Modelling pandemic risks for policy analysis and forecasting

Abstract

What were the economic effects of vaccination campaign, agents’ adaptation to containment measures, and fiscal and monetary measures during the COVID-19 pandemic? To quantify these effects, we augment the ECB’s macro-econometric model with an endogenous epidemiological block, providing one of the first institutional policy models with epidemiological elements. The model tracks closely actual pandemic developments by relying on detailed epidemiological data and by nesting a wide range of features, including vaccination campaigns, emergence of new variants and learning effects. Importantly, it includes an endogenous policy reaction function for containment measures, allowing counterfactual simulations. Our simulation results show that: (i) agents’ adaptation to containment measures over time was key in reducing negative macroeconomic consequences of lockdowns, (ii) the vaccination campaign slowed down infection rates and hospitalizations, enabling a relaxation of containment measures and avoiding a sharp double dip in economic activity and (iii) complementary fiscal and monetary policy interventions provided support to the economy.

1. Introduction

The outbreak of the COVID-19 pandemic emergency together with the related containment and “smart” social distancing measures have shattered the productive sector, households’ behaviour and the financial system through a variety of channels. The unprecedented COVID-19 pandemic shock constituted a formidable challenge for economies, and we have observed a multidimensional response of economic agents to both health and economic emergency. This paper assesses the economic consequences of the COVID-19 pandemic and the adaptation and responses of different economic agents, and in doing so we adapt the central bank modelling apparatus to this new economic landscape.

We augment the ECB-BASE model (Angelini et al., 2019), a large-scale semi-structural model for the euro area, with the predictive dynamics of an augmented epidemiological SIR model. This enables to assess the interplay between the epidemiological fundamentals of the COVID-19, containment policies and the economy. Our work is to our knowledge one of the first attempts to enhance an institutional policy model, used in a central bank, with pandemic fundamentals. In that respect, our work falls into a rapidly growing field of papers related to COVID-19 that have been written since the outbreak of the pandemic,1 and those assessing the economic effects caused by Covid-19 that have been well documented and summarized by Padhan and Prabheesh (2021), extending previous work by Maliszewska et al. (2020) and Goodell (2020).

Specifically, our work relates strongly to recent papers that incorporate extensions of the canonical epidemiological model introduced by Kermack and McKendrick (1927) into macroeconomic models. For example, Eichenbaum et al. (2021) study the equilibrium interactions between economic decisions and epidemic dynamics in a Dynamic Stochastic General Equilibrium (DSGE) model for the U.S. According to their main findings, agents’ decision to cut back on consumption and work reduces the severity of the epidemic but aggravates the size of the recession. The competitive equilibrium is not socially Pareto optimal as people infected with the virus do not fully internalize the effect of their consumption and work decisions on the spread of the virus. In their benchmark model, the optimal containment policy increases the severity of the recession but saves roughly half a million lives. Similarly, Bodenstein et al. (2022) and Bodenstein et al. (2021) assess the economic costs related to drastic public health measures, namely social distancing and lockdowns. They combine a calibrated epidemiological model with a two-sector model featuring a set of industries that produce core inputs used by all other industries, capturing key characteristics of the U.S. Input-Output Tables. They also find that social distancing measures can reduce costs, especially if skewed towards non-core industries and occupations with tasks that can be performed from home. A simplified variation of the SIR model presented by Atkeson (2020) is taken by Alvarez et al. (2021) to assess an optimal lockdown policy, using micro data to calibrate the key model parameters. They find that the optimal policy varies over time as a function of both the fraction of infected and susceptible in the population, and that the intensity of the lockdown depends on the level of the fatality rate.

The effectiveness of lockdown response, considering both, epidemiological and economic perspectives, is likewise analysed by Gori et al. (2021). Relying on the Solow growth model with nested SIR model, the authors find that lockdowns and early prevention of the spread of the disease are a sub-optimal response relative to publicly funded broad-based testing, contact tracing, and early isolation policies.

Apart from seeking the optimal policy mix from the perspective of mitigating epidemiological developments and cyclical impacts on the economy, the literature also evolved around studying policies suitable for addressing long-term economic consequences. For example, the modelling framework by Michl (2021) analyses macroeconomic consequences of the Covid-19 pandemic through the lens of hysteresis and a possible drag on long-term trends, which have been common also in the cases of temporary but exceptionally large macroeconomic shocks in the past. The author uses the modelling framework incorporating hysteresis effects to illustrate how indecisive policy responses can lead to locked-in losses of output.

The aim of this paper is to synthesize the above highlighted modelling advances associated with macroeconomic impacts of the Covid-19 crisis in a large-scale institutional modelling framework applied to produce regular forecasts and policy analyses. This study contributes to the literature in many ways. First, our macroeconomic model nests an endogenous epidemiological dynamics that is informed by detailed and high frequency epidemiological data and wide range of elements related specifically to the Covid-19 crisis, including non-pharmaceutical prevention measures, lockdown policies, vaccination campaigns, emergence of new variants of the disease, and learning effects of the economy. Second, the propagation of epidemiological developments to the economy is analysed through a rich set of transmission channels, incorporating private consumption and investment, supply side and productivity, labour market and wages. Finally, the model derives an endogenous policy reaction function for containment measures, allowing to perform various counterfactual simulations in search for optimal macroeconomic and epidemiological responses to the Covid-19 crisis.

Elaborating on these points, this paper integrates the ECB’s workhorse projection model and the extension of the SIR model into the ECB-BASIR in order to shed light on numerous trade-offs faced by households, governments and health authorities in addressing the public health situation, while limiting the economic fallout of the pandemic. In doing so, we aim to evaluate multitude of macroeconomic channels in combination with various health policies set to curb adverse consequences of COVID-19 pandemic using one coherent modelling framework.

The granularity of the epidemiological module enables to account not only for susceptible, infected and recovered people, but also for vaccinated population and for lockdown measures. In this vain we develop an extended variant of the SIR model, the SIHVDR model with time variant structural parameters.2 The epidemiological module of the ECB-BASIR then generates shocks to agents’ ability to work, consume and invest, which we refer to as “pandemic wedges”. At the same time, the macroeconomic outcomes affect the evolution of epidemiological variables in the SIHVDR module. Finally, the model nests an endogenous policy response function to pandemic developments, allowing us to perform realistic counterfactual scenarios.

In line with Donadelli et al. (2021), we deviate from calibrating pandemic wedges and parameters related to the epidemiological model on the basis of empirical evidence related to past pandemic episodes and instead rely on up-to-date data and empirical literature on the Covid-19 specifically. The calibration and estimation strategy allows us to achieve a satisfactory empirical performance in matching the observed euro area developments over the 2020-to-2021 period for (i) the health situation, (ii) a range of macroeconomic outcomes, and (iii) the stringency of containment measures.

We utilize the quantitative ability of the ECB-BASIR model to construct selected counterfactual scenarios, related to alternative containment policies, the role of medical solutions, or other macroeconomic contingencies.

The first counterfactual policies we consider are designed to uncover the model’s mechanics. The simulation assumes that no specific measure is undertaken to fight the virus. Under this “Laissez-faire” approach, real GDP drops in the second quarter of the pandemic emergency by more than 2%, recovering in the third quarter but remains persistently below the baseline by less than 1% over a three-year horizon. Indeed, after the second quarter, the share of infected people approaches zero, and the economy starts recovering from the slump, while the excessive death toll of the disease exerts a permanent drag on economic activity. Interestingly, prices increase initially and the disinflationary effects remain muted over the simulation horizon due to supply-side factors weighing on labour force and potential output. Overall, while the public health situation dramatically deteriorates in this scenario, the long-term economic costs might still be significant.

We then turn to the analysis of various containment measures and assess their effectiveness in mitigating the spread of the virus as well as their impact on the economy. While general confinement measures reduce the number of deceased people by a factor of six during the first wave compared with the “Laissez-faire” scenario, they carry along much larger economic costs: such interventions, calibrated to match the initial government response in the euro area over the observed period, lead to a V-shaped recession, with real GDP plunging to −12% by 2020Q2, bouncing back to −4% in 2020Q3. The endogenous propagation mechanism of the model points at pervasive slack in the economy and significant disinflationary pressures, of around 0.5 p.p. in annual terms. We also specify an endogenous policy formulation that relies on capping hospitalization rates at the lowest economic costs. Under this endogenous containment policy, the overall economic impact of the first phase of the pandemic is dramatically reduced, with the initial drop in real GDP at roughly 5%. At the same time, a second wave of infections and associated tightening of containment measures would have nonetheless occurred.

In the next sections we assess actual economic responses from different agents in economy. We first evaluate learning by economic agents, which is a key feature of the empirical validation of the model. Namely, the estimation and also circumstantial evidence suggests it is crucial to allow for agents’ learning to mitigate the macro-economic impact from the containment measures. We define learning as a reduction of the initial macro-economic impact of containment measures3 — in case of no-learning the impact from containment measures would not decrease in time, while in case of 100% learning the containment measures would not affect macro-economic dynamics anymore. The estimates suggest fast and considerable learning effects that were crucial in avoiding a considerable slump over the winter of 2021 that rather ended as a milder recession followed by a strong recovery. The estimated achievable maximum level of learning is at 67%, implying in the long-run the containment measures would weigh on economic activity almost 70% less than in initial stages of the pandemic.

Focusing on the risks associated with the medical solution to the pandemic, we construct a counterfactual scenario that assumes the non-availability of vaccines. The vaccination campaign is estimated to have limited economic effects in the first half of 2021 but became instrumental in enabling the relaxation of containment measures in the second half of 2021.

Finally, unravelling the macroeconomic consequences of the pandemic emergency may also require accounting for policy responses. The model simulations reveal complementary transmission channels of fiscal and monetary policies, with fiscal transfers importantly preserving the income and consumption of households, while monetary measures providing supportive role to the business investment via favourable financing conditions.

The remainder of this paper is organized as follows. Section 2 describes the epidemiological module and its integration into the ECB-BASE model. Subsequently, Section 3 defines the calibration and estimation strategy of different parameters, wedges and the policy function estimated to close the model. Section 4 discusses the macroeconomic simulations of selected containment policies while the quantification of learning effects are laid out in Section 5. Section 6 articulates the medical responses via the vaccination to the pandemic crisis with the aid of counterfactual experiments. Section 7 assess the implications of fiscal and monetary policies, followed by Section 8 on policy considerations. Finally Section 9 summarizes and concludes.

2. ECB-BASIR

The ECB-BASIR is an extension of the ECB-BASE model (Angelini et al., 2019) created to address the specific features of the COVID-19 crisis through the lens of an epidemiological satellite SIR module. In what follows we describe both modules, the SIR model and the ECB-BASE, and their endogenous interaction. While this section provides the general modelling principles, Appendix describes key model equations affected by our framework.

2.1. The susceptible-infectious-recovered (SIR) model

To model epidemiological developments we rely on the class of compartmental models designed by Kermack and McKendrick (1927) (see, Kermack and McKendrick, 1927). This mathematical model divides the population into three compartments to predict how a disease can spread: S, the number of susceptible; I, the number of infectious, and R the number of recovered or deceased (or immune) individuals. We go one step further and use a variant of the SIR model that additionally includes V, the share of vaccinated of the susceptible population, H, as a share of hospitalized, and D, as a share of deceased, while accounting also for different types of containment policies.

These S, I, H, V, D, R, compartments of the population vary over time according to the following daily dynamic system.

$$s_t=s_{t-1}-\widetilde{{\beta }_t}{s}_{t-1}{i}_{t-1}-{\delta }_t^v{s}_{t-1}$$ (1)

$$i_t=i_{t-1}+\widetilde{{\beta }_t}{s}_{t-1}{i}_{t-1}+\widetilde{{\beta }_t}{\zeta }^v{v}_{t-1}{i}_{t-1}+\widetilde{{\beta }_t}{\zeta }^r{r}_{t-1}{i}_{t-1}-({\mu }^r+{\mu }^d)i_{t-1}$$ (2)

$$h_t=h_{t-1}+i_{t-1}{\iota }^i(\widetilde{{\beta }_t}{s}_{t-1}+(1-{\iota }^v)\widetilde{{\beta }_t}{\zeta }^v{v}_{t-1}+{\iota }^r\widetilde{{\beta }_t}{\zeta }^r{r}_{t-1}-({\mu }^r+{\mu }^d))$$ (3)

$$v_t=v_{t-1}+{\delta }_t^v{s}_{t-1}-(1-{\zeta }^v)\widetilde{{\beta }_t}{v}_{t-1}{i}_{t-1}$$ (4)

$$d_t=d_{t-1}+{\mu }^d{i}_{t-1}$$ (5)

$$r_t=r_{t-1}-{\zeta }^r\widetilde{{\beta }_t}{r}_{t-1}{i}_{t-1}+{\mu }^r{i}_{t-1}$$ (6)

where $s_t$ is the share of susceptible population at risk of infection, $i_t$ is the share of infected population with or without symptoms, $h_t$ is the share of hospitalized population, $v_t$ is the share of the population which is vaccinated, $d_t$ is the share of population that died due to the infection and $r_t$ is the share of recovered population.

The central parameter is the rate at which the infection occurs and is defined as $\widetilde{{\beta }_t}=\alpha \gamma (1+{\tilde{c}}_t)(1+{\tilde{n}}_t)(1-{\lambda }_t)$.4 The rate of contacts resulting in an infection is denoted by $\alpha$ and $\gamma$.5 Two terms in Eqs. (1), (2), $(1+{\tilde{c}}_t)(1+{\tilde{n}}_t)$ have been added to the standard SIR model, introducing a dependence between consumption and labour decisions (in the macroeconomic allocation) and the spread of the disease as in Eichenbaum et al. (2021). The term, $(1+{\tilde{c}}_t)$, captures the fact that during activities related to consumption, contacts between people are inevitable therefore enhancing the probability of people getting infected. In particular, the exact specification assumes that when agents consume more than in the baseline case (${\tilde{c}}_t$ $>$0), these agents have $(1+{\tilde{c}}_t)$ more contacts, thereby increasing the spread of the disease. The same reasoning applies to labour decisions captured by the term $(1+{\tilde{n}}_t)$. Altogether, this specification opens a channel from the macroeconomic model to the epidemiological module through the sensitivity of the spread of the disease to “economic interactions” among people.

The variable ${\lambda }_t$ captures developments that had a significant effect on the infection rate, capturing, in a reduced-form, a wide range of policies aimed at reducing the effective infection rate, for example lockdowns and other non-pharmaceutical interventions (NPI) such as the general obligation to wear face masks.6 The exact definition of ${\lambda }_t$ is:

$${\lambda }_t=l_t+{\lambda }^{npi}+{\lambda }^s+{\lambda }^{delta}$$ (7)

where $l_t$ is the share of lockdown agents that captures the stringency of containment measures and is discussed in further detail in Section 2.3. Parameter ${\lambda }^{npi}$ captures the decrease of infection rate due to other non-pharmaceutical interventions after April 2020 and ${\lambda }^s$ is the “summer effect” that captures the significant decrease of infections observed during the summer period from 15 May until 15 August of each year. Finally, ${\lambda }^{delta}$ captures the increase of the infection rate due to the “Delta variant”, that appeared in summer 2021. All three parameters are estimated as discussed in Section 3.1.

The last set of parameters is related to transition rates between different groups. ${\mu }^r$ is the recovery rate, and ${\mu }^d$ is the fatality rate. The rate of vaccination is expressed by ${\delta }_t^v$. Since vaccines do not offer a complete protection against the virus, the inefficiency of vaccines is captured by parameter ${\zeta }^v$ which implies a positive but smaller probability of getting infected. Similarly, the probability of reinfection is ${\zeta }^r$. Additionally, being vaccinated and being previously infected are not providing only lower probability of infections, but even more importantly are reducing the probability of hospitalizations as captured by the difference in parameters ${\iota }^i$, ${\iota }^v$ and ${\iota }^r$ that measure the probability of hospitalization for the infected, vaccinated and recovered respectively.

2.2. ECB-BASE model

The ECB-BASE is a large-scale, estimated, semi-structural model for the euro area, featuring optimizing agents constrained by generalized adjustment costs. The model comprises demand, supply and financial blocks. The link to the SIHVDR module is established through the decision problems of agents. The optimization problems can be generalized in the form of a reward function,

$$\begin{array}{ccc}{x}_t^{\ast }\hfill & =\hfill & \underset{x}{argmax}{\mathbb{E}}_t\sum _{t=1}^T{f}_{t+1}(x_t,u_t)\hfill \\ u_{t+1}\hfill & =\hfill & g_t(x_t,u_t)\hfill \\ x_t^{\ast }\hfill & \in \hfill & \Phi \hfill \end{array}$$ (8)

where $u_t$ is the state variable, $x_t$ is the control variable chosen for the optimization problem, the constraint $x_{t+1}$ specifies the influence that the control exerts on the state and the control variable takes values in a given set $\Phi$. This is a generic representation for all optimizing problems in the model, like households’ lifetime utility optimization in consumption, profit maximization by firms subject to capital accumulation to determine investment and optimal level of employment, etc. For a detailed specification of each of those optimization problems see Angelini et al. (2019).

However, agents cannot adapt their behaviour instantaneously in line with the optimal condition. Instead they choose an optimal path of their decision variable subject to minimizing the associated polynomial adjustment costs in line with Tinsley (1993).

The cost function can be expressed as:

$$C_t={\mathbb{E}}_{t-1}\sum _{i=0}^{\infty }{\beta }^i\left[{(x_{t+i}-x_{t+i}^{\ast })}^2+\sum _{k=1}^m{b}_k{\left({(1-L)}^K{y}_{t+i}\right)}^2\right]$$ (9)

where $x_{t+i}$ is the decision variable, $x_{t+i}^{\ast }$ is its desired level, $m$ is the order of the polynomial and $L$ is the lag operator.

Minimizing the cost function yields the following first order condition:

$$(x_t-x_t^{\ast })+\sum _{k=1}^m{b}_K{\left[(1-L)(1-\beta F)\right]}^K{y}_t=0$$ (10)

where $F=L^{-1}$ is the lead operator. Note that $b_K{\left[(1-L)(1-\beta F)\right]}^K$ is a self-reciprocal polynomial, i.e. a polynomial with the property that the coefficients of the forward looking terms can be deduced from the backward-looking terms.

Let us denote $x_t^u$ as the variable of interest not subject to constraints stemming from infections or lockdown. The short run dynamic behaviour for $x_t^u$ is given by,

$$\Delta x_t^u=\left(a_0\left(x_{t-1}^{\ast }-x_{t-1}\right)+\sum _{i=1}^{m-1}{a}_i\Delta x_{t-i}^u+{\beta }_1{x}_t+{\mathbb{E}}_{t-1}\stackrel{\infty }{\sum _{j=0}}{d}_j\Delta x_{t+j}^{\ast }\right)$$ (11)

where $a_0$ is the coefficient on the deviation of the variable of interest from its target and $a_i$ gives the weights on the backward-looking terms. The term ${\mathbb{E}}_{t-1}{\sum }_{j=0}^{\infty }{d}_j\Delta c_{t+j}^{\ast }$ represents the expectations of future targets.

Finally, the link between the macroeconomic model and to the epidemiological model can be expressed by the following:

$$x_t=(1-i_t-l_t-d_t)x_t^u+i_t{\alpha }_x^I{x}_t^u+l_t({\alpha }_x^L+{\psi }_t(1-{\alpha }_x^L))x_t^u$$ (12)

where $(1-i_t-l_t-d_t)$ is a share of agents not affected by the virus, $i_t$ is the share of infected agents, $l_t$ is the share of locked down agents, and $d_t$ is the share of deceased people.7

Parameters ${\alpha }_X^I$ and ${\alpha }_X^L$ determine how much lower consumption, investment and labour of infected and locked down agents is compared to unconstrained agents. Parameter ${\psi }_t$ captures the learning process such that over time the economic effects of lockdown measures dissipate. The calibration and estimation of the wedges is discuss in Section 3.2.8

2.3. Containment policy

In order to conduct counterfactual experiments we need to close the model and specify the policy function that endogenously determines the level of the lockdown. We postulate that the policy makers decide on lockdown measures according to the following policy function:

$$\begin{array}{c}\hfill l_t^{\ast }=\underset{l_t}{argmin}\sum _{\underset{\_}{T}}^{\overline{T}}{\left(l_t\right)}^2\hfill \\ \hfill s.t.\hfill \\ \hfill h_t<{\mu }^{h}max\left(h_z\right)forz<\underset{\_}{T}\hfill \end{array}$$ (14)

where $l_t$ is the level of lockdown ranging between 0%–100%, $h_t$ is the percentage of hospitalized persons, $max\left(h_z\right)$ is the maximum level of hospitalizations in the first wave in 2020 and ${\mu }^h$ is the parameter determining the reference of hospital capacity and T defines the dates of the first wave, first day to last day, from 0 to 200 days. The optimization in (14) determines the target lockdown, while the actual lockdown evolves in a staggered manner:

$$l_t={\rho }^l{l}_{t-1}+(1-{\rho }^l)l_t^{\ast }$$ (15)

The intuition for this specified policy function is straightforward and is designed to mimic the observed behaviour of stringency measures during the pandemic crisis. The policy function postulates that policy makers try to minimize the degree of lockdowns due to their negative effect on economic activity and other possible negative effects. However, they are still constrained by making sure that the infection rate does not lead to a number of hospitalizations which would exceed the existing hospital capacity. The estimation and the characteristics of the policy function are explained in Section 3.3 below.

3. Calibration and estimation strategy

Compared with the ECB-BASE model, there are three main categories of new parameters, which need to be calibrated or estimated: (i) the parameters specific to the SIHVDR module, (ii) parameters, which directly link the SIHVDR variables to the ECB-BASE through “the pandemic wedges” in consumption, investment, labour market and productivity blocks and (iii) parameters related to public health and lockdown policies which reflect an additional economic wedge created by interventions aimed at containing the spread of the disease. A total wedge on the economy can then be perceived as a combination of the wedge due to infected population and the wedge created by lockdown measures. We discuss the estimation and calibration of each block of parameters in turn. The estimation of the model is based on the macroeconomic and epidemiological data until 10th of October 2021.

3.1. SIHVDR estimation and calibration

The parameters of the epidemiological model are partly calibrated based on the empirical work which studies virus dynamics as discussed in Section 2.1 and partly estimated by fitting the implied model fit to the observed data:

$$\widehat{{\rm Y}}=argmin\sum _{d=0}^D{\left({\tilde{I}}_d-I_d\right)}^2$$ (16)

where $\widehat{{\rm Y}}$ contains the parameters of SIHDVR model that are estimated, $I_d$ are the cumulative infections in period from $d=[0,\dots ,D]$ in the data and ${\tilde{I}}_d$ are the cumulative infections based on the model simulation.

The first step in the estimation is to construct the cumulative infection rate from the data. For this we use the data from the European Centre for Disease Prevention and Control. We retrieve the weekly data on the number of tests and of reported cases for France, Italy, Germany, and Spain.9,10 We use the data of these four countries as a proxy for the euro area. The uncertainty in the reported data is large, especially due to the large share of asymptomatic cases. To get a better estimate of the actual infection rate we therefore use an average of three measures. The first measure is the reported number of cases found in the data. The second measure takes into account the increased testing intensity over time and it is obtained by scaling the number of reported cases by testing frequency.11 The last measure is based on the reported deaths — assuming the mortality rate of 0.37% we can calculate the actual number of infections. The final estimate of the actual number of infected is the simple average between these three measures.

The set of parameters in $\widehat{{\rm Y}}$ from (16) includes four parameters. We estimate the initial share of infected population (as of 15 February 2020), $i_0$, the underlying infection rate $\beta =\alpha \gamma$ and the two parameters affecting infection rate, the effect of other NPI, ${\lambda }^{npi}$, and the so-called “summer effect”, ${\lambda }^s$. The estimates are reported in Table 1 and suggest the initial infection rate of 1.98, approximately a 10% decrease of infections due to other NPIs and a 27% decrease during the summer. We use information from medical studies to calibrate the increase of the infection rate due to the appearance of the new variant of the virus, the Delta variant, ${\lambda }^{delta}$. The empirical research suggests that the Delta variant of the virus increased the infection rate by 60%.12

Table 1.

BASIR parameters.

Parameter	Description	Value
SIR parameters
$\beta =\alpha \gamma$	Initial infection rate	1.9846
$i_0$	Initial share of infected	0.004
${\lambda }^{npi}$	Other NPI effect	0.1019
${\lambda }^s$	Summer effect	0.2734
${\lambda }^{delta}$	Delta variant effect	0.6a
${\mu }^r$	Recovery rate	0.0711a
${\mu }^d$	Death rate	0.025%a
${\delta }_1^v$	Vaccination rate from January until March 2021	0.001a
${\delta }_2^v$	Vaccination rate from April 2021	0.01a
${\zeta }_1^v$	Vaccination efficiency	0.1a
${\zeta }_2^v$	Vaccination efficiency after Delta variant	0.6a
${\zeta }^r$	Reinfection probability	0.03a
${\iota }^i$	Hospitalization rate	0.03a
${\iota }^v$	Vaccination efficiency (hospitalizations)	0.85a
${\iota }^r$	Hospitalization probability for reinfected	0.03a
${\overline{v}}_t$	Vaccination share ceiling	0.8a
Wedge and learning parameters
${\alpha }_C^I$	Consumption wedge infected	0.6a
${\alpha }_C^L$	Consumption wedge lockdown	0.6210
${\alpha }_I^I$	Investment wedge infected	0.6a
${\alpha }_I^L$	Investment wedge lockdown	0.5616
${\alpha }_L^I$	Labour wedge infected	0.6a
${\alpha }_L^L$	Labour wedge lockdown	1a
${\alpha }_{LF}^I$	Labour force wedge infected	0.6a
${\alpha }_{LF}^L$	Labour force wedge lockdown	0.9217
${\alpha }_{LF}^I$	Wage wedge infected	1a
${\alpha }_{LF}^L$	Wage wedge lockdown	0.9799
${\alpha }_A^I$	Productivity wedge infected	0.6a
${\alpha }_A^L$	Productivity wedge lockdown	0.9217
${\psi }_1$	Learning ceiling	0.6727
${\psi }_2$	Learning rate	0.9999
${\psi }_3$	Sigmoid’s midpoint in learning	0
Policy function parameters
${\mu }^h$	Hospital capacity	0.5913
${\rho }^l$	Smoothing parameter in policy function	0.5

^aParameters are calibrated.

The last set of parameters related to the SIHDVR model relates to the transition rates between susceptible, infected, vaccinated and recovered. We assume that, infected people either recover at a rate of ${\mu }^r=0.07114296$ or die with a death rate of ${\mu }^d=0.00025704$. The sum of these two parameters ${\mu }^r+{\mu }^d=0.0714$ implies that the outcome of discovering the disease is on average known after 21 days,13 while the calibrated death rate implies a fatality rate of 0.37%, somewhat on the lower end of the estimates but consistent with the evidence collected for Germany.14

The rate of vaccination is expressed by ${\delta }_t^v$ and is calibrated to fit the observed vaccination rate. We assume that the vaccination started in January 2021 and initially at a rate of 0.1%, accelerating to 1% after April 2021 and that the maximum share of vaccinated population is 80%. The vaccines do not offer a complete protection against the virus and this inefficiency of vaccines is captured by parameter ${\zeta }^v$. The initial efficiency of vaccines is assumed to be 90%, dropping to 60% with the appearance of the Delta variant of the virus.15 We calibrate the probability of reinfection on ${\zeta }^r$ to 3% based on the meta-study in Sotoodeh Ghorbani et al. (2022).16 Additionally, vaccinations and being previously infected are not providing only lower probability of infection, but even more importantly reduce the probability of hospitalization as captured by the difference in parameters ${\iota }^i$, ${\iota }^v$ and ${\iota }^r$ that measure the probability of hospitalization for infected, vaccinated and recovered, respectively. We calibrate the general hospitalization rate, ${\iota }^i$, at 3% which matches the number of hospitalizations to the infections in our data. Following the results by Bajema et al. (2021) we calibrate the overall adjusted vaccine effectiveness against COVID-19 associated to hospitalization at 85%. Hospitalization probability of being reinfected, ${\iota }^r$, is set to 3%.

The fit of the model can be seen in Fig. 1. Although the model is relatively parsimonious and depends also on non-optimal proxies for the lockdown intensity, we can see that the model dynamics follow closely the observed infection rates.

Fig. 1.

Actual and fitted cumulative infection rate.

Note: The figure displays actual cumulative infection rate in red and the fitted outcome in blue based on the estimation and calibration described in Section 3.1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.2. Pandemic wedges

The second set of parameters specific to the ECB-BASIR model are the parameters providing the link between the epidemiological developments and macroeconomic outcomes. The epidemiological outcomes are channelled to the macroeconomic part of the model through shares of infected and lockdown population. The calibration of wedges induced by these population cohorts relies partially on empirical data and micro evidence and partially on observed macroeconomic outcomes associated and related to imposition of containment measures.

We start by discussing parameters related to the wedge created on the economy by the infected population. One of the most important statistics for this calibration is the number of infected people that show no symptoms. The intuition behind this kind of calibration strategy rests on the assumption that the asymptomatic people remain undiagnosed and are therefore unconstrained in their consumption decision, either by quarantine measures or by their health situation. Nevertheless, the estimated share of people testing positive for SARS-CoV-2 that are asymptomatic varies considerably between different studies ranging from a minimum of 5% to a maximum of 80%.17 For simulations conducted in this paper, we consider a median calibration of 60% for the asymptomatic cases among population, the value also considered in the related literature (e.g. see Eichenbaum et al., 2021). Taking as an example a consumption wedge, the calibration ${\alpha }_C^I=0.6$ implies an unconstrained consumption for asymptomatic cases among infected people, while 40% of infected is assumed to not consume at all. We apply a homogeneous treatment to the investment decisions and labour demand, setting to 0.6 also ${\alpha }_{IB}^I$, ${\alpha }_N^I$, and ${\alpha }_A^I$. In line with Bodenstein et al. (2022), we assume that the short-falls due to infected population are consistently reflected in the production side of the economy through wedges imposed on total factor productivity and labour supply (${\alpha }_A^I=0.6$ and ${\alpha }_{LF}^I=0.6$). In line with the income retention and other safety-net policies, wage income is expected to be fully compensated for the infected population.

To account for the wedge implied by lockdown measures, we rely on the strategy that aims towards fitting shortfalls in particular demand components in relation to containment measures. To isolate the economic impact of lockdown measures, we resort to empirical estimates and calibrations that explicitly account for mitigating income and job retention economic policies. The wedges for lockdown persons are estimated by minimizing the sum of squared differences between selected observed and simulated macroeconomic outcomes:

$$\hat{\alpha }=argmin\sum _{q=0}^Q\sum _{k=1}^K{\left({\tilde{Y}}_{k,t+q}-Y_{k,t+q}\right)}^2$$ (17)

where $\hat{\alpha }$ contains five parameters, ${\alpha }_C^L$, ${\alpha }_I^L$, ${\alpha }_{LF}^L$, ${\alpha }_W^L$ and ${\alpha }_A^L$. $Y_{k,t+q}$ is a vector of relevant macroeconomic outcomes, while ${\tilde{Y}}_{k,t+q}$ is its model counterpart. Specifically, vector $Y_{k,t+q}$ contains the growth rate of output, consumption, investment, unemployment, wages and core inflation. The values of estimated parameters can be seen in Table 1. We used the first two quarters of 2020 to estimate the initial value of wedges, while the following four quarters are used to estimate the learning coefficients, ${\psi }_t$, which is discussed in detail in Section 5 below. Based on Eq. (17) and relevant shortfalls observed for consumption and investment, the estimates suggest an implied lockdown wedges of ${\alpha }_C^L=0.62$ and ${\alpha }_{IB}^L=0.56$, which are therefore very close to the assumed wedges for these two categories implied by the infected populations. The impact of the lockdown is estimated to be lower for the production side of the economy with respective lockdown wedges for productivity, labour force and wages of ${\alpha }_A^L=0.92$, ${\alpha }_{LF}^L=0.92$, and ${\alpha }_W^L=0.97$. The estimation of wedges for the production side relies crucially on the co-movement between output and inflation. Those wedges determine the dynamics of potential GDP and thus the co-movement between output and output gap. Output gap in turn, via the Philips curve, determines the response of inflation. While estimated production side wedges are lower compared to demand side wedges, the production side of the economy still reacts. This implies more contained response of the output gap compared to the case without those wedges. The adjustment of supply side suggested by estimation therefore reveals contribution of supply shocks leading to a more contained response of inflation to pandemic developments.18 In order to emulate job retention policies, a lockdown wedge for the labour demand, ${\alpha }_L^L$, is calibrated to 1, implying no shortfall from this particular source of pandemic wedge. The comparison between simulated macroeconomic variables, conditional on estimated total wedges, and actual realizations is demonstrated in Fig. 2.

Fig. 2.

Model based and actual macroeconomic outcomes.

Note: The figure shows simulation outcomes in deviation from baseline (pre-pandemic ECB-BASE conditional forecast from March 2020). The solid line shows the model-based outcomes. The dashed line corresponds to actual data outcome. Real variables are expressed as percentage deviations from the baseline levels. Price and wage inflation rates are annualized and expressed as percentage point deviations from baseline. Unemployment rate is expressed as percentage point deviations from baseline.

3.3. Containment policy

The policy function laid out in Section 2.3 is specified following the observed behaviour of policy makers during the pandemic emergency. To evaluate whether the policy function defined in (14) can replicate well the actual developments in lockdown measure we estimate the parameters and compare the simulated lockdown with the one in the data.

One of the main uses of the model is nesting endogenous epidemiological and macroeconomic dynamics informed by detailed and high-frequency data.19 The data is used to construct the model counterparts and to estimate central model parameters. In order to estimate the model we first construct the observable level of the lockdown. To this end we rely on data from mobility reports available from Google, Google (2021) to construct the index of stringency of containment. More specifically, we create a lockdown proxy for the euro area using data for France, Germany, Italy and Spain. We retrieve changes in mobility compared to a baseline value for categories retail and recreation places, transit stations and workplace.20 We average the changes in all three categories for each country and construct the euro area lockdown proxy by computing the weighted average (by population) of each country mobility trends.

The stringency measure obtained from the Google mobility trends is shown by the solid blue line in Fig. 3. Stringency increases strongly around April 2020, reaching level of 60%. Towards the summer stringency measures were released, reaching levels below 20%, and started increasing in autumn and reaching levels around 40% during the winter of 2021. After April 2021 the stringency measures started to be relaxed and released quickly reaching in October 2021 levels below 10%.

Fig. 3.

Actual and model based lockdown stringency.

Note: The figure displays stringency measure based on Google mobility data in blue and in red the fitted outcome as derived by the model as described in Section 2.3.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

We use the observable stringency index to estimate the model, including the two policy function parameters. The reference hospital capacity, ${\mu }^h$, is estimated at around 59% of the maximum of hospitalizations we observed over the first wave in 2020, while the smoothing parameter ${\rho }^l$ is estimated to be around 0.5 as reported in Table 1. The estimation is conditioned on the first 135 days of pandemic. The main reason is that the lockdowns in the first wave were stronger than implied by the policy function. Given the policy reaction in the first wave was highly conditioned by uncertainty on pandemic developments, we rather condition the estimation on this period and use later more systematic responses to estimate the policy function. We perform the counterfactual scenario in Section 4 using the policy function from the outset of the pandemic confirming that, contrary to later periods over the pandemic, the response in the first wave is harder to describe by this type of the rule.

The red line in Fig. 3 shows the fit of the policy function compared to empirical proxy based on Google mobility data. Although the assumed policy function is simple, the simulated stringency of containment is very close to actual developments. In Section 4 we show how the interplay between different policies and pandemic developments leads to exuberant macroeconomic dynamics we have observed in 2020 and 2021.

4. Macroeconomic propagation of pandemic shocks under alternative containment policies

In this section, we analyse further the macroeconomic transmission of the pandemic on agents’ ability to work, consume and invest and emphasize that the propagation mechanism hinges crucially on containment policies.

Three containment policies are contrasted:

• (ii)“Laissez-faire”, assuming no active policy intervention aimed at containing the pandemic developments;
• (i)“Baseline”, incorporating a policy function fit conditioned on the observed stringency in 2020;
• (iii)“Endogenous containment policy”, assuming policy intervention in line with the estimated policy function provided in (14) since the onset of the pandemic.

The “Laissez-faire” policy assumes that no specific policy measure is undertaken to fight the pandemic such that the health policy parameters are set to ${\delta }_t=0$ and ${\lambda }_t=0\forall t$. Such a “Laissez-faire” counterfactual is a useful benchmark against which the effectiveness of other containment policies can be assessed, in terms of the spread of the virus as well as economic costs. The other two policies we consider differ mainly regarding the response to the first wave of the pandemic: we either assume that confinement measures are imposed on the whole population as in the baseline case or follow the endogenous containment policy specification of Section 2.3. Beyond the first wave, both policies are similar and follow the endogenous containment policy conduct.

In Fig. 4, black lines represent epidemiological outcomes under alternative containment scenarios, while red lines depict corresponding macroeconomic impacts. The responses of macroeconomic variables are represented as deviations from the ex-ante pre-pandemic ECB-BASE projection, conditioned on technical assumptions contained in the ECB March 2020 Macroeconomic Projection Exercise (see ECB, 2021a). In performing the simulations, the macroeconomic propagation is fully driven by the development of pandemic wages, while conditioning assumptions remain unchanged with respect to the ex-ante ECB-BASE baseline projection.

Fig. 4.

Simulations with various containment response policies.

Note: The figure shows simulation outcomes in deviation from baseline (pre-pandemic ECB-BASE conditional forecast from March 2020). The solid line shows the baseline case. The dashed line corresponds to the “Laissez-faire” case. The dotted line represents a case with endogenous policy function. Real variables are expressed as percentage deviations from the baseline levels. Price and wage inflation rates are annualized and expressed as percentage point deviations from baseline. Unemployment rate is expressed as percentage point deviations from baseline.

The baseline case tracks closely the observed stringency in the euro area observed in the various waves of the pandemic so far. In this scenario, the share of population subject to the lockdown measures amounted to 60% in the first wave, reaching the second peak of 40% in the first quarter of 2021, and gradually dissipating thereafter (see bottom right panel in Fig. 4). Conversely, in the “Laissez-faire” scenario, no lockdown measures are assumed, meaning that macroeconomic wedges are entirely subject to development in shares of infected and deceased population. In the concrete case, the wedges are expected to bind only by the end of third quarter of 2020 as cumulative share of 60% of recovered population, and therefore “herd-immunity”, is attained already after the first wave of the pandemic (see fourth row, far-right panel in Fig. 4). Finally, the endogenous policy function case represents roughly a mid-way between the baseline case and the “Laissez-faire” scenario in terms of the overall spread of the virus and the speed at which the pandemic developments and binding wedges are expected to dissipate.

While the baseline case reduces the share of infected and deceased by almost a factor of six, the corresponding macroeconomic wedges still remain notably higher, driven by the lockdown population. The loss in the real GDP in the first half of the 2020 amounts to roughly 12%. With the endogenous containment policy function, the overall economic impact is dramatically reduced, with the initial drop in the real GDP at roughly 5%, relative to the 2.5% in the “Laissez-faire” case. The contribution of the lockdown population to the pandemic wedges is particularly big on the demand side of the economy, with real consumption and real investment respectively falling to 17% and 26% in the first half of 2020 in the general confinement case, more than 4 times stronger response than in the “Laissez-faire” case.

Conversely, the wedges related to the labour market and supply side are predominantly driven by the realized spread of the virus as estimated wedge coefficients emulate the mitigating effects of job and income retention schemes for the lockdown and quarantined part of the population. In this regard, the “Laissez-faire” case displays the largest drop in employment among all three scenarios and roughly similar dynamics in the labour-force participation compared to the general-confinement case. Likewise, while the overall effect on the consumer price inflation is strong and persistent for the scenarios incorporating lockdown measures, with peak effect close to 0.5p.p., the effects on the wage inflation remains transitory and roughly similar across all three scenarios. Finally, the “Laissez-faire” case highlights the primary mechanism through which the epidemiological model affects the potential output. Absent the lockdown measures and their impact on demand-side wedges, the inflationary pressures are driven by the negative impact on the potential output, which in the “Leissez-faire” case outweighs the drop in the real output as the spread of the disease propagate to labour force and productivity via infected and deceased parts of population.

5. Quantifying the learning effects

Over the course of the pandemic we witnessed how economic agents have had to adapt to the new social realities. In the initial stages of the lockdown, the new working regime induced an extremely detrimental impact on productivity, but by the second lockdown households and firms have, to an incredible extent, adjusted to new realities. In the data these developments are best represented by the falling correlation between the stringency indicators and economic developments. In this section we explore the role of agents’ adaptation to different containment measures over the pandemic. This adaptation is commonly referred to as the learning effects.

In Section 2.2, we have defined and described the pandemic wedges that link the epidemiological and macroeconomic developments:

$$x_t=(1-i_t-l_t-d_t)x_t^u+i_t{\alpha }_x^I{x}_t^u+l_t({\alpha }_x^L+{\psi }_t(1-{\alpha }_x^L))x_t^u$$ (18)

where we defined the parameter ${\psi }_t\in [0,1]$ that captures the learning processes (for definitions of other parameters please refer to Section 2.2). Learning is ingrained in the scalar $(1-{\psi }_t)$ and applied to wedges related to locked down agents, ${\alpha }_x^L$, in order to capture dissipating economic effects of lockdown measures. For example, when learning is complete, ${\psi }_t=1$, the wedges no longer bind and pandemic developments stop affecting economic dynamics. We decided for a parsimonious modelling with only one general learning parameter affecting all wedges in order to avoid over-fitting the behaviour of specific demand components. The time profile of the learning mechanism is modelled as a logistic process described by the following equation:

$${\psi }_t=\frac{{\psi }_1}{1+exp(-{\psi }_2(t-{\psi }_3))}$$ (19)

The logistic function captures the fact that agents learn fast in initial periods, but the learning rate starts to fall afterwards. The learning rate is captured by parameter ${\psi }_2$, where a higher rate implies faster learning. Sigmoid’s midpoint, ${\psi }_3$, determines the time point at which the sigmoidal learning curve reaches half of its maximum learning. The maximum learning is defined by parameter ${\psi }_1$. The introduction of this parameter allows for the possibility that learning might not be complete, i.e. ${\psi }_1<1$. The parameters are estimated and can are reported in Table 1. We estimate the specific wedges on the first two quarters of 2020 and use the next four quarters to estimate the learning effects. The estimation shows that learning was fast, with the bulk of the learning already taking place in 2020. Additionally, estimates suggest that the maximum achievable level of learning stands at 67%, implying that in the long-run the containment measures would impede on economic activity almost 70% less than in initial stages of the pandemic.

In order to assess how learning contributed to economic activity, we conduct a counterfactual experiment21 in which we compare two simulations, a baseline case that includes learning, as reported in the red solid line in Fig. 5, and an alternative case, depicted by the red dotted line, in which we assume no learning. In both simulations we allow for endogenous lockdown responses.

Fig. 5.

Learning vs. no learning impact.

Note: The figure shows simulation outcomes in deviation from baseline (pre-pandemic ECB-BASE conditional forecast from March 2020). The solid line shows the baseline case including learning. The dashed line depicts the simulation excluding learning. Real variables are expressed as percentage deviations from the baseline levels. Price and wage inflation rates are annualized and expressed as percentage point deviations from baseline. Unemployment rate is expressed as percentage point deviations from baseline.

Focusing on the output dynamics plotted in top left panel of Fig. 5, we can see that learning had a large effect. The initial drop of output is the same in both scenarios as we impose ex-ante no-learning in the first two quarters. However, already in the third quarter of 2020 we estimate learning to reach around 35%, implying that the recovery in 2020q3 was faster than in the counterfactual scenario with no learning. The largest gap between the two scenarios opens in the next two quarters, where we can see that the recession over autumn of 2020 and winter of 2021 would be considerably stronger had agents not adapted to increased stringency of containment measures. Considering the second pandemic wave, the negative impact on the economic activity would in the case of no learning be considerably more pronounced, with additional loss in GDP at around 4% compared to 1% in the learning scenario.

In the later periods, incorporating the start of the vaccination campaign and gradual phase out of containment measures, the difference between the two scenarios becomes less evident. In summary, we estimate fast and considerable learning effects that were crucial in avoiding a considerable slump over the winter of 2021 that rather ended as a milder recession followed by a strong recovery.

6. The medical response: the macroeconomic effects of vaccination

The economic downturn in 2020 and 2021 was caused by the COVID-19 pandemic, which is inherently a medical issue. Although not common in past recessions, the current downturn opens the question about the interplay between macroeconomic developments and medical policies. Over the two years, myriad of medical solutions was proposed in order to prevent or heal the consequences of the COVID-19 virus, but vaccination stands out as the most important of all. In this section we explore the effect vaccination has had on macroeconomic outcomes, considering uncertainty related to pandemic developments, other structural parameters and standard macroeconomic uncertainty.

6.1. Counterfactual design and accounting for uncertainty

To study the effects of vaccine implementation we construct various counterfactual scenarios that assume the non-availability of vaccines. In constructing scenarios we use the benefit of the model that allows us to take into account the uncertainty on some of the structural parameters that determine pandemic and macroeconomic dynamics.22 Namely, ECB-BASIR can also indicate the distribution of risk, spanning relevant sources of uncertainty. In particular, the model can be used to assess a composite measure of risk density combining (i) the standard historical uncertainty captured in the residuals of the model, (ii) uncertainty about the fundamentals of the pandemic (estimated and calibrated epidemiological parameters). and (iii) uncertainty about other structural parameters, like degree of learning.

Considering the uncertainty is crucial in assessing alternative scenarios, as uncertainty about pandemic fundamentals coming from medical studies is large. Table 2 reports the parameter’s distributions we use in construction the risk intervals around the scenarios. For example, two main uncertainties regarding the pandemic developments relate to how more infectious the Delta variant is and how efficient the vaccines are against it. Therefore we do not use only a median estimate, but we rather draw the increase of the infection rate due to the Delta variant from a normal distribution with a mean of a calibrated value and a standard deviation that is based on empirical research on pandemic developments, ${\lambda }^{delta}\sim \mathcal{N}(0.6,0.2)$. Similarly, we consider that vaccination efficiency can range on uniform interval, ${\zeta }_2^v\sim \mathcal{U}(0.3,0.9)$. The other two important sources of uncertainty are the rate of learning and standard macroeconomic uncertainty captured in historical residuals. We consider the uncertainty from September 2021 as of the time of writing up this work. Table 2 summarizes all the distributions we used.23

Table 2.

BASIR parameter’s uncertainty ranges.

Parameter	Description	Distribution
$\beta =\alpha \gamma$	Initial infection rate	$\mathcal{N}(1.98,\hat{\Sigma })$
$i_0$	Initial share of infected	$\mathcal{N}(0.0039,\hat{\Sigma })$
${\lambda }^{npi}$	Other NPI effect	$\mathcal{N}(0.10,\hat{\Sigma })$
${\lambda }^s$	Summer effect	$\mathcal{N}(0.27,\hat{\Sigma })$
${\lambda }^{delta}$	Delta variant effect	$\mathcal{N}(0.6,0.2)$
${\delta }_3^v$	Vaccination after October 2021	$\mathcal{U}(0.0008,0.0012)$
${\zeta }_2^v$	Vaccination efficiency after Delta variant	$\mathcal{U}(0.3,0.9)$
${\zeta }^r$	reinfection probability	$\mathcal{U}(0.01,0.05)$
${\iota }^v$	Vaccination efficiency (hospitalizations)	$\mathcal{U}(0.75,0.95)$
${\psi }_t$	Learning	$\mathcal{N}({\overline{\psi }}_t,0.1)$

6.2. The macroeconomic effects of vaccination: results

In Fig. 6, Fig. 7 the blue line depicts the baseline case and the red line denotes the severe scenario in which we assume no vaccination is available over the considered period. The blue and red areas correspond to 68% risk bands. The baseline GDP profile and HICP inflation profile are centred on the September 2021 ECB staff macroeconomic projection. In the middle right panel we see that in the baseline scenario – that captures actual developments – vaccinations start in the beginning of 2021 with an initial low rate of vaccination. Over the spring the rate of vaccinations accelerated considerably and by September 2021 over 60% of the population was vaccinated. On the other hand, in the counterfactual scenario we assume an extreme case in which no vaccination is available and therefore the share of vaccinated population stays at 0% through the whole period until 2023.

Fig. 6.

Pandemic outcomes for different vaccination start dates.

Note: The figure displays a severe scenario, red line and a baseline case blue line. The blue and red coloured areas represent the 90% risk bands. The distribution is obtained by random simulations considering standard historical uncertainty captured in the residuals of the model, the uncertainty about the fundamentals of the pandemic parameters, and structural parameters as the speed of learning as described in Section 6.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7.

Macroeconomic outcomes for different vaccination start dates.

Note: The figure shows simulation outcomes in deviation from GDP in 2019q4. The blue line represents the baseline scenario, which is centred around the ECB’s staff macroeconomic projections in September 2021. The severe scenario is depicted with the red line. The blue and red coloured areas represent the 90% risk bands. The distribution is obtained by random simulations considering standard historical uncertainty captured in the residuals of the model, the uncertainty about the fundamentals of the pandemic parameters, and structural parameters as the speed of learning as described in 6.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Turning to the infections, after a strong second wave in the baseline scenario, a large share of vaccinated population implies a considerably milder infection wave in autumn 2021. As vaccines offer even better protection against the hospitalizations compared to cases of infections, the wave in hospitalizations is even milder. On the other hand, given that no vaccinations are assumed to take place, the expected infection rates are higher already in spring and summer 2021, demanding somehow stricter containment measures as shown in the middle left panel of Fig. 6. However, the lack of immunity gained via the vaccination hits after the favourable summer conditions and the beginning of the autumn period. The spread of the virus is further fuelled by the outbreak of the Delta variant in summer 2021 that is on average 60% more infectious than the previous variant.24 Containment measures are thus reintroduced by the end of 2021 and the beginning of 2022 in order to keep hospitalizations under control. Containment measures must be additionally higher as the lack of vaccination implies the wedge between infections and hospitalizations remains higher than in the baseline.

The level of GDP can be seen in Fig. 7. In the baseline scenario the level of GDP recovers up to pre-pandemic levels of GDP at the end of 2021 following the complete relaxation of the containment measures. On the other hand, the reintroduction of lockdowns in autumn in the severe scenario would produce the third recession. Due to learning effects discussed in Section 5 the recession would not be as deep as the intensity of lockdowns could suggest, but nevertheless the recession would be comparable to the second recession observed in winter 2021. Output would stay below the pre-pandemic levels also in 2022, also as the pandemic could reappear in 2022 as the share of recovered population would still not provide herd immunity by the end of 2022. Inflation would be around 0.5% lower over 2021 and 2022 mainly due to a more negative output gap.

Interestingly, we can observe that uncertainty around the infection rate in the autumn 2021 is higher in the baseline scenario. This is not surprising, as large part of the uncertainty in the baseline scenario comes from the uncertainty about the actual efficiency of vaccines not present in the no-vaccination scenario. Nevertheless, looking at hospitalizations the picture changes, as there is strong evidence that vaccines are more efficient when it comes to the severe outcomes of the COVID-19 disease. In almost all cases hospitalizations are lower in the baseline scenario implying lower containment measures. This is the main reason why GDP is lower in practically all cases whenever vaccines are not available.

All in all, the economic effects of vaccination campaign were relatively modest in the first half of 2021, while the discovery of vaccines was crucial for the relaxation of containment measures in the second half of 2021.25 The discovery of vaccines thus enabled European economies to recover to pre-pandemic levels already in 2021.

7. Sensitivity to fiscal and monetary policy conduct

This section employs the ECB-BASIR setting to simulate monetary and fiscal policy conducts in response to the pandemic crisis. The discussion of monetary policy response is in the ECB-BASIR importantly facilitated with the comprehensive account financial intermediation, which is in detail described in A.5. In a broader sense, the financial block in the ECB-BASIR is built sequentially, starting from a risk-free rate, which is modelled in terms of a monetary policy rule. The upstream financing conditions are then completed by forming a risk-free yield curve, with yields of particular maturity being constructed as a composite of an average expected short-rate path and term-premium. Finally, in the second stage of financial intermediation, particular lending rates, relevant for investment and consumption decisions, are constructed as an add-on or risk-premium above the risk-free component. In this context, the financial amplification of pandemic shock is realized through term- and risk-premia as they ingrain current and expected macroeconomic conditions.

Considering the framework described above and in more details in A.5, the monetary policy conduct in the context of a pandemic shock can be perceived from two perspectives: (i) preservation of favourable financing conditions and prevention of financial amplification of the shock, (ii) accommodation of monetary policy stance to achieve the primary, price stability, objective of the central bank. The dual operational aspect of the monetary policy mimics the operational modalities of monetary measures employed in practice to mitigate the consequences of the Covid-19 crisis. For example, the guidance for the pace of net asset purchases under specially devised Pandemic Emergency Purchase Programme was distinctly based on the joint assessment of the financing conditions and inflation outlook (Lane, 2021, Lagarde, 2021).26

The prevention of financial amplification of a pandemic shock is in the ECB-BASIR observed through increases in term- and risk-premiums that would prevail in absence of any monetary policy response. In modelling terms, the monetary policy efforts aimed at preventing financial amplification, i.e. keeping spreads unchanged, would be in quantitative terms observationally equivalent to the absolute change in 10-year overnight index spread (OIS) and composite financing conditions to non-financial corporations that would be obtained due to amplification of the pandemic shock via financial spreads, but without an active monetary policy. On the other hand, the additional accommodation of the monetary stance beyond preservation of unchanged financing conditions and consistent with the price stability mandate is within the model derived endogenously by the activation of the standard policy rule.

Both effects are in Fig. 8 respectively depicted by dashed and dotted lines. The financial amplification effect would demand monetary policy efforts in the size of roughly 30 basis points on 10-year OIS on impact to preserve unchanged financing conditions in the wake of the pandemic shock. A similar, 30 basis points accommodation in monetary policy stance, beyond purely preserving unchanged financing conditions, would be suggested by the monetary policy rule in the context of the inflation and output outlook. The latter effect is very similar to the actually observed dynamics in the 10-year OIS rate, which in September 2021 stood roughly 30 basis points lower compared to the pre-pandemic period (e.g. February 2020). The effective total monetary policy measures, combining both preservation of financing conditions and monetary stance accommodation, during the medium-term forecast horizon amount to roughly 60 basis points in the context of 10-year OIS rate. The effects of the pandemic shock on the composite financing conditions is assessed to be significantly more detrimental, with the required monetary policy effort amounting to roughly 160 basis points.

Fig. 8.

Monetary and fiscal developments during the pandemic crisis.

Fig. 9 displays additional losses in the real GDP and inflation that would prevail in the absence of monetary policy. At the end of the medium-term horizon of the monetary policy, the GDP is assessed to be lower by roughly 1.55% had monetary measures, including both preserving financing conditions and accommodation of the stance, not have been employed. Monetary measures and favourable financing conditions have been particularly important in averting the real-financial amplifications for the non-financial corporate sector, where real investments are assessed to be roughly 14% lower absent the monetary policy response. Likewise, the macroeconomic policy acts meaningfully towards averting deflationary risks. The overall contribution of the monetary policy is assessed to amount to roughly 0.7 percent on the price level or roughly 0.25 percentage points in inflation terms.

Fig. 9.

Counterfactual simulations assuming absence of policy responses.

Turning to the fiscal policy, measures taken during the pandemic period could have largely been categorized under income and job preserving policies. Empirically, the macroeconomic effect of fiscal policies could be quantified as a difference between fiscal measures scheduled by budgetary plans ex-ante, before the onset of the pandemic emergency, and the available policy measure observed ex-post in the context of mitigating the effects of the Covid crisis. Concretely, the fiscal measures could be quantified as a revision in assumptions considered respectively in March 2020 and September 2021 ECB’s Macroeconomic Projection Exercises.27

Fig. 8 displays changes in the selected fiscal measures relative to the ex-ante paths assumed in the pre-pandemic period. On the fiscal side, social benefits, transfers and tax reliefs have taken the largest share in the overall response since the onset of the crisis. Expressed in terms of the pre-crisis GDP level, social benefits and tax reliefs together increased by more than 10p.p. compared to the paths assumed in the pre-pandemic period. Considering the counterfactual path of the GDP depicted in Fig. 9, the GDP loss that would have materialized at the end of 2021 in the absence of fiscal transfers is assessed to peak at 0.8% two years after the initial shock. The ECB-BASIR emulates a differing transmission mechanism associated with respective fiscal and monetary policies, where in contrast to the monetary measures, fiscal measures are affecting the macroeconomy predominantly through the household consumption side.

8. Policy implications

The simulation results in Section 4 suggest that the overall policy response to the epidemiological situation faces two main trade-offs. The first one relates to the fact that bold and swift measures to contain the spread of the disease come at the expense of a severe and immediate slump in the aggregate demand. The second trade-off is linked to the short versus long-run effects of policy interventions: a passive response to the deteriorated epidemiological situation, which intends to preserve aggregate demand conditions in the short-run, may actually lead to persistent adverse effects on the supply side of economy and the labour market. Navigating between these short-term and long-term macroeconomic effects, the full set-up of the ECB-BASIR model, incorporating learning effects, vaccination progress, and macroeconomic policy responses, reveals the first trade-off as less costly. In particular, considering the substantial learning effects across epidemiological waves, the model suggests that an active response towards mitigating epidemiological effects can produce meaningful public health benefits at relatively short-lived, albeit quantitatively large, macroeconomic impacts. Moreover, the diminishing effects of pandemic wedges with each epidemiological wave are further exacerbated by vaccination progress that is embedded within our model. The simulations showed that without explicitly considering learning effects and depending on a particular wave of the pandemic, the macroeconomic impact of containment measures could be over-predicted by up to 3%, measured in terms of additional losses in GDP. Likewise, failing to explicitly consider the effects of vaccinations in the model would imply additional general lockdowns, which would lead to overestimation of macroeconomic impacts by up to 5% of GDP. Finally, Section 7 illustrates how meaningful macroeconomic policy responses can mitigate the initial slump in aggregate demand and can boost its recovery in the subsequent period. The versatile macroeconomic transmission channels considered in the ECB-BASIR model suggest that a macroeconomic policy response should draw complementarities between fiscal and monetary measures. Fiscal measures are most effective in preserving disposable income of households and their consumption, while monetary measures ensure favourable financing conditions in the economy that supports investment activity and provides fiscal space for income and job retention measures.

9. Conclusion

This paper presents a model that combines the SIR class of epidemiological models and the ECB’s macroeconomic model for forecasting and policy analysis, the ECB-BASE, to shed an informative view on the macroeconomic consequences of the pandemic crisis. The ECB-BASIR models the joint epidemiological and macroeconomic developments in a two-way linkage, where epidemiological outcomes constrain agents both on demand and supply side, while macroeconomic interactions among agents affect the share of potential infectious contacts among population. Additionally, the model specifies an endogenous policy function for containment measures, allowing to perform counterfactual scenarios on alternative economic and pandemic developments. A special feature of the model is to account for the wide range of elements related specifically to the recent epidemiological crisis, including non-pharmaceutical prevention measures, lockdown policies, vaccination progress, appearance of the new variants of the disease, and the learning effect. In order to track closely past crisis developments, the estimation and calibration of model parameters was informed by various relevant data sources related to past stringency, mobility data, pandemic and public health.

The macroeconomic properties of the ECB-BASIR model shows that while various policy interventions successfully contained a more devastating spread of the Covid-19 virus, the active polices to tackle the pandemic crisis produced a roughly 12% drop in the real GDP by the end of the third quarter of 2020. Nevertheless, the model estimates show that the learning and adaptation of economic agents to the situation was fast and became a crucial component in averting the more persistent macroeconomic consequences from the containment measures in the subsequent waves of the crisis. In particular, simulations reveal positive contributions of the learning effects in the range of the 3% of the GDP. An important contributor towards preventing a more drastic macroeconomic consequences has likewise been the vaccination progress among the euro area countries, especially in the light of the new emerging variants of the virus. Namely, in absence of the vaccination progress, the pre-pandemic GDP level would be attained only by the end of 2022, one year later than currently foreseen, with overall progress towards the ECB’s inflation objective significantly hampered. Finally, the ECB-BASIR was employed to evaluate the contribution of fiscal and monetary policy response. The model reveals complementary transmission channels of fiscal and monetary policies, with fiscal transfers importantly preserving the income and consumption of households, while monetary measures provided supportive role to the business investment via favourable financing conditions.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix. Integrating the SI(Q)R module into the ECB-BASE

ECB-BASE is a large-scale, estimated, semi-structural model for the euro area featuring optimizing agents subject to generalized adjustment costs. The model comprises demand, supply and financial blocks. Altogether, the ECB-BASE model is comprised of roughly 120 behavioural equations and around 140 additional identities. While full exposition of the model is provided in Angelini et al. (2019), this section focuses on key equations and decision problems affected by the inclusion of the SI(Q)R model: this covers consumption, investment and labour market blocks. Variables denoted with lower case letters are expressed in logarithms while upper case letters apply to variables in level. Besides, the time increment in the macroeconomic model is quarterly. For the sake of exposition, we use the same time subscript $t$ as in the previous section but in practice, the integration of the daily SI(Q)R module to the quarterly ECB-BASE model gives rise to a mixed-frequency modelling framework.28

A.1. Consumption

The consumption behaviour in ECB-BASE is determined by two kinds of households, optimizing households and hand to mouth consumers. The first group maximizes their consumption based on their lifetime resource constraint, the second on the changes of their current income. The target consumption for optimizing agents depends on expected permanent labour income, transfer and property incomes, financial and housing wealth:

$$c_t^{\ast }={\eta }_0+{\eta }_{T}ey{h}_t^T+{\eta }_{P}ey{h}_t^P+{\eta }_{D}h{w}_t^D+{\eta }_{L}ey{h}_t^L$$ (20)

where, $ey{h}^L$, $ey{h}^T$, $ey{h}^P$ are labour, transfer and property incomes and $h{w}^D$ represents housing wealth of households.

In the short-run, the adjustment towards the target is only gradual and subject to adjustment costs. Let us denote $c_t^u$ the consumption of agents not subject to constraints stemming from infections or lockdown. The short run dynamic behaviour for $c_t^u$ is then given by,

$$\Delta c_t^u=(1-\theta )\left(a_0\left(c_{t-1}^{\ast }-c_{t-1}\right)+\sum _{i=1}^{m-1}{a}_i\Delta c_{t-i}^u+{\beta }_1{x}_t+{\mathbb{E}}_{t-1}\stackrel{\infty }{\sum _{j=0}}{d}_j\Delta c_{t+j}^{\ast }\right)$$

$$+\theta \Delta (y{h}_t^L+y{h}_t^T)+{ϵ}_t^C$$ (21)

where $\theta$ is the share of rule-of-thumb consumers, $a_0$ is the coefficient indicating the difference closed relative to the target consumption in a given period and $a_i$ represents a persistence of past changes. The term ${\mathbb{E}}_{t-1}{\sum }_{j=0}^{\infty }{d}_j\Delta c_{t+j}^{\ast }$ represents the expected changes in the target consumption.

The final consumption $C_t$ is then comprised of unconstrained consumption and consumption affected by pandemic wedges. In this respect, the final consumption can be derived by considering different shares of agents stemming from the SI(Q)R model so that:

$$C_t=(1-i_t-l_t-d_t)C_t^u+i_t{\alpha }_C^I{C}_t^u+l_t{\alpha }_C^L{C}_t^u$$ (22)

where $(1-i_t-l_t-d_t)$ is a share of agents not affected by the virus, $i_t$ is the share of infected agents, $l_t$ is the share of locked down agents, and $d_t$ is the share of deceased people. Parameters ${\alpha }_C^I$ and ${\alpha }_C^L$ determine how much lower consumption of infected and locked down agents is compared to unconstrained agents.

A.2. Labour market

In the ECB-BASE model, the labour market block is centred around the equation for total employees. The equation derives from firms deciding on optimal target of employment, which is reached only gradually. The target employment is defined as:

$$n_t^{\ast }=mc+log(1-\alpha )+y_t-w_t$$ (23)

where $mc$ is the log of the Lagrange multiplier related to the technology constraint, $\alpha$ is the geometric weight related to physical capital in the production function, $w_t$ represents real compensation of employees and $y_t$ is real GDP.

As in the consumption block, we first define an unconstrained (log) employment dynamics, $n_t^u$, in form of the polynomial adjustment costs:

$$\Delta n_t^u=a_0^n\left(n_{t-1}^{\ast }-n_{t-1}^u\right)+a_1^n\Delta n_{t-1}^u+{\mathbb{E}}_{t-1}\stackrel{\infty }{\sum _{j=0}}{d}_j\Delta n_{t+j}^{\ast }+e^n$$ (24)

where $a_0^n$ denotes the degree of adjustment towards target in time $t$, whereas $a_1^n$ and $d_j$ denote costs associated with past and expected adjustments.

Considering agents constrained by the SI(Q)R dynamics and aggregating across agent epidemiological types, the total labour input in the productive process is then given by:

$$N_t=(1-i_t-l_t-d_t)N_t^u+i_t{\alpha }_N^I{N}_t^u+l_t{\alpha }_N^L{N}_t^u$$ (25)

As before, we introduce ${\alpha }_N^I$ and ${\alpha }_N^L$ to capture the constraints on the productive match between firms and employees related to infected and locked down agents.

Total population and working age population specified in the ECB-BASE model are also adapted to take into account the fatalities due to the disease. Total population $P^b$ and working age population $W{P}^b$ are adjusted as follows:

$$P_t=P_t^b(1-d_t)$$ (26)

$$W{P}_t=W{P}_t^b(1-d_t)$$ (27)

Following the specification of the ECB-BASE model, the equation for the unconstrained labour force participation rate, $lf{p}_t^u$, is given by as

$$lf{p}_t^u=-0.5\ast (lf{p}_{t-1}^u-lf{p}_{t-1}^T)-\beta (u_{t-1}-u_{t-1}^T)+\Delta lf{p}_t^T$$ (28)

where, $lf{p}_t^u$ is the labour force participation rate, $lf{p}_t^T$ is the trend labour force participation rate, $u_t$ is the unemployment rate and $u_t^T$ is the trend unemployment rate.

Again, aggregating across epidemiological types gives the total labour force as:

$$L{F}_t=(1-i_t-l_t-d_t)L{F}_t^u+i_t{\alpha }_{LF}^{I}L{F}_t^u+l_t{\alpha }_{LF}^{L}L{F}_t^u$$ (29)

where ${\alpha }_{LF}^I$ and ${\alpha }_{LF}^L$ map the constraints on the supply of labour from infected and locked down agents.

A.3. Investment

In the ECB-BASE, business investment is derived from a standard optimization problem where firms maximize their profits subject to a capital accumulation equation.29 .

The target for business investment is inversely related to user costs of capital and is given by the following equation:

$$I{B}_t^{\ast }=\left(G_{t+1}^{K^{\ast }}+\delta \right)\frac{S_t^K{Y}_t}{U{C}_t}$$ (32)

where $I{B}^{\ast }$ denotes the target for business investment, $UC$ represents user costs of capital and $G_{t+1}^{K^{\star }}$ is the desired growth rate of the (target) capital stock, approximated by the real GDP growth.

The short-run dynamics for the unconstrained (log-)business investment, $i{b}_t^u$ is given by the following Polynomial adjustment costs specification:

$$\Delta i{b}_t^u=\left(1-{\theta }^{ib}\right)\left(a_0^{ib}\left(i{b}_{t-1}^{\ast }-i{b}_{t-1}^u\right)+\underset{k=1}{\sum ^{m-1}}{a}_k^{ib}\Delta i{b}_{t-k}+{\mathbb{E}}_{t-1}\stackrel{\infty }{\sum _{j=0}}{d}_j^{ib}\Delta i{b}_{t+j}^{\ast }\right)+{\theta }^{ib}\Delta y_{t-1}+{ϵ}_t^{ib}$$ (33)

whereas in the case of consumption, proportion, ${\theta }^{ib}$ of firms do not adhere to the optimal target, but rather fully align the investment growth with the previous period GDP growth, indicating output acceleration effect.

Incorporating epidemiological developments and aggregating agents across epidemiological types then gives the final expression for level of investment in time $t$ as:

$$I{B}_t=(1-i_t-l_t-d_t)I{B}_t^u+i_t{\alpha }_{IB}^{I}I{B}_t^u+l_t{\alpha }_{IB}^{L}I{B}_t^u$$ (34)

where ${\alpha }_{IB}^L$ and ${\alpha }_{IB}^I$ incorporate the constraints on investment stemming from locked down and infected agents.

The same adaptation and calibration strategy is applied to the residential investment block.

A.4. Productive efficiency

Potential output is in the ECB-BASE model derived from a Cobb–Douglas production function approach, which bundles physical capital and labour. As explained above, the capital stock and the labour supply are affected by the SI(Q)R module, which then feeds into potential output.

Additionally, the trend labour productivity component $A_t^{\ast }$ includes dependence to the epidemiological shares as follows:

$$A_t^{\ast }=A_t^{\ast u}(1-i_t-l_t)+{\alpha }_A^I{i}_t{A}_t^{\ast u}+{\alpha }_A^L{l}_t{A}_t^{\ast u}$$ (35)

where $A_t^{\ast u}$ refers to the unconstrained trend labour productivity, whereas ${\alpha }_A^L$ and ${\alpha }_A^I$ account for the lower labour productivity of locked down and infected agents.

A.5. Interest-rate rule and financial transmission

The ECB-BASE model nests a financial block that in the context of epidemiological scenarios allows consideration of financial amplifications of pandemic shocks and at the same time monetary policy to counter them. The financial block is in the ECB-BASE built sequentially, starting from a monetary policy rule for the short-term risk-free rate:

$$i_t={\Phi }_i{i}_{t-1}+(1-{\Phi }_i)(\overline{\pi }+\overline{r})+(1-{\Phi }_i){\Phi }_{\Pi }{\hat{\pi }}_t+{\Phi }_{\Delta \Pi }\Delta \pi +{\Phi }_y\Delta {\hat{y}}_t+e_t$$ (36)

where $\overline{\pi }$ is the inflation target, $\overline{r}$ is the real natural rate, and $\hat{\pi }$ and $\hat{y}$ are inflation and output gaps.

The risk-free euro area yield curve is then constructed around the reference rate in (36) according to the term-structure expectation hypothesis. Specifically, an interest rate, $R$, of particular maturity $m$ is considered to be a sum of an average expected short-term path over horizon $m$ and a term-premium, $TP$:

$$R_t\left(m\right)=\frac{1}{m}\sum _{i=0}^{m-1}{R}_{0,t+i}+T{P}_t\left(m\right)$$ (37)

The financing conditions relevant for investment and consumption decision are then determined by lending rates, which are composed of risk-free part and a risk premium. The model considers 5 particular financing costs related to loans to non-financial corporations, household consumer loans, mortgages, corporate bond rates, and cost-of-equity. The generic specification for a particular lending rate is given by the following representation:

$$L{R}_t^i=v_s^i{R}_t\left(1\right)+v_l^i{R}_t\left(40\right)+RP{R}_t^i$$ (38)

where $v_s^i$ and $v_l^i$ are weights assigned to the short-term rate (3-month) and the long-run rate (10-year), and are obtained using the bank balance sheet statistics data for particular lending segment. $RPR$ denotes a risk spread associated with each particular lending rate.

In the framework designed above, the financial amplification of the pandemic shock is transmitted via term-premium and risk-premium terms as both are modelled as a function of current and expected macroeconomic conditions.

The empirical model for the term-premium is specified by:

$$T{P}_t\left(m\right)={\alpha }^{TP}+{\rho }^{TP}T{P}_{t-1}\left(m\right)+{\beta }_1^{TP}\frac{1}{m}{\mathbb{E}}_t\sum _{i=0}^m{\hat{y}}_{t+i}+{\beta }_2^{TP}T{P}_t^{US}+e_t^{TP}$$ (39)

where ${\alpha }^{TP}$ is a constant, ${\rho }^{TP}$ is the autoregressive coefficient, ${\beta }_1^{TP}$ reflects dependency on expected macroeconomic conditions, and ${\beta }_2^{TP}$ accounts for external financial spillovers.

The risk-premium terms associated with financing conditions follow similar framework and are modelled as:

$$RP{R}_t^i={\alpha }^{RPR}+{\rho }^{RPR}RP{R}_{t-1}+{\beta }^{RPR}\frac{1}{m}{\mathbb{E}}_t\sum _{i=0}^m{\hat{y}}_{t+i}+e_t^{RPR}$$ (40)

The estimates and detailed empirical set-up is laid out in Angelini et al. (2019).

Data availability

Data will be made available on request.