  shocks.  We  conclude  that  the  (more)  agnostic  specifications  preserve  the  main 

message from the benchmark model. 

2. Stylised facts 

The  TBs  of  DE  and  ES  have  followed  distinct  patterns  in  recent  years  (Figure  1).  DE  is 

characterised by a large and persistent TB surplus that has built up since the early 2000s, with 

a pause in the years of the global financial crisis and a peak at around 8% of GDP in 2015. ES 

has run a large trade deficit in the early years of EMU, reaching -6% of GDP on the eve of the 

financial crisis. The TB has turned into a surplus of up to 4% of GDP in recent years. DE's TB 

surplus shows limited co-movement with the output gap, i.e. the surplus has remained high in 

periods  of  positive  and  negative  output  gaps  alike.  Spain's  TB  dynamics,  to  the  contrary, 

displays marked cyclicality, with TB deficits in periods of positive output gaps, and a move 

into surplus in conjunction with negative output gaps after 2008. 

Figure 1: Trade balance and output gap  

Note: TBY is the trade balance in % of GDP; YGAP is the output gap in %. Source: AMECO. 

Figure  2  illustrates  DE-ES  differences  with  respect  to  the  co-movement  between  TB  and 

indicators of price competitiveness, namely the REERs based on the GDP deflator (PGDP) and 

unit  labour  costs  (ULC),  respectively.  The  sustained  increase  in  DE's  TB  surplus  did  not 

coincide with the steady depreciation of DE's REER. The TB of ES, by contrast, co-moved with 

the REER. It appreciated during the pre-crisis boom, when the ES TB moved into deficit, and 

4 

-6-4-202468101991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018Year(a) GermanyTBY (% of GDP)YGAP (%)-10-8-6-4-202461991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018Year(b) SpainTBY (% of GDP)YGAP (%) 
 
 
 
it  depreciated  after  2008,  when  the  economy  contracted  and  the  TB  moved  into  positive 

territory. 

Figure 2: Trade balance and real effective exchange rate  

Note: TBY is the trade balance in % of GDP; REER is the real effective exchange rate, normalised to 2010=100. 
The REER is calculated based on the GDP deflator (PGDP) and unit labour costs (UCL), respectively, compared 
to a group of 37 industrial countries. A REER decline indicates REER depreciation. Source: AMECO. 

3. Model description 

Our analysis uses a set of estimated multi-country models.2 The models are ex-ante identical, 

i.e. they share the same structure and the same set of observed variables used for the estimation. 

Each model consists of an EA Member State (MS), the REA, and the RoW as building blocks 

(with country index 𝑘).. International trade and financial markets link the three regional blocks. 

The  EA  MS  block  is  more  detailed  than  the  other  regions.  It  assumes  two  (representative) 

households, firms and a government. The MS households provide labour services to domestic 

firms. Final good firms combine domestic and imported intermediate inputs. Intermediates are 

produced by monopolistically competitive firms using local labour and capital as inputs. Fiscal 

and monetary authorities follow estimated policy rules. 

3.1. EA Member State households 

The household sector consists of a continuum of households 𝑗 ∈ [0; 1]. There are two types of 

households,  savers  ("Ricardians",  superscript  s)  who  own  firms  and  hold  government  and 

foreign  bonds,  and  liquidity-constrained  households  (superscript  c)  who  only  receive  labour 

and transfer income and do not save. The share of savers in the population is 𝜔𝑠. 

2 The models build on the Global Multi-country (GM) model of the European Commission (Albonico et al., 2019).  

5 

8090100110120130140-2024681019911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182010=100% of GDPYear(a) GermanyTBY (left)REER PGDP (right)REER ULC (right)80859095100105110-8-6-4-2024619911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182010=100% of GDPYear(b) SpainTBY (left)REER PGDP (right)REER ULC (right) 
 
 
                                           
Both households enjoy utility from consumption 𝐶𝑗𝑘𝑡

𝑟  and incur disutility from labour 𝑁𝑗𝑘𝑡

𝑟  (𝑟 =

𝑠, 𝑐).  Ricardian’s  utility  also  depends  on  the  financial  assets  held.  Date  t  expected  life-time 

utility of household r is defined as: 

𝑈𝑗𝑘𝑡

∞
𝑟 = ∑ 𝑒𝑥𝑝(𝜀𝑘𝑡
𝑠=𝑡

𝑐 )𝛽𝑠−𝑡

𝑟 (∙), 

𝑢𝑗𝑘𝑡

𝑐  
where 𝛽 is the (non-stochastic) discount factor (common for both types of households) and 𝜀𝑘𝑡
𝑟 (∙)  denotes  per  period  utiliy 
is  a  saving  shock,  which  is  limited  to  saver  households.3  𝑢𝑗𝑘𝑡

described below. 

3.1.1. Ricardian households 

The Ricardian households work, consume, own firms and receive nominal transfers 𝑇𝑗𝑘𝑡

𝑠  from 

the government. Ricardians are the only households with full access to financial markets. The 

financial wealth of household j consists of bonds and shares, where 𝑃𝑘𝑡

𝑆  is the nominal price of 

shares in t, 𝐵𝑗𝑘𝑡−1

𝑆

 the number of shares held by the household, and 𝑃𝑘𝑡

𝐶,𝑣𝑎𝑡 is the consumption 

price, including VAT. The period t budget constraint of a saver household j is: 

(1 − 𝜏𝑘

𝑁)𝑊𝑘𝑡𝑁𝑗𝑘𝑡

𝑔
)𝐵𝑗𝑘𝑡−1

+ (1 + 𝑖𝑙𝑡−1

𝑏𝑤 )𝑒𝑅𝑜𝑊𝑘𝑡𝐵𝑗𝑘𝑡−1

𝑔

𝑠 + (1 + 𝑖𝑘𝑡−1
𝑆 + 𝑃𝑘𝑡

+ (𝑃𝑘𝑡

𝑌 𝑑𝑘𝑡)𝐵𝑗𝑘𝑡−1

𝑆

+ 𝑇𝑗𝑘𝑡

𝑠 − 𝑡𝑎𝑥𝑠

𝑗𝑘𝑡 = 𝑃𝑘𝑡

𝑟𝑓

𝑏𝑤 + (1 + 𝑖𝑡−1
𝐶,𝑣𝑎𝑡𝐶𝑗𝑘𝑡

𝑟𝑓 )𝐵𝑗𝑘𝑡−1
𝑠 + 𝐴𝑗𝑘𝑡 + 𝑎𝑑𝑗𝑡
𝑊, 

where 𝑊𝑘𝑡 is the nominal wage rate, 𝑁𝑗𝑘𝑡

𝑠  is the employment in hours, and 𝜏𝑘

𝑁 the labour tax 

𝑔

rate.  𝐵𝑗𝑘𝑡−1

𝑟𝑓
, 𝐵𝑗𝑘𝑡−1

  and  𝐵𝑗𝑘𝑡−1

𝑏𝑤  are domestic government  bonds, foreign bonds,  and risk-free 

bonds  with  returns  𝑖𝑘𝑡−1
denotes the bilateral exchange rate. 𝑇𝑗𝑘𝑡

,   𝑖𝑙𝑡−1

𝑔

𝑏𝑤  ,  and  𝑖𝑡−1

𝑟𝑓 ,  respectively.4  𝑃𝑘𝑡

𝑠  are government transfers to savers, and 𝑡𝑎𝑥𝑗𝑘𝑡

𝑌   is  the  GDP  price  deflator.  𝑒𝑙𝑘𝑡 
𝑠  are lump-

sum  taxes  paid  by  savers.  Intermediate  goods  producers  pay  dividends  𝑃𝑘𝑡

𝑌 𝑑𝑘𝑡  to  savers. 

𝑎𝑑𝑗𝑡

𝑊 denotes wage adjustment costs. 

We define the gross nominal return on domestic shares as: 

1 + 𝑖𝑘𝑡

𝑠 =

𝑌 𝑑𝑘𝑡

𝑆 + 𝑃𝑘𝑡
𝑃𝑘𝑡
𝑆
𝑃𝑘𝑡−1

The instantaneous utility functions of savers, 𝑢𝑠(∙), is defined as: 

3 Unless stated differently, all exogenous random variables in the model follow independent autoregressive processes. 
4 As in Benigno (2009) and Ratto et al. (2009), we assume that only the RoW bond is traded internationally. 

6 

 
 
                                           
𝑠 (𝐶𝑗𝑘𝑡
𝑢𝑗𝑘𝑡

𝑠 ,
𝑠 , 𝑁𝑗𝑘𝑡

𝐴
𝑈𝑗𝑘𝑡−1
𝑐,𝑣𝑎𝑡 ) =
𝑃𝑘𝑡

1
1 − 𝜃𝑘

(𝐶𝑗𝑘𝑡

𝑠 − ℎ𝑘𝐶𝑘𝑡−1

𝑠

1−𝜃𝑘 
)

−

𝑈
𝑁𝜀𝑘𝑡
𝜔𝑘
𝑁 (𝐶𝑘𝑡)
1 + 𝜃𝑘

1−𝜃𝑘(𝑁𝑗𝑘𝑡
𝑠 )

𝑁
1+𝜃𝑘

−   (𝐶𝑘𝑡

𝑠 − ℎ𝑘𝐶𝑘𝑡−1

𝑠

)−𝜃𝑘  

𝐴
𝑈𝑗𝑘𝑡−1
𝑐,𝑣𝑎𝑡 , 
𝑃𝑘𝑡

where 𝐶𝑘𝑡

1
𝑠
𝑠 = ∫ 𝐶𝑗𝑘𝑡
0

𝑑𝑗, and 𝐶𝑘𝑡 = 𝜔𝑠𝐶𝑘𝑡

𝑠 + (1 − 𝜔𝑠)𝐶𝑘𝑡

𝑐  , ℎ𝑘 ∈ (0; 1) measures the strength of 

external habits in consumption, 𝜔𝑘
labour supply (or wage mark-up) shock.  

𝑁 the weight of the disutility of labour, and 𝜀𝑘𝑡

𝑈  captures a 

The disutility of holding risky financial assets, 𝑈𝑗𝑘𝑡−1

𝐴

, is defined as: 

𝐴
𝑈𝑗𝑘𝑡−1

= ∑ 𝐵𝑗𝑘𝑡−1
𝒬  

𝒬 

(𝛼𝑘

𝒬

𝒬 + 𝜀𝑘𝑡−1

) . 

The asset-specific risk premium shock depends on an asset-specific exogenous shock 𝜀𝑡
{𝑔, 𝑆, 𝑏𝑤} (government bonds, stocks, and foreign assets) and an asset-specific intercept 𝛼𝒬.5 

𝒬, 𝒬 ∈

Similar  to  Krishnamurthy  and  Vissing-Jorgensen  (2012)  and  Fisher  (2015),  introducing  a 

disutility of holding risky assets captures the households’ preferences for the safe short-term 

bonds and introduces an endogenous wedge between the return on risky assets and safe bonds.  

An uncovered interest rate parity condition links the interest rate of the MS to the EA interest 

rate: 

(1 + 𝑖𝑘𝑡

𝑟𝑓) = (1 + 𝑖𝐸𝐴𝑡) − (𝛼𝑘

𝑊
𝑏𝑤1 𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡𝐵𝑘𝑡
𝑃𝑘𝑡

𝑌 𝑌𝑘𝑡

𝐹𝑄 
) + 𝜀𝑘𝑡

where 𝛼𝑘

𝑊
𝑏𝑤1 𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡𝐵𝑘𝑡
𝑌 𝑌𝑘𝑡
𝑃𝑘𝑡

 captures a debt-dependent country risk premium on net foreign asset 

(NFA) holdings to ensure the long-run stability of foreign debt (see, e.g., Schmitt-Grohe and 

Uribe, 2003; Adolfson et al., 2008). The ‘flight-to-safety’ shock, 𝜀𝑘𝑡

𝐹𝑄, creates a wedge between 

the EA interest rate, 𝑖𝐸𝐴𝑡, and 𝑖𝑘𝑡
assets and the cost of capital, reducing consumption and investment simultaneously. Appendix 

𝑟𝑓. A positive shock increases the required return on domestic 

B.3 provides additional information on the transmission and the relative importance of domestic 

demand shocks. 

5 Internationally traded bonds are also subject to transaction costs in form of a function of the average net foreign asset position relative to 
GDP. 

7 

 
 
 
                                           
3.1.2. Liquidity-constrained household 

The  liquidity-constrained  household  consumes  her  disposable  after-tax  wage  and  transfer 

income in each period (“hand-to-mouth”), which gives the period t budget constraint: 

(1 + 𝜏𝐶 )𝑃𝑘𝑡

𝐶 𝐶𝑗𝑘𝑡

𝑐 = (1 − 𝜏𝑘

𝑁)𝑊𝑘𝑡𝑁𝑘𝑡

𝑐 + 𝑇𝑘𝑡

𝑐 − 𝑡𝑎𝑥𝑐

𝑗𝑘𝑡. 

3.1.3. Wage setting 

Households  provide  differentiated  labour  services,  𝑁𝑗𝑘𝑡

𝑟 ,  in  a  monopolistically  competitive 

market. A labour union bundles labour hours provided by both types of domestic households 

and resells homogeneous labour services to intermediate goods producing firms.6 The resulting 

wage rule equates a weighted average of the marginal utility of leisure to a weighted average 

of the marginal utility of consumption times the real wage adjusted for a wage mark-up. Wage 

adjustment costs give rise to nominal wage rigidity. We also allow for real wage rigidity as in 

Blanchard and Galí (2007), parametrized by 𝛾𝑘

𝑤𝑟. 

3.2. EA Member State production sector 

Perfectly  competitive  firms  produce  total  output,  𝑂𝑘𝑡,  by  combining  value  added,  𝑌𝑘𝑡,  with 

energy input, 𝑂𝑖𝑙𝑘𝑡, using the following CES production function: 

𝑂𝑘𝑡 = [(1 − 𝑠𝑘

𝑂𝑖𝑙)

1
𝑜(𝑌𝑘𝑡)
𝜎𝑘

𝜎𝑘

𝑜−1
𝑜
𝜎𝑘

+ (𝑠𝑘

𝑂𝑖𝑙)

1
𝑜(𝑂𝑖𝑙𝑘𝑡)
𝜎𝑘

𝜎𝑘

𝑜−1
𝑜
𝜎𝑘

𝑜
𝜎𝑘
𝑜−1

𝜎𝑘

]

, 

𝑂𝑖𝑙 is the energy input share in total output and 𝜎𝑘

𝑜 the elasticity of substitution between 

where 𝑠𝑘
the two components.  

Domestic final good firms assemble different intermediate varieties into a homogenous good 

and  sell  it  to  domestic  final  demand  packers  and  exporters  (see  below  3.3.2).  Demand  for 

individual intermediate goods 𝑖 ∈ [0; 1] is downward-sloping and follows 𝑌𝑖𝑘𝑡 = (

−𝜎𝑦

𝑌
𝑃𝑖𝑘𝑡
𝑌 )
𝑃𝑘𝑡

𝑌𝑘𝑡. 

Each variety 𝑖 is produced by a single firm using total capital, 𝐾𝑖𝑘𝑡−1
are combined by a Cobb-Douglas production function: 

𝑡𝑜𝑡

, and labour, 𝑁𝑖𝑘𝑡, which 

𝑌𝑖𝑘𝑡 = [𝐴𝑘𝑡

𝑌  (𝑁𝑖𝑘𝑡 − 𝐹𝑁𝑖𝑘)]𝛼(𝑐𝑢𝑖𝑘𝑡 𝐾𝑖𝑘𝑡−1

𝑡𝑜𝑡

 )1−𝛼 − 𝐴𝑘𝑡

𝑌 𝐹𝐶𝑖𝑘, 

6 Since both households face the same labour demand schedule, each household works the same number of hours as the average of the economy. 
It  follows  that  the  individual  union's  choice  variable  is  a  common  nominal  wage  rate  for  both  types  of  households.  See  Appendix  A  for 
additional details. 

8 

 
                                           
where  𝛼  is  the  steady-state  labour  share,  𝐴𝑘𝑡
common  to  all  firms  𝑖.7  𝑐𝑢𝑖𝑘𝑡  and  𝐹𝑁𝑖𝑘  are  the  firm-specific  level  of  capital  utilization  and 
𝑡𝑜𝑡, is the sum of private installed capital, 𝐾𝑖𝑘𝑡, 
labour hoarding, respectively.8 Total capital, 𝐾𝑖𝑘𝑡

𝑌   is  exogenous  labour-augmenting  productivity 

and public capital, 𝐾𝑖𝑘𝑡

𝐺 . 𝐹𝐶𝑖𝑘𝑡 captures fixed costs in production.  

The monopolistically competitive producers maximize the real value of the firm, 𝑉𝑘𝑡, equal to 
a discounted stream of future dividends 𝑑𝑘𝑡, 𝑉𝑘𝑡 = 𝑑𝑘𝑡 + 𝐸𝑡[𝑠𝑑𝑓𝑘𝑡+1𝑉𝑘𝑡+1], with the stochastic 

discount factor: 

𝑠𝑑𝑓𝑘𝑡 = (1 + 𝑖𝑘𝑡+1

𝑠

⁄
) (1 + 𝜋𝑘𝑡+1

𝑦

)

≈ (1 + 𝑖𝑘𝑡

𝑟𝑓 + 𝑟𝑝𝑟𝑒𝑚𝑘𝑡

𝑠 ) (1 + 𝜋𝑘𝑡+1

⁄

𝑦

),

which depends directly on the investment risk premium, 𝑟𝑝𝑟𝑒𝑚𝑘𝑡
as: 

𝑠 . The dividends are defined 

𝑑𝑖𝑘𝑡 = (1 − 𝜏𝐾 ) (

𝑌
𝑃𝑖𝑘𝑡
𝑌 𝑌𝑖𝑘𝑡 −
𝑃𝑘𝑡

𝑊𝑘𝑡
𝑌 𝑁𝑖𝑘𝑡) + 𝜏𝐾 𝛿𝑘
𝑃𝑘𝑡

𝐼
𝑃𝑘𝑡
𝑌 𝐾𝑖𝑘𝑡−1 −
𝑃𝑘𝑡

𝐼
𝑃𝑘𝑡
𝑌 𝐼𝑖𝑘𝑡 − 𝑎𝑑𝑗𝑖𝑘𝑡, 
𝑃𝑘𝑡

where 𝐼𝑖𝑘𝑡 is physical investment, 𝑃𝑘𝑡

𝐼  is the investment price, 𝜏𝐾  is the corporate tax, and 𝛿𝑘 is 
the capital depreciation rate. 𝑎𝑑𝑗𝑖𝑘𝑡 summarizes adjustment costs on production factors, namely 

capital and labour, and on capacity utilization, labour hoarding and investment. 

3.3. Trade 

3.3.1 Import sector 

The EA MS final  aggregate demand component goods,  𝐶𝑘𝑡  (private consumption  good),  𝐼𝑘𝑡 
𝐺   (government 

(private  investment  good),  𝐺𝑘𝑡  (government  consumption  good),  and  𝐼𝑘𝑡

investment good), as well as 𝑋𝑘𝑡 (export good) are produced by perfectly competitive firms by 
𝑍 , where 𝑍 = {𝐶, 𝐼, 𝐺, 𝐼𝐺, 𝑋}, using 

𝑍 , with imported goods, 𝑀𝑘𝑡

combining domestic output, 𝑂𝑘𝑡
the following CES technology: 

𝑝𝑧
𝑍𝑘𝑡 = 𝐴𝑘𝑡

[(1 − 𝜀𝑘𝑡

𝑀 𝑠𝑘

𝑀,𝑍)

1
𝑧 (𝑂𝑘𝑡
𝑍 )
𝜎𝑘

𝑧 −1
𝜎𝑘
𝑧
𝜎𝑘

+ (𝜀𝑘𝑡

𝑀 𝑠𝑘

𝑀,𝑍)

1
𝑧 (𝑀𝑘𝑡
𝑍 )
𝜎𝑘

𝑧 −1
𝜎𝑘
𝑧
𝜎𝑘

]

𝑧
𝜎𝑘
𝑧 −1
𝜎𝑘

, 

𝑝𝑧
where 𝐴𝑘𝑡

 is a shock to productivity in the sector producing goods, 𝜀𝑘𝑡

𝑀  is a shock to the share 

of  good-specific  import  demand  components,  𝑠𝑘

𝑀,𝑍,  and  𝜎𝑘

𝑧  is  the  elasticity  of  substitution 

7 Productivity is a non-stationary stochastic process subject to trend and level shocks (see Appendix A). 
8  According to  Burnside  and  Eichenbaum  (1996),  firms  prefer  not  to  lay  off  workers  when  the  demand  is temporarily  low  because  firing 
workers may be more costly than hoarding them. Additionally, the inclusion of labour hoarding helps matching the observed co-movement 
between output and working hours. 

9 

 
 
                                           
between domestic output and imports. It follows that the demand for 𝑂𝑘𝑡

𝑍  and imported goods 

𝑍  are given by:  

𝑀𝑘𝑡

𝑝𝑧
𝑍 = (𝐴𝑘𝑡

𝑂𝑘𝑡

)

𝜎𝑧−1

(1 − 𝜀𝑘𝑡

𝑀 𝑠𝑘

𝑀,𝑍) (

𝑧
−𝜎𝑘

𝑂
𝑃𝑘𝑡
𝑍 )
𝑃𝑘𝑡

𝑍𝑘𝑡, 

𝑝𝑧
𝑍 = (𝐴𝑘𝑡

𝑀𝑘𝑡

)

𝜎𝑧−1

𝑀 𝑠𝑘
𝜀𝑘𝑡

𝑀,𝑍 (

𝑧
−𝜎𝑘

𝑀
𝑃𝑘𝑡
𝑍 )
𝑃𝑘𝑡

𝑍𝑘𝑡, 

where 𝑃𝑘𝑡

𝑂  and 𝑃𝑘𝑡
total final good deflator 𝑃𝑘𝑡

𝑍  is: 

𝑀 are the price deflators associated with 𝑂𝑘𝑡

𝑍  and 𝑀𝑘𝑡

𝑍 , respectively, and the 

𝑝𝑧
𝑍 = (𝐴𝑘𝑡
𝑃𝑘𝑡

)

−1

[(1 − 𝜀𝑘𝑡

𝑀 𝑠𝑘

𝑀,𝑍)(𝑃𝑘𝑡

𝑧
𝑂 )1−𝜎𝑘

+ 𝜀𝑘𝑡

𝑀 𝑠𝑘

𝑀,𝑍(𝑃𝑘𝑡

𝑧
𝑀)1−𝜎𝑘

1
𝑧
1−𝜎𝑘

]

Perfectly competitive firms produce final imported goods, 𝑀𝑘𝑡, by combining country-specific 

final import goods, 𝑀𝑙𝑘𝑡, using a CES production function: 

𝑀)
𝑀𝑘𝑡 = [∑ (𝑠𝑙𝑘

𝑙

1
𝐹𝑀
𝜎𝑘

(𝑀𝑙𝑘𝑡

𝑠𝑖𝑧𝑒𝑙
𝑠𝑖𝑧𝑒𝑘

)

𝐹𝑀

𝜎𝑘
𝐹𝑀−1
𝜎𝑘

, 

𝐹𝑀−1
𝜎𝑘
𝐹𝑀
𝜎𝑘

]

where 𝜎𝑘

𝐹𝑀 is the price elasticity of demand for country 𝑙’s goods and 𝑠𝑖𝑧𝑒𝑙 denotes the share 
of country 𝑙 in world output. Since all products from foreign country 𝑙 are initially purchased at 
𝑋, 
𝑀 = 𝑒𝑙𝑘𝑡𝑃𝑙𝑡

export price, 𝑃𝑙𝑡
where 𝑒𝑙𝑘𝑡 is the bilateral exchange rate between domestic country k and foreign country l. 

𝑋, the economy-specific import good price can be expressed as: 𝑃𝑙𝑘𝑡

3.3.2. Export sector 

The exporting firms are competitive and export a good 𝑋𝑘𝑡 that is a combination of domestic 

output and import content. The corresponding export price is given by: 

𝑃𝑘𝑡

𝑋 = 𝑒𝑥𝑝(𝜀𝑘𝑡

𝑋 )[(1 − 𝑠𝑘

𝑀,𝑍)(𝑃𝑘𝑡

𝑧
𝑂 )1−𝜎𝑘

+ 𝑠𝑘

𝑀,𝑍(𝑃𝑘𝑡

𝑧
𝑀)1−𝜎𝑘

1
𝑧 , 
1−𝜎𝑘
]

where 𝜀𝑘𝑡

𝑋  captures an export-specific price shock. 

3.4. Monetary and fiscal policy 

3.4.1. EA Taylor rule 

The ECB sets the policy rate 𝑖𝐸𝐴𝑡 in response to the annualized EA-wide inflation gap, 𝜋𝐸𝐴𝑡
and the annualized EA output gap: 

𝑐,𝑣𝑎𝑡,𝑄𝐴, 

10 

 
 
𝑖𝐸𝐴𝑡 − 𝑖̅ = 𝜌𝑖(𝑖𝐸𝐴𝑡−1 − 𝑖̅) + (1 − 𝜌𝑖) [𝜂𝐸𝐴

𝑖𝜋 0.25(𝜋𝐸𝐴𝑡

𝑐,𝑣𝑎𝑡,𝑄𝐴 − 𝜋̅𝐸𝐴

𝑐,𝑣𝑎𝑡,𝑄𝐴) +

𝑖𝑦 (𝑙𝑜𝑔(0.25 ∑
𝜂𝐸𝐴

4
𝑟=1

𝑌𝐸𝐴𝑡−𝑟

) − 𝑙𝑜𝑔(0.25 ∑

4
𝑟=1

𝑝𝑜𝑡
𝑌𝐸𝐴𝑡−𝑟

))] + 𝜀𝐸𝐴𝑡

𝑖

, 

where 𝑖̅ = 𝑟 + 𝜋̅ 𝑌 is the steady-state nominal interest rate, equal to the sum of the steady-state 

real  interest  rate and  GDP inflation in  the steady state. The policy parameters (𝜌𝑖, 𝜂𝑖𝜋, 𝜂𝑖𝑦) 

capture the interest rate inertia and the response to the annualized inflation and output gaps, 

respectively. 𝜀𝐸𝐴𝑡

𝑖

 captures unexpected monetary policy changes. 

3.4.2. Member State fiscal policy 

𝑁, capital, 𝜏𝐾 , and consumption, 𝜏𝐶 , as well as lump-

The government collects taxes on labour, 𝜏𝑘
sum taxes, 𝑡𝑎𝑥𝑘𝑡, and constant excise duties on oil imports from RoW, 𝜏𝑂𝑖𝑙𝑃𝑌0, and it issues 
𝑔 .  Government  spending  includes  public  consumption,  𝐺𝑘𝑡,  public 
𝐺 , and 𝑇𝑘𝑡  follow 

𝐺 , transfers, 𝑇𝑘𝑡 , and the servicing of the outstanding debt. 𝐺𝑘𝑡, 𝐼𝑘𝑡

one-period  bonds,  𝐵𝑘𝑡

investment, 𝐼𝑘𝑡

𝒢 : 
autoregressive processes with shocks 𝜀𝑘𝑡

𝒢𝑘𝑡
𝑌 𝑌𝑘𝑡
𝑃𝑘𝑡

− 𝒢̅ = 𝜌𝑘

𝒢 (

𝒢𝑘𝑡−1
𝑌 𝑌𝑘𝑡−1
𝑃𝑘𝑡−1

𝒢 , 
− 𝒢̅) + 𝜀𝑘𝑡

where 𝒢 ∈ {𝐺, 𝐼𝐺, 𝑇} 𝑎𝑛𝑑 The government budget constraint is: 

𝑔 = (1 + 𝑖𝑘𝑡−1
𝐵𝑘𝑡

𝑔

)𝐵𝑘𝑡−1

𝑔 − 𝑅𝑘𝑡

𝐺 + 𝑃𝑘𝑡

𝐺 𝐺𝑘𝑡 + 𝑃𝑘𝑡

𝐼𝐺𝐼𝑘𝑡

𝐺 + 𝑇𝑘𝑡, 

where nominal government revenues, 𝑅𝑘𝑡

𝐺 , are: 

𝐺 = 𝜏𝐾 (𝑃𝑘𝑡
𝑅𝑘𝑡

𝑌 𝑌𝑘𝑡 − 𝑊𝑘𝑡𝑁𝑘𝑡 − 𝑃𝑘𝑡

𝐼 𝛿𝑘𝐾𝑘𝑡−1) + 𝜏𝑘

𝑁𝑊𝑘𝑡𝑁𝑘𝑡 + 𝜏𝐶 𝑃𝑘𝑡

𝐶 𝐶𝑘𝑡 + 𝜏𝑂𝑖𝑙𝑃𝑌0𝑂𝑖𝑙𝑡 + 𝑡𝑎𝑥𝑘𝑡. 

The government uses lump-sum taxes as a budget closure and increases (lowers) them when 

government debt and deficit are above (below) the respective targets, 𝐵̅
𝑘

𝑔 and 𝐷𝐸𝐹𝑘

𝑇:  

𝑡𝑎𝑥𝑘𝑡
𝑌 𝑌̅̅̅̅̅̅
𝑃𝑘𝑡
𝑘𝑡

= 𝜌𝑡𝑎𝑥 (

𝑡𝑎𝑥𝑘𝑡−1
𝑌 𝑌̅̅̅̅̅̅
𝑃𝑘𝑡
𝑘𝑡

) + 𝜂𝑘

𝐷𝐸𝐹 (

𝑔
Δ𝐵𝑘𝑡−1
𝑌 𝑌𝑘𝑡−1

𝑃𝑘𝑡−1

− 𝐷𝐸𝐹𝑘

𝑇) + 𝜂𝑘

𝐵 (

𝑔
𝐵𝑘𝑡−1
𝑌 𝑌𝑘𝑡−1

𝑃𝑘𝑡−1

− 𝐵̅
𝑘

𝑔) + 𝜀𝑘𝑡

𝑡𝑎𝑥. 

3.5. The trade balance and aggregate accounting  

Market clearing requires that: 

𝑌𝑘𝑡𝑃𝑘𝑡

𝑌 + 𝜏𝑡

𝑂𝑖𝑙𝑂𝑖𝑙𝑘𝑡𝑃𝑌0 = 𝑃𝑘𝑡

𝐶 𝐶𝑘𝑡 +   𝑃𝑘𝑡

𝐼 𝐼𝑘𝑡 + 𝑃𝑘𝑡

𝐺 𝐺𝑘𝑡 + 𝑃𝑘𝑡

𝐼𝐺𝐼𝐺𝑘𝑡 + 𝑇𝐵𝑘𝑡, 

where  the  trade  balance,  𝑇𝐵𝑘𝑡,  is  defined  as  the  difference  between  nominal  exports  and 

imports, with domestic importers buying the imported good at the price 𝑃𝑙𝑡

𝑋: 

11 

 
𝑇𝐵𝑘𝑡 = 𝑃𝑘𝑡

𝑋 𝑋𝑘𝑡 − ∑ 𝑠𝑖𝑧𝑒𝑙
𝑠𝑖𝑧𝑒𝑘

𝑙

𝑒𝑙𝑘𝑡𝑃𝑙𝑡

𝑋𝑀𝑙𝑘𝑡

− 𝑒𝑅𝑜𝑊𝑘𝑡𝑃𝑅𝑜𝑊𝑡

𝑂𝑖𝑙 𝑂𝐼𝐿𝑅𝑜𝑊𝑡. 

Exports  are  the  sum  of  imports  by  other  countries  from  the  domestic  economy,  i.e.  𝑋𝑘𝑡 =
∑ 𝑀𝑙𝑘𝑡

,  where  𝑀𝑙𝑘𝑡  stands  for  imports  of  economy  l  from  the  domestic  economy  k.  Total 

𝑙

imports are: 

𝑀𝑡𝑜𝑡𝑀𝑘𝑡
𝑃𝑘𝑡

𝑡𝑜𝑡 = 𝑃𝑘𝑡

𝑀𝑀𝑘𝑡 + 𝑃𝑘𝑡

𝑜𝑖𝑙𝑂𝐼𝐿𝑘𝑡, 

where non-oil imports are 𝑃𝑘𝑡
𝑤 , evolve according to:9 

𝐵𝑘𝑡

𝑀𝑀𝑘𝑡 = 𝑃𝑘𝑡

𝑀(𝑀𝑘𝑡

𝐶 + 𝑀𝑘𝑡

𝐼 + 𝑀𝑘𝑡

𝐺 + 𝑀𝑘𝑡

𝐼𝐺). Net foreign assets (NFA), 

𝑒𝑅𝑜𝑊𝑘,𝑡𝐵𝑘,𝑡

𝑤 = (1 + 𝑖𝑡−1

𝑏𝑤 )𝑒𝑅𝑜𝑊𝑘,𝑡𝐵𝑘,𝑡−1

𝑤 + 𝑇𝐵𝑘𝑡 + 𝐼𝑇𝑅𝑘𝑃𝑘𝑡

𝑌 𝑌𝑘𝑡. 

NFA sum to zero at the global level, i.e. ∑ 𝑁𝐹𝐴𝑙𝑡𝑠𝑖𝑧𝑒𝑙

𝑙

= 0. 

3.6. The REA and RoW blocks  

The REA and RoW (subscript  k=REA, RoW) model blocks follow a simplified structure. It 

consists of a budget constraint for the representative household, demand functions for domestic 

and imported goods, a linear production technology, a New Keynesian Phillips curve, and a 

Taylor rule. The REA and RoW blocks abstract from capital accumulation.10 There are shocks 

to labour productivity, price mark-ups for final output, the subjective discount rate, the relative 

preference for domestic vs. imported goods, as well as monetary policy shocks. 

The budget constraint for the representative household in REA, as an oil importer, is: 

𝑌 𝑌𝑅𝐸𝐴𝑡 + 𝜏𝑂𝑖𝑙𝑃𝑌0𝑂𝑖𝑙𝑅𝐸𝐴𝑡 = 𝑃𝑅𝐸𝐴𝑡
𝑃𝑅𝐸𝐴𝑡

𝐶

𝐶𝑅𝐸𝐴,𝑡 + 𝑇𝐵𝑅𝐸𝐴𝑡, 

where 𝜏𝑂𝑖𝑙𝑃𝑌0𝑂𝑖𝑙𝑅𝐸𝐴𝑡 captures the excise duty.11 Total nominal exports of final goods for REA 

and RoW are defined as: 𝑃𝑘𝑡

𝑋 𝑋𝑘𝑡 = ∑ 𝑃𝑙𝑘𝑡

𝑋 𝑀𝑙𝑘𝑡

𝑙

,with the bilateral export price being defined as 

the domestic price subject to a bilateral price shock, 𝑃𝑙𝑘𝑡

𝑋 = exp (𝜀𝑙𝑘𝑡

𝑌 . 
𝑋 )𝑃𝑘𝑡

We  combine  the  FOCs  of  REA  and  RoW  with  respect  to  international  bonds  to  obtain  the 

uncovered interest parity (UIP) condition: 

𝐸𝑡 [

𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡+1
𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡

] (1 + 𝑖𝑅𝑜𝑊𝑡) = (1 + 𝑖𝐸𝐴𝑡) + 𝜀𝐸𝐴𝑡

𝑏𝑤 + 𝛼𝐸𝐴

𝑏𝑤0 + 𝛼𝐸𝐴

𝑤
𝑏𝑤1 𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡𝐵𝐸𝐴𝑡
𝑃𝐸𝐴𝑡

𝑌 𝑌𝐸𝐴𝑡

9 Since we allow for a non-zero trade balance in the steady state, we include an international transfer, 𝐼𝑇𝑅𝑘, calibrated to satisfy zero NFA in 
equilibrium. 
10 Appendix B.5 shows that our main results remain unaffected when we extend the model by capital formation and multi-input production 
functions in the REA and the RoW. For clarity, we thus choose the simpler approach outlined here as the benchmark. 
𝑂𝑖𝑙 𝑂𝑖𝑙𝑙𝑡 =
11  In  contrast,  since  RoW  is  an  oil  exporter,  the  budget  constraint  for  the  representative  household  is:  𝑃𝑅𝑜𝑊𝑡
𝐶
 and 𝑂𝑖𝑙𝑅𝑜𝑊𝑙𝑡 are price and volume of 
 and 𝑌𝑅𝑜𝑊𝑡 are price and volume of RoW final good output, 𝑃𝑅𝑜𝑊𝑙𝑡
𝑃𝑅𝑜𝑊𝑡
oil exports to country l=(EMU regions), and 𝑇𝐵𝑅𝑜𝑊𝑡 is the trade balance. For simplicity, oil is an unstorable exogenous endowment of RoW 
and is supplied inelastically. The price of oil, 𝑃𝑅𝑜𝑊𝑡

𝐶𝑅𝑜𝑊,𝑡 + 𝑇𝐵𝑅𝑜𝑊𝑡, where 𝑃𝑅𝑜𝑊𝑡

, is determined in RoW currency. 

𝑌𝑅𝑜𝑊𝑡 + 𝑃𝑅𝑜𝑊𝑙𝑡

𝑂𝑖𝑙

𝑂𝑖𝑙

𝑌

𝑌

12 

 
 
                                           
where 𝜀𝐸𝐴𝑡

𝑏𝑤  captures a bond premium shock between EA and RoW (exchange rate shock), and 

𝑏𝑤1 is a debt-dependent country risk premium on NFA holdings.12  

𝛼𝐸𝐴

In  the  absence  of  investment  and  government  spending  in  the  REA  and  RoW  blocks,  final 

domestic demand, 𝐶𝑘𝑡, is a CES aggregate of domestic output, 𝑌𝑘𝑡, and imported goods, 𝑀𝑘𝑡: 

𝐶𝑘𝑡 = 𝐴𝑘𝑡

𝑝 [(1 − 𝑠𝑘

𝑀)

1
𝑐 (𝑌𝑘𝑡
𝐶 )
𝜎𝑘

𝑐 −1
𝜎𝑘
𝑐
𝜎𝑘

1
𝑐 (𝑀𝑘𝑡
𝐶 )
𝜎𝑘

𝑐 −1
𝜎𝑘
𝑐
𝜎𝑘

+ (𝑠𝑘

𝑀)

𝑐
𝜎𝑘
𝑐 −1
𝜎𝑘

]

, 

where 𝑠𝑘

𝑀 the import share. 

The  intermediate  good  producers  use  labour  to  manufacture  domestic  goods  :𝑌𝑘𝑡 = 𝐴𝑘𝑡

𝑌 𝑁𝑘𝑡, 
𝑌   captures  a  trend  in  productivity.  Price  setting  follows  a  New  Keynesian  Phillips 

where  𝐴𝑘𝑡
curve: 

𝑌 − 𝜋̅𝑘
𝜋𝑘𝑡

𝑌 = 𝛽

𝜆𝑘𝑡+1
𝜆𝑘𝑡

[𝑠𝑓𝑝𝑘(𝜋𝑘𝑡+1

𝑌 − 𝜋̅𝑘

𝑌) + (1 − 𝑠𝑓𝑝𝑘)(𝜋𝑘𝑡−1

𝑌 − 𝜋̅𝑘

𝑌)] + 𝜑𝑘

𝑌 ln(𝑌𝑘𝑡 − 𝑌̅𝑘) +

𝑀𝑈𝑌, 
𝜀𝑘𝑡

where 𝜆𝑘𝑡 = (𝐶𝑘𝑡 − ℎ𝑘𝐶𝑘𝑡−1)−𝜃𝑘 is the marginal utility of consumption, 𝑠𝑓𝑝𝑘 is the share of 
forward-looking price-setters, and 𝜀𝑘𝑡

𝑀𝑈𝑌 is a cost-push shock.  

The  intertemporal  equation  for  aggregate  domestic  demand  follows  from  the  FOC  for 

consumption: 

𝛽𝑡

𝜆𝑘𝑡+1
𝜆𝑘𝑡

1 + 𝑖𝑘𝑡
𝐶
1 + 𝜋𝑘𝑡+1

= 1 

with 𝛽𝑡 = exp (𝜀𝑘𝑡

𝐶 ) 𝛽, and 𝜀𝑘𝑡

𝐶  as the REA and RoW demand shock, respectively.  

Monetary policy in RoW follows a Taylor-type rule similar to the EA (estimated parameters 

are region-specific). 

12 The endogenous risk premium ensures long-run stability of the NFA position (see, e.g., Adolfson et al., 2008; Schmitt-Grohe and Uribe, 
2003). 

13 

 
 
                                           
4. Model solution and econometric approach 

The following non-linear system summarizes the state-space representation of our model: 

𝐸𝑡[ℱ(𝑦𝑡+1, 𝑦𝑡, 𝑦𝑡−1, 𝜀𝑡; 𝜃)] = 0, 

where  𝑦𝑡  collects  all  endogenous  variables  of  the  model,  while  𝜀𝑡  is  a  vector  of  exogenous 

shocks.  We  compute  an  approximate  model  solution  by  linearizing  the  model  around  its 

deterministic  steady  state.  Given  the  structural  parameters  collected  in  𝜃,  the  linear  rational 

expectation solution takes the following form: 

where Φ1 and Φ𝜀 govern the decision rules of the model.  

𝑦𝑡 = Φ1(𝜃) + Φ𝜀(𝜃)𝜀𝑡,  

We  calibrate  a  subset  of  parameters  to  match  long-run  data  properties,  and  we  estimate  the 

remaining  parameters  with  Bayesian  methods  using  data  for  the  period  1999q1-2018q4.  To 

perform a large number of robustness checks, we use a computationally efficient parallelized 

slice sampling algorithm.13  Appendix C provides information on data transformations and our 

data set. 

The  calibration  of  parameters  for  the  long  run  replicates  average  historical  ratios  and  trade 

shares for the respective MS (see Table B.1.1 in the appendix). All real GDP components on 

the demand side (deflated by the GDP deflator) are assumed to grow at the average growth rate 

of output over the sample period. Prices in steady state grow at a rate of 2% per year. We set 

the steady-state share of Ricardian households according to the survey evidence in Dolls et al. 

(2012). The parameters of the EA monetary policy rule have been estimated in a two-region 

(EA-RoW) version of the model and are imposed here to ensure an identical policy rule for both 

EA configurations, i.e. DE-REA-RoW and ES-REA-RoW.  

13 We use the DYNARE software (Adjemian et al., 2011). The estimated model includes 39 exogenous shocks, as it appears that many shocks 
are needed to capture the dynamic properties of the macroeconomic and financial data (e.g., Kollmann et al., 2015). The large number of shocks 
is also dictated by the fact that we use a large number of observables (38) for the estimation. For details on slice sampling, see Neal (2003) and 
Planas et al. (2015). 

14 

 
                                           
Table 1: Selected estimated model parameters  

Consumption habit persistence 

Risk aversion 

Share of forward-looking wage setters 

Inverse Frisch elasticity 

Share of forward-looking price setters 

Elasticity of substitution of imports  

Bilateral price elasticity of imports 

Oil price elasticity 

Price adjustment cost 

ℎ 

𝜃 

𝑠𝑓𝑤 

𝜃𝑁 

sfp 

𝜎 𝑧 

𝜎𝐹𝑀 

𝜎𝑂 

𝛾𝑃 

Beta 

Gamma 

Normal 

Gamma 

Prior distribution 
Mean 
Distr 
St.dev. 
Preferences 
0.5 
0.1 
1.5 
0.2 
1 
0.5 
2.5 
0.5 
1 
0.5 
2 
0.4 
2 
1 
0.5 
0.2 

Gamma 

Gamma 

Gamma 

Normal 

Nominal and real frictions 
Gamma 

Nominal wage adjustment cost 

𝛾𝑤    

Gamma 

Real wage rigidity 

Employment adjustment cost 

𝛾𝑤𝑟 

Beta 

𝛾𝑛 

Gamma 

Labour hoarding adjustment cost 

𝛾𝑓𝑛,2 

Gamma 

Capacity utilization adj. cost 

Capital stock adjustment cost 

Investment adjustment cost 

𝛾𝑢,2 

𝛾𝐼,1 

𝛾𝐼,2 

Gamma 

Gamma 

Gamma 

Lump-sum tax persistence 

Lump-sum tax response to deficit 

Lump-sum tax response to debt 

𝜌𝑡𝑎𝑥 

Beta 

𝜂𝐷𝐸𝐹 

Beta 

𝜂𝐵  

Beta 

Consumption habit persistence 

Risk aversion 

Import price elasticity 

Phillips curve slope 

ℎ 

𝜃 

𝜎𝐶 

𝜑𝑌  

Beta 

Gamma 

Gamma 

Gamma 

Share of forward-looking price setters 

sfp

REA 

Normal 

Consumption habit persistence 

Risk aversion 

Import price elasticity 

Phillips curve slope 

ℎ 

𝜃 

𝜎𝐶 

𝜑𝑌 

Beta 

Gamma 

Gamma 

Gamma 

Share of forward-looking price setters 

sfp

RoW 

Normal 

60 
40 
5 
2 
0.5 
0.2 
60 
40 
2 
0.5 
0.003 
0.0012 
60 
40 
60 
40 

Fiscal policy 
0.5 
0.2 
0.03 
0.008 
0.02 
0.01 
REA region 
0.7 
0.1 
1.5 
0.2 
2 
0.4 
0.025 
0.01 
1 
0.5 
RoW region 
0.7 
0.1 
1.5 
0.2 
2 
0.4 
0.025 
0.01 
1 
0.5 

Posterior distribution 

DE 

ES 

0.68 
(0.67, 0.80) 
1.45 
(1.18, 1.80) 
0.75 
(0.47,0.90) 
2.43 
(1.83, 3.14) 
0.98 
(0.89,1.00) 
1.48 
(1.13, 1.49) 
2.00 
(0.57,2.86) 
0.19 
(0.02, 0.33) 

28.33 
(12.62, 38.30) 
4.40 
(2.64, 6.44) 
0.96 
(0.95, 0.98) 
41.68 
(15.78, 66.53) 
1.52 
(1.21, 1.84) 
0.004 
(0.002, 0.006) 
46.68 
(33.39,65.58) 
9.66 
(0.98, 19.90) 

0.88 
(0.90, 0.97) 
0.02 
(0.01, 0.04) 
0.003 
(0.001, 0.006) 

0.87 
(0.80, 0.89) 
1.49 
(1.22, 1.78) 
1.37 
(1.10, 1.40) 
0.03 
(0.02, 0.05) 
0.79 
(0.38,0.82) 

0.92 
(0.88, 0.93) 
1.31 
(1.28, 2.05) 
1.38 
(1.14, 1.54) 
0.01 
(0.01, 0.05) 
0.25 
(0.01,0.60) 

0.70 
(0.68, 0.81) 
1.75 
(1.39, 1.96) 
0.77 
(0.32,0.89) 
2.23 
(1.45, 2.58) 
0.98 
(0.93, 1.00) 
1.21 
(1.11, 1.40) 
0.85 
(0.37,2.44) 
0.25 
(0.03, 0.42) 

22.42 
(14.70, 29.70) 
1.53 
(1.41, 3.77) 
0.97 
(0.97, 0.99) 
10.07 
(5.17, 19.90) 
1.30 
(1.08, 1.52) 
0.004 
(0.001, 0.004) 
34.49 
(17.92, 51.88) 
55.93 
(51.96, 128.75) 

0.94 
(0.92, 0.98) 
0.03 
(0.02, 0.04) 
0.003 
(0.002, 0.005) 

0.84 
(0.79, 0.89) 
1.37 
(1.25, 1.79) 
1.39 
(1.11, 1.35) 
0.03 
(0.02, 0.05) 
0.72 
(0.17,0.72) 

0.88 
(0.87, 0.92) 
1.64 
(1.37, 2.04) 
1.39 
(1.16, 1.59) 
0.05 
(0.01, 0.06) 
0.90 
(0.03,0.92) 

Note: Cols. (1)-(2) list model parameters. Cols. (3)-(4) indicate the prior distribution function. Identical priors 
are assumed for DE and ES parameters. Cols. (5)-(8) show the mode and the (10% and 90% ) HPD intervals of 
the posterior distributions.  

15 

 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 1 presents the chosen priors and posterior estimates for key parameters. Consumption 

habit  persistence  of  around  0.7  in  DE  and  ES  suggests  relatively  sluggish  adjustment  of 

consumption demand to changes in income. The model estimation indicates a slightly higher 

risk  aversion  and  labour  supply  elasticity  in  ES.  Aggregate  import  price  elasticities  are 

estimated at 1.5 and 1.2 in DE and ES, respectively. Lower employment adjustment costs in ES 

relate  to  the  highly  cyclical  unemployment  dynamics  observed  in  the  last  two  decades.  The 

estimates also suggest substantial nominal rigidities in prices and wages.  

Demand shocks are highly serially correlated, as shown in Table 2.14 Appendix B.2 shows that 

model-implied  moments  are  close  to  the  data  and  that  the  estimated  model  successfully 

replicates business cycles features in DE and ES. 

14 Table B.1.2 in Appendix B.1 provides the estimated exogenous shock processes in REA and RoW for both model versions (DE and ES). 

16 

 
 
                                           
Subjective discount factor 

Investment risk premium 

Domestic price mark-up 

Labor supply 

Flight-to-safety 

Trade share 

Export price 

International bond preferences 

Government consumption 

Government transfers 

Government investment 

Government tax 

Permanent TFP growth 

Subjective discount factor 

Investment risk premium 

Price mark-up 

Labor supply 

Flight-to-safety 

Trade share 

Export price 

Table 2: Selected estimated exogenous shock processes 

Prior distribution 
Mean 
Distr 
St.dev. 

Posterior distribution 

DE 

ES 

Autocorrelation of forcing variables 

𝜌𝑈𝐶 

𝜌𝑆 

𝜌𝑀𝑈𝑌 

𝜌𝑈 

𝜌𝐹𝑄 

𝜌𝑀 

𝜌𝑋 

𝜌𝐵𝑊 

𝜌𝐺  

𝜌𝑇  

𝜌𝐼𝐺  

𝜌𝑇𝐴𝑋  

𝜌𝐺𝐴𝑌 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

Beta 

0.5 
0.2 
0.85 
0.05 
0.5 
0.2 
0.5 
0.2 
0.85 
0.05 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.7 
0.1 
0.5 
0.2 
0.5 
0.2 

0.87 
(0.81, 0.91) 
0.90 
(0.87, 0.95) 
0.67 
(0.54, 0.76) 
0.90 
(0.87, 0.96) 
0.96 
(0.94, 0.99) 
0.87 
(0.86, 0.96) 
0.97 
(0.96, 0.99) 
0.94 
(0.88, 0.94) 
0.96 
(0.91, 0.96) 
0.96 
(0.95, 0.98) 
0.85 
(0.78, 0.90) 
0.88 
(0.88,0.97) 
0.96 
(0.94, 0.97) 

Standard deviation (%) of innovations to forcing variables 

𝜀𝑈𝐶 

𝜀𝑆 

Gamma 

Gamma 

𝜀𝑀𝑈𝑌 

Gamma 

𝜀𝑈 

𝜀𝐹𝑄 

𝜀𝑀 

𝜀 𝑋 

Gamma 

Gamma 

Gamma 

Gamma 

1 
0.4 
0.1 
0.04 
2 
0.8 
1 
0.4 
1 
0.04 
1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
0.01 
0.004 
0.01 
0.004 
1 
0.4 

0.74 
(0.51, 1.34) 
0.20 
(0.14, 0.31) 
5.70 
(3.10, 6.40) 
1.40 
(0.86, 1.97) 
0.08 
(0.07, 0.10) 
2.50 
(2.00, 2.52) 
0.34 
(0.31, 0.42) 
0.14 
(0.15, 0.28) 
0.12 
(0.11, 0.16) 
0.13 
(0.11, 0.14) 
0.07 
(0.06,0.08) 
0.62 
(0.53, 0.65) 
0.006 
(0.005, 0.007) 
0.002 
(0.001, 0.002) 
0.097 
(0.080, 0.099) 

0.84 
(0.81, 0.89) 
0.94 
(0.94, 0.97) 
0.21 
(0.14, 0.59) 
0.88 
(0.80, 0.92) 
0.96 
(0.92, 0.98) 
0.89 
(0.84, 0.94) 
0.86 
(0.86,0.96) 
0.90 
(0.85, 0.95) 
0.92 
(0.90, 0.93) 
0.96 
(0.94, 0.97) 
0.94 
(0.92, 0.97) 
0.94 
(0.92,0.98) 
0.97 
(0.95, 0.98) 

1.00 
(0.63, 1.37) 
0.23 
(0.17, 0.31) 
5.80 
(4.10, 7.10) 
1.50 
(1.50, 3.16) 
0.07 
(0.06, 0.09) 
2.40 
(2.20, 2.91) 
0.64 
(0.61,0.80) 
0.23 
(0.14, 0.34) 
0.11 
(0.11, 0.13) 
0.23 
(0.19, 0.25) 
0.24 
(0.23,0.29) 
1.04 
(0.97, 1.27) 
0.010 
(0.001, 0.003) 
0.002 
(0.001, 0.003) 
0.090 
(0.082, 0.109) 

International bond preferences 

𝜀𝐵𝑊 

Gamma 

Government consumption 

Government transfers 

Government investment 

Government tax 

Permanent TFP growth 

Permanent TFP level 

EA monetary policy 

𝜀𝐺 

𝜀𝑇 

𝜀𝐼𝐺 

𝜀𝑇𝐴𝑋 

𝜀𝐺𝐴𝑌 

𝜀𝐿𝐴𝑌 

Gamma 

Gamma 

Gamma 

Gamma 

Gamma 

Gamma 

𝜀𝑖 

Gamma 

Note: Cols. (1)-(2) list model innovations. Cols. (3)-(4) indicate the prior distribution function. Identical 
priors are assumed for DE and ES parameters. Cols. (5)-(8) show the mode and the (10% and 90%) HPD 
intervals of the posterior distributions. 

17 

 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5. Estimated drivers of the trade balance in the benchmark model 

This  section  quantifies  the  main  drivers  of  the  TBs  of  DE  and  ES  based  on  the  estimated 

benchmark model. Figure 3 and Figure 4 assess the role of different shocks as drivers of the TB 

for DE and ES, respectively. We first consider the historical decomposition of DE TB as the 

EA's emblematic surplus country in Figure 3.  

Figure 3: Shock decomposition of the German trade balance-to-GDP ratio 

Note: Units on the  x-axis are  years and units on the  y-axis  measure  the trade balance as  a share  of  GDP 
relative  to its sample  mean,  where  0.01 corresponds to 1% of GDP. The mean (steady state) of the trade 
balance-to-GDP ratio in DE is 4.0%. The solid lines represent the historical series of the trade balance-to-
GDP  ratio  from  which  we  have  subtracted  the  sample  average.  Vertical  bars  measure  the  estimated 
contribution  of  different  shock  groups.  Bars  above  (below)  the  x-axis  indicate  positive  (negative) 
contributions to the trade balance relative to its average in a given year. The sum of positive and negative 
contributions matches the data (solid black line) for any point in time. We have assigned shocks to distinct 
groups, mainly focusing on demand versus supply shocks originating in different regions (domestic, REA, 
and RoW). In addition, we report shocks to preferences for foreign goods and mark-up shocks to import and 
export  prices  as  “trade  shocks”,  and  shocks  to  EA  monetary  policy  and  the  interest  rate  parity  condition 
between the EA and the RoW as "EXR and monetary policy shocks." The group "Others + Initial Values" 
summarizes any remaining factors and the effect of initial conditions. Initial conditions (“initial disbalances”) 
are estimated measures of how much the starting values in the data deviate from the model steady state. 

18 

 
 
 
 
The  estimates  suggest  that  domestic  demand  conditions,  namely  excess  saving  and  adverse 

investment  shocks,  account  for  a  large  share  of  the  surplus  build-up.  The  shocks  are  very 

persistent,  which  explains  the  non-cyclical  upward  trend  in  Figure  1  above.  Exchange  rate 

shocks (euro depreciation) in recent years have also contributed to the surplus. Trade shocks, 

notably higher demand for DE goods and services (preference shift), have contributed to the 

rising DE TB surplus in recent years. Positive trade shocks cannot explain the persistent upward 

trend in DE TB, however, given that the former have also been present (and even stronger) in 

the early 2000s, before switching sign in the Global financial crisis and recession that saw a 

pronounced  slowdown  in  world  trade.  Strong  (weak)  aggregate  demand  in  the  REA  has 

strengthened (lowered) DE TB before (during and after) the EA crisis.  

The global recession as a negative shock to RoW demand has been an important driver behind 

the decline in DE TB in 2009, and the RoW recovery has contributed to its renewed rise in the 

2010s. The positive contribution by domestic supply shocks reflects competitiveness gains from 

the  labour  market  (“Hartz”)  reforms  after  2004-05  and  wage  moderation,  but  the  effect  is 

temporary.15 External supply factors (REA and RoW) have little impact on DE TB and do not 

contribute to explaining the main pattern of a rising TB over the sample horizon.  

The dynamics of ES TB is more cyclical, as illustrated in Figure 1 above. The TB has displayed 

a  large  and  growing  deficit  during  the  first  decade  of  EMU  and  sharp  imbalance  correction 

afterwards.  The  historical  decomposition  in  Figure  4  shows  that  ES  TB  has  been  primarily 

driven  by  the  boom-bust  cycle  of  domestic  demand,  according  to  the  model  estimates.  The 

loosening of credit constraints, asset price bubbles, and the construction boom  led to  strong 

import  demand  and  pronounced  TB  deficits  in  the  pre-crisis  period.  Subsequently,  the 

contraction of domestic demand and the double-dip recession have led to a sharp TB reversal. 

The results suggest that the ES TB (in % of nominal GDP) would have been more than 5 pp 

higher in 2008 in the absence of positive domestic demand shocks, and the subsequent reversal 

about 4 pp weaker. Foreign (REA and RoW) demand has played a similar role as in the case of 

DE, and foreign supply shocks likewise have little impact. Trade shocks are noticeable, but, as 

for DE, they do not explain the overall pattern of ES TB. The role of euro exchange rate has 

been similar to DE's case and has supported the ES TB reversal after the global recession and 

EA crisis.  

15 We model the (“Hartz”) reforms as permanent shock to the unemployment benefit replacement rate. The estimated trade balance effects of 
this policy change are highly persistent. Appendix B.4 provides additional details.  

19 

 
                                           
Figure 4: Shock decomposition of the Spanish trade balance-to-GDP ratio 

Note: Units on the x-axis are years and units on the y-axis measure the trade balance as a share of GDP relative to 
its sample mean, where 0.01 corresponds to 1% of GDP. The mean (steady state) of the trade balance-to-GDP ratio 
in ES is -1.1%. For additional information see also the description below Figure 3. 

Appendix B.3 provides further details on the role of different shocks in the "domestic demand" 

group and stresses the minor role of the estimated fiscal shocks in the TB decompositions. In 

line with Giovannini et. al. (2019), it also shows that oil price shocks weigh negatively on DE 

and ES TBs, when the shocks correspond to a price increase, and positively, when the shocks 

imply a decline in oil prices, as e.g., in (2015-17), and the associated decline in the import bill. 

The contribution  of oil  price shocks to  DE and  ES TB dynamics remains modest,  however, 

compared to the impact of, notably, domestic demand shocks ES. 

In  sum,  the  estimated  benchmark  version  of  the  model  suggests  that  spillover  from  foreign 

shocks,  particularly  foreign  demand  shocks,  has  played  a  notable  but  limited  role  for  TB 

dynamics in DE and ES. The estimation provides little evidence for quantitatively important 

supply-driven  spillover,  such  as  exogenous  “competitive  gains/losses”  or  “competitive 

20 

 
 
 
pressure”,  on  the  TBs  of  DE  and  ES.  The  rest  of  the  paper  examines  the  secondary  role  of 

foreign shocks in more detail in a more agnostic setting.  

6. Inspecting the robustness of the benchmark results 

The estimated benchmark specification suggests that domestic demand conditions are the key 

drivers  of  DE  and  ES  TBs,  whereas  foreign  shocks,  and  in  particularly  foreign  supply-side 

shocks, play a much smaller role. The estimated model thus supports the hypothesis of primarily 

demand-  and  domestically-driven  TB  dynamics  in  the  two  countries.  This  section  presents 

econometric tests to assess the robustness of this result. Section 6.1 directly includes domestic 

and  foreign  mark-up  shocks  in  the  trade  equations  to  allow  for  a  stronger  presence  of 

competitiveness effects in trade, reflecting the idea that price and wage pressure from abroad 

may have affected net exports of EA Member States more strongly than foreseen by the standard 

trade equations, so that competitive pressure may explain part of the benchmark model’s trade 

shocks. Section 6.2 enriches the empirical specification more generally. It augments the model 

with agnostic structural disturbances (ASDs), proposed by Den Haan and Drechsel (2020), as 

a  “theory-free”  alternative  to  structural  shocks  (“drivers”)  that  we  identified  as  drivers  in 

Section 5.  

6.1 Strengthening the competitiveness channel  

This subsection inspects the role of price and wage dynamics for TB. We extend the benchmark 

specification  by  including  shocks  to  price  and  wage  dynamics  directly  in  the  behavioural 

equations describing import and export dynamics. Price and wage setting  equations remains 

identical to the benchmark model. We then re-estimate the model to test for a direct impact of 

price and wage shocks in the trade equations that goes beyond the impact via current prices. 

We consider four different specifications for each country, i.e. a total of eight estimated model 

versions. The first specification looks at domestic wage mark-up shocks and their potential to 

explain trade, notably exports. The second set-up does the same for domestic price mark-up 

shock.  For  completeness,  we  allow  the  domestic  shocks  to  also  enter  REA  and  RoW  trade 

equations  directly  in  the  first  two  variants.  The  two  remaining  experiments  incorporate, 

respectively,  REA  and  RoW  price  mark-up  shocks  in  the  trade  equations  to  allow  for  more 

direct  effects  of competitive pressure. Specifically,  DE  and ES  export and import equations 

include the REA and RoW mark-up shocks (𝜀𝑘𝑡
factors  in  these  experiments.  The  procedure  is  agnostic  in  the  sense  of  allowing  structural 

𝑀𝑈𝑌 with 𝑘 ∈ {𝑅𝐸𝐴, 𝑅𝑜𝑊}) as additional additive 

21 

 
 
disturbances  to  enter  additional  model  equations  without  constraining  the  sign  and  size  of 

additional effects and, hence, letting the data speak more freely. We assign wide priors with 

zero mean such that the four variants remain a priori identical to the benchmark specification 

of Section 5. Table 3 provides the data density of the four variants as the criterion for model 

selection  in  the  Bayesian  context.  The  data  density  evaluates  the  fit  of  the  model,  but  also 

penalizes models with more parameters, giving a preference to simplicity.16 Table 3 shows that 

the data reject all four augmented specifications for the case of ES, i.e. supports the benchmark 

results  that  spillover  from  supply-side  shocks  have  played  little  role  ES  TB  dynamics. 

Interestingly, however, the estimation favours a reinforced role for  foreign (REA and RoW) 

and  domestic  price  pressure  in  the  case  of  DE,  whereas  the  data  reject  the  inclusion  of  the 

domestic wage mark-up also for the DE model.  

Table 3: Data density of models with augmented trade equations 

Benchmark model 

REA price markup 

RoW price markup 

DE 

ES 

11571.80  10804.74 

11573.79  10802.54 

11573.91  10804.33 

Domestic price mark-up  

11590.25  10798.94 

Domestic wage mark-up  

11563.51  10795.16 

Note: The data density is reported in log points using a Laplace approximation. 

Figure  5  shows  impulse  response  functions  (IRFs)  for  negative  domestic  and  foreign  price 

mark-up shocks (increase in prices relative to production costs) in the augmented versions of 

the DE model. The responses correspond to the benchmark model in qualitative terms, i.e. the 

transmission  of the shocks  remains essentially  intact. The reactions of domestic and foreign 

economic activity are stronger in the augmented model, however, implying stronger spillover 

of  competitiveness  differentials  to  economic  activity.  Consistently  with  the  reinforced 

transmission,  REA  and  RoW  supply  shocks  explain  slightly  more  of  the  DE  TB  dynamics 

relative to the benchmark specification. Nonetheless, the overall share of foreign supply shocks 

in the DE TB decomposition remains small, which provides additional evidence in favour of 

the results from the estimated benchmark specifications for DE and ES.  

16 For example, a difference in the log data density of 1 implies that a model is preferred by a log Bayes factor of 1. See e.g., Kass and Raftery 
(1995). 

22 

 
  
 
                                           
Figure 5: Dynamics effects of augmented shocks in Germany 

Panel A. Domestic price mark-up shock 

Panel B. REA price mark-up shock 

Panel C. RoW price mark-up shock 

Note:  Dynamic  effects  of  mark-up  shocks  (shock  sizes  are  normalized  to  1%  to  ensure  comparability  of  the 
transmission mechanism). Solid black lines refer to the benchmark model, dashed blue to the augmented model 
with  price  mark-up  shocks  in  the  trade  equations.  An  increase  in  the  real  exchange  rate  corresponds  to  a  real 
effective depreciation. Units on the x-axis are quarters, and units on the y-axis are percentage-point deviations 
from the steady state for the real interest rate, inflation, and the trade balance, and per-cent deviations from steady 
state for all other variables. 

23 

 
 
 
 
6.2 Agnostic structural disturbances 

This  subsection  generalises  the  empirical  specification  further  to  soften  model-imposed 

restrictions on the shock transmission. Based on the "agnostic structural disturbances" (ASD) 

approach  of  Den  Haan  and  Drechsel  (2020),  it  investigates  whether  estimated  shocks  that 

mainly drive the TB in the benchmark decompositions are correctly specified, or whether an 

alternative  shock  structure  would  change  the  relative  importance  of  domestic  and  foreign 

shocks.  

Formally, ASDs are structural shocks (disturbances) that enter the model like regular structural 

shocks. Their role in explaining the observed data is a priori unrestricted, however. We can 

rewrite the model representation as: 

𝐸𝑡[ℱ(𝑦𝑡+1, 𝑦𝑡, 𝑦𝑡−1, 𝜀𝑡

𝑅; 𝜃)] + Υ̂𝜀𝑡

𝐴𝑆𝐷 = 0, 

where we partition the set of disturbances into regular shocks, 𝜀𝑡

𝑅, and the ASDs, 𝜀𝑡

𝐴𝑆𝐷.  Υ̂  is an 

estimated vector of coefficients that determines the impact of the ASD on all model equations, 

with one coefficient for each model equation. A zero coefficient in a specific equation means 

that the ASD will have no impact on this equation. A coefficient different from zero implies 

that  the  ASD  does  enter  the  particular  equation.  Hence,  ASDs  enter  the  model  without 

theoretical restrictions and may capture any “missing” shock. The tests conducted in Subsection 

6.1 may be viewed as a “constrained” ASD procedure, where Υ̂ contains a few estimated non-

zero entries, whereas the other  coefficients  are set  to zero.17  In this section, by  contrast,  the 

ASDs enter the main behavioural equations. Once the coefficients in Υ̂ are estimated, we can 

assess the relevance of the respective ASD for macroeconomic and TB dynamics and interpret 

the ASD transmission from the point of economic theory to classify its nature.18  

The ASD procedure is especially insightful when we replace a key shock from our baseline set-

up. The replacing ASD enters the model in the same equation as the original shock and many 

other equations. The impact in all equations is a priori zero, including in the original location. 

In this way, the model estimation can detect potential misspecification of structural shocks. The 

estimation then agnostically determines the properties of the ASD. If, for instance, the resulting 

ASD assigns a large coefficient to the place of the original shock and the ASD behaves similarly 

17 In the approach in Subsection 6.1, the original shocks remain in the price or wage equations, i.e. the coefficients on the initial shocks equal 
one.  
18 In practice, the size of Υ̂ in a multi-region macro model is very large. We do not include ASDs in equations that are pure definitions (e.g., 
of  growth  rates)  or  accounting  identities.  Given  the  size  of  our  model  and  the  data  set,  we  focus  discussion  on  entries  of  Υ̂  in  the  main 
behavioural equations.  

24 

 
                                           
to  the  omitted  shock  (similar  IRFs),  the  procedure  supports  the  original  specification. 

Otherwise,  the  data  may  point  to  a  “theory-free”,  but  econometrically  preferred  alternative 

shock structure. As in Subsection 6.1, we use the estimated data density to evaluate the fit of 

the model. 

We  focus  the  analysis  on  shocks  to  domestic  demand  and  exogenous  changes  in 

competitiveness,  which  reflect  competing  hypotheses  about  the  sources  of  external 

imbalances.19 For each shock replaced by an ASD, we re-estimate the model parameters and 

shock processes.  

Table 4 shows that the data indeed prefer some of the agnostic specifications to the benchmark, 

suggesting that the extended models provide a better fit. 

Table 4: Data density of augmented models (ASDs) 

Benchmark model 

Flight-to-safety ASD 

Wage mark-up ASD 

Savings ASD 

DE 

ES 

11571.80  10804.74 

11585.42  10820.53 

11590.73  10808.48 

11563.54  10833.99 

Investment risk premium ASD 

11579.04  10814.97 

Note: The data density is reported in log points using a Laplace approximation. 

6.2.1 Replacing a key domestic demand shock 

The flight-to-safety shock is critical in the estimated benchmark model in Section 5, where it is 

the main driver of domestic demand and the TB-to-GDP ratio in ES (Figure 4 above). Replacing 

this flight-to-safety shock by an ASD therefore opens the possibility of decomposing the TB 

dynamics in an entirely different way. The estimated ASD specification, however, shows the 

benchmark result to be robust to the modification. In particular, the decomposition of the TB-

to-GDP ratio remains similar, supporting the benchmark estimates.  

19 Theoretically, it would be interesting to extend the ASD approach to all shocks entering the model and even allow for more than one ASD 
at once. Given the large number of shocks and possible configurations, this remains virtually impossible, however.  

25 

 
  
 
 
                                           
Figure 6: Trade balance-to-GDP ratio with "flight-to-safety" ASD 

Panel A: ASD replacing flight-to-safety in Germany (DE) 

Panel B: ASD replacing flight-to-safety in Spain (ES) 

Note: Units on the x-axis are years and units on the y-axis measure the trade balance (as share of GDP) 
relative to its sample mean, where 0.01 corresponds to 1% of GDP. Black bars show the contributions 
in the baseline version and red bars the contributions in the ASD specification. 

26 

 
 
 
Figure  6  compares  shock  contributions  of  the  benchmark  model  and  the  alternative  ASD 

specification. The group of domestic demand shocks in the figure excludes the flight-to-safety 

shock in the benchmark model and the respective ASD in the ASD specification. While there 

are  small  quantitative  differences,  the  relative  importance  of  the  different  groups  remains 

almost unchanged for both DE and ES. In particular, the original flight-to-safety shock and the 

replacing ASD shock display remarkably similar contributions for both countries, and the role 

of  other  shocks  remain  (largely)  unchanged,  thereby  preserving  the  conclusions  from  the 

historical decomposition of the fully micro-founded model. 

Figure 7 shows that the main estimated demand shocks in the benchmark model and the ASD 

extension follow very similar paths. In particular, the estimated ASD closely follows the path 

of the flight-to-safety shock that it replaces, with higher persistence in recent years. 

Does the transmission of the ASD resemble a domestic demand shock? Figure 8 illustrates that 

the responses to this shock display strong similarity to the original flight-to-safety specification. 

At the same time, the ASD generates significant positive co-movement between domestic and 

foreign  economic  activity,  in  particular  activity  in  REA.  This  co-movement  indicates  the 

estimated ASD shock to be more global than the original domestic flight-to-safety shock. It also 

leans more towards lower investment, to the benefit of higher consumption demand. 

27 

 
 
Figure 7: Smoothed estimates of key demand shocks  

Panel A. Germany (DE) 

Panel B. Spain (ES) 

Note: Solid black lines refer to the benchmark model and dashed blue ones to the ASD set-up. 
All shocks are standardized (to zero mean and standard deviation of one). 

28 

 
 
 
 
 
 
Figure 8: IRFs for flight-to-safety and corresponding ASD in Spain (ES) 

Note: Dynamic effects of flight-to-safety shocks (we normalize the shock size to 1%). Solid black lines refer 
to  the  benchmark  model,  dashed  blue  to  the  agnostic  model.  An  increase  in  the  real  exchange  rate 
corresponds  to  a  real  effective  depreciation.  Units  on  the  x-axis  are  quarters,  units  on  the  y-axis  are 
percentage-point deviations from the steady state (trade balance) and per cent (%) deviations from steady 
state (all other variables), respectively. 

The literature on business cycle synchronization has highlighted the role of common exposure 

to global risk factors (e.g., Bacchetta and Wincoop, 2011) and cross-country transmission of 

shocks to explain the international co-movement in economic activity, in particular with respect 

to the global financial crisis. Several papers have explained international synchronisation by 

global financial intermediation. Perri and Quadrini (2018), e.g., offer a theory based on financial 

frictions and self-fulfilling expectations.20 Kalemli-Ozcan (2011), Kollmann et. al. (2011), and 

Kollmann (2013) build on a microfounded propagation mechanism based on globally operating 

banks.  Born  and  Enders  (2019)  support  the  role  of  financial  frictions,  but  their  calibration 

exercise suggests a dominance of the collapse in trade over financial factors in explaining DE 

output dynamics. Darracq, Paries and Papadopoulou (2019) calibrate a model with a rich set of 

financial  frictions  (banking,  portfolio  adjustment  frictions,  and  bonds  of  different  maturity) 

similar to Kollmann et al. (2015) to analyse (spillover effects of) non-conventional monetary 

policy. Sovereign default risk may further hamper financial intermediation. Bocola (2016), e.g., 

finds a sizable pass-through of sovereign risk to the private sector. The ASD estimates in this 

20 See also Devereux and Sutherland (2011) on the role of leverage constraints for the international transmission of shocks. 

29 

 
 
 
                                           
section support the idea of domestic demand conditions being linked to international (financial) 

factors. 

6.2.2 Replacing a key competitiveness shock 

Wage  moderation  (wage  mark-up)  shocks  have  contributed  to  the  DE  TB  surplus,  notably 

during the period of the  “Hartz” labour market reforms, according to the benchmark model. 

This section presents a model variant that replaces the wage mark-up shock by an ASD. Table 

4 suggests related improvements in the model fit for ES and, in particular, for DE. The estimated 

IRFs in Figure 9 characterise the ASD in the model for DE. The ASD replacing the wage mark-

up  shock  combines  characteristics  of  demand  and  supply  shocks.  Output  increases  in 

conjunction with a decline in the price level and REER depreciation, which is characteristic for 

positive supply shocks. At the same time, domestic demand increases sharply, driven notably 

by strong consumption demand from Ricardian households. TB falls in response to the ASD, 

contrary  to  the  TB  improvement  in  response  to  a  negative  wage  mark-up  shock  in  the 

benchmark model. 

Figure 9: IRFs for wage mark-up and replacing ASD shock in Germany 

Note: Dynamic effects of wage mark-up shocks (we normalize the shock size to 1%). Solid black lines refer to the 
benchmark model, dashed blue ones to the agnostic model. An increase in the real exchange rate corresponds to a 
real effective depreciation. Units on the x-axis are quarters, units on the y-axis are percentage-point deviations 
from  the  steady  state  (trade  balance)  and  per  cent  (%)  deviations  from  steady  state  (all  other  variables), 
respectively. 

30 

 
 
 
7. Conclusion 

This  paper  examines  the  trade  balance  (TB)  dynamics  of  Germany  (DE)  and  Spain  (ES), 

emblematic cases with very distinct TB dynamics since the start of EMU in 1999, in estimated 

multi-region  open-economy  DSGE  models  that  feature  rich  trade  linkages  and  international 

financial  markets.  In  line  with  previous  results  from  this  class  of  models,  the  estimated 

benchmark models ascribes a large part of TB dynamics to domestic drivers, notably domestic 

demand shocks, although international (foreign demand) and supply factors also matter for the 

TB profile, particularly  for  DE. We  revisit  the benchmark result by  adopting more agnostic 

approaches with respect to shock transmission and use the "agnostic structural disturbances" of 

Den Haan and Drechsel (2020). Letting the data speak more freely suggests that the benchmark 

model  neglects  elements  of  international  co-movement,  but  these  additional  factors  do  not 

fundamentally  alter  the  decomposition  of  the  TB  dynamics.  The  domestic  (demand)  drivers 

remain dominant also when theoretical restrictions on the shock transmission are relaxed. 

The  distinction  between  domestic  versus  foreign  and  demand  versus  supply  shocks  is, 

admittedly, less sharp in reality. Domestic demand shocks in the model reflect, e.g., financial 

constraints, such as credit supply by foreign and domestic financial intermediaries, and may be 

subject to financial contagion that is unrelated to the structural linkages included in the model. 

In this sense, positive (negative) private domestic demand shocks, notably in the model for ES, 

may,  e.g.,  also  relate  to  softening  (tightening)  financial  constraints  and  strengthening 

(weakening) credit supply by foreign lenders. 

31 

 
 
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34 

 
 
 
Appendices 

A. Model description 

This Appendix provides the full equilibrium conditions of the household and firm optimization 

problems. 

Households 

The Ricardian household problem leads to the following first-order conditions (FOC): 

The FOC w.r.t. savers' consumption produces: 

𝐶 (𝐶𝑘𝑡
𝜀𝑘𝑡

𝑠 − ℎ𝐶𝑘𝑡−1

𝑠

𝑠 , 
)−𝜃 = 𝜆𝑘𝑡

where 𝜆𝑘𝑡

𝑠  is the Lagrange multiplier on the budget constraint. 

The FOC w.r.t. domestic risk-free bond: 

𝛽𝐸𝑡 [

𝑠
𝜆𝑘𝑡+1
𝑠
𝜆𝑘𝑡

𝑟𝑓
1 + 𝑖𝑘𝑡
𝐶,𝑣𝑎𝑡] = 1 
1 + 𝜋𝑘𝑡+1

The FOC w.r.t. domestic government bonds: 

𝛽𝐸𝑡 [

𝑠
𝜆𝑘𝑡+1
𝑠
𝜆𝑘𝑡

1 + 𝑖𝑘𝑡

𝑔 − 𝜀𝑘𝑡
𝑏0
𝐵 − 𝛼𝑘𝑘
𝐶,𝑣𝑎𝑡
1 + 𝜋𝑘𝑡+1

] = 1 

𝐶,𝑣𝑎𝑡 the consumption deflator inflation rate and  𝜀𝑘𝑡

𝐵  the risk-premium on government 

with 𝜋𝑘𝑡
bonds. 

The FOC w.r.t. domestic stocks: 

𝛽𝐸𝑡 [

𝑠
𝜆𝑘𝑡+1
𝑠
𝜆𝑘𝑡

(1 + 𝑖𝑘𝑡+1

𝑠

𝑠0
𝑆 − 𝛼𝑘𝑘

) − 𝜀𝑘𝑡
𝐶,𝑣𝑎𝑡
1 + 𝜋𝑘𝑡+1

] = 1 

𝑆  the risk premium on stocks. The above optimality conditions are similar to a textbook 

where 𝜀𝑘𝑡
Euler equation, but incorporate asset-specific risk premia that depend on an exogenous shock 

𝑄  as well as the size of the asset holdings as a share of GDP; see Vitek (2017) for a similar 
𝜀𝑘𝑡
formulation. Taking into account the Euler equation for the risk-free bond and approximating 

simplifies the FOCs to the familiar expressions: 

𝑔 = 𝑖𝑘𝑡
𝑖𝑘𝑡

𝑔  
𝑟𝑓 + 𝑟𝑝𝑟𝑒𝑚𝑘𝑡

𝑠 = 𝑖𝑘𝑡
𝑖𝑘𝑡

𝑟𝑓 + 𝑟𝑝𝑟𝑒𝑚𝑘𝑡
𝑠  

35 

 
In  the  equations  above,  𝑟𝑝𝑟𝑒𝑚𝑘𝑡
𝑟𝑝𝑟𝑒𝑚𝑘𝑡

𝑠  is a risk premium on domestic equity (shares).21 

𝑔   is  the  risk  premium  on  domestic  government  bonds,  and 

Given the monetary union setting, we assume that an uncovered interest rate parity condition 

links the interest rate of the individual EMU region to the EA interest rate (set by the central 

bank): 

(1 + 𝑖𝑘𝑡

𝑟𝑓) = (1 + 𝑖𝐸𝐴𝑡) − (𝛼𝑘

𝑊
𝑏𝑤1 𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡𝐵𝑘𝑡
𝑌 𝑌𝑘𝑡
𝑃𝑘𝑡

𝐹𝑄 
) + 𝜀𝑘𝑡

where 𝛼𝑘

𝑊
𝑏𝑤1 𝑒𝑅𝑜𝑊,𝐸𝐴,𝑡𝐵𝑘𝑡
𝑌 𝑌𝑘𝑡
𝑃𝑘𝑡

 captures a debt-dependent country risk premium on net foreign asset 

(NFA) holdings to ensure the long-run stability of foreign debt (see, e.g., Schmitt-Grohe and 

Uribe, 2003; Adolfson et al., 2008). Following Smets and Wouters (2007), we also introduce 

an additional risk premium shock, 𝜀𝑘𝑡

𝐹𝑄 (‘flight-to-safety’), which creates a wedge between the 

EA interest rate, 𝑖𝐸𝐴𝑡, and the return on domestic risk-free assets, 𝑖𝑘𝑡
increases  the  required  return  on  domestic  assets  and  the  cost  of  capital,  it  reduces  current 

𝑟𝑓. Since a positive shock 

consumption  and  investment  simultaneously  and  helps  explaining  the  co-movement  of 

consumption and investment. 

The instantaneous utility functions for liquidity-constrained households, 𝑢𝑐(∙), is defined as: 

𝑐 (𝐶𝑗𝑘𝑡
𝑢𝑗𝑘𝑡

𝑐 , 𝑁𝑗𝑘𝑡

𝑐 ) =

1
1 − 𝜃𝑘

(𝐶𝑗𝑘𝑡

𝑐 − ℎ𝑘𝐶𝑘𝑡−1

𝑐

1−𝜃𝑘 − (𝐶𝑘𝑡)
)

1−𝜃𝑘 𝜔𝑘

𝑈
𝑁𝜀𝑘𝑡
𝑐 )
𝑁 (𝑁𝑗𝑘𝑡
1 + 𝜃𝑘

𝑁
1+𝜃𝑘

with 𝐶𝑘𝑡

𝑐1
𝑐 = ∫ 𝐶𝑗𝑘𝑡
0

𝑑𝑗. 

Total output  

Perfectly  competitive  firms  produce  total  output,  𝑂𝑘𝑡,  by  combining  value  added,  𝑌𝑘𝑡,  with 

energy input, 𝑂𝑖𝑙𝑘𝑡, using the following CES production function: 

𝑂𝑘𝑡 = [(1 − 𝑠𝑘

𝑂𝑖𝑙)

1
𝑜(𝑌𝑘𝑡)
𝜎𝑘

𝜎𝑘

𝑜−1
𝑜
𝜎𝑘

+ (𝑠𝑘

𝑂𝑖𝑙)

1
𝑜(𝑂𝑖𝑙𝑘𝑡)
𝜎𝑘

𝜎𝑘

𝑜−1
𝑜
𝜎𝑘

𝑜
𝜎𝑘
𝑜−1

𝜎𝑘

]

, 

where  𝑠𝑘

𝑂𝑖𝑙  is  the  energy  input  share  in  total  output  and  𝜎𝑘

𝑜  is  the  elasticity  of  substitution 

between both components. It follows that demand for 𝑌𝑘𝑡 and 𝑂𝑖𝑙𝑘𝑡 by total output producers 

is, respectively: 

21 Observationally, this approach is equivalent to exogenous risk premia as well as risk premia derived in the spirit of Bernanke et al. (1996). 

36 

 
 
                                           
𝑌𝑘𝑡 = (1 − 𝑠𝑘

𝑂𝑖𝑙) (

𝑂𝑖𝑙𝑘𝑡 = 𝑠𝑘

𝑂𝑖𝑙 (

𝑜
−𝜎𝑘

𝑂𝑖𝑙
𝑃𝑘𝑡
𝑂 )
𝑃𝑘𝑡

𝑜
−𝜎𝑘

𝑌
𝑃𝑘𝑡
𝑂 )
𝑃𝑘𝑡

𝑂𝑘𝑡, 

𝑂𝑘𝑡, 

where  𝑃𝑘𝑡

𝑌   and  𝑃𝑘𝑡

imported from RoW, the oil price is given by: 𝑃𝑘𝑡

𝑂𝑖𝑙  are  price  deflators  associated  with  𝑌𝑘𝑡  and  𝑂𝑖𝑙𝑘𝑡,  respectively.  Oil  is 
𝑂𝑖𝑙 + 𝜏𝑂𝑖𝑙𝑃𝑌0, where 𝜏𝑂𝑖𝑙𝑃𝑌0 

𝑂𝑖𝑙 = 𝑒𝑅𝑜𝑊𝑘𝑡𝑃𝑅𝑜𝑊𝑡

is the excise duty. The price index of total output 𝑃𝑘𝑡

𝑂  is: 

𝑂 = [(1 − 𝑠𝑘
𝑃𝑘𝑡

𝑂𝑖𝑙)(𝑃𝑘𝑡

𝑜
𝑌 )1−𝜎𝑘

+ 𝑠𝑘

𝑂𝑖𝑙(𝑃𝑘𝑡

𝑂𝑖𝑙)

𝑜
1−𝜎𝑘

1
𝑜
1−𝜎𝑘

]

. 

Firms 

Each variety 𝑖 is produced by a single firm using total capital, 𝐾𝑖𝑘𝑡−1
are combined by a Cobb-Douglas production function: 

𝑡𝑜𝑡

, and labour, 𝑁𝑖𝑘𝑡, which 

𝑌𝑖𝑘𝑡 = [𝐴𝑘𝑡

𝑌  (𝑁𝑖𝑘𝑡 − 𝐹𝑁𝑖𝑘)]𝛼(𝑐𝑢𝑖𝑘𝑡 𝐾𝑖𝑘𝑡−1

𝑡𝑜𝑡

 )1−𝛼 − 𝐴𝑘𝑡

𝑌 𝐹𝐶𝑖𝑘, 

where 𝛼 is the steady-state labour share, 𝐴𝑘𝑡
firms in the differentiated goods sector, and 𝑐𝑢𝑖𝑘𝑡 and 𝐹𝑁𝑖𝑘 are the firm-specific levels of capital 
𝑡𝑜𝑡,  is  the  sum  of  privately 
utilization  and  labour  hoarding,  respectively.22  Total  capital,  𝐾𝑖𝑘𝑡

𝑌  is labour-augmenting productivity common to all 

installed  capital,  𝐾𝑖𝑘𝑡,  and  public  capital,  𝐾𝑘𝑡

𝐺 .  𝐹𝐶𝑖𝑘𝑡  captures  fixed  costs  in  production. 

Economy-wide total Factor Productivity, 𝑇𝐹𝑃𝑘𝑡, is: 

𝑇𝐹𝑃𝑘𝑡 = (𝐴𝑘𝑡

𝑌 )𝛼. 

Since TFP is a non-stationary process, we allow for two types of shocks that are related to a 

non-stationary process and its autoregressive component, respectively:  

𝑙𝑜𝑔(𝐴̅

𝑌 ) − 𝑙𝑜𝑔(𝐴̅
𝑌
𝑘𝑡−1
𝑘𝑡

) =   𝑔𝑘𝑡

𝐴𝑌̅̅̅̅ + 𝜀𝑘𝑡

𝑙𝑎𝑦, 

𝐴𝑌̅̅̅̅ =   𝜌𝐴𝑌̅̅̅̅𝑔𝑘𝑡−1
𝑔𝑘𝑡

𝐴𝑌̅̅̅̅ + (1 − 𝜌𝐴𝑌̅̅̅̅)𝑔𝐴𝑌0̅̅̅̅̅̅ + 𝜀𝑘𝑡

𝑔𝑎𝑦, 

where  𝑔𝑡

𝐴𝑌̅̅̅̅  and  𝑔𝐴𝑌0̅̅̅̅̅̅  are  the  time-varying  growth  and  the  long-run  growth  of  technology, 

respectively. 𝜀𝑘𝑡

𝑙𝑎𝑦 and 𝜀𝑘𝑡

𝑔𝑎𝑦 are permanent technology level and growth rate shock, respectively.  

22 According to Burnside and Eichenbaum (1996), firms prefer to keep workers when demand is temporarily low, because firing workers may 
be more costly than hoarding them. Additionally, the inclusion of labour hoarding helps matching the observed co-movement between output 
and working hours. 

37 

 
                                           
The monopolistically competitive producers maximize the real value of the firm, 𝑉𝑘𝑡, equal to 
the  discounted  stream  of  future  dividends  𝑑𝑘𝑡,  𝑉𝑘𝑡 = 𝑑𝑘𝑡 + 𝐸𝑡[𝑠𝑑𝑓𝑘𝑡+1𝑉𝑘𝑡+1],  with  the 

stochastic discount factor: 

𝑠𝑑𝑓𝑘𝑡 = (1 + 𝑖𝑘𝑡+1

𝑠

⁄
) (1 + 𝜋𝑘𝑡+1

𝑦

)

≈ (1 + 𝑖𝑘𝑡

𝑟𝑓 + 𝑟𝑝𝑟𝑒𝑚𝑘𝑡

𝑠 ) (1 + 𝜋𝑘𝑡+1

⁄

𝑦

),

which depends directly on the investment risk premium, 𝑟𝑝𝑟𝑒𝑚𝑘𝑡
as: 

𝑠 . The dividends are defined 

𝑑𝑖𝑘𝑡 = (1 − 𝜏𝐾 ) (

𝑌
𝑃𝑖𝑘𝑡
𝑌 𝑌𝑖𝑘𝑡 −
𝑃𝑘𝑡

𝑊𝑘𝑡
𝑌 𝑁𝑖𝑘𝑡) + 𝜏𝐾 𝛿𝑘
𝑃𝑘𝑡

𝐼
𝑃𝑘𝑡
𝑌 𝐾𝑖𝑘𝑡−1 −
𝑃𝑘𝑡

𝐼
𝑃𝑘𝑡
𝑌 𝐼𝑖𝑘𝑡 − 𝑎𝑑𝑗𝑖𝑘𝑡, 
𝑃𝑘𝑡

where 𝐼𝑖𝑘𝑡 is physical investment, 𝑃𝑘𝑡
the capital depreciation rate.  

𝐼  is the investment price, 𝜏𝑘

𝐾 is the corporate tax, and 𝛿𝑘 is 

Adjustment costs, 𝑎𝑑𝑗𝑖𝑘𝑡, are associated with the output price, 𝑃𝑖𝑘𝑡
utilization, 𝑐𝑢𝑖𝑘𝑡, investment, 𝐼𝑖𝑘𝑡, and labour hoarding, 𝐹𝑁𝑖𝑘𝑡:  

𝑌 , labour input, 𝑁𝑖𝑘𝑡, capacity 

𝑎𝑑𝑗𝑖𝑘𝑡 = 𝑎𝑑𝑗(𝑃𝑖𝑘𝑡

𝑌 ) + 𝑎𝑑𝑗(𝑁𝑖𝑘𝑡) + 𝑎𝑑𝑗(𝑐𝑢𝑖𝑘𝑡) + 𝑎𝑑𝑗(𝐼𝑖𝑘𝑡) + 𝑎𝑑𝑗(𝐹𝑁𝑖𝑘𝑡), 

where: 

𝑎𝑑𝑗𝑖𝑘𝑡

𝑃𝑌 =

𝛾𝑝
2

𝑌𝑘𝑡 (

𝑌
𝑃𝑖𝑘𝑡
𝑌
𝑃𝑖𝑘𝑡−1

2

− 1)

𝑎𝑑𝑗𝑖𝑘𝑡

𝑁 =

𝛾𝑛
2

𝑌𝑘𝑡 (

2

− 1)

𝑁𝑖𝑘𝑡 − 𝐹𝑁𝑖𝑘𝑡
𝑁𝑖𝑘𝑡−1 − 𝐹𝑁𝑖𝑘𝑡−1
𝛾𝑢,2
2

𝑎𝑑𝑗𝑖𝑘𝑡

𝑐𝑢 =

𝑎𝑑𝑗𝑖𝑘𝑡

𝐼 =

𝐼
𝑃𝑘𝑡
𝑌 𝐾𝑖𝑘𝑡−1 (𝛾𝑢,1(𝑐𝑢𝑖𝑘𝑡 − 1) +
𝑃𝑘𝑡
𝐼
𝑃𝑘𝑡
𝑌 [
𝑃𝑘𝑡

𝐼𝑖𝑘𝑡
𝐾𝑘𝑡−1

2
− 𝛿)

𝛾𝐼,1
2

𝐾𝑘𝑡−1 (

+

(𝑐𝑢𝑖𝑘𝑡 − 1)2) 

𝛾𝐼,2
2

(𝐼𝑖𝑘𝑡 − 𝐼𝑖𝑘𝑡−1)2
𝐾𝑘𝑡−1

] 

𝑎𝑑𝑗𝑖𝑘𝑡

𝐹𝑁 = 𝑌𝑘𝑡 [𝛾𝑓𝑛,1 (

𝐹𝑁𝑖𝑘𝑡
𝐴𝑐𝑡𝑟𝑘𝑡𝑃𝑜𝑝𝑘𝑡

− 𝐹𝑁) +

𝛾𝑓𝑛,2
2

(

𝐹𝑁𝑖𝑘𝑡
𝐴𝑐𝑡𝑟𝑘𝑡𝑃𝑜𝑝𝑘𝑡

2

− 𝐹𝑁)

] 

in which the 𝛾-s capture the degree of adjustment costs, and 𝐴𝑐𝑡𝑟𝑘𝑡𝑃𝑜𝑝𝑘𝑡 is the active labour 

force.  The  maximization  is  subject  to  the  production  function,  the  standard  capital 

accumulation equation, 𝐾𝑖𝑘𝑡 = (1 − 𝛿)𝐾𝑖𝑘𝑡−1 + 𝐼𝑖𝑘𝑡, and the usual demand condition that 

inversely links the demand for variety i goods to the price of the variety: 

𝑌𝑖𝑘𝑡 = (

𝑌
𝑃𝑖𝑘𝑡
𝑌 )
𝑃𝑘𝑡

−𝜎𝑦

𝑌𝑘𝑡. 

The usual equality between the marginal product of labour and labour cost holds, with a wedge 

driven by the labour adjustment costs: 

38 

 
 
 
 
𝑦 𝛼
𝜇𝑘𝑡

𝑌𝑘𝑡
𝑁𝑘𝑡 − 𝐹𝑁𝑘𝑡

− 𝑎𝑑𝑗𝑖𝑘𝑡

𝑁 = (1 − 𝜏𝑘
𝐾)

𝑊𝑘𝑡
𝑌  
𝑃𝑘𝑡

𝑦  being inversely related to the price mark-up. The capital optimality condition reflects 

with 𝜇𝑘𝑡
the usual dynamic trade-off faced by the firm: 

𝑦
1+𝜋𝑘𝑡+1
𝑠
1+𝑖𝑘𝑡+1

𝐼
𝑌⁄
𝑃𝑘𝑡+1
𝑃𝑘𝑡+1
𝑌⁄
𝐼 𝑃𝑘𝑡
𝑃𝑘𝑡

𝑦
(𝜇𝑘𝑡+1

𝑌

(1 − 𝛼) 𝑃𝑘𝑡+1
𝐼
𝑃𝑘𝑡+1

𝑌𝑖𝑘𝑡+1
𝑡𝑜𝑡 + 𝜏𝐾 𝛿 −
𝐾𝑖𝑘𝑡

𝑐𝑢
𝑎𝑑𝑗𝑘𝑡
𝐾𝑖𝑘𝑡

+ (1 − 𝛿)𝑄𝑘𝑡+1) = 𝑄𝑘𝑡, 

where 𝑄𝑘𝑡 has the usual Tobin's interpretation. 

FOC w.r.t. investment implies that Tobin's Q varies due to investment adjustment costs: 

𝑄𝑘𝑡 = 1 + 𝑎𝑑𝑗𝑖𝑘𝑡

𝐼

. 

Firms adjust their capacity utilization and labour hoarding depending on market conditions in 

line with the respective optimality conditions: 

𝑦
𝜇𝑘𝑡
𝑌⁄
𝐼 𝑃𝑘𝑡
𝑃𝑘𝑡

(1 − 𝛼)

𝑌𝑘𝑡
𝑐𝑢𝑘𝑡

𝑐𝑢  
= 𝑎𝑑𝑗𝑖𝑘𝑡

𝑦 𝛼
𝜇𝑘𝑡

𝑌𝑘𝑡
𝑁𝑘𝑡−𝐹𝑁𝑘𝑡

𝐹𝑁. 
= 𝑎𝑑𝑗𝑖𝑘𝑡

Finally, the FOC w.r.t. the price of differentiated varieties of goods pins down the price mark-

up: 

𝜎𝑦
(𝜎𝑦−1)

𝑦 = (1 − 𝜏𝐾 ) +
𝜇𝑘𝑡

𝑃𝑌
𝑎𝑑𝑗𝑖𝑘𝑡
(𝜎𝑦−1)

+  𝜀𝑘𝑡

𝑀𝑈𝑌, 

𝑀𝑈𝑌 being the mark-up shock. The latter equation, combined with the FOC w.r.t. labour 

with 𝜀𝑘𝑡
and symmetry in pricing behaviour, implies the Phillips curve of the familiar form: 

𝑦 𝜎𝑘
𝛾𝑘𝑡

𝑌 = (1 − 𝜏𝐾 )(𝜎𝑘

𝑌 − 1) + 𝛾𝑘

𝑃𝜎𝑘

𝑌
𝑌 𝑃𝑘𝑡
𝑌
𝑃𝑘𝑡−1

[𝜋𝑘𝑡

𝑌 − 𝜋̅] −

𝑃𝜎𝑘
𝛾𝑘

𝑌 [

𝑌
1+𝜋𝑘𝑡+1
𝑠
1+𝑖𝑘𝑡+1

𝑌
𝑃𝑘𝑡+1
𝑌
𝑃𝑘𝑡

𝑌𝑘𝑡+1
𝑌𝑘𝑡

(𝜋𝑘𝑡+1

𝑌 − 𝜋̅)] + 𝜎𝑘

𝑌𝜀𝑘𝑡

𝑀𝑈𝑌, 

where 𝜀𝑘𝑡

𝑀𝑈𝑌 is the inverse of the price mark-up shock.  

Labour markets 

The optimality condition for the equilibrium wage is given by: 

39 

 
(𝜇𝑘

𝑁
𝑤 𝑈𝑘𝑡
𝜆𝑘𝑡

𝑤𝑟

1−𝛾𝑘

𝑃𝑘𝑡

𝐶,𝑣𝑎𝑡
𝑌 )
𝑃𝑘𝑡

𝑤𝑟
𝛾𝑘

((1 − 𝜏𝑘

𝑁) 𝑊𝑘𝑡−1
𝐶,𝑣𝑎𝑡 )
𝑃𝑘𝑡−1

= (1 − 𝜏𝑘

𝑁) 𝑊𝑘𝑡
𝐶,𝑣𝑎𝑡 +𝛾𝑘
𝑃𝑘𝑡

𝑤 (

𝑊𝑘𝑡
𝑊𝑘𝑡−1

− 1 −

(1 − 𝑠𝑓𝑘

𝑤)(𝜋𝑘𝑡−1

𝑦 − 𝜋̅) − 𝜋𝑤)

𝑊𝑘𝑡
𝑊𝑘𝑡−1

𝑊𝑘𝑡
𝑌   − 𝛾𝑘
𝑃𝑘𝑡

𝑤𝐸𝑡 [𝛽̃

𝑘𝑡

𝜆𝑘𝑡+1
𝜆𝑘𝑡

𝑁𝑘𝑡+1
𝑁𝑘𝑡

𝐶,𝑣𝑎𝑡
𝑃𝑘𝑡
𝐶,𝑣𝑎𝑡 (
𝑃𝑘𝑡+1

𝑊𝑘𝑡+1
𝑊𝑘𝑡

− 1 −

(1 − 𝑠𝑓𝑘

𝑤)(𝜋𝑘𝑡

𝑦 − 𝜋̅) − 𝜋𝑤)

𝑊𝑘𝑡+1
𝑊𝑘𝑡

𝑊𝑘𝑡
𝑌 ] + 𝜀𝑘𝑡
𝑃𝑘𝑡

𝑈 𝑊𝑘𝑡
𝑌 , 
𝑃𝑘𝑡

where  𝜀𝑘

𝑤 is  the wage mark-up, 𝛾𝑘

𝑤𝑟  is  the degree of real  wage rigidity, 𝛾𝑘

𝑤  is  the degree of 

nominal  wage  rigidity,  and  𝑠𝑓𝑘

𝑤  is  the  degree  of  forward-lookingness  in  the  labour  supply 

equation. 𝑈𝑘𝑡

𝑁  is the marginal disutility of labour: 

𝑈𝑘𝑡

𝑁 = 𝜔𝑘

𝑁(𝐶𝑘𝑡)1−𝜃𝑘(𝑁𝑘𝑡)

𝑁
−𝜃𝑘

. 

In the case of Germany, the real wage term on the left-hand side accounts for unemployment 

benefits, i.e. we modify  (1 − 𝜏𝑘

Similalry, the term (1 − 𝜏𝑘

𝑁) to (1 − 𝜏𝑘
𝑁) becomes (1 − 𝜏𝑘

𝑈
𝑁 − 𝑏𝑘𝑡−1
𝑁 − 𝑏𝑘𝑡

𝑈 ) on the right-hand side. 

), where  𝑏𝑘𝑡−1

𝑈

 is the replacement rate. 

REA and RoW demand functions 

From profit maximization we obtain the demand for domestic and foreign goods: 

𝑝 )
𝐶 = (𝐴𝑘𝑡
𝑌𝑘𝑡

𝑐−1

𝜎𝑘

(1 − 𝑠𝑘

𝑀) (

𝑌
𝑃𝑘𝑡
𝐶 )
𝑃𝑘𝑡

𝑀𝑘𝑡

𝑝 )
𝐶 = (𝐴𝑘𝑡

𝑐−1

𝜎𝑘

𝑀 (
𝑠𝑘

𝑐
−𝜎𝑘

𝑀
𝑃𝑘𝑡
𝐶 )
𝑃𝑘𝑡

𝑐
−𝜎𝑘

𝐶𝑘𝑡 

𝐶𝑘𝑡, 

where the consumer price deflator, 𝑃𝑘𝑡

𝐶  , is given by: 

𝑝 )
𝐶 = (𝐴𝑘𝑡
𝑃𝑘𝑡

−1

RoW monetary policy 

[(1 − 𝑠𝑘

𝑀)(𝑃𝑘𝑡

𝑐
𝑌 )1−𝜎𝑘

+ 𝑠𝑘

𝑀(𝑃𝑘𝑡

𝑐
𝑀)1−𝜎𝑘

1
𝑐
1−𝜎𝑘

]

. 

Monetary policy in RoW follows a Taylor-type rule similar to the EA one: 

𝑖𝑅𝑜𝑊𝑡 − 𝑖̅ = 𝜌𝑅𝑜𝑊

𝑖

(𝑖𝑅𝑜𝑊𝑡−1 − 𝑖̅)

+ (1 − 𝜌𝑅𝑜𝑊

𝑖

) [𝜂𝑅𝑜𝑊

𝑖𝜋 0.25(𝜋𝑅𝑜𝑊𝑡

𝑐,𝑣𝑎𝑡,𝑄𝐴 − 𝜋̅𝑅𝑜𝑊

𝑐,𝑣𝑎𝑡,𝑄𝐴)

4

4

+ 𝜂𝑅𝑜𝑊

𝑖𝑦 (𝑙𝑜𝑔 (0.25 ∑ 𝑌𝑅𝑜𝑊𝑡−𝑟

) − 𝑙𝑜𝑔 (0.25 ∑ 𝑌𝑅𝑜𝑊𝑡−𝑟

𝑝𝑜𝑡

))] + 𝜀𝑅𝑜𝑊𝑡

𝑖

. 

𝑟=1

𝑟=1

40 

 
RoW oil endowment  

The RoW supplies inelastically its unstorable exogenous endowment: 

𝑂𝑖𝑙𝑅𝑜𝑊𝑡 = ∑
𝑙

𝑠𝑖𝑧𝑒𝑙
𝑠𝑖𝑧𝑒𝑅𝑜𝑊

𝑂𝑖𝑙𝑙𝑅𝑜𝑊𝑡,

the price of which, 𝑃𝑅𝑜𝑊𝑡

𝑂𝑖𝑙

 is set in RoW currency. 

41 

 
 
 
B. Additional results 

B.1 Calibrated parameters, steady state ratios and estimated exogenous processes 

Parameters 

DE 

ES 

Table B.1.1: Selected calibrated parameters 

Intertemporal discount factor 
Share of Ricardian households 
Weight of disutility 
Degree of openness 
Preference for domestic risky assets 
Preference for government bond 
Euro Area preference for international bonds 
Member State preference for international bonds 
Preference for imports from RoW 
Preference for imports from REA 
Import share in consumption 
Import share in investment 
Import share in government expenditure 
Import share in export 

Cobb-Douglas labor share 
Depreciation of capital stock 
Elasticity of substitution between differentiated goods 
Depreciation of public capital stock 
Share of commodities in total output 
Linear capacity utilization adj. costs 
Linear labour hoarding adj. cost  
Excise duty 

Consumption tax 
Corporate profit tax 
Labour tax 
Deficit target (in % of GDP) 
Debt target (in % of GDP) 

Private investment share 
Government consumption share 
Government investment share 
Transfers share 
Trade balance share 

Interest rate persistence 
Response to inflation 
Response to output gap 

Member State size (in % of world GDP) 
Rest of Euro Area size (in % of world GDP) 
Rest of the World size (in % of world GDP) 

Preferences 
𝛽 
𝜔𝑠 
𝜔𝑁 
𝑠𝑀 
𝛼𝑆0 
𝛼𝐵0 
𝐵𝑊0 
𝛼𝐸𝐴
𝛼𝐵𝑊0 
𝑀  
𝑠𝑅𝑜𝑊
𝑀  
𝑠𝑅𝐸𝐴
𝑠𝑀,𝐶 
𝑠𝑀,𝐼 
𝑠𝑀,𝐺 
𝑠𝑀,𝑋 
Production 
𝛼 
𝛿 
𝜎𝑌 
𝛿𝐺  
𝑠𝑜𝑖𝑙 
𝛾𝑢,1 
𝛾𝑓𝑛,1 
τOil 
Fiscal policy 
𝜏𝑐 
𝜏𝑘 
𝜏𝑁 
𝐷𝐸𝐹𝑇  
𝐵̅ 𝑔  
Steady-state shares (in % of GDP) 
𝐼/𝑌 
𝐺/𝑌 
𝐼𝐺/𝑌 
𝑇/𝑌 
𝑇𝐵/𝑌 
EA Monetary policy 
𝜌𝑖 
𝜂𝑖𝜋 
𝜂𝑖𝑦 
Others 
𝑠𝑖𝑧𝑒 
𝑠𝑖𝑧𝑒𝑅𝐸𝐴 
𝑠𝑖𝑧𝑒𝑅𝑜𝑊 

0.610 
1.095 
0.394 
0.003 
-0.001 
0.015 
-0.006 
0.526 
0.474 
0.264 
0.365 
0.098 
0.313 

8.04 
0.014 
0.015 
0.017 
-0.439 

0.389 
0.500 
62.80 

0.173 
0.188 
0.022 
0.165 
0.004 

4.63 
12.23 
83.14 

0.998 

0.65 
0.014 

0.30 

0.20 
0.30 

0.898 
1.390 
0.085 

0.690 
4.340 
0.308 
-0.001 
0.0002 
0.008 
-0.006 
0.473 
0.527 
0.216 
0.288 
0.097 
0.312 

5.53 
0.012 
0.015 
0.015 
-0.440 

0.352 
0.500 
60.02 

0.203 
0.185 
0.035 
0.137 
-0.011 

1.85 
15.01 
83.14 

42 

 
 
 
 
 
 
 
 
 
 
Table B.1.2: Estimated exogenous shock processes in REA and RoW 

Prior distribution 
Mean 
Distr 
St.dev. 

Posterior distribution 

DE 

ES 

Autocorrelation of forcing variables 

REA subjective discount factor 

𝜌𝑈𝐶  

Beta 

REA mark-up shock 

𝜌𝑀𝑈𝑌  

Beta 

RoW subjective discount factor 

𝜌𝑈𝐶  

Beta 

RoW mark-up shock 

𝜌𝑀𝑈𝑌  

Beta 

Bilateral export price MS vs RoW 

Bilateral export price REA vs RoW 

RoW import demand 

Bilateral import demand MS vs RoW 

𝜌𝑋 

𝜌𝑋 

𝜌𝑀 

𝜌𝑀 

Beta 

Beta 

Beta 

Beta 

0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 
0.5 
0.2 

0.73 
(0.70,0.86) 
0.21 
(0.05, 0.027) 
0.88 
(0.74,0.9) 
0.86 
(0.82, 0.93) 
0.97 
(0.95, 0.98) 
0.43 
(0.29,0.86) 
0.98 
(0.98, 0.99) 
0.95 
(0.91,0.97) 

Standard deviation (%) of innovations to forcing variables 

REA subjective discount factor 

𝜀𝑈𝐶 

Gamma 

REA mark-up shock 

𝜀𝑀𝑈𝑌  Gamma 

RoW subjective discount factor 

𝜀𝑈𝐶 

Gamma 

RoW mark-up shock 

𝜀𝑀𝑈𝑌  Gamma 

Bilateral export price MS vs RoW 

RoW import demand 

Bilateral import demand MS vs RoW 

RoW monetary policy 

𝜀 𝑋 

𝜀𝑀 

𝜀𝑀 

𝜀𝑖 

Gamma 

Gamma 

Gamma 

Gamma 

1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
1 
0.4 
2 
0.8 
1 
0.4 

2.00 
(1.03, 2.53) 
0.17 
(0.14,0.20) 
0.48 
(0.39, 1.15) 
0.11 
(0.05, 0.14) 
2.47 
(1.86, 2.61) 
2.98 
(2.69,3.76) 
5.12 
(4.14,5.21) 
0.07 
(0.06, 0.08) 

0.74 
(0.73, 0.84) 
0.18 
(0.10, 0.35) 
0.87 
(0.77, 0.89) 
0.91 
(0.84, 0.94) 
0.84 
(0.82, 0.95) 
0.45 
(0.14, 0.81) 
0.98 
(0.97, 0.99) 
0.95 
(0.87, 0.95) 

1.43 
(0.74, 1.88) 
0.19 
(0.15, 0.21) 
0.52 
(0.35, 0.91) 
0.02 
(0.02, 0.13) 
3.16 
(2.50, 3.24) 
3.03 
(2.85, 3.80) 
4.58 
(3.84, 4.92) 
0.06 
(0.06, 0.08) 

Note: Cols. (1)-(2) list model innovations. Cols. (3)-(4) indicate the prior distribution function. Identical priors 
are assumed for REA and RoW parameters. Cols. (5)-(8) show the mode and the (10% and 90%) HPD intervals 
of the posterior distributions. 

B.2 Theoretical moments and model fit 

Tables B.2.1 and B.2.2 compare sample and model-implied moments for a subset of statistics 

to evaluate the capability of the benchmark model to fit the data. Specifically, we report the 

volatilities of real GDP, consumption, investment, the trade balance-to-GDP ratio, and the GDP 

deflator  as  well  as  the  cross-correlation  of  GDP  with  its  main  components.  We  use  first 

differences for the trade balance-to-GDP ratio and quarter-on-quarter growth rates for all other 

variables. Most of the correlations between GDP growth and its components are well captured. 

Our estimated model for DE tends to overestimate the volatility of real variables, while the ES 

model matches the data moments reasonably well. The relative magnitudes are preserved. In 

43 

 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
particular, the high volatility of investment is in line with the data. These theoretical moments 

show that the estimated structural models successfully replicate key business cycle features in 

DE and ES. 

The last column reports the r2 of the 1-year ahead forecast. We define the r2 as 1 minus the ratio 

between the k-step ahead forecast error and the deviation of the observed time series from the 

model-implied  steady  state.  This  definition  implies  that  r2  has  an  upper  bound  at  1  and  is 

unbounded from below. In the perfect case where the model generates no forecast error, the r2 

is equal to one, whereas in the case where the volatility of the forecast error is larger than the 

volatility of the observed time series, the r2 is negative. The positive r2 values indicate that the 

model forecast errors are not very large. However, the model-implied volatility of consumption 

growth in DE is higher than its empirical counterpart. 

Table B.2.1: Model fit for DE baseline model 

Variable 

GDP growth (GY) 
Consumption growth (GC) 
std(GC)/std(GY) 
Investment growth (GI) 
std(GI)/std(GY) 
GDP deflator 
Δ Trade balance to GDP 

GDP growth (GY) 
GDP deflator 
Δ Trade balance to GDP 

GDP growth (GY) 
GDP deflator 
Δ Trade balance to GDP 

Std(%) 

Data 

Corr 
(x,GDP) 

DE 

Model 

Std(%) 

Corr 
(x,GDP) 

r2 

1y-ahead 

0.84 
0.57 
0.68 
2.14 
2.55 
0.33 
0.73 

0.55 
0.30 
0.44 

0.62 
0.35 
0.08 

1.00 
0.25 

0.78 

-0.20 
0.33 

REA 

1.00 
0.24 
-0.22 

RoW 

1.00 
0.78 
0.07 

1.04 
1.12 
1.08 
2.35 
2.26 
0.54 
0.79 

0.60 
0.32 
0.61 

0.35 
0.25 
0.11 

1.00 
0.43 

0.60 

-0.39 
0.34 

1.00 
0.10 
-0.16 

1.00 
0.48 
-0.04 

0.49 
-3.35 

0.39 

0.69 
0.82 

0.73 
0.89 
0.88 

0.96 
0.86 
0.88 

Note: The r2 is reported for the absolute nominal trade balance. 

44 

 
 
 
 
 
 
 
 
 
Table B.2.2: Model fit for ES baseline model 

Variable 

GDP growth (GY) 
Consumption growth (GC) 
std(GC)/std(GY) 
Investment growth (GI) 
std(GI)/std(GY) 
GDP deflator 
Δ Trade balance to GDP 

GDP growth (GY) 
GDP deflator 
Δ Trade balance to GDP 

GDP growth (GY) 
GDP deflator 
Δ Trade balance to GDP 

Std(%) 

Data 

Corr 
(x,GDP) 

ES 

Model 

Std(%) 

Corr 
(x,GDP) 

r2 

1y-ahead 

0.68 
0.85 
1.26 
2.46 
3.62 
0.48 
0.66 

0.61 
0.22 
0.42 

0.62 
0.36 
0.08 

1.00 
0.82 

0.67 

0.58 
-0.44 

REA 

1.00 
0.02 
0.09 

RoW 

1.00 
0.78 
0.08 

0.62 
0.97 
1.56 
2.45 
3.95 
0.41 
0.72 

0.67 
0.26 
0.58 

0.32 
0.25 
0.11 

1.00 
0.64 

0.39 

-0.10 
-0.12 

1.00 
0.06 
-0.01 

1.00 
0.59 
0.02 

0.80 
0.86 

0.53 

0.91 
0.92 

0.79 
0.92 
0.69 

0.96 
0.65 
0.82 

Note: The r2 is reported for the absolute nominal trade balance. 

B.3 Details on the estimated effects of private demand shocks, discretionary fiscal policy, and 

oil price shocks 

This section provides additional details on the contributions of private demand shocks (B.3.1), 

fiscal policy (B.3.2), and oil price shocks (B.3.3) to the dynamics of the TB. 

B.3.1 Private domestic demand shocks 

The model includes three private domestic demand shocks: Shocks to preferences for risk-free 

bonds (“flight-to-safety” shocks), shocks to the discount factor (“savings shocks”), and shocks 

to the investment risk premium. While our main results are robust to the exclusion of one of 

these shocks, the model fit and identification critieria support the specification with all three 

shocks. 

45 

 
 
  
  
  
 
 
 
 
 
 
Figure B.3.1: IRFs for key demand shocks in Germany (DE) 

Note: Simulations use the DE baseline  model. Shock sizes correspond to one  estimated standard deviation. An 
increase in the real exchange rate corresponds to  a real effective depreciation. Units on the x-axis are quarters, 
units on the y-axis are percentage-point deviations from the steady state (trade balance) and per cent (%) deviations 
from steady state (all other variables), respectively. 

Figure B.3.1 illustrates that each of the three private domestic demand shocks triggers distinct 

dynamics in the economy, which allows to identify all three shocks separately. Adverse demand 

shocks improve the TB relative to GDP (TBY) in all three cases, but the transmission differs 

markedly. The private savings shocks (dashed blue) reduces consumption and lowers domestic 

and foreign GDP and inflation. Yet, the shock crowds in private investment. By contrast, the 

investment risk premium shock (dotted red) dampens investment. The fall in aggregate demand 

lowers GDP and inflation, but the model-predicted crowding-in of consumption is at odds with 

the observed co-movement of domestic demand components. The flight-to-safety shock (solid 

black) reduces aggregate demand (consumption  and investment), inflation, and GDP, which 

suggests that this shock can account for salient features of the recent recessions, especially in 

the  case  of  ES..  The  boom-bust  cycle  in  ES  has  featured  a  simultaneous  strong  decline  in 

consumption and investment, together with a reversal of TB from high deficit to surplus (Figure 

B.3.3).  

B.3.2 Fiscal shocks 

Fiscal shocks play only a small role for DE TBY dynamics (Figure B.3.2). In ES, the initial 

fiscal stimulus during the Global financial crisis counteracted the private demand contraction, 

which shows up as negative contribution to TBY. Starting around 2012, however, the model 

46 

 
 
 
 
estimation  identifies  reductions  in  government  spending  and  investment  (“austerity”)  as 

contributions to the post-crisis TB reversal in ES (Figure B.3.3). 

B.3.3 Oil price shocks 

The model includes an oil price shock as exogenous supply-side change in the price of oil (in 

RoW currency). Because EA and its MS are oil importers, any change in the oil price will affect 

the  TBY,  i.e.  a  lower  (higher)  oil  price  will  reduce  (increase)  the  import  bill  and  improve 

(deteriorate)  the  TB.  Giovannini  et  al.  (2019)  show  that  oil  prices  (and  a  broader  bundle  of 

commodities) were indeed relevant drivers of the TBY in the EA and the US after the Great 

Recession.23 We find that oil price hikes deteriorated the TBY in 2008 and 2011/12, whereas 

the oil price decline in 2015-17 led to an improvement in DE and ES external positions relative 

to the long-term average. The estimated dynamics are similar for both DE and ES, i.e. they do 

not explain differences in the overall TBY pattern between the two economies. 

23 Their model includes a richer specification of oil and commodities, including shocks to the demand of oil. 

47 

 
 
                                           
Figure B.3.2: Selected shock contributions to TBY in Germany (DE) 

Note: Units on the x-axis are years and units on the y-axis measure the trade balance (as a share of GDP) relative 
to its sample mean, where 0.01 corresponds to 1% of GDP. Black bars show the contributions of the respective 
shock group. 

Figure B.3.3: Selected shock contributions to TBY in Spain (ES) 

Note: Units on the x-axis are  years and  units on the  y-axis  measure the trade balance (as  a share of GDP) 
relative to its sample mean, where 0.01 corresponds to 1% of GDP. Black bars show the contributions of shock 
groups. 

48 

 
 
 
 
 
B.4 Hartz reforms - estimated effects of replacement rate shocks 

In 2003-2005, the DE government implemented a far-reaching labour market deregulation, the 

so-called  ‘Hartz’  reforms,  which  aimed  at  better  job  matching  and  reduced  the  length  and 

generosity of unemployment benefits (the benefit replacement rate fell permanently from 62% 

to  53%  on  average  in  2004-2005).  The  discussion  and  model  implementation  here  closely 

follows Kollmann et al. (2015). In particular, we capture the structural change by observing the 

benefit  replacement  rate  (see  lower  panel  in  Figure  B.4.1)  in  this  model.  Unemployment 

benefits (paid to unemployed workers in the labour force) enter the budget constraints of the 

households  and  the  government.  A  random-walk  shock  to  the  replacement  rate  captures  the 

observed (permanent) structural change. Appendix A above provides the formal details. 

Figure B.4.1 displays dynamic responses to the shock to the benefit replacement rate. A cut in 

the replacement rate stimulates DE labour supply, which lowers the real wage rate and increases 

employment in DE persistently. Initially, GDP increases faster than the TB, but after around 10 

quarters the competitiveness gain improves the TBY persistently. The aggregate supply shock 

is thus consistent with the increasing TB surplus after 2005.  

49 

 
 
Figure B.4.1: Replacement rate shocks in Germany (DE) 

Note: Dynamic effects of shock to the replacement rate (shock size of 1 pp.). Simulations use the DE 
baseline  model.  An increase in the real exchange  rate  corresponds to  a real effective depreciation. 
Units on the x-xis are quarters, units on the y-axis are percentage-point deviations from the steady 
state (trade balance) and percent (%) deviations from steady state (all other variables), respectively. 
The real interest rate is expressed in annualized basis points. The lower two panels depict the observed 
replacement rate and the corresponding estimated shock process in the model. 

B.5 Model extension - adding capital to the REA and RoW model blocks 

As a further robustness check, we have extended the REA and RoW model blocks by including 

capital and investment decisions to assess whether the simplified structure of the benchmark 

model may bias results against a stronger impact of foreign drivers by omitting "pull factors" 

of  net  capital  exports.24  Figure  B.5.1  shows  that  domestic  demand  factors  remain  the  main 

driver of the DE TBY ratio.  

24 We have also tested and estimated a fully detailed REA model structure (similar to the individual EA country), which provides similar results 
compared to the model version with capital extension. 

50 

 
 
 
 
                                           
Figure B.5.1: Shock decomposition of the German trade balance-to-GDP ratio 

Note: Units on the x-axis are years and units on the y-axis measure the trade balance as share of GDP relative to 
its sample mean, where 0.01 corresponds to 1% of GDP. 

The total contribution of REA and RoW demand shocks in Figure B.5.1 is similar to Figure 3. 

The extended model rather decomposes the contribution of foreign aggregate demand shocks 

to  DE  TBY  further  into  foreign  household  savings  versus  investment  risk  premium  shocks 

(Figure B.5.2 and Figure B.5.3). 

51 

 
 
 
 
Figure B.5.2: Disaggregation of REA demand shocks in decomposition of DE TBY 

Note: Units on the x-axis are years and units on the y-axis measure the trade balance as share of GDP relative to 
its sample mean, where 0.01 corresponds to 1% of GDP. 

Figure B.5.3: Disaggregation of RoW demand shocks in decomposition of DE TBY

Note: Units on the x-axis are years and units on the y-axis measure the trade balance as share of GDP relative 
to its sample mean, where 0.01 corresponds to 1% of GDP. 

52 

 
 
 
 
 
C. Data transformations 

We use quarterly and annual data for the period 1999q1 to 2018q4. Data for EMU countries 

(DE and ES) and the Euro Area aggregate (EA19) are taken from Eurostat (in particular, from 

the European System of National Accounts ESA2010). Bilateral trade flows are based on trade 

shares from the GTAP trade matrices for trade in goods and services. The  rest of the world 

(RoW) data are annual  data and are constructed using  IMF  International  Financial Statistics 

(IFS) and World Economic Outlook (WEO) databases.  

Series for GDP and prices in the RoW start in 1999 and are constructed on the basis of data for 

the  following  58  countries:  Albania,  Algeria,  Argentina,  Armenia,  Australia,  Azerbaijan, 

Belarus, Brazil, Bulgaria, Canada, Chile, China, Colombia, Croatia, Czech Republic, Denmark, 

Egypt,  Georgia, Hong Kong, Hungary,  Iceland,  India,  Indonesia,  Iran,  Israel,  Japan, Jordan, 

Korea, Lebanon, Libya, FYR Macedonia, Malaysia, Mexico, Moldova, Montenegro, Morocco, 

New Zealand, Nigeria, Norway, Philippines, Poland, Romania, Russia, Saudi Arabia, Serbia, 

Singapore,  South  Africa,  Sweden,  Switzerland,  Syria,  Taiwan,  Thailand,  Tunisia,  Turkey, 

Ukraine, United Arab Emirates, United Kingdom, and Venezuela.  

When  not  available,  quarterly-frequency  data  are  obtained  by  interpolating  annual  data.  We 

seasonally adjust the following time series using the TRAMO-SEATS package developed by 

Gómez and Maravall (1996): nominal  public investments  (for EA19,  DE, and ES), nominal 

social  benefits  other  than  transfers  in  kind  (for  EA19,  DE,  and  ES),  government  interest 

expenditure (for EA19, DE, and ES), compensation of employees (for DE, and ES), and general 

government net lending (for ES). 

Table  C.1  lists  the  observed  time  series.  We  apply  logarithmic  transformations  to  all 

observables, with the exception of the trade balance-to-GDP ratio, the oil price, and nominal 

interest rates. GDP deflators and relative prices of demand components are computed as the 

ratios of the current-price value to the chain-indexed volume series. The trend component of 

total factor productivity is computed using the DMM package developed by Fiorentini et al. 

(2012). The resulting series at quarterly frequency is then used to estimate potential output. In 

DE, we additionally observe the historical average unemployment benefit ratio (constructed as 

the ratio of unemployment benefits to the wage rate). 

53 

 
RoW  

Real GDP  
GDP trend  
Oil price  
Nominal interest rate 
Population  

Table C.1: Observed time series 

Member State (DE and ES)  

Euro Area  

Real GDP  
GDP trend  
Effective exchange rate (nom.)  
Nominal interest rate 
Nominal trade balance to GDP 
Nominal exports 
Population  

Real GDP  
TFP trend  
Worked hours  
Nominal wage share to GDP 
Import share to GDP 
Export share to GDP 
Nominal government transfers to GDP  
Nominal government debt to GDP 
Nominal government interest payments to GDP  
Nominal government consumption to GDP 
Nominal total investment to GDP 
Nominal private consumption to GDP  
Nominal exports to GDP 
Nominal imports to GDP 
GDP deflator 
Government consumption to GDP deflator 
Government investment to GDP deflator 
Private consumption to GDP deflator 
Total investment to GDP deflator 
Nominal import to GDP deflator 
Nominal exports to GDP deflator 
Nominal trade balance to GDP 
Active population rate 
Population  

Note:  We  observe  EA  aggregate  variables  and  compute  model-consistent  REA  observation  equations.  We 
observe the first quarter of the capital stock and the net international investment position to initialise the starting 
point. 

We make a few transformations  to  the raw investment  series.  In particular, we compute the 

deflator  of  public  investments  based  on  annual  data  and  then  obtain  its  quarterly  frequency 

counterpart through interpolation. This series together with nominal public investments is then 

used  to  compute  real  quarterly  public  investments.  In  order  to  assure  consistency  between 

nominal GDP and the sum of the nominal components of aggregate demand, we impute  the 

change in inventories to the series of investments. 

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doi:10.2760/117627 

ISBN 978-92-76-19936-6