The COVID-19 Recession on Both Sides of the Atlantic: A Model-Based Comparison (European Economy, July 2023)

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European Economy Discussion Paper 191, dated July 2023, "The COVID-19 Recession on Both Sides of the Atlantic: A Model-Based Comparison," by Roberta Cardani, Philipp Pfeiffer, Marco Ratto and Lukas Vogel, published by the European Commission's Directorate-General for Economic and Financial Affairs. The abstract says the paper compares the COVID-19 recession in the euro area (EA) and the US using an estimated multi-region New Keynesian macroeconomic model. It states that transitory ('forced') savings are central to account for the behavior of economic activity in both regions during the pandemic. It also says EA inflation has a stronger supply component, including commodity prices, compared to a stronger demand component in the US.

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ISSN 2443-8022 (online)

The COVID-19 Recession
on Both Sides
of the Atlantic:
A Model-Based
Comparison

Roberta Cardani, Philipp Pfeiffer,
Marco Ratto and Lukas Vogel

DISCUSSION PAPER 191 | JULY 2023

EUROPEAN ECONOMY

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CREDIT
Cover photography: © iStock.com/g-stockstudio
European Commission
Directorate-General for Economic and Financial Affairs

The COVID-19 Recession on Both Sides of the Atlantic:
A Model-Based Comparison

Roberta Cardani, Philipp Pfeiffer, Marco Ratto and Lukas Vogel

Abstract
This paper compares the COVID-19 recession in the euro area (EA) and the US using an estimated multi-
region New Keynesian macroeconomic model. To capture quarterly dynamics from 2020 onwards, we
introduce relevant extensions such as `forced' savings, extensive versus intensive employment margins, and
trade in commodities as inputs to production and final demand. Transitory (`forced') savings are central to
account for the behaviour of economic activity in both regions during the pandemic, which was strongly driven
by private consumption, alongside shocks to domestic demand and foreign activity. The model highlights the
importance of demand recovery and rising commodity prices for the inflation acceleration during 2021-22. EA
inflation has a stronger supply component (including commodity prices) compared to a stronger demand
component in the US.

JEL Classification: C11, E1, E20.

Keywords: DSGE model, Bayesian estimation, COVID-19, Euro Area, United States.

Acknowledgements: We thank our discussants Raf Wouters and Pablo Guerron-Quintana, two anonymous
referees as well as Christian Bayer, Martin Eichenbaum, Jan in 't Veld, Rafal Raciborski, Sergio Rebelo, Werner
Roeger, Mathias Trabandt, Kristine van Herck, and participants of the CEF 2023 conference (Nice), the CEBRA
2023 meeting (New York), and the ECFIN-CEPR-EER conference “The COVID-shock and the new
macroeconomic landscape” (Brussels, October 2022) for useful comments and suggestions. We are
particularly grateful to Lorenzo Frattarolo and Susanne Hoffmann for preparing the dataset. Most of this
paper was written while Roberta Cardani was working with the European Commission. The views expressed in
this paper are those of the authors and should not be attributed to the European Commission or the ESM.

Contact: Marco Ratto, European Commission, Joint Research Centre, marco.ratto@ec.europa.eu; Roberta
Cardani, European Stability Mechanism (ESM), r.cardani@esm.europa.eu; Philipp Pfeiffer, European
Commission, Directorate-General for Economic and Financial Affairs, philipp.pfeiffer@ec.europa.eu; Lukas
Vogel, European Commission, Directorate-General for Economic and Financial Affairs,
lukas.vogel@ec.europa.eu.

EUROPEAN ECONOMY Discussion Paper 191
CONTENTS

1 Introduction 4

2 Stylised macro facts 5

3 Related literature 7

4 The multi-region model 9
4.1 Multi-stage production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 Wage setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Monetary and fiscal policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.5 Commodities: energy and industrial supplies . . . . . . . . . . . . . . . . . . . . . . . 14
4.6 Resource constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.7 Rest of the world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Econometric approach 16
5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.2 Model solution and filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.3 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6 Impulse response functions 18

7 Shock decompositions 24

8 Comparison to off-model evidence 28

9 Robustness checks 28
9.1 Size of fiscal multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
9.2 Unconventional monetary policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

10 Conclusion 31

Appendix A Model details 38
A.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
A.1.1 Savers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
A.1.2 ‘Hand-to-mouth’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
A.1.3 Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2
A.2 Wage setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
A.3 Intermediate goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
A.4 Fiscal policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
A.5 Commodity importers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
A.6 Exporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A.7 RoW details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A.8 US commodity supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Appendix B Data, calibration, and posterior estimates 47
B.1 Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
B.2 Calibration and posterior estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Appendix C Additional results 52
C.1 Shock decomposition full sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
C.2 Shadow rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
C.3 Fiscal policy: dynamic effects of fiscal shocks . . . . . . . . . . . . . . . . . . . . . . . 55
C.4 Savings shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
C.5 COVID-specific labour demand shock . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
C.6 Preferences over safe assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Appendix D Effective lower bound: simulation and smoothing algorithm 62
D.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
D.2 Details on the OccBin algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
D.3 Nonlinear smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
D.3.1 Additive representation of shock decompositions . . . . . . . . . . . . . . . . . 63
D.3.2 Implied regime sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
D.4 Counterfactual: no effective lower bound . . . . . . . . . . . . . . . . . . . . . . . . . 63

3
1 INTRODUCTION

This paper compares the COVID-19 recession and recovery in the Euro Area (EA) and the United States
(US), using an estimated three-region dynamic stochastic general equilibrium (DSGE) model (EA, US,
RoW). The model is a variant of the European Commission’s Global Multi-country (GM) model (Albon-
ico et al. (2019)), augmented by COVID-specific shocks (Cardani et al. (2022)), an explicit distinction
between the intensive and extensive margins of employment, and an enriched representation of commod-
ity use (input to production and component of final demand) and trade, in which the US is a commodity
supplier along with the RoW.
Combining ex-ante identical EA and US blocks (except for the difference in commodity endowment)
in a multi-country setting and estimating them jointly on the same set of observable variables provides an
appropriate framework for cross-country comparison. The model captures many possible demand-side
and supply-side drivers of GDP growth and inflation, including private domestic demand, monetary and
fiscal policy, foreign activity and trade, wage and price setting, productivity, and commodity prices, and
jointly assesses their quantitative importance in the estimation.
Our model is a fairly rich but standard estimated one-sector multi-region DSGE model in the New
Keynesian tradition. It incorporates additional macro shocks to accommodate COVID-period data, a
distinction between employment in persons and hours worked, and a richer structure of commodity supply
and use. The setup includes an endogenous and occasionally binding effective lower bound (ELB) on
nominal short-term interest rates.
Additional features of relevance during the pandemic, such as the multi-sector structure of production
(with contact-intensive and other activities), or an explicit interaction between economic activity and the
spread of the virus, are omitted. However, evidence from different models and empirical work at different
levels of aggregation is helpful for a more structural interpretation of some of the model shocks.
The model is estimated on data over the period 2020q1-2022q4. It covers the COVID-19 pandemic
and recovery as well as the energy crisis in 2021-22 and other early economic consequences of Russia’s
war of aggression against Ukraine.
The analysis attributes an important role to transitory consumption (‘forced’ savings) shocks in ac-
counting for the volatility (contraction and recovery) of EA and US economic activity at quarterly fre-
quency in 2020-21. More persistent consumption and investment shocks, as well as shocks to foreign
activity and trade, have also played a role. Fiscal policy has stabilised aggregate activity during the pan-
demic. Rising inflation in 2021-22 has been driven by recovering domestic and foreign demand and rising
commodity prices. Fiscal policy also added to price pressure. Appreciation (depreciation) pressure on
the USD (euro) dampened (added to) inflation in the US (EA). Particularly for the EA, the estimation also
points to inflation from retail price shocks. Overall, the results align with the hypothesis that inflation in
2021-22 had a stronger supply-side component in the EA and a more substantial demand-side component
in the US.
The paper proceeds as follows. Section 2 presents stylised macro facts for the EA and the US macroe-
conomic adjustment to the COVID-19 shock. Section 3 discusses the connections to the literature with
respect to modelling pandemic-specific developments and empirical literature on the COVID shock and
its macroeconomic repercussions. Section 4 outlines the main elements of the model. Section 5 describes

4
Real GDP per capita Inflation Private consumption
120 140
6

110 4 120

100 2 100

0 80
90
2000 2005 2010 2015 2020 2000 2005 2010 2015 2020 2000 2005 2010 2015 2020
Private investment Primary budget balance Policy rate
0
160 6

140 -5 4

120 2
-10
100
0
-15
2000 2005 2010 2015 2020 2000 2005 2010 2015 2020 2000 2005 2010 2015 2020
Real wage growth Hours worked Employment
170
5 280
EA US
270 160
260
0
250 150

240
-5 140
2000 2005 2010 2015 2020 2000 2005 2010 2015 2020 2000 2005 2010 2015 2020

Figure 1: Macro time series for EA and US (1999-2022)

Notes: Annual series for GDP, consumption and investment are at constant prices (real terms) and normalised to 100 in 2010.
Annual inflation (in %) refers to the HICP for the EA and the PCE index for the US. The policy rate and real wage growth
are also expressed in % per year. The primary government balance is expressed in % of GDP. Hours are in billions, whereas
employment is reported in millions (persons). Sources: AMECO, BEA, and Eurostat.

the econometric approach and reports parameter estimates. The propagation of COVID-specific and other
important model shocks is analysed in more detail in Section 6. Section 7 discusses the main drivers of
EA and US growth and inflation during and after the pandemic on the basis of shock decompositions.
Section 8 provides additional off-model evidence for the plausibility of the estimated COVID-specific
shocks. Section 9 discusses robustness checks concerning the role of fiscal and monetary policy (fiscal
multipliers and unconventional monetary policy). Finally, Section 10 concludes.

2 STYLISED MACRO FACTS

Comparing macroeconomic time series for the EA and the US points to similarities and differences in
response to the COVID-19 shock and the recovery. Figures 1 and 2 summarise six general observations
that an estimated multi-region macro model has to account for.
The first observation is that economic activity (measured by real GDP per capita in Figures 1 and 2)
fell in both regions in 2020 but more strongly in the EA. US activity had recovered to pre-pandemic levels
by spring 2021, whereas EA activity reached the 2019q4 level only in autumn 2021. The sharp decline
in private consumption in 2020 was an important driver of the pandemic recession, which contrasts with
previous (‘standard’) recessions (including the 2008-09 financial crisis) that exhibit the opposite pattern,
i.e. a more critical role for investment demand in the business cycle. Private consumption recovered
faster in the US, where it was back to its 2019q4 level in 2021q1, whereas EA consumption reached the

5
Real GDP per capita Inflation Private consumption
10 110
100
100
5
95
90
90
0
80
20q1 20q3 21q1 21q3 22q1 22q3 20q1 20q3 21q1 21q3 22q1 22q3 20q1 20q3 21q1 21q3 22q1 22q3

Private investment Oil price (Brent index) Nominal effective exchange rate
120
100
1
100 80

60 0.95
EA US
80 40
0.9
20q1 20q3 21q1 21q3 22q1 22q3 20q1 20q3 21q1 21q3 22q1 22q3 20q1 20q3 21q1 21q3 22q1 22q3

Figure 2: Quarterly macro time series for EA and US (2019q4-2022q4)

Notes: Quarterly GDP, private investment, and private consumption are levels at constant prices (real terms), normalised to 100
in 2019q4. Consumption inflation is the annualised y-o-y growth (%) of the HICP for the EA and the PCE price index for the
US. The Brent price is measured in USD per barrel. The nominal effective exchange rate (NEER) is normalised to 1 in 2019q4,
and an increase indicates NEER depreciation of the domestic currency. Sources: BEA and Eurostat.

2019q4 level only in 2022q3.
Second, EA and US inflation increased strongly after 2020. US CPI inflation accelerated early in
the recovery and moderated in the second half of 2022. EA CPI inflation followed with some lag but
remained elevated in the second half of 2022. Given that the US depends less on commodity imports
than the EA, commodity price shocks had milder adverse terms-of-trade effects on the US economy.
Third, US fiscal policy has been more expansionary than its EA counterpart, as indicated by the
substantial deterioration of the US (primary) government balance in 2020-21. In addition, the COVID-
19 shock hit the EA economy at the ELB. Short-term interest rates in the US were above the ELB in
2019, to the contrary, providing space for some conventional monetary stimulus, followed by tightening
in light of rising inflation.
Fourth, EA and US real wages grew in 2020 as nominal wages outpaced price inflation. This pattern
reversed in 2021-22. Part of the real wage growth in 2020 can be ascribed to composition effects. Less-
skilled, younger and temporary-contract workers with less-paid jobs face a higher risk of unemployment
during recessions, which increases the average hourly wage in the economy of the workers remaining
employed without a rise in individual wages.1
Fifth, employment patterns during the pandemic differed markedly between the two regions. Em-
ployment in persons and hours co-moved closely in the US but decoupled in the EA in 2020-21. In
the EA, hours worked declined, whereas employment in persons remained relatively stable (even in the
most affected sectors), which indicates quantitatively important labour hoarding (‘short-time work’) to
preserve existing matches.2
1
See, e.g., Anderton et al. (2021), Bodnár et al. (2023), Christodoulopoulou and Kouvavas (2022) and Howard et al. (2022)
on the role of composition effects for aggregate wage dynamics.
2
For a detailed discussion of EA-US differences in employment dynamics, notably a more detailed breakdown of adjustment

6
Finally, prices of fossil fuels (oil in Figure 2) declined at the start of the pandemic and recovered in
the second half of 2020. Oil prices and prices for gas and electricity rose steeply in 2021-22, notably
in the EA, in reaction to the pandemic recovery, geopolitical tensions, and Russia’s war of aggression
against Ukraine. In the EA, the price increase has also been amplified by NEER depreciation between
mid-2020 and 2022, whereas the USD gained value in 2021-22 in nominal effective terms.

3 RELATED LITERATURE

This paper offers a comparative perspective on the macroeconomic impact of the COVID-19 pandemic.
It connects to three strands of the literature. The first relates to the class of estimated multi-country
structural models for cross-country comparison. Christiano et al. (2008), as an early example, investigates
the role of shocks, structure (such as wage and price stickiness) and monetary policy in accounting for
differences in EA and US business cycles after 2001. Smets and Wouters (2003) and Smets and Wouters
(2007) estimate their (single-country) model on EA and US data alike and compare outcomes in terms
of structural parameters and exogenous shock. Kollmann et al. (2016) and Giovannini et al. (2019) have
estimated EA-US-RoW models similar to the present one to compare the EA and US economies during
and after the Global Financial Crisis (GFC) and the impact of commodity price and emerging market
shocks on the EA and the US, respectively.
The second strand of the literature focuses on modelling the economic impact of COVID-19. By now,
there is extensive literature on the micro and macro implications of the pandemic, including goods, labour
and financial markets. ‘Non-standard’ structural models have been developed to capture elements of the
pandemic. This strand includes papers that merge epidemiological and economic dynamics to understand
the interplay between the pandemic, containment policies, and economic activity (Eichenbaum et al.
(2021, 2022); Jones et al. (2021)), and multi-sector models that show the importance of cross-sector
linkages and (demand) externalities (Guerrieri et al. (2022), Corrado et al. (2021)). Concerning price
dynamics, Benigno and Eggertsson (2023), Hall (2023) and Harding et al. (2023) argue that models with
non-linear Phillips curves can explain the acceleration of post-pandemic inflation through a steepening of
the slope of the Phillips curve, where the motivation (micro foundation) for the steepening varies across
the three contributions.3
Other authors have adapted established macro models used in policy institutions (‘workhorse mod-
els’) to allow estimation based on data including the period of the pandemic (Chen et al., 2020; Cardani
et al., 2022). We follow the pragmatic approach in Cardani et al. (2022) to augment the European Com-
at the intensive and extensive margins, see Bodnár et al. (2023). Kiss et al. (2022) gives a broad account of EA labour market
developments during and after the pandemic. 15-34% of employees in Germany, France, Italy, and Spain were on job retention
schemes in April 2020 compared to 1-3% on average during the financial crisis in 2009. In most large EA countries, benefits
paid under these schemes go directly to employees and are recorded as social transfers, whereas, e.g., the Netherlands pays
them as wage subsidies to employers, leading to increasing compensations per hour worked in the data (Anderton et al. (2021)).
Giupponi et al. (2022) provides a theory-based comparison between short-time work schemes and unemployment insurance in
positive and normative (welfare) terms, as well as a wider cross-country comparison.
3
In particular, Hall (2023) stresses that the Phillips curve can become much steeper in times of highly volatile price deter-
minants (costs, productivity) in models with constant costs of price adjustment, i.e. the sensitivity of inflation to demand and
supply shocks may depend on the shock size. Benigno and Eggertsson (2023) develop a non-linear NK Phillips curve in which
inflation reacts to labour market tightness (vacancies relative to the number of unemployed) and argue that recent high inflation
was compatible with an exceptionally tight labour market (labour shortage). Harding et al. (2023), instead, derive non-linearity
in the Phillips curve from non-linearity in the demand for goods.

7
mission’s GM model with short-lived (‘forced’) savings shocks and labour hoarding (short-time work) to
map important characteristics of data from the COVID-19 period. We extend our earlier work by explic-
itly modelling labour hoarding that distinguishes between hours worked per employee (intensive margin)
and the numbers of employees (extensive margin) broadly along the lines of Merz and Yashiv (2007)
to account for total hours worked. The model in this paper also accounts for commodity extraction in
the US. The US block becomes a commodity supplier, implying a wedge between the demand for com-
modities in the US and US net commodity imports. The role of commodities in the economy as input to
production and part (energy) of final consumption demand is modelled along the lines of Blanchard and
Gali (2007), Blanchard and Riggi (2013), Bodenstein et al. (2012), and Gagliardone and Gertler (2023).
Third, a rich empirical literature on economic developments during the pandemic and in the post-
pandemic environment developed in recent years and months, drawing on different approaches. Inflation
dynamics on both sides of the Atlantic have attracted particular attention as EA and US price levels have
grown at a pace not seen for decades. The general tendency in the debate is to assign a more prominent role
to demand versus supply factors in the US compared to the EA. Pasimeni (2022) observes that energy and
food prices account for almost 3/4 of EA post-COVID headline inflation, which started rising in early
2021, and that price pressure stems mainly from sectors with high import content and concerns goods
more than services. He also suggests a dominance (4/5) of supply factors in producer price inflation
at the sector level. Similarly, Hansen et al. (2023) emphasise the importance of import prices for EA
post-pandemic inflation. For the US, di Giovanni (2022) attributes 60% of consumer price inflation in
2019-21 to increased goods demand and 40% to supply-side constraints. di Giovanni et al. (2023) find
2/3 of the increase in US inflation between December 2019 and June 2022 to be demand-driven.4
Ball et al. (2022) emphasise the importance of labour market tightness (defined as vacancies over
unemployment) for US (core) inflation in 2021-22, part of which (1.0 pp y-o-y in July 2022) is attributed
to demand deriving from US fiscal stimulus, in addition to pass-through from headline to core.5 Bernanke
and Blanchard (2023), by contrast, attribute most of US inflation since 2021 to price shocks (commodity
prices, sectoral demand shifts, supply constraints) for given wages. Ferrante et al. (2023) estimate a
multi-sector New Keynesian (NK) model on US data and find an important role of cross-sector demand
reallocation (from services to goods) for inflation in the presence of (labour) adjustment frictions that
constrain a shift in supply, suggesting that reallocation could explain up to 4 pp of the increase in US
inflation in recent years.
Cavallo and Kryvtsov (2023) use detailed micro data on product availability from seven countries
to document a substantial increase in product shortages (supply disruptions) during the pandemic, with
significant inflationary effects within a quarter. Comin et al. (2023) build a multi-sector open-economy
model with temporarily binding domestic and foreign supply chain constraints, which bind in case of
positive demand or negative supply shocks. The impact of binding constraints on activity and inflation is
similar to the effect of price markup shocks, i.e. it could provide a structural interpretation of the latter.
Comparing the model with binding constraints to a counterfactual in which the constraints are slack at
any time, the authors attribute around half of the increase in US consumer price inflation in 2021-22 to
binding supply chain constraints.6
4
Similar (institutional) perspectives on EA versus US inflation are provided by Boone (2022) and Lane (2023).
5
Related to that, Blanchard et al. (2022) emphasise the role of dampening labour market tightness for controlling inflation.
6
More than inflation through labour market tightness, the Comin et al. (2023) channel would be consistent with rising profit

8
Reis (2022) lists supply disruptions, less well-anchored inflation expectations, and expansionary
monetary and fiscal policies as possible inflation drivers. Jorda and Nechio (2023) underline the role
of fiscal stimulus and inflation expectations for wage and price setting during the pandemic in a sample
of 18 OECD countries. Hale et al. (2023) find inflationary effects of fiscal support to households, but not
to firms, in a sample of ten large countries, notably in an environment of improving economic conditions.
Bayer et al. (2023) use a heterogeneous-agent New Keynesian (HANK) model and find an important role
of fiscal transfers to explain the stronger post-pandemic recovery and higher inflation in the US compared
to the EA.7 di Giovanni et al. (2023) attribute as much as 1/3 of the US inflation increase between end-
2019 and mid-2022 to fiscal stimulus. Gagliardone and Gertler (2023) develop a simple New Keynesian
(NK) model with oil as complementary consumption good and production input and find an important
role for oil price shocks combined with ‘easy’ monetary policy to explain recent US inflation, notably its
persistence in 2022.
From a different perspective, Cavallo (2020) and Diewert and Fox (2022) emphasise measurement
problems, notably the underestimation (overestimation) of inflation in 2020 (2021) due to the use of a
CPI with a fixed basket of goods and services which contrast with strong shifts in relative demand at
sector and goods level during the pandemic.
The present paper adds to the literature by providing a comparative perspective on EA versus US
macroeconomic dynamics during and after the COVID-19 pandemic, using an estimated workhorse
DSGE model with three regions and ex-ante largely identical model blocks for the EA and the US.8
The rich structure of the model with many observable variables implies that a plausible narrative of re-
cent macroeconomic developments has to account for a large number of observations at the same time,
including the macro facts summarised in Figures 1 and 2 above. The model captures a large number of
possible demand-side and supply-side drivers of GDP growth and inflation, including private domestic
demand, monetary and fiscal policy, foreign activity and trade, wage and price setting, productivity, and
commodity prices, and jointly assesses their quantitative importance in the estimation.

4 THE MULTI-REGION MODEL

The analysis builds on an estimated three-region DSGE model consisting of the EA, the US, and the
RoW.9 The model needs to be rather elaborate in terms of economic structure and shocks to allow for a
quantitative account of the macroeconomic dynamics in the three regions, notably in light of the large
number of observable time series in the estimation.
In light of the salient differences between the EA and the US economies during the COVID-19 re-
margins in the post-COVID recovery (Arce et al. (2023); Glover et al. (2023)), although some of the work on profit dynamics
also attributes a significant role to expected future increases in production costs in an environment of infrequent price adjustment
(Glover et al. (2023)).
7
Some countries, such as Germany, have also implemented less conventional fiscal policy measures during the pandemic,
such as temporary VAT cuts that mimic the effect of interest rate reduction (Bachmann et al. (2021); Baudisch and Neuenkirch
(2023); Clemens and Röger (2021)).
8
The main structural difference imposed by facts is the modelling of the US economy as a commodity supplier.
9
The model builds on and extends the European Commission’s Global Multi-country (GM) model (Albonico et al., 2019;
Giovannini et al., 2019; Kollmann et al., 2016). The description in this section introduces only the key elements. It abstracts from
linear taxes and contains only the main exogenous shocks. Readers can find a comprehensive model description in Appendix
A.

9
cession, discussed in Section 2, we extend the model in Cardani et al. (2022) in two directions. First,
we improve the modelling of commodities (energy and non-energy commodities) by including the US
as a supplier of commodities along the RoW block. In line with the data, this modification distinguishes
between US domestic demand for commodities and US net commodity imports. Second, we differentiate
between the extensive (workers) and intensive (hours per worker) margin of employment adjustment in
light of the discrepancy between the US (co-movement between total hours and employment in persons)
and the EA (short-time work) during the pandemic. Finally, the present analysis will also draw on a
longer sample, extending the coverage of the post-pandemic period, which now covers the energy crisis
in 2021-22.
Each model region features households, non-financial firms operating in the domestic market or the
import-export sector, and a central bank. Short-lived savings and labour hoarding shocks are introduced
as in Cardani et al. (2022) to replicate distinctive features of the pandemic recession, i.e. strong and
short-lived volatility in quarterly consumption and the wedge, especially in the EA, between employment
and hours worked. Separating the extensive versus intensive margins of adjusting total hours worked
broadly follows Merz and Yashiv (2007). Monopolistic trade unions set EA and US wages. Intermediate
goods prices and nominal wages are sticky. Each region has a central bank conducting monetary policy
following a Taylor-type rule. The EA and US central banks face an occasionally binding effective lower
bound (ELB) on nominal short-term policy rates. The EA and US blocks also include a government sector
with taxation and public spending. The three regions are linked through trade in goods (final goods and
industrial supplies) and an internationally traded financial asset (bond).
The US and the RoW supply commodities, which enter as industrial supplies in the production process
for manufactured output and as energy directly in the households’ consumption basket. This two-stage
use of commodities corresponds to the modelling of oil demand in Blanchard and Gali (2007), Blanchard
and Riggi (2013), Bodenstein et al. (2012) and Gagliardone and Gertler (2023).
Due to limited data availability, the RoW block (which comprises a group of 56 countries) is more
stylised. Another difference between the regions and with respect to previous versions of the GM model
(e.g., Giovannini et al. (2019)) is that the US and RoW both supply commodities. The model includes
nominal and real rigidities to provide an empirically plausible account of macroeconomic dynamics and
persistence at a quarterly frequency. Unless stated otherwise, the exogenous random variables follow
autoregressive processes of order 1. Time is discrete and indexed by t.
The following subsections present the key elements of the EA model block. The US block has the
same structure, except that the US economy also supplies and exports commodities.10 While the EA and
US block are ex-ante identical (except for commodity supply), model estimation and the calibration of
selected parameters imply that parameter values can differ between the EA and the US.

4.1. MULTI-STAGE PRODUCTION

Final goods. The EA final good is produced from the domestic output and imported outputs of the US
and RoW economies. Let Zt ∈ {CtF G , Gt , It , IGt , Xt } be the demand for final goods by households
and the government, private and government investors, and exporters of final goods, respectively. Per-
10
To ease notation, we omit country-specific indices when not explicitly needed (e.g., for the common parts of the EA and
US block).

10
fectly competitive firms assemble Z;, using domestic output (O/) and imported output (M7) into a CES
production function:

Z, = AZ

(1 si") (OR) + (si"7)* one | , (1)

where A? denotes a productivity shock in sector Z, and 0 < sM ~ < 1 is the stochastic import share

associated with the different components of final demand.'! The parameter o* > 0 is the elasticity of
substitution between domestic output and imports in the assembly of the final good. This elasticity is
assumed to be the same across all final demand components.

Output. Perfectly competitive firms produce output (O;) by combining domestic value added (Y;) and
imported industrial supplies (J.S;) in a CES production function:

oP 1
o°2-1

a oo 1
Op = | (1 85) (%4)o™ + (sf) 7? (15) (2)

where s/° is the input share of commodities (industrial supplies) used in production. This share is stochas-
tic and captures fluctuations in the CO intensity of production.The parameter 0° > 0 is the elasticity of
substitution between the two components. Industrial supplies in the EA are imported from the RoW and
the US subject to an excise duty T°, so that: PC? = prom + 7©° P,, where prom denotes the
import price in terms of domestic currency.'*

Value added. Value added Y; aggregates the EA intermediate goods:

1 vt 5 _ot
Y= i Yi di| ort (3)
0

where Y; denotes intermediate good i € [0,1]. The parameter o¥ > 0 is the elasticity of substitution
between the varieties Y;4. The production function for good 2 is:

l-ag

Yit = (AP (Nis — FN))* (cuitK; 4-1) ° (KE4) — ®, (4)
where A} is exogenous stochastic total factor productivity (TFP), subject to trend and level shocks. Nj.1,
Kya and cu; are firm 7’s labour input (minus overhead labour F'N), capital stock, and endogenous
capacity utilisation, respectively, and ©, are fixed costs (indexed to trend).!3 Gross investment I; ; drives
the law of motion for capital K;; = Kiz-1(1 — 6) + [i 4, with the depreciation rate 0 < 6 < 1. Public

capital (K © ,) follows an analogous accumulation equation and features an output elasticity ag.
p t—1 2 q p y

16M.Z M,Z

=s exp(e}"7), where s“’7 denotes the steady-state import share of the demand component Z and ei4 isa
shock to the import demand (preference).
The excise duty is also levied on domestically supplied commodities in the US block.

'3On a balanced growth path, 6, = © x (Ay) aFagat |

11
Labour input and labour hoarding. The EA and the US differ in the relative importance of the ex-
tensive and intensive margins for labour adjustment. To account for this disparity, we distinguish be-
tween persons employed (mpl; ;) and hours worked per employee (Hpere;,). Overall hours paid are
NP i id — Empl; ,Hpere;,, and firms can adjust at both margins subject to specific adjustment costs.

In light of the restrictions on work during the COVID-19 pandemic, we introduce a transitory labour

hoarding shock (¢#”), which creates a discrepancy between hours paid (wage income) and actual hours
worked (production function):

“= (1%). (5)
A positive innovation to </” implies that employees work fewer hours compared to their wage income. '+
Incorporating the shock into firm dividends and the government budget allows for the inclusion of sub-
sidies related to short-time work schemes. Firm nominal dividends in period t are then given by:

: paid LU paid I
divig = Pitan — WeNPRM +760 W; (NPE — Nia) —PLTie —Tise (6)
Sa
Wage bill Hoarding

where W; and P/ are the nominal wage rate and the price of investment goods, respectively. 7’ is the
share of publicly financed labour hoarding. I’; ; collects quadratic price and factor adjustment costs. Each
intermediate goods firm 7 sets the good’s price P; ; in a monopolistically competitive market, subject to

Pi\ 70"
2) Y;. Appendix A

provides additional details and the equilibrium conditions for the production sector.

Rotemberg (1982) price adjustment costs and the demand function Y;, =

4.2. HOUSEHOLDS

Two groups of households consume and provide labour to intermediate goods producers.

Savers. A share w* of households are savers (s), who own domestic firms and participate in financial
markets by saving and borrowing. Savers choose consumption C;, (which includes energy as explained
below) and financial assets B to maximise welfare:

N
(ce, — © — h(Chy - fe) (apr) _
t ’ N Js
Eo >) BE 3 4 Ta 9N
t=0

(7)

where Ep denotes the expectations operator and 0 < 6 and 0 < 6%. The parameter h governs the
importance of external consumption habits. The shock €; captures stochastic disturbances to the discount
factor 3.!5 The term wj\ is a stochastic labour disutility factor.!°

'4Put differently, actual hours are given Ni, = EmpliHperes.(1 — ef”).

Se. 14/€ = exp (ef) implies that the Euler equation features the time ¢ shock ef.

'©To ensure a balanced growth path, labour disutility includes a multiplicative term ci, such that wi = w™ exp(eY)C}-°,
where e/ is exogenous.

12
Utility maximisation is subject to the budget constraint:
X X
Q
PtC Cj,t
s
+ Bj,t+1 s,paid
= Wt Nj,t + divtT OT + RtQ Bj,t
Q s
+ Tj,t , (8)
Q Q

divtT OT and Tj,t
s summarises the taxes and transfers, which are detailed in Appendix A.

As in Cardani et al. (2022), the households face non-persistent ‘forced’ savings shocks, εtC
t , that
constrain consumption outside of habit persistence and are zero before 2020 in the benchmark version of
the model.17
P Q
The portfolio Q Bj,t+1 with gross nominal returns RtQ includes risk-free private domestic bonds
(rf ), government bonds (g), an internationally traded bond (bw), and domestic corporate shares (S).18
The model allows for asset-specific risk premia shocks εQt with Q ∈ {bw, g, S}.
19

‘Hand-to-mouth’. The remaining households (1 − ω s ) with the label (c) are ‘hand-to-mouth’. They
face a liquidity constraint (or zero-borrowing constraint) and consume their net disposable period in-
come (wages and transfers minus taxes paid). The financing constraint binds every period, except during
COVID-19 when even ‘hand-to-mouth’ consumers accumulate ‘forced’ savings that they spend gradually
upon exit from the pandemic.20 Therefore, the budget constraint of ‘hand-to-mouth’ households is:
!
c,paid 1 X
13
PtC Cj,t t −
c c
= Wt Nj,t + Tj,t + PtC εtC εtC
t−i . (9)
6
i=8

Aggregation across households. Per-capita consumption and hours worked by EA households are
Ct = (1 − ω s ) Ctc + ω s Cts and Nt = (1 − ω s ) Ntc + ω s Nts , respectively.

4.3. WAGE SETTING

A monopolistic trade union differentiates homogeneous labour hours provided by the two households into
imperfectly substitutable labour services. The union then offers these services to local intermediate goods
firms. The labour input (Ni,t ) in the production function is a CES aggregate of the differentiated labour
services. The union sets wage rates at a markup over the marginal rate of substitution between leisure
and consumption. The wage markup is inversely related to the substitutability among labour varieties in
intermediate goods production.
We introduce nominal wage rigidity through quadratic wage adjustment costs (γ w ). In addition, the
parameter γ wr adds real wage rigidity in the spirit of Blanchard and Galí (2007) and Coenen and Straub
(2005). A share (1 − sf w) of unions indexes wages to past inflation. Per-capita employment is the same
17
Given its large estimated contribution to the pandemic recession, we discuss the ‘forced’ savings shock and its macroeco-
nomic transmission compared to standard persistent savings shocks in more detail below.
18
Like in, e.g., Benigno (2009) and Ratto et al. (2009), only the RoW bond is traded internationally.
19
Appendix A provides a microfoundation of these shocks by incorporating assets in the utility function, as proposed by Fisher
g
(2015). The term εS bw
t is an investment-specific risk premium shock; εt is a risk premium on government debt; εt distorts the
first-order condition for foreign bond demand and amounts to a disturbance to the uncovered interest parity (UIP) condition.
20
Evidence that also liquidity-constrained households saved the largest part of transfer income during the pandemic is pro-
vided by Parker et al. (2022).

13
across both household types.

4.4. MONETARY AND FISCAL POLICY

Monetary policy. Monetary policy follows a Taylor (1993)-type rule subject to an occasionally binding
ELB constraint. The target interest rate inot
t responds sluggishly to (quarterly annualised) deviations of
gap,QA
inflation and the output gap (Yt ) from their respective target levels:
" #
η iπ
inot
t − ī = ρi (it−1 − ī) + (1 − ρi ) πtC,QA − π̄ C,QA + η iy Ytgap,QA , (10)
4

where ī is the steady-state nominal interest rate, πtC,QA is quarterly annualised CPI inflation, and π̄ C,QA is
the latter’s steady-state value.21 The variable it in the persistence term is the actual or effective short-term
interest rate. The parameters ρi , η iπ and η iy govern interest rate inertia and the response to annualised
inflation and output gap, respectively. The output gap is the (log) difference between actual and potential
output. Potential output at date t is the output level that would prevail if the labour input equalled the
amount of hours worked in the absence of nominal wage rigidity, as in Galí (2011), the capital stock was
utilised at full capacity, and the TFP equalled its trend value.
The effective policy rate it corresponds to the target nominal short-term rate only when the latter is
above the ELB (ilb ). The effective policy rate hence satisfies:

t , i } + εt ,
it = max{inot lb i
(11)

where εit is a monetary policy shock following an ARMA(1,1) structure.22

Fiscal policy. The fiscal authority collects constant linear taxes on consumption, wage income, and
corporate profits, a commodity import duty, and a lump-sum tax (introduced to close the government
budget) to finance consumptive purchases, public investment, and transfers.23 The individual govern-
ment expenditure components follow feedback rules. Appendix C.3 provides impulse response functions
(IRFs) illustrating the transmission of the main fiscal shocks.

4.5. COMMODITIES: ENERGY AND INDUSTRIAL SUPPLIES

Commodities trade at flexible, destination-specific prices, driven by exogenous supply (price) shocks.24
The total demand for commodities, COt , is the sum of household energy consumption, CtE , and demand
(∑ ) (∑ )
r=0 Pt−r − log
3 7
21
Quarterly annualised inflation is defined as πtC,QA = log C C
r=4 Pt−r . We have also tested spec-
ifications with separate targets on core versus headline inflation. Estimation results suggest that US monetary policy compared
to EA targets more core inflation. Since overall results are similar, we limit the discussion of results to the simpler formulation.
22
Compared to a white noise process, the predictable MA-component helps capture forward guidance policies at the ELB.
23
For simplicity, the different taxes are omitted from equations in the overview in Section 4 and instead included in the
detailed model description in Appendix A.
24
We also tested model versions in which commodity demand affects global commodity prices. In light of the additional
complexity, we have kept the more stylised assumption of exogenous supply shocks as drivers of commodity prices, leaving a
more detailed treatment of demand versus supply factors in commodity markets in recent years for future work. For a distinction
between the two in earlier work, see Giovannini et al. (2019).

14
for industrial supplies in final goods production, ISt .

Energy goods. Final household consumption is a CES aggregate of commodities used for consumption
(‘energy’, denoted CtE ) and final manufactured goods C F G :

" # EσE
1 σEE−1 1 σ E −1 σ −1
Ct = (1 − sE
t ) σE CtFG σ + (sE
t ) σE (CtE ) σE , (12)

with energy share sE E
t and the elasticity of substitution σ > 0.

US commodity supply. While all commodities used in the EA are imported, the US not only uses com-
modities but also supplies them (while remaining a net importer). A share of value-added is used for com-
modity extraction (YtCO,U S ).25 Commodity producers maximise dividends, divi,t U S,CO
= COtU S PtCO −
αCO
YtCO,U S PtU S , using a decreasing return to scale technology, COtU S = ACO Y CO,U S t , where ACO
is a scaling parameter. With αCO < 1, US production is an increasing function in the (relative) price of
commodities.

4.6. RESOURCE CONSTRAINT

The resource constraint of the EA economy is:

Pt Yt + τ CO Pt COt = PtC Ct + PtI It + PtIG IGt + PtG Gt + T Bt , (13)

where PtIG and PtG are the prices of investment and consumption goods purchased by the government,
respectively, and: X
T Bt = PtX Xt − PtCO,M COt − PtM MtZ (14)
z

defines the EA trade balance as the difference between exports and imports in value terms. The US trade
balance, in addition, includes US commodity exports to the RoW and the EA.

4.7. REST OF THE WORLD

The RoW block adopts a simplified structure, excluding ‘hand-to-mouth’ households and fiscal policy.
Perfectly competitive final goods firms bundle the final consumption good Ct∗ , the investment good It∗ ,
and the RoW (non-commodity) export good Xt∗ following a structure analogous to the production of
aggregate demand components in the EA outlined in Subsection 4.1 (bundling of domestic and imported
output).
Monopolistically competitive intermediates goods firms in the RoW use a Cobb-Douglas technology
as in equation (4) to produce domestic (non-commodity) output. The price setting for non-commodity
output follows a New Keynesian Phillips curve with cost-push shock.
25 int
Thus, output production (eq. 2) in the US uses Yi,t = Yi,t − Yi.t
CO
.

15
In addition to final goods, RoW is a commodity exporter. Compared to the US, the supply of com-
modities by RoW is residual, satisfying global demand. A competitive sector supplies commodities CO,
namely Brent oil and other commodities materials, to foreign firms.26 Both supply schedules follow
exogenous stochastic processes (see Appendix A.7).
Preferences of RoW households include consumption with external consumption habits and endoge-
nous labour supply. RoW output combines industrial supplies and final goods. The latter are also required
for commodity extraction. However, for simplicity, consumption in the RoW does not feature an energy
component. Monetary policy in RoW follows a Taylor-type interest rate rule targeting inflation and GDP
growth.

5 ECONOMETRIC APPROACH

This section describes the econometric approach to estimating the three-region model and retrieving the
exogenous shocks. Subsection 5.1 describes the data for estimation, and Subsection 5.2 the model solu-
tion and the filtering. Subsection 5.3 summarises important calibrated and estimated parameters.

5.1. DATA

The data set covers 1998q4-2022q4.27 EA and US data (quarterly national accounts, fiscal aggregates,
quarterly interest and exchange rates) are taken from Eurostat and the BEA. Annual RoW series are
compiled from the IMF International Financial Statistics (IFS) and World Economic Outlook (WEO)
databases.28 The data for RoW short-term nominal interest rates are available only until 2021 (included).
The observed data also include commodity prices (Brent oil and other commodities, including natural
gas) from the Eurostat Comext database, allowing us to observe import prices (total and commodities)
for each region.29 Appendix B provides additional details on the data sources and the RoW aggregation.

5.2. MODEL SOLUTION AND FILTERING

State-space representation. We construct a linear solution of the economy’s dynamic equilibrium.
The model also includes a stochastic productivity trend (as a component of AYt ), which affects all real
variables. Let Θ denote the parameters of the DSGE model. Using the de-trended model solution, we
can specify the following system of observation and state equations:

Ytdata = Ψ1 (Θ)St , (15)
St = Φ1 (Θ)St−1 + Φε (Θ)εt εt ∼ N (0, Qt I). (16)
26
We do not specify separate demand functions for the different commodity types but allow for different prices (and, hence,
supply schedules).
27
In estimations, we include a pre-sample of five quarters.
28
RoW series include GDP, prices, investment, and the short-term nominal interest rate with some gaps for 2022. Annual
data points are treated as last quarter observations (as quarterly annualised variables) to ensure model-consistent interpolation.
29
Due to data limitations, we do not observe the prices of bilateral imports and exports.

16
The observation equation (15) links the vector of observed variables Ytdata at time t to the model vari-
ables St through the coefficient matrix Ψ1 (Θ). The state equation (16) describes the transition of the
system’s state variables St using the coefficient matrices Φ1 (Θ) and Φε (Θ). The model shocks εt follow
a normal distribution with time-varying covariance matrix Qt I. With this formulation, we incorporate
deterministic heteroskedasticity in the subset of COVID-related shocks, following the approach of Lenza
and Primiceri (2022), previously used in Cardani et al. (2022). Specifically, for the COVID-19 period
t ∈ 2020q1:2022q4, Qt = QCOV ID includes temporary shocks specific to the pandemic. Prior to the
pandemic, i.e. for t < 2020q1, Qt = Q assumes zero standard deviations for these shocks. This approach
implies that expectations regarding COVID-19 were zero before its occurrence.

Two-step estimation. The estimation proceeds in two steps. First, we estimate the model parameters
(Θ) using data until 2019q4. Then, in the second step, we estimate the variances of heteroskedastic,
COVID-specific shocks using data for 2020q1-2022q4 while keeping all other parameters unchanged
and initialising the system’s state (16) and covariance matrix at their estimates from the first step (i.e., at
the pre-COVID Kalman filter recursions). This approach is equivalent to using the full dataset starting
from 1998q4, but it is more efficient given the large model size. Both estimation steps employ a linear
Kalman filter and a parallelised slice sampling algorithm (Neal, 2003) to draw parameters from their
posterior distribution using Markov Chain Monte Carlo methods. The simulations and estimations are
performed using DYNARE (Adjemian et al., 2022).

Nonlinear smoothing. Based on the estimated parameter values, we run a piecewise linear Kalman
filter, as in Giovannini et al. (2021), to identify the structural shocks, where we account for endogenous
ELB periods using the OccBin approach (Guerrieri and Iacoviello, 2015). The smoothing algorithm cov-
ers observations until 2022q4, given the parameter estimates. Appendix D provides additional method-
ological details. In particular, counterfactual simulations suggest that the ELB played a substantial role
in constricting monetary policy, which intensified the recessionary shocks and deflationary dynamics.

5.3. MODEL PARAMETERS

Calibration. We calibrate a subset of model parameters to match long-run data averages and targets.
The values are summarised in table B.2. All real variables grow at the average annual growth rate of EA
GDP (1.3%). The trend growth of the price level corresponds to the targeted annual inflation rate (2%).
The time preference rate, together with trend output growth and trend inflation, determines the steady-
state nominal interest rate (4% p.a.). The steady-state shares of main economic aggregates in GDP match
historical averages over the estimation period. Furthermore, the share of saver households is set to 0.67
in the EA and 0.73 in the US, in line with the evidence in Dolls et al. (2012). The Cobb-Douglas labour
share, α, is 0.65 in both regions. We calibrate the import content in aggregate demand components,
sM,Z , to Bussiere et al. (2013). The steady-state share of industrial supplies in output, sCO , matches
the average of imported commodities to GDP for the EA (0.04). For the US, this includes domestically
produced commodities and the US (0.05).

17
Posterior estimates. We estimate the remaining parameters using Bayesian full information methods
applied to the linearised model. Table 1 reports estimates for key parameters of the three model regions.
Appendix B collects the estimates for the remaining parameters and processes. Overall, the parameter
estimates are similar to the ones in Kollmann et al. (2016) and Giovannini et al. (2019). On the household
side, EA and US display consumption habits of similar size (0.87 and 0.92) and similar risk aversion (1.57
and 1.49). Labour supply is estimated to be more elastic in the US. The demand for imports and energy
commodities (oil) is (somewhat) more price elastic in the EA (2.55 and 0.44) compared to the US (1.67
and 0.38).
On the production side, estimated investment adjustment costs are higher in the EA. In line with the
stylised facts presented above, employment adjustment costs are substantially lower in the US, while
hours are more flexible in the EA. The degree of nominal price and wage rigidity is similar for the EA
and the US, but EA estimates point to stronger real wage persistence.30
Concerning monetary policy, estimates of the Taylor rule parameters indicate somewhat less interest
inertia (0.83 and 0.90) and a weaker response to inflation (1.55 and 1.71) in the EA compared to the US.
The Taylor rule response to the output gap is modest (0.06 versus 0.02) in both regions, according to the
estimates.
Table 2 reports second-step estimation results, specifically focused on the period influenced by COVID-
19. Compared to the US, the model estimation indicates a more pronounced incidence of ‘forced savings’.
It also suggests more substantial labour hoarding shocks in the EA, in line with the economic measures and
labour market policies adopted by many European countries. Conversely, the estimation finds stronger
US employment shocks (in addition to lower structural employment adjustment costs).

6 IMPULSE RESPONSE FUNCTIONS

This section discusses impulse response functions (IRFs) for selected shocks that are characteristic of the
pandemic and recovery period according to the estimated model to understand the dynamics of the model
given the parameter estimates. In particular, we display IRFs for the transitory ‘forced’ savings shock
compared to the standard persistent savings (time preference) shock, the COVID-specific labour demand
shock, a shock to commodity (oil) prices, a persistent government transfer shock, and a consumption-
specific retail price shock. The IRFs in this section consider an economy away from the ELB in which
monetary policy can adjust short-term interest rates up and down.31

Savings shocks. Figure 3 displays IRFs for the temporary (‘forced’) savings shock (blue solid lines)
that accounts for most of the contraction of private consumption demand in 2020 at quarterly frequency,
in comparison to a persistent ‘forced’ savings (time preference) shock (red dashed lines). This section
30
The price adjustment cost estimate here is difficult to compare to evidence from the literature about the stickiness of retail
prices (e.g., Karadi et al. (2023)) because price rigidity in our model occurs at the level of intermediate goods production, i.e.
before the levels of output assembly (adding industrial supplies) and final demand (adding household energy consumption and
imports). Moreover, inflation inertia interacts with real rigidities, which are higher in the EA (Christiano et al., 2005).
31
Appendix C.5, in addition, provides IRFs for the temporary labour demand shock, which is a transitory shock to the firm’s
first-order condition for employment during the pandemic and recovery period. A negative labour demand shock implies lower
employment for given real wages. It can be understood as a shock to labour costs other than wages. It may equally proxy a
mark-down of wages associated with the increased market power of employers in labour markets.

18
Prior distribution Posterior mode distribution
Distr. Mode EA US
Std. (10%-90%) (10%-90%)
Preferences and technology
Habit persistence h Beta 0.50 0.87 0.92
0.10 (0.83-0.93) (0.89-0.95)
Risk aversion θ Gamma 1.50 1.57 1.49
0.20 (1.29-2.01) (1.20-1.75)
Inverse Frisch elasticity of labour supply θN Gamma 2.50 2.48 1.68
0.50 (2.08-3.77) (1.37-2.23)
Import price elasticity σz Gamma 2.00 2.55 1.67
0.40 (1.47-2.75) (1.41-2.08)
Commodity price elasticity σo Beta 0.50 0.44 0.38
0.08 (0.35-0.60) (0.31-0.50)
Energy consumption elasticity σE Beta 0.50 0.43 0.38
0.08 (0.36-0.57) (0.32-0.52)
Commodity extraction elasticity αCO 0.13
(0.07-0.20)
Nominal and real frictions
Price adj. cost γP Gamma 20.00 55.48 72.06
12.00 (40.26-79.77) (55.26-106.15)
Capacity utilisation adj. cost γ U,2 Gamma 0.03 0.02 0.03
0.01 (0.01-0.02) (0.02-0.04)
Investment adj. cost 1 γ I,1 Gamma 60.00 122.72 92.28
20.00 (79.44-166.03) (40.18-120.01)
Investment adj. cost 2 γ I,2 Gamma 60.00 63.62 47.16
40.00 (25.39-168.10) (9.57-122.46)
Employment adj. cost (pers.) γ E,2 Gamma 20.00 27.23 10.38
12.00 (20.45-36.93) (6.92-14.06)
Hours adj. cost γ H,2 Gamma 20.00 11.95 28.74
12.00 (8.67-16.08) (19.47-47.89)
Nominal wage adj. cost γw Gamma 20.00 14.28 18.62
12.00 (1.08-22.56) (12.32-27.84)
Real wage rigidity γ wr Beta 0.85 0.95 0.82
0.06 (0.94-0.98) (0.80-0.94)
Policy
Interest rate persistence ρi Beta 0.85 0.83 0.90
0.08 (0.75-0.87) (0.82-0.93)
Response to inflation η i,ϕ Inv.Gamma 1.70 1.55 1.71
0.15 (1.42-1.68) (1.53-1.92)
Response to output gap η i,y Beta 0.20 0.06 0.02
0.08 (0.04-0.11) (0.01-0.04)
Tax rule persistence ρτ Beta 0.85 0.91 0.95
0.06 (0.85-0.95) (0.92-0.98)
Tax rule deficit response η DEF Beta 0.03 0.03 0.02
0.01 (0.02-0.04) (0.01-0.04)
RoW region
Habit persistence h∗ Beta 0.70 0.92
0.10 (0.91-0.95)
Risk aversion θ∗ Gamma 1.50 1.31
0.20 (1.18-1.52)
Commodity price elasticity σ C,∗ Gamma 2.00 2.05
0.40 (1.52-2.30)
Price adj. cost γ P,∗ Gamma 20.00 18.08
6.00 (12.72-27.85)
Response to inflation η i,ϕ,∗ Inv.Gamma 1.70 1.55
0.15 (1.42-1.68)
Response to GDP growth η i,y,∗ Beta 0.20 0.06
0.08 (0.04-0.11)

Table 1: Prior and posterior distribution of key estimated model parameters.

Notes: This table reports the mode and the standard deviation
19(std) of the posterior distributions of EA and US parameters,
respectively. RoW parameters are reported below. Identical priors are assumed for EA and US parameters.
Prior distribution Posterior mode distribution
Distr. Mode EA US
Std. (10%-90%) (10%-90%)
Shock processes (domestic) COVID-19
Forced savings - std εtC Gamma 0.01 0.04 0.03
0.00 (0.03-0.05) (0.02-0.04)
Labour hoarding - std εLU Gamma 0.01 0.02 0.01
0.00 (0.02-0.03) (0.01-0.01)
Temporary employment - std εN D,covid Gamma 0.05 0.19 0.28
0.02 (0.16-0.23) (0.23-0.29)
Shock processes (rest of the world) COVID-19 RoW
tC,∗
Forced savings - std ε Gamma 0.05 0.27
0.02 (0.22-0.29)
Temporary productivity - std εAY,∗ Gamma 0.05 0.30
0.02 (0.24-0.30)

Table 2: Selected estimated COVID-specific shock variances

Notes: This table reports the mode and the standard deviation (std) of the posterior distributions of EA and US COVID-specific
shock parameters, respectively. RoW parameters are reported below. Identical priors are assumed for EA and US parameters.

shows the IRFs for the EA. Appendix C.4 compares EA and US responses. The shock is a temporary
increase in private savings, i.e. a temporary contraction in consumption demand. Private consumption
and real GDP decline (and, by consequence, hours worked, mitigated by labour adjustment costs), as does
the government’s primary balance due to the working of automatic stabilisers (government expenditure
relative to GDP increases, whereas tax revenue declines).
Monetary policy reacts by lowering the short-term nominal interest rate, which stimulates investment
demand and depreciates the exchange rate. Together with the decline in total domestic demand, the depre-
ciation contributes to an increase in the trade balance. The real wage increases temporarily given down-
ward price adjustment (in reaction to lower demand) combined with nominal wage stickiness, whereas,
in the case of the persistent savings shock, the decline in hours worked also weighs negatively on real
wage growth.
IRFs for the persistent savings shock (positive shock to the rate of time preference, depicted as red
dashed in Figure 3) are more persistent but qualitatively similar otherwise. A notable difference is the sim-
ilar initial inflation response despite the much bigger initial GDP contraction associated with the ‘forced’
savings shock. Compared to the demand and output contraction, the inflation response to transitory higher
savings is modest. As the ‘forced’ savings shock is short-lived, it has little impact on expectations about
future inflation, which dampens its impact on inflation compared to the persistent demand shock in an
environment with price stickiness described by the New Keynesian Phillips curve (NKPC). In the case
of the persistent shock, the lasting contraction of economic activity also lowers expectations of future
inflation, which feeds into lower current inflation through the NKPC.

Oil price shock. Figure 4 shows the macroeconomic response to an increase in the price of energy
commodities (‘oil price’ for short). The higher oil price, which affects consumers indirectly through
higher costs for industrial supplies that feed into higher prices of domestic manufactured products and
directly through the energy component in the final demand bundle, increases headline inflation. Monetary

20
GDP Policy rate Consumption inflation
0 0 0.1

-1 -0.05 0

-0.1
-2 -0.1

-0.2
-3 -0.15
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0 0.2 0

-1 0.15
-0.2
-2 0.1
-0.4
-3 0.05
-0.6
-4 0
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP Trade balance to GDP
0.2 0.4
0
Forced savings
0.3 Persistent savings
0
-0.5 0.2

-0.2
0.1

-1 0
-0.4
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure 3: Response to different savings shocks in EA

Notes: All variables are displayed in % deviations from the steady state, except for the trade balance relative to GDP, the
government primary balance relative to GDP, the policy rate (annualised), and consumption inflation (annualised), which are
expressed in percentage-point deviations from the steady state instead. Periods correspond to quarters. The shock sizes corre-
spond to one estimated standard deviation.

21
policy tightens, which leads to higher real rates in the medium term and further dampens domestic demand
and output. The EA (blue solid lines) trade balance deteriorates due to the higher commodity import bill.
The US (red dashed lines) trade balance is rather stable (small surplus) instead. Given that the US is
a commodity supplier in our model, an oil price increase has less of a negative wealth effect (resource
transfer to RoW), which contributes to the resilience of domestic consumption and activity in the US.
GDP Policy rate Consumption inflation
0 0.4

0.3 0.6
-0.05

-0.1 0.2 0.4

-0.15 0.1 0.2

-0.2 0 0
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0 0 0.05

-0.1 -0.1 0

-0.2 -0.2 -0.05

-0.3 -0.3 -0.1

-0.4 -0.4 -0.15
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP Trade balance to GDP
0 0.05
0 EA
-0.1 US
-0.05
0
-0.2 -0.1

-0.3 -0.15
-0.05 -0.2
-0.4
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure 4: Response to oil price shock in EA and US

Notes: See Figure 3 for additional details on the variable units and the simulation setup. The shock size corresponds to an
approximately 10 USD increase in global oil prices.

Government transfer shock. An important part of the fiscal response to the COVID-19 pandemic has
been government transfers rather than purchases. The literature has argued that the appropriate fiscal
response to lockdowns consists of household income insurance rather than additional demand (Guerrieri
et al. (2022)).
Figure 5 plots the IRFs for a persistent increase in government transfers (1% of GDP on impact).
Private consumption increases in the presence of ‘hand-to-mouth’ consumers and triggers a monetary
tightening away from the ELB, with an increase in the real interest rate that partly crowds out private
investment. The private consumption response is stronger in the EA (blue solid lines), owing to a higher
share of ‘hand-to-mouth’ consumers than in the US (red dashed lines). The trade balance declines in re-
sponse to higher domestic demand and declining price competitiveness (appreciation of the real effective
exchange rate (REER)) of domestic output. Domestic inflation increases in response to stronger activity.
In light of the persistence of the shock and the output response, the inflation effect is relatively strong in

22
GDP Policy rate Consumption inflation
0.2 0.08 0.1

0.06
0.1
0.04 0.05
0
0.02

-0.1 0 0
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0
0.4 0.05

0.3
-0.05 0
0.2

0.1 -0.05
-0.1
0
-0.1
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP Trade balance to GDP
0.2 0 0.02
EA
0.15 0 US

0.1 -0.5 -0.02

0.05 -0.04

0 -1 -0.06
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure 5: Response to persistent government transfer shock in EA and US

Notes: The shock size corresponds 1% of GDP on impact. See Figure 3 for additional details on the variable units and the
simulation setup.

23
relation to the initial GDP increase, given the impact of shock persistence on inflation expectations and
current inflation in the NKPC.

Retail price shock. Figure 6 plots IRFs for a positive retail price shock. This shock is a wedge between
the costs of output (aggregation of the final good and energy consumption) and the consumer price.
Technically, the shock is a negative shock to productivity in the provision of the final consumption good
(ACF
t
G in eq. (1)). It can also be interpreted as a proxy for a consumption-specific price markup collected

by retailers.
The shock increases consumer prices and lowers consumption demand, which, in turn, dampens eco-
nomic activity. The central bank raises interest rates in response to inflation. Investment falls in response
and contributes to the decline in GDP. Net exports (the trade balance) weaken in response to the REER
appreciation, following monetary tightening, despite the converse effect of lower domestic demand on
imports.
The response of consumption and activity to the shock is stronger in the EA (blue solid lines) than
in the US (red dashed lines), which reflects the different shock persistence (substantially higher in EA).
By contrast, the estimated shock size is larger in the US block, implying a stronger initial price impact in
the US. Together with smaller rigidities, this difference explains the larger US inflation response despite
a smaller initial GDP response to the shock. Higher estimated real wage rigidity explains the stronger
negative response of employment to the shock in the EA.

7 SHOCK DECOMPOSITIONS

Shock decompositions (SDs) split the dynamics of endogenous model variables into their main exogenous
drivers (shocks), thereby providing information about the relative importance of individual factors. This
section compares quarterly SDs for GDP growth and headline CPI inflation in the EA and the US, focusing
on the COVID-19 period and recovery (2019-22). SDs for GDP growth and inflation starting in 2000q1-
2022q4 are presented in Appendix C (Figures C.1-C.2) for completeness.

Real GDP growth. Figure 7 shows the decompositions of year-on-year real GDP growth in the US
(left) and the EA (right) for 2019q1-2022q4. It illustrates the dominant role that the model ascribes to
the transitory (‘forced’) savings shock to explain the contraction of economic activity in 2020 and the
recovery in 2021 and early 2022.32 The dominant role of ‘forced’ savings also echoes the important role
of declining consumption demand in the pandemic recession, contrary to the average recessions with a
stronger role for investment demand.
Additional downside factors in 2020 are other private domestic demand shocks, including the standard
persistent savings (time preference) shock and a shock to private investment demand, as well as negative
shocks to foreign activity and international trade, which dampen net export demand.33 Fiscal shocks
32
The transitory ‘forced’ savings shock is the one that dominates the contribution of the group of ‘lockdown’ shocks in the
EA and US SDs for real GDP growth. Other elements of this group are the labour hoarding shock and a COVID-specific labour
demand shock.
33
The negative shock to foreign activity implies a contraction of foreign activity but no change in trade openness. On the
contrary, the shock to international trade is a negative shock to trade, which accounts for the fact that world trade contracted

24
GDP Policy rate Consumption inflation
0 0.3 1

-0.1 0.2
0.5
-0.2 0.1

-0.3 0 0
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0 0
0
-0.05
-0.2 -0.05
-0.1
-0.1
-0.4
-0.15 -0.15

-0.6 -0.2 -0.2
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP Trade balance to GDP
0 0.05
0 EA
-0.1 US
0 -0.02
-0.2
-0.04
-0.3
-0.05
-0.06
-0.4
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure 6: Response to a retail price shock

Notes: The shock size corresponds one estimated standard deviation. See Figure 3 for additional details on the variable units.

(discretionary fiscal policy) play a stabilising role in 2020, especially in the US, whereas they dampen
the 2021 recovery, i.e. the phasing out of fiscal support becoming a drag on US growth.
Falling commodity prices supported growth in 2020 (though moderate in their quantitative contribu-
tion). In contrast, the rise of commodity prices in 2021-22 was a downside factor in more recent quarters.
Domestic supply shocks play little role in explaining the EA and US fluctuation in activity in 2020-21.
They are a downside factor more in 2021-22, notably positive shocks to retail prices; the latter are nega-
tive retail-specific productivity shocks but can also be understood as positive price markup shocks on the
domestic component of final aggregate demand.
Overall, the SDs explain the milder US recession (trough at around 10% yoy contraction in 2020q1
compared to circa 15% in the EA) through less pronounced ‘forced’ savings, stronger fiscal expansion,
less shocks to export demand and more favourable supply conditions compared to the EA.

Consumer price inflation. Figure 8 provides the decompositions for US (left) and EA (right) consumer
price inflation (yoy). Strikingly, the main driver of activity at quarterly frequency in 2020, ‘forced’
savings (as part of the lockdown shocks), has only a minor effect on inflation during the pandemic and in
the recovery. This result is linked to the transitory nature of the shock, which excludes a relevant impact
on expected future inflation that would feed back into current inflation in the NKPC.
more strongly than world output, implying a decline in trade openness.

25
United States Euro Area
16 16

Domestic supply
12 12
Commodities

8 8
Monetary

4 4
Domestic demand
1.3 1.3
Lockdown

-4 -4 Fiscal

International trade
-8 -8

Foreign activity
-12 -12

Exchange rate
-16 -16
Others + Initial Values

9q
1
9q
3
0q
1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3
1 1 2 20 021 021 022 022 19 19 20 20 21 21 22 22
20 20 20 20 2 2 2 2 20 20 20 20 20 20 20 20

Figure 7: Real GDP growth (yoy) decomposition (2019q1-22q4)

Notes: The panels show shock decompositions of quarterly real GDP growth (year-on-year). All structural shocks together
recover the observed time series of GDP growth (continuous black line). Units on the y-axis are in % (1=1%). We have grouped
the estimated shocks into the following categories: (1) domestic supply shocks, including TFP, price and wage markup shocks
(blue); (2) commodity price shocks (light green); (3) monetary policy, i.e. innovations to the estimated Taylor rule (red); (4)
shocks to private domestic demand (excluding COVID-specific transitory shocks), such as persistent saving and investment risk
premium shocks (black); (5) lockdown shocks since 2020, i.e. transitory (‘forced’) saving and temporary labour hoarding shocks
(pink); (6) discretionary fiscal policy shocks, which capture deviations from estimated fiscal policy rules (dark green); (7) shocks
to international trade, which include deviations of trade volumes and prices from the estimated export and import demand and
pricing equations (yellow); (8) shocks to foreign activity, which include shocks to demand and supply in the respective foreign
regions (light blue); (9) exchange rate shocks, which are shocks to the UIP that affect the exchange rate for given ‘fundamentals’
(brown); (10) any remaining factors (grey).

According to the SDs, the rise in inflation in both regions in 2021-22 was, instead, driven by rising
commodity prices, the recovery of foreign demand and domestic consumption and investment (reversal
of the negative persistent demand shocks), and an increase in price markups.34 Supply shocks had a
sizable impact on EA inflation already during the pandemic in 2020-21, also reflecting the absence of
deflation despite the strength of downside factors. For the US, there was a role for the pandemic-specific
labour cost shock (i.e., an increase in labour costs other than wages) as a contributor to rising inflation
since 2020.35
Fiscal expansion had a persistent and positive impact on inflation in the US and EA, especially in
the US during 2020-21, when the stimulus was largest.36 The persistence of fiscal stimulus effects on
inflation is linked to the persistence of the stimulus effect on output levels as well as the presence of strong
34
The commodity price effect on inflation is stronger in the EA given the larger commodity price increase in the region in
2021-22 that has to do with the previous sourcing of EA commodity imports and the need to find short-term replacements at
elevated world market prices.
35
The stronger role of the labour demand shock for US inflation reflects the fact that this shock applies to the external margin
of employment, where changes were more pronounced in the US.
36
The observation that a substantial part of transfers to households has been saved rather than spent by the latter would
be interpreted by the model as a positive contribution from fiscal stimulus combined with a positive household savings (i.e.,
negative household consumption) shock.

26
real wage rigidity in the model that leads to delayed inflation effects through nominal wage growth. The
(small) positive contribution of monetary shocks in 2021-22 reflects the cautious reaction of monetary
policy to rising inflation, i.e. more gradual tightening than suggested by the model’s estimated Taylor
rules.
A notable difference between the two regions regarding inflation concerns the role of exchange rate
shocks. Appreciation pressure on the USD during the pandemic and since (‘flight to safety’) has partly
offset push factors through a dampening effect on import and commodity prices in USD terms. In EA, to
the contrary, depreciation pressure added to consumer price inflation via the impact on commodity and
manufactured import prices and second-round effects associated with high real wage rigidity.
Overall, the shock decompositions for CPI inflation are in line with the result from previous literature
(di Giovanni (2022); Pasimeni (2022); di Giovanni et al. (2023)) that inflation in 2021-22 had a stronger
supply-side component in the EA and a more substantial demand-side component in the US.

United States Euro Area
10 10

Domestic supply

8 8
Commodities

6 6 Monetary

Domestic demand
4 4
Lockdown

2 2 Fiscal

International trade
0 0

Foreign activity

-2 -2
Exchange rate

Others + Initial Values
-4 -4
q 1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3
19 19 20 20 021 021 022 022 19 019 020 020 021 021 022 022
20 20 20 20 2 2 2 2 20 2 2 2 2 2 2 2

Figure 8: Consumer price inflation (yoy) decomposition (2019q1-22q4)

Notes: Inflation rates are year-on-year, i.e. they measure consumer price deflator growth relative to the same period of the
previous year. Units on the y-axis are in % (1=1%). The solid black line represents the data. Bars below (above) the dashed line
(trend inflation) indicate negative (positive) contributions to consumer price inflation. All structural shocks together recover
the observed time series of GDP growth (continuous black line). We have grouped the estimated shocks into the following cat-
egories: (1) domestic supply shocks, including TFP, price and wage markup shocks (blue); (2) commodity price shocks (light
green); (3) monetary policy, i.e. innovations to the estimated Taylor rule (red); (4) shocks to private domestic demand (exclud-
ing COVID-specific transitory shocks), such as persistent saving and investment risk premium shocks (black); (5) lockdown
shocks since 2020, i.e. transitory ‘forced saving’ and temporary labour hoarding shocks (pink); (6) discretionary fiscal policy
shocks, which capture deviations from estimated fiscal policy rules (dark green); (7) shocks to international trade, which include
deviations of trade volumes and prices from the estimated export and import demand and pricing equations (yellow); (8) shocks
to foreign activity, which include shocks to demand and supply in the respective foreign regions (light blue); (9) exchange rate
shocks, which are shocks to the UIP that affect the exchange rate for given ‘fundamentals’ (brown); (10) any remaining factors
(grey).

27
EA US
0 3 0.02 2.5
Lockdown (savings) shock
0 Stringency indicator 2
-0.02 2 Mobility indicator
1.5
-0.02

-0.04 1 1
-0.04
0.5
-0.06
-0.06 0 0
-0.08
-0.5
-0.08 -1
-0.1 -1

-0.1 -2 -0.12 -1.5
20q1 20q2 20q3 20q4 21q1 21q2 21q3 21q4 20q1 20q2 20q3 20q4 21q1 21q2 21q3 21q4

Figure 9: Lockdown shocks and indicators

Notes: The model shock (blue solid line) corresponds to the estimated ‘forced savings’ shock as described in equation (7). The
data are time series of the Oxford stringency index (Hale et al., 2020) (red solid line) and Google’s mobility indicator (red dashed
line). All series are standardised. For the EA, we aggregate indicators across countries using GDP weights.

8 COMPARISON TO OFF-MODEL EVIDENCE

The decomposition above of GDP growth dynamics in the EA and the US assigns an important role to
lockdown shocks, notably ‘forced’ savings. This section provides additional support for this channel
by comparing the estimated shock profile with off-model evidence. In particular, Figure 9 compares
the shape of the transitory savings shock to available indicators of pandemic-related restrictions that
are not part of the data set used for model estimation. More precisely, the smoothed estimates of the
transitory ‘forced’ savings shocks are displayed together with empirical measures of lockdown stringency
and mobility restrictions for the EA and the US.
The time profiles of these series are similar across the EA and the US blocks throughout the year
2020, with close co-movement between the estimated ‘forced’ savings shocks and the mobility indicators,
especially in 2020q1-3. There is some decoupling after the first wave of the pandemic. Notably, private
consumption recovers faster than restriction ease, reflecting possible adjustments in the retail and service
sectors (more online retail, sanitary measures, and less compliance with legal restrictions).
The positive co-movement of the estimated shock with the off-model indicators of lockdown strin-
gency in both regions suggests that ‘forced’ savings in the model relate to contact and mobility restrictions.
We interpret the evidence in Figure 9 as supporting the modelling of the COVID-related contraction of
economic activity in this paper.

9 ROBUSTNESS CHECKS

This section explores two model modifications to explore the robustness of our results around the baseline
specification. The first exercise considers a model with government debt in utility that can generate larger
fiscal multipliers, notably for government transfers. The second extension uses shadow estimated rates
to proxy for the effect of unconventional monetary policy.

28
9.1. SIZE OF FISCAL MULTIPLIERS

Non-targeted government transfer shocks have small output and inflation effects in the standard New
Keynesian model, where optimising households would balance the income gain with the expectation of
higher future tax liabilities. This channel is relevant in particular for the US block, where government
transfers to households accounted for a large part of fiscal stimulus during COVID-19 and are more
important in the SD of real GDP growth than for the EA, where government purchases dominate the
impact of the fiscal shock. Targeted transfers to ‘hand-to-mouth’ consumers have a larger multiplier, but
the share of these households in the population is modest (33% in the EA and 27% in the US), which
dampens the overall effect.
A model mechanism that increases the transfer multiplier with intertemporally maximising consumers
is to introduce government bonds as a safe asset with a concave functional form in household utility, as
proposed by Rannenberg (2021). Debt-financed fiscal expansions increase the households’ stock of safe
assets, which implies a decreasing marginal utility of government debt. Households react by reducing
their savings by means of higher consumption spending (and lower labour supply).37
The approach by Rannenberg (2021) with preferences over safe assets (POSA) has the advantage of
being easy to implement in a standard NK DSGE framework. We augment our baseline model structure
accordingly to assess the implications for the size of the transfer multiplier and the associated inflation
effects.
Figure 10 shows IRFs for a standard US transfer shock, comparing the benchmark version of the
model with the POSA extension away from as well as at the ELB. The model with preferences over safe
assets (POSA) implies a stronger consumption and GDP response to a given transfer shock, i.e. a stronger
fiscal multiplier. It also affects the initial ratio of inflation over output impacts, which one could frame
as the slope of the Phillips curve. In particular, the inflation response becomes stronger for a given size
of the output response. This is even more the case with the economy at the ELB or with partial monetary
accommodation.38
In sum, the POSA extension increases the transfer multiplier and (especially at the ELB) the inflation
response for given GDP effects. It could therefore strengthen the contribution of fiscal shocks to 2021-22
inflation, notably in the US. It would also imply larger inflation effects of fiscal stimulus at times when
observed inflation was more moderate.

37
Alternative approaches would be available in heterogeneous-agent NK (HANK) models (e.g., Bayer et al. (2023)). Agents
in HANK models face non-insurable income risk, and income risk raises private precautionary savings. Targeted transfers reduce
individual income risk, which, by implication, lowers precautionary savings, strengthens private consumption, and increases
the fiscal multiplier. Analysis with a HANK model by Bayer et al. (2023) introduced a liquidity channel of fiscal policy. In this
framework, debt-financed fiscal expansions lower the liquidity premium (government debt being a liquid asset) and increase
liquid asset holdings, which act as insurance against individual income risk.
38
The hump-shape pattern of the POSA consumption and output response follows the path of government debt. Private
consumption increases when debt increases and declines when outstanding debt is reduced. The POSA version of the model
requires a more aggressive fiscal debt stabilisation rule. Imposing the more aggressive fiscal closure rule in a no-POSA setting
with Ricardian households would not affect the dynamics when the fiscal closure rule operates through lump-sum taxes.

29
Real GDP level Private consumption Inflation
0.4 0.5 0.5
Baseline
0.4 0.4 Baseline 8Q ZLB
0.3 POSA
POSA 8Q ZLB
0.3 0.3
0.2
0.2 0.2
0.1
0.1 0.1

0
0 0

-0.1 -0.1 -0.1
5 10 15 20 5 10 15 20 5 10 15 20

Figure 10: Transfer shock with preferences over safe assets

Notes: This graph reports results for the US. All variables are displayed in % deviations from the steady state, except for
consumer price inflation (annualised), which is expressed in percentage-point deviations from the steady state instead. Periods
correspond to quarters. The label ‘8Q ZLB’ indicates a duration of the (exogenous) ELB of eight quarters. Appendix C.6 reports
additional details on this illustrative application.

9.2. UNCONVENTIONAL MONETARY POLICY

Central banks have increasingly applied unconventional monetary policy (UMP) at the ELB in recent
years. The benchmark model with endogenous ELB on the short-term nominal policy rate does not
account directly for the impact of UMP, however. Without explicit modelling, the effects of UMP are
hidden in other estimated shocks instead. Priftis and Vogel (2016), e.g., illustrate that quantitative easing
(QE) corresponds to a combination of foreign-bond preference, investment risk premium and private
savings shocks in standard open-economy NK models. Accounting for UMP, by implication, should
affect the quantitative importance of exogenous financial market shocks as drivers of economic activity.
Similarly, a decomposition of exchange rate dynamics in our benchmark model suggests that ex-
change rates are driven mainly by preference shocks for foreign versus domestic-currency bonds in the
short term. This result is in line with the finding in Eichenbaum et al. (2021) of the US dollar exchange
rate being driven mainly by disturbances in the foreign demand for dollar-denominated bonds. Simi-
larly, Itskhoki and Mukhin (2021) emphasise the importance of financial market shocks to account for
the disconnect between nominal exchange rate dynamics and macroeconomic fundamentals in the data.
In this subsection, we use estimated shadow rates by Wu and Xia (2016, 2020) as a measure for UMP
in an ELB environment.39 In particular, we replace the constrained short-term rate with the shadow rate
when the economy operates at the ELB.40 For simplicity, the estimated shadow rates are plugged into the
estimated Taylor rule of the baseline model, i.e., the coefficients of the policy rule are not re-estimated.
Figure 11 provides a comparison of the decomposition of annual EA real GDP growth (2004-22) in
the baseline model with occasionally binding ELB and the shadow-rate version that replaces the actual
short-term policy rate with the shadow-rate equivalent of UMP measures when the economy reaches the
ELB.
39
The data is available at https://sites.google.com/view/jingcynthiawu/shadow-rates.
40
Away from the ELB, the short-term policy rate and shadow rate are (almost) identical. The shadow-rate approach translates
the impact of UMP on the yield curve into a sequence of short-term rates with the equivalent effect.

30
The decomposition in Figure 11 focuses on the monetary, private savings, investment and exchange
rate shocks. It shows that when UMP took off in the EA in 2015, it positively contributed to GDP growth,
implying that UMP measures in their shadow-rate equivalent provided stronger stimulus than would have
been foreseen by the estimated Taylor rule, given inflation and output. Interestingly, the contribution of
UMP shifts the sign in 2021-22, indicating a change towards monetary tightening and leaving the ELB
environment. This tightening step has been larger compared to the shadow rate metric than compared to
an interest rate at the ELB in 2020 so that the negative contribution of monetary shocks to GDP growth in
2021-22 becomes more pronounced. Finally, accounting for UMP shocks affects the growth contribution
of private savings, investment and exchange rate shocks in Figure 11, which would otherwise absorb the
omitted UMP effect in a model with occasionally binding ELB. However, the quantitative discrepancies
in the SDs between both model variants remain moderate.
Baseline
6

2
1.3
Monetary

-2

-4

-6 Private savings

2004 2006 2008 2010 2012 2014 2016 2018 2020 2022
Shadow rate
Investment risk premia
6

2
1.3 Exchange rate

-2

-4
Others + Initial Values
-6

2004 2006 2008 2010 2012 2014 2016 2018 2020 2022

Figure 11: EA annual real GDP growth decomposition (2004-22) in different model versions

10 CONCLUSION

This paper has estimated a three-region (EA, US, and RoW) DSGE model to compare drivers of the
COVID-19 recession and recovery in the EA and the US. We have augmented the European Commission’s
Global Multi-country (GM) model (Albonico et al. (2019); Giovannini et al. (2019)) with shocks and
channels that have been specific to, or particularly relevant during, the pandemic. These elements include
transitory ‘forced’ savings shocks, an explicit distinction between the extensive and intensive margins of
employment, and a richer structure of commodity trade and use.
Overall, the paper adopts a parsimonious approach to adapt a workhorse policy model to salient
features of the COVID-19 recession. The model extensions allow the inclusion of the pandemic period
in the data set while preserving plausible model dynamics prior to COVID-19.

31
The analysis attributes an important role to transitory consumption (‘forced’ savings) to explain the
quarterly profile of EA and US economic activity in 2020-21. More persistent consumption and invest-
ment shocks and shocks to foreign activity and trade also played a role. Fiscal policy stabilised aggregate
activity during the pandemic. Rising inflation in 2021-22 was driven by recovering domestic and foreign
demand and rising commodity prices. Fiscal policy added to price pressure. Appreciation (depreciation)
pressure on the USD (euro) dampened (added to) inflation in the US (EA). Particularly for the EA, the
estimation also points to inflation from retail price shocks. Overall, the shock decompositions align with
the result from existing literature that inflation in 2021-22 had a stronger supply-side component in the
EA and a more substantial demand-side component in the US.
The robustness checks on fiscal multipliers show that a model with government debt (safe bonds) in
household utility increases the multiplier of debt-financed fiscal expansion. Especially at the ELB, it also
leads to a steepening of the Phillips curve, i.e. more inflation for a given output response. Accounting
for unconventional measures as a substitute for lower short-term policy rates at the ELB implies a more
stabilising impact of monetary policy during ELB episodes, which affects the contribution of domestic
savings and investment as well as exchange rate shocks in the shock decompositions.
In sum, our enhanced multi-region model can provide interesting insights into output and inflation
dynamics during and after the pandemic. In particular, it allows for joint testing of the quantitative rele-
vance of different drivers on the demand and the supply side rather than focusing the discussion on one
or a few elements.

32
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37
Appendices
A MODEL DETAILS
This appendix provides additional model details omitted in the main text. The model shares many standard elements
with Albonico et al. (2019), and we also refer to the model description contained therein. The US and EA regions
are isomorphic, and we omit explicit country indices unless required for understanding.

A.1. HOUSEHOLDS

Two groups of representative households consume and provide labour to intermediate goods producers. A share ω s
of households are savers (s), who own domestic firms and participate in financial markets (saving and borrowing).

A.1.1. Savers

Savers maximise lifetime utility over consumption and leisure:
∞
( )
X s
(Cj,t t−1 − h(Ct−1 − εt ))
− εtC s tC 1−θ s,,paid 1+θ N
(Nj,t ) λt X Q Q
s
Q
max E0 t
(β) ξt − ωt
N
− C Bj,t (α − εt ) ,
Q
Cj,t ,Bj,t 1−θ 1 + θN Pt
t=0 Q
(A.1)

where 0 < θ, θ N . h governs the importance of external
consumption habits. ξt captures stochastic disturbances to
the discount factor β, where ξt+1 /ξt = exp εC t implies that the Euler equations are affected by the time t cyclical
saving shock process εC t ; while the forced saving shock, εtC
t , is a transitory shock outside the habit persistence.
ωtN represents a stochastic labour disutility term.41
We allow for asset-specific risk premia shocks εQ t with Q ∈ {bw, g, S}, which we incorporate in the utility
function, as proposed by Fisher (2015). εSt is an investment-specific risk premium shock. εbw t distorts the first-
order condition for the foreign bond and amounts to a disturbance to the uncovered interest parity (UIP) condition.
Asset-specific intercepts, αQ , capture the steady-state risk premia, except for risk-free bonds.
Savers maximise utility subject to a sequence of budget constraints:
X X Q
Q s,paid Q
PtC Cj,t
s
+ Bj,t+1 = Wt Nj,t + divtT OT + Rt Bj,t s
+ Tj,t , (A.2)
Q Q

s,paid
where Nj,t s
= Nj,t /(1 − εTt LU ) indicates total hours paid by the intermediary firms and divtT OT redistributed
by (all domestic) firms to households. The portfolio consists of risk-free domestic bonds (rf ), one internationally
traded asset (bw), denoted in euro currency, and domestic firm shares (S). We also include government bonds (G)
in the portfolio. Each asset has gross nominal return RtQ (returns to bonds are pre-determined, whereas the return
on firm shares is unknown at time t). The net of transfers and taxes is:
s,paid
s
Tj,t s
= T Rj,t − taxsj,t − τ N Wt Nj,t − τ C PtC Cj,t
s
, (A.3)
s
where T Rj,t , taxsj,t , τ C and τ N denote transfers, lump-sum taxes, the consumption (sales) tax and the labour tax
rate, respectively.
41
To ensure a balanced growth path, labour disutility includes a multiplicative term Ct1−θ , such that ωtN = ω N exp(εU 1−θ
t )Ct
s
where εUt is exogenous. Similarly, we scale asset utility by marginal utility λ t .

38
Optimality. Saver households are identical and make identical choices. The first-order necessary conditions in
a symmetric equilibrium are for Q ∈ {rf, bw, S, G}:
" #
R Q + εQ
t −α
Q
1 = Et Λst,t+1 t C,vat
, (A.4)
1 + πt+1

tC −θ λs
where αrf = 0, λst = (Cts − εtC
t − h (Ct−1 − εt ))
s s
, and Λst,t+1 = β exp(εC t+1
t ) λs . t

Approximating the first-order condition for investment in foreign bonds gives a standard uncovered interest
parity (UIP) condition:
hE i
t+1 W
Et i = irf
t + rpremt ,
W
(A.5)
Et t
where iW W
t and rpremt are the return and risk premium on the foreign bond, respectively.

A.1.2. ‘Hand-to-mouth’

The remaining households with a population share 1 − ω s are ‘hand-to-mouth’ consumers (c) who face a zero-
borrowing constraint. In each period, they consume their current disposable wage and transfer income:

1 X
13
c,paid
PtC Cj,t
c
= Wt Nj,t c
+ Tj,t − PtC t −
εtC εtc
t−i . (A.6)
6 i=8

During COVID-19, these households accumulate forced savings that will be spent gradually upon exit from the
pandemic.

A.1.3. Aggregation

Total consumption by households (in per-capita terms) is:

Ct = (1 − ω s ) Ctc + ω s Cts (A.7)

and total labour supply:
Nt = (1 − ω s ) Ntc + ω s Nts . (A.8)

A.2. WAGE SETTING

The labour market structure follows Albonico et al. (2019). Households are providing differentiated labour services
in a monopolistically competitive market. A labour union bundles hours worked provided by both types of domestic
households into a homogeneous labour service and resells it to intermediate goods-producing firms. We assume
that Ricardian (saver) and liquidity-constrained (hand-to-mouth) households’ hours are distributed proportionally
to their respective population shares. 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.
The union maximises the discounted future stream of the weighted average of lifetime utility of its members
with respect to the wage and subject to the weighted sum of their budget constraints, Cj,t . Unions bargain over
contractual hours, i.e. Ntpaid = 1−ε
Nt
LU :
t

∞
X paid
max Uj,t = (βt )t U (Cj,t , Nj,t , ·) (A.9)
Wj,t
t=0

39
subject to:

POCS, + Birr + EW = Wye NPE + w8 (RE B54 + ivf?) + Tj (A.10)
. W; —o” .
aid st aid
Nie = ( W, ) NP" (A.11)

wan . 2
where ry _ vite w, np me — nv —(1- sfw)(nor" - 7)) is a quadratic wage adjustment cost that
is bore by the households, and 1-s fw is the share of wage setters that index the growth rate of wages to the
previous period inflation. o” is the inverse of the steady-state gross wage markup. Additionally, we allow for

a slow adjustment of real wages in the spirit of Blanchard and Gali (2007). Specifically, P©’*''"9 in equa-
tion A.12 implies a gradual adjustment of the past real wages to changes in the price level, ie. PO?™'9 =

ppevat pO-wvatlag | (1 _ ppevat) pCval.@A here PC-4-@A denotes quarterly annualised consumption prices
including taxes.

The resulting wage equation is:

yer
Cyvat
Unt P,
Mt POrattag

where ju,” is the fluctuating gross wage markup:

| Wi

pC watlag (1 — TN ut (A. 12)
t-1

_ C,vat,lag
P;

sy ae 4 OT? yg pet THs ly
‘ LarN | ow, Oe Sh OW, yet |
be = (7) is the steady state markup, 7” and y” govern real and nominal rigidity, respectively. <V is a labour

supply shock. Uy, is the derivative of the utility function with respect to labour. Prat is the price of consumption
goods adjusted for the sales tax (PO = (1+ 7°) PC).

A.3. INTERMEDIATE GOODS

Each firm i € [0, 1] produces a variety of the domestic good, which is an imperfect substitute for varieties produced
by other firms. Firms are monopolistically competitive and face a downward-sloping demand function for goods.

Differentiated goods are produced using capital, A; ;_, and labour, N;,z, which are combined in a Cobb-
Douglas production function:

l-ag

Yi = (AY (Nin — FN))* (cuieKita)* (K&_1) °° — (AY) Pe ©, (A.13)

where a is the steady-state labour share, A} represents the labour-augmenting productivity common to all firms in
the differentiated goods sector, cu; , denotes firm-specific capital utilisation. ® captures fixed costs in production.
ag denotes the output elasticity of public capital. AY is a non-stationary process, and we allow for two types of
technology shocks, <4 and e/. They are related to a non-stationary process and its autoregressive component p*:

log(Ay) — log(Af_,) = gf +e7, (A.14)

Gf = Pr gitat+(— p*)g* + ef", (A.15)
where gf‘ and g4 are the time-varying growth and the long-run growth of technology, respectively.

Total hours paid are N? aid = Empl, ,Hpere;, and firms can adjust at both margins (employment in persons
and hours per worker) subject to specific adjustment costs. In light of the restrictions on work during the COVID-
19 pandemic, we introduce a transitory labour hoarding shock (c/”), which creates a discrepancy between hours

40
paid (wage income) and actual hours worked (production function):

Nit

paid
Nia

=(1—-ef"). (A.16)

Ss
Monopolistically competitive firms maximise the real value of the firm FE Sto, that is the discounted stream

of expected future profits, subject to the output demand Y;, = (ee ) 7 Y;, the technology constraint (A.13),

and the capital accumulation equation Kj. = I; + (1 — 6)K, it—1-” Their optimisation problem can be written
as:

oe divi.s, (A.17)
PraNia le neuy 1K i,t

where the stochastic discount factor, D?, is

1+rp

D? = =
‘ T7_,(1 +r?)

(A.18)

with 1 +r? = a being the real stock return and 7/ the change in the investment price deflator. P; 1 is the
t+1

price of intermediate inputs, and the corresponding price index is:
1
1l-oY

_ : . \l-o% 4
P= (/ (Pit) d ; (A.19)

The period ¢ dividend of an intermediate goods firm 2 in real terms is given by:

div; t K f at W t nrpaid 7k Pe ig l Pi
P; ( ) P; PP, at pk tL P, it ( )

where J; , is the physical investment at price PLT ,, 7 is the corporate tax, and 6 is the capital depreciation rate.
Firms face quadratic factor adjustment costs, I’; ;, measured in terms of production input factors:

Die =P, +02, +0 +0), +084. (A.21)

Specifically, the adjustment costs are associated with the output price P;,, employment (Empl; ;, extensive mar-
gin), hours per employee (Hpere; +, intensive margin), investment J; ,, as well as capacity utilisation variation
CUi,t:

P P, 2
re, soy, | mH exp(n)| . (A.22)
2 Pit-1
E 2
Y Empl, i
pe. =! | 2 et pop ADB
Al Wi trend at 1 nyt 2
Di = p, Empl :Hpere; *(Hpere;4—1) + gy (Hperei.s —1)*}, (A.24)
I
r= PE vg ( Tie af) 7 yl? Tie — Tie—1exp(g™ +9” ))? (A.25)
at P, 2 t-1 K,_ 1 t =a Ki ; :
PL cu,2
rat Fw [yous 1) + (ee 1] (A.26)
t

where y-parameters capture the degree of adjustment costs. 7 denotes steady-state inflation. g?°?, gY , and g”! are
trend factors of population, GDP and prices for investment goods, respectively. Hpere’"°"¢ is an exogenous trend

“We assume that the total number of shares Stet = 1,

41
in hours per employee. 6 4 6 is a function of the depreciation rate adjusted for the capital trend to have zero
adjustment costs on the trend path. Given the Lagrange multiplier associated with the technology constraint, j1¥,
the FOCs with respect to employment, hours, capital, investments and capital utilisation are given by:

y
Mi PY Hi H2 ( jipere))
=H + A —l+e A.27
° W,Empl;Hpereien4 penet | 7 Pave ‘ ( )
WwW, Y; Ore 1+ e441 Ory
1—7rkK) t= y __ ND _ t + A.28
( ™) P, ° (Hi “t ) Empl, -FN OEmpIl; ae i244 OEmpl; , ( )

Q: = FE,

L+ mi Pa Pe (-* _ ory"

Praia Yeesi
+ 1-—6)+0- y ; A.29
14%.) Pos PI aKi4 Qr41( ) + ( Ot) Mi yy Pl ( )

t+1 ky

I 1 —-Th Y 4 gP?
t yk = 1 9,-1 yolk t—1exp(g' +9" ))
Ky} yi Ky-1
LE 1+ m1 Pia F xp(g” tg yh? (Li41 — Lexp(g’ + 9”’)) (A.30)
‘\ 1+, Pa PP ky
Yi Pi u u
HI = 0) or = Kala +9" (cu = 0), (A31)

where Q; = p13 / Fe In equations (A.27) and (A.28), e/7?°"° and ce’ are shocks to labour demand on the intensive
and extensive margin, respectively. We also allow for temporary one-off shocks during the COVID period.

In a symmetric equilibrium (P;; = P,), the FOC with respect to P; , yields the New Keynesian Phillips curve:

(ne —*)
1-7
Poi!

14 me41 Pro Yiqi (« _ i)
lth, BY, t41

pio’ = (L—T™)(o¥ —1) tay”

— oy? + ove, (A.32)

where e+’ is a white noise markup shock.

A.4, FISCAL POLICY

The government collects taxes on labour, 7, corporate profits, 7“, consumption, 7”, and lump-sum taxes, ta2,,
and issues one-period bonds, BG, to finance government consumption, G;, public investment, J, transfers, 77,
and the servicing of the outstanding government debt. The tax on commodity imports from RoW, 7, is fixed.
TY denotes a labour hoarding subsidy. The government budget constraint is:

Br = (1+ 8 ,) Be, — RP + PEG. + PISIP + TPs, (A.33)
where nominal government revenues, R@, are defined as:
RE = 7* (PY, — WNP — PLE Ki) + TN WNP 4 Oo POO,
4+ 7©°P,CO; + tar,P.¥, + EUW; (pw - Ni) (A.34)

“We specify 6{* = exp(g® + g”") — (1 — 4), so that 4 — 6* ¢ O along the trend path.

42
The government closes its budget via lump-sum taxes:

tary = pTtary1 +1" (an dé f) 4B an _ BG) 4 eta, (A.35)
Yi-1Pr-1 Yi-1Pr-1

where def and BG are the targets for the government deficit and the government debt level, with debt rule coeffi-
cients 7% and 7”, respectively. ¢{** is a white noise shock. p7 governs the debt rule persistence. The accumulation
equation for government capital is:
KP =(1-0) KE, +1, (A.36)
where 6 is the depreciation rate.
We use the following fiscal rules for government consumption, G;, investment, [@, and transfers, T;:

G
pyr = ef (A.37)

G pIG
Byer = el%, (A.38)
o =, (A.39)

where e@, e/°, ce? represent shocks to government consumption, investment and transfers, respectively.

COVID-specific features. To account for the substantial fiscal packages in the EA and US, we introduce two
COVID-specific features. Firstly, considering the large-scale US transfer packages, we re-estimate the variance
of US transfer shocks (see eq. A.39) during the COVID period.* Secondly, in the EA, we incorporate COVID-
specific lump-sum taxes (distributed to households based on population shares), broadly capturing tax reductions
and similar policies. These two features, while having comparable macroeconomic effects, are identified based on
distinct data series (transfers for the US and revenue data for the EA), reflecting the varying compositions of fiscal
support in these two regions.

5. COMMODITY IMPORTERS

Commodity importers seek to maximise the dividends subject to the inverse-sloping demand equation for each

variety with respect to PO:
2
PCO pco.M P,CO(gCOMM —1) peo [{ Pc?
max Fi ‘DP if ft 00 | Co, _7 CO,-t ity
max Eo y B (5 PR 2 PR | Poe,
—gCOMM
Pe
st. COit = peo CO:, (A.40)
where D? is the stochastic discount factor, and POOM is the import price of energy commodities. y?C° is the

COMM

adjustment cost parameter for the energy commodity price, and o is the elasticity of substitution between

different energy commodity varieties. Rearranging the first-order condition with respect to Pge gives*
poo? poco
pce = pCoM 4 ,COp _ ~P.cO ( to 1)
' PE? \ PE?
2
+p Pia ~P:CO COur Pr PSY” (PSS 4 (A.41)
CO; Prst Pee Pee , ‘

“' Additionally, we allow for a portion oi targeted transfers to *hand-to-mouth’ households. The estimated parameter value
suggests that approximately 55% of transfers were targeted.

SWe also impose symmetry across importer and assume that c7?™™ jis sufficiently large so that in the limit ZCOMM =
——1,— ~ 1, allowing to eliminate the steady-state markup.
1— comma

43
A.6. EXPORTERS

The exporters in each region use a mix of domestic-cost pricing and destination-market pricing. The mix of pricing

strategies is specific for each destination /, including also a destination-specific shock term ¢€ 1 x ”

X = exp(eP**) (pe) (g,,Pe)eh® AA42
Prt = exp(€, 1; )( t ) ( Lt 4) : (A.42)
Total nominal exports of final goods (excluding commodities) are defined as:

PXX,=S° PAM». (A.43)
l

A.7. ROW DETAILS

The RoW final good. As for the EA and the US, final goods producers combine domestic output, yin and
imported goods, /;*, ina CES production function:

ote

(1 = si) (COP) + (8th) (le) =] , (AAA)

x 4Z,x
4; ~~ A;

where Z7 € {C*t, I;', Xf} denotes the demand for final goods by households, private investors, and exporters of

final goods, respectively. AZ ™ denotes a productivity shock in sector Z, and 0 < sM 4" < 1 is the stochastic im-

port share associated with the different components of final demand. This is given by sha = 5“2* exp (ch A ),
where s:4:* denotes the steady-state import share of the demand component Z, and ef 1 is an import demand
(preference) shock. The parameter o*’* > 0 is the elasticity of substitution between domestic output and imports

in the assembly of the final good. This elasticity is assumed to be common across all final demand components.

Output. Perfectly competitive firms produce output (O;) by combining domestic value added (Y;) and imported
industrial supplies (IS;) in a CES production function:

OF =

(1— si) (vey + (87) (157) =] . (A.45)

where s} °* is the RoW share of commodities use.4° The specification in eq. (A.45) leads to optimality conditions

for the demand for commodities as in the detailed regions of the model.

Intermediate goods. The intermediate good producers use labour and capital to manufacture domestic goods
(non-commodity output) according to a Cobb-Douglas production function and are subject to a standard CES de-
mand function of RoW output packers (analogously to the EA and US blocks):
* yk * * l-a *\ a
Yet = Ar (cuj Ay) (Ne), (A.46)

where Al* captures a trend in the productivity, and N;* = Actr# Pop; is the active population in the economy.

Kj, denotes capital. It is utilised at rate cuj', and follows a law of motion analogous to the detailed regions in

“SUnlike the EA and US, the RoW block does not feature energy commodities as an additional (direct) element in the house-
holds’ consumption good.

44
the model. RoW adjustment costs are given by:

2
Y,* ,,P,* P*
y=? + Y; ( pele -) (A.47)
it—1
CU,* P* Bo U,* * yw ok 2
Vie = pe Bit-1 10" (cuz, — 1) + “9 (cuj, — 1) (A.48)
t
2
I,* pl,* * 2 I,x pl,x (I*, — [* xX You Pl x
* P I; P, ( it — 4i,t—1 ©XP (s g
yy = Ke (Se -5,) + (A.49)
2 PF Key 2 PF Key

The first-order condition with respect to [**, reads:

* * u
= ¥ x 7 x
t 0 Ke, t 1 Ke,

* Tx * * _ T* Y Py)
Ata Pid Pw (it. If exp (s Tg

_E ex ( y Pe) . A.50
t re pis Px V1 Ke Pig +9 ( )
where QF = “4 is Tobin’s marginal Q. The first-order condition with respect to K;, solves:
;
“pF

U,*

rN tt Pi* P* + 9
f =E, | FEE ( ( 99" (cut, —1) — 4 (cut yy, -1
Q; t dM, Pay pls Yo (CUR p41 ) 5) (cUj rp )

+(1— 6") Qi, + (= 0") wp SE ke J (A.51)
Piya i,t
The first-order condition with respect to cu; , yields:
Pi* * U,* U,* * Y,* * Yi
pe Kiana (90 +11" (cuzs —1)) = we* (1 0*) cur (A.52)
Price setting for non-oil output follows a New Keynesian Phillips curve:
nm _ Ay _ Be NEw (nx _ a) +4 gu lo YP +4 et* (A 53)
t = Pt M t+1 8 Y« t > :

where \¥ = (C¥ — h*C*_,)~®" is the marginal utility of consumption, and ¢?* is a cost push shock.

RoW commodity supply. In the RoW, a competitive sector supplies two distinct commodities, namely oil (o,
Brent) and non-oil commodities (no, e.g. natural gas and materials) to domestic and foreign firms. There is a supply
disturbance eC°* that captures exogenous commodity supply shocks, such as the discovery of new raw material
deposits. EA, US and local demand for commodities is determined by final good producers in these regions (see
above). The producer combines oil (0*) and non-oil (no*) commodities into bundles of CO* that are exported to
EA and US or used locally. The price of the CO* bundle is destination-specific. The prices of CO* exports to EA
and US contain shock terms Ef. CO where | = (EA,US). This specification accounts for price differences due,
e.g., to different commodity baskets. Thus:

_gCOMM,«

; (A.54)

~ <Ot

poo» — P.O. [spn (pen yeeene + sp )(Broryreonn) 1/(1

_—g COMM, «

+ (1—s*)(PP°") (A.55)

COMM,
econ) 1/(1-o *)

peo = [s(Pe")!

45
Commodity prices are exogenous in this model specification, i.e.:

. PF
PRY = Fox: (A.56)
t

where A?” is the exogenous oil-specific productivity technology (analogously for prices of non-oil commodities).

The total supply of commodities by RoW is residual, i.e. it satisfies global demand given US production (see
below).

Non-commodity exporters. The exporters of final goods follow a mix of domestic-cost pricing and destination-
market pricing, which is specific for each destination 1 = {EA, US}, including also a destination-specific shock

PX,*,
term € ;

PX,* px PX,*

; * l-a a
Pe sete (PO) (EPR (A.57)

Euler equation. RoW households maximise utility subject to the aggregate budget constraint:
PYY# + div’ = PO*Ce + PO* IS + TBF, (A.58)

where div; are dividends from intermediate good producers, and T'B; are net exports. J;* denotes investment. The
consumption Euler equation is:
Ri
Cx
T+ my

1=E; , (A.59)

x
Ae etd

—~@e*
Ch, —n*Ce ,
(Cisr“h° Cr) e* and </°* denote persistent and COVID-specific

(Cy—h*Cx_,) t é

temporary discount factor shocks, respectively.

where Aj,,, = (* exp(eC™ + ef")

A.8. US COMMODITY SUPPLY

While all commodities used in the EA are imported, the US not only uses commodities but also supplies them. The
supply of intermediate goods comprises commodity extraction, i.e. Y;4 = Y;'?’ + Y,°?. Thus, commodities are
produced with the same production function, capital and labour input as other intermediate goods. US commodity
producers maximise dividends:

divi O° _ CoY¥s pce _ Y,CO-US pus. (A.60)

COPS = Ave (ycousy (A.61)

using a decreasing return to scale technology, where A@® is a scaling parameter. With aco < 1, US commodity
extraction is an increasing function in the (relative) price of commodities:

CO pCO \ 1!-4co
yCous _ (seer: P; )
t —_— — _FrTaq .

pos (A.62)

46
B DATA, CALIBRATION, AND POSTERIOR ESTIMATES

B.1. DATA SOURCES

The analysis uses quarterly and annual data for the period 1998q4 to 2022q4 based on the data set of the European
Commission’s Global Multi-country Model (Albonico et al., 2019). This appendix repeats the description contained
therein for convenience. Data for EMU countries and the Euro Area aggregate (EA20) are taken from Eurostat (in
particular, from the European System of National Accounts). US data come the BEA. 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 56
countries: Albania, Algeria, Argentina, Armenia, Australia, Azerbaijan, Belarus, Brazil, Bulgaria, Canada, Chile,
China, Colombia, 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 quarterly-frequency data is not available, mixed frequency data estimation is used. In this case, we
observe annual RoW data in the last quarters of each year (as quarterly annualised variables) and allow the Kalman
smoother to interpolate the annual data in the other three quarters in a model-consistent manner.
Table B.1 lists the observed time series. GDP deflators and relative prices of aggregates are computed as
the ratios of current price value to chained indexed volume. The trend component of total factor productivity is
computed using the DMM package developed by Fiorentini et al. (2012). The obtained series at quarterly frequency
is then used to estimate potential output.
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 change in inventories to the series of investments.

47
Euro Area and US
i Nominal short term interest rate
log(actrk ) Log of active rate population
g
log( BY ) Log of nominal gov. bonds share
g
log( CY ) Log of nominal gov. consumption share
log( YC ) Log of nominal consumption share
log(e) Log effective nominal exchange rate
g
log( iY ) Log of nominal gov. interest payments share
g
log( IY ) Log of nominal gov. investment share
log( YI ) Log of nominal investment share
log( MY
) Log of nominal total import share
log(Empl) Log of employment
log(N ) Log of hours
log(HpereT ) Log of hours per employee trend
T
gN Potential hour growth
c,vat
log( P P ) Log of consumption price final to observed GDP price
g
log( PP ) Log of gov. observed price to observed GDP price
IG
log( PP ) Log of govt. investment price to observed GDP price
PI
log( P ) Log of observed total investment price to observed GDP price
M
log( PP ) Log of import price to observed GDP price
log(P op) Log of population
X
log( PP ) Log of export price to GDP price
log(P ) Log of observed GDP price
log(tf¯p) Log of TFP trend
log( YT ) Log of nominal gov transfers share
log( WY
) Nominal wage share
log( XY
) Log of nominal export share
log(Y ) Log of observed GDP
CO
Y
Nominal industrial supply import share
CO
P Price of industrial supply
log TYB Nominal trade balance share
P CO,O Oil price in US dollars
Rest of the World
∗
i RoW nominal Interest rate
log(P op∗ ) Log of population
log(P ∗ ) Log of observed GDP price
log(Y ∗ ) Log of observed GDP
∗
log( YI ∗ ) Log of nominal investment share
log(Y¯∗ ) Log of GDP trend

Table B.1: List of observables.

48
B.2. CALIBRATION AND POSTERIOR ESTIMATES

Table B.2 reports the calibrated parameter values. Table B.3 collects main estimated parameter values.

49
EA US
Households
Preference for government bonds αB -0.001 0.002
Preference for stocks αS 0.005 0.011
Preference for foreign bonds αBW 0.010 0.010
Intertemporal discount factor β 0.998 0.998
Savers share ωS 0.670 0.730
Import share in consumption sM,C 0.099 0.053
Import share in investment (private and gov) sM,I 0.150 0.125
Import share in exports sM,X 0.140 0.058
Weight of disutility of labor ωN 3.342 18.319
Production
Cobb-Douglas labor share α 0.650 0.650
Depreciation of private capital stock δ 0.014 0.017
Share of oil in total output sOil 0.037 0.048
Linear capacity utilisation adj. costs γ u,1 0.028 0.040
Value-added demand elasticity σy 6.085 11.543
Monetary and fiscal policy
Nominal interest rate in SS ī 0.004 0.005
Nominal interest rate in SS ī 0.004 0.005
CPI inflation in SS π̄ c,vat 0.005 0.005
Interest rate persistence ρi 0.807 0.852
Consumption tax τC 0.200 0.100
Corporate profit tax τk 0.300 0.300
Labour tax τN 0.436 0.348
Deficit target def T 0.024 0.028
Debt target BG ¯ 3.025 3.416
Long-run growth and ratios
Private consumption share in SS C/Y 0.559 0.700
Private investment share in SS I/Y 0.176 0.148
Govt consumption share in SS C G /Y 0.204 0.150
Govt investment share in SS I G /Y 0.031 0.036
Transfers share in SS T /Y 0.163 0.131

Table B.2: Selected calibrated parameters.

50
Prior distribution Posterior mode distribution
Distr. Mode EA US
Std. (10%-90%) (10%-90%)
Shock processes (domestic)
Price markup - std εµ Gamma 0.02 0.02 0.02
0.01 (0.01-0.03) (0.01-0.04)
Labour supply - std εU Gamma 0.01 0.00 0.02
0.00 (0.00-0.00) (0.01-0.03)
Temporary TFP level - std εLAY Gamma 0.00 0.00 0.00
0.00 (0.00-0.00) (0.00-0.00)
Labour demand - AR(1) coeff. ρN D Beta 0.50 0.70 0.77
0.20 (0.63-0.83) (0.72-0.86)
Labour demand -std εN D Gamma 0.01 0.01 0.02
0.00 (0.01-0.02) (0.02-0.02)
Government consumption - AR(1) coeff. ρG Beta 0.70 0.94 0.93
0.10 (0.90-0.97) (0.89-0.96)
Government consumption - std εG Gamma 0.01 0.00 0.00
0.00 (0.00-0.00) (0.00-0.00)
Government investment - AR(1) coeff. ρIG Beta 0.70 0.92 0.93
0.10 (0.88-0.97) (0.90-0.95)
Government investment - std εIG Gamma 0.01 0.00 0.00
0.00 (0.00-0.00) (0.00-0.00)
Transfers - AR(1) coeff. ρT Beta 0.70 0.95 0.97
0.10 (0.91-0.97) (0.94-0.98)
Transfers - std εT Gamma 0.01 0.00 0.00
0.00 (0.00-0.00) (0.00-0.00)
Tax - AR(1) coeff. ρT AX Beta 0.85 0.91 0.95
0.06 (0.85-0.95) (0.92-0.98)
Tax - std εT AX Gamma 0.01 0.01 0.01
0.00 (0.01-0.01) (0.01-0.01)
Import - AR(1) coeff. ρM,Z Beta 0.50 0.96 0.90
0.20 (0.93-0.98) (0.84-0.94)
Import - std εM,Z Gamma 0.01 0.02 0.02
0.00 (0.02-0.03) (0.01-0.02)
Bilateral export price - AR(1) coeff. ρX Beta 0.30 0.17 0.17
0.10 (0.09-0.26) (0.09-0.26)
Bilateral export price - std εX Gamma 0.00 0.01 0.01
0.00 (0.01-0.01) (0.01-0.01)
International bond preference - AR(1) coeff. ρBW Beta 0.50 0.83 0.95
0.20 (0.84-0.93) (0.94-0.98)
International bond preference - std εBW Gamma 0.01 0.01 0.00
0.00 (0.00-0.01) (0.00-0.00)
Monetary policy - std εI Gamma 0.00 0.00 0.00
0.00 (0.00-0.00) (0.00-0.00)
Shock processes (rest of the world)
Time preference - AR(1) coeff. ρC Gamma 0.01 0.01
0.00 (0.01-0.02)
Time preference - std εC Beta 0.50 0.73
0.20 (0.62-0.81)
Investment risk prem. - AR(1) coeff. ρS Beta 0.01 0.01
0.00 (0.01-0.02)
Investment risk prem. - std εS Beta 0.50 0.68
0.20 (0.62-0.82)
Price markup εµ Gamma 0.01 0.01
0.00 (0.00-0.02)
Import - AR(1) coeff. ρM,Z Beta 0.50 0.97
0.20 (0.95-0.98)
Import - std εM,Z Gamma 0.01 0.02
0.00 (0.02-0.02)
Monetary policy - std εI Gamma 0.01 0.00
0.00 (0.00-0.00)
51
Table B.3: Selected estimated shock processes.
C ADDITIONAL RESULTS

C.1. SHOCK DECOMPOSITION FULL SAMPLE

Figure C.1: Real GDP growth shock decomposition (yoy)

52
Figure C.2: Inflation shock decomposition (yoy)

53
C.2. SHADOW RATES

Shadow rates represent hypothetical short-term interest rates determined through the application of term structure
models. These models provide a basis to derive the trajectory of short-term interest rates in line with shifts in long-
term rates, particularly in reaction to the impact of unconventional monetary policy (UMP) on long-term yields.
In standard economic circumstances (i.e., away from the ELB), or ‘normal times’, shadow rates align with
short-term policy rates. However, when the effective lower bound (ELB) comes into play—when the short-term
policy rate touches the ELB and long-term rates are lowered by UMP—shadow rates go into negative territory.
For our research, we utilise shadow rate estimates provided by Wu and Xia (2016, 2020). In Figure C.3, we
graphically represent these rates for both the Euro Area (EA) and the United States (US), alongside the actual
short-term policy rates (bold blue). This illustration effectively highlights the disparity between shadow rates and
short-term policy rates when the latter hit the ELB, and central banks implement UMP measures.

US EA
8 8

6
6
4
4
2

2 0

-2
0
-4
Nom. int. rate (baseline)
-2 Shadow rate (Wu and Xia)
-6
Combined
-4 -8
1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020

Figure C.3: Shadow rates and nominal short-term interest rates

Notes: This graph depicts the interest rate measures used in the baseline (bold blue) and shadow-rate (dashed yellow) versions
of the model.

54
C.3. FISCAL POLICY: DYNAMIC EFFECTS OF FISCAL SHOCKS

Figure C.4 shows the macroeconomic response to a persistent increase in government purchases. Domestic output
increases, and the government’s primary balance deteriorates as the purchases are only partly offset by higher
tax revenue. Monetary policy tightens away from the ELB, which raises real interest rates and reduces private
consumption and investment demand. The exchange rate appreciates in reaction to monetary tightening, which
reinforces the initial negative trade balance effect from higher import demand. The inflation response is similar in
strength to the persistent private savings shock in the main text. The shock transmission in the EA versus the US is
similar in quantitative terms, except for stronger crowding out of investment and a weaker trade balance response
in the US.
Compared to the shock to government purchases, government investment shocks lead to a more persistent
increase in GDP and generate less crowding out of private investment (Figure C.5). Finally, for comparison, Figure
C.6 shows the effect of an untargeted transfer shock, which we discuss in the main text.
GDP Government consumption Government investment Transfers
1 8 0.02
0.5
6
0
0.5 4 0
-0.02
2

-0.5
0 0 -0.04
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40

Policy rate Consumption inflation Private consumption Private investment
0.4 0 0
0.2
0.3 -0.1
0.15 -0.1
0.2 -0.2
0.1
-0.2
0.05 0.1 -0.3

0 0 -0.4 -0.3
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
Hours worked Real wages Gov. primary balance to GDP Trade balance to GDP
0.2 0.05
0.6 0
EA
0 US
0.4 0.1 -0.2
-0.05
0.2 0 -0.4
-0.1
-0.6
0 -0.1 -0.15
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40

Figure C.4: Response to a government consumption shock

55
GDP Government consumption Government investment Transfers
1 0.6 40 0

30
0.4 -0.5
0.5 20
0.2 -1
10

0 0 0 -1.5
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40

Policy rate Consumption inflation Private consumption Private investment
0.4 0.6 0.3
0.1

0.2
0 0.2 0.4
0.1

-0.1 0 0.2
0

-0.2 -0.2 0 -0.1
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
Hours worked Real wages Gov. primary balance to GDP Trade balance to GDP
0.6 0.6
0 EA
0 US
0.4 0.4
-0.2

0.2 0.2 -0.4 -0.1

0 -0.6 -0.2
0
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40

Figure C.5: Response to a government investment shock

56
GDP Government consumption Government investment Transfers
0.2 0 0 8

6
0.1
-0.05 -0.05 4
0
2

-0.1 -0.1 -0.1 0
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40

Policy rate Consumption inflation Private consumption Private investment
0.08 0.1 0
0.4
0.06
0.3
-0.05
0.04 0.05 0.2

0.1
0.02
-0.1
0
0 0
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
Hours worked Real wages Gov. primary balance to GDP Trade balance to GDP
0.2 0 0.02
0.05
EA
0.15 0 US
0
0.1 -0.5 -0.02

-0.05
0.05 -0.04

-0.1 0 -1 -0.06
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40

Figure C.6: Response to an untargeted government transfer shock

57
C.4. SAVINGS SHOCKS

This section presents additional details on the IRFs of the two types of savings shocks.
GDP Policy rate Consumption inflation
0 0
0
-0.05
-0.1 -0.05
-0.1
-0.2
-0.1
-0.3 -0.15

-0.4 -0.15 -0.2
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0.2
0 0
0.15
-0.2
-0.1
0.1
-0.4
-0.2
0.05
-0.6

0 -0.3
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP Trade balance to GDP
0 0.1
0
EA
-0.05 US
-0.1 0.05
-0.1
-0.2
-0.15 0
-0.3
-0.2
-0.4 -0.05
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure C.7: Response to a persistent savings shock

58
GDP Policy rate Consumption inflation
0.2
0
0 0.1
-1
0
-0.05
-2 -0.1

-0.2
-3 -0.1
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0 0.06 0

0.04
-2
0.02 -0.5
-4
0
-6
-0.02 -1
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP Trade balance to GDP
0 0.6
0.1 EA
-0.5 US
0.05 0.4
-1
0
0.2
-0.05 -1.5

0
-0.1 -2
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure C.8: Response to a temporary savings (lockdown) shock

59
C.5. COVID-SPECIFIC LABOUR DEMAND SHOCK

Figure C.9 shows the effects of a temporary labour demand shock. This disturbance is active only during the
COVID period to help fit the employment dynamics, notably in the US. The estimated contribution of this shock
to GDP growth and inflation in the pandemic period is relatively minor with the exception of a small inflationary
effect in the US in 2021 (included in the contribution of ‘lockdown shocks’).
GDP Policy rate Consumption inflation
0.05 0.04 0.2

0.02
0.1
0 0
0
-0.02

-0.05 -0.04 -0.1
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Private consumption Private investment Hours worked
0.2 0.04 0

0.02
0.1 -0.5
0
0 -1
-0.02

-0.1
-0.04 -1.5
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40
Real wages Gov. primary balance to GDP -3 Trade balance to GDP
10
0.2 20
0
EA
15
-0.1 US
0.1
10
-0.2
0 5
-0.3
0
-0.1
-0.4
5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Figure C.9: Response to a COVID-specific labour demand shock

Notes: The shock size corresponds to one estimated standard deviation. All variables are displayed in % deviations from the
steady state, except for the trade balance relative to GDP, the government primary balance relative to GDP, the policy rate
(annualised), and consumption inflation (annualised), which are expressed in percentage-point deviations from the steady state
instead. Periods correspond to quarters.

60
C.6. PREFERENCES OVER SAFE ASSETS

We incorporate preferences over safe assets (POSA), as proposed in Rannenberg (2021), by extending the utility
function outlined in equation (7) to include preferences towards government debt. The modified utility function is
presented in equation (C.1):

where x, > 0 introduces POSA and oy governs the curvature of the safe asset preferences. bg, = on — BG
denotes deviations of the government debt-to-GDP ratio from the steady-state government debt-to-GDP ratio. We
assume government debt to be (almost) risk-free and explicitly associate the interest rate of risk-free assets with
government bonds, such that 7 = i, + a@, with av being very small.

The first-order condition for government bond holdings is provided by equation (C.2):

Nar Pr 1

1= (PE
a A, Pil+a%+eP

((1+%)) | + x0 (be). (C.2)

As clarified in Rannenberg (2021) (p.1026), POSA results in a discount wedge, 67°54, which is the net value that
the household savers assign to the marginal utility of consumption in the following period.*” Emulating his paper,
our illustrative application sets (o,,070°4) = (0.15, 0.96). All other parameters persist at their estimated values.

The introduction of an extra benefit from saving in government bonds, beyond the utility associated with future
consumption, reduces consumption smoothing over time. This is because the current period’s consumption does not
only depend on the benefit of future consumption but also on the benefit of holding government bonds. Moreover,
the additional utility value implies that the interest rate offered may be lower than households would naturally
discount their future earnings. We refer to Rannenberg (2021) for additional discussion of the effects of POSA.

“"In the steady state, 9POS4 = Bi/mOr™,

61
D EFFECTIVE LOWER BOUND: SIMULATION AND SMOOTHING AL-
GORITHM

D.1. OVERVIEW

We build on the OccBin toolkit (Guerrieri and Iacoviello 2015) to account for the occasionally binding constraint
on nominal interest rates. This method handles the constraints as different regimes of the same model in which
the constraints are either slack or binding. Consequently, our model consists of the following four regimes: an
unconstrained baseline; two variations, which include either an ELB constraint in the EA or the US leaving the
other constraint slack; and a regime in which both constraints are active. Importantly, the dynamics in all regimes
depend on the endogenous length of that regime. The expected duration, in turn, depends on the state variables
and exogenous disturbances. As emphasised in Guerrieri and Iacoviello (2015), this interaction can result in highly
nonlinear dynamics. We lay out the details below in Section D.2.
Following Giovannini et al. (2021), we integrate the nonlinear solution into a specially adapted Kalman filter
to estimate shocks in the model with the two occasionally binding constraints. We summarise the algorithm for the
shock decompositions in Section D.3.

D.2. DETAILS ON THE OCCBIN ALGORITHM

For ease of exposition, this Appendix assumes a single occasionally binding constraint. The reference regime (e.g.,
ELB constraint is slack) can be expressed as a linearised system (M1):

A1 Et [Xt+1 ] + A0 Xt + A−1 Xt−1 + Eut = 0

Here, Xt denotes the model variables in deviation from the steady state.
The alternative regime (e.g., ELB constraint is binding) features a constant D∗ (M2):

A∗1 Et [Xt+1 ] + A∗0 Xt + A∗−1 Xt−1 + D∗ + E ∗ ut

M1 and M2 are linearised around the same point.

Regimes The solution for M1 (reference regime) can be written as:

Xt = T Xt−1 + Cut

In this case, the transition matrices T and C are constant. The Blanchard-Kahn conditions hold for M1.
The solution for the alternative regime (M2) can be written as:
(
Tt Xt−1 + Rt + Ct ut for t = 1
Xt =
Tt Xt−1 + Rt for t ≥ 2

Here, the time-varying matrices depend on the expected regime length. The system’s behaviour, exhibiting certainty
equivalence, does not depend on shocks ut+j for j ≥ 1.

Guess and verify The guess and verify approach begins by guessing regime 1 (M1): If ut = 0 for all future
periods, the system returns to M1. We then check whether we are indeed in M1 (e.g., the constraint is slack), and if
regime M2 is in period t given state Xt−1 and shocks ut . This approach involves guessing T such that for τ ≥ T ,
we are in M1, then verifying whether the guess is correct, following the process outlined in Guerrieri and Iacoviello
(2015). If not, an update is required.

D.3. NONLINEAR SMOOTHING

62
D.3.1. Additive representation of shock decompositions

This section provides additional details on obtaining an additive shock decomposition for the nonlinear model. To
fix ideas, consider a piecewise-linear Kalman smoother, which estimates the sequence of regimes in the historical
time interval. The sequence of regimes triggers a sequence of state-space matrices:

xt = T(xt−1 , εt ; θ)xt−1 + C(xt−1 , εt ; θ) + R(xt−1 , εt ; θ)εt , (D.1)

where xt stacks all endogenous variables in deviation from steady state, ut are the smoothed shocks, and Ct is a
constant, which is triggered by the regime, i.e. C(·) = 0 in the unconstrained regime.48
The algorithm estimates the additive shock decompositions in two steps. The first step exploits the piecewise-
linear Kalman smoother that provides the smoothed estimate of the sequence of regimes together with the historical
series of exogenous shocks. Given the sequence of regimes, the shocks are propagated individually through the
sequence of state-space matrices T(·) and R(·). The array C(·) is treated as an additional exogenous process,
labelled “regime effect”.
A second step extends this procedure to obtain an additive shock decomposition. Note that the regime effect
results from the interaction of all shocks simultaneously hitting the system ∀τ ≤ t. Hence, the regime effect is a
function of exogenous shocks. For each t and variable j, we compute the absolute value of the contribution of each
shock ui,t onto a variable xRj :
wj,i,t = |xR
t (ui,t )|, (D.2)
where wj,i,t is a set of weights which apportion the regime effect to all shocks, and xR
j is a variable determining
the regime sequence.

D.3.2. Implied regime sequences

Figure D.1 reports the identified regime sequences for the US and EA.

D.4. COUNTERFACTUAL: NO EFFECTIVE LOWER BOUND

Figure D.2 reports the counterfactual simulations on the role of the ELB. The baseline simulation, depicted in
solid blue, introduces the estimated shocks into the baseline model, incorporating the occasionally binding ELB
constraints. By design, these shocks, in the baseline model, replicate the observed time series of real GDP and
inflation (and the other endogenous variables not shown here). According to our model, the second simulation
(depicted in dashed red lines) measures the macroeconomic effects attributable to the ELB. For this purpose, the
simulation introduces the identical set of estimated shocks into a linear model variant without the ELB constraints.
This generates a counterfactual trajectory of endogenous variables and shows the output losses and deflationary
effects associated with the ELB in the two regions (neglecting the potential offsetting effects of unconventional
monetary policy implemented during ELB episodes).

48
Note that at the ELB, the Taylor rule it = ilb violates the steady-state condition (ilb < ī).

63
EA
10

regime expected start
5

0
2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022
historic period
US

regime expected start
10

0
2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022
historic period
Unbinding Binding

Figure D.1: Model-identified ELB periods

Notes: This graph reports the ELB regime sequences. The vertical axes show the expected length in each period as simulated
using the piecewise-linear model.

64
Real GDP level EA Real GDP level US
10 10

5 5

0 0

-5 -5

-10 -10

-15 -15

-20 -20
2006 2008 2010 2012 2014 2016 2018 2020 2022 2006 2008 2010 2012 2014 2016 2018 2020 2022
Inflation EA (quarterly annualised) Inflation US (quarterly annualised)
6 6
Data
5 5 Counterfactual no ELB

4 4

3 3

2 2

1 1

0 0

-1 -1
2006 2008 2010 2012 2014 2016 2018 2020 2022 2006 2008 2010 2012 2014 2016 2018 2020 2022

Figure D.2: No-ELB Counterfactual

Notes: This graph reports the level of real GDP (de-trended) and inflation (annualised) in the data (baseline, blue) and the
counterfactual simulations (red, dashed), where the latter feeds the estimated shocks into a linear model version.

65
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