Germany’s macroeconomic drivers during the pandemic and inflation surge

Hohberger, Stefan Article — Published Version Germany’s macroeconomic drivers during the pandemic and inflation surge International Economics and Economic Policy Provided in Cooperation with: Springer Nature Suggested Citation: Hohberger, Stefan (2025) : Germany’s macroeconomic drivers during the pandemic and inflation surge, International Economics and Economic Policy, ISSN 1612-4812, Springer, Berlin, Heidelberg, Vol. 22, Iss. 1, https://doi.org/10.1007/s10368-024-00651-7 This Version is available at: https://hdl.handle.net/10419/319168 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ 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 macroeconomic 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 synchronised 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. BStefan Hohberger stefan.hohber[email protected] 1HM Business School, Munich University of Applied Sciences, Munich, Bavaria, Germany 2Centre for Applied Macroeconomic Analysis (CAMA), Australian National University, Canberra, Australia 123 25 Page 2 of 49 International Economics and Economic Policy (2025) 22 :25 This paper analyses the main drivers of the COVID-19 pandemic and subsequent inflation period for Germany through the lens of an estimated structural macroeconomic 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. Additionally, 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 supplyside disruptions and rising commodity prices. Adverse productivity and supply shocks reflectglobalsupplychainandcapacityconstraints.Theestimatedshockscloselyalign with off-model indicators, reinforcing the empirical credibility of the findings. The remainder of the paper is organised as follows: Section 2reviews recent studies related to modelling COVID-specific developments and the empirical literature on the post-pandemic inflation surge. Section3presents stylised macroeconomic facts for the German economy since 2008. Section4presents the model’s structure. Section5 details the model solution, data, estimation methodology, and discusses the posterior estimates. Section6examines the dynamic responses to shocks characteristic of the COVID-19 period. Section7quantifies the main drivers of GDP growth, CPI inflation, and wage growth in Germany. Section8compares model-based results with off-model evidence. Section9conducts a sensitivity analysis without COVID-specific shocks. Section10 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 123 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.1For the EA, studies such as Neri et al. (2023) and Pasimeni (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 influential for US inflation, while supply factors dominate in the EA. However, Giannone and Primiceri (2024) find unexpectedly strong demand forces in the Post-covid inflation, 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 member 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 methodological approach of Cardani et al. (2022a) and incorporates heteroscedastic domestic and foreign COVID-19 shocks, such as a domestic consumptionand investmentspecific lockdown shock, a shock to labour demand (labour hoarding) to account for the wedge between hours worked and employees (intensive margin) due to shorttime 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, occasionally binding constraints to account for ELB periods; and (v) it provides off-model evidence for the fit of the model-implied estimated shock pattern. 1Given 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;diGiovanni2022; 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). 123 25 Page 4 of 49 International Economics and Economic Policy (2025) 22 :25 3 Stylised facts Figure1presents 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 123 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 recession, both private consumption and investment declined simultaneously during the 2020 pandemic. The model accounts for these patterns by incorporating transitory consumptionand 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, whenaccounting for the2%steady state. Theco-movementbetweenGDPand 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, sectorspecific goods prices, and import/export prices, to capture supply-side disruptions through various disturbances. 4Themodel 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 produce 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 foreign 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. 123 25 Page 6 of 49 International Economics and Economic Policy (2025) 22 :25 The DE government purchases final goods and provides lump-sum transfers to households. To finance its expenditure, the government issues debt and imposes distortionary taxes on labour, capital, and consumption, along with non-distortionary lump-sum taxes. Monetary authorities set short-term nominal interest rates by following 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, εtC t, to capture the lockdown-imposed drop in consumption, (2) a transitory labour demand shock (labour hoarding), εtN t, to capture short-time work arrangements, i.e. to distinguish between hours worked and hours paid, (3) a transitory VAT shock, εtvat t, to capture the reduction of the German VAT consumption tax during 2020q3–2020q4, and (4) a transitory investment-specific lockdown shock, εtS t, 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 households (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: Us j=E0 ∞  t=0 (˜ βt)tus j,t(.), (1) where ˜ βtis the stochastic discount factor.2Ricardian households have full access to financial markets, which allows them to accumulate wealth, Aj,t, consisting of domestic private risk-free bonds, Brf j,t, domestic government bonds, BG j,t, one internationally traded bond, BW j,t, and internationally traded shares, PS tSj,t: Aj,t=Brf j,t+BG j,t+eRoW,tBW j,t+PS tSj,t(2) 2˜ βt=βexp(εc t−1)features a shock to the subjective rate of time preference (saving shock) εc t. 123 International Economics and Economic Policy (2025) 22 :25 Page 7 of 49 25 where PS tis the nominal price of shares. The international bond is issued and denominated 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, Cs j,t, and experience disutility from labour, Ns j,t, as well as from holding risky financial assets, UA j,t−1.The instantaneous utility function of savers, us(.), is defined as: us j,t(Cs j,t,Ns j,t, UA j,t−1 PC,vat t )=(Cs j,t−εtC t−h(Cs t−1−εtC t−1))1−θ 1−θ −ωNεU t(Ct)1−θ(Ns j,t+εtN t)1+θN 1+θN −(Cs j,t−εtC t−h(Cs t−1−εtC t−1))−θUA j,t−1 PC,vat t ,(3) where Cs t=1 0Cs j,tdj,hmeasures the strength of external habits in consumption, and ωNis the stochastic weight of the disutility of labour. εU tcaptures a labour supply shock. εtC tcaptures the non-persistent lockdown shock (forced saving) that constrains consumption outside of habit persistence, εtN tcaptures a labour hoarding shock.3The disutility of holding risky financial assets, UA j,t−1, takes the following form: UA j,t−1=αb0+εB t−1BG j,t−1+αbw0+εbw t−1eRoW,tBW j,t−1 +αbw1 2 (eRoW,t−1NFA t−1)2 PY t−1Yt−1 +αS0+εS t−1PS t−1Sj,t−1.(4) 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 εx,x∈{B,S,bw}, and an asset-specific intercept αx,x∈{b0,S0,bw0}. 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 jth Ricardian household faces the following budget constraint: PC,vat tCs j,t+Aj,t=(1−τN)Wt(Ns j,t+εtN t)+(1+irf t−1)Brf j,t−1+(1+iG t−1)BG j,t−1 +(PS t+PY tDt)Sj,t−1+(1+iW t−1)eRoW,tBW j,t−1 +Ts j,t−taxs j,t,(5) 3Aggregate consumption, Ct, in the second term of the right-hand side is introduced as normalisation to ensure a balanced steady-state growth path. 123 25 Page 8 of 49 International Economics and Economic Policy (2025) 22 :25 where PC,vat tis the private consumption deflator,4Wtdenotes the nominal wage rate, Ns j,tis the employment in hours, Ts j,tare government transfers and taxs j,tlumpsum taxes paid by savers. irf t,iG t, and iW tare returns on domestic private risk-free bonds, domestic government bonds, and internationally traded bonds, respectively. Transfers include unemployment benefits, BENs j,t, defined as the gap between actual and potential hours multiplied with benefit replacement rate, τu: Ts j,t=BENs j,t+ωsPtTt,(6) BENs j,t=τuWtNpot t−(Ns j,t+εtN t).(7) Ricardian households receive nominal profits in the form of dividends, Dt. Gross nominal return on shares Stis defined as: 1+iS t=PS t+PY tDt PS t−1 .(8) Ricardian households maximise the present value of the expected stream of future utility by choosing the amount of consumption, Cs j,t, and next period asset holdings, Brf j,t,BG j,t,Sj,t,BW j,t, subject to their budget constraint (Eq.5), The optimality conditions 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, uc(.),is: uc j,t(Cc j,t,Nc j,t)=(Cc j,t−εtC t−h(Cc t−1−εtC t−1))1−θ 1−θ −ωNεU t(Ct)1−θ 1+θN(Nc j,t+εtN t)1+θN.(9) Ineachtimeperiod, theyconsume their entire net disposableincome,whichconsists of after-tax (paid) labour income and lump-sum transfers from the government: PC,vat tCc j,t=(1−τN)Wt(Nc j,t+εtN t)+Tc j,t−taxc j,t+PC,vatεtC t−1 6 13  i=8 εtC t−i. (10) During the COVID-19 pandemic, this constraint is eased such that even LC households can save (forced savings), εtC t, which will be gradually spent post-pandemic. 4PC,vat tis the VAT adjusted private consumption deflator, PC,vat t=(1+τC+εtVAT t)PC t,where τCis the tax rate on consumption (VAT) and εtV AT tcaptures the VAT-tax cut during 2020q3–2020q4 implemented by the German government. 123 International Economics and Economic Policy (2025) 22 :25 Page 15 of 49 25 ITRrepresents 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:  l NFA l,tsizel=0.(41) 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: YREA,tPY REA,t+τCOCOREA,tPY0=PC REA,tCREA,t+TB REA,t,(42) where τCOCOREA,tPY0represents the excise duty. Final aggregate demand, Ck,t, is a combination of domestic output, YC k,t, and imported goods, MC k,t, using the following CES function: Ck,t=Ap k,t(1−εM k,tsM k) 1 σc k(YC k,t) σc k−1 σc k+(εM k,tsM k) 1 σc k(MC k,t) σc k−1 σc k σc k σc k−1.(43) σc krepresents the import elasticity of substitution, ApC tis a shock to productivity in the sector producing goods, C, and sM tis the import share. The demand for domestic and imported goods is obtained from profit maximisation: YC k,t=(ApC k,t)σc k−11−εM k,tsM kPY k,t PC k,t−σc kCk,t,(44) MC k,t=(ApC k,t)σc−1εM k,tsM kPM k,t PC k,t−σc kCk,t,(45) where the consumer price deflator, PC k,t,is: PC k,t=(ApC k,t)−1(1−εM k,tsM k)(PY k,t)1−σc k+εM k,tsM k(PM k,t)1−σc k1 1−σc k.(46) The good producers use labour as input factor, Yk,t=AY k,tNk,t, where AY k,trepresents trend productivity. The price-setting equation follows a New Keynesian Phillips 123 25 Page 16 of 49 International Economics and Economic Policy (2025) 22 :25 curve: πY k,t−¯πY k=βλk,t+1 λk,t (πY k,t+1−¯πY k)+φY klog(Yk,t ¯ Yk )+εY k,t,(47) where λk,t=(Ck,t−hkCk,t−1)−θkis the marginal utility of consumption, and εY k,tis a cost-push shock. REA and RoW total nominal exports are defined as: PX k,tXk,t=lPX l,k,tMl,k,t, with the bilateral export price being defined as the domestic price subject to a bilateral price shock, PX l,k,t=exp(εX l,k,t)PY k,t. Combining the two regions’ FOCs with respect to international bonds derives the uncovered interest parity (UIP) condition: EteRoW,EA,t+1 eRoW,EA,t(1+iRoW,t)=(1+iEA,t)+εbw EA,t+αbw0 EA +αbw1 EA eRoW,EA,tBw EA,t PY EA,tYEA,t , (48) where εbw EA,tcaptures a euro exchange rate shock (shock to the bond premium between EA and RoW), and αbw1 EA 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, COOil and non-oil commodities, COIS, such as natural gas and materials, to domestic and foreign firms. εCO tcaptures exogenous commodity supply shocks. The RoW producer combines oil (Oil) and non-oil (IS) commodities into bundles, CO, 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, εP,CO l,t, where l=(DE,REA), aiming to reflect price variations due to differing commodity baskets. Therefore: PCO l,t=εPCO l,tsOil lPOil t1−σCO +(1−sOil l)PIS t1−σCO1 1−σCO ,(49) PCO t=sOilPOil t1−σCO +(1−sOil)PIS t1−σCO1 1−σCO .(50) Commodity prices are exogenous and follow: PCO t=Pt ACO t ,where CO=(Oil, IS) (51) where ACO tis the exogenous commodity-specific productivity technology. 123 International Economics and Economic Policy (2025) 22 :25 Page 17 of 49 25 5 Model solution and econometric approach 5.1 Model solution The following non-linear system summarises the observation and state equations of the model: yobs t=1()St,(52) St=1()St−1+ε(θ)εt,ε t∼N(0,QtI)(53) In observation Eq.52,yobs tdenotes the vector of observables at time t, and 1() links the model variables to the data. The state Eq.53 describes the transition of the system’s state variables, St, where 1() and εare the coefficient matrices. Following (Cardani et al. 2022a), the model shocks, εt, follow a normal distribution with timevarying covariance matrix QtI, such that the state Eq.53 incorporates deterministic heteroscedasticity: Qt=QCOVID for t∈{2020q1:2021q4}, Qotherwise.(54) For the pandemic period 2020q1–2021q4, Qt=QCOVID incorporates temporary COVID-specific shocks, whereas prior to COVID-19, Qt=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. Section9includes a sensitivity analysis examining the model’s fit and economic narrative in the absence of COVIDspecific shocks. 123 25 Page 18 of 49 International Economics and Economic Policy (2025) 22 :25 2. The remaining parameters and shocks are estimated using data over the sample period1999q1–2023q4. Thefull-sample estimationprocedure incorporatesthe estimation of heteroscedastic COVID-specific variances during the period 2020q1–2021q4, thereby allowing for time-varying shock disturbances Qt.7The likelihood function (evaluated by implementing the Kalman filter) and the prior distribution of the parameters 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).8We 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%, and21%,respectively.Theglobaltrend GDPgrowthrateandtrend 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 3in Appendix 2 provides an overview of calibrated parameters. Table 1reports 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 7Cardani 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 COVIDspecific 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. 8The 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). 123 International Economics and Economic Policy (2025) 22 :25 Page 19 of 49 25 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 ρiG 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,yG 0.10 0.05 0.04 (0.03, 0.11) Preferences Consumption habit persistence hB 0.50 0.90 0.20 (0.83, 0.92) Risk aversion θG 1.50 1.33 0.20 (1.16, 1.70) Inverse Frisch elasticity of labour supply θNG 2.50 3.72 0.50 (2.21, 4.86) Import price elasticity σzG 2.00 1.93 0.40 (1.64, 2.19) Oil price elasticity σoG 0.5 0.40 0.1 (0.32, 0.48) Nominal and real frictions Price adjustment cost γPG 20 40.8 12 (33.7, 49.9) Nominal wage adjustment cost γwG 20 17.3 12 (9.2, 19.4) Real wage rigidity γwrB 0.47 0.85 0.20 (0.54, 0.89) Employment adjustment cost γNG20 1.8 12 (1.5, 2.3) Capacity utilisation quadratic adj cost γCU,2G 0.003 0.003 0.0012 (0.002, 0.005) Investment adjustment cost γI,2G 40 38.2 25 (19.1, 67.5) Fiscal policy Lump-sum tax persistence ρtax B 0.85 0.82 0.06 (0.75, 0.89) Tax response to deficit ηdef 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 distribution; G: Gamma distribution). Col. (5) shows the mode and the 90% HPD intervals of the posterior distributions of model parameters 123 25 Page 20 of 49 International Economics and Economic Policy (2025) 22 :25 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 εtC G 5 [20q1 - 21q3] 4.75 2 (4.03, 7.36) Investment-specific lockdown shock εtS G 5 [20q1 - 20q2] 2.27 2 (1.10, 5.80) labour hoarding shock εtN G 5 [20q2 - 21q1] 2.57 2 (1.85, 4.77) VAT-tax shock εtVAT G 2 [20q3 - 20q4] 1.70 0.8 (0.91, 3.03) REA COVID-specific shocks (standard deviations in %) Consumption-specific lockdown shock εtC G 5 [20q1 - 20q2] 6.97 2 (4.99, 9.78) Risk shock εtβG 5 [20q1 - 21q4] 8.30 2 (3.91, 10.13) RoW COVID-specific shocks (standard deviations in %) Risk shock εtβG5 [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 4in Appendix 2. Tables 5and 6in Appendix 2report the main estimated shock processes for DE, and REA and RoW, respectively. Table 2provides the posterior estimates of pandemic-specific shocks, revealing a mix of demand-side (lockdown) and supply-side shocks (labour market).9Specifically, 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. Figure12 in 9For 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. 123 International Economics and Economic Policy (2025) 22 :25 Page 21 of 49 25 Appendix 2provides the prior and posterior distributions of the estimated COVIDspecific 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 variables 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 7in 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 sequenceinTable7,a period where the ELBisbindingfor5 more quarters. Remove the specificshock(e.g., the consumption-specificlockdown shock) andsimulatethe 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 illustrates 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 (annualised), 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, negativesupply-side shocksdrivingupinflationandslowingeconomicactivityarecompoundedby monetary tightening aimed at reducing inflation. 123 25 Page 22 of 49 International Economics and Economic Policy (2025) 22 :25 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) Figure2compares the estimated dynamic responses to the transitory consumptionspecific 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 supplyside 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 123 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 Figure3compares 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 (unconstrained) Taylor rule, responding to the negative shocks by decreasing the rate. 123 25 Page 24 of 49 International Economics and Economic Policy (2025) 22 :25 declines, leading to a fall in investment. However, households maintain real consumption levels, keeping overall income (GDP) and inflation relatively stable. The economy’s estimated response to the standard labour demand shock (solid line) differs 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 contraction 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) Figure13 in Appendix 2compares the estimateddynamicresponsestothe 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 Figure4compares 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 generates 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 qualitative patterns that help explain key features of the pandemic period (see Fig.1). Consumptionand investment-specific lockdown shocks lead to sharp declines in consumption, investment, and output, followed by a swift recovery. Labour hoarding 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 RoWprovideinsightsinto the global impactofthe pandemic and theassociateddecline in Germany’s trade balance. Consequently, incorporating additional pandemic-related shocks is necessary to fully capture the information from our comprehensive data set. 123 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. Figure9b compares the estimated retail import price markup shock with the Global Supply Chain Pressure Index (GSCPI) by Benigno et al. (2022), which measures pressures 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 counterfactual 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 Figure10 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. 123 25 Page 32 of 49 International Economics and Economic Policy (2025) 22 :25 2018 2019 2020 2021 2022 2023 2024 -0.1 -0.05 0 0.05 0.1 0.15 Initial Values COVID-19 World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 2018 2019 2020 2021 2022 2023 2024 -0.1 -0.05 0 0.05 0.1 0.15 Initial Values World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 2018 2019 2020 2021 2022 2023 2024 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 Initial Values COVID-19 World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 2018 2019 2020 2021 2022 2023 2024 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 Initial Values World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 2018 2019 2020 2021 2022 2023 2024 -0.1 -0.05 0 0.05 0.1 0.15 Initial Values COVID-19 World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 2018 2019 2020 2021 2022 2023 2024 -0.1 -0.05 0 0.05 0.1 0.15 Initial Values World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply Fig. 10 CounterfactualwithoutCOVID-specificshocks.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. Figures10a, c, and e present identical historical decompositions as Figs.6,7,and8, 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 estimation 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. 123 International Economics and Economic Policy (2025) 22 :25 Page 33 of 49 25 2018 2019 2020 2021 2022 2023 2024 -0.1 -0.05 0 0.05 0.1 0.15 Initial Values COVID-19 World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 2018 2019 2020 2021 2022 2023 2024 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 Initial Values COVID-19 World activity International trade Oil and Energy Fiscal policy Monetary policy Domestic demand Domestic supply 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 Figure11 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 Thispaperestimatesathree-regionDSGE modeltoanalysethemacroeconomicdrivers 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). 123 25 Page 34 of 49 International Economics and Economic Policy (2025) 22 :25 in Germany during 2020, with significant stabilising effects from fiscal policy measures. 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 inflation 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 developments, 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, Cs j,t, and next period asset holdings, Brf j,t,BG j,t,Sj,t,BW j,t. The resulting FOCs are: λs j,t=Cs j,t−εtC t−h(Cs t−1−εtC t−1)−θ ,(A.1) 1=˜ βtEtλs j,t+1 λs j,t (1+irf t 1+πC,vat t+1,(A.2) 1=˜ βtEtλs j,t+1 λs j,t (1+iG t)−αb0+εB t 1+πC,vat t+1,(A.3) 1=˜ βtEtλs j,t+1 λs j,t (1+iS t+1)−αS0+εS t 1+πC,vat l,t+1,(A.4) 1=˜ βtEtλs j,t+1 λs j,t (1+iW t)eRoW,t+1 eRoW,t−εbw t+αbw0+αbw1eRoW,tNFA t PY tYt 1+πC,vat t+1,(A.5) where αbw1eRoW,tNFA t PY tYtcaptures a debt-dependent country risk premium on net foreign asset holdings as external closure to ensure long-run stability (see Schmitt-Grohe and Uribe 2003; Adolfson et al. 2008). 123 International Economics and Economic Policy (2025) 22 :25 Page 35 of 49 25 The optimality conditions are similar to standard Euler equations, but incorporate asset-specific risk premia which depend on exogenous shocks εB kt,εS kt,εbwkt.Combining the Euler equation for the risk-free bond (A.2) with (A.3), (A.4), and (A.5), we obtain the following approximated expressions: iG t=irf t+rpremG t,(A.6) iS t=irf t+rpremS t,(A.7) EteRoW,t+1 eRoW,tiW t=irf t+rpremW t,(A.8) where rpremG tand rpremW tare risk premia on domestic government bonds and foreign bonds, respectively, rpremS l,tare the country-specific risk premia on domestic and foreign shares, and rpremra ta global financial shock to the risk appetite. A.2 Firms Following (Rotemberg 1982), firms face quadratic adjustment costs, adji,t, measured in terms of production input factors. Specifically, the adjustment costs are associated with the output price, PY i,t, labour input, Ni,t, capital stock and investment, Ii,t,aswell as capacity utilisation variation, CUi,t: adjPY i,t=σYγP 2YtPY i,t PY i,t−1 −exp(¯π)2 ,(A.9) adjN i,t=γN 2YtNi,t Ni,t−1 −exp(gpop)2 ,(A.10) adjI i,t=PI t PY tγI,1 2Kt−1Ii,t Kt−1 −δK t2+γI,2 2 (Ii,t−Ii,t−1exp(gY+gPI))2 Kt−1, (A.11) adjCU i,t=PI t PY t Ktot i,t−1γCU,1(CUi,t−1)+γCU,2 2(CUi,t−1)2,(A.12) where γ-s capture the degree of adjustment costs, ¯π,gpop,gY,gPIare the steady-state growth rates of inflation, population, and country-specific GDP and investment price deflator, respectively. δK t= δis a function of the depreciation rate adjusted for the capital trend in order to have zero adjustment costs on the trend path.23 Given the Lagrange multiplier associated with the technology constraint, μy,the FOCs with respect to labour, capital, investment, and capacity utilisation are given 23 We specify δK t=exp(g¯ Y+GAPI0)−(1−δ),whereg¯ Yand GAPI0 are the global GDP trend and the investment-specific technology growth, respectively, so that I K−δk= 0 along the trend path. 123 25 Page 36 of 49 International Economics and Economic Policy (2025) 22 :25 by: (1−τK)Wt PY t =αμy t−εND tYt Nt−FN −∂adjN t ∂Nt +Et1+πY t+1 1+is t+1 ∂adjN t+1 ∂Nt, (A.13) Qt=Et1+πY t+1 1+is t+1 PI t+1 PY t+1 PY t PI t τKδ−∂adjCU t ∂Kt−1 +Qt+1(1−δ) +(1−α)μY t+1 PY t+1 PI t+1 Ykt+1 Ktot t,(A.14) Qt=1+γI,1(It+εtS t) Kt−1−δK t+γI,2((It+εtS t)−(It−1+εtS t−1)exp(gY+gPI)) Kt−1 −Et1+πY t+1 1+is t+1 PI t+1 PY t+1 PY t PI t exp(gY+gPI) ·γI,2((It+1+εtS t+1)−(It+εtS t)exp(gY+gPI)) Kt,(A.15) μy t(1−α) Yt CUt PY t PI t =Ktot t−1γu,1+γu,2(CUt−1),(A.16) where Qt=μt/PI t PY t represents Tobin’s Q and ActrtPoptis the active labour force of the domestic country. Equation (A.13) characterises the optimal level of labour input, taking into account labour overhead. EquationsA.14 and A.15 define the Tobin’s Q, which is equal to the replacement cost of capital (the relative price of capital). εtS tis 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 i,t= PY t, the FOC with respect to PY i,tyields the New Keynesian Phillips curve: μy tσY=(1−τK)(σY−1)+σYγPPY t PY t−1πY t−¯π −σYγPEt1+πY t+1 1+is t+1 PY t+1 PY t Yt+1 YtπY t+1−¯π+σYεμY t,(A.17) where εμY tis the inverse of the markup shock. 123 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 β0.998 0.998 0.998 Savers share ωs0.61 1.00 1.00 Weight of disutility of labour ωN2.5 −− Degree of openness sM0.36 0.28 0.06 Import share in consumption sM,C0.22 0.17 0.05 Import share in investment sM,I0.31 −− Import share in government expenditure sM,G0.31 −− Import share in export sM,X0.26 0.31 0.15 Preference for imports from REA sM,REA 0.33 −0.67 Preference for imports from RoW sM,RoW 0.23 0.77 − Preference for imports from DE sM,DE −0.52 0.48 Production Cobb-Douglas labour share α0.65 1.00 1.00 Depreciation of private capital stock δ0.014 −− Elasticity of substitution between differentiated goods σY6.50 −− Share of commodities in total output sCO 0.06 0.04 0.05 Linear capacity utilisation adj. costs γCU,10.03 −− Fiscal policy Consumption tax τC0.20 −− Corporate profit tax τK0.20 −− Labour tax τN0.41 −− Deficit target (in % of GDP) Def T0.50 −− Debt target (in % of GDP) ¯ BG61.6 −− Steady-state ratios Private consumption share C/Y0.55 0.68 0.72 Private investment share I/Y0.19 −− Government consumption share G/Y0.19 −− Government investment share IG/Y0.02 −− Transfer share T/Y0.17 −− Trade balance share TB/Y0.04 −0.02 −0.02 Size of the country (% of world) size 5.4 14.5 80.1 123 25 Page 38 of 49 International Economics and Economic Policy (2025) 22 :25 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 ρiG 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,yG 0.10 0.05 0.07 0.04 (0.03, 0.11) (0.05, 0.15) Preferences Consumption habit persistence hB 0.50 0.73 0.87 0.20 (0.72, 0.83) (0.85, 0.90) Risk aversion θG 1.50 1.50 1.29 0.20 (1.19, 1.71) (1.18, 1.72) Phillips curve coefficient φYG 0.025 0.04 0.06 0.01 (0.02, 0.05) (0.03, 0.07) Import price elasticity σzG 2.00 3.13 1.28 0.40 (2.62, 3.88) (1.11, 1.43) Oil price elasticity σoG 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 ρUC Beta 0.50 0.83 0.20 (0.75, 0.90) Investment risk premium ρSBeta 0.85 0.94 0.05 (0.88, 0.94) Labour demand ρND Beta 0.50 0.78 0.20 (0.74, 0.83) Trade share ρMBeta 0.50 0.91 0.20 (0.88, 0.95) Government consumption ρGBeta 0.50 0.97 0.20 (0.95, 0.98) Government transfers ρTBeta 0.50 0.94 0.20 (0.90, 0.95) 123 International Economics and Economic Policy (2025) 22 :25 Page 39 of 49 25 Table 5 continued Prior distribution Posterior distribution Mean Distr St.Dev DE Commodity imports ρCO Beta 0.50 0.82 0.20 (0.76, 0.86) Productivity growth ρGA Beta 0.50 0.82 0.20 (0.94, 0.98) International bond preference ρBW EA Beta 0.50 0.87 0.20 (0.71, 0.89) Standard deviations (%) of innovations to forcing variables Subjective discount factor εUC Gamma 1.00 1.74 0.40 (0.64, 2.50) Investment risk premium εSGamma 0.10 0.25 0.04 (0.20, 0.44) Price mark-up εMUY Gamma 2.00 8.77 0.80 (5.39, 9.80) Labour demand εND Gamma 1.00 2.81 0.40 (2.56, 2.94) Trade share εMGamma 1.00 1.94 0.40 (1.74, 2.05) International bond preference εBW EA Gamma 1.00 0.21 0.40 (0.15, 0.40) Labour supply εUGamma 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 εGGamma 1.00 0.19 0.40 (0.16, 0.22) Government transfers εTGamma 1.00 0.15 0.40 (0.13, 0.17) Commodity imports εCO Gamma 1.00 5.05 0.40 (4.02, 5.86) Productivity growth εGA Gamma 0.10 0.05 0.04 (0.02, 0.06) Productivity trend εAGamma 0.10 0.02 0.04 (0.01, 0.05) Monetary policy εi EA 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 123 25 Page 40 of 49 International Economics and Economic Policy (2025) 22 :25 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 ρUC Beta 0.50 0.69 0.79 0.20 (0.59, 0.74) (0.73, 0.87) Price mark-up ρYBeta 0.50 0.57 0.62 0.20 (0.33, 0.63) (0.52, 0.69) Trade share ρMBeta 0.50 0.94 0.97 0.20 (0.90, 0.96) (0.95, 0.99) Commodity imports ρCO Beta 0.50 0.90 − 0.20 (0.85, 0.96) Productivity growth ρGA 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 εUC Gamma 1.00 1.95 0.69 0.40 (1.53, 2.69) (0.46, 1.01) Price mark-up εMUY Gamma 1.00 0.17 0.43 0.40 (0.14, 0.28) (0.34, 0.53) Trade share εMGamma 1.00 3.14 2.89 0.40 (2.69, 3.42) (2.53, 3.16) Commodity imports εCO Gamma 1.00 4.86 − 0.40 (4.02, 5.86) Productivity growth εGA Gamma 0.10 0.03 0.08 0.04 (0.03, 0.04) (0.07, 0.10) Monetary policy εiGamma 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 123 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 chainindexed 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 Multicountry (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 Thedataused forestimationareavailableonopen-accessdatabases. Theyarealso available from the corresponding author upon request. Declarations Conflict of interest The author declares no competing interests. Open Access This article is licensed underaCreative Commons Attribution4.0InternationalLicense, 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. 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