Macroeconomic policies and the pandemic-driven recession

Abstract

We build a three-country DSGE model to address the economic fallout from the COVID-19 shock. First, three different scenarios –optimistic, baseline and pessimistic– are drawn where economic authorities are assumed to not react to the disturbance. We find that the pandemic brings about a prolonged economic depression in the latter scenario –the most realistic one–, as GDP and hours worked fall by 20% (from trend) and they never recover their pre-crisis levels over the span of time studied. We then move on to analyze the effectiveness of conventional fiscal and monetary policy tools in curbing the recessionary consequences of the pandemic. The most powerful instruments are government purchases and expansionary monetary policy, although these two measures come with some trade-offs. In addition, we explore how a binding zero lower bound (ZLB) that renders conventional monetary policy ineffective can affect our findings. We show that the lower constraint deepens the recession caused by the pandemic, primarily because the central bank cannot lower the policy rate further, and because fiscal policy tightens in order to ensure government debt sustainability. Naturally, we next ask ourselves what would happen in this context did the monetary authority rely on unconventional monetary policy to try to dampen the recessionary consequences of the pandemic. Our results reveal that quantitative easing (QE) prevents private consumption, inflation, and to a much lesser extent, output from falling as much due to the shock.

1. Introduction

At the time of the writing, in addition to wreaking havoc worldwide and causing myriad human losses, which is of course the most pressing and heartbreaking side of this disease, the outbreak of the new coronavirus COVID-19 is currently rocking the world economy and throwing most of the countries into a profound recession. There is a broad consensus that the surge of this virus constitutes a war-like shock. Along these lines, in the following blog post Dell’Ariccia et al. (2020) assert that:

“The COVID-19 pandemic is a crisis like no other. It feels like a war, and in many ways it is. People are dying. Medical professionals are on the front lines. Those in essential services, food distribution, delivery, and public utilities work overtime to support the effort. And then there are the hidden soldiers: those who fight the epidemic confined in their homes, unable to fully contribute to production.

In a war, massive spending on armaments stimulates economic activity and special provisions ensure essential services. In this crisis, things are more complicated, but a common feature is an increased role for the public sector.

At the risk of oversimplifying, policy needs to distinguish two phases:

Phase 1: the war. The epidemic is in full swing. To save people’s lives, mitigation measures are severely curtailing economic activity. This may be expected to last at least one or two quarters.

Phase 2: the post-war recovery. The epidemic will be under control with vaccines/drugs, partial herd immunity, and continued but less disruptive containment measures. As restrictions are lifted, the economy returns–perhaps haltingly–to normal functioning.

The success of the pace of recovery will depend crucially on policies undertaken during the crisis. If policies ensure that workers do not lose their jobs, renters and homeowners are not evicted, companies avoid bankruptcy, and business and trade networks are preserved, the recovery will occur sooner and more smoothly (IMFBlog, Giovanni Dell’Ariccia, Paolo Mauro, Antonio Spilimbergo, and Jeromin Zettelmeyer, April 1, 2020).

Dell’Ariccia et al. (2020) highlight the existing trade-off between measures to deter contagion and the acute deterioration of the economy. In effect, as the virus spreads, governments find themselves at the crossroad of choosing between letting people get infected, with a huge cost in term of human lives, and compelling them to self-quarantine, with a huge cost in term of output and employment. After a certain initial resistance, authorities by and large have finally opted for the latter option, although at a varying degree. The economic consequences prove to be quite visible. COVID-19 has caused a severe breakdown in the global supply which has been compounded by an abrupt fall in aggregate demand, because both consumption and investment are expected to plunge due to the lockdown and the increased uncertainty arising from the pandemic itself. As a result, unemployment levels are set to skyrocket. Economic authorities have rushed to put in place a broad battery of bold fiscal and monetary policies designed to prop up economic activity. Central banks have not hesitated to slash interest rates so as to stem the sharp deterioration of the economic environment. Further, some monetary authorities (i.e., the FED, the ECB and the Bank of England) have just entered into another round of Quantitative Easing (QE),1 as their policy rates are close to or at the zero lower bound. These large-scale central bank purchases of assets are viewed as a stabilizing device, for they help governments issue long-term bonds (Myles, 2020).

Concerning fiscal policy, governments have spared no efforts in helping shore up the battered financial situation of consumers and firms. For instance, Spain’s government has taken steps to fight back the COVID-19 shock by rolling out a huge stimulus package accounting for roughly one-fifth of the country’s GDP.2 This program comprises measures such as extended unemployment benefits to all workers, regardless of whether they qualify for the financial aid or not, the possibility of postponing the payments of the mortgage, rent or utility bills for some type of workers, unlimited liquidity to firms in the form of public guarantees, etc. Needless to say, when it became evident how critical the situation was, most governments desperately embarked on large purchases of medical supplies. Similar policies have been implemented in many other countries. Although not a priority as matters currently stand, another policy proposal that seems to be currently on the table across countries is large infrastructure investments. Several countries (i.e., the US and UK) have long been suffering from crumbling infrastructure and see the current situation as an opportunity to make heavy investments in public capital. Within the European context, some leaders are now calling on the European Commission to launch a new Marshall Plan that would encompass large infrastructure projects to jumpstart the economy.3

But such a significant increase in government expenditure may prove hard for some countries to finance, even in times of very low interest rates. Debt-GDP ratios will likely soar in the aftermath of this crisis, thereby inflicting hardship on both those debt-ridden developed countries with relatively low credibility (Italy and Spain come to mind) and developing economies and emerging markets. The ensuing higher tax burden, coupled with government expenditure cuts in some non-priority items, that these countries will have to incur can impair the economy and therefore render the job of stabilizing government debt more difficult. Sooner or later, investors would panic and end up shedding bonds, thus putting upward pressure on the yields. Higher interest rates would in turn drive debt-GDP ratios up and make this vicious circle feed on itself. At the European level, a way to stop this process that has relentlessly been called on is the creation of the eurobonds or even some type of COVID-related bonds, often referred to as coronabonds or COVID perpetual bonds (Giavazzi & Tabellini, 2020). The rationale behind this proposal is that, like in a war, the optimal economic policy response should be to spread the fiscal cost across several generations, backed by a joint tax capacity. Other advantages would be the swiftness with which they can be issued and the “whatever-it-takes” signal that they send. Other authors have just proposed mutualizing the sizable fiscal burden through the creation of a European wealth tax (Landais et al., 2020).

One step further in that direction would be the implementation of the so-called “helicopter money”. While not a new concept, it has gained some traction at the current juncture. Some prominent economists have vigorously called for its urgent execution (Buiter, 2020; De Grauwe, 2020; Gali, 2020a and 2020b) on the grounds that extraordinary problems require extraordinary and bold solutions. Gali, 2020a, Gali, 2020b finds that money-financed fiscal expansions in a Real Business Cycle (RBC) model gives rise to a small effect on output and a quick spike in inflation. Things look very different when the author turns to a New Keynesian model with wage stickiness. The same policy measure leads to sizable expansionary effects on output with almost no cost in terms of inflation. Contrary to the flexible-price case, consumption and investment now react strongly to the sharp drop in real interest rates. On top of that, debt-GDP ratio declines over time and welfare can increase if output lies sufficiently below its natural level to begin with.

The literature on pandemics and macroeconomics is somewhat scant. It should be noted, however, that the ongoing crisis is sparking a great deal of interest in the subject. In a short paper, Fornaro and Wolf (2020) use an undergraduate-like New Keynesian model to depict a rather pessimistic scenario in which the COVID-19 supply shock depresses aggregate demand, which can in turn lead to lower investment and lower productivity growth. The latter would act to reduce aggregate demand further. Thus, a genuine supply-demand loop would be set in motion. Of course, central banks could be quick to cushion these negative effects by adopting a very expansionary stance. Problems arise, nevertheless, if the zero lower bound were to bind, because monetary policy would be rendered rather ineffective. The economy might then be subject to stagnation traps. Against this complex backdrop, policymakers would be left with fiscal policy as the only actual powerful tool to get the economy back on track.

By means of a DSGE model calibrated to the US, Faria e Castro (2020) illustrates the effects of fiscal policy throughout a pandemic. Although the shock is assumed to take place only in the contact-intensive services sector, it rapidly gets transmitted into the rest of the economy. The results of the pandemic simulation are bleak: the recession lasts for three quarters, and it implies both a stunning output fall of 15% (percentage deviation from steady state) and a significant jump in unemployment that ends up hovering around 20%. The author then analyzes how different fiscal shocks would help dampen the recessionary effects of the pandemic. He finds that the group of people that loses the most from the crisis, borrowers, is also the group that gains the most from unemployment insurance measures or other unconditional cash transfers. Besides, liquidity support to the firms can play an instrumental role in bolstering income and employment.

Boscá et al. (2020) employ the REMS model (a taylor-made DSGE model for the Spanish economy) to study the economic effects of the COVID shock, as well as a host of policies designed to combat the recession in Spain. Making an optimistic assumption about the length of the lockdown, they show that the year-by-year decrease in output would exceed 4% in the no-policy change scenario. The policies they propose in order to partially offset the impact of the crisis in an effective manner would be a loosening of the current EU fiscal rule, the ECB’s QE program, the provision of state guarantees to firms, and social insurance measures. Under three distinct scenarios differing in the duration of the crisis and in the adverse effect of the lockdown on the labor supply, Mihailov (2020) draws on Galí-Smets-Wouters (2012) model to estimate the covid-19 shock in the hardest-hit industrialized countries: the US, France, Italy, Germany and Spain. He finds that even in the most optimistic scenario in terms of the duration of the pandemic and of the lockdown, per-capita consumption and per-capita output would fall significantly, although both variables would recover fast (1–2 years). When more gloomy assumptions are made, however, the per-capita consumption and per-capita output losses would be shockingly large and long-lasting (more than 10–15 years). In the case of a permanent supply shock, these variables would be 1.5 percentage points lower on a permanent basis.

Jordá et al. (2020) focus on the medium-term to longer-term effects of European pandemics. Using a very long dataset that dates back to the 14th century, they show that, due to the strong contraction of the labor supply, real returns on assets plummet, real wages tend to rise, investment wanes and saving increases. Governments would be given some additional fiscal space owing to the significant decline in the real interest rates. Correia et al. (2020) rely on disaggregated data across US cities of the 1918 Flu Pandemic to show that manufacturing output fell by 18% in those geographical areas more exposed to the pandemic. They also show that those cities that were quicker and firmer in acting against the health crisis did recover faster after this was over.

Guerrieri et al. (2020) argue that a pure supply shock can trigger a negative demand-side shock if the model at hand is a multi-sector model featuring low substitutability across sectors, incomplete markets, as well as hand-to-mouth consumers. Building on such a model, they go on to explore a rich array of policy options targeted at overcoming the economic crisis, finding that the optimal policy is a combination of very loose monetary policy and social insurance measures. Farhi and Baqaee ​(2020) contend that the new coronavirus is not a regular shock but a messy combination of disaggregated supply and demand shocks affecting all sectors of the economy to varying degrees. They use a general disaggregated model featuring an arbitrary number of sectors, factors, unrestricted input-output linkages and elasticities of substitution, downward nominal wage rigidities, credit-constraints, and a zero lower bound on nominal interest rates. Both resorting to the analysis of local and global comparative statics and to the results yielded by a calibrated model, they show how important complementarities in the production network are in amplifying negative supply shocks and in dampening adverse demand shocks. These outcomes tend to hold even if the intersectoral and intertemporal elasticities of substitution in consumption are identical.

From a different perspective, Eichenbaum et al. (2020) extend a SIR model to allow for the interplay between epidemics and economics. This interaction causes supply and demand effects that combine to produce large and deep downturns. They show that containment measures exacerbate recessions but tend to raise welfare because they save human lives. Using a similar SIR ​+ ​DSGE model, Jones et al. (2020) estimate the optimal late response to the pandemic, which requires a brutal front-loaded slowdown of the economy by 25% to save as many human lives as possible. Along similar lines, Glover et al. (2020) embed an epidemiological diffusion framework into a multi-sector model with heterogeneous agents (young and old). Their results are that older individuals are found to gain more from the lockdown, whereas young workers in the non-essential sectors stand to lose the most. When it comes to the optimal policy package, they find that it differs across the different kinds of individuals according to their preferences, and the policies that a planner would favor are also different from the ones that each type of agent would advocate.

With a view to providing simple and straightforward intuition on the macroeconomic consequences of the COVID crisis, we next turn to one of the most familiar graphical apparatus at the undergraduate level, the aggregate supply (AS)-aggregate demand (AD) model. The pandemic is known to affect both the economy’s supply side and demand side simultaneously, and as such, its effects on output and unemployment are likely to be highly recessive. Things turn out to be different regarding variables like inflation and the interest rate, for how the COVID shock ends up impacting them will hinge on both the relative strength of the shifts and the slopes of the supply and demand curves. For the sake of simplicity, we first assume that the government does nothing to counteract the recession spawned by the pandemic. Fig. 1 depicts such a situation. Starting out at the initial equilibrium point E where observed unemployment is at its NAIRU level, the supply shock, as a temporary disruption in the production process, raises the marginal cost of firms and shifts up the AS schedule to AS′. At the same time, the natural level of output shifts in as a result of a lower total factor productivity4 from $\overline{Y}$ to ${\overline{Y}}^{\prime }$.

Fig. 1.

Economic effects of the pandemic under the no-policy change scenario. Source: Authors’ elaboration.

Other things being equal, the initial supply shock would prompt a higher price level and a lower output. Graphically, consumers would slide up the AD curve, capturing the decrease in aggregate demand. The transmission mechanism underlying this movement is as follows: the rise in the price level reduces real balances and puts upward pressure on the interest rate, which ends up denting investment. Throughout the process, consumption also declines. The short-run equilibrium now lies at the point E′, where short-run output, Y, outweighs natural output, ${\overline{Y}}^{\prime }$, and the new price level, P′, is above the initial one. If the contractionary effects of the pandemic were to be long-lasting, the AD curve could shift in because of falling expected future income. In this case, the new AD curve, AD′, moves all the way down the AS′ curve until point E″, thus reducing output further, which tends to buffer the early inflationary pressures. Moreover, quarantine practices followed to prevent the spread of the virus also make up an additional demand-side shock inasmuch as they restrict individuals’ mobility and hence, their consumption activities. In terms of the graphical model, the AD curve would shift further down up to the new short-run equilibrium point E‴ where AD″ intersects AS′.

It is worthwhile to note that ex-ante, there is no way to ensure whether this new short-run equilibrium point will be located above or below the initial one, that is to say, whether the final price level will be higher or lower than the initial one. What can be ensured, however, is that output will be hit hard by the described shock propagations, with its final value possibly lying below the natural level, which is in turn lower than the initial one. It is worth noting as well that in a conventional situation, we would expect the economy to return to the full-employment output level at point E′, still below the initial output level, point E. But the post-COVID world may not be a normal one, and longer-lasting quarantines, along with the difficulties to formulate correct price expectations, can hamper the functioning of the economy’s transmission channels, thereby retarding the adjustment process.

Against this critical background, a coordinated fiscal-monetary response aimed at mitigating the adverse effects of the crisis should be implemented in no time. Fig. 2 displays the implementation of such measures. We start out at point E‴, which represents the final short-run equilibrium following the COVID shocks. To simplify the analysis, let us call this initial point A and the alluded curves AD″ and AS′ AD _p e AS _p, respectively. As illustrated in Fig. 2 , monetary and fiscal policies exert a direct influence on the aggregate demand. Both policies act to displace the AD curve to the right until $A{D}_p^{″}$, taking the economy to point A′, and stabilizing output at ${\overline{Y}}^{\prime }$. Nevertheless, there is a clear trade-off facing policymakers: given the supply constraints, the efforts to stabilize output through pumping up demand would lead to inflationary pressures and higher government deficits and debts. The economy would then come closer to entering a stagflation period when compared to the initial situation before the pandemic hit. From this simple graphical approach, it should be evident that without the proper calibration regarding the COVID shocks and the parameters concerned, it proves hard to analyze how deep the recession, and its associated effects on variables like the price level and the interest rate, will be.

Fig. 2.

Fiscal and monetary policy responses to the pandemic. Source: Authors’ elaboration.

In this paper we use a three-country New Keynesian DSGE model to answer a number of relevant questions:

• ●How deep and persistent will this supply-side disruption be?
• ●By how much will aggregate demand be affected?
• ●Will the conventional economic policy levers –monetary policy and fiscal policy – be effective in fighting this shock? Size wise, what will be the most adequate response?
• ●Will the recovery be V-shaped, U-shaped, W-shaped, or L-shaped?
• ●What are the macroeconomic effects of the pandemic in the presence of a binding ZLB?
• ●To what extent can unconventional monetary policy help the economy recover faster?

Our results suggest that except for the optimistic scenario, to which we attach low chances to play out, the pandemic takes a big toll on production and hours worked. Specifically, in the pessimistic case, both variables sharply drop by 20% (from trend) and a full recovery over a timespan of almost 4 years is nowhere to be seen. Fortunately, economic authorities have some tools at their disposal to curb the pandemic’s blow. We find that the most successful policy measures in terms of their contribution to the fight against recession are government purchases and conventional monetary policy, with the latter being more effective in helping the economy soften the impact and return quicker to its pre-crisis level. Its only side effect would be temporary higher inflation, which in a deflationary context like the one the pandemic would generate does not seem to be much of a side effect after all. Furthermore, compared to spending-based fiscal expansions, tax-based stimuli are found to be less powerful in combating the crisis, as the vast literature on fiscal multipliers has long underscored. Amongst the tax instruments, cutting labor-income tax would be the most appropriate measure. Conversely, we do not find significant effects from using the remaining tax tools: consumption tax and import tariffs from China and the ROW. It should be pointed out that all the policies encompassed in our analysis have been calibrated to account for the large stimulus packages that the authorities of the most industrialized countries have recently announced.

Next, in order to make the analysis more realistic, we consider the macroeconomic effects of the pandemic-driven crisis in the presence of a binding ZLB that leaves standard monetary measures ineffective. As expected, this constraint is found to aggravate the recession, as this interest rate floor keeps the central bank from further lowering the monetary policy rate. In effect, both private and government consumption decrease, with the former falling more on impact, but recovering faster, than in the unrestricted situation, and with the latter being cut in a decisive manner over the whole timespan studied to prevent the government debt from getting out of control. Besides, inflation, wages and marginal cost all follow a similar pattern according to which the variable drops on impact but bounces back more swiftly as time goes by. It is worth underlining that the exchange rate depreciation arising from the pandemic-induced recession contributes to the rise of exports to, and the decline of imports from, both geographical areas (China and the ROW), thereby improving the external accounts. Finally, to complete the analysis, we ask ourselves what would be the effects of the monetary authority resorting to unconventional policies to fight back the recession under the ZLB. Our exercise indicates that QE is not particularly effective in impeding a sharp economic downturn and in promoting a faster recovery of output. This unconventional policy, however, spurs both private consumption and inflation, and engineers an exchange rate depreciation that helps improve the trade balance.

2. Model

The model used in this work consists of three economies5 : United States of America, China and the rest of the world –ROW– (Europe). In presenting the model, only objective functions, budget constraints, etc. of the Home economy (h) relative to the other two foreign economies (f1, f2) will be laid out. That is to say, this way of setting up the model can be thought of as a loop in which in each iteration one of the three economies is regarded as the benchmark. It is worth remarking that differently from other open economy models featuring small open economies,6 ours deals with three economies endogenously.

2.1. Covid-19 in the model

The aim of this paper is to study the impact of the covid-19 crisis on the American economy. Due to the fact that up to now papers dealing with pandemics in DSGE models had been in short supply, there is no a well-established way in the literature to model a shock like this. However, there exists a widespread consensus among economists and policymakers about the economic effects of this event. On the one hand, Chinese measures to shut down trade and other non-essential activities and to enforce travel bans have caused a sharp drop in China’s industrial production - a 13.5% drop in industrial production in the first two months of 2020 (Fig. 3 ). In the model, this shock can be thought of as arising through a drop in productivity in the production of inputs in China, used domestically and exported.

Fig. 3.

China’s industrial production. Source: NBS.

On the other hand, the effect identified by the sudden stops in consumption and labor, due to social isolation in the three countries of the model,7 is captured by declines in preferences about consumption and labor supply, an empirically grounded assumption actually, as the sharp fall in sales in the Chinese retail sector indicates (Fig. 4 ). In short, we have a negative supply shock captured by a drop in China’s input production, and two negative shocks represented by declines in consumption and labor supply preferences.

Fig. 4.

China’s retail sales. Source: NBS.

2.2. Households in the benchmark country (h)

There is a continuum of households indexed by j ​∈ ​[0, 1]. This representative household maximizes its intertemporal utility by choosing consumption, savings and leisure. The consumption decision involves choosing between goods produced domestically or abroad. In other words, this agent decides how much to consume, how much to work and how much to save, accumulating assets to maximize the discounted flow of expected utility:

$$\underset{C_{h,j,t}^h,C_{f1,j,t}^h,C_{f2,j,t}^h,L_{j,t}^h,B_{h,j,t+1}^h}{\max }{E}_t\sum _{t=0}^{\infty }{\beta }^t{S_t^P}^h\left(\frac{{C_{j,t}^h}^{1-\sigma }}{1-\sigma }-{S_t^L}^h\frac{{L_{j,t}^h}^{1+\varphi }}{1+\varphi }\right)$$ (1)

subject to the following budget constraint,

$$\left(1+{\tau }_t^{c,h}\right)C_{h,j,t}^h{P}_t^{c,h}{S}_t^h+\left(1+{\tau }_t^{imp,h,f1}\right)C_{f1,j,t}^h{S}_t^{f1}{P}_t^{c,f1}+\left(1+{\tau }_t^{imp,h,f2}\right)C_{f2,j,t}^h{S}_t^{f2}{P}_t^{c,f2}$$

$$+S_t^h\frac{B_{h,j,t+1}^h}{R_t^h}=\left(1-{\tau }_t^{l,h}\right)W_t^h{S}_t^h{L}_{j,t}^h+S_t^h{B}_{h,j,t}^h$$ (2)

The aggregation of domestic consumption is done as follows:

$$C_{j,t}^h={C_{h,j,t}^h}^{1-{\omega }_c^h}{C_{F,j,t}^h}^{{\omega }_c^h}$$ (3)

and,

$$C_{F,j,t}^h={C_{f1,j,t}^h}^{{\vartheta }_{f1}^h}{C_{f2,j,t}^h}^{1-{\vartheta }_{f1}^h}$$ (4)

where E _t is an expectation operator, β denotes the intertemporal discount rate, σ is the relative risk aversion parameter, ϕ is the marginal disutility of work, ${\omega }_C^h$ is the participation of the good produced abroad in the basket of household goods, ${\vartheta }_{f1}^h$ is the participation of the foreign country f1 in the basket of imported goods, $C_h^h$ are the goods produced and consumed domestically,8 $C_F^h$ it is the basket of goods produced abroad and consumed domestically, with $C_{f1}^h$ and $C_{f1}^h$ originating in countries f1 and f2, respectively. The price level of the domestic consumption good is P ^c,h, P ^C,f1, P ^C,f2, S ^f1 and S ^f2 are the consumption goods price levels and the exchange rates in f1 and f2, respectively, with S ^h being the domestic country’s exchange rate.9 $B_h^h$ is the bond of the domestic government whose return (basic interest rate) is R ^h, W ^h is the wage level of the domestic country, L ^h is the number of hours worked by households in the country domestic, τ ^c,h, τ ^l,h, τ ^imp,h,f1 and τ ^imp,h,f1 represent the tax rates on consumption of household goods, on labor income and on the consumption of goods imported from f1 and f2, respectively.

Additionally, the model presents two shocks on the side of the household’s preferences, where, S ^P is the shock of intertemporal preference, which alters the family’s choice between present and future consumptions, with the following movement rule:

$$\log {S_t^P}^h={\rho }_P^h\log {S_{t-1}^P}^h+{ϵ}_{P,t}^h-{\phi }_{covid-19,P}^h{S}_{t+1}^{covid-19}$$ (5)

where ${\rho }_P^h$ is the autoregressive component of this shock and ${ϵ}_{P,t}^h~N(0,{\sigma }_P^h)$, $S_{t+1}^{covid-19}$ is the effect of covid-19 being $\log S_t^{covid-19}={\rho }_{covid-19}\log S_{t-1}^{covid-19}+{ϵ}_{covid-19,t}$ with ρ _covid−19 being the autoregressive component of this shock, ϵ _covid−19,t ~ N(0, σ _covid−19) and ${\phi }_{covid-19,P}^h$ a scale parameter of the effects of covid-19 on the domestic economy. The second shock is the labor supply, S ^L, which affects the households’ willingness to work, with the following rule:

$$\log {S_t^L}^h={\rho }_L^h\log {S_{t-1}^L}^h+{ϵ}_{L,t}^h+{\phi }_{covid-19,L}^h{S}_{t+1}^{covid-19}$$ (6)

where ${\rho }_L^h$ is the autoregressive component of this shock and ${ϵ}_{L,t}^h~N(0,{\sigma }_L^h)$.

The first-order conditions of the representative household’s problem are:

$$\left(\frac{1-{\omega }_c^h}{{\omega }_c^h{\vartheta }_{f1}^h}\right)\left(\frac{C_{f1,j,t}^h}{C_{h,j,t}^h}\right)=\frac{\left(1+{\tau }_t^{c,h}\right)P_t^{c,h}{S}_t^h}{\left(1+{\tau }_t^{imp,h,f1}\right)P_t^{c,f1}{S}_t^{f1}}$$ (7)

$$\left[\frac{1-{\omega }_C^h}{{\omega }_c^h\left(1-{\vartheta }_{f1}^h\right)}\right]\left(\frac{C_{f2,j,t}^h}{C_{h,j,t}^h}\right)=\frac{\left(1+{\tau }_t^{c,h}\right)P_t^{c,h}{S}_t^h}{\left(1+{\tau }_t^{imp,h,f2}\right)P_t^{c,f2}{S}_t^{f2}}$$ (8)

$$\left(\frac{1}{1-{\omega }_C^h}\right)S_t^{L,h}{L_{j,t}^h}^{\varphi }{C_{j,t}^h}^{\sigma -1}{C}_{h,j,t}^h=\frac{\left(1-{\tau }_t^l\right)W_t}{\left(1+{\tau }_t^{c,h}\right)P_t^{c,h}}$$ (9)

$$\left[\frac{{C_{j,t}^h}^{1-\sigma }}{\left(1+{\tau }_t^{c,h}\right)P_t^{c,h}{S}_t^h{C}_{h,j,t}^h}\right]=R_t^h\beta E_t\left[\frac{{C_{j,t+1}^h}^{1-\sigma }}{\left(1+{\tau }_{t+1}^{c,h}\right)P_{t+1}^{c,h}{S}_{t+1}^h{C}_{h,j,t+1}^h}\right]$$ (10)

Equations (7), (8), (9), (10) account for the relative demands for imported consumption goods (for the two foreign countries), the labor supply and the Euler equation for the government bond (IS curve), respectively.

2.3. Firms in the benchmark country

2.3.1. Firms producing final goods

From an aggregate perspective, monopolistic competition involves, among other things, confronting two distinct issues: the fact that consumers purchase a great variety of goods with the need of modeling the consumer as buying only a specific kind of good (a bundle comprised of all goods), $Y_t^h$. This aggregate good is sold by a perfectly competitive retail firm. In other words, all the retailers are assumed to be identical. In order to produce this aggregate good, the assembler must purchase a large quantity of intermediate goods, $Y_{j,t}^h$ with individual prices for each good j, $P_{j,t}^{c,h}$. These are the inputs used in this production process. Thus, the assembler must solve the following problem:

$$\underset{Y_{j,t}^h}{\max }{P}_t^{c,h}{Y}_t^h-{\int }_0^1{P}_{j,t}^{c,h}{Y}_{j,t}^{h}dj$$ (11)

subject to the following technology given by the Dixit-Stiglitz aggregator (Dixit and Stiglitz, 1977),

$$Y_t^h={\left({\int }_0^1{Y_{j,t}^h}^{\frac{{\psi }_h-1}{{\psi }_h}}dj\right)}^{\frac{{\psi }_h}{{\psi }_h-1}}$$ (12)

where ψ _h is the elasticity of substitution between intermediate goods.

By solving the previous problem, we obtain the demand for product j, $Y_{j,t}^h$:

$$Y_{j,t}^h=Y_t^h{\left(\frac{P_{j,t}^{c,h}}{P_t^{c,h}}\right)}^{-{\psi }_h}$$ (13)

and replacing equation (13) in equation (12), we arrive at the general price level for final domestically produced goods:

$$P_t^{c,h}={\left({\int }_0^1{P_{j,t}^{c,h}}^{1-{\psi }_h}dj\right)}^{\frac{1}{1-{\psi }_h}}$$ (14)

2.3.2. Firms producing domestic inputs and intermediate goods

2.3.2.1. Domestic input production

At this stage, the firm must choose the quantities of labor in order to maximize its profit:

$$\underset{L_{j,t}^h}{\max }{P}_t^{INP,h}{S}_t^{h}IN{P}_{j,t}^h-W_t^h{S}_t^h{L}_{j,t}^h$$ (15)

subject to the following technology:

$$IN{P}_{j,t}^h=A_t^h{L_{j,t}^h}^{1-\alpha }$$ (16)

where INP ^h is the domestic production of input with price $P_t^{INP,h}$, 1 ​− ​α is the participation of labor in the production process of the domestic input and A ^h is the technological level that follows the law of movement10 :

$$\log A_t^h={\rho }_A^h\log A_{t-1}^h+{ϵ}_{A,t}^h$$ (17)

where ${\rho }_A^h$ is the autoregressive component of this shock and ${ϵ}_{A,t}^h~N(0,{\sigma }_A^h)$.

The first order conditions for the previous problem are:

$$W_t^h{L}_{j,t}^h=(1-\alpha )P_t^{INP,h}IN{P}_{j,t}^h$$ (18)

And total domestic input production is,

$$IN{P}_{j,t}^h=IN{P}_{h,j,t}^h+IN{P}_{h,j,t}^{f1}+IN{P}_{h,j,t}^{f2}$$ (19)

where $IN{P}_h^h$ is the input produced and used domestically, while $IN{P}_h^{f1}$ and $IN{P}_h^{f1}$ are the inputs produced domestically, but used in f1 and f2, respectively.

2.3.2.2. Production of intermediate goods

At this stage of production, this firm seeks to minimize its cost by choosing between inputs produced domestically and abroad:

$$\underset{IN{P}_{h,j,t}^h,IN{P}_{f1,j,t}^h,IN{P}_{f2,j,t}^h}{\min }IN{P}_{h,j,t}^h{P}_t^{INP,D}{S}_t^h+IN{P}_{f1,j,t}^h{S}_t^{f1}{P}_t^{INP,f1}+IN{P}_{f2,j,t}^h{S}_t^{f2}{P}_t^{INP,f2}$$ (20)

subject to the following aggregator technology,

$$Y_{j,t}^h={IN{P}_{h,j,t}^h}^{1-{\omega }_{INP}^h}{IN{P}_{F,j,t}^h}^{{\omega }_{INP}^h}$$ (21)

$$IN{P}_{F,j,t}^h={IN{P}_{f1,j,t}^h}^{{\vartheta }_{f1}^h}{IN{P}_{f2,j,t}^h}^{1-{\vartheta }_{f1}^h}$$ (22)

where $Y_j^h$ is the production of the intermediate good j, ${\omega }_{INP}^h$ is the share of the input from abroad in the production of the domestic intermediate good, ${\vartheta }_{f1}^h$ is the share of the input from the source f1 in the basket of imported inputs.

The first order conditions for the previous problem are:

$$IN{P}_{h,j,t}^h{P}_t^{INP,D}{S}_t^h=\left(1-{\omega }_{INP}^h\right)M{C}_{j,t}^h{Y}_{j,t}^h$$ (23)

$$IN{P}_{f1,j,t}^h{S}_t^{f1}{P}_t^{INP,f1}={\omega }_{INP}^h{\vartheta }_{f1}^{h}M{C}_{j,t}^h{Y}_{j,t}^h$$ (24)

$$IN{P}_{f2,j,t}^h{S}_t^{f2}{P}_t^{INP,f2}={\omega }_{INP}^h\left(1-{\vartheta }_{f1}^h\right)M{C}_{j,t}^h{Y}_{j,t}^h$$ (25)

where MC ^h is the marginal cost of the domestic country.

2.3.2.3. Pricing a la Calvo

The firm producing intermediate goods must decide the price of its good following a rule by Calvo (Calvo, 1983). There is a probability θ ^h that firms will maintain the price level of the previous period and the probability (1 −θ ^h) to price their asset optimally. Once the price is set at t, there is a probability θ ^h to remain fixed at t + 1, a probability ${{\theta }^h}^2$ to remain fixed at t + 2, and so on against. Therefore, this firm must consider these probabilities when setting the price in t. Thus, the problem of the firm that adjusts its price in t is:

$$\underset{{P_{j,t}^{c,h}}^{\ast }}{\max }{E}_t\sum _{i=0}^{\infty }{(\beta {\theta }^h)}^i\left({P_{j,t}^{c,h}}^{\ast }{Y}_{j,t+i}^h-T{C}_{j,t+i}^h\right)$$ (26)

subject to equation (13), where θ ^h is the rigidity factor in the price adjustment and TC ^h is the total cost.

The first order condition of this problem is:

$${P_{j,t}^{c,h}}^{\ast }=\left(\frac{{\psi }_h}{{\psi }_h-1}\right)E_t\sum _{i=0}^{\infty }{(\beta {\theta }^h)}^{i}M{C}_{j,t+i}^h$$ (27)

combining the pricing rule in equation (16) with the assumption that all firms in similar conditions define the price in the same way, the general price level is reached:

$$P_t^{c,h}={\left[{\theta }^h{P_{t-1}^{c,h}}^{1-{\psi }_h}+(1-{\theta }^h){P_t^{c,h}}^{\ast 1-{\psi }_h}\right]}^{\frac{1}{1-{\psi }_h}}$$ (28)

2.4. Government in the benchmark country

The government is split into two different entities, the fiscal authority and the monetary authority. The former is held responsible for conducting the model’s fiscal policy, while the latter is tasked with maintaining price stability through a Taylor rule.

2.4.1. Fiscal authority

The fiscal authority is assumed to tax households and issue debt to finance its current expenses, G ^h:

$$\frac{B_{h,t+1}^h}{R_t^h}-B_{h,t}^h+{\tau }_t^{c,h}{C}_{h,t}^h{P}_t^{c,h}{S}_t^h+{\tau }_t^{imp,h,f1}{C}_{f1,t}^h{S}_t^{f1}{P}_t^{c,f1}$$

$$+{\tau }_t^{imp,h,f2}{C}_{f2,t}^h{S}_t^{f2}{P}_t^{c,f2}+{\tau }_t^{l,h}{W}_t^h{L}_t^h=P_t^{c,h}{G}_t^h$$ (29)

$$\frac{Z_t^h}{Z_{ss}^h}={\left(\frac{Z_{t-1}^h}{Z_{ss}^h}\right)}^{{\gamma }_Z^h}{\left(\frac{B_{h,t}^h}{Y_{t-1}^h{P}_{t-1}^{c,h}}\frac{Y_{ss}^h{P}_{ss}^{c,h}}{B_{h,ss}^h}\right)}^{(1-{\gamma }_Z^h){\phi }_Z^h}{S_t^Z}^h$$ (30)

where $Z^h=\{G_t^h,{\tau }_t^{c,h},{\tau }_t^{l,h},{\tau }_t^{imp,h,f1},{\tau }_t^{imp,h,f2}\}$, and ${\gamma }_Z^h$ is the smoothing parameter for changes in variable Z and ${\phi }_Z^h$ is a scale parameter for each variable Z in public debt sustainability. Each fiscal shock takes the following form:

$$\log {S_t^Z}^h={\rho }_Z^h\log {S_{t-1}^Z}^h+{ϵ}_{Z,t}^h$$ (31)

where ${\rho }_Z^h$ is the autoregressive component of this shock, and ${ϵ}_{Z,t}^h~N(0,{{\sigma }^Z}^h)$.

2.4.2. Monetary authority

The monetary authority has a dual goal: stabilizing output and achieving price stability. To that end, the following Taylor rule is used:

$$\frac{R_t^h}{R_{ss}^h}={\left(\frac{R_{t-1}^h}{R_{ss}^h}\right)}^{{\gamma }_R^h}{\left[{\left(\frac{Y_t^h}{Y_{ss}^h}\right)}^{{\gamma }_Y^h}{\left(\frac{{\mathrm{\Pi }}_t^{c,h}}{{\mathrm{\Pi }}_{ss}^{c,h}}\right)}^{{\gamma }_{{\pi }^h}}\right]}^{1-{\gamma }_R^h}{S_t^m}^h$$ (32)

where ${\gamma }_Y^h$ and ${\gamma }_{\pi }^h$ are the sensitivities of the basic interest rate relative to the product and the inflation rate, respectively. ${S^m}^h$ is the monetary policy shock that evolves according to the following law of motion:

$$\log {S_t^m}^h={\rho }_m^h\log {S_{t-1}^m}^h+{\epsilon }_{m,t}^h$$ (33)

where ${\rho }_m^h$ is the autoregressive component of this shock, and ${ϵ}_{m,t}^h~N(0,{{\sigma }^m}^h)$.

And the gross inflation rate is given by:

$${\mathrm{\Pi }}_t^{c,h}=\frac{P_t^{c,h}}{P_{t-1}^{c,h}}$$ (34)

2.5. Good market equilibrium conditions and the balance of payments in the benchmark country

To close the model, two equilibrium conditions are required. In the goods market:

$$Y_t^h=C_{h,t}^h+G_t^h+C_{h,t}^{f1}+C_{h,t}^{f2}$$ (35)

And in the balance of payments:

$$\left(C_{h,j,t}^{f1}{P}_t^{c,h}{S}_t^h+IN{P}_{h,j,t}^{f1}{P}_t^{INP,h}{S}_t^h\right)+\left(C_{h,j,t}^{f2}{P}_t^{c,h}{S}_t^h+IN{P}_{h,j,t}^{f2}{P}_t^{INP,h}{S}_t^h\right)=$$

$$S_t^{f1}\left(C_{f1,j,t}^h{\tau }_t^{imp,h,f1}{P}_t^{c,f1}+IN{P}_{f1,j,t}^h{P}_t^{INP,f1}\right)+S_t^{f2}\left(C_{f2,j,t}^h{\tau }_t^{imp,h,f2}{P}_t^{c,f2}+IN{P}_{f2,j,t}^h{P}_t^{INP,f2}\right)$$ (36)

3. Empirical analysis

In this section some counter-factual exercises are conducted to explore the adverse effects of the COVID-19 crisis and the macroeconomic policies that can be used to alleviate them. In subsection 3.1 we first focus on a thorough analysis of the effects of the pandemic, where a no-policy baseline scenario is assumed throughout. Then, in subsection 3.2 we move on to assess the economic policy tools available to soften the blow of the COVID recession.

3.1. COVID-19 shock

This subsection seeks to study the effects of the pandemic on the benchmark economy, the US economy. Thus, the initial challenge is to calibrate the amplitude and persistence of negative productivity shock in China’s input production function.11 Concerning the amplitude, the strategy is to adjust the drop in productivity needed to affect Chinese industrial production in the proportion shown in Fig. 3, that is, a value of ϵ _covid−19,t ​= ​1.15. As for the persistence of the shock, three scenarios are defined: optimistic; base; and pessimistic. In the optimistic scenario, the effects of the pandemic die out in the very short term. Model-wise, this corresponds to the choice of an auto-regressive component in the amount of 0.1. In the base and pessimistic scenarios, the autoregressive components are 0.5 and 0.9, respectively.

As the pandemic progresses, it becomes more and more evident that all the scenarios considered in our exercise but the optimistic one can potentially play out. More and more economists and analysts alike predict a big drop in economic activity followed by a U- or L-shaped (or even a W-shaped) recovery, instead of a V-shaped one. Kapoor and Buiter (2020), for instance, write:

As GDPs crumble …

With the pause button pressed on nearly half of economic activity in the US and the EU for what is likely to be at least a period of three months, consumption, investment and trade have all collapsed. A contraction of as much as 10–20% of GDP or worse is possible. Pervasive uncertainty about the timing of the development of a viable treatment and/or vaccine means there is no light at the end of the tunnel yet. Even when we get there, the trauma of the COVID-19 meltdown will keep investors and consumers on the sidelines.

… tax revenues will collapse …

This will blow a massive hole through tax revenues. Corporate taxes that derive from profits will collapse first. Sales and value-added taxes will register a dramatic fall in line with the collapse in economic activity. The gigantic scale of job losses and/or job subsidies to stem such losses will depress income taxes. Tax revenues may fall by 30%–40%, maybe more.

… and deficits balloon …

Even as tax revenues dry up, governments need to spend unprecedented sums of money not just on healthcare and social interventions to fight COVID-19, but also on welfare payments and job guarantees. Mortgage and rental market interventions, rescuing and resuscitating private sector firms, even whole industries, and inevitably bailing out large tracts of the financial sector will require record fiscal interventions. The pincer movement of falling taxes and rising spending will drive eye-popping fiscal deficits of 10%–20% of GDP, and beyond.

… leading to counterproductive austerity

The double whammy of crumbling GDPs and ballooning deficits may drive OECD debt/GDP ratios up by 30% or so by the end of 2020 as countries scramble to borrow, mirroring the effect of the global financial crisis and its aftermath. It may push Italy and Japan past the 160% and 270% of GDP mark, respectively, and no country would be immune. Inevitably, this will fuel future calls for austerity, with the counterproductive logic and toxic politics of the EU’s Stability and Growth Pact and Fiscal Compact, driving long-suffering euro area economies further into the ground.

As Kapoor and Buiter (2020), we think that the odds this crisis will resemble something along the lines of the Great Depression only grow as time elapses. In this respect, let us lay out in a straightforward way the intuition behind the emergence of an economic depression of the sort our pessimistic scenario portends: Hesitantly at first, governments go for a strict lockdown that ends up taking longer than expected. Once the situation appears to improve, the quarantine is lifted, which enables the virus to start spreading rapidly again. The quick propagation of the virus forces countries to go back to strict lockdowns, this time for longer periods. This situation is likely to cause many firms to go bankrupt and exit the market on which they operate, many workers to lose their jobs and have real difficulties making end meets, and many indebted governments to adopt growth-killing fiscal austerity at some point. A disrupting financial crisis could even be triggered in this context. This process could be reinforced by the existence of bureaucratic barriers that hinder the discovery of a vaccine or some life-saving treatment. The base scenario just lies in between the optimistic and the pessimistic one, and in it, things get straightened out faster because for example, a more lenient/shorter lockdown suffices to contain contagion, a financial crisis can be averted, and/o a vaccine is found earlier than expected.

Fig. 5, Fig. 6 portray the outcomes of this exercise, which, for convenience, are grouped into demand variables and inputs (Fig. 5), and fiscal variables and prices (Fig. 6). As regards the effects on the AD components, in the optimistic scenario US output would fall by 5%, relative to its steady state value, but it would bounce back quite rapidly. In the base scenario, the output plunge would be 10%, and it would take the economy roughly 10 quarters to pull itself back out of recession. However, the most worrisome situation would be the pessimistic scenario, since the decrease in output would be very deep, attaining 20% in the fourth period, and very protracted, as after 15 quarters, the economy would have not returned to the initial steady state. In the three scenarios studied, the intense reduction in private consumption is the major driving force of the lower aggregate demand. This process of falling output is aided by the cuts in current expenditure that the government is forced to undertake to keep public debt stable, as tax collection plummets by means of the weak economic activity (equation (30)).

Fig. 5.

Impulse response of the aggregate-demand variables and inputs to the COVID-19 shock. Source: Authors’ elaboration.

Fig. 6.

Impulse response of price variables and fiscal variables to the COVID-19 shock. Source: Authors’ elaboration.

Fig. 6 shows that the smaller stock of nominal government debt is not enough to ensure fiscal sustainability, so current spending has to be trimmed and tax rates have to be raised. While imports of consumption goods across the three scenarios are adversely affected, it is in the pessimistic one where this variable falls the most: 40% and 60% in relation to goods imported from China and from the rest of the worlds (ROW), respectively. It bears pointing out that such outcomes of weaker demand for inputs are amplified by the rise of tariffs enacted to make up for the public sector’s revenue loss. The combination of a lower income level and a more depreciated nominal exchange rate (Fig. 6) encourages domestic firms to search for sales opportunities abroad. The upshot is that exports of consumption goods to the ROW and China increase. In the former country, this occurs in the three scenarios. As for the latter, exports wane for the pessimistic case. Both hours worked and the production of domestic inputs, which decreases 25% relative to the steady state before the fifth quarter, follow same pattern as the production of final goods.

With regard to prices and wages(Fig. 6), for the optimistic and base scenarios, a deflationary process sets in. Interestingly, in the pessimistic scenario, the more persistent recession induces a stagflation period with rising input prices, wages and hence, marginal costs on impact. Indeed, as laid out in the introduction section, stagflation can arise if the effects of the supply shock outweigh those of the demand shock. By the same token, an analogous pattern applies to the monetary policy rate, which, in the pessimistic case, moves in tandem with prices. It is interesting to notice that the policy rate undershoots its steady-state value for an extended timespan, helping to partially offset consumption and production losses, and contributing to ensuring debt sustainability over time. Regarding the base scenario, this variable again traces the price movement and thus falls on impact, returning to the steady state within the range of the fifth and the tenth quarters. As mentioned above, the weaker economic activity sets off a process whereby tax rates are increased and government spending is slashed in order to restore debt sustainability.

3.2. Conventional macroeconomic policy responses

In the preceding subsection, we provided an in-depth analysis of the macroeconomic consequences of the pandemic. It should be stressed that back in that exercise, the fiscal and monetary authorities were constrained on the grounds that they were only allowed to react to economic changes to meet the equilibrium conditions indicated by equations (30), (32)), respectively. In this subsection, we now relax this constraint to permit the economic authorities to rely on a set of conventional monetary and fiscal tools available to cushion the virus-induced deterioration of the economy: current government spending, consumption taxes, tariffs on imports from China and the ROW, labor-income taxes, and the monetary policy rate. For the sake of clarity, we stick to the base scenario throughout the entire exercise.

All the fiscal shocks were calibrated so as to reproduce an expansionary fiscal policy amounting to 10% of annual GDP in the US, in accordance with the information on the stimulus package released by the US government. Conversely, monetary policy was calibrated using a standard deviation of the estimated value for that shock. Fig. 7, Fig. 8 and 9 display the results of: (1) an increase in current government spending and a lower consumption tax rate; (2) lower tariffs on imports from China and from the ROW; and (3) a labor-income tax cut, as well as an expansionary monetary policy, respectively. In that vein, there are three countercyclical policies that were found to be effective in returning output to its state state level: current public spending, a cut in the labor-income tax rate, and a looser monetary stance. It is apparent from the visual inspection of the graphs that all policies have advantages and disadvantages. Higher current spending (Fig. 7) leads to a fast recovery of GDP and hours worked over the first five quarters, but the expansionary effect dies off thereafter, with hours worked even falling below trend. The ultimate reason why it does not take long before these variables peak is the need to increase taxes or slash spending to keep debt stable over time. Specifically, the fiscal instruments making most of the adjustment to comply with the fiscal rule are tariffs and the labor-income tax, all of which follow a similar path. In this sense, it is interesting to note that the peak of the hours worked curve coincides with the time at which the latter tax rate starts increasing. Unsurprisingly, greater public spending is found to exert upward pressure on final consumption prices and the interest rate.

Fig. 7.

Impulse response of the macroeconomic variables to an increase in government spending and a reduction in the consumption tax to combat the COVID-19 crisis. Source: Authors’ elaboration.

Fig. 8.

Impulse response of the macroeconomic variables to reductions in tariffs on imports from China and from the ROW to combat the COVID-19 crisis. Source: Authors’ elaboration.

When it comes to the labor-income tax (Fig. 9 ), the effects on PIB and hours worked are milder than those analyzed above, but on the other hand, this measure does not require adjusting taxes up and/or cutting expenditure as much as when public spending is used as a policy lever. This has a direct implication especially on the evolution of hours worked, for they do not go below trend over the span of time of our experiment. In regards to monetary policy (Fig. 9), we find that the central bank can act as a buffer against the pronounced drop in economic activity by lowering the policy rate in a firm and decisive manner. In the labor market, its demand-stimulating effects take longer to materialize but are more long-lasting. Also, it gives rise to a mild fall in consumption vis-à-vis the other proposals. In terms of the fiscal rule, using monetary policy to tackle the recession presents the advantage of creating fiscal space via lower interest payments on public debt, which helps to maintain fiscal sustainability while at the same time allowing tax and spending instruments to be used to boost the economy. In addition, to the extent that the lower interest rate makes it possible to cut import tariffs, there are both a rise in imports and a fall in exports relative to the base scenario. This difference tends to fade away over time as the exchange-rate effects intensify. Finally, a strong positive monetary shock considerably increases inflation on impact, which is certainly an advantage in a deflationary environment like the one we consider here. Things would be different in this regard if the pessimistic stagflation scenario were to prevail. Curiously enough, embarking on a trade liberalization process would have negligible effects on all macroeconomic variables but the consumption price and, to a lesser extent, the interest rate (only when tariffs from the ROW get cut).

Fig. 9.

Impulse response of the macroeconomic variables to a reduction in labor-income tax and to an expansionary monetary policy to combat the COVID-19 crisis. Source: Authors’ elaboration.

The punchline is that among all the policy tools considered in our exercise, the most efficient ones in dealing with the COVID-driven recession would be increasing current government spending and a more expansionary monetary policy. It bears emphasizing that the medium-run costs associated with the former policy in terms of future fiscal retrenchment and of future inflation would be higher. On the contrary, a monetary expansion would incur the trade-off of boosting the economy in an effective fashion at the cost of rapid inflation, although in a deflationary environment like the one proposed here, the appearance of inflationary pressures should not be thought of as a cost at all. On the fiscal front, when comparing the use of public spending to the use of taxes, we find that expenditure-based fiscal expansions do a better job of getting the economy back on track than tax-based ones do. This is partly because in increasing public spending, the government injects resources into the economy directly, whereas with the tax cut in an uncertain situation, part of the stimulus can go to raise saving, and partly because the resulting fiscal consolidation needed to ensure a stable debt is stronger in the case of taxes. Lastly, in comparing taxes efficacy, using labor-income tax to spur economic activity seems to work better than the other kinds of tax instruments studied here.

3.3. COVID-19 shock and the zero lower bound (ZLB)

Up until now, we abstracted from the existence of a ZLB on the policy rate. It could be argued that the US economy was out of the ZLB when the pandemic-induced crisis hit, and therefore, there existed some room for monetary manoeuvre at that time to attempt to mitigate the steep fall in output. It should be noted, though, that the aforementioned leeway for monetary stimulus was small and a large negative shock like the covid-19 crisis indeed has the potential to render the ZLB binding. When an economy gets stuck at the ZLB,12 and a large negative demand shock arises, a deflationary spiral may set in: the pronounced fall in demand leads to both lower current and future inflation. The latter tends to drive up the real interest rate, which in turn feeds back into consumption, investment and output. Thus, aggregate demand falls further. The bottom line is that the contraction in economic activity, when the economy is unfavorably shocked, should be larger at the ZLB vis-á-vis normal times in which the central bank has the ability to counter the recession by cutting the policy rate. It is therefore paramount to bring this restriction into our analysis to fully capture the macroeconomic effects of a pandemic shock.

In terms of modeling strategy, the ZLB imposes additional hurdles on the tractability of DSGE models. Fernández-Villaverde et al. (2015) argue that both the monetary policy decision rules and the equilibrium dynamics of macroeconomic models are intrinsically affected by the non-linear characteristics driven by the ZLB. Along the same lines as the preceding authors, Adjemian and Juillard (2010) assert that “the usual likelihood approach is based on a first order approximation of the model around its deterministic steady state. This is not possible when we deal with a model with occasionally binding constraints, because the model is non differentiable everywhere and because, putting this first problem aside, the agents in the approximated model do not anticipate that the economy may hit the zero lower bound in the future”.

Fortunately, there are several ways of introducing a binding ZLB into a DSGE model. We choose to use the toolkit developed by Guerrieri and Iacoviello (2015), which adopts a first-order perturbation approach and applies it “in a piecewise fashion to solve dynamic models with occasionally binding constraints”. Furthermore, compared with a high-quality numerical solution, this method captures the main properties of the particular models. The authors state that a key advantage of this toolkit lies in its applicability to models with a large number of state variables.

Fig. 10, Fig. 11 plot the impulse response functions of this exercise. Compared to the base scenario, the COVID-19 crisis expectedly causes output to contract significantly more on impact under the ZLB. In effect, as laid out above, even though the monetary authority would want to partially offset the fall in demand by adjusting the policy rate below zero, it finds itself unable to do so. In a deflationary environment, this floor on the nominal interest rate results in a higher real interest rate that ends up curtailing aggregate demand and production even further. The recovery over ten quarters is never complete with the economy stuck at the ZLB. Concerning the demand components, on impact total consumption plummets by 20% (percentage deviation from trend) at the ZLB versus 15% in the situation with no constraint, but it recovers faster in the former situation than in the latter.

Fig. 10.

Impulse response of the aggregate-demand variables and inputs to the COVID-19 shock under the ZLB. Source: Authors’ elaboration.

Fig. 11.

Impulse response of price variables and fiscal variables to the COVID-19 shock under the ZLB. Source: Authors’ elaboration.

Regarding the fiscal side of the economy, sinking output (and income) drags down tax collection and forces the government to engage in fiscal retrenchment –by cutting back on public expenditure and raising taxes– so as to ensure debt sustainability, which is also worsened by the rise of the real interest rate. This fiscal austerity disrupts economic activity relative to a situation where the economy is out of the ZLB. None of the fiscal variables returns to its steady-state value under the ZLB. In addition, the external sector improves initially as exports to, and imports from, both China and the ROW increase and decrease more in the presence of the ZLB, respectively. The driving force behind this outcome is the higher (more depreciated) exchange rate following the new coronavirus shock. On the supply side, neither hours worked nor input production get affected on impact by the shock. As expected, wages and the marginal cost move in tandem, falling substantially more under the ZLB than in normal times. It is worth highlighting that in this constrained economy, in spite of the higher initial fall, wages bounce back faster than those in the baseline, getting close to their steady-state value at the end of the horizon studied.

3.4. Quantitative easing (QE) responses to the COVID-19 shock

The existence of the ZLB is known to render conventional monetary policy fruitless. However, central banks still have other weapons at their disposal to provide the needed monetary accommodation via the compression of long-term yields and stem further financial distress. These extra tools that the monetary authority can deploy when running out of conventional ammunition on account of a binding ZLB are referred to as unconventional monetary policy. A number of distinct measures can be grouped into this category: forward guidance, negative interest rates, extended liquidity operations, and quantitative easing (QE). In this paper, we resort to the latter policy, defined as large-scale purchases of securities by the central bank. QE normally comes about through the acquisition of long-term government bonds in exchange for an increase in the reserve accounts held by the commercial banks at the central bank. The ultimate goal of this measure is flattening long-term yields and therefore, being able to implement an additional stimulus when the interest rate is near or at zero (Dell’Ariccia et al., 2018).

In order to capture the targeted change in the long-term yield, we increase the supply of short-term bonds by 12% of the US GDP (which corresponds to a shrinkage in the supply of long-term bonds of the same magnitude). This policy brings about a rise in the price of long-term securities and consequently, a drop in their return. The specific modeling strategy that we pursue is to insert a term structure of interest rates into our three-country DSGE model, in line with Costa Junior (2019), where the author uses the idea of preferred habitat. Thus, some new terms were included into the US households’ budget constraint13 :

$$\dots +\frac{B_{us,j,t+1}}{R_t^{us}}+\frac{B_{us,L,j,t+1}}{R_{L,t}^{us}}\left(1+A{C}_t^L\right)+\dots =\dots +B_{us,j,t}+\frac{B_{us,L,j,t}}{{\prod }_{i=2}^{N_L}{R}_{t+i-1}^{us}}+\dots$$ (37)

where households allocate their income between two types of zero-coupon bond, short-term (B _us) and long-term (B _us,L), whose yields are expressed by R ^us and $R_L^{us}$, respectively. Lastly, N _L represents the maturity of the long-term bond. On the left-hand side of equation (37) the bonds are priced according to the appropriate interest rates. Meanwhile, on the right-hand side, the secondary market for the trading of bonds is incorporated, i.e. bonds with different maturities are priced according to the short-term rate. Thus, in t, a household that purchases a bond with a longer maturity and plans to sell it in the following period, will not be certain about its gains, as $R_{t+1}^{us}$ is not known in t – price risk for this asset.

The differentiation in bond maturities is obtained by introducing a portfolio adjustment friction, representing an impediment to households’ arbitrage behavior – which would tend to equalize bond yields. AC ^L is a friction in the portfolio adjustment of maturity L whose structure is as follows:

$$A{C}_t^L=\left[\frac{{\vartheta }_L}{2}{\left(\frac{B_{us,L,t+1}}{B_{us,L,t}}\right)}^2\right]Y_t^{us}$$ (38)

where ϑ _L is the sensitivity of the portfolio adjustment friction of maturity L. As mentioned above, the economic motivation related to this friction stems from the preferred-habitat theory. Given this perspective, the transaction cost represents the inertial behavior of the investor positioned at each maturity. In equation (38), an increase in the supply of a bond should be accompanied by an increase in the adjustment cost to maintain equilibrium between the demand and supply for this asset. Moreover, the extent of these adjustment costs is given by the parameter ϑ _L.

Fig. 12 displays the results of the proposed QE experiment. On impact, output decreases slightly less under a gigantic stimulus program like this, but on the other hand, this policy makes the recovery slower than in the benchmark economy, where there is no QE. Behind this more sluggish growth over time lies the behavior of hours worked, which, although in both scenarios they fall the same on impact (10% below trend), do not return to their pre-shock value in the presence of QE. On the demand side, this unconventional monetary policy gives rise to private consumption not dropping as much as in the base scenario at any horizon of our exercise. Conversely, due to the fiscal rule, the government is compelled to cut down substantially more on its consumption and to raise all taxes in the QE scenario. The reason is that the QE program implies more short-term debt being put on the market which at some point will have to be served by pursuing a fiscal consolidation process. This tighter fiscal policy also helps account for the slower recovery of output. As far as the trade balance is concerned, QE leads exports to the ROW to not rise as much as in the base scenario over the whole period of analysis, while there is no difference between the two scenarios when it comes to exports to China. As for imports, they fall slightly less owing to the monetary stimulus. Regarding consumer price inflation, not only does QE cushion the deflationary pressures stemming from the pandemic-related shock, but it also helps it turn into positive numbers before the fifth quarter.

Fig. 12.

Impulse response of the macroeconomic variables to a quantitative easing policy to combat the COVID-19 crisis. Source: Authors’ elaboration.

It is also worth mentioning that both bond yields, short-term and long-term, drop on impact. The reason why the latter falls is straightforward, since the central bank acquires an awful lot of long-term securities which tends to raise their equilibrium price (the so-called portfolio-balance channel). However, the explanation as to why the short-term bond yield falls over the first quarters relates to portfolio reallocation decisions, whereby the falling long-term bond yield triggers an excess demand for short-term securities that binds up the price of these assets. This effect would somehow capture what comes to be known as the signaling channel, through which the central bank commits to not raising short-tem interest rates during the process of large-scale asset purchases.

4. Concluding remarks

In this paper we built a three-country DSGE model to provide answers as to how the COVID-19 crisis is likely to affect the world economy, as well as ascertaining which macroeconomic policies can be useful in palliating the negative economic consequences of the pandemic. To capture the highly uncertain economic environment, under a no-policy change hypothesis, we consider three distinct situations: an optimistic scenario, a base scenario and a pessimistic scenario. Our results show that the pandemic wreaks economic havoc in the latter scenario, as GDP and hours worked drop by 20% from trend or more. Moreover, they never return to the pre-crisis levels over the 15-quarter horizon that we consider. In contrast, in the most optimistic scenario, the COVID shock is observed to lead to a relatively mild and temporary crisis as far as most variables are concerned. The analysis of the intermediate case, the base scenario, shows that the harm inflicted in terms of output and hours worked would be considerable, a 10% decline from trend in both cases, although it is worth stating that the recovery would be much faster than in the pessimistic scenario.

We then assess which macroeconomic policies are more powerful in lessening the negative consequences of the crisis.14 To that end, we only consider the base scenario. We find that the most effective macroeconomic levers in fighting the COVID-caused recession would be increasing current government spending and a more expansionary monetary policy. These policies would involve some trade-offs, though. The fiscal rule dictates that as a result of a higher public spending, taxes be raised in the near future, partially offsetting the expansionary effects of the government purchases. As far as monetary policy, the very expansionary stance contemplated in our exercise acts to enhance debt dynamics and therefore, allows freeing up fiscal resources that lead to lower tax burden and/or higher spending in the coming quarters. Its side-effects, though, would be soaring prices on impact, which, in a situation in which deflation may be an issue, can be more of a blessing. Tax-based fiscal stimuli were found to be less potent in attenuating the impact of the shock.

To give our analysis an extra bit of realism, we now look at what the effects of the pandemic would be if the policy rate were near or at the ZLB. We find that quite expectedly, output declines further over the whole horizon of analysis. Moreover, more deflationary pressures translate into higher real interest rates, which coupled with lower government revenues due to the weaker economic activity, sets public debt dynamics on an unsustainable path. Thus, to prevent debt from spiraling, the fiscal rule dictates that government spending be cut and taxes be raised. This is in itself a factor contributing to the worsening of the recession. It is interesting to note that private consumption, wages, marginal costs and CPI inflation all drop on impact, but they also end up recovering faster than in the unrestricted situation. Lastly, the trade balance improves in the wake of the shock, as the generated exchange rate depreciation induces an increase of exports and a decrease of imports, to both China and the ROW.

We next evaluate the efficacy of one of the most commonly used unconventional measures when the ZLB binds, QE. We do not find conclusive evidence in our model that this policy plays a significant role in accelerating the economic recovery. Nonetheless, we find a beneficial impact of QE in terms of a faster recovery of private consumption. In closing, the external accounts slightly worsen, as exports to, and imports from, the ROW fall and rise, respectively. Trade with China virtually remains unaltered.

Having come this far, it should be stated that in this article we have purposely stayed away from the realm of some unconventional macroeconomic policies that have been hotly debated during the current juncture. For future value-added contributions widening the scope of this line of research, a strategy worth pursuing could be the use of these policies to overcome the economic fallout from the COVID-19 shock. Proposals for refinement of our DSGE model could therefore be the deployment of a richer collection of economic policy instruments, such as Helicopter Money (HM) or just another kind of money-financed fiscal expansions destined to bolster public infrastructure or transfer resources directly to households and firms.

Author statement

• 1Celso J. Costa Junior: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - Original Draft, Project administration.
• 2Alejandro Garcia-Cintado: Conceptualization, Investigation, Data Curation, Writing - Original Draft, Writing - Review Editing, Visualization, Supervision.
• 3Karlo Marques Junior: Conceptualization, Investigation, Writing - Original Draft, Writing - Review Editing, Visualization.

Appendix

5.1. Data processing

The model was estimated using quarterly date spanning 2000:Q2-2019:Q3. The database is described in table 1. When necessary, the data were processed to remove the seasonality and trends of the series – through the X12-ARIMA algorithm and the difference in logarithms, respectively.

Table 1.

Observable variables. Source: Authors’ elaboration.

Series	Source
Real Personal Consumption Expenditures	Federal Reserve
for the United States	Bank of St. Louis
Government total expenditures	Federal Reserve
for the United States	Bank of St. Louis
Consumer Price Index: Total All Items	Federal Reserve
for the United States	Bank of St. Louis
Effective Federal Funds Rate	Federal Reserve
for the United States	Bank of St. Louis
Federal government current tax receipts	Federal Reserve
for the United States	Bank of St. Louis
Weekly Hours Worked: Manufacturing	Federal Reserve
for the United States	Bank of St. Louis
Exports: Value Goods for China	Federal Reserve
for the United States	Bank of St. Louis
Imports: Value Goods for China	Federal Reserve
for the United States	Bank of St. Louis
National Currency to US Dollar Exchange	Federal Reserve
Rate for the Euro Area	Bank of St. Louis
National Currency to US Dollar	Federal Reserve
Exchange Rate for China	Bank of St. Louis
Current Price Gross Domestic	Federal Reserve
Product in China	Bank of St. Louis
Interest Rates, Discount Rate	Federal Reserve
for China	Bank of St. Louis
Consumer Price Index:	Federal Reserve
All Items for China	Bank of St. Louis
Real Gross Domestic Product	Federal Reserve
for Euro area	Bank of St. Louis
Consumer Price Index: Harmonized Prices:	Federal Reserve
Total All Items for the Euro Area	Bank of St. Louis
Interest Rates, Discount Rate	Federal Reserve
for Euro Area	Bank of St. Louis
Exports: Value Goods for China	Eurostat
for Euro Area
Imports: Value Goods for China	Eurostat
for Euro Area

Source: Authors’ elaboration.

5.2. Calibration

Table 2 reports the values of the calibrated parameters.

Table 2.

Parameter calibration.

Parameter	value	source
α	0.33	Del Negro et al. (2013)
β	0.989	Sensitivity analysis
σ	2	Del Negro et al. (2013)
ϕ	1.5	Del Negro et al. (2013)
${\gamma }_{{\pi }_{us}}$	2	Del Negro et al. (2013)
${\gamma }_{R_{us}}$	0.5	Del Negro et al. (2013)
${\gamma }_{Y_{us}}$	0.2	Del Negro et al. (2013)
θus	0.75	Del Negro et al. (2013)
${\omega }_c^{us}$	0.3	US Census Bureau Foreign Trade Statistics
${\omega }_{INS}^{us}$	0.3	US Census Bureau Foreign Trade Statistics
${\vartheta }_{ch}^{us}$	0.25	US Census Bureau Foreign Trade Statistics
${\gamma }_{{\pi }_{ch}}$	0.7098	Zheng and Guo (2013)
${\gamma }_{R_{ch}}$	0.9237	Zheng and Guo (2013)
${\gamma }_{Y_{ch}}$	0.3893	Zheng and Guo (2013)
θch	0.75	Zheng and Guo (2013)
${\omega }_c^{ch}$	0.2	World Integrated Trade Solution
${\omega }_{INS}^{ch}$	0.2	World Integrated Trade Solution
${\vartheta }_{us}^{ch}$	0.0838	World Integrated Trade Solution
${\gamma }_{{\pi }_{rw}}$	1.7	Gomes et al. (2015)
${\gamma }_{R_{rw}}$	0.87	Gomes et al. (2015)
${\gamma }_{Y_{rw}}$	0.1	Gomes et al. (2015)
θrw	0.92	Gomes et al. (2015)
${\omega }_c^{rw}$	0.35	World Integrated Trade Solution
${\omega }_{INS}^{rw}$	0.35	World Integrated Trade Solution
${\vartheta }_{us}^{rw}$	0.07	World Integrated Trade Solution

Source: Authors’ elaboration.

5.3. Estimation

The model was estimated using a Markov chain process via the Metropolis-Hastings algorithm with 500,000 iterations, a scale value of 0.1 and 2 parallel chains. Tables 3 and 4, as well as Figs. 13 and 14 show the prior and subsequent distributions of each of the estimated parameters.

Table 3.

Posterior distribution of the model.

Parameters	prior	posterior	90% Intervals	dist	pstdev
Structural parameters
${\tau }_{ss}^{imp,us,ch}$	0.125	0.1226	0.1157 0.1300	unif	0.0433
${\tau }_{ss}^{imp,us,rw}$	0.125	0.1871	0.1828 0.1917	unif	0.0433
${\gamma }_{G^{us}}$	0.5	0.7924	0.7455 0.8441	beta	0.25
${\phi }_G^{us}$	−0.5	−0.8123	−0.8368–0.7902	unif	0.2887
${\gamma }_{{\tau }^{c,us}}$	0.5	0.5615	0.5396 0.5819	beta	0.25
${\phi }_{{\tau }^{c,us}}$	0.5	0.1311	0.1123 0.1484	unif	0.2887
${\gamma }_{{\tau }^{imp,us,ch}}$	0.5	0.6837	0.6705 0.6988	beta	0.25
${\phi }_{{\tau }_{imp,us,ch}}$	0.5	0.4991	0.4706 0.5289	unif	0.2887
${\gamma }_{{\tau }^{imp,us,rw}}$	0.5	0.5656	0.5476 0.5866	beta	0.25
${\phi }_{{\tau }_{imp,us,rw}}$	0.5	0.7192	0.6973 0.7484	unif	0.2887
${\gamma }_{{\tau }^{l,us}}$	0.5	0.8930	0.8694 0.9150	beta	0.25
${\phi }_{{\tau }^{l,us}}$	0.5	0.7636	0.7197 0.8040	unif	0.2887
${\gamma }_{G^{ch}}$	0.4	0.3504	0.3430 0.3595	unif	0.0577
${\phi }_{G^{ch}}$	−0.8	−0.9637	−0.9745–0.9533	unif	0.1155
${\gamma }_{{\tau }^{c,ch}}$	0.5	0.8796	0.8612 0.8971	beta	0.25
${\phi }_{{\tau }^{c,ch}}$	0.5	0.1020	0.0646 0.1401	unif	0.2887
${\gamma }_{{\tau }^{imp,ch,rw}}$	0.4	0.3292	0.3192 0.3378	unif	0.0577
${\phi }_{{\tau }^{imp,ch,rw}}$	0.4	0.0050	0.0000 0.0110	unif	0.2309
${\gamma }_{{\tau }^{imp,ch,us}}$	0.5	0.7642	0.7351 0.7919	beta	0.25
${\phi }_{{\tau }^{imp,ch,us}}$	0.75	0.8112	0.7958 0.8247	unif	0.1443
${\gamma }_{{\tau }^{l,ch}}$	0.5	0.2983	0.2703 0.3215	beta	0.25
${\phi }_{{\tau }^{l,ch}}$	0.6	0.5281	0.5221 0.5337	unif	0.0577
${\tau }_{ss}^{imp,rw,ch}$	0.125	0.1223	0.1182 0.1259	unif	0.0433
${\tau }_{ss}^{imp,rw,us}$	0.125	0.0537	0.0500 0.0573	unif	0.0433
${\gamma }_{G^{rw}}$	0.75	0.7541	0.7437 0.7625	unif	0.1443
${\phi }_{G^{rw}}$	−0.15	−0.0967	−0.1033–0.0899	unif	0.0866
${\gamma }_{{\tau }^{c,rw}}$	0.5	0.6714	0.6399 0.6953	beta	0.25
${\phi }_{{\tau }^{c,rw}}$	0.25	0.0251	0.0041 0.0431	unif	0.1443
${\gamma }_{{\tau }^{imp,rw,ch}}$	0.5	0.5346	0.4780 0.5865	beta	0.25
${\phi }_{{\tau }^{imp,rw,ch}}$	0.5	0.2218	0.1963 0.2406	unif	0.2887
${\gamma }_{{\tau }^{imp,rw,us}}$	0.5	0.5510	0.5185 0.5892	beta	0.25
${\phi }_{{\tau }^{imp,rw,us}}$	0.5	0.1817	0.1367 0.2278	unif	0.2887
${\gamma }_{{\tau }^{l,rw}}$	0.25	0.2141	0.1965 0.2333	unif	0.1443
${\phi }_{{\tau }^{l,rw}}$	0.75	0.7780	0.7658 0.7878	unif	0.1443

Source: Authors’ elaboration.

Table 4.

Posterior distribution of the model (cont).

Parameters	prior	posterior	90% Intervals	dist	pstdev
Autoregressive parameters
${\rho }_{A^{us}}$	0.5	0.5047	0.4695 0.5470	beta	0.25
${\rho }_{G^{us}}$	0.5	0.8667	0.8417 0.8889	beta	0.25
${\rho }_{{S^L}^{us}}$	0.5	0.8851	0.8690 0.8988	beta	0.25
${\rho }_{{S^m}^{us}}$	0.5	0.7752	0.7519 0.7993	beta	0.25
${\rho }_{{S^P}^{us}}$	0.5	0.5579	0.5252 0.5922	beta	0.25
${\rho }_{{\tau }^{c,us}}$	0.5	0.2684	0.2439 0.2952	beta	0.25
${\rho }_{{\tau }^{imp,us,ch}}$	0.5	0.7693	0.7531 0.7831	beta	0.25
${\rho }_{{\tau }^{imp,us,rw}}$	0.5	0.8669	0.8583 0.8743	beta	0.25
${\rho }_{{\tau }^{l,us}}$	0.5	0.2902	0.2536 0.3280	beta	0.25
${\rho }_{{S^m}^{ch}}$	0.5	0.4802	0.4435 0.5177	beta	0.25
${\rho }_{{S^m}^{rw}}$	0.5	0.6750	0.6591 0.6906	beta	0.25
Standard deviations
${ϵ}_{{S^P}^{us}}$	1.0	0.1479	0.1275 0.1696	invg	Inf
${ϵ}_{{S^L}^{us}}$	1.0	0.2877	0.2427 0.3307	invg	Inf
${ϵ}_{A^{us}}$	1.0	0.1942	0.1613 0.2390	invg	Inf
${ϵ}_{G^{us}}$	1.0	0.1200	0.1176 0.1232	invg	Inf
${ϵ}_{{\tau }^{c,us}}$	1.0	0.9337	0.5283 1.3156	invg	Inf
${ϵ}_{{\tau }^{imp,us,ch}}$	1.0	10.9760	10.4212 11.5694	invg	Inf
${ϵ}_{{\tau }^{imp,us,rw}}$	1.0	1.6311	1.4231 1.8188	invg	Inf
${ϵ}_{{\tau }^{l,us}}$	1.0	0.2986	0.2208 0.3514	invg	Inf
${ϵ}_{{S^m}^{us}}$	1.0	0.1199	0.1176 0.1227	invg	Inf
${ϵ}_{{S^P}^{ch}}$	1.0	0.2336	0.1777 0.2846	invg	Inf
${ϵ}_{G^{ch}}$	1.0	0.8963	0.7677 1.0512	invg	Inf
${ϵ}_{{\tau }^{c,ch}}$	1.0	2.4443	2.3229 2.5681	invg	Inf
${ϵ}_{{\tau }^{imp,ch,us}}$	1.0	6.1788	5.8639 6.4694	invg	Inf
${ϵ}_{{\tau }^{imp,ch,rw}}$	1.0	0.3572	0.2432 0.4764	invg	Inf
${ϵ}_{{\tau }^{l,ch}}$	1.0	0.8454	0.5125 1.1710	invg	Inf
${ϵ}_{{S^m}^{ch}}$	1.0	0.1212	0.1176 0.1254	invg	Inf
${ϵ}_{{S^P}^{rw}}$	1.0	0.6193	0.4710 0.7459	invg	Inf
${ϵ}_{{S^L}^{rw}}$	1.0	0.4549	0.3179 0.6043	invg	Inf
${ϵ}_{{\tau }^{c,rw}}$	1.0	0.5259	0.2889 0.7805	invg	Inf
${ϵ}_{{\tau }^{imp,rw,us}}$	1.0	1.5013	0.9170 2.0241	invg	Inf
${ϵ}_{{\tau }^{imp,rw,ch}}$	1.0	6.1649	5.9212 6.4100	invg	Inf
${ϵ}_{{\tau }^{l,rw}}$	1.0	4.6887	4.4222 4.9410	invg	Inf
${ϵ}_{{S^m}^{rw}}$	1.0	0.1203	0.1176 0.1233	invg	Inf

Source: Authors’ elaboration.

Fig. 13.

Prior and posterior of the model. Source: Authors’ elaboration.

Fig. 14.

Prior and posterior of the model (cont). Source: Authors’ elaboration.