Germany's Macroeconomic Drivers During the Pandemic and Inflation Surge — Stefan Hohberger (2025)
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Paper by Stefan Hohberger, Germany's macroeconomic drivers during the pandemic and inflation surge, International Economics and Economic Policy (2025) 22:25, accepted 23 December 2024 and published online 15 January 2025. The abstract says the paper estimates a three-region macroeconomic model of Germany's GDP, inflation and wage growth, and that the results attribute the 2020-2021 downturn as primarily driven by domestic and global lockdown shocks and the 2021-2022 inflation surge as resulting from rising commodity prices, recovering global demand and supply-side pressures. It says wage growth per hour was shaped by opposing demand and supply forces and that the model's shocks closely align with external indicators. These are the author's model-based findings.
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“Germany's Macroeconomic Drivers During the Pandemic and Inflation Surge — Stefan Hohberger (2025).”
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International Economics and Economic Policy (2025) 22:25
https://doi.org/10.1007/s10368-024-00651-7
ORIGINAL PAPER
Germany’s macroeconomic drivers during the pandemic
and inflation surge
Stefan Hohberger1,2
Accepted: 23 December 2024 / Published online: 15 January 2025
© The Author(s) 2025
Abstract
This paper estimates a three-region macroeconomic model to analyse the key drivers
of Germany’s GDP, inflation, and wage growth during the COVID-19 pandemic and
inflation surge. Incorporating COVID-related demand and supply shocks, trade in
commodities, and endogenous ELB periods, the results highlight that (i) the 2020–
2021 downturn was primarily driven by domestic and global lockdown shocks, (ii) the
2021–2022 inflation surge resulted from rising commodity prices, recovering global
demand, and supply-side pressures, and (iii) wage growth per hour was shaped by
opposing demand and supply forces. The model’s estimated shocks closely align with
external indicators, supporting its empirical plausibility.
Keywords COVID-19 · Inflation · Open-economy DSGE model ·
Bayesian estimation · Germany
JEL Classification C51 · E32 · E52 · F41 · F45
1 Introduction
The COVID-19 pandemic and subsequent energy crisis have led to significant macroe-
conomic consequences for Germany and the global economy. The immediate response
to COVID-19 through the implementation of containment measures and widespread
lockdowns, brought many economic activities and international trade to a halt. As a
consequence, heightened uncertainties, disrupted global supply chains, and a sharp
decline of domestic activity accelerated the economic downturn, leading to a synchro-
nised global recession in 2020. Simultaneously, governments rolled out unprecedented
fiscal stimulus packages. The energy crisis in 2021–2022 has amplified the surge in
inflation, leading to a strong tightening of monetary policy.
B Stefan Hohberger
stefan.hohberger@hm.edu
1 HM Business School, Munich University of Applied Sciences, Munich, Bavaria, Germany
2 Centre for Applied Macroeconomic Analysis (CAMA), Australian National University,
Canberra, Australia
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This paper analyses the main drivers of the COVID-19 pandemic and subsequent
inflation period for Germany through the lens of an estimated structural macroeco-
nomic model. The model is a three-region monetary union DSGE model, consisting
of Germany (DE), the rest of the euro area (REA), and the rest of the world (RoW).
Following the approach of Cardani et al. (2022a), the model incorporates several
COVID-related demand and supply shocks to account for the lockdown-imposed drop
in consumption, fiscal stimulus packages, or short-time work arrangements. Addition-
ally, the model extends the use of commodities to account for the impact of rising
commodity prices during 2021–2022 along the lines of Giovannini et al. (2019).
The model is estimated using a parallelised slice sampling algorithm with data over
the period 1999q1–2023q4. Incorporating a large number of time series information
(observables) in the estimation process involves a large number of shocks, but allows
to assess the main drivers of macroeconomic variables and to provide a plausible
narrative of economic developments. Additionally, the model allows for endogenous
occasionally binding constraints to account for effective lower bound (ELB) periods
during the COVID-19 pandemic.
The estimation results highlight the pivotal role of transitory lockdown shocks in
driving Germany’s economic contraction and recovery during 2020–2021, with fiscal
policy measures providing significant stabilisation. The GDP recovery in 2021–2023
shows offsetting effects between domestic and foreign demand normalisation and a
slowdown in international trade, alongside growing supply chain bottlenecks. The
surge in CPI inflation in 2021–2022 is largely driven by domestic and global supply-
side disruptions and rising commodity prices. Adverse productivity and supply shocks
reflect global supply chain and capacity constraints. The estimated shocks closely align
with off-model indicators, reinforcing the empirical credibility of the findings.
The remainder of the paper is organised as follows: Section 2 reviews recent studies
related to modelling COVID-specific developments and the empirical literature on the
post-pandemic inflation surge. Section 3 presents stylised macroeconomic facts for
the German economy since 2008. Section 4 presents the model’s structure. Section 5
details the model solution, data, estimation methodology, and discusses the posterior
estimates. Section 6 examines the dynamic responses to shocks characteristic of the
COVID-19 period. Section 7 quantifies the main drivers of GDP growth, CPI inflation,
and wage growth in Germany. Section 8 compares model-based results with off-model
evidence. Section 9 conducts a sensitivity analysis without COVID-specific shocks.
Section 10 provides a summary and concludes the paper.
2 Related literature
The analysis relates broadly to two strands of literature. The first strand relates to
studies that have explored the impact of COVID-19 on economic dynamics, using
structural macroeconomic models. For the US, for example, Chen et al. (2020) extend
the New York Fed DSGE model, finding the pandemic recession primarily driven
by demand shocks, while (Corrado et al. 2021) attribute it to a combination of large
demand and supply shocks. Ferroni et al. (2024) propose a framework to estimate
a general ‘Covid shock’, which loads onto model wedges to capture the pandemic’s
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International Economics and Economic Policy (2025) 22:25 Page 3 of 49 25
unique macroeconomic dynamics, using data from professional forecasts to update
agents’ beliefs. In the Euro Area (EA), Cardani et al. (2022a) enhance the European
Commission’s DSGE model with COVID-specific shocks and financially-constrained
investors, highlighting the importance of ‘forced savings’ in explaining GDP growth
during the 2020 recession. Cardani et al. (2023) offer a model-based comparison of the
pandemic’s economic impact in the US and EA. Regarding German-specific studies,
Funke and Terasa (2022) examines the temporary VAT rate cut during 2020q3–2020q4
in a calibrated DSGE model for Germany, while (Hinterlang et al. 2023) simulate the
German fiscal stimulus packages.
The second strand relates to the growing number of studies with a focus on the
(global) inflation dynamics.1 For the EA, studies such as Neri et al. (2023) and Pasi-
meni (2022) identify rising commodity prices as key drivers, contributing to over half
of the post-COVID headline inflation. Pasimeni (2022) also highlights price pressures
in sectors with high import content, pointing to international supply chain disruptions.
Similarly, Hansen et al. (2023) attributes 40% of the EA’s change in the consumption
deflator in 2022 to import prices. Cardani et al. (2023) finds demand factors more influ-
ential for US inflation, while supply factors dominate in the EA. However, Giannone
and Primiceri (2024) find unexpectedly strong demand forces in the Post-covid infla-
tion, not only in the US, but also in the EA. Blanchard and Bernanke (2023) explore US
inflation during the pandemic, identifying commodity prices, sectoral demand shifts,
and supply constraints as key sources. This approach is applied to the EA and its mem-
ber states by Menz (2024) (Germany), Pisani and Tagliabracci (2024) (Italy), Ghomi
et al. (2024) (Spain), and Arce et al. (2024) (EA), all of whom find that commodity
price shocks and supply bottlenecks were the primary inflation drivers.
This paper contributes to this discussion along several dimensions: (i) It develops
and estimates a state-of-the-art multi-country DSGE model for the German economy
(DE-REA-RoW) using data from 1999q1 to 2023q4; (ii) it applies the methodolog-
ical approach of Cardani et al. (2022a) and incorporates heteroscedastic domestic
and foreign COVID-19 shocks, such as a domestic consumption- and investment-
specific lockdown shock, a shock to labour demand (labour hoarding) to account for
the wedge between hours worked and employees (intensive margin) due to short-
time work arrangements in Germany, and foreign risk shocks to account for spillover
effects; (iii) it extends the use of commodities in production and final consumption
demand to account for rising commodity prices; (iv) it allows for endogenous, occa-
sionally binding constraints to account for ELB periods; and (v) it provides off-model
evidence for the fit of the model-implied estimated shock pattern.
1 Given the focus on Germany and the EA, I provide only a brief summary of the growing body of studies
on US inflation dynamics, where the main drivers during the 2021–2022 US inflation surge are attributed
to a combination of binding supply chain constraints (Comin et al. 2023; di Giovanni 2022; Blanchard
and Bernanke 2023), fiscal stimulus (di Giovanni et al. 2023; Bayer et al. 2023; Jorda and Nechio 2023),
rising commodity prices combined with expansionary policies (Gagliardone and Gertler 2023; Reis 2022;
Blanchard and Bernanke 2023), and tight labour markets (Ball et al. 2022) that point to a non-linear Phillips
curve in explaining the surge of post-pandemic inflation (Benigno and Eggertsson 2023, 2024; Harding
et al. 2023).
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3 Stylised facts
Figure 1 presents stylised facts about selected macroeconomic variables in Germany
during the Global Financial Crisis (GFC) and the COVID-19 pandemic. First, the
V-shaped contraction of economic activity in 2020q2 was sharper than the more
Fig. 1 Stylised facts of the pandemic and recovery period in Germany. Note: Real demand components
(inflation rates) are shown in percentage-point deviations from the steady state, which is calibrated to 1.35%
(2%) per year, respectively. 1 on the y-axes correspond to 1 pp. Sources: Eurostat and Comext data
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International Economics and Economic Policy (2025) 22:25 Page 5 of 49 25
prolonged U-shaped recession of the GFC (Fig. 1a). Unlike the 2008–2009 reces-
sion, both private consumption and investment declined simultaneously during the
2020 pandemic. The model accounts for these patterns by incorporating transitory
consumption- and investment-specific lockdown shocks during 2020.
Second, despite a significant decline in hours worked, the number of employees
remained relatively stable during the onset of the pandemic (Fig. 1b). The gap between
hours worked and employment during can be attributed to the introduction of job
retention schemes (short-time work), which were designed to mitigate employment
losses despite the sharp drop in GDP. The model addresses the wedge by introducing
a labour hoarding shock that reduces effective hours worked.
Third, Fig. 1c illustrates that CPI and GDP inflation (left axis) rose significantly
from 2021 onward, peaking at 8% and 6.8% in 2022q3 and 2023q2, respectively,
when accounting for the 2% steady state. The co-movement between GDP and inflation
during the 2020 lockdown, similar to the 2008–2009 recession, indicates a stronger
initial demand-side driver (positive correlation). Commodity prices (right axis) fell at
the onset of the pandemic, but surged in 2021–2022 due to the pandemic recovery,
global supply chain bottlenecks, geopolitical tensions, and, ultimately, Russia’s war
against Ukraine. By 2023, oil and energy prices had dropped significantly to pre-crisis
levels, contributing to the decline in CPI inflation. The model incorporates the most
relevant time series, including commodity prices, GDP deflator, CPI inflation, sector-
specific goods prices, and import/export prices, to capture supply-side disruptions
through various disturbances.
4 The model
The structural setup builds upon the model used in Hohberger et al. (2020) and Cardani
et al. (2022b). The economy of DE consists of various sectors including households,
firms that operate domestically or in the import–export sector, as well as a government
and a central bank. In contrast, the regional blocks of REA and RoW have a simpler
structure. Within the DE block, there are two types of households: Ricardian and
liquidity-constrained (LC). The former have access to financial markets, smooth their
consumption, and own the firms through equity. LC households do not have access
to financial markets and consume all their disposable wage and transfer income each
period. Both household types supply labour to domestic firms at a common wage
established by a labour union with monopoly power.
In the DE production sector, firms operate under monopolistic competition and pro-
duce a variety of differentiated intermediate goods. These intermediate goods are then
aggregated into domestic value added by perfectly competitive firms. In the subsequent
stage, total domestic output is produced by perfectly competitive firms by combining
the domestic value added with commodities. The RoW region is the sole producer
of commodities, which includes both energy and non-energy commodities. In the
import sector (import retailers), perfectly competitive firms purchase goods from for-
eign regions and assemble them into a final import good, which is then combined with
domestic output by final good packagers to create final aggregate demand-component
goods.
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The DE government purchases final goods and provides lump-sum transfers to
households. To finance its expenditure, the government issues debt and imposes dis-
tortionary taxes on labour, capital, and consumption, along with non-distortionary
lump-sum taxes. Monetary authorities set short-term nominal interest rates by follow-
ing a Taylor rule, which reacts to inflation and the output gap.
Following the methodological approach in Cardani et al. (2022a), the model
incorporates the following COVID-specific demand and supply disturbances: (1) A
transitory consumption-specific lockdown shock in DE and REA, εttC , to capture the
lockdown-imposed drop in consumption, (2) a transitory labour demand shock (labour
hoarding), εtt N , to capture short-time work arrangements, i.e. to distinguish between
hours worked and hours paid, (3) a transitory VAT shock, εttvat , to capture the reduc-
tion of the German VAT consumption tax during 2020q3–2020q4, and (4) a transitory
investment-specific lockdown shock, εtt S , to capture the lockdown-imposed drop in
investment demand. To capture COVID-specific demand contraction in the simplified
REA and RoW model blocks, the model also incorporates additional foreign shocks
to the time preference (risk shock). The following description highlights the primary
aspects of the model, with further details available in Appendix 1.
4.1 Households
There is a continuum of households, indexed by j ∈ [0, 1], whereas a share of house-
holds (Ricardians ωs ) owns firms and trades assets. The remaining share (1-ωs ) is
liquidity-constrained (c) and consumes its entire disposable income in each period
(‘hand-to-mouth’). Household preferences are defined over consumption and leisure.
Additionally, Ricardian utility is determined by the holdings of financial assets.
4.1.1 Ricardian households
Ricardian preferences are given by the infinite horizon expected life-time utility:
∞
U sj = E 0 (β̃t )t u sj,t (.), (1)
t=0
where β̃t is the stochastic discount factor.2 Ricardian households have full access to
financial markets, which allows them to accumulate wealth, A j,t , consisting of domes-
rf
tic private risk-free bonds, B j,t , domestic government bonds, B G
j,t , one internationally
traded bond, B W j,t , and internationally traded shares, P SS :
t j,t
rf
A j,t = B j,t + B G
j,t + e RoW ,t B j,t + Pt S j,t
W S
(2)
2 β̃ = β exp(ε c ) features a shock to the subjective rate of time preference (saving shock) ε c .
t t−1 t
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International Economics and Economic Policy (2025) 22:25 Page7of49 25
where P,° is the nominal price of shares. The international bond is issued and denomi-
nated in foreign currency, therefore, the financial wealth in terms of domestic currency
is also influenced by the nominal exchange rate, erow,t-
Ricardian households gain utility from consumption, Ci, * , and experience disu-
tility from labour, Nin * , as well as from holding risky financial assets, Us, _,- The
instantaneous utility function of savers, u*(.), is defined as:
Cs NS UA 4 _ (Ci, — [© — A(Ch_y — eff)?
Wo Jit it? peat) = 1—6
N
Ne? (Cr)! FNS , + ef Nyl+e
1+0N
A
9 Uj, t-1
= (C¥, = 6 = h(Ce_ — &(54)) ? pow @)
P,
where C? = Io Cc j ,2j, h measures the strength of external habits in consumption,
and w’ is the stochastic weight of the disutility of labour. eu captures a labour supply
shock. é/ © captures the non-persistent lockdown shock (forced saving) that constrains
consumption outside of habit persistence, ¢ v captures a labour hoarding shock.* The
disutility of holding risky financial assets, uA, _,, takes the following form:
A _ bo B G bwo bw Ww
Uji = (« + ef) BS, + (a + oP erow. By
a”! (erowr—-1N FA;-1)"
Y
2 PYY,—
+(e 405 JPL Si. A)
Internationally traded bonds are subject to transaction costs which are a function of
the average NFA position relative to GDP. The asset-specific risk premium depends on
an asset-specific exogenous shock e*, x € {B, S, bw}, and an asset-specific intercept
a*, x € {bg, So, bwo}. By incorporating a disutility for holding risky assets, the model
reflects households’ preference for safe assets, such as risk-free short-term bonds. This
preference creates an endogenous gap between the returns on risky assets and those
on safe bonds (Albonico et al. 2019).
The j’” Ricardian household faces the following budget constraint:
Peete’ 4 Aj, = (L—tN) WANS, +e “y4a4+it: tp _j + +i7 By, 4
+ (PS + PY D))Sjr-1+ +i, Jerow Bert
+}, — tax}, (5)
3 Aggregate consumption, C;, in the second term of the right-hand side is introduced as normalisation to
ensure a balanced steady-state growth path.
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25 Page 8 of 49 International Economics and Economic Policy (2025) 22:25
where porat is the private consumption deflator,+ W, denotes the nominal wage
rate, N j _, 1s the employment in hours, T?, are government transfers and taxi , lump-
sum taxes paid by savers. if , iG , and i” are returns on domestic private risk-free
bonds, domestic government bonds, and internationally traded bonds, respectively.
Transfers include unemployment benefits, BEN; ,, defined as the gap between actual
and potential hours multiplied with benefit replacement rate, t”:
T;, = BEN} ,+0'P,T,, (6)
BEN}, = c"W.(N?" —(N5, +1"). (7)
Ricardian households receive nominal profits in the form of dividends, D;. Gross
nominal return on shares S; is defined as:
PS + PD
t-1
Ricardian households maximise the present value of the expected stream of future
utility by choosing the amount of consumption, C jj ,, and next period asset holdings,
Bi ' BY, Sits By, subject to their budget constraint (Eq. 5), The optimality condi-
tions can be found in Appendix A.1.
4.1.2 Liquidity-constrained households
Liquidity-constrained (LC) households do not have access to financial markets. Their
instantaneous utility function, u°(.), is:
(Ci, — fC — A(Cy_y — ef©,))h-%
1-@
c Cc Cy
Wit Cje Ni) =
NU 1-0
or és (Cr) c tNy1+0N
_ Tn Nit + €,"") . (9)
Ineach time period, they consume their entire net disposable income, which consists
of after-tax (paid) labour income and lump-sum transfers from the government:
13
1
Pomc’ = (1— tN) WANS, + e)%) +76, —taxe, + PO («° -@ y ef).
i=8
(10)
During the COVID-19 pandemic, this constraint is eased such that even LC house-
holds can save (forced savings), ¢/ ©, which will be gradually spent post-pandemic.
4 povrar is the VAT adjusted private consumption deflator, pCvvat = (1+ 4+ ef VAT) pC. where
© is the tax rate on consumption (VAT) and ef VAT captures the VAT-tax cut during 2020q3—2020q4
implemented by the German government.
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International Economics and Economic Policy (2025) 22:25 Page 9 of 49 25
4.1.3 Wage setting
Households supply differentiated labour services, N rj,t , with r = {s, c}, in a monop-
olistically competitive labour market. A labour union aggregates labour hours from
both types of households into a unified labour service and supplies it to the intermedi-
ate goods-producing firms. Given the same labour demand schedule, each household
works the same average number of hours. The union maximises the weighted average
of the members’ discounted future utility stream with respect to the wage, subject to
the combined budget constraints of the households and the demand for differentiated
labour by intermediate-goods producers.
Nominal wage rigidity takes the form of quadratic adjustment costs for changing
w n
nominal wages according to ad jtw = γ (σ2 −1) Wt Nt (πtw − π w )2 , where σ n is the
inverse of the steady gross wage markup and πtw is the wage inflation. Real wage
rigidity is modelled in the spirit of Blanchard and Galí (2007), implying a gradual
adjustment of past reals wages to changes in the price level. The wage rule is determined
by equating the marginal utility of leisure, UtN , to the weighted average of the marginal
utility of consumption, λt , times the real wage adjusted for a wage markup. The wage
equation is:
1−γ wr γ wr
w UtN Wt Wt−1 Wt
μ − τ u C,vat − μw
t (1 − τ ) N
= (1 − τ N ) ,
λt Pt C,vat
Pt−1 PtC,vat
(11)
where μw
t is the cyclical gross wage markup:
w
∂ad jtw λt+1 1 ∂ad jt+1
μw
t =γ
w
− β Et + εtU . (12)
∂ Wt λt π C,vat
+1 ∂ W t
t+1
μw is the steady-state gross wage markup, γ w and γ wr represent the degree of nominal
and real wage rigidity, respectively, and εtU captures a labour supply shock (wage
markup). The marginal utility of leisure is defined as: UtN = ω N (Ct )1−θ (Nt )−θ , and
N
λt the weighted average of the marginal utility of consumption.
4.2 Production sector
The total domestic output is a combination of domestic value added and commodities.
Value added consists of a bundle of differentiated goods produced by monopolistically
competitive firms, which utilise capital and labour in their production processes.
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4.2.1 Total output demand
Perfectly competitive firms produce total output, O;, by combining value added, Y;,
with (imported) commodities, C O;, using the following CES production function:
0?
Gon
o2-1 | o?-l
O
1 o. 1
0, = (a _ s©) expler?)) yy a 4 (s° exp(ef))’ (CO,)
(13)
° represents the commodity input share, influenced by the exogenous process ef 0.
o° refers to the elasticity of substitution between factors. Each firm maximises its
expected profits:
gf
max P20, — PYY, — P©°CO,, (14)
Y;,CO;
subject to the production function Eq. 13. The first-order conditions for the demand
for value added and commodities are:
PY \-0°
_ co co t
¥, = (1 —s©) exp(e' (50) Or, (15)
pce —o?
— .cO co t
CO, = 5° exples (Sr) O;. (16)
Commodities are assumed to be produced only by RoW. Consequently, all com-
modities used by Germany are imported from RoW, and their price is taken as given:
Pe? = eRow.t PRows + TOO Pr, (17)
where €row,r is the exchange rate, t©9 and P¥°® are the excise duty and the (global)
GDP trend deflator, respectively. The total output aggregate price index is given by:
1
° 0 T-o?
Po? _— ja _ seP yO) PY ye -1 + s©P ul? (PO)? *| . (18)
4.2.2 Value added and intermediate goods producers
Value added, Y;, is produced by firms operating in a perfectly competitive market.
These firms combine a variety of differentiated goods, Y;,+, which are produced by
firms in a monopolistically competitive market. The differentiated goods are produced
using a Cobb-Douglas production function with labour, Nj; +, private capital, Kj +-1,
and public capital, K ane as input factors:
a
Yie= [ A? (Nin +e!) — FN) (CU; 1K; 1)! -*(KE 1)! = AY FC. (19)
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International Economics and Economic Policy (2025) 22:25 Page 11 of 49 25
α is the steady-state labour share, AtY is an exogenous common labour-augmenting
stochastic productivity scalar, CUi,t and F N are firm-specific levels of capacity utilisa-
tion and labour overhead, respectively. FCi represents fixed costs in production. Gross
investment, Ii,t , drives the law of motion for private capital K i,t = Ii,t +(1−δ)K i,t−1 ,
with the depreciation rate δ. Public capital, K i,t−1
G , follows an analogous accumulation
equation with output elasticity αG . AtY is a non-stationary process with two types of
technology shocks, εtA and εtG A . They are related to a non-stationary process and its
autoregressive component ρ A :
log(AtY ) − log(At−1
Y
) = gtA + εtA , (20)
gtA = ρ A gt−1
A
+ (1 − ρ A )g A + εtG A , (21)
where gtA and g A are the time-varying growth and the long-run growth of technology,
respectively.
The model incorporates a transitory labour demand shock (labour hoarding, εtt N )
to capture short-time work arrangements during the onset of COVID-19. Specifically,
employees working fewer hours while remaining employed, thereby introducing a
wedge between hours worked (production function) and hours paid (wage income). It
enters as a transitory shock to hours worked. Dividends are defined as:
Di,t = Pi,t
Y
Yi,t − Wt (Ni,t + εtt N ) − PtI (Ii,t + εtt S ) − ad ji,t , (22)
where Wt and Pi,t I are the nominal wage rate and the price of investment goods, respec-
tively. εtt S represents an investment-specific lockdown shock. Following (Rotemberg
1982), firms face quadratic adjustment costs, ad ji,t , associated with the output price,
Y , labour input, N , private investment, I , and capacity utilisation, CU . The
Pi,t i,t i,t i,t
adjustment cost definitions and optimality conditions can be found in Appendix A.2.
4.3 International trade
Final good packagers combine domestic output and imported goods to supply different
sectors in the economy with components of aggregate demand. Imported goods are
a bundle of imports sourced from different origins and are put together by import
retailers.
Final good packagers
The final aggregate demand-component goods are manufactured by perfectly com-
petitive firms that combine domestic output, OtZ , with imported goods from REA
and RoW, MtZ , using a CES production function. The demand for final goods,
Z = {C, G, I , I G , X }, comes from households and the government, private and
public investors, as well as exporters of final goods, respectively:
σz
pZ σ z −1 σ z −1
(1 − stM,Z ) σ z (OtZ ) σ z + (stM,Z ) σ z (MtZ ) σ z
1 1 σ z −1
Zt = At , (23)
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Zz
o* represents the elasticity of substitution of imports, and A? is a shock to produc-
tivity in the sector producing goods, Z. sM isa sector-specific stochastic import
share, where 3M 2 exp(eM 2) 5M ‘2 sM-2 denotes the steady-state import share
of Z. Demand for domestic output and imported goods is given by:
2 Gt PP, -0
OF = (AP (1s) (45) © 2, (24)
P;
Zz Gt PM \ -o%
MZ = (AP y's (2) 2, (25)
t
The price deflator associated with the demand components is:
1
Pe = arya = sf \(POye + stop (26)
Total non-commodity imports are defined as:
M, = Mo + M/ +ME+M/¢ + MX. (27)
Import retailers
Final non-commodity imports are produced by perfectly competitive firms that
combine goods from the foreign regions into a final import good. The demand for
goods from country / is:
PM. —oFM size
M = (7) 28
eS ht pM " size] 8)
and the import prices deflator is:
ru | i-ot™
pM = [strep . (29)
1
o'™ represents the price elasticity of demand for country /’s goods, and pM is the
price of its good. The good from country / is purchased at the export price of country
l, Px, Hence, the import price for the domestic country is defined as:
PM =e Pi. (30)
4.4 Fiscal policy
The government raises taxes on consumption, t©, corporate profits, t*, lump-sum
taxes, tax;, and wage income tax, 7N . & VAT is the COVID-related shock to VAT
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during 2020q3-—2020q4. It finances consumptive purchases, G;, investments, 1G;,
and transfers, T;. The tax on commodity imports, t©9 is fixed. t*% denotes a labour
hoarding subsidy. Nominal debt evolves as:
S=(1+i°)BO, —RO+PG,+ PIG, + PT, (31)
where R@ are the nominal government revenues:
= (© + 247) PC +8 (Pr¥s — WiC; + 8,") = 5P,Ki-1) (32)
+ oN (N, + ef!) W, + 1©° P©°CO, + oN Ww, ((N, 4 ef) Ni) + tax;.
(33)
Lump-sum taxes, tax,, adjust residually as government budget closure:
_ [ ABE
tax, = p! tax;_, + nf" —— — DEFTAR
Y;-1 1
BG
+8" (—+*_ — BTAR) +2'®, (34)
Y;— Pe 1
where DEFT AR and BT AR are the targets on government deficit and government
debt, respectively, and e/“* captures a shock. The government increases (decreases)
taxes when the level of government debt and the government deficit is above (below) the
debt and deficit target. On the spending side, government consumption, G;, investment,
IG;,, and transfers, T; follow AR(1) processes and are subject to idiosyncratic shocks
(e%, e!©, and’).
4.5 Monetary policy
Monetary policy follows a Taylor (1993)-type policy rule subject to an ELB constraint.
The target interest rate, PA, , responds sluggishly to (uae annualised) deviations
of EA-wide CPI inflation (7; ee ) and EA output gap re? BA, ‘) from their respective
target levels?:
. > j . > C,QA -~C,QA y
PAs ~1 = Pga@igas—-1 —i) + rica) |e 40-25 ( p45 Fe )+ neale PA ai
(35)
i =7 +7 is the steady-state nominal interest rate, which equals the sum of the
steady-state real interest rate and trend inflation. The policy parameters (p', 7/7, n/)
5 Potential output, Y pa Ar is defined as the output level that prevails when labour input equals steady-state
per capita hours worked, the capital stock is utilised at full capacity, and TFP equals its trend component.
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capture interest rate inertia and the response to the EA inflation and EA output gap,
respectively.
The effective policy rate, i E A,t , corresponds to the target nominal short-term rate
as long as the latter is above the ELB, (i L B ). The effective policy rate satisfies:
i E A,t = max{i EnotA,t , i L B } + εiE A,t , (36)
where εiE A,t captures a monetary policy shock. More details on the ELB treatment
will be explained in Section 5.5.
4.6 Commodities
Commodities are traded at destination-specific prices, influenced by exogenous sup-
ply shocks.6 The total demand for commodities, C Ot , comprises household energy
consumption, CtE , and the demand for industrial supplies in final goods production,
I St . Following (Cardani et al. 2023), final household consumption is represented as a
CES aggregate of commodities used for consumption and final manufactured goods
CtF G :
σE
1 σ E −1 1 σ E −1
σ E −1
Ct = (stE ) σ E (CtE ) σ E + (1 − stE ) σ E (CtF G ) σ E , (37)
where stE represents the energy share and σ E the elasticity of substitution.
4.7 Closing the economy
The resource constraint of the DE economy is:
Yt PtY + τ C O C Ot PtY 0 = PtC Ct + PtI It + PtI G I G t + PtG G t + T Bt , (38)
where T Bt is the trade balance, defined as the difference between exports and (non-
commodity) imports:
si zel
T Bt = PtX X t − M
Pl,t Ml,t − PRoW
CO
,t C O RoW ,t e RoW ,t . (39)
si ze
l
Domestic holding of the internationally traded bond, BtW , evolves according to:
e RoW ,t BtW = (1 + i t−1
bw
)e RoW ,t Bt−1
W
+ T Bt + I T R PtY Yt . (40)
6 Unlike (Giovannini et al. 2019), this model incorporates an endogenous supply equation where commodity
demand affects global commodity prices.
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IT R represents international transfers that allow to calibrate a non-zero steady state
of the trade balance. The sum of all countries’ net foreign assets are zero:
Y> NFA/,size; = 0. (41)
1
4.8 The REA and RoW blocks
The REA and RoW (subscript k = REA, RoW) model blocks include a budget
constraint for the representative household, demand functions for both domestic and
imported goods, a linear production technology, a New Keynesian Phillips curve,
and a Taylor rule. Both regions do not take capital accumulation into account. The
simplified model blocks are subject to various shocks, including those affecting labour
productivity, price markups on the final output, the subjective discount rate, the relative
preference for domestic versus imported goods, and monetary policy surprises.
The household budget constraint in the REA, as a commodity importer, is defined
as:
YreasPReas + 1©?COrEAt PY? = PrreatCREAs +TBreat, (42)
where t©°C Ope AtP YO represents the excise duty.
Final aggregate demand, C;,;, is a combination of domestic output, Y, ia and
imported goods, M@ fa , using the following CES function:
c
oy -!
ot 1 a
(VG) & + (el sl) (ME) % |" i (43)
1
P M My ot
Cer = AP, [C= eft sit)
Cc
o, represents the import elasticity of substitution, A? is a shock to productivity in
the sector producing goods, C, and sM is the import share. The demand for domestic
and imported goods is obtained from profit maximisation:
Y
c c_ Py —O;
YE, = (AR, )% ‘(1 ett st") (Se) Cer, (44)
k,t
Coe P98
Me, = (AR, )” ‘etist! (Se) Cit (45)
k,t
where the consumer price deflator, PL, 1S:
1
Cc. ie _ oe | Hoh
PE, = (A?,) f= etfstcre % + ef st (PY)! “| (46)
The good producers use labour as input factor, Y;.; = Al /Nk,t, where Al; repre-
sents trend productivity. The price-setting equation follows a New Keynesian Phillips
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curve:
_ Akt+1 _ Vx,
Thy KE = BIC bret — FE) + Op los(S*) + ek (47)
where Ax¢ = (Ct — heCx1—1) is the marginal utility of consumption, and Eh, is
a cost-push shock.
REA and RoW total nominal exports are defined as: Pex kt = PA Mik.
with the bilateral export price being defined as the domestic price subject to a bilateral
price shock, P PN kta = expe) Pe
Combining the two regions’ FOCs with respect to international bonds derives the
uncovered interest parity (UIP) condition:
CROW,EA 1 . .
b,] BEAN reo = (l+igartepy pap ton
€RoW,EA,t PL, Yeas
(48)
where a , captures a euro exchange rate shock (shock to the bond premium between
EA and RoW), and ae “1 is a debt-dependent country risk premium on NFA holdings
to ensure long-run stability of the model (Schmitt-Grohe and Uribe 2003).
4.9 RoW commodity supply
The RoW exclusively supplies two distinct commodities, namely oil, CO? and
non-oil commodities, C O/5, such as natural gas and materials, to domestic and for-
eign firms. 660 captures exogenous commodity supply shocks. The RoW producer
combines oil (Oil) and non-oil (J $) commodities into bundles, C O, that are either
exported to DE and REA or used domestically. The price of the commodity bundle is
specific to its destination and includes a shock term, ef, ; co , where / = (DE, REA),
aiming to reflect price variations due to differing commodity baskets. Therefore:
ere) ; Jo CO 1
Pe? _ = «f “fs pip") +(1— s?")(PIS) yer, (49)
co co 1
: \ l-o . l-—o 1
poo _ [so"(Re") +(1 — 52")(PIS) °° (50)
Commodity prices are exogenous and follow:
P,
poe = 500° where CO=(Oil, IS) (51)
t
where ACO is the exogenous commodity-specific productivity technology.
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5 Model solution and econometric approach
5.1 Model solution
The following non-linear system summarises the observation and state equations of
the model:
yes — Wi (O)S;, (52)
Si =Wi(@)S;-1+ O.)er, er ~ NO, O:1) (53)
In observation Eq. 52, yobs denotes the vector of observables at time ¢, and ¥;(©)
links the model variables to the data. The state Eq. 53 describes the transition of the sys-
tem’s state variables, S,;, where Y; (©) and ©, are the coefficient matrices. Following
(Cardani et al. 2022a), the model shocks, ¢;, follow a normal distribution with time-
varying covariance matrix Q;/, such that the state Eq.53 incorporates deterministic
heteroscedasticity:
COVID for t € {2020q1 : 202194},
0, = Q ort € { q q4} (54)
Q otherwise.
For the pandemic period 2020q1-2021q4, 0, = Q©?!” incorporates temporary
COVID-specific shocks, whereas prior to COVID-19, Q; = Q, implies zero standard
deviations (and zero expectations) for these shocks.
5.2 Data
The model is estimated quarterly, using data for Germany and the Euro Area (EA19)
from Eurostat. Bilateral trade flows are based on GTAP trade matrices, covering goods
and services. Annual data for the rest of the world (RoW) are sourced from the
IMF’s International Financial Statistics (IFS) and World Economic Outlook (WEO)
databases. The model includes 41 observed series and 41 exogenous shocks. Details
on the time series are provided in Appendix 4.
5.3 Estimation procedure and filtering
The estimation proceeds in three steps:
1. A subset of parameters is calibrated to align with historical long-run properties,
such as steady-state ratios. The heteroscedastic filter enables the ex-ante specification
of shock standard errors for each period between 2020q1 and 2021q4. The timing of
the COVID-related shocks is calibrated to reflect the imposed lockdown periods and
policy-induced VAT reductions, as detailed in Table 2. Section 9 includes a sensitivity
analysis examining the model’s fit and economic narrative in the absence of COVID-
specific shocks.
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2. The remaining parameters and shocks are estimated using data over the sample
period 1999q1–2023q4. The full-sample estimation procedure incorporates the estima-
tion of heteroscedastic COVID-specific variances during the period 2020q1–2021q4,
thereby allowing for time-varying shock disturbances Q t .7 The likelihood function
(evaluated by implementing the Kalman filter) and the prior distribution of the param-
eters are combined to calculate the posterior distribution. The posterior Kernel is then
simulated numerically using the slice sampler algorithm as proposed by Planas et al.
(2015).8 We use the Dynare software to solve the linearised model and to perform the
estimation Adjemian et al. 2024.
3. The model accounts for endogenous effective lower bound (ELB) periods using
the OccBin approach by Guerrieri and Iacoviello (2015). More precisely, the paper
employs a piecewise linear Kalman filter, as in Giovannini et al. (2021), to identify
the structural shocks until 2023q4 given the parameter estimates, accounting for ELB
periods.
5.4 Calibrated parameters and posterior estimates
Steady-state ratios in the model are calibrated to match the average historical data for
DE, REA, and RoW. The steady-state shares of DE, REA, and RoW in world GDP
are 5.4%, 14.5%, and 80.1%, respectively. The trade-related parameters, specifically
the degree of openness and import preferences, reflect the average import content of
demand components as computed by Bussière 2013. For Germany, the steady-state
ratios of private consumption, investment, and government expenditure to GDP are
55%, 19%, and 21%, respectively. The global trend GDP growth rate and trend inflation
rate are 1.25% and 2% per year, respectively. The steady-state share of Ricardian
households is calibrated at 61%, based on Dolls et al. (2012). Table 3 in Appendix 2
provides an overview of calibrated parameters.
Table 1 reports prior and posterior estimates for selected model parameters. The
estimated EA monetary policy parameters suggest a strong response to EA inflation
(1.78) compared to the EA output gap (0.05), together with relatively high interest
rate inertia (0.91). Estimated habit persistence is 0.90, implying a slow adjustment
of consumption to changes in income. Risk aversion and the inverse labour supply
elasticity are 1.33 and 3.72, respectively, and similar to those in the literature (e.g.,
Hohberger et al. 2020; Cardani et al. 2022b). Concerning international trade estimates,
the price elasticity of import demand is 1.93, and the price elasticity of commodity
demand is 0.40. The posterior estimates also suggest sticky prices (40.8), wages (17.3),
and investments (38.2). The estimated parameters for REA and RoW can be found in
7 Cardani et al. (2022a, 2023) employ a two-step approach, where the parameters are estimated using data
only until 2019q4 in a first step. In the second step, they estimate the variances of heteroscedastic COVID-
specific shocks using data for the pandemic period (2020q1–2021q4), while keeping all other parameters
unchanged by initialising the system’s state and covariance matrix at their estimates from the first step.
8 The slice sampler algorithm was introduced by Neal (2003). Planas et al. (2015) reconsider the slices
along the major axis of the ellipse to better fit the distribution than any Euclidean slices. The slice sampler
has been shown to be more efficient and to offer better-mixing properties than the Metropolis-Hastings
sampler Calés et al. 2017. The slice sampler has been used, e.g., by Giovannini et al. (2019) and Hohberger
et al. (2019, 2023).
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Table 1 Prior and posterior distribution of key estimated DE model parameters
Prior distribution Posterior distribution
Mean
Distr St.Dev DE
EA monetary policy
Interest rate persistence ρi G 0.85 0.91
0.05 (0.88, 0.93)
Response to inflation ηi,φ G 2.00 1.78
0.20 (1.56, 2.19)
Response to GDP ηi,y G 0.10 0.05
0.04 (0.03, 0.11)
Preferences
Consumption habit persistence h B 0.50 0.90
0.20 (0.83, 0.92)
Risk aversion θ G 1.50 1.33
0.20 (1.16, 1.70)
Inverse Frisch elasticity of labour supply θN G 2.50 3.72
0.50 (2.21, 4.86)
Import price elasticity σz G 2.00 1.93
0.40 (1.64, 2.19)
Oil price elasticity σo G 0.5 0.40
0.1 (0.32, 0.48)
Nominal and real frictions
Price adjustment cost γP G 20 40.8
12 (33.7, 49.9)
Nominal wage adjustment cost γw G 20 17.3
12 (9.2, 19.4)
Real wage rigidity γ wr B 0.47 0.85
0.20 (0.54, 0.89)
Employment adjustment cost γN G 20 1.8
12 (1.5, 2.3)
Capacity utilisation quadratic adj cost γ CU ,2 G 0.003 0.003
0.0012 (0.002, 0.005)
Investment adjustment cost γ I ,2 G 40 38.2
25 (19.1, 67.5)
Fiscal policy
Lump-sum tax persistence ρ tax B 0.85 0.82
0.06 (0.75, 0.89)
Tax response to deficit ηde f B 0.03 0.03
0.008 (0.02, 0.04)
Cols. (1)–(2) list model parameters. Cols. (3)–(4) indicate the prior distribution function (B: Beta distri-
bution; G: Gamma distribution). Col. (5) shows the mode and the 90% HPD intervals of the posterior
distributions of model parameters
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Table 2 Prior and posterior distribution of estimated COVID-specific innovations
Prior distribution Posterior
distribution
Mean
Distr St.Dev Time
DE COVID-specific shocks (standard deviations in %)
Consumption-specific lockdown shock ε tC G 5 [20q1 - 21q3] 4.75
2 (4.03, 7.36)
Investment-specific lockdown shock εt S G 5 [20q1 - 20q2] 2.27
2 (1.10, 5.80)
labour hoarding shock εt N G 5 [20q2 - 21q1] 2.57
2 (1.85, 4.77)
VAT-tax shock ε t V AT G 2 [20q3 - 20q4] 1.70
0.8 (0.91, 3.03)
REA COVID-specific shocks (standard deviations in %)
Consumption-specific lockdown shock ε tC G 5 [20q1 - 20q2] 6.97
2 (4.99, 9.78)
Risk shock ε tβ G 5 [20q1 - 21q4] 8.30
2 (3.91, 10.13)
RoW COVID-specific shocks (standard deviations in %)
Risk shock ε tβ G 5 [20q1 - 21q4] 13.76
2 (12.63, 17.44)
Note: The table reports the mode and the standard deviation (in %) of the posterior distributions of DE,
REA, and RoW COVID-specific shock innovations. Time refers to the ex-ante assumed periods of the
heteroscedastic shock
Table 4 in Appendix 2. Tables 5 and 6 in Appendix 2 report the main estimated shock
processes for DE, and REA and RoW, respectively.
Table 2 provides the posterior estimates of pandemic-specific shocks, revealing a
mix of demand-side (lockdown) and supply-side shocks (labour market).9 Specifically,
it shows a significant incidence of consumption-specific lockdown shocks (4.75%)
and substantial labour hoarding shocks (2.57%), reflecting Germany’s adopted labour
market policies. The estimated VAT cut in 2020q3–2020q4 is 1.7%. The simplified
REA and RoW structure suggests persistent saving shocks (risk shocks) to capture
the COVID-19 pattern during 2020 and the recovery from 2021 to 2022. Figure 12 in
9 For robustness, I incorporated additional domestic and foreign heteroscedastic productivity shocks for
the pandemic period (2020q1–2021q4) and the inflationary period (2022q1–2023q4) to assess whether
the model might be missing key supply-side drivers not captured by the standard shocks. The analysis
indicates that these additional shocks are weakly identified and have only a marginal impact on GDP and
inflation compared to the standard incorporated and estimated supply shocks. This result suggests that the
model effectively captures the dynamics of both the pandemic and the inflationary surge using the observed
supply-side series and shocks.
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Appendix 2 provides the prior and posterior distributions of the estimated COVID-
specific shocks.
5.5 ELB environment—non-linear smoothing
The model accounts for binding ELB periods using the piecewise linear Kalman filter
algorithm from Giovannini et al. (2021). Based on the model’s parameter estimates, it
identifies structural shocks that account for endogenous ELB periods using the OccBin
approach of Guerrieri and Iacoviello (2015), generating a sequence of smoothed vari-
ables and shocks consistent with the occasionally binding constraint.10 The sequence
of regimes for Germany, indicating whether the ELB is binding or not, is shown in
Table 7 in Appendix 2.
6 Dynamic transmission of shocks
This section examines the estimated dynamic effects of shocks characteristic of the
COVID-19 pandemic and the subsequent inflation surge. For the pandemic period, it
compares the COVID-specific shocks with their standard counterparts in a scenario
where the ELB on the short-term nominal interest rate is binding.11 Specifically, it
presents generalised impulse response functions (GIRFs), which are simulated as
follows: The starting point of the simulations is set to 2020q2. Based on the regime
sequence in Table 7, a period where the ELB is binding for 5 more quarters. Remove the
specific shock (e.g., the consumption-specific lockdown shock) and simulate the model
with all remaining shocks. Then, reintroduce this shock and rerun the simulation. The
difference between the two scenarios yields the GIRFs under the ELB (shown as
dashed lines in the Figures).
All shocks are simulated using one estimated standard deviation. Each panel illus-
trates the dynamic responses of real GDP, the policy rate, CPI inflation, private
consumption, private investment, total hours worked, the real interest rate, the real
effective exchange rate (REER), and the trade balance-to-GDP ratio. Real variables
are shown as percent deviations from their steady states, while the policy rate (annu-
alised), CPI inflation (annualised), and the trade balance-to-GDP ratio are expressed
as deviations in basis points and percentage points, respectively.
6.1 Pandemic-related responses
This subsection presents the dynamic responses to the estimated COVID-specific
disturbances, namely (i) the transitory consumption-specific lockdown shock (forced
10 Similar ELB implementations are found in Hohberger et al. (2019) and Croitorov et al. (2020).
11 When the ELB is binding, the economic contraction during the COVID-19 period, marked by declining
output and inflation, is not mitigated by expansionary monetary policy. In contrast, during 2022–2023,
negative supply-side shocks driving up inflation and slowing economic activity are compounded by monetary
tightening aimed at reducing inflation.
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saving, (ii) the shock to labour hoarding, (iii) the investment-specific lockdown shock,
and (iv) foreign risk shocks in REA and RoW.
Transitory forced saving shock (consumption-specific lockdown)
Figure 2 compares the estimated dynamic responses to the transitory consumption-
specific lockdown shock (forced saving) and the standard persistent savings shock.
The transitory lockdown shock (dashed), combined with a binding ELB on interest
rates, leads to an 8.5% drop in private consumption and a 3.6% drop in real GDP,
both lasting for one quarter (2020q2). The fall in GDP causes a temporary dip in
employment (hours worked), although the decline is mitigated by labour adjustment
costs. In the short term, the trade balance improves due to lower domestic demand and
reduced imports. It is important to note that this transitory lockdown shock captures
both demand-side effects, such as precautionary household behaviour, and supply-
side effects, such as forced business closures. The relatively modest impact on CPI
inflation reflects the shock’s temporary nature and the presence of sticky prices. Unlike
persistent savings shocks, transitory shocks do not influence medium-term inflation
expectations, which play a crucial role in determining actual inflation.
Fig. 2 Dynamic responses to saving shocks. Note: The trade balance (normalised by GDP), inflation (p.a.),
and real interest rate (p.a.) responses are expressed as percentage point, the policy rate (p.a.) as basis point,
deviations from steady state. All other responses are percent deviations from steady state. The size of the
shock corresponds to one estimated standard deviation. Periods correspond to quarters
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International Economics and Economic Policy (2025) 22:25 Page 23 of 49 25
Fig. 3 Dynamic responses to labour shocks. Note: The trade balance (normalised by GDP), inflation (p.a.),
and real interest rate (p.a.) responses are expressed as percentage point, the policy rate (p.a.) as basis point,
deviations from steady state. All other responses are percent deviations from steady state. The size of the
shock corresponds to one estimated standard deviation. Periods correspond to quarters
The economy’s response to the standard savings shock (solid line) is qualitatively
similar, characterised by a hump-shaped pattern in domestic demand driven by habit
persistence. Moreover, the persistent savings shock remains deflationary when the
economy exits the ELB environment after seven quarters, prompting the central bank
to lower interest rates in the medium term relative to the no-shock baseline.12 This
policy response boosts investment, stabilises private demand and output, and leads to
domestic currency depreciation, which in turn improves the trade balance.
Labour hoarding shock
Figure 3 compares the estimated responses to the standard labour demand shock
(solid line) and the COVID-specific labour hoarding shock (dashed line). Labour
hoarding represents a shock to labour demand that accounts for the wedge between
hours worked and employment. This transitory shock reduces effective hours worked
by 1.5% on impact. As the capital-labour ratio increases, the marginal return to capital
12 Note that the starting point of the simulations is 2020q2, a period during which the ELB is initially
expected to bind for seven more quarters (see Table 7). Afterward, the policy rate transitions to the (uncon-
strained) Taylor rule, responding to the negative shocks by decreasing the rate.
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declines, leading to a fall in investment. However, households maintain real con-
sumption levels, keeping overall income (GDP) and inflation relatively stable. The
economy’s estimated response to the standard labour demand shock (solid line) dif-
fers notably, as the persistent decline in employment reduces real wages and weakens
domestic demand components. The accompanying real exchange rate appreciation
worsens the trade balance, resulting in a much sharper and more prolonged contrac-
tion in output. Inflation rises due to higher import prices, prompting an increase in
interest rates once the economy exits the ELB environment.
Transitory investment shock (investment-specific lockdown)
Figure 13 in Appendix 2 compares the estimated dynamic responses to the transitory
investment-specific lockdown shock (dashed line) and the standard persistent shock to
the investment risk premium. The economy’s reaction to the lockdown shock closely
resembles that of the consumption-specific lockdown shock, reflecting its one-off
nature. Private investment drops by 11%, and real GDP falls by 1.4% in 2020q2, with
only a marginal effect on CPI inflation. In contrast, the response to the investment
risk shock (solid line) is characterised by a persistent decline in domestic demand
components, exerting downward pressure on CPI inflation. This leads to lower interest
rates in the medium term (after exiting the ELB), which in turn boosts consumption
by reducing savings, stabilises private demand and output, and improves the trade
balance.
Foreign demand shocks
Figure 4 compares the dynamic effects of a negative foreign demand shock in REA
(solid line) and RoW (dashed line) on the German economy, modelled as a temporary
increase in foreign household savings during the COVID-19 pandemic. This shock
reduces foreign consumption, output, and prices. For Germany, the REA shock gener-
ates significantly larger spillovers, causing a 0.4% drop in real GDP without monetary
support. This is primarily due to an appreciation of the real effective exchange rate
(REER), which negatively impacts the trade balance by reducing foreign demand. The
resulting decline in economic activity lowers employment, real wages, and domestic
consumption. With the ELB constraint in place in 2020, these spillovers resemble the
effects of an additional risk shock, characterised by the co-movement of consumption
and investment, for Germany.
In summary, the dynamic responses to the COVID-specific shocks capture qual-
itative patterns that help explain key features of the pandemic period (see Fig. 1).
Consumption- and investment-specific lockdown shocks lead to sharp declines in
consumption, investment, and output, followed by a swift recovery. Labour hoard-
ing accounts for the discrepancy between reduced hours worked and relatively stable
employment during the pandemic. Neither transitory savings and investment shocks
nor labour hoarding result in a significant change in inflation. Spillovers from REA and
RoW provide insights into the global impact of the pandemic and the associated decline
in Germany’s trade balance. Consequently, incorporating additional pandemic-related
shocks is necessary to fully capture the information from our comprehensive data set.
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Fig. 4 Dynamic responses to foreign risk shocks. Note: The trade balance (normalised by GDP), inflation
(p.a.), and real interest rate (p.a.) responses are expressed as percentage point, the policy rate (p.a.) as basis
point, deviations from steady state. All other responses are percent deviations from steady state. The size
of the shock corresponds to one estimated standard deviation. Periods correspond to quarters
6.2 Inflation-related responses
Figure 5 presents the dynamic responses to two key supply-side shocks characteristic
of the inflationary period from 2022 to 2023: A retail price markup shock (solid lines),
and a permanent increase in DE export prices (dashed lines). The retail price markup
shock acts as a wedge between production costs and consumer prices, which can be
interpreted as a consumption-specific price markup by retailers.13 Note that the IRFs in
Fig. 5 display linear responses since both shocks significantly contributed to GDP and
CPI inflation dynamics in 2022–2023, during which the ECB began raising interest
rates away from the ELB.
Both shocks can be viewed as proxies for binding capacity constraints, reflecting
dynamics captured by the Global Supply Chain Pressure Index (GSCPI) developed by
Benigno et al. (2022) and simulating the effects of supply chain disruptions. They both
suppress domestic economic activity (consumption and investment), but only the retail
price markup shock notably drives up CPI inflation. As a result, these shocks present
different inflation-output trade-offs: the retail markup shock increases CPI inflation
Z
13 The shock, A p , is modelled as a negative productivity shock for the final consumption good, C, as
t
detailed in Eq. 23
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Fig. 5 Dynamic responses to supply-side shocks. Note: The trade balance (normalised by GDP), inflation
(p.a.), and real interest rate (p.a.) responses are expressed as percentage point, the policy rate (p.a.) as basis
point, deviations from steady state. All other responses are percent deviations from steady state. All other
responses are percent deviations from steady state. The size of the shock corresponds to one estimated
standard deviation. Periods correspond to quarters
by nearly 2 pp while causing a smaller drop in real GDP (up to 0.4%). In contrast, the
export price shock leads to a larger decline in real GDP (up to 0.7% after one year)
with less pronounced inflationary effects.
7 Estimated drivers of macroeconomic variables
Historical shock decompositions (SDs) offer a quantitative evaluation of the main
estimated drivers of Germany’s historical data pattern. Figures 6, 7, and 8 exhibit the
SDs of real GDP growth, CPI inflation, and nominal wage growth from 2018q1 to
2023q4.14 The assessment considers the endogenous ELB periods obtained from non-
linear smoothing, as discussed in Subsection 5.5. The approach for extending standard
linear (additive) historical shock decomposition to account for occasionally binding
constraints is detailed in C.15
14 Figs. 14 and 15 in Appendix 2 display the historical drivers of real GDP growth and inflation over the
full-sample period.
15 A similar methodology for adapted piecewise linear smoothed shock decomposition is presented in
Croitorov et al. (2020) and Cardani et al. (2023).
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International Economics and Economic Policy (2025) 22:25 Page 27 of 49 25
Fig. 6 Historical decomposition of real GDP growth (yoy) Note: Real GDP growth is shown in percentage-
point deviations from steady state, which is calibrated to 1.25% per year. 0.01 on the y-axis corresponds to
1 pp. Continuous black lines represent the historical data. The vertical red bars illustrate the contribution
of each respective (group of) exogenous shocks to the data, whereas stacked light grey bars summarise the
contributions of all remaining shocks. The sum of the contributions equals the historical data
In each subplot in Figs. 6, 7, and 8, the continuous black line represents the histori-
cal data, from which the steady state (1.25% p.a. for GDP, 2.0% p.a. for inflation, and
2.9% p.a. for wage growth) has been subtracted. The vertical red bars illustrate the con-
tribution of each respective (group of) exogenous shocks to the data, whereas stacked
light grey bars summarise the contributions of all remaining shocks. Bars above the
horizontal axis (steady state) represent positive shock contributions; bars below the
horizontal axis show negative shock contributions. The sum of the contributions by all
shocks equals the historical data in each period. The group of shocks are categorised
as follows: (1) domestic supply, which includes productivity, price, labour supply
and demand, and wage markup shocks; (2) domestic demand, encompassing private
savings and investment risk premium; (3) monetary policy; (4) fiscal policy; (5) com-
modity prices, including oil and industrial supplies; (6) international trade, involving
preferences for domestically produced versus foreign goods, export and import price
markups, and exchange rate shocks; (7) world demand and supply, containing foreign
(REA and RoW) demand and supply shocks; (8) COVID-19, covering lockdown and
labour market shocks; and (9) initial values.
Real GDP growth
Figure 6 shows that the COVID-19 recession was driven by both demand and supply
shocks. The model emphasises the significant impact of lockdowns in DE and REA,
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Fig. 7 Historical decomposition of CPI inflation (yoy) Note: CPI inflation is shown in percentage-point
deviations from steady state, which is calibrated to 2% per year. 0.01 on the y-axis corresponds to 1 pp.
Continuous black lines represent the historical data. The vertical red bars illustrate the contribution of
each respective (group of) exogenous shocks to the data, whereas stacked light grey bars summarise the
contributions of all remaining shocks. The sum of the contributions equals the historical data
notably through a transitory savings shock that reduced domestic consumption and
increased investment risk, leading to an 8 percentage-point (pp) contraction in 2020q2
from trend. Global spillovers further contributed to the 2020 GDP decline, averaging
1 pp. However, international trade positively affected GDP growth due to reduced
German import demand from REA and RoW, boosting net exports. Discretionary
fiscal policy helped stabilise GDP, contributing up to 2 pp on average, consistent with
findings by Funke and Terasa (2022) and Hinterlang et al. (2023).
The recovery phase during 2021–2023 was shaped by counterbalancing factors.
The normalisation of domestic demand (as lockdowns eased) and recovering global
demand supported real GDP growth. However, a slowdown in international trade and
negative supply shocks exerted downward pressure, keeping growth rates modest. A
significant export price shock, driven by supply chain bottlenecks, reduced economic
activity in Germany by up to 4 pp in 2021–2022. Despite monetary tightening in
2022, moderate positive contributions from monetary policy arose because our model-
implied rate was higher than the observed rate. This gap was offset by easing monetary
policy shocks, suggesting the model would have advocated earlier or more aggressive
rate hikes.16
16 Monetary policy refers only to Taylor rule shocks, excluding the tapering of unconventional measures.
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International Economics and Economic Policy (2025) 22:25 Page 29 of 49 25
Fig. 8 Historical decomposition of wage growth (compensation per hour) (yoy) Note: Nominal wage
growth, measured as compensation per hour, is shown in percentage-point deviations from steady state,
which is calibrated to 2.9% per year. 0.01 on the y-axis corresponds to 1 pp. Continuous black lines
represent the historical data. The vertical red bars illustrate the contribution of each respective (group of)
exogenous shocks to the data, whereas stacked light grey bars summarise the contributions of all remaining
shocks. The sum of the contributions equals the historical data
CPI inflation
Figure 7 shows that transitory lockdown shocks had a minimal impact on inflation
during the pandemic, as they did not influence inflation expectations. The CPI inflation
surge in 2021–2022 was primarily driven by rising commodity prices and supply-
side factors, with energy prices contributing up to 4.5 pp in 2022. The reversal of
persistent negative global demand shocks signals recovery from pre-COVID trends.
Expansionary fiscal policy moderately boosted inflation, while the VAT reduction in
late 2020 contributed to a 1.5 pp dip.
In 2023, falling commodity prices put downward pressure on inflation, offset by
consumption-specific price markup shocks from retailers. These increased import
markups, due to capacity constraints and supply chain disruptions, added up to 4
pp to above-trend inflation. The moderate inflationary impact of monetary policy in
2022 reflects again a cautious approach to tightening relative to the model-implied
policy rule.
Nominal wage growth (compensation per hour)
Pandemic-related support measures in Germany created a significant gap between
compensation per employee (CPE) and compensation per hour (CPH). The volatility
in hours worked, mainly due to job retention schemes like short-time work (STW),
contributed to this disparity. Since the government’s compensation for wage losses
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25 Page 30 of 49 International Economics and Economic Policy (2025) 22:25
Fig. 9 Off-model indicators and estimated model shocks. Note: In Panel a), the model shock (blue solid
line) represents the estimated lockdown shock as described in Eq. 3. The data used are time series for
Google’s mobility indicator (red dotted line) and the Oxford stringency index (Hale et al. 2021) (yellow
dashed line), both of which are scaled to their maximum absolute values. In Panel b), the model shock (blue
solid line) represents the estimated price markup shock by import retailers. The data for the Global Supply
Chain Pressure Index (GSCPI) are taken from the NY Fed website based on Benigno et al. (2022). Data on
the GSCPI have been adjusted using a linear transformation to align the mean and standard deviation of the
adjusted series with the corresponding moments of the estimated model shocks
is paid as social transfers while wages decrease with reduced hours, STW schemes
caused a marked drop in CPE. As CPE growth fell sharply in early 2020, CPH rose
due to the significant reduction in hours worked.17
Figure 8 illustrates the effects of STW schemes through the COVID-specific labour
hoarding shock. The reduction in hours worked positively impacted wage growth (per
hour) by about 4 pp in 2020 (COVID-19 shock group), though it had negative effects
in 2021, partly due to base effects from 2020.18 The decline in domestic demand
was a primary negative driver in 2020. In contrast, the normalisation and recovery of
domestic and foreign demand boosted wage growth during the recovery phase from
2022 to 2023. However, these gains were partly offset by domestic supply-side factors,
such as retail import price markups and capacity constraints, as reflected in export price
shocks and international trade components.
8 Comparison of shocks to off-model indicators
To assess the empirical plausibility of two identified shocks, Fig. 9 compares the esti-
mated COVID-specific lockdown shock and the retail import price markup shock with
their real-world counterparts.
Figure 9a examines the estimated lockdown shock alongside two pandemic-related
restriction indicators for Germany: Google’s mobility indicator and the Oxford
COVID-19 Government Response Tracker (Hale et al. 2021), which reflects govern-
ment policies on closures, containment, and health measures. The estimated lockdown
shock closely aligns with both indicators. The slight decoupling from the strin-
17 Bodnár et al. (2023) and Da Silva et al. (2020) discuss wage developments and STW schemes during
the pandemic in detail.
18 The estimated labour hoarding shock during the COVID-19 period can also indicate labour market
tightness, consistent with Menz (2024).
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International Economics and Economic Policy (2025) 22:25 Page 31 of 49 25
gency indicator after the first lockdown (2020q2) indicates that private consumption
rebounded faster than the easing of restrictions, likely due to the increased adoption
of online retail. Both the alternative indicators and the estimated lockdown shock also
correspond during the subsequent improvement in the epidemiological situation in
2021.
Figure 9b compares the estimated retail import price markup shock with the Global
Supply Chain Pressure Index (GSCPI) by Benigno et al. (2022), which measures pres-
sures within the global supply chain and indicates potential disruptions. The estimated
price markup closely follows the GSCPI pattern. Notably, during the pandemic from
2020 to 2022, the estimated price markup rose sharply alongside increasing global
supply constraints, before both showed reduced pressures on the supply chain toward
the end of 2022 and the beginning of 2023.
9 Sensitivity analysis
This section explores the sensitivity of the model’s results through two counterfac-
tual analyses: (i) the absence of heteroscedastic COVID-specific shocks, and (ii) the
robustness of observing shadow rates instead of the short-term nominal interest rate
to proxy for the effect of unconventional monetary policy (UMP).
9.1 Counterfactual without COVID-specific shocks
Figure 10 presents the shock decomposition of real GDP growth, CPI inflation, and
wage growth for two model variants: (i) one including COVID-specific shocks and (ii)
one excluding these shocks. The latter variant is generated by running a smoother with
identical estimated parameters, but with all COVID-specific shocks deactivated. The
exogenous shock groups are similar, except the former variant separately visualises
all COVID-related shocks (light blue).
The counterfactual model without COVID-specific shocks attributes the 2020 GDP
drop to persistent savings shocks (10b). This model’s slower consumption response
affects future expectations, leading to (i) a stronger negative demand impact on CPI
inflation in 2020 and (ii) more pronounced offsetting supply-side factors, like price
and wage markup shocks, to match observed data. For nominal wage growth, positive
wage markup shocks (negative supply shocks) are needed in 2020 to reconcile the
decline in hours worked without COVID-related labour hoarding shocks (10f).19 In
the absence of COVID-specific shocks, the model requires higher shock variances to
match the observed data patterns, particularly during 2020. The implied adjustment
dynamics with COVID-specific shocks are more closely aligned with the observed
data during the pandemic period, indicating a better model fit.
From an empirical standpoint, data density serves as a valuable global criterion
for model evaluation in the Bayesian context. It assesses the model fit, favouring
19 In an early ex-ante assessment of the COVID-19 pandemic, Mckibbin and Fernando (2020) used
preference and risk shocks to predict the initial phase of the pandemic without explicitly incorporating
lockdown-related shocks. This approach is comparable to Fig. 10b, which provides a reasonable economic
interpretation. However, the added value of transitory lockdown shocks lies in their marginal impact on
future expectations and, consequently, the improved fit of nominal variables.
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0.15 0.15
Domestic supply Domestic supply
0.1 Domestic demand 0.1 Domestic demand
Monetary policy
Monetary policy
0.05 0.05
Fiscal policy
Fiscal policy
0 Oil and Energy 0
Oil and Energy
International trade
-0.05 -0.05 International trade
World activity
COVID-19 World activity
-0.1 -0.1
Initial Values Initial Values
2018 2019 2020 2021 2022 2023 2024 2018 2019 2020 2021 2022 2023 2024
Domestic supply Domestic supply
0.12 0.12
0.1 Domestic demand 0.1 Domestic demand
0.08 Monetary policy 0.08
Monetary policy
0.06 Fiscal policy 0.06
Fiscal policy
0.04 0.04
Oil and Energy
0.02 0.02 Oil and Energy
International trade
0 0 International trade
World activity
-0.02 -0.02
COVID-19 World activity
-0.04 -0.04
Initial Values Initial Values
2018 2019 2020 2021 2022 2023 2024 2018 2019 2020 2021 2022 2023 2024
0.15 0.15
Domestic supply Domestic supply
0.1 Domestic demand 0.1
Domestic demand
Monetary policy
Monetary policy
0.05 0.05
Fiscal policy
Fiscal policy
Oil and Energy
0 0
Oil and Energy
International trade
International trade
-0.05 World activity -0.05
COVID-19 World activity
-0.1 -0.1
Initial Values Initial Values
2018 2019 2020 2021 2022 2023 2024 2018 2019 2020 2021 2022 2023 2024
Fig. 10 Counterfactual without COVID-specific shocks. Note: Real GDP growth, CPI inflation, and nominal
wage growth are shown as percentage-point deviations from their steady states, calibrated to 1.25%, 2%,
and 2.9% per year, respectively. 0.01 on the y-axis corresponds to 1 pp. Figures 10a, c, and e present identical
historical decompositions as Figs. 6, 7, and 8, respectively
simplicity by penalising models with more parameters, assuming an equal fit. In the
baseline model, the data density (12.225) is significantly higher than that of the model
excluding COVID-specific shocks (11.407), indicating that the estimation process
supports the inclusion of heteroscedastic disturbances.20
9.2 Counterfactual with shadow rates
During the observed period, the European Central Bank (ECB) extensively employed
unconventional monetary policy (UMP) measures. As the model uses a first-order
approximation, it does not account for occasionally binding constraints during esti-
mation but applies an ex-post evaluation of the ELB via the Occbin smoother. Given
the rich set of observed time series and estimated shocks, UMP effects are, hence,
implicitly captured through domestic demand shocks and exchange rate depreciation.
20 The data density is reported in log points using a Laplace approximation.
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International Economics and Economic Policy (2025) 22:25 Page 33 of 49 25
0.15
Domestic supply Domestic supply
0.12
0.1 Domestic demand 0.1 Domestic demand
Monetary policy 0.08 Monetary policy
0.05
Fiscal policy 0.06 Fiscal policy
0.04
0 Oil and Energy Oil and Energy
0.02
International trade International trade
-0.05 0
World activity World activity
-0.02
-0.1 COVID-19 COVID-19
-0.04
Initial Values Initial Values
2018 2019 2020 2021 2022 2023 2024 2018 2019 2020 2021 2022 2023 2024
Fig. 11 Counterfactual with shadow rates. Note: Real GDP growth and CPI inflation are shown as
percentage-point deviations from their steady states, calibrated to 1.25% and 2% per year, respectively.
0.01 on the y-axis corresponds to 1 pp
To explicitly account for UMP, this robustness check introduces a counterfactual using
shadow rates to proxy both conventional and unconventional interventions.
Following Hohberger et al. (2023), I use the estimated EA shadow rate from Wu
and Xia (2017, 2016) as a measure of UMP, replacing the constrained short-term rate
with the shadow rate when the economy operates at the ELB.21 For simplicity, the
estimated shadow rate is incorporated into the baseline model’s estimated Taylor rule
without re-estimating its coefficients.22
Figure 11 illustrates the decomposition of real GDP growth and CPI inflation from
2018 to 2023 under the shadow rate model. The results show that UMP measures
positively contributed to GDP growth (until 2020) and CPI inflation (until 2022) in
Germany, indicating a stronger stimulus than predicted by the estimated Taylor rule.
From 2021 onward, UMP contributions shift toward monetary tightening, with a more
pronounced effect compared to a short-term interest rate constrained by the ELB
(see Fig. 6). This results in a sharper negative impact of monetary shocks on GDP
growth during 2021–2022. The ECB’s gradual phasing out of UMP measures in 2021
dampened their contribution to CPI inflation, though it remained positive. By 2022,
as interest rates increased, monetary policy’s contribution to CPI inflation approached
zero, aligning with the model’s estimated interest rate rule. Incorporating UMP shocks
also alters the contributions of private savings, investment, and exchange rate shocks,
which would otherwise absorb omitted UMP effects in a model with a binding ELB.
Nonetheless, the differences in standard deviations between the two model variants
are relatively minor.
10 Conclusion
This paper estimates a three-region DSGE model to analyse the macroeconomic drivers
of the pandemic and inflation surge in Germany. The results suggest a central role for
lockdown shocks via forced savings in explaining the contraction of economic activity
21 Shadow rate data is available at: https://sites.google.com/view/jingcynthiawu/shadow-rates.
22 Shadow rates, derived from term structure models, align with the short-term policy rate under normal
conditions and turn negative when the ELB binds. For further discussion on the substitutability between
policy rates and shadow rates, see, e.g., Hohberger et al. (2023).
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25 Page 34 of 49 International Economics and Economic Policy (2025) 22:25
in Germany during 2020, with significant stabilising effects from fiscal policy mea-
sures. Global demand and supply shocks also affected Germany’s economic conditions
during the pandemic.
The GDP recovery from 2021 to 2023 reflects a balance between domestic and
foreign demand normalisation and a slowdown in international trade, exacerbated by
supply chain bottlenecks. The surge in CPI inflation during 2021-2022 is primarily
attributed to rising commodity prices and domestic and foreign supply-side factors,
which mimic the effects of increasing supply chain disruptions. The increase in energy
prices alone contributed up to 4.5 pp to CPI inflation in 2022, accounting for roughly
two-thirds of the inflation surge. In 2023, normalising commodity prices are offset
by consumption-specific price markups from retailers, slowing the decline in infla-
tion rates. The estimation results align well with off-model indicators, confirming the
robustness of the identified shocks.
This analysis offers a plausible narrative for Germany’s macroeconomic develop-
ments, highlighting the importance of accounting for various domestic and global
factors, as well as demand and supply dynamics, in understanding the significant
fluctuations driven by the COVID-19 pandemic and the subsequent inflation surge.
Appendix 1: Model description
A.1 Households
The Ricardian households maximise the present value of the expected stream of future
utility, subject to Eq. 5, by choosing the amount of consumption, C* _,, and next period
. je
rf BS,, Sits By. The resulting FOCs are:
asset holdings, Bi,
Ss Ss tC s tC “6
= [Chet WC -ei)] (A.1)
7 nS 1+ rf
l= jue] a Oth cai} (A.2)
je Lamy)
pg +i?) — (a + eP)
l= fue] a oa |: (A.3)
jt 1 + Tp]
l= fue] a Cat |: (A.4)
jt P+ mp4)
‘ -W)eRoW,t+1 _ ( bw bwo bw cna NFA)
1=B,E Natl LF) er («; fore Pry AS
—_ B; t a» C,vat ’ ( . )
jit I+a4)
where qv! CkoWaNFAr captures a debt-dependent country risk premium on net foreign
PrY,
asset holdings as external closure to ensure long-run stability (see Schmitt-Grohe and
Uribe 2003; Adolfson et al. 2008).
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International Economics and Economic Policy (2025) 22:25 Page 350f49 25
The optimality conditions are similar to standard Euler equations, but incorporate
asset-specific risk premia which depend on exogenous shocks eB, EPs ewe. Com-
bining the Euler equation for the risk-free bond (A.2) with (A.3), (A.4), and (A.5), we
obtain the following approximated expressions:
i? = if + rprem®, (A.6)
i? = if + rprem®, (A.7)
e .
E, |e = if + rprem}" , (A.8)
CRoW,t
where rprem? and rprem\” are risk premia on domestic government bonds and
foreign bonds, respectively, rprem > , are the country-specific risk premia on domestic
and foreign shares, and rprem/“ a global financial shock to the risk appetite.
A.2 Firms
Following (Rotemberg 1982), firms face quadratic adjustment costs, adj;,+, measured
in terms of production input factors. Specifically, the adjustment costs are associated
with the output price, PY , labour input, N;,;, capital stock and investment, J; ,;, as well
as capacity utilisation variation, CU; ;:
y yP Pe, °
adj, = 0" >-¥, | sy" — expt) |, (A.9)
Pit
N 2
N;
adj’, = Y iy, a expte?™)| , (A.10)
, 2 i,t—1
7 Pil yt! Tit gk 2 yl? i — Tia-rexp(g’ +g?)
adj; , => pY a Ket K — O; + 2 K >
t t—1 t-1
(A111)
CU P/ CU, you? 2
adj;, = py Rivet E “(CU;,-D+ 5} (CU;,, — 1) ; (A.12)
t
where y-s capture the degree of adjustment costs, 7, g??, g¥, g? " are the steady-state
growth rates of inflation, population, and country-specific GDP and investment price
deflator, respectively. 5x # 6 is a function of the depreciation rate adjusted for the
capital trend in order to have zero adjustment costs on the trend path.”
Given the Lagrange multiplier associated with the technology constraint, 1”, the
FOCs with respect to labour, capital, investment, and capacity utilisation are given
23 We specify 5K = exp(g? + GAPIO) — (1 — 4), where ral and GAP 10 are the global GDP trend and
the investment-specific technology growth, respectively, so that x — 6k 4 0 along the trend path.
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25 Page 36 of 49 International Economics and Economic Policy (2025) 22:25
by:
W, Y, dad jN 1+2”, aadj®
(=) a (ni — ei") t — eh + E,| ch),
(A.13)
Y I
0, = [re TE
1 = E;| ———
T+ityy Pha Pi
Ks dadjC¥
OKt-1
PY Yer
+ O41 — 8) + (=a) aY, ) ory
Prat K;
I
Q [1+ 11 Cy +e!) sk) 4 19 (Ue + 819) = Uri + €f5 exp(g? + g? ))
pa [et ED a) ay
Ky] ‘ Kr
link, Pl, pY I
t+1 “41 “0
12 (Urri + eth) — Un + €f)exp(g” +e) (A.15)
Y K; ,
t CU, PEt!
I
where Q; = LU; / a represents Tobin’s Q and Actr; Pop; is the active labour force of
the domestic country. Equation (A.13) characterises the optimal level of labour input,
taking into account labour overhead. Equations A.14 and A.15 define the Tobin’s Q,
which is equal to the replacement cost of capital (the relative price of capital). eS is the
investment-specific lockdown shock. Finally, Eq. A.16 describes capacity utilisation,
where the left-hand side indicates the additional output produced while the right-hand
side captures the costs of higher utilisation rate.
Given the Rotemberg set-up and imposing the price symmetry condition, PY r=
PY , the FOC with respect to Py, yields the New Keynesian Phillips curve:
py
wot =(1- t*)(o" —1) tolyl sy (x) — z)
t-1
1 ay py y
YP ttl *rt4+1 at ( Y z) Y oHY
—o E - Ui,—-t)|}+o'e , (A.17)
” | 1+it,) PY Y, + ‘
where e/" is the inverse of the markup shock.
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International Economics and Economic Policy (2025) 22:25 Page 37 of 49 25
Appendix 2: Additional results
Table 3 Selected calibrated structural parameters
DE REA RoW
Preferences
Intertemporal discount factor β 0.998 0.998 0.998
Savers share ωs 0.61 1.00 1.00
Weight of disutility of labour ωN 2.5 − −
Degree of openness sM 0.36 0.28 0.06
Import share in consumption s M,C 0.22 0.17 0.05
Import share in investment s M,I 0.31 − −
Import share in government expenditure s M,G 0.31 − −
Import share in export s M,X 0.26 0.31 0.15
Preference for imports from REA s M,R E A 0.33 − 0.67
Preference for imports from RoW s M,RoW 0.23 0.77 −
Preference for imports from DE s M,D E − 0.52 0.48
Production
Cobb-Douglas labour share α 0.65 1.00 1.00
Depreciation of private capital stock δ 0.014 − −
Elasticity of substitution between differentiated goods σY 6.50 − −
Share of commodities in total output sC O 0.06 0.04 0.05
Linear capacity utilisation adj. costs γ CU ,1 0.03 − −
Fiscal policy
Consumption tax τC 0.20 − −
Corporate profit tax τK 0.20 − −
Labour tax τN 0.41 − −
Deficit target (in % of GDP) De f T 0.50 − −
Debt target (in % of GDP) B̄ G 61.6 − −
Steady-state ratios
Private consumption share C/Y 0.55 0.68 0.72
Private investment share I /Y 0.19 − −
Government consumption share G/Y 0.19 − −
Government investment share I G/Y 0.02 − −
Transfer share T /Y 0.17 − −
Trade balance share T B/Y 0.04 −0.02 −0.02
Size of the country (% of world) si ze 5.4 14.5 80.1
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Table 4 Prior and posterior distribution of estimated model parameters in REA and RoW
Prior distribution Posterior distribution
Mean
Distr St.Dev REA RoW
Monetary policy
Interest rate persistence ρi G 0.85 0.91 0.95
0.05 (0.88, 0.93) (0.94, 0.96)
Response to inflation ηi,φ G 2.00 1.78 1.77
0.20 (1.56, 2.19) (1.47, 1.91)
Response to GDP ηi,y G 0.10 0.05 0.07
0.04 (0.03, 0.11) (0.05, 0.15)
Preferences
Consumption habit persistence h B 0.50 0.73 0.87
0.20 (0.72, 0.83) (0.85, 0.90)
Risk aversion θ G 1.50 1.50 1.29
0.20 (1.19, 1.71) (1.18, 1.72)
Phillips curve coefficient φY G 0.025 0.04 0.06
0.01 (0.02, 0.05) (0.03, 0.07)
Import price elasticity σz G 2.00 3.13 1.28
0.40 (2.62, 3.88) (1.11, 1.43)
Oil price elasticity σo G 0.5 0.31 0.12
0.1 (0.30, 0.35) (0.01, 0.29)
Note: Cols. (1)–(2) list model parameters. Cols. (3)–(4) indicate the prior distribution function (B: Beta
distribution; G: Gamma distribution). Col. (5)–(6) show the mode and the 90% HPD intervals of the posterior
distributions of REA and RoW model parameters
Table 5 Selected estimated exogenous shock processes for DE
Prior distribution Posterior distribution
Mean
Distr St.Dev DE
Autocorrelations of forcing variables
Subjective discount factor ρU C Beta 0.50 0.83
0.20 (0.75, 0.90)
Investment risk premium ρS Beta 0.85 0.94
0.05 (0.88, 0.94)
Labour demand ρN D Beta 0.50 0.78
0.20 (0.74, 0.83)
Trade share ρM Beta 0.50 0.91
0.20 (0.88, 0.95)
Government consumption ρG Beta 0.50 0.97
0.20 (0.95, 0.98)
Government transfers ρT Beta 0.50 0.94
0.20 (0.90, 0.95)
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Table 5 continued
Prior distribution Posterior distribution
Mean
Distr St.Dev DE
Commodity imports ρC O Beta 0.50 0.82
0.20 (0.76, 0.86)
Productivity growth ρG A Beta 0.50 0.82
0.20 (0.94, 0.98)
International bond preference ρ EBW
A Beta 0.50 0.87
0.20 (0.71, 0.89)
Standard deviations (%) of innovations to forcing variables
Subjective discount factor εU C Gamma 1.00 1.74
0.40 (0.64, 2.50)
Investment risk premium εS Gamma 0.10 0.25
0.04 (0.20, 0.44)
Price mark-up ε MU Y Gamma 2.00 8.77
0.80 (5.39, 9.80)
Labour demand εN D Gamma 1.00 2.81
0.40 (2.56, 2.94)
Trade share εM Gamma 1.00 1.94
0.40 (1.74, 2.05)
International bond preference ε EBW
A Gamma 1.00 0.21
0.40 (0.15, 0.40)
Labour supply εU Gamma 1.00 2.73
0.40 (1.94, 2.88)
Export price εPX Gamma 1.00 0.49
0.40 (0.39, 0.59)
Government consumption εG Gamma 1.00 0.19
0.40 (0.16, 0.22)
Government transfers εT Gamma 1.00 0.15
0.40 (0.13, 0.17)
Commodity imports εC O Gamma 1.00 5.05
0.40 (4.02, 5.86)
Productivity growth εG A Gamma 0.10 0.05
0.04 (0.02, 0.06)
Productivity trend εA Gamma 0.10 0.02
0.04 (0.01, 0.05)
Monetary policy εiE A Gamma 1.00 0.10
0.40 (0.08, 0.11)
Note: Cols. (1)–(2) list model parameters. Cols. (3)–(4) indicate the prior distribution function (B: Beta
distribution; G: Gamma distribution). Cols. (5) shows the mode and the 90% HPD intervals of the posterior
distributions
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Table 6 Selected estimated exogenous shock processes for REA and RoW
Prior distribution Posterior distribution
Mean
Distr St.Dev REA RoW
Autocorrelations of forcing variables
Subjective discount factor ρU C Beta 0.50 0.69 0.79
0.20 (0.59, 0.74) (0.73, 0.87)
Price mark-up ρY Beta 0.50 0.57 0.62
0.20 (0.33, 0.63) (0.52, 0.69)
Trade share ρM Beta 0.50 0.94 0.97
0.20 (0.90, 0.96) (0.95, 0.99)
Commodity imports ρC O Beta 0.50 0.90 −
0.20 (0.85, 0.96)
Productivity growth ρG A Beta 0.50 0.93 0.94
0.20 (0.90, 0.95) (0.91, 0.95)
Standard deviations (%) of innovations to forcing variables
Subjective discount factor εU C Gamma 1.00 1.95 0.69
0.40 (1.53, 2.69) (0.46, 1.01)
Price mark-up ε MU Y Gamma 1.00 0.17 0.43
0.40 (0.14, 0.28) (0.34, 0.53)
Trade share εM Gamma 1.00 3.14 2.89
0.40 (2.69, 3.42) (2.53, 3.16)
Commodity imports εC O Gamma 1.00 4.86 −
0.40 (4.02, 5.86)
Productivity growth εG A Gamma 0.10 0.03 0.08
0.04 (0.03, 0.04) (0.07, 0.10)
Monetary policy εi Gamma 1.00 0.10 0.09
0.40 (0.08, 0.11) (0.08, 0.11)
Note: Cols. (1)–(2) list model parameters. Cols. (3)–(4) indicate the prior distribution function (B: Beta
distribution; G: Gamma distribution). Cols. (5) shows the mode and the 90% HPD intervals of the posterior
distributions
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International Economics and Economic Policy (2025) 22:25 Page 41 of 49 25
Fig. 12 Prior and posterior identification of COVID-specific shocks. Note: The light grey lines represent the
prior distributions, while the black lines show the posterior distributions of the estimated COVID-specific
disturbances. The green vertical lines indicate the posterior mode (see Table 2)
Table 7 Historical sequence of
Time Regime sequence Starting period of regime
occasionally binding regimes
2012Q1 0 1
2012Q2 0 1
2012Q3 0 1
2012Q4 0 1
2013Q1 0 1
2013Q2 010 146
2013Q3 010 146
2013Q4 010 136
2014Q1 010 145
2014Q2 010 136
2014Q3 010 126
2014Q4 10 16
2015Q1 10 16
2015Q2 10 15
2015Q3 10 15
2015Q4 10 16
2016Q1 10 17
Note: First column: [0] unconstrained; [0 1 0] indicates an uncon-
strained regime, but agents expect to be binding in the future; [1
0] indicates a constrained regime. Second column: [1 4 6] indicates
an expected constrained regime starting in 4 periods ahead and last
for additional 2 periods; [1 8] indicates a constrained regime with an
expected duration of additional 7 periods
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Table 7 continued
Time Regime sequence Starting period of regime
2016Q2 10 16
2016Q3 10 15
2016Q4 10 14
2017Q1 10 13
2017Q2 10 13
2017Q3 10 13
2017Q4 10 13
2018Q1 10 13
2018Q2 10 13
2018Q3 10 13
2018Q4 10 13
2019Q1 10 13
2019Q2 10 13
2019Q3 10 13
2019Q4 10 13
2020Q1 10 13
2020Q2 10 18
2020Q3 10 15
2020Q4 10 15
2021Q1 10 13
2021Q2 10 13
2021Q3 10 13
2021Q4 10 13
2022Q1 10 12
2022Q2 0 1
2022Q3 0 1
2022Q4 0 1
2023Q1 0 1
2023Q2 0 1
2023Q3 0 1
2023Q4 0 1
Note: First column: [0] unconstrained; [0 1 0] indicates an uncon-
strained regime, but agents expect to be binding in the future; [1
0] indicates a constrained regime. Second column: [1 4 6] indicates
an expected constrained regime starting in 4 periods ahead and last
for additional 2 periods; [1 8] indicates a constrained regime with an
expected duration of additional 7 periods
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International Economics and Economic Policy (2025) 22:25 Page 43 of 49 25
Fig. 13 Dynamic responses to investment shocks. Note: The trade balance (normalised by GDP), inflation
(p.a.), and real interest rate (p.a.) responses are expressed as percentage point, the policy rate (p.a.) as basis
point, deviations from steady state. All other responses are percent deviations from steady state. The size
of the shock corresponds to one estimated standard deviation. Periods correspond to quarters
Fig. 14 Historical decomposition of real GDP growth (yoy). Note: Real GDP growth is shown in percentage-
point deviations from steady state, which is calibrated to 1.25% per year. 0.01 on the y-axis corresponds to
1 pp
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Fig. 15 Historical decomposition of CPI inflation (yoy). Note: CPI inflation is shown in percentage-point
deviations from steady state, which is calibrated to 2% per year. 0.01 on the y-axis corresponds to 1 pp
Appendix 3: Piecewise linear smoothed shock decomposition
This appendix describes the extension of the standard linear (additive) historical shock
decomposition to occasionally binding constraints. The piecewise linear smoother
provides an estimate of the historical sequence of regimes, i.e. identifies periods in
which the ELB has been binding (Table 7). The sequence of regimes triggers a sequence
of state space matrices:
yt = C(t) + T (t)yt−1 + R(t)t ,
where y are endogenous variables in deviation from steady state, ε are the smoothed
shocks, and C(t) is a constant which is triggered by the ELB regime. While C = 0
in normal times, the constant is triggered by the fact that, under the ELB regime, the
Taylor rule becomes i E A = i EL BA and violates the steady-state solution as i EL BA < ī.
The smoothed shock decomposition is performed similarly to the usual linear case:
Given the smoothed series of regimes, the shocks are propagated individually through
the sequence of state space matrices T and R. The array C is, instead, treated as an
additional ‘exogenous’ process, the so-called ‘regime effect’. The regime effect results
from the interaction of all shocks hitting the system simultaneously, for all times <= t.
Hence, we can assume that such a regime effect is also a function of the model shocks,
which allows us to compute, at each time point and for each y j of interest, the absolute
value of the contribution of each shock εi onto variable y j :
w j,i (t) = |y j (ei , t)|,
which provides a set of weights that can be used to apportion the regime affect among
all shocks in the model. The intuition behind this procedure is the following: If a
shock is relevant for y at a given point in time t, it will also be relevant in triggering
the regime effect. For example, if it is an expansionary shock, it would contribute
to mitigate the duration of the constrained regime and vice versa. By doing so, we
obtain a historical shock decomposition in terms of the usual model shocks, which
also includes the regime effect.
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International Economics and Economic Policy (2025) 22:25 Page 45 of 49 25
Appendix 4: Data source and transformations
Table 8 Observed times series
DE EA RoW
GDP (nominal and real) GDP (nominal and real) GDP (nominal and real)
TFP trend GDP trend GDP trend
Private consumption (nominal 3-month interest rate (nomi- 3-month interest rate (nomi-
and real) nal) nal)
Total investment (nominal and Effective exchange rate (nom- Oil price (Brent) in USD
real) inal)
Hours worked Exports (nominal and real) Population
Wages (nominal) Imports (nominal and real)
Exports (nominal and real) Commodities import share
(nominal)
Imports (nominal and real) Price of commodity imports
(from RoW)
Government debt (nominal) Population
Gov. consumption (nominal)
Gov. investment (nominal)
Government transfers (nomi-
nal)
Gov. interest payments (nom-
inal)
Commodities import share
(nominal)
Price of commodity imports
(from RoW)
Active population rate
Population
Data sources
Data for the Germany and EA (quarterly national accounts, fiscal aggregates, quar-
terly interest and exchange rates) are taken from Eurostat. DE and EA imports of
commodities from RoW are based on BEA data and on Eurostat Comext data. RoW
series are constructed on the basis of the IMF International Financial Statistics (IFS)
and World Economic Outlook (WEO) databases.
List of observables
The estimation uses the time series information for 41 endogenous variables. We
additionally observe the first quarter of the capital stock and the net international
investment position to initialise the starting point. Table 8 lists the observed time
series. We apply logarithmic transformations to all observables, with the exception of
the trade balance-to-GDP ratio, the oil price (Brent), the commodities import share
to GDP, the price of commodities imports, and nominal interest rates. Figure 16 plots
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25 Page 46 of 49 International Economics and Economic Policy (2025) 22:25
Fig. 16 Observed DE time series
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International Economics and Economic Policy (2025) 22:25 Page 47 of 49 25
the observed DE data pattern for the estimation. GDP deflators and relative prices of
demand components are computed as the ratios of the current-price value to the chain-
indexed volume series. Note that we observe EA aggregate variables and compute
model-consistent REA variables given the size of Germany.
Acknowledgements I thank the Editor Joscha Beckmann as well as an anonymous referee for very helpful
and constructive comments. I also thank Marco Ratto for the extensive discussions on the Global Multi-
country (GM) model as well as Warwick McKibbin and research seminar participants at the Munich
University of Applied Sciences for very helpful comments and discussions.
Funding Open Access funding enabled and organized by Projekt DEAL.
Data availability The data used for estimation are available on open-access databases. They are also available
from the corresponding author upon request.
Declarations
Conflict of interest The author declares no competing interests.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence,
and indicate if changes were made. The images or other third party material in this article are included
in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If
material is not included in the article’s Creative Commons licence and your intended use is not permitted
by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the
copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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