The COVID19-pandemic in the EU : macroeconomic transmission and economic policy response.
Date: 2020-08-12
Institutions: Directorate-General for Economic and Financial Affairs
Subjects: European Union, coronavirus disease, economic cycle, fiscal policy, labour economics, macroeconomics, monetary union, short-time working

6

ISSN 2443-8022 (online)

The COVID19-Pandemic
in the EU: Macroeconomic 
Transmission & Economic 
Policy Response

Philipp Pfeiffer, Werner Roeger 
and Jan in ’t Veld 

DISCUSSION PAPER 127 | JULY 2020

EUROPEAN ECONOMY

EUROPEAN 
ECONOMY

Economic and 
Financial Affairs

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European Commission 
Directorate-General for Economic and Financial Affairs 

The COVID19-Pandemic in the EU:   
Macroeconomic Transmission and Economic Policy Response 

Philipp Pfeiffer, Werner Roeger and Jan in ’t Veld  

Abstract  

This  paper  uses  a  macroeconomic  model  to  analyse  the  transmission  of  the  COVID19-pandemic  and  its 
associated lockdown and quantify the stabilising effects of the economic policy response. Our simulations 
identify firm liquidity problems as crucial for shock propagation and amplification. We then quantify the 
effects of short-term work allowances and liquidity guarantees - central policy strategies in the European 
Union. The measures reduce the output loss of COVID19 and its associated lockdown by about one fourth. 
However, they cannot prevent a sharp but temporary decline in production. 

JEL Classification: E32, E6, F45, J08. 

Keywords: fiscal policy, COVID19, Monetary union, short-work allowances, liquidity constraints. 

Acknowledgements:  We  would  like  to  thank  Declan  Costello,  Björn  Döhring,  Robert  Kuenzel,  João 
Leal,  José  Leandro,  Hauke  Vierke,  Lukas  Vogel,  Milan  Vyskrabka  and  many  colleagues  involved  in 
Directorate-General for Economic and Financial Affairs’ forecast for useful comments and suggestions.  

Contact:  Philipp  Pfeiffer,  philipp.pfeiffer@ec.europa.eu;  Werner  Roeger,  werner.roeger@ec.europa.eu; 
Jan  in  ’t  Veld,  jan.intveld@ec.europa.eu.  European  Commission,  Directorate-General  for  Economic  and 
Financial Affairs, 

EUROPEAN ECONOMY                                                                                      Discussion Paper 127 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CONTENTS 

1.

Introduction ........................................................................................................................................ 5 

1.1. 

Related literature ................................................................................................................................... 6 

1.2. 

Road map ............................................................................................................................................... 7 

2.

Model

 ........................................................................................................................................ 7 

2.1.  Households .............................................................................................................................................. 7 

2.1.1.  The Ricardian household ........................................................................................................................... 8 

2.1.2.  The liquidity-constrained household ........................................................................................................ 9 

2.2. 

Intermediate goods firms ..................................................................................................................... 9 

2.2.1.  Labour input constraints: Lockdown shocks ......................................................................................... 10 

2.2.2.  Investment liquidity constraints ............................................................................................................... 10 

2.3. 

Final good firms .................................................................................................................................... 11 

2.4.  Wage setting ........................................................................................................................................ 11 

2.5. 

Public policy ......................................................................................................................................... 11 

2.5.1.  Monetary policy ........................................................................................................................................ 11 

2.5.2.  Fiscal policy ................................................................................................................................................ 12 

2.6.  Model calibration and solution ......................................................................................................... 12 

3.

Lockdown and pandemic in a macro model .......................................................................... 14 

4.

Macroeconomic transmisson of the pandemic ....................................................................... 14 

4.1. 

The Covid-19 Shock Absent Liquidity Constraints .......................................................................... 14 

4.2. 

The impact of liquidity constraints .................................................................................................... 16 

3 

5.

Economic policy response ............................................................................................................ 16 

5.1.  Overview stabilisation measures ....................................................................................................... 16 

5.2. 

Short-term work allowances .............................................................................................................. 17 

5.2.1.  Stabilisation gains under identical ex-ante costs ................................................................................. 17 

5.2.2.  The generosity of STW allowances ......................................................................................................... 17 

5.3. 

Liquidity support ................................................................................................................................... 19 

6.

Robustness  ...................................................................................................................................... 21 

7.

Discussion 

 ...................................................................................................................................... 22 

REFERENCES 

ANNEX A  DETAILS ON FIRM LIQUIDITY CONSTRAINTS ....................................................................... 25 

ANNEX B 

FUNCTIONAL FORMS ............................................................................................................ 28 

ANNEX C  ADDITIONAL RESULTS ............................................................................................................ 29 

4 

1.  INTRODUCTION  

COVID19 is a rare disaster requiring  urgent and targeted policy action. The economic fallout of the 
pandemic  has  triggered  an  intense  debate  on  effective  policies.  Governments  have  announced  and 
implemented  exceptional  stabilisation  efforts.  Our  paper  contributes  to  this  debate  using  a  dynamic 
general equilibrium model and an up-to-date collection of fiscal policy measures in the EU. We assess 
the  economic  transmission  of  COVID-19  and  quantify  gains  from  stabilisation  policies  in  the 
European Union (EU). Our model is two-region TANK model (two-agent New Keynesian) consisting 
of  the  EU-27  and  the  rest-of-the  world  (RoW)  based  on  the  European  Commission’s  QUEST  III 
model (Ratto et al., 2009). We extend the baseline model with a parsimonious model of heterogeneous 
firms and liquidity constraints. 

Our  analysis  proceeds  in  two  steps.  First,  a  set  of  scenarios  analyses  the  essential  economic 
characteristics of the pandemic.1 Stylised shocks capture the dynamic adjustment of the economy to (i) 
supply shocks through precautionary measures and (ii) shortfalls in consumer demand. Precautionary 
supply-side measures constrain labour input in production. The demand lockdown prevents consumers 
from  undertaking  certain  consumption  activities  by  either  legal  restrictions  or  voluntary  protection. 
We  quantify  the  impact  of  these  shocks  on  the  depth  and  duration  of  the  recession.  In  addition,  a 
simple  financial  accelerator  mechanism  via  firm  liquidity  constraints  amplifies  the  shocks.  Without 
policy support, the simulations show an output contraction by more than 20% in the second quarter of 
2020 compared to a no-pandemic baseline. Firm liquidity constraints almost double the depth of the 
recession and substantially prolong the slump. This amplification leads to a more U-shaped recovery. 
Output  in  2021  remains  markedly  below  a  no-pandemic  baseline  (almost  40%  of  the  2020  impact 
remains  in  2021).  By  contrast,  a  standard  model  without  borrowing  constraints  does  not  generate  a 
(large)  fall  investment  based  on  the  temporary  lockdown  shocks  to  demand  and  supply  alone.  As  a 
result, the simulations without firm liquidity constraints (and in the absence of other shocks), show a 
V-shaped recovery. 

In  a  second  step,  we  turn  to  an  early  assessment  of  economic  policy.  The  predicted  collapse  is 
unprecedented in post-war history. It warrants systematic comparison and quantification of the main 
policy strategies based on the identified transmission channels. Concretely, we focus on stabilisation 
gains  from  short-term  work  (STW)  allowances  and  government  guarantees.  Besides  automatic 
stabilisers, STW allowances and government guarantees are the dominant forms of fiscal response in 
the EU. Exploiting a dataset of planned fiscal measures of EU-27 Member States, we then show that 
together  economic  policies  likely  eliminate  about  one-fourth  of  the  macroeconomic  fallout  of  the 
pandemic.  

At the heart of our policy analysis are two interacting adjustment inefficiencies, namely employment 
adjustment  costs  and  liquidity  constraints  for  firms.  Measures  targeted  at  reducing  these  distortions, 
such  as  STW  allowances  and  loan  guarantees,  prevent  a  considerable  revision  of  investment  plans. 
Alleviating liquidity constraints supports spending in wages, intermediates, investment, and servicing 
of  loans.  STW  allowances  are  particularly  effective.  Since  workers  stay  in  the  firm,  firms  avoid 
matching frictions and hiring or firing costs. This cost-saving channel, in turn, improves the corporate 
liquidity  position  by  stabilising  the  gross  operating  surplus.  As  a  result,  fewer  firms  become 
constrained,  limiting  the  amplification  arising  from  the  occasionally  binding  constraint.  Apart  from 
short-run  expansionary  effects,  these  measures  may  avoid  that  temporary  liquidity  problems  morph 
into  insolvency  issues.  Together  STW  and  guarantees  reduce  the  output  loss  of  COVID19  and  its 

1 As discussed in Section 1.1, the scenarios are based on stylised versions of the simulations done in the context 
of  the  European  Commission’s  Spring  Forecast  published  on  May  7,  2020:  https://ec.europa.eu/info/business-
economy-euro/economic-performance-and-forecasts/economic-forecasts/spring-2020-economic-forecast-deep-
and-uneven-recession-uncertain-recovery_en  

5 

 
 
                                                           
associated lockdown by around four percentage points: one fourth of the negative economic impact of 
the pandemic.  

The  policies,  however,  cannot  prevent  a  temporary  decline  in  production  because  of  sickness, 
restrictions  on  the  mobility  of  workers  or  supply  chain  interruptions.  Moreover,  additional 
consumption from transfers can only (fully) materialise after the lockdown period. It cannot prevent a 
sharp drop in consumer spending during the pandemic. 

We analyse our results for a given short-lived pandemic. This optimistic simplification is designed to 
transparently  distil  essential  model  features,  in  particular  the  internal  propagation  mechanism  in 
response  to  the  exogenous  pandemic  shocks.  An  additional  longer  pandemic  scenario  relaxes  this 
assumption to show the sensitivity in a stylised way.  

1.1. 

RELATED LITERATURE 

There  have  been  widespread  calls  for  policies  to  mitigate  the  impact  of  the  COVID-19  shock  (e.g., 
Brunnermeier et al., 2020; Gopinath, 2020; and papers in Baldwin and Weder di Mauro, 2020). While 
monetary  policy  plays  a  crucial  role  in  safeguarding  liquidity  conditions  in  the  banking  system  and 
protecting  the  continued  flow  of  credit  to  the  real  economy,  the  space  of  central  banks  is  largely 
constrained. It is generally recognised that the ECB should not be expected to do all the heavy lifting. 
Economists have therefore emphasised that governments must step in with generous loans and other 
support  programs  to  prevent  mass bankruptcies,  and direct  fiscal  measures to  support  demand  when 
the lockdowns are lifted (e.g. Bénassy-Quéré et al. (2020), Lane (2020), Claes and Wolff (2020), and 
others). 

In an assessment of the efficacy of fiscal policies in the financial crisis, Coenen et al. (2012) compare 
transfer  multipliers  in  seven  large-scale  DSGE  models.  In  these  models,  spending  multipliers  are 
typically largest, often exceeding unity when the zero lower bound (ZLB) constrains monetary policy. 
By  contrast,  tax  multipliers  remain  lower.  Typically,  transfer  multipliers  are  also  lower  than 
government  consumption  and  investment  shocks.  However,  targeted  transfers  to  constrained 
households entail multipliers closer to those of spending shocks. Guerrieri et al. (2020) emphasise that 
when  some  sectors  are shut  down,  a  traditional fiscal  stimulus is less effective, as  any  money  spent 
cannot  go  to  “closed”  sectors,  whose  workers  have  the  greater  marginal  propensity  to  consume.  As 
long  as  there  are  sectors  shut  down,  there  is  a  unit  government  spending  multiplier  and  a  transfer 
multiplier  equal  to  the  average  marginal  propensity  to  consume.  Faria  e  Castro  (2020)  analyses 
different types of fiscal policies and finds that unemployment insurance benefits are the most effective 
tool to stabilise income for borrowers, who are the hardest hit, while savers may favour unconditional 
transfers. Liquidity assistance programs are effective if the policy objective is to stabilise employment 
in  the  affected  sector.  Bayer  et  al.  (2020)  also  emphasise  the  importance  of  conditional  transfers. 
Fornaro  and  Wolf  (2020)  emphasise  the  role  expectations  and  the  risks  of  demand-induced  growth 
slowdowns. 

Our  paper  considers  firm  and  household  heterogeneity.  Yet,  the  model  remains  parsimonious. 
Important related work complements our analysis by considering a more granular economic structure. 
Hagedorn and Mitman (2020) apply a HANK  model to study the interaction of fiscal and monetary 
policy.  Guerrieri  et  al.  (2020)  as  well  as  Baqaee  and  Farhi  (2020)  use  multi-sector  models  to  show 
amplification effects through complementarities and incomplete markets. Bigio et al. (2020) compare 
transfers to credit policy and highlight the role of debt.  

The economic literature on COVID19 is growing rapidly. Important contributions also link economic 
models  with  epidemiological  frameworks  (e.g.,  Acemoglu  et  al.,  2020;  Eichenbaum  et  al.,  2020; 
Glover et al., 2020; and Jones et al., 2020; and references therein).   

6 

 
 
We  contribute  to  this  literature  by  implementing  a  lockdown  shock  in  a  standard  macro  model  and 
highlighting  the  role  of  liquidity  constraints.  Exploiting  information  about  size  and  composition  of 
fiscal measures announced by EU member states, our paper then shows the depth of the recession and 
the shape of the recovery with and without fiscal measures.  

The paper is closely related to the scenario analysis published in the Spring Forecast of the European 
Commission (2020). Compared to the present paper, the simulations reported in the forecast document 
consider a richer modelling environmental with deeper regional and sectoral disaggregation and more 
transmissions channels (e.g. uncertainty shocks) and time patterns of the pandemic. By contrast, here 
we stress the role of inefficiencies arising from employment adjustment and liquidity constraints in a 
more stylised way. Another difference is that the paper quantifies national fiscal measures, whereas 
the forecast document included estimates of the EU-level measures. 

1.2. 

ROAD MAP 

The  next  two  sections  present  the  model,  its  calibration,  and  the  underlying  assumptions  of  the 
pandemic  shock.  Section  4  shows  simulations  results  absent  policy  intervention,  while  Section  5 
summarises  announced  policy  measures  and  the  mapping  into  the  model.  Section  6  conducts 
robustness analysis and Section 7 concludes.  

2.  MODEL  

We conduct our analysis in a two-region TANK model (two-agent New Keynesian) consisting of the 
EU-27 and the RoW. The framework is based on the European Commission’s QUEST III model suite 
(see,  e.g.,  Ratto  et  al.,  2009).  Our  discussion,  therefore,  focusses  on  the  main  model  elements  and 
refers for standard features to Ratto et al. (2009). We extend the baseline model with a parsimonious 
model of firm liquidity constraints. 

The model structure of all regions is symmetric. It includes nominal price and wage rigidities as well 
as adjustment costs associated with employment and investment. Households provide labour services 
to domestic firms. A share of households is liquidity constrained. Monopolistic trade unions set sticky 
wage  rates.  Governments  purchase  the  local  final  good;  make  transfers  to  households;  levy  labour, 
profit,  and  consumption  taxes;  and  issue  debt.  We  integrate  automatic  fiscal  stabilisation  via  tax 
revenues, constant spending in real terms and unemployment insurance. Trade and financial markets 
link the EU (based on EU-27 shares) and the rest-of-world. A limited interest rate response captures 
restricted monetary policy. We next present the core of the EU model block. The RoW block has the 
same structure except for the zero lower bound (ZLB) constraint on monetary policy (but features a 
-superscript  denotes  RoW  variables.2  To  ease  notation,  the  presentation 
block-specific  calibration). 
abstracts from linear taxation of consumption, labour, and profits. 

∗

2.1. 

HOUSEHOLDS 

The  household  sector  consists  of  two  representative  households
Ricardian  household,  indexed 

,  of  total  mass  one.  The 
,  enjoys  full  access  to  financial  markets.  The  other  household  is 

 ℎ ∈ {𝑅𝑅, 𝐶𝐶}

2 Parameters such as the degree of openness differ across the EU and RoW. See the discussion below. 

𝑅𝑅

7 

 
 
 
 
                                                           
liquidity-constrained and indexed by C. This household does not trade on asset markets. Instead, she 
consumes her entire disposable wage and transfer income in each period. Both households have this 
utility function over consumption

 and leisure (

)3:  

ℎ,𝑈𝑈

 𝐶𝐶𝑡𝑡
∞

𝑡𝑡

��

𝐸𝐸0 � 𝛽𝛽
𝑡𝑡=0

𝑖𝑖
1 − 𝑁𝑁𝑡𝑡

ℎ,𝑈𝑈

1

1 + 𝜓𝜓𝑡𝑡� log�𝐶𝐶𝑡𝑡
  >  0.   

� − 𝜒𝜒

1

𝑖𝑖
𝜅𝜅+1
(𝑁𝑁𝑡𝑡
)
𝜅𝜅 + 1

�

(1)

  captures  a  self-imposed  demand 

where 

  is  the  subjective  discount  factor  and 

  as  in  Eichenbaum  et  al.  (2020).  Moreover, 

constraint  in 
𝛽𝛽
constraint  on  consumption  (binding  in 
regulatory constraint by

. 

𝑡𝑡

𝜅𝜅

  represents  a  regulatory 
,  see  below).  We  denote  the  multiplier  attached  to  the 
≤ 𝐶𝐶̅

1+𝜓𝜓𝑡𝑡� < 1
ℎ,𝑈𝑈

𝐶𝐶𝑡𝑡

ℎ,𝑈𝑈

�

The aggregate value of any household-specific variable 

, where 

 𝜙𝜙𝑡𝑡

, in per-capita terms, is given by
 denotes the relative size of the liquidity constrained household.  
𝑋𝑋𝑡𝑡

 𝑋𝑋𝑡𝑡 = (1 −

𝑙𝑙𝑙𝑙

𝑟𝑟
)𝑋𝑋𝑡𝑡

𝑠𝑠

𝑙𝑙𝑙𝑙

𝑙𝑙
𝑋𝑋𝑡𝑡

+ 𝑠𝑠

𝑙𝑙𝑙𝑙

𝑠𝑠

𝑡𝑡

2.1.1. 

The Ricardian household 

The Ricardian household maximises utility subject to a sequence of budget constraints 

𝑅𝑅,𝑈𝑈

𝐿𝐿

,

, 

 and 

∆𝐿𝐿𝑡𝑡 + ∆𝐵𝐵𝑡𝑡 + ∆𝑉𝑉𝑡𝑡 = 𝑟𝑟𝑡𝑡−1𝐵𝐵𝑡𝑡−1 + 𝑟𝑟𝑡𝑡−1
𝑅𝑅
𝑟𝑟
𝑇𝑇𝑅𝑅𝑡𝑡
𝑊𝑊𝑡𝑡
  (the  return 

𝑟𝑟
𝐿𝐿𝑡𝑡−1 + 𝐷𝐷𝑡𝑡 − 𝐶𝐶𝑡𝑡
+ 𝑊𝑊𝑡𝑡
(2)
where 
denote the real wage rate (same for both households), labour supply, direct 
taxes paid by households, household-specific transfers, respectively. Assets of the household are made 
𝑁𝑁𝑡𝑡
 𝑇𝑇𝑡𝑡,
  (an 
up  of  loans  to  firms 
internationally traded bonds4 and
, yielding 
𝐵𝐵𝑡𝑡
:5 
dividends 
𝑉𝑉𝑡𝑡
𝑢𝑢𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡

, and unemployment benefits, 
𝑟𝑟𝑡𝑡−1

  includes  a  loan  default  risk  premium),  bonds 

government bonds) with net return 

summarises STW allowances, 

, and firm shares 

𝑅𝑅
+ 𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡

𝑅𝑅
+ 𝑇𝑇𝑅𝑅𝑡𝑡

𝑅𝑅
𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡

− 𝑇𝑇𝑡𝑡,

𝑠𝑠𝑡𝑡𝑤𝑤𝑡𝑡

𝑅𝑅
𝑁𝑁𝑡𝑡

𝐿𝐿
𝑟𝑟𝑡𝑡

𝐷𝐷𝑡𝑡

𝐿𝐿𝑡𝑡

. 

𝑅𝑅
𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡

  and 

𝑅𝑅
= (𝑢𝑢𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡)(1 − 𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑡𝑡 − 𝑁𝑁𝑡𝑡
(3)
  denote  the  labour  force  participation  rate  and  baseline  labour  demand, 

𝑅𝑅
) + 𝑠𝑠𝑡𝑡𝑤𝑤𝑡𝑡(𝑁𝑁𝑡𝑡

𝑅𝑅
− 𝑁𝑁0

 ),

where 
respectively. 

(1 − 𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑡𝑡)

𝑁𝑁0

In equilibrium, intertemporal consumption-saving choice satisfies: 

𝑅𝑅
�(1 + 𝜓𝜓𝑡𝑡
denotes the risk-free rate. Both constraints imply a negative shock to consumption in 

𝑅𝑅
)(1 + 𝜙𝜙𝑡𝑡

𝑓𝑓
𝑅𝑅 = 𝛽𝛽�1 + 𝑟𝑟𝑡𝑡

),

𝑅𝑅
𝐶𝐶𝑡𝑡+1
𝐶𝐶𝑡𝑡

where 
consumption constraint 
both  consumption  constraints,  self-imposed  (

𝑓𝑓
𝑟𝑟𝑡𝑡

𝑅𝑅,𝑈𝑈

𝑅𝑅,𝑈𝑈

𝐶𝐶𝑡𝑡

≤ 𝐶𝐶̅

 becomes binding in period 

 and 

)  and  regulatory  (

𝑡𝑡

𝑅𝑅
𝜙𝜙𝑡𝑡

𝑅𝑅

𝑡𝑡

𝜓𝜓

(4)
. The 
. Note that 
𝑡𝑡
),  have  the  same  effect  on  the 
𝑅𝑅
𝜙𝜙𝑡𝑡
= 𝐶𝐶

𝑅𝑅
𝐶𝐶𝑡𝑡

𝑅𝑅
����

> 0

 if 

3  Households  supply  differentiated  types  of  labour  services 
,  which  we  assume  to  be  distributed  equally  over 
both household types. Unions bundle the differentiated labour services provided by the two types of households 
and maximise a joint utility function for each type of labour 

𝑖𝑖
. See below. 

4  The  international  bond  features  a  country  risk  premium  which  depends  on  the  net  foreign  asset  position  to 
ensure long-run stability of the model (Schmitt-Grohé and Uribe, 2003). 

𝑖𝑖

5 The unemployed (
replacement rate. 

) receive benefits 

, where 

 is the exogenous benefit 

1 − 𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑡𝑡 − 𝑁𝑁𝑡𝑡

𝑟𝑟
𝑢𝑢𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡 = 𝑏𝑏𝑏𝑏𝑛𝑛𝑟𝑟𝑟𝑟 𝑊𝑊𝑡𝑡

𝑏𝑏𝑏𝑏𝑛𝑛𝑟𝑟𝑟𝑟

8 

 
 
 
 
 
 
 
 
 
                                                           
Euler equation.6 In the following, we assume
consumption in the Euler equation. 

 and 

, corresponding to a shock to current 

 𝜙𝜙𝑡𝑡 > 0 

𝜓𝜓𝑡𝑡 = 0

2.1.2. 

The liquidity-constrained household 

Voluntary social distancing and regulatory constraints on consumption also apply to the constrained 
household; namely a self-imposed consumption constraint 

and a regulatory constraint  

𝑟𝑟
𝑊𝑊𝑡𝑡

𝐿𝐿
𝑁𝑁𝑡𝑡

𝐶𝐶
− 𝑇𝑇𝑡𝑡 + 𝑇𝑇𝑅𝑅𝑡𝑡

𝐶𝐶
+ 𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡

𝐶𝐶
> 𝐶𝐶𝑡𝑡

> 𝐶𝐶̅
As a result, the constrained household features forced savings: 

𝑟𝑟
𝑊𝑊𝑡𝑡

𝐿𝐿
𝑁𝑁𝑡𝑡

𝐶𝐶
+ 𝑇𝑇𝑅𝑅𝑡𝑡

𝐶𝐶
+ 𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡

𝐶𝐶

.

and  dissaving  in  periods  following  the  lockdown 

𝐶𝐶
+ 𝑇𝑇𝑅𝑅𝑡𝑡
 denotes the post-lockdown period. 

𝑟𝑟
= 𝑊𝑊𝑡𝑡

𝐶𝐶
∆𝐵𝐵𝑡𝑡

𝐶𝐶
𝑁𝑁𝑡𝑡

, where 

𝐶𝐶
𝑠𝑠𝐵𝐵𝑡𝑡+𝜏𝜏−1
2.2. 

INTERMEDIATE GOODS FIRMS 

𝜏𝜏

𝐶𝐶
+ 𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡
𝐶𝐶
𝐶𝐶𝑡𝑡+𝜏𝜏

𝐶𝐶
− 𝑇𝑇𝑡𝑡 − 𝐶𝐶𝑡𝑡
𝐶𝐶
𝑟𝑟
𝑁𝑁𝑡𝑡+𝜏𝜏

= 𝑊𝑊𝑡𝑡+𝜏𝜏

(5)

(6)

(7)

𝐶𝐶

+ 𝑇𝑇𝑅𝑅𝑡𝑡+𝜏𝜏

𝐶𝐶

+ 𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡+𝜏𝜏

− 𝑇𝑇𝑡𝑡+𝜏𝜏 +

𝑡𝑡

where 

and

There is a continuum of intermediate goods indexed by 
Firms  face  symmetric  decision  problems  and  make  identical  choices.  Firm 

. A single firm produces each good. 

  has  technology 

  where 

𝛼𝛼
�

𝑗𝑗
𝐾𝐾𝑡𝑡

𝑗𝑗
𝑗𝑗
and capital stock, respectively. 
1−𝛼𝛼
𝐴𝐴�𝑁𝑁𝑡𝑡
(𝑢𝑢𝑡𝑡
)
’s  capital  stock  is 
period 
𝑗𝑗

𝐽𝐽
, 𝑁𝑁𝑡𝑡
𝐴𝐴 
= (1 − 𝛿𝛿)𝐾𝐾𝑡𝑡−1

 dividend of intermediate good firm 
𝑗𝑗
+ 𝐼𝐼𝑡𝑡

𝑗𝑗
𝐾𝐾𝑡𝑡

𝑗𝑗
𝑌𝑌𝑡𝑡

𝑗𝑗

𝑗𝑗 ∈ [0,1]

  and 

  are  the  firm’s  output,  labour  input,  capacity  utilisation 
=
𝑗𝑗
is a constant common productivity level. The law of motion of firm 
, 𝑢𝑢𝑡𝑡
.  The 

  and  gross  investment 

𝑗𝑗
𝐾𝐾𝑡𝑡

𝑗𝑗

𝑗𝑗
𝑌𝑌𝑡𝑡

with  depreciation  rate 
 is: 
, 
𝑗𝑗

𝛿𝛿

𝑗𝑗
𝐼𝐼𝑡𝑡

𝑗𝑗
𝐷𝐷𝑡𝑡

𝑗𝑗
= 𝑛𝑛𝑡𝑡

𝑗𝑗
𝑌𝑌𝑡𝑡

𝑗𝑗
− 𝑊𝑊𝑡𝑡𝑁𝑁𝑡𝑡

𝐾𝐾
− 𝑛𝑛𝑡𝑡

𝑗𝑗
𝐼𝐼𝑡𝑡

𝑗𝑗

𝑗𝑗
+ 𝐿𝐿𝑡𝑡

𝑗𝑗
+ Γt

𝐾𝐾
 are one-period loans. 
 𝑛𝑛𝑡𝑡

− 𝑟𝑟𝑡𝑡−1𝐿𝐿𝑡𝑡−1
(8)
denote the price charged by the firm and the price of production capital, respectively. 
summarises quadratic price and factor adjustment costs.7 Firm 
,  where 

maximises 
  denotes  the  discount  factor  of 

𝑗𝑗
the  present  value  of  dividends 
𝐿𝐿𝑡𝑡
Ricardian households. For later purpose, it useful to define the (real) gross operating surplus: 

𝑗𝑗
𝑛𝑛𝑡𝑡

𝑗𝑗
Γt

𝑗𝑗 

𝑗𝑗

,

𝑗𝑗
𝑉𝑉𝑡𝑡

𝑗𝑗
= 𝐷𝐷𝑡𝑡

+ Λ𝑡𝑡,𝑡𝑡+1𝑉𝑉𝑡𝑡+1

Λ𝑡𝑡,𝑡𝑡+1

. We model labour and capital/investment adjustment costs as8: 

𝑗𝑗
𝑁𝑁𝑡𝑡

𝑟𝑟
− 𝑊𝑊𝑡𝑡

𝑗𝑗
𝑌𝑌𝑡𝑡
6  However,  consumption  responds  different  to  policies  for  the  two  shocks.  With  a  self-imposed  reduction  of 
consumption,  household  consumption  will  respond  to  fiscal  measures  (e.g.  a  reduction  of  VAT),  while  the 
government  imposed  constraint  on  consumption  is  a  quantity  constraint  which  cannot  be  affected  by  fiscal 
measures.  
7  Quadratic  price  adjustment  costs  imply  that  the  inflation  rate  of  local  intermediates  obeys  an  expectational 
Phillips curve. See Annex B. 

𝑗𝑗
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

=

8 Given substitutability between capital and labour allowed by the production technology, firms could increase 
the utilisation of capital to partly offset the labour input constraint. We find this an unrealistic option in the short 
run given the scale of the supply constraint. Therefore, we impose a partial short-run complementarity between 
labour and utilised capital 

∆𝑁𝑁𝑡𝑡
𝑁𝑁𝑡𝑡 ≈

∆𝑈𝑈𝐶𝐶𝑡𝑡
𝑈𝑈𝐶𝐶𝑡𝑡 .

9 

 
 
 
 
 
 
 
                                                           
 
𝑁𝑁,𝑗𝑗

𝛤𝛤𝑡𝑡

𝑗𝑗
�𝑁𝑁𝑡𝑡

� ≡

𝑁𝑁

𝛾𝛾
2

�

𝑁𝑁𝑡𝑡−1

𝑗𝑗
𝑁𝑁𝑡𝑡
𝑗𝑗 − 1�

2

(9)

𝐾𝐾,𝑗𝑗

𝛤𝛤𝑡𝑡

𝐾𝐾

𝛾𝛾
2

2

𝑗𝑗
𝐼𝐼𝑡𝑡
𝑗𝑗 − 𝛿𝛿�

𝐼𝐼
𝑛𝑛𝑡𝑡

𝐽𝐽
𝐾𝐾�𝑡𝑡−1

𝐼𝐼

𝛾𝛾
2

𝐼𝐼
𝑛𝑛𝑡𝑡

𝑗𝑗
�𝛥𝛥𝐼𝐼𝑡𝑡

2
�

≡

(10)
Next, we discuss the two transmission channels of the pandemic on the production side: Labour input 
restrictions and liquidity constraints. Lockdown measures imply a downward shift in labour demand. 
In  addition,  the  reduction  in  output  induced  by  the  pandemic  and  its  associated  demand  and  supply 
lockdown measures leads to falling investment via liquidity problems for firms.  

𝐾𝐾𝑡𝑡−1

+

�

2.2.1. 

Labour input constraints: Lockdown shocks 

To  prevent  infections  at the  workplace,  governments  impose  restrictions  on  labour  input.  Firms  can 
  employees  during  the  lockdown.  Precautionary  distancing  measures  at  the  workplace 
only  use 
imply then 
𝑁𝑁�𝑡𝑡
𝑁𝑁𝑡𝑡 ≤ 𝑁𝑁�𝑡𝑡

. A binding constraint shifts down the labour demand schedule: 

𝜕𝜕𝑁𝑁𝑡𝑡
 is the Lagrange multiplier of the labour input constraint.  

𝑗𝑗
𝜕𝜕𝑌𝑌𝑡𝑡

𝑟𝑟
𝑗𝑗 = 𝑊𝑊𝑡𝑡

𝑁𝑁
+ 𝜃𝜃𝑡𝑡

,

(11)

where 

𝑁𝑁
𝜃𝜃𝑡𝑡

≥ 0

2.2.2. 

Investment liquidity constraints 

Below  we  consider  an  extended  model  in  which  a  subset 
faces temporary binding liquidity constraints of the form:9  

of  intermediate  goods  firms 

𝑙𝑙𝑖𝑖
0 ≤ 𝑠𝑠𝑡𝑡

< 1 

𝐿𝐿𝑡𝑡 ≤ 𝜇𝜇𝐾𝐾𝑡𝑡−1,
(12)
  is  the  loan-to-value  ratio.  For  these  firms,  adverse  demand  and  supply  shocks  increase 
where 
liquidity  needs  and  trigger  a  credit  tightening.  A  binding  collateral  constraint  binding  imposes  a 
reduction in investment. Therefore, the investment rate for constrained firms follows: 

𝜇𝜇

𝑗𝑗
𝐼𝐼𝑡𝑡
(13)
𝑗𝑗 − 𝛿𝛿� = ℋ �
 govern the strength of the liquidity constraint. The share of constrained 

𝑗𝑗 − 𝛿𝛿� −   𝜁𝜁2,

𝑗𝑗 � ≡   𝜁𝜁1 �

𝑗𝑗
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝑗𝑗
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐾𝐾𝑡𝑡−1

𝐾𝐾𝑡𝑡−1

𝐾𝐾𝑡𝑡−1

�
 and 

where parameters 
firms is endogenous and follows:  

𝜁𝜁1

𝜁𝜁2

As  shown  in  Annex  A,  this  reduced-form  equation  with  parameters 
micro-founded liquidity constraint.  

= 𝑛𝑛0 − 𝑛𝑛1𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡.

𝑙𝑙𝑖𝑖
𝑠𝑠𝑡𝑡

and 

(14)
is  consistent  with  a 

𝑛𝑛0 

𝑛𝑛1 

9 By contrast, in the baseline model 

. 

𝑙𝑙𝑖𝑖
𝑠𝑠𝑡𝑡

= 0 ∀𝑡𝑡

10 

 
 
 
 
 
 
 
 
 
                                                           
,  where 

𝑗𝑗,′

𝑗𝑗
𝐼𝐼𝑡𝑡
𝑗𝑗
𝛤𝛤𝑡𝑡
�
𝐾𝐾𝑡𝑡
function of 

�

𝑗𝑗
𝑄𝑄𝑡𝑡
, i.e. 

The remaining unconstrained firms decide investment according to a standard 

-equation 

represents  the  discounted  value  of  physical  capital. The  net investment rate  is  a 
  = 1 +

𝑄𝑄

𝑗𝑗
𝑄𝑄𝑡𝑡

𝑗𝑗
𝐼𝐼𝑡𝑡
𝑗𝑗
�
𝐾𝐾𝑡𝑡−1

 for 

. Thus, the aggregate net investment follows: 

𝑗𝑗
− 𝛿𝛿� =  ℱ�𝑄𝑄𝑡𝑡

�

𝑙𝑙𝑖𝑖
𝑗𝑗 ∈ [𝑠𝑠𝑡𝑡

, 1]

𝑗𝑗
𝑄𝑄𝑡𝑡

𝑙𝑙𝑙𝑙
𝑠𝑠𝑡𝑡

𝐼𝐼𝑡𝑡
�
𝐾𝐾𝑡𝑡−1 − 𝛿𝛿� = � ℋ �

0

2.3. 

FINAL GOOD FIRMS  

𝑗𝑗
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐾𝐾𝑡𝑡−1

𝑗𝑗 �  𝑑𝑑𝑗𝑗

1

𝑗𝑗
+ � ℱ�𝑄𝑄𝑡𝑡

𝑙𝑙𝑙𝑙
𝑠𝑠𝑡𝑡

� 𝑑𝑑𝑗𝑗

.

(15)

Final  good  producers  have  access  to  a  CES  production  technology 

𝜈𝜈−1

𝜈𝜈 ,  with  home  bias 

. 

𝑑𝑑

1/𝜈𝜈
)

𝜈𝜈
𝜈𝜈−1
intermediates,  where 
  denotes 
𝑠𝑠
�
intermediate  imports  from  the  RoW.  The  final  good  is  used  for  domestic  private  and  government 
consumption, and investment. 

1
𝑗𝑗
  is  the  exogenous  substitution  elasticity  between  varieties. 
𝐺𝐺𝑡𝑡 = �∫ �𝑌𝑌𝑡𝑡
0

0.5 < 𝑠𝑠

< 1

𝑀𝑀𝑡𝑡

𝑀𝑀𝑡𝑡

𝑑𝑑𝑗𝑗

𝜀𝜀

�

�

𝑑𝑑

𝜀𝜀−1
𝜀𝜀

𝜈𝜈
𝜈𝜈−1

𝑑𝑑

1/𝜈𝜈
+ (1 −
)
𝜀𝜀−1  is  an  aggregate  of  the  local 

𝑌𝑌𝑡𝑡 = �(𝑠𝑠

𝐺𝐺𝑡𝑡

𝜀𝜀

2.4. 

WAGE SETTING  

A trade union ‘differentiates’ homogenous labour hours provided by the two domestic households into 
imperfectly substitutable labour services. Both households work the same hours and receive the same 
in the production process of intermediate goods is a CES aggregate of these 
wage. The labour input 
over  the  marginal  rate  of 
differentiated  labour  services.  The  union  sets  wage  rates  at  a  mark-up
𝑁𝑁𝑡𝑡 
  is  inversely  related  to  the  degree  of  substitution 
substitution  between  leisure  and  consumption. 
between labour varieties. The mark-up is countercyclical because of nominal wage adjustment costs. 
𝑊𝑊
𝜇𝜇𝑡𝑡
Following Blanchard and Gali (2007), we allow for real wage inertia; the current period real wage rate 
is a weighted average of the desired net real wage and the past (net) real wage:   

𝑊𝑊
 𝜇𝜇𝑡𝑡

where 
consumption and leisure. The parameter 

1−𝜉𝜉
𝜉𝜉
(1 − 𝜏𝜏𝑡𝑡−1
)]
(16)
is  a  weighted  average  of  the  two  households’  marginal  rates  of  substitution  between 
 is an index of real wage rigidity.  

𝑊𝑊
= [(1 + 𝜇𝜇𝑡𝑡

𝑁𝑁
(1 − 𝜏𝜏𝑡𝑡

)𝑚𝑚𝑟𝑟𝑠𝑠𝑡𝑡]

𝑟𝑟
)𝑊𝑊𝑡𝑡

𝑟𝑟
[𝑊𝑊𝑡𝑡

,

𝑁𝑁

𝑚𝑚𝑟𝑟𝑠𝑠𝑡𝑡 

𝜉𝜉

2.5. 

PUBLIC POLICY 

2.5.1.  Monetary policy 

EU  monetary  policy  is  subject  to  a  ZLB  constraint.10  The  notional  interest  rate  follows  a  smooth 
Taylor rule with respect to inflation and the output gap: 

10 Monetary policy in the RoW does not hit the ZLB. 

11 

 
 
 
 
 
 
 
                                                           
𝑖𝑖𝑡𝑡 = max �0, 𝜌𝜌𝑖𝑖𝑖𝑖𝑡𝑡−1 + (1 − 𝜌𝜌𝑖𝑖) �𝑟𝑟̅ + 𝜋𝜋

+ 𝜏𝜏𝜋𝜋 �

− 𝜋𝜋

� + 𝜏𝜏𝑦𝑦𝑦𝑦𝑡𝑡

�� .

(17)

, adjusts its policy rate relative to the steady-state value 

𝑡𝑡𝑡𝑡𝑟𝑟

𝑡𝑡𝑡𝑡𝑟𝑟

𝑔𝑔𝑡𝑡𝑔𝑔

𝐶𝐶
𝜋𝜋𝑡𝑡,𝑦𝑦𝑦𝑦𝑦𝑦
4

The central bank has an inflation target 
when actual CPI inflation deviates from the target, where 
inflation, or in case of a non-zero output gap (

).11 

𝑡𝑡𝑡𝑡𝑟𝑟

𝜋𝜋

𝑔𝑔𝑡𝑡𝑔𝑔

𝑦𝑦𝑡𝑡

2.5.2. 

Fiscal policy 

We  assume  that  the  government  keeps  its  expenditure  (
debt evolves as:

𝐺𝐺𝑡𝑡) 

𝐶𝐶
𝜋𝜋𝑡𝑡,𝑦𝑦𝑦𝑦𝑦𝑦

𝐶𝐶
≡ 𝑃𝑃𝑡𝑡

𝐶𝐶
/𝑃𝑃𝑡𝑡−4

− 1

 is year-on-year CPI 
𝑟𝑟̅

constant  in  real  terms.  Real  government 

𝐺𝐺
𝐵𝐵𝑡𝑡
where 
labour, and profit taxes. Time-varying labour taxation stabilises the debt-to-GDP ratio: 

𝐿𝐿
+ 𝐺𝐺𝑡𝑡 + (𝑢𝑢𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡)(1 − 𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑡𝑡 − 𝑁𝑁𝑡𝑡) + 𝑠𝑠𝑡𝑡𝑤𝑤𝑡𝑡(𝑁𝑁𝑡𝑡 − 𝑁𝑁0 ) + 𝑇𝑇𝑅𝑅𝑡𝑡

 denotes the government interest rate. 

, (18)
, government revenues, are the sum of consumption, 

𝑅𝑅
+ 𝑇𝑇𝑅𝑅𝑡𝑡

𝐺𝐺
)𝐵𝐵𝑡𝑡−1

𝐺𝐺
− 𝑅𝑅𝑡𝑡

𝐺𝐺
= (1 + 𝑟𝑟𝑡𝑡
𝐺𝐺
𝑟𝑟𝑡𝑡

𝐺𝐺
𝑅𝑅𝑡𝑡

� ,
�𝜏𝜏
  being  the  target  level  of  government  debt-to-GDP.  Parameters 

�

������� + 𝜏𝜏

𝑁𝑁
𝜏𝜏𝑡𝑡

𝑁𝑁
= 𝜏𝜏𝑡𝑡−1

𝐺𝐺
+ 𝒹𝒹𝑡𝑡

𝐵𝐵

𝑑𝑑𝑑𝑑𝑓𝑓

𝐺𝐺
𝛥𝛥𝐵𝐵𝑡𝑡

𝐺𝐺
𝐵𝐵𝑡𝑡
4𝑌𝑌𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑛𝑛𝑟𝑟

  and 

(19)
  control  the 

 is a dummy that allows to turn off the debt rule temporarily. 
𝜏𝜏

𝑑𝑑𝑑𝑑𝑓𝑓

𝐵𝐵

𝜏𝜏

with 
feedback rule. 
������
𝑏𝑏𝑡𝑡𝑛𝑛𝑟𝑟

𝐺𝐺
𝒹𝒹𝑡𝑡

2.6. 

MODEL CALIBRATION AND SOLUTION 

In  our  model  calibration,  one  period  corresponds  to  one  quarter.  Tables  1  summarises  the  main 
parameter  values.  Table  2  features  block-specific  parameter  values.  Macroeconomic  aggregates  that 
characterise the steady state, like private and public consumption and investment, trade openness, and 
trade linkages match block-specific data from national accounts and the GTAP database (Narayanan 
and Walmsley, 2008). 

𝑁𝑁

Behavioural parameters that govern the dynamic adjustment to shocks are based on earlier estimates of 
QUEST  model  versions.  In  particular, the  model  estimations  have identified  high  labour  adjustment 
).12  Annex  B  shows  additional  details  on  the  convex  adjustment  costs 
costs  for  the  EU  (
related to price setting and capacity utilisation. Concerning financial market frictions, we set the share 
of the Ricardian household to 60% - close to the estimates in Ratto et al. (2009), Dolls et al. (2012) 
and  Kaplan  et  al.  (2014).  We  microfound  the  firm  liquidity  needs  based  on  collateral  constraints  in 
Annex A. In our simulation, the endogenous share of constrained firms reaches around 30 per cent in 
2020Q2 (including policy). This value is in line with recent estimates (OECD, 2020) and based on a 
 of 0.3.13 The labour supply elasticity is set at 0.2 slightly below the 
collateral constraint parameter 
estimate  in  Kollmann  et  al.  (2016).  Concerning  adjustment  costs  on  labour,  goods,  and  capital,  we 
broadly follow earlier QUEST-based estimates. The tax rule parameters assure a smooth transition to 

= 25

𝜇𝜇

𝛾𝛾

11 The output gap concepts comes from a production function framework. See Ratto et al. (2009).  

12 See, for example, in 't Veld et al. (2015) and Kollmann et al. (2016). 

13 EU corporate debt is around 30% of the private capital stock. 

12 

 
 
 
 
 
 
 
 
 
                                                           
the  long-run  debt-to-GDP  ratio.  The  latter  reflects  average  pre-pandemic  EU  data.  Taylor  rule 
parameters are standard values in the literature. 

We solve the model nonlinearly under perfect foresight using a Newton-Raphson algorithm. 

Table 1: Selected parameter values 

Parameter 

Value 

Description 

0.997 
0.2 
25 
20 
0.04 
0.1 
20 
75 
0.8 
1.2 
0.12 
0.65 
0.17 
0.2 
0.015 
1.1 
0.1 
42 
0.3 
0 
0.05 
0.1 
0.8 
2 
0.1 

Discount factor  
Labour supply elasticity 
Head-count adjustment costs parameter 
Price adjustment costs parameter 
Linear capacity-utilisation adjustment cost 
Quadratic capacity-utilisation adjustment cost 
Capital adjustment cost 
Investment adjustment cost 
Real wage inertia 
Elasticity of substitution in total trade 
Price mark-up 
Cobb-Douglas labour share parameter 
Government expenditure (share in GDP) 
Steady-state wage mark-up  
Depreciation rate (quarterly) 
Intensity of liquidity-constraints (firms) parameter 1 
Intensity of liquidity-constraints (firms) parameter 2 
Share of liquidity-constrained firms parameter  
LTV in affected sectors 
Steady-state share of liquidity-constrained firms 
Tax rule parameter on debt 
Tax rule parameter on deficit 
Taylor rule persistence 
Reaction to inflation in Taylor rule 
Reaction to output gap in Taylor rule 

𝛽𝛽
1/𝜅𝜅
𝑁𝑁
𝛾𝛾
𝛾𝛾
𝑢𝑢𝑙𝑙𝑡𝑡𝑔𝑔,1

𝑃𝑃

𝑢𝑢𝑙𝑙𝑡𝑡𝑔𝑔,2

𝐾𝐾

𝛾𝛾
𝛾𝛾

𝐼𝐼

𝛾𝛾
𝛾𝛾
𝜉𝜉
𝜈𝜈
1 − 1/𝜀𝜀
𝛼𝛼
𝐺𝐺̅
𝑊𝑊
𝜇𝜇
𝛿𝛿
𝜁𝜁1
𝜁𝜁2
𝑛𝑛1
𝜇𝜇
𝑙𝑙𝑖𝑖
𝑠𝑠̅
𝜏𝜏
𝑑𝑑𝑑𝑑𝑓𝑓
𝜏𝜏

𝑏𝑏

𝜌𝜌𝑖𝑖
𝜏𝜏𝜋𝜋
𝑦𝑦
𝜏𝜏

Source: Commission services. 

Table 2: Region-specific parameter values 

Parameter 

𝑙𝑙𝑙𝑙

𝑠𝑠

1 − 𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑡𝑡

𝑁𝑁

𝑏𝑏𝑏𝑏𝑛𝑛𝑟𝑟𝑟𝑟
𝑇𝑇𝑅𝑅����
𝑑𝑑

𝑠𝑠

EA 

0.4 

0.71 

0.64 

0.40 

0.16 

0.22 

0.8 

RoW 

Description 

0.5 

Share of liquidity-constrained households 

0.76 

0.66 

0.30 

0.12 

0.06 

Labour force to population 

Steady-state employment to population 

Benefit replacement rate 

Transfer share (share in GDP) 

Steady-state share of imports  

0.4 

Baseline government debt-to-GDP ratio 

𝑏𝑏𝑡𝑡𝑛𝑛𝑟𝑟
Source: Commission services. 

13 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
3.  LOCKDOWN AND PANDEMIC IN A MACRO MODEL 

We  now  discuss  our  assumption  on  exogenous  shocks.  For  clarity,  we  assume  that  containment 
measures are active in March until June with a peak early in Q2. The pandemic shocks thus last two 
quarters, with a stronger effect in the second quarter. The shocks end in the third quarter. As discussed 
above,  the  pandemic  shocks  are  the  two  shocks  associated  with  supply  and  demand  disruptions,  i.e. 
restrictions on labour input and consumption (see Jonung and Roeger, 2006). In reality, the separation 
of  demand  and  supply  is  difficult.  For  example,  supply  constraints  are  only  one  factor  behind  the 
closure  of  shops  and  factories.  Moreover,  we  do  not  necessarily  see  a  trade-off  between  economic 
costs and lockdown. Timely containment measures may also prevent disruptions by avoiding larger-
scale  outbreak  at  a  later  stage.  Moreover,  in  multi-sector  models  with  incomplete  markets,  supply 
shocks can have “Keynesian” features (Guerrieri et al., 2020).  

All shocks are global, i.e. they are symmetric in both regions of the model. We calibrate the shock size 
as  roughly  consistent  with  the  Spring  Forecast  of  the  European  Commission  (2020).  The  forecast 
employed  detailed  sectoral  assumptions,  e.g.  particularly  strong  declines 
transport, 
accommodations, restaurants, tourism etc.  

in  air 

Two  remarks  are  in  order.  First,  we  do  not  believe  that  the  exogenous  pandemic  shocks  materialise 
only in 2020Q2. Yet, this assumption allows us to distinguish the direct pandemic shocks from their 
endogenous  transmission  in  a  transparent  way.    Second,  we  do  not  consider  the  exogenous  shocks 
included  in  the  simulations  to  be  the  only  economic  disruptions  caused  by  the  pandemic.  Other 
channels,  such  as  heightened  uncertainty  (e.g.  Baker  et  al.,  2020),  financial  risks  such  as  cascading 
bankrupticies,  or  permanent  changes  in  consumption  patterns,  complement  the  analysis  presented  in 
this paper.14  

Regarding public policy, the simulations assume an inactive debt rule for 40 periods, i.e. 

 for 
  and  1  otherwise.  This  setting  allows  a  clearer  assessment  of  the  budgetary 
effects of the pandemic and the economic policy response. In our simulations, the ZLB binds for two 
𝑡𝑡 = 2020𝑄𝑄1: 2030𝑄𝑄1
years. The simulations without discretionary policy intervention assume that governments only rely on 
automatic  stabilisers  (in  particular  unemployment  benefits).  All  scenarios  assume  that  government 
consumption and other transfers are constant in real terms (unless explicitly specified). 

𝐺𝐺
𝒹𝒹𝑡𝑡

= 0

4.  MACROECONOMIC TRANSMISSON OF THE 

PANDEMIC  

This section looks at the transmission channels of the pandemic shock and quantifies its impact. The 
next section then adds the economic policy response to the analysis. 

4.1. 

THE COVID-19 SHOCK ABSENT LIQUIDITY CONSTRAINTS 

The COVID-19 crisis has a very large detrimental economic impact on the EU and the world economy 
as  shown  in  Figure  1.  In  the  basic  model  version  without  firm  liquidity  constraints,  the  economic 

14 As mentioned above, our related work in the European Commission’s (2020) spring forecast addresses these 
two points. It considers additional channels, relaxes the assumption on duration, and considers other pandemic 
patterns such as second waves.   

14 

 
 
 
 
 
 
 
                                                           
impact  closely  follows  the  pandemic  and  required  containment  measures  (shown  with  red  dashed 
lines).15 The result for this model is essentially a V-shaped recession in Q1 and Q2. There is a massive 
decline  in  consumption,  where  reduced  labour  income  adds  to  the  adverse  impact  of  the  demand 
shock.  Some  persistence  in  adjustment  frictions  in  employment  prevent  an  immediate  adjustment. 
Higher  capacity  utilisation  partly  offsets  a  delayed  response  of  the  labour  inputs,  which,  however, 
remains  limited  as  we  assume  a  partial  short-run  complementarity  between  capital  and  labour.  The 
crisis also has a distributional dimension. Consumption of the constrained households depends more 
on labour income and falls more strongly than the consumption of the Ricardian household.  

The  baseline  model  version  only  generates  a  small  decrease  in  investment.  Investors  foresee  the 
temporary nature of the shock (as we abstract from uncertainty effects). Supply and demand shocks 
alone cannot generate a fall of investment. Yet, we find a strong decline in the gross operating surplus 
since  labour  costs  remain  high.  This  result  indicates  the  relevance  of  liquidity  constraints,  as  we 
discuss next. 

Figure 1: Simulations absent policy response 

Output

Labor input

Investment

Cap. utilisation

0

-5

-10

-15

-20

-25

-30

0

-2

-4

-6

-8

-10

-12

0

-5

-10

-15

-20

-25

-30

10

0

-10

-20

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Consumption

Inflation

Consumption savers

Consumption constr.

0

-10

-20

-30

-40

2

1.5

1

0.5

0

-0.5

10

0

-10

-20

-30

0

-20

-40

-60

-80

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Gross operating surplus

20

10

0

-10

-20

-30

-40

15

10

5

0

-5

Wage share

Gov. balance over GDP

Pandemic shock

0

-5

-10

-15

-20

0

-5

-10

-15

-20

-25

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

With liquidity constraints

W/o liquidity constraints

Note:  This  figure  expresses  the  wage  share,  quarterly  inflation,  and  the  government  balance  in 
percentage  point  deviation  from  steady  state.  All  other  variables  are  expressed  in  percent  deviation 
from steady state.  The pandemic shock is an illustrative index of the exogenous shock process.  Source: 
Commission services. 

15 We always maintain the assumptions that a share of households is liquidity constrained. 

15 

 
 
                                                           
4.2. 

THE IMPACT OF LIQUIDITY CONSTRAINTS 

We  now  show  that  the  firm  liquidity  constraints  lead  to  a  deeper  and  more  U-shaped  recession.  In 
contrast  to  the  baseline  setup,  the  firm  liquidity  channel  in  this  model  version  amplifies  supply  and 
demand shocks and generates a sizable decline in investment as shown in Figure 1 (blue solid lines). 
The  endogenous  fall  in  the  GOS  increases  the  share  of  liquidity-constrained  firms  and  generates  a 
sizable contraction in private investment. Investment adjustment costs, a plausible empirical feature, 
generate  additional  persistence. The  magnitude of the  investment decline is roughly  in  line  with  the 
Commission’s  investment  forecast  (European  Commission,  2020).  In  the  baseline  model  supply 
constraints  dominate  and  generate  (quarterly)  inflationary  pressure.  By  contrast,  the  impact  from 
liquidity  constraints  amplifies  the  deflationary  demand  effects  leading  to  a  more  balanced  picture. 
Once  the  lockdown  can  be  lifted,  higher  capacity  utilisation  and  recovering  consumption  lead  to  an 
increase prices.  

The  amplification  from  the  occasionally  binding  liquidity  constraints  also  renders  the  reduction  in 
labour input more persistent even though the constraint binds only in the first and second quarter. This 
effect strongly reduces output growth in 2020 and 2021 as shown in Table 4. GDP growth falls by 13 
per cent below the no-shock path, compared to -8 per cent in the absence of the liquidity constraints. 
In  sum,  the  amplification  leads  to  a  more  U-shaped  pattern  of  output  and  motivates  the  focus  on 
liquidity constraints when analysing the EU policy response in the next section. 

5.  ECONOMIC POLICY RESPONSE 

This  section  analyses  the  economic  policy  response  in  the  EU  with  a  focus  on  (i)  short-time  work 
allowances and (ii) loan guarantees. Both measures target the distortion arising from firms’ liquidity 
constraints. As shown above, given the sharp fall in the gross operating surplus, liquidity constraints 
substantially  prolong  the  recession,  if  not  addressed  appropriately  by  economic  policy.  These 
measures, however, cannot prevent a temporary decline in production because of sickness, restrictions 
on the mobility of workers or supply chain interruptions. 

5.1. 

OVERVIEW STABILISATION MEASURES 

Table 3. Overview of announced measures by EU-27 Member States 

1. Measures with a direct budgetary impact 
2. Liquidity measures without budgetary impact 

a. Tax delays 
b. Public guarantees 
c. Others 
Total liquidity support 

Source: Commission services. Cut-off date 29/04/2020. 

bln EUR 

% of GDP 

 368 

248 
2301 
334 
2882 

 2.8 

1.9 
17.6 
2.6 
22.1 

The  fiscal  measures  announced  in  the  Member  States  consist  of  stimulus  measures  with  a  direct 
impact on the budget, as well as liquidity measures without direct budgetary impact. Table 3 provides 
information about fiscal measures and their composition for the EU-27. Total liquidity support by EU 
Member States amounts to approximately 22% of GDP, mostly in form guarantees and tax delays. In 
addition,  the  stimulus  measures  amount  to  around  2.8%  of  GDP,  mainly  as  STW  allowances  and 
transfers. We leave the analysis of the sizable supranational EU support for future work.  

16 

 
  
 
 
 
5.2. 

SHORT-TERM WORK ALLOWANCES 

Our modelling focuses on two differences of STW allowances compared to unemployment benefits: 
First,  STW  reduces  employment  adjustment  costs.  Unemployment  benefits  are paid to  workers  who 
have  lost  their  job.  By  contrast,  STW  allowances  are  paid  for  workers  staying  in  the  firm.  Since 
workers  stay  in  the  firm,  firms  avoid  matching  frictions  and  hiring  or  firing  costs.  We  capture  this 
  –  a  parsimonious  way  to  capture  the 
improved  allocative  efficiency  under  STW  by  setting 
absence  of  matching  frictions.  Second,  STW  allowances  are  more  generous  than  unemployment 
benefits. We capture this effect by including additional transfers to liquidity-constrained households, 
, which can be spent only after the pandemic.16 For analytical purposes, we separate 

= 0

𝛾𝛾

𝑁𝑁

𝐶𝐶

the two channels via two simulations. 
𝑇𝑇𝑅𝑅2020𝑄𝑄3:2020𝑄𝑄4

5.2.1. 

Stabilisation gains under identical ex-ante costs 

We  first  compare  stabilisation  gains  of  STW  under  identical  ex-ante  fiscal  cost,  i.e.  the  STW  rate 
equals  the  benefit  replacement  rate.  Assuming  the  same  generosity  of  STW  allowance  and 
unemployment  benefits,  allows  us  to  highlight  the  difference  in  allocative  efficiency.  Temporary 
unemployment  entails  layoff  and  search  costs,  which  STW  schemes  avoid.  To  keep  capture  the 
absence of matching friction and employment adjustment costs, we eliminate labour adjustment costs 
from the model. Figure 2 then compares the dynamics under STW (red dotted lines) to those of the 
baseline model discussed in Section 4.2, where only unemployment benefits active (solid blue line). 

The absence of employment adjustment frictions under STW allows firms to adjust their labour input 
more  strongly  during  the  peak  of  the  shock  (2020Q2).  However,  by  the  same  logic,  STW  schemes 
support the exit from the pandemic shock by avoiding a costly and time-consuming hiring process and 
allowing firms to increase labour input more rapidly.  

The interaction of STW with liquidity constraints. STW addresses two interacting frictions in the 
model:  Employment  and  liquidity  frictions.  The  cost-saving  effect  of  STW  improves  the  corporate 
liquidity position. By allowing for a stronger reduction of labour input, STW schemes help lower the 
wage  bill  without  incurring  firing  costs.  Importantly,  the stabilisation of the  gross  operating  surplus 
reduces  the  impact  of  firm  liquidity  constraints,  as  fewer  firms  become  constrained.  The  smaller 
distortion  from  liquidity  constraints  implies that  investment  declines  less,  and  labour input  recovers 
faster  and  more  strongly  –  especially  after  the  pandemic.  This,  in  turn,  makes  the  recession  less 
persistent.  This  result  highlights  the  gains  from  allocative  efficiency  even  under  identical  ex-ante 
fiscal costs.  

STW implies a larger government deficit in 2020. The expenditure on STW allowances is higher than 
under unemployment benefits scheme since firms reduce labour input more strongly (even under same 
generosity). However, once the government can lift the lockdown restrictions, STW policy achieves 
higher revenues from labour, consumption, and profit taxation. In annual terms, the (total) government 
balance to GDP ratio falls by around 9 percentage points in 2020 and remains at -3 pps in 2021.  

The  fact  that  STW  is  a  desirable  policy  depends  on  the  significant  labour  adjustment  costs  in 
European  countries.  The  relative  gains  compared  to  unemployment  benefits  could  be  smaller  for 
economies (or sectors) with a higher degree of labour market churning.17 

5.2.2. 

The generosity of STW allowances 

We  now  turn  to  the  more  realistic  case,  where  the  generosity  under  STW  is  higher  than  under 
unemployment  benefits.  Unlike  in  the  previous  simulation,  STW  allowances  entail  higher  ex-ante 

16 The Annex shows results for transfers to both households (non-targeted).  
17 See, e.g., Davis et al. (2012) for a discussion on labour market flows in the US. 

17 

 
                                                           
budgetary  costs  than  unemployment  benefits.  A  second  simulation  captures  this  aspect  by  adding 
transfers  to  constrained  households  of  2.8%  of  EU-27  GDP.  This  value  corresponds  to  the  policy 
measures credibly announced as of now (see Table 3). Since the containment measures partially curtail 
spending opportunities, households can spend transfers only in Q3 and Q4. Moreover, we assume that 
transfers target liquidity-constrained households. The Annex relaxes this assumption. 

Figure 2:  Short-term work allowances 

Output

Labor input

Investment

Cap. utilisation

0

-5

-10

-15

-20

-25

-30

0

-5

-10

-15

0

-10

-20

-30

-40

10

0

-10

-20

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Consumption

Inflation

10

0

-10

-20

-30

-40

2

1.5

1

0.5

0

-0.5

-1

0

-5

-10

-15

-20

-25

-30

Consumption savers

Consumption constr.

40

20

0

-20

-40

-60

-80

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Gross operating surplus

20

10

0

-10

-20

-30

-40

15

10

5

0

-5

Wage share

Gov. balance over GDP

Pandemic shock

0

-5

-10

-15

-20

0

-5

-10

-15

-20

-25

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Baseline w/ liquidity constraints

STW (same generosity as UBEN)

STW incl. higher transfers

Only transfers without STW

Note:  This  figure  expresses  the  wage  share,  quarterly  inflation,  and  the  government  balance  in 
percentage  point  deviation  from  steady  state.  All  other  variables  are  expressed  in  percent  deviation 
from steady state. The pandemic shock is an illustrative index of the exogenous shock process.  

The  higher  generosity  implies  sizable  output  gains.  Constrained  households  have  a  high  marginal 
propensity  to  consume,  implying  a  higher  multiplier  than  non-targeted  transfers.  Since  the 
containment measures partially curtail spending opportunities, we assume that transfers are paid and 
spent in Q3 and Q4. A sizable rebound of consumption materialises in these periods. The simulation 
shows that the support for household consumption facilitates exit. In 2020, the level of consumption is 
2.7% higher than without discretionary policy intervention. Higher transfers provide a strong boost to 
employment,  which  under  STW  can  expand  more  rapidly.  STW  thereby  also  improves  risk-sharing 
among  households,  with  a  more  balanced  distribution  of  consumption  across  households.  In  sum, 
STW  and  associated  higher  transfer  allowances  cushion  the  fall  in  real  GDP  by  around  2.2  pps.  in 
2020. 

18 

 
The  higher  generosity  of  STW  also  implies  ex-ante  a  stronger  deterioration  of  the  government 
balance.18  However,  the  faster  recovery  implies  increased  tax  revenues  (from  relative  increases  in 
consumption, labour, and profits) as well as lower unemployment benefits. In sum, STW allowances 
increase the deterioration in the deficit-to-GDP ratio by less than 1 pps. (on average in 2020 and 2021) 
compared to the baseline simulations with only unemployment benefits active.  

Interestingly,  the  two  aspects  of  STW  analysed  here,  namely  avoiding  job  match  destruction  and 
higher generosity, interact. The improved allocative efficiency under STW leads to stronger effects of 
transfers. Figure 2 shows the results by adding a simulation with “only transfers” where employment 
adjustment  costs  remain  at  the  baseline  values.  In  this  case,  additional  transfers  provide  smaller 
stabilisation  gains,  because  employment  adjustment  costs  slow  down  the  response  of  hours  worked 
and wages, translating into a smaller increase in household income. 

Finally, note that the effectiveness of transfers depends on the marginal propensity to consume of the 
receiving  households.  The  Annex  shows  that  targeted  transfers  are  significantly  more  efficient  by 
supporting  households  with  a  higher  marginal  propensity  to  consume  in  line  with  the  findings 
provided by Bayer et al. (2020).  

5.3. 

LIQUIDITY SUPPORT 

Liquidity  support  in  the  form  of  lending  guarantees  amounts  to  a  maximum  of  22%  of  GDP.  One 
important goal of these programs is to stabilise investment of liquidity-constrained firms.  

It  is  challenging  to  operationalise  the  liquidity  guarantees  in  a  macro  model.  Since  there  is  some 
heterogeneity of initial conditions and on how severely individual firms are affected by the shock, a 
fraction of firms will defer investment even with guarantees. There are also specific eligibility criteria, 
which exclude certain types of firms from the schemes or restrict the schemes to certain sectors. Also 
generally,  an  upper  bound  on  the  guarantee  per  firm  is  imposed.  Modelling  the  take  up  rate  would 
require more information about the distribution of the shock across firms and the constraints imposed 
by governments.  

In the absence of detailed up-to-date information, we will assume that 50% of the liquidity-constrained 
firms  are  not  revising  their  investment  plans  or  are  excluded  from  funding.  This  allows  us  to  say 
something  about  the  ’guarantee  multiplier’.  Under  the  assumption  that  firms  keep  dividend  payouts 
stable and that investment does not affect gross operating surplus of the firm in the current period, the 
investment multiplier to a loan increase for liquidity-constrained firms is one.  

.  The  budget  constraint  restricts 
To  see  this,  consider  a  liquidity-constrained  firm  (superscript
restricts  investment  of  this  firm  to  the  loan  supply  of  the  bank  and  current  gross  operating  surplus 
minus debt service and dividend payments  

 𝐶𝐶)

𝐶𝐶
Keeping current period dividends and GOS constant, the increase in investment due to a (guarantee-
+ 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
(20)
secured) extension of the loan is given by 

𝐶𝐶
− 𝑟𝑟𝐿𝐿𝑡𝑡−1 − 𝐷𝐷𝑡𝑡

𝐶𝐶
= ∆𝐿𝐿𝑡𝑡

𝐶𝐶
𝐼𝐼𝑡𝑡

𝐺𝐺
 denotes 
 is the loan expansion fully guaranteed by the government and supescript 
where 
= ∆𝐿𝐿𝑡𝑡
(21)
variables following the provision of guarantees. This is likely to be an upper bound since some of the 
additional funds may be diverted to increase dividends. However, apart from firm specific preferences, 
diversion  of  funds  is  limited  because  guarantee  schemes  by  EU  governments  generally  impose 
temporary  restrictions  on  dividend  payments  for  firms,  which  receive  funding  under  public  loan 

𝐶𝐶
− ∆𝐿𝐿𝑡𝑡

𝐶𝐶
− ∆𝐿𝐿𝑡𝑡

𝐶𝐶
− 𝐼𝐼𝑡𝑡

𝐺𝐺
∆𝐿𝐿𝑡𝑡

𝐺𝐺
𝐼𝐼𝑡𝑡

𝐺𝐺

,

18 We assume that the government covers the additional generosity. There are no additional costs for the firms. 

19 

 
 
 
                                                           
guarantee schemes. Based on information about non-performing loans19, we can assume that about ten 
per cent of these loans will default. This value gives a guarantee-multiplier of 

𝐶𝐶
− 𝑌𝑌𝑡𝑡
𝐶𝐶
(22)
𝑚𝑚
Thus,  essential  for  the  fiscal  multiplier  is  the  investment  multiplier  (
)  and  the  loss  rate  of  the 
− ∆𝐿𝐿𝑡𝑡
guaranteed  loan.20  This  multiplier  is  an  upper  bound  since  it  ignores  possible  windfall  gains  to  the 
banking  sector.  The  banking  sector  might  use  the  loan  guarantees  also  for  loans  to  unconstrained 
firms, thereby covering losses, which would otherwise be borne by the banking sector. 

𝐺𝐺
𝑌𝑌𝑡𝑡
𝐺𝐺
(∆𝐿𝐿𝑡𝑡

∗ 𝑙𝑙𝑙𝑙𝑠𝑠𝑠𝑠

= 𝑚𝑚

𝑚𝑚

=

)

𝐺𝐺

I

I

Figure 3: Lending guarantees 

Output

Labor input

Investment

Cap. utilisation

0

-5

-10

-15

-20

-25

-30

0

-2

-4

-6

-8

-10

-12

0

-5

-10

-15

-20

-25

-30

5

0

-5

-10

-15

-20

-25

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Consumption

Inflation

Consumption savers

Consumption constr.

0

-10

-20

-30

-40

1.5

1

0.5

0

-0.5

0

-5

-10

-15

-20

-25

-30

0

-20

-40

-60

-80

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Gross operating surplus

10

0

-10

-20

-30

-40

15

10

5

0

-5

Wage share

Gov. balance over GDP

Pandemic shock

0

-5

-10

-15

-20

0

-5

-10

-15

-20

-25

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Baseline w/ liquidity constraints

Guarantees

 Note:  This  figure  expresses  the  wage  share,  quarterly  inflation,  and  the  government  balance  in 
percentage  point  deviation  from  steady  state.  All  other  variables  are  expressed  in  percent  deviation 
from steady state. The pandemic shock is an illustrative index of the exogenous shock process 

19 Consolidated banking data from the ECB shows a ratio of lower non-performing loans to total loans. However, 
during  peak 
also:   
https://www.ecb.europa.eu/press/pr/date/2019/html/ecb.pr191106_1~a993d312e7.en.html  

eight  percent.  See 

around  2013, 

around 

times 

reach 

share 

crisis 

the 

20 The loss rate is defined by how much of the value of the investment project associated with defaulting loans 
must be written off. 

20 

 
 
 
                                                           
6.  ROBUSTNESS  

For analytical clarity, we have considered a very short pandemic. Yet, it is increasingly clear that the 
pandemic and the associated lockdown will continue for a longer time. Therefore, Figure 4 considers 
also a longer pandemic, extending partially also into 2021 (see bottom right figure). Dashed red lines 
show the simulations of the longer pandemic, while blue solid lines correspond to the main simultions 
(with firm liquidity constraints) as shown in Figure 1. 

Figure 4 shows that the duration of the pandemic is crucial for the length of the economic downturn: 
the adverse impact on investment and output increases and becomes more persistent into the second 
year (see final columns in Table 4 below). Note that the longer pandemic scenario includes automatic 
stabilisers,  but  no  STW  and  guarantees.  The  Commission’s  forecast  (European  Commission,  2020) 
has also considered other pandemic scenarios such as a second wave. 

Figure 4: Longer pandemic 

Output

Labor input

Investment

Cap. utilisation

0

-10

-20

-30

-40

0

-5

-10

-15

-20

0

-10

-20

-30

-40

5

0

-5

-10

-15

-20

-25

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Consumption

Inflation

0

-10

-20

-30

-40

-50

1.5

1

0.5

0

-0.5

-1

0

-10

-20

-30

-40

Consumption savers

Consumption constr.

0

-20

-40

-60

-80

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Gross operating surplus

10

0

-10

-20

-30

-40

15

10

5

0

-5

Wage share

Gov. balance over GDP

Pandemic shock

0

-5

-10

-15

-20

-25

0

-10

-20

-30

-40

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Baseline w/ liquidity constraints

Longer pandemic (w. liq. constraints)

Note:  This  figure  expresses  the  wage  share,  quarterly  inflation,  and  the  government  balance  in 
percentage  point  deviation  from  steady  state.  All  other  variables  are  expressed  in  percent  deviation 
from steady state. The pandemic shock is an illustrative index of the exogenous shock process. 

21 

 
 
 
 
7.  DISCUSSION 

COVID-19 is a rare disaster with enormous economic costs. This paper has analysed the transmission 
channels  of  the  pandemic  using  a  TANK  model.  In  the  baseline  model,  demand  and  supply  shocks 
lead to a V-shaped recession. However, an augmented model with firm liquidity constraints provides a 
different  picture.  In  this  framework,  the  strong  decline  in  the  gross  operating  surplus  following  the 
pandemic and its associated lockdown induces a strong reduction in investment due to a tightening of 
liquidity  constraints.  This  effect  amplifies  the  economic  fallout  and  generates  persistence.  It  also 
provides an important entry point for economic policy. 

Table 4: Overview of results (EU-27) 

Variable/Scenario

GDP 

Consumption

Investment

Labor input

GOS

Wage share

Gov. balance/GDP 

No liq. constr.

Liq. constraints

2020

-7.9

-12.9

-0.5

-4.8

-4.4

0.4

-5.3

2021

-0.9

-1.2

-0.6

-0.9

3.8

0.4

-0.8

2020

-13.0

-14.1

-20.2

-7.8

-10.1

2.6

-7.7

2021

-4.8

-3.0

-13.6

-4.1

-2.2

2.6

-3.2

STW (without add. 
transfers)
2020

2021

-12.1

-15.0

-14.3

-8.6

-6.8

0.7

-8.0

-3.7

-2.9

-10.0

-3.7

-0.7

-1.1

-2.9

STW

Guarantees

STW 
+ Guarantees

Longer pandemic 
(absent policy)

2020

-10.8

-11.4

-16.9

-6.6

-3.9

0.8

-9.2

2021

-4.2

-3.2

-11.8

-3.7

-1.6

-0.8

-3.2

2020

-10.7

-13.4

-10.7

-6.6

-8.1

1.4

-7.0

2021

-3.1

-2.1

-7.4

-2.6

0.6

-1.1

-2.1

2020

-8.7

-10.8

-8.6

-5.3

-1.9

0.0

-8.4

2021

-2.5

-2.3

-6.3

-2.3

0.7

-1.0

-2.1

2020

-19.8

-23.3

-27.0

-12.2

-15.9

4.4

-12.5

2021

-7.9

-5.6

-19.6

-6.4

-2.1

-1.5

-5.2

This table expresses the wage share and the government balance in percentage point deviation from steady state. 
All other variables are expressed in percent deviation from steady state. Source: Commission services. 

Our  analysis  then  quantifies  two  central  policy  responses  in  the  EU-27:  Short-term  work  (STW) 
allowances and liquidity support. Both policies support the recovery after the pandemic shocks. Given 
that  the  demand  effects  of  lockdowns  cannot  be  stabilised  at  the  time  of  implementation,  policies 
should target a rapid exit, once the pandemic ceases and governments can lift the associated lockdown. 
Our  paper  shows  that  STW  is  a  desirable  policy,  given  the  significant  labour  adjustment  costs  in 
European countries. Apart from reducing stress for employees associated job loss, STW allows more 
labour input flexibility and softens liquidity constraints of firms. In addition, liquidity guarantees target 
investment  and  employment  and  address  the  externalities  arising  from  constrained  firms.  Together 
both policies reduce the output loss of COVID19 and its associated lockdown by about one fourth (see 
Table 4): Instead of dropping by 13.0 per cent in 2020, the simulated fall in real GDP reaches 8.7%. 
However,  the  policy  measures  cannot  prevent  a  sharp  temporary  decline  in  production  during  the 
lockdown phase. 

The focus  of  the  paper  has  been  on time-limited  short-term  support  schemes.  In  particular,  we  have 
abstracted  from  the  negative  impact  that  these  support  policies  may  have  on  medium-run  allocative 
efficiency through reducing exit-entry rates and labour market churning. Moreover, we have focussed 
on the fiscal policy response of Member States, abstracting from important EU-level measures such as 
the  European  Stability  Mechanism  (ESM)  and  the  Support  to  mitigate  Unemployment  Risks  in  an 
Emergency (SURE). We leave these important topics for future research. 

22 

 
 
 
 
 
  
  
 
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24 

 
Annex A 

DETAILS ON FIRM LIQUIDITY CONSTRAINTS 

The  main  text  has  used  the  following  equations  describing  the  investment  behaviour  of  constrained 
firms: 

𝑗𝑗
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐾𝐾𝑡𝑡−1

𝑗𝑗
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐾𝐾𝑡𝑡−1

ℋ �

𝑗𝑗 � ≡   𝜁𝜁1 �

𝑗𝑗 − 𝛿𝛿� −   𝜁𝜁2,

Liquidity-constrained investment 

𝑙𝑙𝑖𝑖
𝑠𝑠𝑡𝑡

= 𝑛𝑛0 − 𝑛𝑛1𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

In  this  appendix,  we  show  how  a  share  of  firms  can  become  liquidity  constrained  if  a  shock  hits in 
period  t,  which  reduces  the  gross  operating  surplus  of  the  firm.  First,  we  look  at  an  individual  firm 
with budget constraint (dropping 

 indices to ease notation) 

𝑖𝑖

(A.1) 

To  facilitate  our  discussion,  we  make  three  assumptions:  (i)  the  economy  is  initially  on  a  balanced 
 does not 
growth path, (ii) all firms are financially unconstrained before the shock occurs, and (iii) 
change  much  across  constrained and  unconstrained  regimes  (see Jermann  and  Quadrini (2012)  for  a 
discussion). The firm faces an upper limit on loans which is determined by its capital stock 

𝐿𝐿𝑡𝑡 = (1 + 𝑟𝑟𝑡𝑡−1)𝐿𝐿𝑡𝑡−1 + 𝐷𝐷𝑡𝑡 + 𝐼𝐼𝑡𝑡 − 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐷𝐷𝑡𝑡

Prior to the unanticipated adverse shock, the firm is not constrained,  

𝐿𝐿𝑡𝑡 ≤ 𝜇𝜇𝐾𝐾𝑡𝑡

(A.2) 

(A.3) 

and becomes constrained after receiving a temporary negative GOS shock in period 
borrowing to the collateral limit. 

𝐿𝐿𝑡𝑡−1 < 𝜇𝜇𝐾𝐾𝑡𝑡−1

, which increases 

Since the firm is unconstrained in 

𝐶𝐶
𝐿𝐿𝑡𝑡

𝐶𝐶
= 𝜇𝜇𝐾𝐾𝑡𝑡

.

𝑡𝑡 − 1

Since collateral constraint is binding in period 

𝐾𝐾𝑡𝑡−1 = �
,  

1
𝜇𝜇 + 𝑥𝑥� 𝐿𝐿𝑡𝑡−1 >

𝑡𝑡

(A.4) 

(A.5) 

(A.6) 

1
𝜇𝜇1 𝐿𝐿𝑡𝑡−1

𝑡𝑡

𝐶𝐶
∆𝐾𝐾𝑡𝑡

𝐶𝐶
= (𝐾𝐾𝑡𝑡

− 𝐾𝐾𝑡𝑡−1) =
where the inequality indicates that capital stock falls more than the loan since the firm is now facing a 
financial constraint. How much does investment decline relative to a situation where the firm is not hit 
by a negative GOS shock and a standard (unconstrained) 
-equation determines investment. Without 
adverse  shock  in 
,  balanced  growth  implies  that  the  change  in  the  capital  stock  (denoted  by 
superscript 

) would have exceeded 

− 𝑥𝑥𝐿𝐿𝑡𝑡−1 <

𝑄𝑄

: 

,

1
𝐶𝐶
𝜇𝜇 ∆𝐿𝐿𝑡𝑡

1
𝐶𝐶
𝜇𝜇 ∆𝐿𝐿𝑡𝑡

𝑡𝑡

𝐵𝐵

𝐶𝐶
∆𝐾𝐾𝑡𝑡

(A.7) 

The difference between the change of capital with and without constraint 

𝐵𝐵
∆𝐾𝐾𝑡𝑡

1
𝐵𝐵
𝜇𝜇 + 𝑥𝑥� ∆𝐿𝐿𝑡𝑡

𝐶𝐶
> ∆𝐾𝐾𝑡𝑡

.

= �

. Thus, 

𝑥𝑥𝐿𝐿𝑡𝑡−1 − �

1
𝐵𝐵
𝜇𝜇 + 𝑥𝑥� ∆𝐿𝐿𝑡𝑡

Since 

1
𝐶𝐶
𝜇𝜇+𝑧𝑧 (∆𝐿𝐿𝑡𝑡

𝐵𝐵
− ∆𝐿𝐿𝑡𝑡

𝐶𝐶
) = ∆𝐾𝐾𝑡𝑡

𝐵𝐵
− ∆𝐾𝐾𝑡𝑡

<

1
𝐶𝐶
𝜇𝜇 (∆𝐿𝐿𝑡𝑡

𝐵𝐵
− ∆𝐿𝐿𝑡𝑡

)

𝐶𝐶
∆𝐾𝐾𝑡𝑡

𝐵𝐵
− ∆𝐾𝐾𝑡𝑡
25 

𝐶𝐶
= 𝐼𝐼𝑡𝑡

𝐵𝐵
− 𝐼𝐼𝑡𝑡

𝐶𝐶
∆𝐾𝐾𝑡𝑡

𝐵𝐵
− ∆𝐾𝐾𝑡𝑡

=

1
𝐶𝐶
𝜇𝜇 ∆𝐿𝐿𝑡𝑡

−

(A.8) 

(A.9) 

 
 
 
   
 
 
 
 
 
 
 
 
 
 
 
 
 
   
 
  
 
 
 
 
   
 
 
We get 

(A.10) 

𝐵𝐵
From the budget constraint of the firm (and neglecting differences in dividend payouts in both 
− 𝐼𝐼𝑡𝑡
regimes) we obtain the following relationship between investment and GOS in the constrained and 
unconstrained regime  

𝐶𝐶
(𝜇𝜇 + 𝑧𝑧)(𝐼𝐼𝑡𝑡

𝐶𝐶
) = (∆𝐿𝐿𝑡𝑡

𝐵𝐵
− ∆𝐿𝐿𝑡𝑡

)

𝐶𝐶
                       (∆𝐿𝐿𝑡𝑡

𝐵𝐵
− ∆𝐿𝐿𝑡𝑡

𝐶𝐶
) = (𝜇𝜇 + 𝑧𝑧)(𝐼𝐼𝑡𝑡

𝐵𝐵
− 𝐼𝐼𝑡𝑡

𝐶𝐶
) = (𝐼𝐼𝑡𝑡

𝐵𝐵
− 𝐼𝐼𝑡𝑡

𝐶𝐶
) − (𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐵𝐵
− 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

)       

(A.11) 

(A.12) 

This result holds for the individual firm or for the case with all firms becoming liquidity constrained. 
) =
The next section discusses the case when only a fraction of firms becomes constrained.  

)

𝐶𝐶
(𝐼𝐼𝑡𝑡

𝐵𝐵
− 𝐼𝐼𝑡𝑡

1

𝐶𝐶
1−(𝜇𝜇+𝑧𝑧) (𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

𝐵𝐵
− 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

Aggregate relationship between GOS and Investment  

In  this  section,  we  show  how  movement  of  (average)  GOS  affect  the  share  of  constrained  firms  by 
introducing a minimum amount of heterogeneity across firms.  We first introduce some notation. There 
are 

. GOS has an aggregate and an idiosyncratic component governed by 

 firms with 

.   

𝑖𝑖

𝑖𝑖 ∈ [0,1]

(A.13) 
𝜎𝜎

 Firm i will respond to a temporary decline of gross operating surplus by increasing borrowing because 
of  a  smoothness  restriction  on  dividend  payouts,  and  convex  investment  adjustment  costs,  which 
makes investment a function of the present discount value of profits. Investment of the unconstrained 
 without the COVID 
firm deviates marginally from the investment the firm would have undertaken in 
shock (see scenario 1). We denote this difference 

𝐺𝐺𝐺𝐺𝑆𝑆𝑖𝑖𝑡𝑡 = 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡 + 𝜎𝜎(𝑖𝑖 − 0.5)

We denote the marginal firm, which stays unconstrained with 

= (1 + 𝑟𝑟𝑡𝑡−1)𝐿𝐿𝑡𝑡−1

𝐵𝐵
+ 𝐼𝐼𝑡𝑡

𝐵𝐵
− 𝑏𝑏𝑡𝑡 − 𝐺𝐺𝐺𝐺𝑆𝑆𝑖𝑖𝑡𝑡 = 𝜇𝜇𝐾𝐾𝑡𝑡

𝐶𝐶
𝐿𝐿𝑖𝑖𝑡𝑡

𝑈𝑈
𝐼𝐼𝑡𝑡

𝐵𝐵
= 𝐼𝐼𝑡𝑡

𝐵𝐵

𝑏𝑏𝑡𝑡.
− 𝑏𝑏𝑡𝑡
𝐵𝐵
+ 𝐷𝐷𝑡𝑡

𝑡𝑡

(A.14) 

(A.15) 

𝚤𝚤̅
𝐵𝐵
+𝐼𝐼𝑡𝑡
 declines 
 increases, i.e. the profitability threshold increases for firms to remain unconstrained. 
 ranges between zero and one, it can also be interpreted as the share of constrained firms and the 

𝐵𝐵
(1+𝑟𝑟𝑡𝑡−1)(𝜇𝜇+𝑥𝑥)𝐾𝐾𝑡𝑡

𝐵𝐵
+𝐷𝐷𝑡𝑡
𝐵𝐵
𝜇𝜇𝐾𝐾𝑡𝑡

( 𝚤𝚤̅ − 0.5) =

(A.16) 

𝜎𝜎
𝐵𝐵
𝜇𝜇𝐾𝐾𝑡𝑡

−𝑑𝑑𝑡𝑡−𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

 and 

 can be approximated linearly (where we ignore the term 

If 
Since 
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
relationship between 
𝚤𝚤̅

𝚤𝚤̅

𝐶𝐶

𝚤𝚤̅

𝐺𝐺𝐺𝐺𝑆𝑆

𝑏𝑏𝑡𝑡)
(A.17) 

𝑙𝑙𝑖𝑖
𝑠𝑠𝑡𝑡

𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐵𝐵
𝐾𝐾𝑡𝑡

= 𝚤𝚤̅ = 𝑛𝑛0 − 𝑛𝑛1
Equation  (A.17)  corresponds  to  the  firm  share  equation  presented  in  the  main  text.  The  parameter 
values  can  be  determined  using  information  about  the  share  of  liquidity  constrained  firms  in  the 
constrained and unconstrained regime. For the unconstrained regime, we assume a share equal to zero. 
By contrast, in the constrained regime, we use information about the share of output produced by firms 
directly  affected  from  lockdown  measures  to  set  a  lower  bound  of  investment  undertaken  by 
constrained firms in the COVID regime. This share is set to 0.3. Therefore, we have two equations to 
determine the two parameter 

and 

0.3 = 𝑛𝑛0 − 𝑛𝑛1

Given the investment rule of constrained firm 

0.0 = 𝑛𝑛0 − 𝑛𝑛1

𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐵𝐵
𝐾𝐾𝑡𝑡

𝐵𝐵
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐵𝐵
𝐾𝐾𝑡𝑡

𝑖𝑖 𝜖𝜖(0, 𝚤𝚤̅)
𝐵𝐵
− 𝐼𝐼𝑡𝑡

� =
26 

𝐶𝐶
�𝐼𝐼𝑖𝑖𝑡𝑡

1

𝐶𝐶
1−(𝜇𝜇+𝑧𝑧) �𝐺𝐺𝐺𝐺𝑆𝑆𝑖𝑖𝑡𝑡

𝐵𝐵
− 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

�

(A.18) 

(A.19) 

(A.20) 

 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
 
 
   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
We obtain total investment of constrained firm by 

𝐶𝐶
𝐼𝐼𝑡𝑡

𝐶𝐶𝚤𝚤̅
= ∫ 𝐼𝐼𝑖𝑖𝑡𝑡
0

𝐵𝐵𝚤𝚤̅
𝑑𝑑𝑖𝑖 = ∫ 𝐼𝐼𝑡𝑡
0

1

𝚤𝚤̅
𝐶𝐶
1−(𝜇𝜇+𝑧𝑧) ∫ �𝐺𝐺𝐺𝐺𝑆𝑆𝑖𝑖𝑡𝑡
0

𝐵𝐵
− 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

�

𝑑𝑑𝑖𝑖

𝑑𝑑𝑖𝑖 +

𝐶𝐶
𝐼𝐼𝑡𝑡

𝐵𝐵
= 𝚤𝚤̅𝐼𝐼𝑡𝑡

+ 𝚤𝚤̅

𝐶𝐶
𝐼𝐼𝑡𝑡

𝐵𝐵
= 𝚤𝚤(�𝐼𝐼𝑡𝑡

With 

1
1 − (𝜇𝜇 + 𝑧𝑧)
1

𝐵𝐵
�(𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡 − 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

2
) + 𝜎𝜎0.5(𝚤𝚤̅

− 𝚤𝚤̅)�

𝐵𝐵
1−(𝜇𝜇+𝑧𝑧) ��𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡 − 𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡

+

� + 𝜎𝜎0.5(𝚤𝚤̅ − 1)�) 

Firm i which is not constrained invests according to the Q equation 

𝜎𝜎0.5(𝚤𝚤̅ − 1) < 0

𝑈𝑈
𝐼𝐼𝑖𝑖𝑡𝑡

 because firms are identical in t-1 

= 𝜙𝜙(𝑄𝑄𝑖𝑖𝑡𝑡 − 1)𝐾𝐾𝑖𝑖𝑡𝑡−1 + 𝛿𝛿𝐾𝐾𝑖𝑖𝑡𝑡−1 = 𝜙𝜙(𝑄𝑄𝑡𝑡 + 𝜑𝜑(𝑖𝑖 − 0.5) − 1)𝐾𝐾𝑡𝑡−1 + 𝛿𝛿𝐾𝐾𝑡𝑡−1

𝐾𝐾𝑖𝑖𝑡𝑡−1 = 𝐾𝐾𝑡𝑡−1

1

𝑈𝑈
𝐼𝐼𝑡𝑡

𝑈𝑈
= � 𝐼𝐼𝑖𝑖𝑡𝑡
𝚤𝚤̅

1

𝑑𝑑𝑖𝑖 = � (𝜙𝜙(𝑄𝑄𝑡𝑡 + 𝜑𝜑(𝑖𝑖 − 0.5) − 1)𝐾𝐾𝑡𝑡−1 + 𝛿𝛿𝐾𝐾𝑡𝑡−1)

𝚤𝚤̅

𝑑𝑑𝑖𝑖

 (A.21) 

(A.22) 

(A.23) 

𝑈𝑈
2
= (1 − 𝚤𝚤̅)(𝜙𝜙(𝑄𝑄𝑡𝑡 − 1)𝐾𝐾𝑡𝑡−1 + 𝛿𝛿𝐾𝐾𝑡𝑡−1) + 𝜑𝜑0.5�(1 − 𝚤𝚤̅
𝐼𝐼𝑡𝑡
𝑈𝑈
2
Total investment 
= (1 − 𝚤𝚤̅)(𝜙𝜙(𝑄𝑄𝑡𝑡 − 1)𝐾𝐾𝑡𝑡−1 + 𝛿𝛿𝐾𝐾𝑡𝑡−1) + 𝜑𝜑0.5(𝚤𝚤̅ − 𝚤𝚤̅
𝐼𝐼𝑡𝑡

)𝐾𝐾𝑡𝑡−1

) − (1 − 𝚤𝚤̅)�𝐾𝐾𝑡𝑡−1

(A.24) 

𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 =

𝑈𝑈
𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 +

𝐶𝐶
𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1
2
= (1 − 𝚤𝚤̅)(𝜙𝜙(𝑄𝑄𝑡𝑡 − 1) + 𝛿𝛿) + 𝜑𝜑0.5(𝚤𝚤̅ − 𝚤𝚤̅

𝐵𝐵
𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 +

+ 𝚤𝚤̅ �

1
1 − (𝜇𝜇 + 𝑧𝑧)

��

𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐾𝐾𝑡𝑡−1 −

)
𝐵𝐵
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐾𝐾𝑡𝑡−1 � +

𝜎𝜎0.5
𝐾𝐾𝑡𝑡−1 (𝚤𝚤̅ − 1)�� 

𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 − 𝛿𝛿 =

𝑈𝑈
𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 − (1 − 𝚤𝚤̅)𝛿𝛿 +

𝐶𝐶
𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 − 𝚤𝚤̅𝛿𝛿 =

2
(1 − 𝚤𝚤̅)�𝜙𝜙(𝑄𝑄𝑡𝑡 − 1)� + 𝜑𝜑0.5(𝚤𝚤̅ − 𝚤𝚤̅

) + 𝚤𝚤̅ �

𝐵𝐵
𝐼𝐼𝑡𝑡
𝐾𝐾𝑡𝑡−1 − 𝛿𝛿 +

1

1−(𝜇𝜇+𝑧𝑧) ��

𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐾𝐾𝑡𝑡−1 −

𝐵𝐵
𝐺𝐺𝐺𝐺𝑆𝑆𝑡𝑡
𝐾𝐾𝑡𝑡−1 � +

𝜎𝜎0.5
𝐾𝐾𝑡𝑡−1 (𝚤𝚤̅ − 1)�� 

(A.25) 

We assume that 

 is small since 

 does not respond a lot to temporary shocks. 

2
𝜑𝜑0.5(𝚤𝚤̅ − 𝚤𝚤̅

)

𝑄𝑄𝑖𝑖𝑡𝑡

27 

 
     
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Annex B 

FUNCTIONAL FORMS 

Price and capacity utilisation costs follow convex functions: 

 with 

𝑃𝑃,𝑗𝑗

Γ𝑡𝑡

𝑗𝑗
≡ 0.5𝛾𝛾𝑃𝑃(𝜋𝜋𝑡𝑡

2
)

𝑗𝑗
𝑃𝑃𝑡𝑡−1

𝑗𝑗
𝑌𝑌𝑡𝑡

𝑗𝑗
𝜋𝜋𝑡𝑡

𝑗𝑗
≡ 𝑃𝑃𝑡𝑡

𝑗𝑗
/𝑃𝑃𝑡𝑡−1

− 1#

𝑢𝑢𝑙𝑙𝑡𝑡𝑔𝑔,𝑗𝑗

Γ𝑡𝑡

𝑗𝑗
≡ �𝛾𝛾𝑢𝑢𝑙𝑙𝑡𝑡𝑔𝑔,1 (𝑢𝑢𝑡𝑡

− 1) +

𝛾𝛾𝑢𝑢𝑙𝑙𝑡𝑡𝑔𝑔,2
2

𝑗𝑗
(𝑢𝑢𝑡𝑡

2
− 1)

�

𝐼𝐼
𝑛𝑛𝑡𝑡
𝑗𝑗
𝑗𝑗 𝐾𝐾𝑡𝑡
𝑛𝑛𝑡𝑡

28 

 
 
 
 
Annex C 

ADDITIONAL RESULTS 

Figure 1: Non-targeted transfers  

Output

Labor input

Investment

Cap. utilisation

0

-5

-10

-15

-20

-25

-30

0

-5

-10

-15

0

-5

-10

-15

-20

-25

-30

10

0

-10

-20

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Consumption

Inflation

10

0

-10

-20

-30

-40

2

1.5

1

0.5

0

-0.5

-1

0

-5

-10

-15

-20

-25

-30

Consumption savers

Consumption constr.

20

0

-20

-40

-60

-80

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Gross operating surplus

20

10

0

-10

-20

-30

-40

15

10

5

0

-5

Wage share

Gov. balance over GDP

Pandemic shock

0

-5

-10

-15

-20

0

-5

-10

-15

-20

-25

-30

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

2019Q4

2020Q2

2020Q4

2021Q2

2021Q4

Baseline w/ liquidity constraints

STW incl. higher transfers

STW incl. transfers (non-targeted)

Note:  This  figure  expresses  the  wage  share,  quarterly  inflation,  and  the  government  balance  in 
percentage  point  deviation  from  steady  state.  All  other  variables  are  expressed  in  percent  deviation 
from steady state. The pandemic shock is an illustrative index of the exogenous shock process. 

29 

 
 
 
 
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