The response of household debt to COVID-19 using a neural networks VAR in OECD

Abstract

This paper investigates responses of household debt to COVID-19-related data like confirmed cases and confirmed deaths within a neural networks panel VAR for OECD countries. Our model also includes a plethora of non-pharmaceutical and pharmaceutical interventions. We opt for a global neural networks panel VAR (GVAR) methodology that nests all OECD countries in the sample. Because linear factor models are unable to capture the variability in our data set, the use of an artificial neural network (ANN) method permits to capture this variability. The number of factors, as well as the number of intermediate layers, is determined using the marginal likelihood criterion and we estimate the GVAR with MCMC techniques. We also report δ-values that capture the dominance of each individual country in the network. In terms of dominant countries, the UK, the USA, and Japan dominate interconnections within the network, but also countries like Belgium, Netherlands, and Brazil. Results reveal that household debt positively responds to COVID-19 infections and deaths. Lockdown measures such as stay-at-home advice, and closing schools, all have a positive impact on household debt, though they are of transitory nature. However, vaccinations and testing appear to negatively affect household debt.

1 Introduction

The paper sheds light on household financial behaviour in relation to household debt during the pandemic to inform policy making interventions and economic recovery. We investigate the responses of household debt in OECD countries to shocks in COVID-19-related data like confirmed cases and confirmed deaths within a neural networks panel VAR. We provide evidence that disentangles the impact of the pandemic and government interventions on household debt in the OECD.

The importance of household debt for macroeconomic and financial stability is unequivocal. Zabai (2020) and OECD (2020) report recent data that show that household consumption is about 60% of GDP in OECD, whereas household debt, mostly in the form of mortgages, captures up to 40% of banks’ asset. Franklin et al. (2021) presented descriptive analysis to argue that many UK households have managed to weather the crisis of COVID-19, though the Authors also argue that households with unsecured loans could face financial difficulties. Georgarakos and Kenny (2022), using a new consumer expectations survey data for EU, show that policy makers by clearly communicating their COVID-19 interventions (see Christelis et al. 2020), i.e. fiscal measures, would enhance consumers perception about the adequacy of these interventions and thereby they would incentivise household spending, including debt payment.¹ Kubota et al. (2021) employ a natural experiment in Japan to show that household would increase their spending as response to COVID-19 pandemic governments’ interventions that take the form of cash transfers (see also Chetty et al. 2020 for US; and Carvalho et al. 2020 for the UK).

This paper builds on the above empirical studies to provide evidence of responses of household debt, in particular, to shocks due to the pandemic within a unique panel global Vector Autoregressive model that nests neural networks and postulates forecasts over 24 months period under various COVID-19 scenarios while controlling for non-pharmaceutical and pharmaceutical interventions as shocks in the GVAR. For example, government interventions in the form of lockdowns play a prominent role in our modelling. Because linear factor models may be unable to capture the variability in the data, we use an artificial neural network (ANN) method. The number of factors as well as the number of intermediate layers is determined using the marginal likelihood criterion and we estimate the GVAR with MCMC techniques. We also employ Mixed Data Sampling (MIDAS) that allows the use of data of different frequencies and identifies household debt responses under different COVID-19 scenarios. Note that household and macroeconomic data in OECD are country specific on annual frequency while COVID-19-related data are on a daily frequency. Also, we provide a detailed map of interconnectedness of the underlying causal nodes of various contributing factors to household finances as well as interactions between household debt repayment, relating comparisons between the UK and advanced countries. We, therefore, follow Pesaran and Yang (2016) to identify “strong” and “weak” dominant countries in the network based in measures of eigenvector degrees and centrality of Acemoglu et al. (2012). To this end, we estimate pervasiveness scores to identify the dominant countries in OECD. Last, we rank the principal contributing factors to household debt repayment so to inform policy makers to prioritise actions on specific factors.

Results reveal that household debt positively responds to COVID-19 infections and death. Lockdown measures such as stay at home advise, closing schools, all have a positive impact on household debt repayments in GVAR, though of transitory nature. However, pharmaceutical interventions like vaccinations and testing appear to negatively affect household debt. In terms of dominant countries, the UK, the USA, and Japan dominate interconnections within the network, but also countries like Belgium, Netherlands and Brazil.

In what follows Sect. 2 presents the global VAR model. Section 3 reports the data set and provides descriptive statistics. Section 4 discusses results. The last section presents some concluding remarks.

2 The global VAR model

Suppose ${Y}_{t}=[{y}_{1,t},{y}_{2,t},...,{y}_{n,t}{]}^{\mathrm{^{\prime}}}$ is an $n\times 1$ vector time series which can be described by a vector autoregression (VAR):

$${Y}_{t}=B{Y}_{t-1}+{\varepsilon }_{t}, t=1,...,T,$$

(1)

where ${\varepsilon }_{t}\sim {\mathcal{N}}_{n}(\varvec{0},\Omega )$. Following previous contributions (Koop 2017; Primiceri 2005; Eisenstat et al., 2016; and Carriero et al., 2015) we use a triangular decomposition of $\Omega$ as follows:

$$A\Omega {A}^{\mathrm{^{\prime}}}=\mathrm{\Sigma \Sigma },$$

(2)

where $\Sigma =\mathrm{diag}[{\sigma }_{1},...,{\sigma }_{n}]$, and $A$ is a lower triangular matrix with ones on the main diagonal. Define $A={I}_{n}+\widetilde{A}$, where $\widetilde{A}$ is a lower triangular matrix with zeros on the main diagonal. Therefore, we can write the VAR as follows:

$${Y}_{t}=B{Y}_{t-1}+{A}^{-1}\Sigma {\xi }_{t},$$

(3)

where ${\xi }_{t}\sim {\mathcal{N}}_{n}(0,{I}_{n})$.

In turn, we can write:

$${Y}_{t}=\Theta {Z}_{t}+\Sigma {\xi }_{t},$$

(4)

where $\Theta =\left[\Gamma ,\widetilde{A}\right]$ and $\Gamma =AB$. The advantage of the representation is that this is a recursive system. The first equation involves only ${Y}_{t-1},$ the second equation includes $({{Y}^{\mathrm{^{\prime}}}}_{t-1},-{y}_{1,t})$, the third equation includes $({{Y}^{\mathrm{^{\prime}}}}_{t-1},-{y}_{1,t},-{y}_{2,t})$, etc. Moreover, $\widetilde{A}$ controls for the error covariances.

2.1 The artificial neural network (ANN)

In GVARs it is typical that various VARs are connected through some observed variables like exchange rate converted to lie between zero and one. Here, we connect the different VARs through several common dynamic factors (an $M\times 1$ vector, ${f}_{t}$). The VAR model for each country is as follows.

$${Y}_{t}^{(c)}={B}^{(c)}{Y}_{t-1}^{(c)}+{\Delta }^{(c)}{Z}_{t}^{(c)}+{\varepsilon }_{t}^{(c)}, t=1,...,T,$$

(5)

where ${\varepsilon }_{t}^{(c)}\sim {\mathcal{N}}_{n}(0,{\Omega }^{(c)})$, for country $c\in \{1,...,C\},$ and ${Z}_{t}$ is a $K\times 1$ vector of covariates whose coefficients are given in the $n\times K$ matrix $\Delta$.

We suppose that the dynamic factors are given as:

$${f}_{t}=\Lambda {f}_{t-1}+{u}_{t},$$

(6)

where $\Lambda$ is an $M\times M$ matrix of unknown coefficients, and ${u}_{t}\sim {\mathcal{N}}_{M}(0,V)$, where $V$ is an unknown covariance matrix, assumed to be diagonal with different elements along the main diagonal.

As linear factor models may be unable to capture the variability in the data, we use an artificial neural network (ANN):

$${f}_{t}=\Lambda {f}_{t-1}+\sum_{g=1}^{G}{a}_{g}\varphi ({b}_{g}{f}_{t-1})+{\varepsilon }_{t},$$

(7)

where ${a}_{g}$ and ${b}_{g}$ are unknown parameters, $\varphi (z)=\frac{1}{1+{e}^{-z}}$ is the logistic activation function, and $G$ is the unknown number of components in the ANN. The number of factors $f$ as well as the number of intermediate layers ($G$) is determined using the marginal likelihood criterion (Diccio et al., 1997). In the next section, we discuss our dataset and the factors $f$ that are in line with the household finance literature (Georgarakos and Kenny 2022; Christelis et al. 2020; Kubota et al. 2021).

In terms of estimation of the ANN, we use the MCMC technique in (see Appendix A1). In detail, we use 150,000 iterations, the first 50,000 of which are discarded to mitigate possible start up effects. In addition, we use a flat prior for the coefficients in (7). We shall discuss the robustness of priors in the empirical Section.

In turn, we modify (5) as follows:

$${Y}_{t}^{(c)}={B}^{(c)}{Y}_{t-1}^{(c)}+{\Delta }^{(c)}{Z}_{t}^{(c)}+{\Phi }^{(c)}{f}_{t}+{\varepsilon }_{t}^{(c)}, t=1,...,T,$$

(8)

where ${\varepsilon }_{t}^{(c)}\sim {\mathcal{N}}_{n}(0,{\Omega }^{(c)})$, and ${\Phi }^{(c)}$ is an $n\times M$ matrix of unknown coefficients. So, we couple the dynamic factor model in (7) with the VAR models in (5). In our case, the vector ${Y}_{t}$ contains household debt, household savings, household spending, GDP, real exchange rate, government deficit, share prices, and the long-term interest rate ($n$=11). The dynamic factors in (6) are computed beforehand to simplify computations so, for all equations of the GVAR as well as different countries.

For the diagonal elements of ${A}^{(c)}$ we assume that they are normally distributed with mean 1 and standard deviation 0.2. The non-diagonal elements have a normal prior with mean zero and standard deviation 0.2. For the elements of ${\Delta }^{(c)}$ and ${\Phi }^{(c)}$ we assume that they have a standard normal distribution. Suppose that the $j$ th typical equation of (8) has the form

$${Y}_{t,j}^{(c)}={{B}_{j}^{(c)}}^{\mathrm{^{\prime}}}{Y}_{t-1}^{(c)}+{{\Delta }_{j}^{(c)}}^{\mathrm{^{\prime}}}{Z}_{t}^{(c)}+{{\Phi }_{j}^{(c)}}^{\mathrm{^{\prime}}}{f}_{t}+{\varepsilon }_{t,j}^{(c)}, t=1,...,T,j=1,...,8,$$

(9)

where ${{B}_{j}^{(c)}}^{\mathrm{^{\prime}}}, {\Delta }_{j}^{(c)}, {\Phi }_{j}^{(c)}$ denotes the jth row of matrices ${B}^{(c)},{\Delta }^{(c)},{\Phi }^{(c)}$, respectively. We keep in mind that (9) is estimated in the form of (4) so, in fact, the indices are $j\in \{1,...,8\}$ and $c\in \{1,...,C\}$. The GVAR can be estimated now for each country and VAR variable on an equation-by-equation basis, using  Markov Chain Monte Carlo techniques (MCMC, Geweke, 1999).

2.2 The pervasiveness scores within the ANN

Following from Pesaran and Yang (2016) that identify “strong” and “weak” dominant countries in the network based in measures of eigenvector degrees and centrality of Acemoglu et al. (2012), we also estimate δ-values per country in Eq. (9) (see Pesaran and Yang 2016 and Tsionas et al. 2016). The δ-values capture the dominance of each individual country in the network of Eq. (9) whereby if a country has δ-value close to one then that country would be the most dominant in the network. So low δ-values imply low dominance in the network. Pesaran and Yang (2016) call these δ-values pervasiveness scores.

The covariates ${Z}_{k,t}^{(c)}$ in (9) are available monthly, whereas the variables in the VARs are annually observed. Khalaf et al. (2021) propose to follow Ghysels et al. (2004) and use the exponential Almon (1965) lag polynomial of length $H$ (Almon, 1965) defined for the $k$ th variable, as:

$${Z}_{k,t}(\vartheta )=\sum_{j=1}^{m}{Z}_{k,t,j}{w}_{k,j}({\vartheta }_{k}),$$

(10)

so the high-frequency data for a variable ${Z}_{k,t,j}$ (variable $k$, year $t$ and date $j=1,...,m$ are aggregated into the annual variable ${z}_{i,t}(\vartheta )$, where $\vartheta$ is a vector of parameters, and the weights ${w}_{j}(\vartheta )$(omitting the variable index, $k$, for simplicity) are

$${w}_{j}(\vartheta )=\frac{{\prod }_{h=1}^{H}{e}^{{j}^{h}{\vartheta }_{h}}}{{\sum }_{j=1}^{m}\left({\prod }_{h=1}^{H}{e}^{{j}^{h}{\vartheta }_{h}}\right)}.$$

(11)

Khalaf et al. (2021) set $H=2$ on the basis that it can model a variety of patterns, see also Ghysels (2016). When ${\vartheta }_{h}=0$ for all $h$, then all weights are equal to $\frac{1}{m}$. In fact, we can choose the appropriate value of $H$ using the marginal likelihood of the model.

The elements of ${Z}_{t}^{(c)}$ are vaccine prioritisation, testing policy, confirmed cases, confirmed deaths, vaccination policy, school closing, workplace closing, cancel public events, restrictions on gatherings, close public transport, stay at home requirements, international restrictions, contact tracing, and stringency index. Therefore, instead of (9) we have:

$${Z}_{t,k}^{(c)}(\vartheta )=\sum_{j=1}^{m}{Z}_{k,t,j}{w}_{k,j}(\theta ),k=1,...,14.$$

(12)

To simplify the computations, the weighting is performed before estimating the GVAR, using the MCMC technique in Appendices A1 and A2 Girolami a. We use 150,000 iterations, the first of which are discarded to mitigate possible start up effects. In turn, we consider Generalised Impulse Response Functions (GIRFs; Koop et al. 1996; Pesaran and Shin 1998).

3 The data set

We draw on three data sources. The non-pharmaceutical interventions data is from the Oxford COVID-19 government response tracker (OxCGRT) (Hale et al. 2020). The daily COVID-19 case data are from the Johns Hopkins University’s Center for Civic Impact. OxCGRT collects publicly available information on 19 indicators of government responses related to containment and closure policies, economic policies, and health system policies, which are combined into four indices ranging from 0 to 100. The indices include the number and strictness of government policies and do not indicate appropriateness or effectiveness response.

Data on government interventions concern three main areas of interventions: (a) containment and closure, (b) health system, and (c) economic stimulus. All the indicators are available on a daily and monthly basis. The containment and closure interventions include eight sub-indicators: (i) school closing, (ii) workplace closing, (iii) cancellation of public events, (iv) restrictions on gatherings size, (v) public transport closed, (vi) stay at home requirements, vii) restrictions on internal movement, and (viii) restrictions on international travel. The second area of interventions includes health system: (i) public information campaigns, (ii) testing policy, and (iii) contact tracing. Since these policies help to cope with the pandemic quicker, they may be also discounted in stock prices. The third area includes economic stimulus packages such as: income support, and debt or contract relief for households. These stimuluses affect the economy through various channels. For instance, stimulus supports consumption and spending in times of distress; hence, they may significantly affect local equity markets. Finally, besides the individual measures, we also consider the overall Stringency Index by Hale et al. (2020). The index aggregates the data pertaining and is re-scaled to create a score between 0 and 100. This index provides a synthetic measure of the intensity of different non-medical government interventions during the pandemic. Table 1 reports the main descriptive statistics of our sample.

Table 1 COVID-19-related data

In some detail in term of the data, we measure exposure to the pandemic by computing the growth rate of the cumulative number of confirmed cases (and deaths) in each country on daily frequency starting from 1st of January 2020 to end of 2021 (see Table 1 for COVID-19-related data). In some detail, COVID-19 and lockdown variables include: vaccines; tests; confirmed deaths; hospitalisations; ICU data; school closing; workplace closing; cancel events; gatherings restrictions; transport closing; stay home restrictions; internal movement restrictions; international movement restrictions; information campaigns; testing policy; contact tracing; stringency index. All the changes in government policies are tracked daily and monthly. Therefore, when we perform the regressions based on weekly returns, we calculate the weekly averages for the considered period.

In addition, we also control for health care and include health expenditures, both in per capita terms and as % of GDP, as well as number of hospital beds, nurses, and physicians per 1,000 people. We consider how healthy the population is with the life expectancy at birth in years and infant mortality rate per 1000 births. As composite indexes of health care quality we employ Healthcare Access and Quality Index obtained from Institute for Health Metrics and Evaluation and the UHC Service Coverage Index by WHO.

In terms of household finance-related data and macroeconomic data (see Table 2), we follow the household finance literature (Georgarakos and Kenny 2022; Christelis et al. 2020; Kubota et al. 2021) and include in the GVAR: household debt as percentage of household disposable income; household savings; household spending; GDP; the real exchange rate with dollar; government deficit; share price of country’s i stock exchange, and long-term interest rate (below we define the data in detail). The OECD countries that we include in the analysis are: Australia (AUS), Austria (AUT), Belgium (BEL), Brazil (BRA), Canada (CAN), Switzerland (CHE), Chile (CHL), Check Republic (CZE), Germany (DEU), Denmark (DNK), Spain (ESP), Estonia (EST), Finland (FIN), France (FRA), United Kingdom (UK), Greece (GRC), Hungary (HUN), Ireland (IRL), Italy (ITA), Japan (JPN), South Korea (KOR), Lithuania (LTU), Luxemburg (LUX), Latvia (LVA), Mexico (MEX), Netherland (NLD), Norway (NOR), New Zealand (NZL), Poland (POL), Portugal (PRT), Russia (RUS), Slovakia (SVK), Slovenia (SVN), Sweden (SWE), and the USA. The period of the sample is from 1981 to 2021 (for 2021 data are provisional).

Table 2 Household and macroeconomic data in OECD

It is worth noting that other variables could be introduced in the ANN such as trade and financial flows. Preliminary testing shows that the maximal rank correlation between such variables and factors we include was low at 0.057. Although, there is a plethora of potential variables, we follow the literature (Georgarakos and Kenny 2022; Christelis et al. 2020; Kubota et al. 2021) and include variables like GDP and government deficit that capture the macroeconomic conditions, share prices, reflecting financial markets, and real exchange rate and interest rate for monetary policy.

Figure 1 presents household debt in OECD countries in 2020. It is defined as all liabilities of households (including non-profit institutions serving households) that require payments of interest or principal by households to the creditors at a fixed dates in the future. Debt is calculated as the sum of the following liability categories: loans (primarily mortgage loans and consumer credit) and other accounts payable. The indicator is measured as a percentage of net household disposable income. Denmark has the highest debt with Mexico the lowest. The UK household debt is at 148% and comes second highest among G7 countries where Canada reports household debt at 177%. Most OECD countries are above 100%, insinuating the indebtedness of households should be a concern at a global level.

Fig. 1

Source: OECD (2022)

Household debt as percentage of disposable income

In Fig. 2 we show the household debt in G7 countries over time. For most countries but the USA and Canada, household debt was following an upwards trend as COVID-19 pandemic hit the world economy. As this figure is percentage of disposable income, the latter could also explain the upwards trajectory of household debt.

Fig. 2

Source: OECD (2022)

Household debt as percentage of disposable income over time

Figure 3 reports the household disposable income change from previous year. It reports household disposable income gross, per capita, percentage change, previous period, Q3 2021 or latest available.² Note that Fig. 3 reports “real” growth rates adjusted to remove the effects of price changes. It is worth noticing that for US and G7 the real growth of disposable income is negative, while for OECD total is at low levels of 0.17. For the UK the real growth rate is low at 0.36, in particular, if compared with Germany’s 1.12. The negative real growth rate of disposable income shows that ceteris paribus of the effects COVID-19 households in G7 would face challenges to serve their household debt. The impact of COVID-19 on household debt came at a time that the latter posed uncertainties for the economy. Early indications showed that household debt repayments increase as the pandemic shocked countries across the world. In this paper, we model the impact of shocks related to the pandemic on household debt.

Fig. 3

Source: OECD (2022), National Accounts

Disposable income, percentage change from previous period

In our analysis we employ, net household saving, defined as household net disposable income plus the adjustment for the change in pension entitlements less household final consumption expenditure (households also include non-profit institutions serving households). The adjustment item concerns (mandatory) saving of households, by building up funds in employment-related pension schemes. Household saving is the main domestic source of funds to finance capital investments, a major impetus for long-term economic growth. The net household saving rate represents the total amount of net saving as a percentage of net household disposable income. It thus shows how much households are saving out of current income and how much income they have added to their net wealth. All OECD countries compile their data according to the 2008 System of National Accounts (SNA).

Household spending is also a variable in GVAR and it is defined as the amount of final consumption expenditure made by resident households to meet their everyday needs, such as food, clothing, housing (rent), energy, transport, durable goods (notably cars), health costs, leisure, and miscellaneous services. It is typically around 60% of gross domestic product (GDP) and is therefore an essential variable for economic analysis of demand. Household spending including government transfers (referred to as “actual individual consumption” in national accounts) is equal to households' consumption expenditure plus those expenditures of general government and non-profit institutions serving households (NPISHs) that directly benefit households, such as health care and education. “Housing, water, electricity, gas, and other fuels”, one out of the twelve categories distinguished, consist of both actual rentals (for tenants) and imputed rentals (for owner-occupied housing), housing maintenance, as well as costs for water, electricity, gas. Total household spending is measured in million USD (in current prices and Private consumption PPPs), as a percentage of GDP, and in annual growth rates. Household spending including government transfers is measured as a percentage of GDP. Spending in housing is presented as a percentage of household disposable income. All OECD countries compile their data according to the 2008 system of national accounts (SNA 2008).

4 Empirical results

4.1 The ANN network: dominant countries

As a first step in our empirical estimations, we present the OECD weighted network as in Eq. (9). Figure 4 shows this OECD network. To facilitate the presentation of all OECD countries we note countries with numbers by first reporting G7 countries so that: 1 notes the USA, 2 notes the United Kingdom, 3 notes Japan, 4 Germany, 5 France, 6 Italy and 7 Canada. Then the remaining countries are 8 Austria, 9 Australia, 10 Belgium, 11 Brazil (not a member but affiliated), 12 Chile, 13 notes Colombia, 14 notes Czech Republic, 15 Denmark, 16 Estonia, 17 Finland, 18 Greece, 19 notes Hungary, 20 notes Iceland, 21 Ireland, 22 notes Israel, 23 Korea, 24 notes Latvia, 25 notes Lithuania, 26 notes Luxembourg, 27 notes Mexico, 28 notes the Netherlands, 29 notes New Zealand, 30 notes Norway, 31 notes Poland, 32 notes Portugal, 33 notes Slovak Republic, 34 notes Slovenia, 35 notes Spain, 36 notes Sweden, 37 notes Switzerland, 38 notes Turkey. It is worth noting at the outset that the network has a cyclical shape as all nodes are interconnected with each other. Clearly the large economies of OECD like the USA, the UK, Japan, Germany, France, and Italy are the most important ones in terms of their underlying weight in the network. However, other countries also carry a substantial weight like Belgium, Netherlands and to less degree Brazil. Fig. 4 reveals that the global network is a complex synthesis of multiple interconnections and when it comes to impact of the pandemic the whole world is interconnected without borders.

Fig. 4

Source: Authors’ estimations

Network of OECD countries

As in Pesaran and Yang (2016), we also report the pervasiveness based on its δ-value of each country’s node in the network, see Eq. (9). Pesaran and Yang (2016) call these δ-values pervasiveness scores. Table 3 reports δ-values pervasiveness scores for each country. Note that according to Pesaran and Yang (2016) a score below 0.5 will imply very low to none network effect (see also Acemoglu et al. 2012).

Table 3 Degree of pervasiveness. Authors’ estimations

Table 3 shows that there are several countries with δ-value above 0.8, see the USA, the UK, Japan, Germany, France, Italy, Canada from G7 but also Belgium, Netherlands, and Brazil to less extent. These values confirmed the findings of Fig. 4 that shows that there are multiple nodes of importance in the network and that the pandemic has been reaching across the globe. Results show that there are several countries that are dominant and would impact upon the global network. The remaining countries with low δ-value might not be dominant but can assert localised effects in the network.

Table 3 also reports the eigenvector centrality and degree of centrality to identify the dominant country in the network. Note that values below 0.5 would imply that the corresponding country is of significance for the network, while the highest value will imply the dominant country. The results reveal that the USA, closely matched by the UK, is dominant in the network both in terms of degree of centrality and eigenvector centrality. These results may not come as a surprise given then importance of those countries in the global economy.

4.2 Evidence of the impact of COVID-19 infections and COVID-19 deaths on household debt.

It is worth noting that we test for the robustness of our priors. We have used Sampling–Importance–Resampling (SIR) to examine robustness of priors. The results were insensitive to 1000 alternative priors chosen. In some detail, we change the prior of parameters to N(a,V) where α is a vector of means and V is a diagonal matrix. The elements of a are drawn randomly from a uniform distribution in ( − 100, 100). The diagonal elements of V are sampled uniformly from (0.0001, 100). The SIR technique produces new posteriors corresponding to the new priors. In Figs. 5 and 6 we report results from 1000 different priors and posteriors drawn as above for the parameters and the GIRFs. Figures show that results are highly robust to the prior.

Fig. 5

Source: Authors’ estimations

Prior sensitivity analysis of parameters

Fig. 6

Prior sensitivity analysis of GIRFs. Authors’ estimations

In what follows we report the Global Impulse Response Functions (GIRFs) of global panel VAR variables to shocks in COVID-19 confirmed cases and COVID-19 mortality. The first line of diagrams in Fig. 7 shows that a shock in confirmed cases will increase household debt over the two months period before converging to zero by the fifth month. The response of household savings and household spending is positive but it lasts for one month. The case of household savings is of some interest as the response turns negative in month 2 and onwards, insinuating the underlying variability in dynamics. The remaining GIRFs are consistent with a positive response to infections shock that is of transitory nature.

Fig. 7

Source: Authors’ estimations

Impact of shocks in confirmed cases to global panel VAR variables

Interestingly, Fig. 8 shows that a shock in deaths would reduce household debt up to the first month. This result confirms empirical evidence of the first wave of the pandemic in spring–summer 2020 when household debt repayments increased, in particular in the UK. Our modelling reveals that deaths, not infections, would influence household preferences towards repaying their debt. Clearly, the mortality rate of COVID-19 pandemic has been detrimental. However, it is worth noting the response of household debt to a shock in deaths turns upwards beyond the first month and is positive beyond the fifth month. Higher mortality would reduce household debt, but this response is transitory and is reversed beyond the fifth month. The remaining GIRFs present positive responses of a bell type of shape that implies convergence towards the zero after a few periods. It is worth noting that when the GIRFs are crossing the zero line the statistical significance should be treated with some caution, though standard errors bands provide some guidance.

Fig. 8

Source: Authors’ estimations

Impact of shocks in COVID-19 mortality

4.3 GIRFs of government interventions to control COVID-19

In the early stages of the pandemic, in spring 2020, governments across the world imposed draconian lockdowns and restrictions in economic activity to control the exponential growth of COVID-19 infections. These lockdowns scaled down during summer months before returning the following winter of 2020–2021 but also in the winter of 2021–2022 as new variants of the virus emerged.

Lockdowns and economic restrictions would have influenced household debt. To examine the response of household debt to such measures we present GIRFs. First, we employ the stringency index, which is a function of nine restrictions and lockdowns such as school closures, workplace closures, and travel bans. The index is provided by Oxford COVID-19 Government Response Tracker (OxCGRT) and it is scaled from 0 to 100 with 100 being the strictest restrictions.

In Fig. 9 we present the GIRFs of the response of household debt to the stringency index (see first graph, in the first line from the left). The response of household debt to stringency is positive in the first month, though statistical significance is not high as the standard errors band is wide. The GIRFs show that a shock related to lockdowns will increase household debt while its impact on household saving is zero. Similarly, it is the picture for household spending. Interestingly a shock in lockdown measures would increase GDP in the first month but it turns negative thereafter.

Fig. 9

Source: Authors’ estimations

Impact of shocks in stringency index to global panel VAR variables

In Fig. 10 we report the GIRFs of the response of household debt to cancelling of public events. The GIRFs show the response of GDP is zero. Standards errors bands are wide implying that there is strong statistical significance though cancelling public events assert a positive effect on household debt.

Fig. 10

Source: Authors’ estimations

Impact of shocks in cancel public events to global panel VAR variables

Figure 11 shows the GIRFs of the response of household debt to school closing. These GIRFs confirm the above responses.

Fig. 11

Source: Authors’ estimations

Impact of shocks in school closing to global panel VAR variables.

Lastly, Fig. 12 presents the GIRFs of the response of household debt to stay at home advise, respectively. These GIRFs confirm the above responses.

Fig. 12

Source: Authors’ estimations

Impact of shocks in stay at home to global panel VAR variables

4.4 Evidence of the impact of pharmaceutical interventions: vaccination, testing, contact tracing

Next, we report the GIRFs from medical interventions to combat COVID-19 like testing, vaccination, and contact tracing. We begin by reporting in Fig. 13 the responses to vaccinations. Interestingly, vaccination programs would reduce household debt (though beyond one period significance bands are wide), suggesting that the rapid development of vaccines and their deployment would restore household confidence and assist in reducing household debt. Moreover, our evidence appears to confirm changes in behavioural perceptions of households in earlier studies that examine the effectiveness of government interventions. In a recent study, Georgarakos and Kenny (2022) argue that policy makers by clearly communicating their COVID-19 interventions would enhance households’ confidence because households would consider that government interventions are adequate to combat the pandemic. Similar implications are reported by Kubota et al. (2021), Chetty et al. 2020 for the US, and Carvalho et al. 2020 for the UK. Our GIRFs in Fig. 13 provide evidence that higher levels of vaccinations prioritisations would restore household confidence that they are protected against the pandemic and contribute to reducing their debts.

Fig. 13

Source: Authors’ estimations

Impact of shocks in vaccination to global panel VAR variables

Note that the responses of household savings and household spending to vaccinations prioritisation are all positive. The cases of household savings and spending are of interest because they further demonstrate that vaccination prioritisation restores household confidence. Similarly, the reported remaining GIRFs in Fig. 13 are consistent with positive responses to vaccination prioritisation. Moreover, vaccination prioritisation would increase GDP and positively affect the stock exchange. However, we also demonstrate that the real exchange rate will depreciate, and the government deficit will increase as well as the long-term interest rate. Recent macroeconomic developments confirm the evidence of our GIRFs as both government deficits and interest rates are on an upwards trend though other factors like the energy cost crisis have recently contributed to worsening the macroeconomic prospects.

Figure 14 presents the GIRFs of the response of household debt to testing. These GIRFs in these Figures are broadly consistent with the GIRFs in Fig. 13. It is worth noting though that in contrast with vaccinations, a shock in testing policy would increase household debt though the statistical band is quite wide, and it could imply low statistical significance. Existing evidence shows that tests compared to the development of vaccinations have failed to restore household confidence that the pandemic is under control (see Georgarakos and Kenny 2022; Christelis et al. 2020). Our evidence appears to confirm this evidence as the first plot of GIRFs shows that testing enhances household debt.

Fig. 14

Source: Authors’ estimations

Impact of shocks in testing to global panel VAR variables

Figure 15 presents the GIRFs of the response of household debt to contact tracing. These GIRFs in these Figures are broadly consistent with the GIRFs in Fig. 14. Once more, out GIRFs show that a sock in tracing would increase households’ debt in line with existing literature that argue that test and trace policies could not be as effective as vaccinations in controlling the pandemic (see Georgarakos, and Kenny 2022; Christelis et al. 2020).

Fig. 15

Source: Authors’ estimations

Impact of shocks in contact tracing to global panel VAR variables

5 Conclusions

The reported δ-values that capture the dominance of each individual country in the network reveal that dominant countries are the UK, the USA and Japan within the network, but Belgium, Netherlands and Brazil also have high dominance. The GVAR results show that household debt would decline as a response to COVID-19 mortality, though this response is valid in the short term. However, shocks in infections, test and trace programs would increase household debt. Lockdown measures such as stay-at-home advice, and closing schools, all have also a positive impact on household debt, though they are of transitory nature.

In addition, the GIRFs show that household debt responses vary to COVID 19 shocks. For example, vaccinations prioritisation reduces household debt while testing and tracing increases household debt. This evidence implies that key to controlling the COVID-19 pandemic and ensuring low household debt is to prioritise medical innovation that protects against COVID 19 rather than testing. Lockdown restrictions alleviate the consequences of COVID 19 in terms of infections and mortality but come at economic and financial cost as fiscal deficits have been increasing and the stock markets have been negatively affected. As gradually the pandemic eases the economic and financial costs of COVID-19 seem to abide while supply chains have been severely disrupted and energy costs have been rising. Our findings suggest that caution is warranted when it comes to imposing draconian economic restrictions. The latter are not as effective as vaccinations. It is fortunate that new vaccination has been engineered and manufactured at a large scale in a record time. A main policy implication of our findings that serves as a useful guide for future pandemics is the importance of medical innovation and fast drag discovery.

Lastly, we show that the dominant countries in the underlying network of OECD countries are the USA, the UK and the remaining G7 countries. Our results demonstrate that there are a plethora of nodes and interconnections across OECD countries. Therefore, when it comes to a pandemic the global economy is highly interconnected and no country is immune to a pandemic. Given the results of our network analysis, and in terms of policy implication, we argue that global coordinated action is required to deal effectively with the pandemic. Future research could further study issues related to vaccination policies and distribution of vaccines across the world.

Appendix

1.1 The Creal and Tsay (2015) procedure

We use a recent advance in sequential Monte Carlo methods known as the particle Gibbs (PG) sampler, see Andrieu et al. (2010). The algorithm allows us to draw paths of the state variables in large blocks. Particle filtering is a simulation-based algorithm that sequentially approximates continuous, marginal distributions using discrete distributions. This is performed by using a set of support points called ‘‘particles’’ and probability masses; see Creal (2012) for a review. The PG sampler draws a single path of the latent or state variables from this discrete approximation. As the number of particles M goes to infinity, the PG sampler draws from the exact full conditional distribution. As mentioned in Creal and Tsay (2015, p. 339): “The PG sampler is a standard Gibbs sampler but defined on an extended probability space that includes all the random variables that are generated by a particle filter. Implementation of the PG sampler is different than a standard particle filter due to the ‘‘conditional’’ resampling algorithm used in the last step. Specifically, for draws from the particle filter to be a valid Markov transition kernel on the extended probability space, Andrieu et al. (2010) note that there must be positive probability of sampling the existing path of the state variables that were drawn at the previous iteration. The pre-existing path must survive the resampling steps of the particle filter. The conditional resampling step within the algorithm forces this path to be resampled at least once. We use the conditional multinomial resampling algorithm from Andrieu et al. (2010), although other resampling algorithms exist, see Chopin and Singh (2013)”. We follow Creal and Tsay (2015). Suppose the posterior is $p(\theta ,{\Lambda }_{1:T}|{{\varvec{y}}}_{1:T})$ where ${\Lambda }_{1:T}$ denotes the latent variables whose prior can be described by $p({\Lambda }_{t}|{\Lambda }_{t-1},\theta )$. In the PG sampler we can draw the structural parameters $\theta |{\Lambda }_{1:T},{{\varvec{y}}}_{1:T}$ as usual, from their posterior conditional distributions. This is important because, in this way, we can avoid mixture approximations or other Monte Carlo procedures that need considerable tuning and may not have good convergence properties. As such posterior conditional distributions, we omit the details and focus on drawing the latent variables. Suppose we have ${\Lambda }_{1:T}^{(1)}$ from the previous iteration. The particle filtering procedure consists of two phases.

Phase I: Forward filtering (Andrieu et al., 2010).

• Draw a proposal ${\Lambda }_{i,t}^{(m)}$ from an importance density $q({\Lambda }_{i,t}|{\Lambda }_{i,t-1}^{(m)},\theta ),m=2,\dots ,M$.

• Compute the importance weights:

  $${w}_{i,t}^{(m)}=\frac{p({y}_{i,t};{\Lambda }_{i,t}^{(m)},\theta )p({\Lambda }_{i,t}^{(m)}|{\Lambda }_{i,t-1}^{(m)},\theta )}{q({\Lambda }_{i,t}|{\Lambda }_{i,t-1}^{(m)},\theta )},m=1,\dots ,M.$$

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• Normalise the weights: ${\widetilde{w}}_{i,t}^{(m)}=\frac{{w}_{it}^{(m)}}{{\sum }_{{m}^{^{\prime}}=1}^{M}{w}_{it}^{({m}^{^{\prime}})}},m=1,\dots ,M$.

• Resample the particles $\{{\Lambda }_{i,t}^{(m)},m=1,\dots ,M\}$ with probabilities $\{{\widetilde{w}}_{i,t}^{(m)},m=1,\dots ,M\}$.

  In the original PG sampler, the particles are stored for $t=1,\dots ,T$ and a single trajectory is sampled using the probabilities from the last iteration. An improvement upon the original PG sampler was proposed by Whiteley (2010), who suggested drawing the path of the latent variables from the particle approximation using the backwards sampling algorithm of Godsill et al. (2004). In the forwards pass, we store the normalised weights and particles, and we draw a path of the latent variables as we detail below (the draws are from a discrete distribution).

  Phase II: Backward filtering (Chopin and Singh 2013, Godsill et al., 2004).

• At time $t=T$ draw a particle ${\Lambda }_{i,T}^{*}={\Lambda }_{i,T}^{(m)}.$

• Compute the backward weights: ${w}_{t|T}^{(m)}\propto {\widetilde{w}}_{t}^{(m)}p({\Lambda }_{i,t+1}^{*}|{\Lambda }_{i,t}^{(m)},\theta )$.

• Normalise the weights: ${\widetilde{w}}_{t|T}^{(m)}=\frac{{w}_{t|T}^{(m)}}{{\sum }_{{m}^{^{\prime}}=1}^{M}{w}_{t|T}^{({m}^{^{\prime}})}},m=1,\dots ,M$.

• Draw a particle ${\Lambda }_{i,t}^{*}={\Lambda }_{i,t}^{(m)}$ with probability ${\widetilde{w}}_{t|T}^{(m)}$.

Therefore, ${\Lambda }_{i,1:T}^{*}=\{{\Lambda }_{i1}^{*},\dots ,{\Lambda }_{iT}^{*}\}$ is a draw from the full conditional distribution. The backwards step often results in dramatic improvements in computational efficiency. For example, Creal and Tsay (2015) find that $M=100$ particles is enough. There remains the problem of selecting an importance density $q({\Lambda }_{i,t}|{\Lambda }_{i,t-1},\theta )$. We use an importance density implicitly defined by ${\Lambda }_{i,t}={a}_{i,t}+{\sum }_{p=1}^{P}{b}_{i,t}{\Lambda }_{i,t-1}^{p}+{h}_{i,t}{\xi }_{i,t}$ where ${\xi }_{i,t}$ follows a standard (zero location and unit scale) Student-t distribution with $\nu =5$ degrees of freedom. That is, we use polynomials in ${\Lambda }_{i,t-1}$ of order $P$. We select the parameters ${a}_{i,t},{b}_{i,t}$ and ${h}_{i,t}$ during the burn-in phase (using $P=1$ and $P=2$) so that the weights $\{{\widetilde{w}}_{i,t}^{(m)},m=1,\dots ,M\}$ and $\{{\widetilde{w}}_{t|T}^{(m)},m=1,\dots ,M\}$ are approximately not too far from a uniform distribution. Chopin and Singh (2013) have analysed the theoretical properties of the PG sampler and proved that the sampler is uniformly ergodic. They also prove that the PG sampler with backwards sampling strictly dominates the original PG sampler in terms of asymptotic efficiency.

Alternatively, when the dimension of the state vector is large, we can draw ${\Lambda }_{i,1:T},$ conditional on all other paths ${\Lambda }_{-i,1:T}$ that are not path $i$. Therefore, we can draw from the full conditional distribution $p({\Lambda }_{i,1:T}|{\Lambda }_{-i,1:T},{{\varvec{y}}}_{1:T},\theta )$.

1.2 The Girolami and Calderhead (2011) procedure

We use a Girolami and Calderhead (2012, GC) algorithm to update draws for a parameter ${\varvec{\theta}}$ which in our case is ${\varvec{\beta}}$. The algorithm uses local information about both the gradient and the Hessian of the log-posterior conditional of ${\varvec{\theta}}$ at the existing draw. A Metropolis test is again used for accepting the candidate so generated, but the GC algorithm moves considerably faster relative to our naive scheme previously described. The GC algorithm is started at the first stage GMM estimator and MCMC is run until convergence. It has been found that the GC algorithm performs vastly superior relative to the standard MH algorithm and autocorrelations are much smaller. Suppose $L\left({\varvec{\theta}}\right)=\mathrm{log }p\left({\varvec{\theta}}|{\varvec{X}}\right)$ is used to denote for simplicity the log posterior of ${\varvec{\theta}}$.

Moreover, define

$${\varvec{G}}\left({\varvec{\theta}}\right)=\mathrm{est}.\mathrm{cov}\frac{\partial }{\partial{\varvec{\theta}}}\mathrm{log }p\left({\varvec{X}}|{\varvec{\theta}}\right)$$

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the empirical counterpart of

$${{\varvec{G}}}_{o}\left({\varvec{\theta}}\right)=-{E}_{Y|{\varvec{\theta}}}\frac{{\partial }^{2}}{\partial{\varvec{\theta}}\partial {{\varvec{\theta}}}^{^{\prime}}}\mathrm{log }p\left({\varvec{X}}|{\varvec{\theta}}\right)$$

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The Langevin diffusion is given by the following stochastic differential equation:

$$d{\varvec{\theta}}\left(t\right)=\frac{1}{2}{\widetilde{\nabla }}_{{\varvec{\theta}}}L\left\{{\varvec{\theta}}\left(t\right)\right\}dt+d{\varvec{B}}\left(t\right)$$

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where

$${\widetilde{\nabla }}_{{\varvec{\theta}}}L\left\{{\varvec{\theta}}\left(t\right)\right\}=-{{\varvec{G}}}^{-1}\left\{{\varvec{\theta}}\left(t\right)\right\}\cdot {\nabla}_{{\varvec{\theta}}}L\left\{{\varvec{\theta}}\left(t\right)\right\}$$

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is the so-called natural gradient of the Riemann manifold generated by the log posterior.

The elements of the Brownian motion are

$${{\varvec{G}}}^{-1}\left\{{\varvec{\theta}}\left(t\right)\right\}d{{\varvec{B}}}_{i}\left(t\right)=|{\varvec{G}}\left\{{\varvec{\theta}}\left(t\right)\right\}{|}^{-1/2}\sum_{j=1}^{{K}_{\beta }}\frac{\partial }{\partial{\varvec{\theta}}}\left[mbol{G}^{-1}{\left\{{\varvec{\theta}}\left(t\right)\right\}}_{ij}|{\varvec{G}}\left\{{\varvec{\theta}}\left(t\right)\right\}{|}^{1/2}\right]dt+{\left[\sqrt{{\varvec{G}}\left\{{\varvec{\theta}}\left(t\right)\right\}}d{\varvec{B}}\left(t\right)\right]}_{i}$$

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The discrete form of the stochastic differential equation provides a proposal as follows:

$${\widetilde{{\varvec{\theta}}}}_{i}={{\varvec{\theta}}}_{i}^{o}+\frac{{\varepsilon }^{2}}{2}{\left\{{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right){\nabla }_{{\varvec{\theta}}}L\left({{\varvec{\theta}}}^{o}\right)\right\}}_{i}-{\varepsilon }^{2}{\sum }_{j=1}^{{K}_{\theta }}{\left\{{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)\frac{\partial {\varvec{G}}\left({{\varvec{\theta}}}^{o}\right)}{\partial {{\varvec{\theta}}}_{j}}{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)\right\}}_{ij} +\frac{{\varepsilon }^{2}}{2}{\sum }_{j=1}^{{K}_{\theta }}{\left\{{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)\right\}}_{ij}\mathrm{tr}\left\{{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)\frac{\partial {\varvec{G}}\left({{\varvec{a}}}^{o}\right)}{\partial {{\varvec{\theta}}}_{j}}\right\}+{\left\{\varepsilon \sqrt{{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)}{{\varvec{\xi}}}^{o}\right\}}_{i}={\varvec{\mu}}{\left({{\varvec{\theta}}}^{o},\varepsilon \right)}_{i}+{\left\{\varepsilon \sqrt{{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)}{{\varvec{\xi}}}^{o}\right\}}_{i},$$

where ${{\varvec{\beta}}}^{o}$ is the current draw.

The proposal density is

$$q\left(\widetilde{{\varvec{\theta}}}|{{\varvec{\theta}}}^{o}\right)={\mathcal{N}}_{{K}_{\theta }}\left(\widetilde{{\varvec{\theta}}},{\varepsilon }^{2}{{\varvec{G}}}^{-1}\left({{\varvec{\theta}}}^{o}\right)\right),$$

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and convergence to the invariant distribution is ensured by using the standard form Metropolis–Hastings probability

$$\mathrm{min }\left\{1, \frac{p\left(\widetilde{{\varvec{\theta}}}|\cdot ,Y\right)q\left({{\varvec{\theta}}}^{o}|\widetilde{{\varvec{\theta}}}\right)}{p\left({{\varvec{\theta}}}^{o}|\cdot ,Y\right)q\left(\widetilde{{\varvec{\theta}}}|{{\varvec{a}}}^{o}\right)}\right\}.$$

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