Bayesian estimation of a dynamic stochastic general equilibrium model with health disaster risk

Abstract

Pandemics are not new, but they continue to prevail in the last three decades. A variety of reasons such as globalization, trade growth, urbanization, human behavior change, and the rise of the prevalence of viral diseases among animals can account for this issue. Outbreaks of COVID-19 indicated that viral diseases have spread easily among nations, influencing their economic stability. In this vein, the motivation behind the present study was to get an understanding of the effect of the rise of the health disaster risk on the dynamics of Iran's macroeconomic variables by using Bayesian Dynamic Stochastic General Equilibrium. As opposed to Computable General Equilibrium models, DSGE models can be evaluated in a stochastic environment. Since the duration of the virus outbreak and its effect on the economy is not known, it is more appropriate to use these models. The results demonstrated that increased health disaster risk has a remarkable negative effect on macroeconomic variables. According to the findings of the research and the significance of public vaccination as an essential solution for improving health status and quality of life, it was suggested that the government pave the path for the thriving of businesses and socio-economic activities as early as possible by employing specific policies such as tax exemption or budget allocation for vaccine manufacturing companies or importers.

Introduction

Globalization, trade increase, urbanization, human behavior change, and the prevalence of viral diseases among animals have given rise to the spread of pandemic diseases and global crisis (Madhav et al. 2017; Verikios 2020). Given the increased pandemic disease incidence, some researchers, e.g. Keogh-Brown, McDonald, Edmunds, Beutels, and Smith (2008) and Fan et al. (2018), affirmed a global pandemic at a large scale. Recently, the outbreak of COVID-19 demonstrated that infectious diseases have spread easily in nations, affecting their economic stability. The rapid outbreak of the disease has become a public health crisis, insofar as the World Health Organization identified it as an unprecedented global disease (World Health Organization 2020). Based on past experience, a pandemic will have economic impact around the world (Bloom, Wit and Jose 2005; McKibbin and Sidorenko 2006). On the other hand, delays in manufacturing therapeutic drugs and licensing have led to high mortality rates of COVID-19 as well as severe economic effects. The COVID-19 pandemic spotlights the inefficiency of the capitalism because it gives prominence to making a profit, and vaccine production was not profitable for pharmaceutical companies. (Shang, Li and Zhang 2021).

In general, pandemics have significant negative effects on the quality of life of households. On one hand, pandemics disrupt economic activities by lowering labor supply and productivity, increasing absenteeism, and more importantly adopting lockdown measures to cut virus transmission. On the other hand, Pandemics have a negative effect on social (education, health, etc.) and ecological (clean environment, etc.) components (Bobylev 2020). In addition to this, with increased uncertainty in such circumstances, domestic and foreign investment suffered a decline. That is, the general demand decreased as businesses were closed and household budgets dropped, which caused economies to face crises on a large scale (World Health Organization 2009).

In Iran, the first confirmed case of COVID-19 was reported on February 19, 2020, in the city of Qom. The fall in the price of oil and oil products because of the spread of the disease was more likely the major channel through which Coronavirus effects and economic crisis were felt in Iran. Although other factors may contribute to this paucity, the Coronavirus was the chief cause, which can be due to China’s remarkably low demand for oil. Additionally, with China’s major role in the global economy, any disruption in China’s economy was expected to have a considerable negative impact on the world economy (Arezki and Liu 2020). Following the outbreak, the government adopted a wide range of measures to restrict the spread of the virus, including the suspension of China flights, the closure of universities, and schools, shopping malls, markets, and major religious venues, as well as a ban on cultural and religious gatherings. As for the state's financial measures, we can refer to government support for the Unemployment Insurance Fund, gratuitous allowance for the vulnerable and subsidized loans to affected enterprises (International Monetary Fund 2021).

With Coronavirus beginning to spread worldwide, conventional Dynamic Stochastic General Equilibrium (DSGE) models underwent certain changes; adding health blocks to these models linked them to epidemiological models and provided room to understand the consequences of disease outbreaks. In what follows, initial studies on health and its impacts on economy will be approached. Next, we present studies related to the addition of health block in DSGE models.

Using human capital theory, Grossman (2000) developed a model in which disease hinders labor's work activity and equivalent to the time period of regaining health, time will be wasted. Halliday et al. (2009) calibrated a model for the US to study health investment in life cycle. The results indicated, the factor that enhances consumption motivation is the downward marginal utility of health. Torój (2013) designed the open-economy new Keynesian model to simulate the economic consequences of the flu epidemic in Poland. The results indicated that the indirect costs simulations in the new Keynesian model are less than the estimates that can be obtained using a human capital approach. Vasilev (2017) investigated real business cycles and their impacts on labor productivity in the US economy by incorporating health status into a household’s utility function. The results indicated that health status did not create business cycles. Yang et al. (2020) examined the state of tourism in the Chinese economy under the spread of infectious diseases using a DSGE model in different scenarios. They concluded that the prevalence of COVID-19 disease hinders the consumption of goods and tourism services, and with the deterioration of health, welfare also decreases. Asoyan, Davtyan, Igityan, Kartashyan, and Manukyan (2020) developed a New Keynesian DSGE model for simulating the effect of health impulse on the Armenian economy. The results indicated that people’s decisions on reducing consumption and work hours, due to health crisis, would result in an economic downturn. Eichenbaum et al. (2021) developed a conventional epidemiological model for the US economy with an aim to analyze the interaction between economic decisions and pandemic diseases. In this model, a pandemic affects the economy in demand–supply respect, which would give rise to a sharp downturn.

A review of empirical studies suggests that due to the novelty of the health literature in macroeconomics, this issue is still in its infancy and needs to be further developed. In this vein, the purpose of the present research is to analyze the economic impacts of the outbreak of pandemic disease by using a DSGE model. DSGE modeling is a sub-branch of macroeconomics that conforms to the principles of microeconomics and can optimally evaluate economic performance under a stochastic environment. These models are new versions of a general equilibrium put forward following Locus critique (Lucas 1976). As opposed to Computable General Equilibrium models, DSGE models can be evaluated in a stochastic environment. Since the duration of the virus outbreak and its effect on the economy is not known, it is more appropriate to use these models (Yang et al. 2020).

The study enjoys innovation and creativity with at least three distinctive features as follows:

1. Health shock and its economic impact suffer a research gap when using dynamic stochastic general equilibrium models.

2. Health expenditures are divided into two parts-private and public.

3. In most similar studies, the parameter calibration method is used for simulation purposes, but the present study utilized a Bayesian method for estimating parameters.

The rest of the study is organized as follows. Section 2 is theoretical foundations, methodology, and deals with the model; Section 3 encompasses the model estimation; Section 4 deals with impulse-response functions; and, finally, Section 5 is a conclusion and recommendations.

Theoretical foundations and model description

Theory of real business cycles

The theorists of real business cycles laid emphasis on the supply side in their analyses. In a model developed by Kydland and Prescott (1982) during the early 1980s, they described real business cycles based on supply. As the second version of the new classic macroeconomics, their study is a serious challenge to all theories stressing total demand shocks, particularly monetary shocks. The crucial point in this model is the emphasis on economic equilibrium at each stage of the business cycle (peak and low). According to the theorists, the market would not fail; as recessions are the consequences of economic agents’ reactions to inevitable changes in economic constraints. That is to say, economic agents demonstrate optimal reactions to the constraint changes. Thus, market consequences are efficient.

Nelson and Plosser (1982) challenged the macroeconomic models underscoring demand-side disturbances (monetary shocks). According to them, monetary disturbances viewed as the main source of temporary fluctuations in production cannot account for stochastic production changes that ensue from real factors. If real factors are the source of fluctuations, then business cycles cannot be construed as temporary. Their findings suggest that if technology shocks, are random and reiterative, then the production path follows a stochastic behavior. Nevertheless, the crucial point is that the fluctuations observed in total production are those in the natural rate of production. As a result, trend-determining forces are not different from those causing fluctuations; therefore, it is pointless to dissociate growth theory from fluctuation analysis (King, Plosser, & Rebelo, 1988a, b). One can imagine various shocks in the supply part, which could result in significant changes in productivity:

1. Unfavorable physical conditions that have a negative effect on agricultural crops; floods, earthquakes, droughts, etc.

2. Considerable changes in the price of energy carriers: oil price shock in 1973

3. War, political developments that affect economy performance and structure

4. State regulations such as import quotas and measures that lead to the prevalence of economic rent seeking.

5. Productivity shocks caused by changes in the quality of work and capital inputs, new management performance, new product development, and the introduction of new technology. Pandemic diseases inversely affect labor's quality and even capital, affecting economic performance by a large-scale health shock.

Model description

The core of the present study was shaped according to the incorporation of Grossman (2000), Vasilev (2017) and Yang et al. (2020), Asoyan et al. (2020) models. By expanding them, the impact of a pandemic infectious disease on the dynamics of Iran's macroeconomic variables was investigated. In this respect, DSGE model includes households with an infinite planning horizon, a firm producing homogeneous goods in a competitive condition, the government and the oil sector.

Problem of households

The purpose of a sample household is to maximize the reduced sum of planning horizon utilities (reduced expected utility) for its life span. In the present research, household preferences in this utility function encompass an array of consumption, working hours, and health status. Accordingly, every household maximizes the expected utility of its lifetime:

$$E_0\sum _{t=0}^{\infty }{\beta }^t\left\{\left(l,n,C_t,{-\psi }_n,H_t^w,+,{\psi }_s,\frac{S_t^{1-v}}{1-v}\right\},,\right)$$ 1

where $E_0$ is the operator's expected value, $0<\beta <1$ is a discount factor for utility function, $C_t$ is consumption, $H_t^w$ is working hour, $S_t$ health (stock) capital1 in t-time. ${\psi }_n>0$ is a parameter for the lack of work offer preferences, ${\psi }_s>0$ is the weight (significance) of health in the household’s utility function, and $v$ is the inverse elasticity of intertemporal substitution for health status.

A household assigns every t time to $H_t^w$ work, $H_t^q$ (quarantine) recreation activities, and $L_t^H$ leisure; this time is normalized into number 1 in Eq. 2.

$$H_t^w+H_t^q{+L}_t^H=1$$ 2

Each household gets a rate of $W_t$(nominal) wage in return for each work hour and earns an income equal to ${W_t.H}_t^w$.

In addition, health can be depreciated over time with a rate of ${\mathrm{\delta }}^s$, so it has to be kept up by investing on it $I_t^s$. The health transition equation is as follows:

$$S_{t+1}=\left[i_t^s,+,(1-{\delta }^s),S_t\right]-(Z_t.\omega )$$ 3

$Z_t$ is the health disaster risk, and a first-order autoregressive process (Asoyan et al. 2020):

$$ln\left(\frac{Z_t}{\overline{Z}}\right)={\rho }_{z}ln\left(\frac{Z_{t-1}}{\overline{Z}}\right)+{\epsilon }_t^z,{\epsilon }_t^z\sim N\left(0,.,{\sigma }_z^2\right)$$ 4

In this equation, $\overline{Z}>0$ is the steady state level of health disaster risk, ${0<\rho }_Z<1$ is the first-order autoregressive persistence parameter, and ${\epsilon }_t^z$ random shocks to the health disaster risk process.

$\omega$ is the size of the crisis,2 and $I_t^s$ investment in health and a function of total health expenditure $X_t^s$, and $(H_t^q)$ is quarantine time completion:

$$I_t^s=(X_t^s{)}^{\varphi }(w_t{H}_t^q{)}^{1-\varphi }$$ 5

In this equation, $0<\varphi <1$ and $1-\varphi$ are the elasticity of health investment versus health expenditures, and the costs of quarantine hours opportunity, respectively. Also, the expenditures of health are incurred by households and the public sector:

$$X_t^s=X_t^{\mathit{sp}}+X_t^{\mathit{sg}}$$ 6

where $X_t^{\mathit{sp}}$ is the household’s health expenditure and $X_t^{\mathit{sg}}$ is the public sector’s health expenditure. Figure 1 shows how health capital is accumulated:

Fig. 1.

Accumulation of health capital Source: Current Research

In the end, each household makes an investment in physical capital, and as a capital owner earns an interest income $R_t^k{.K}_t$ by renting the capital to an enterprise. $R_t^k$ is the nominal rent rate, and $K_t$ is the capital deposit in t time.

Additionally, the households own the shares of economic enterprises. A household’s physical capital is developed according to the following transition law:

$$K_{t+1}=I_t^k+(1-{\mathrm{\delta }}^k)K_t$$ 7

where ${\mathrm{\delta }}^k$ is the depreciation rate of physical capital. Each household faces a budget constraint as follows:

$$W_t.H_t^w+R_t^k.K_t+p_t\left(1,-,{\delta }^k\right)K_t+{p_t.D}_t\ge p_t.C_t+{\mathit{oop}}_t.p_t.X_t^s+p_t.K_{t+1}+p_t.T_t+W_t.H_t^q$$ 8

where $p_t$ is the general price level, ${\mathrm{T}}_{\mathrm{t}}$ is the net taxes payed by household to the state, $D_t$ is enterprise dividend, and ${\mathit{oop}}_t$ household quota for out-of-pocket payments. By dividing Eq. 8 into $p_t$, household's budget constraint is revised in real terms:

$$w_t.H_t^w+r_t^k.K_t+\left(1,-,{\delta }^k\right)K_t+D_t\ge C_t+{\mathit{oop}}_t.X_t^s+K_{t+1}+T_t+w_t.H_t^q$$ 9

As for household's real budget constraint, $w_t$ is real wage, $r_t^k$ is real capital rent rate which is defined as follows:

$$w_t=Wt/Pt$$ 10

$$r_t^k=R_t^k/P_t$$ 11

Maximizing utility function 1 relative to household's budget constraint 9, and health transition Eq. 3 would lead to household optimization (Appendix 1).

Firms

Following Torój (2013), an agency firm produces a homogenous final product by using a Cub Douglas function that requires physical capital and labor:

$$Y_t=A_t{K}_t^{\alpha }({S_t.H}_t^w{)}^{1-\alpha }$$ 12

$A_t$ depicts the neutral technology level of Hicks3(total factors productivity) which is accessible in an economy in t time. $0<\alpha ,\left(1,-,\alpha \right)<1$ is the productivity of labor and capital. It is assumed that the productivity of the total factors follows a first-order autoregressive process:

$$\mathit{ln}\left(\frac{A_t}{\overline{A}}\right)={\rho }_{A}ln\left(\frac{A_{t-1}}{\overline{A}}\right)+{\epsilon }_t^A,{\epsilon }_t^A\sim N\left(0,.,{\sigma }_a^2\right)$$ 13

where A > 0 is steady state level of the total factor productivity process, ${0<\rho }_a<1$ is the first-order autoregressive persistence parameter and ${\epsilon }_t^a$ are random shocks to the total factor productivity process.

The firm aims to maximize profit at each target period:

$$D_t=A_t{K}_t^{\alpha }({S_{t}H}_t^w{)}^{1-\alpha }-r_t^k.K_t-w_t.H_t^w$$ 14

In a long-run equilibrium, enterprises' profit is zero, and each production factor receives their marginal production:

$$w_t=(1-\alpha )\frac{Y_t}{H_t^w}$$ 15

$$r_t^k=\alpha \frac{Y_t}{K_t}$$ 16

Government

Government administers a balanced budget at each epoch. Government's expenses are covered by oil income and taxes:

$$p_t{G}_t+\left(1,-,{\mathit{oop}}_t\right)p_t{X}_t^s={p_{t}R}_t^{\mathit{oil}}+p_t.T_t$$ 17

where $R_t^{\mathit{oil}}$ are oil revenue, $T_t$ are tax incomes, $G_t$ government expenditure, and ${\mathrm{X}}_{\mathrm{t}}^{\mathrm{s}}$ health expenses, and $(1-{\mathit{oop}}_t)$ is government quota on health expenditure.

Government non-health expenditure follows a first-order autoregressive process:

$$ln\left(\frac{G_t}{\overline{G}}\right)={\rho }_{G}ln\left(\frac{G_{t-1}}{\overline{G}}\right)+{\epsilon }_t^G,{\epsilon }_t^G\sim N\left(0,.,{\sigma }_G^2\right)$$ 18

where $\overline{G}>0$ is the steady state level of government non-health expenditure process, ${0<\rho }_G<1$ is the first-order autoregressive persistence parameter, and ${\epsilon }_t^G$ is random shocks to government non-health expenditure process.

Health expenditure of public sector follows a first-order autoregressive process:

$$ln\left(\frac{X_t^{\mathit{sg}}}{{\overline{X}}^{\mathit{sg}}}\right)={\rho }_{X^{\mathit{sg}}}ln\left(\frac{X_{t-1}^{\mathit{sg}}}{{\overline{X}}^{\mathit{sg}}}\right)+{\epsilon }_t^{X^{\mathit{sg}}},{\epsilon }_t^{X^{\mathit{sg}}}\sim N\left(0,.,{\sigma }_{X^{\mathit{sg}}}^2\right)$$ 19

In this equation:$X_t^{\mathit{sg}}$: The health expenditure of public sector in t time${\overline{X}}^{\mathit{sg}}$: The steady state level of public sector health expenditure${\rho }_{X^{\mathit{sg}}}$: The first-order autoregressive persistence parameter of public health expenditure${\epsilon }_t^{X^{\mathit{sg}}}$: Random shocks of public sector health expenditure.

Oil revenues in most oil-exporting countries account for a large share of government budget. That is, government budget is highly dependent on oil revenues due to the inefficiency of the tax system in these countries.

Oil

In the present research, the purpose of this sector is to maximize revenue, because the National Iranian Oil Company as a main oil supplier hardly follow the goal of maximizing revenue just like other state-owned companies (Sayadi and Khoshkalam Khosroshahi 2020).

Since oil revenues are injected into the economy in oil-rich countries, and changes in exchange rates besides oil prices, may be effective in reducing or increasing oil revenues, it seems Oil revenue shocks should be more appropriate for oil-exporting countries than oil price shocks. The change in oil revenues can be due to a change in the amount of oil exports ${\mathit{EXP}}_t^{\mathit{oil}}$ or a change in the price of oil $P_t^{\mathit{oil}}$ or a change in the exchange rate ${\mathit{EX}}_t$, or a combination of them, which in the present study, these shocks are gathered into stochastic shocks of oil revenues ${\epsilon }_t^{\mathit{Roil}}$.

$$R_t^{\mathit{oil}}={\mathit{EX}}_t.{\mathit{EXP}}_t^{\mathit{oil}}.P_t^{\mathit{oil}}$$ 20

Indeed, one can design a completely distinctive model for each of the variables, but, given the objective of the present research, the foregoing impulses have been taken into account in the oil revenue impulse. We suppose that oil is entirely exported, and the revenue from it made available to the government.

The first-order autoregressive process of oil revenues is as follows:

$$ln\left(\frac{R_t^{\mathit{oil}}}{{\overline{R}}^{\mathit{oil}}}\right)={\rho }_{R^{\mathit{oil}}}ln\left(\frac{R_{t-1}^{\mathit{oil}}}{{\overline{R}}^{\mathit{oil}}}\right)+{\epsilon }_t^{R^{\mathit{oil}}},{\epsilon }_t^{R^{\mathit{oil}}}\sim N\left(0,.,{\sigma }_{\mathit{Roil}}^2\right)$$ 21

where $R_t^{\mathit{oil}}$ is oil revenue in t time and ${\overline{R}}^{\mathit{oil}}$ is the real revenue from the sale of oil in steady state, ${0<\rho }_{R^{\mathit{oil}}}<1$ is the first-order autoregressive persistence parameter, and ${\epsilon }_t^{\mathit{Roil}}$ is random shocks of oil revenues.

General constraint of resources

Under market settlement conditions, total supply and total demand are equal:

$$Y_t+R_t^{\mathit{oil}}=C_t+X_t^s+I_t^k+G_t+w_t{H}_t^q$$ 22

Accordingly, the sum of final non-oil products and oil revenues are earmarked for households’ final use, health expenditure, private sector investment in production, public expenditure, and the cost of quarantine time, such that the final product market is stabilized.

Competitive equilibrium

When households and enterprises optimize their objective functions with respect to the existing constraints and government estimates its budget constraint and also all markets are settled, economic stability can be investigated under the circumstances. Rational expectation stability is a sequence of endogenous variables, which provides a set of equations derived from optimization, government budget constraint and market settlement condition as a whole. In equilibrium, economic factors follows a similar behavior; the equilibrium conditions are presented in the Appendix 2 as a linear logarithm Uhlig (1995), which comprise 18 variables and 18 equations.

Model estimation

To estimate the model indexes, Bayesian method, and Random Walk Metropolis–Hastings algorithm were used. The data of the model’s observable variables include seasonal adjusted data, GDP, private consumption, private investment, government expenditure, and oil revenues from January of 1992 to April 2020, which underwent de-trending procedure by using Hodrick-Prescott filter. Prior to the model estimation, the indexes which could be excluded from estimation were identified and calibrated. Accordingly, the indexes that can be calibrated according to Iran’s economy variables are presented in Table 1.

Table 1.

Calibrated indexes of the model according to Iran’s economy variables

Indicators	Description	Value	Method
$\frac{C}{Y}$	Stable ratio of private consumption to non-oil production	0.62	[1]
$\frac{I^k}{Y}$	Stable ratio of Investment expenditures to non-oil production	0.16	[1]
$\frac{G}{Y}$	Stable ratio of private government expenditures to non-oil production	0.31	[1]
$\frac{R^{\mathit{oil}}}{Y}$	Stable ratio of oil revenues to non-oil production	0.26	[1]
$\frac{T}{G}$	Stable ratio of tax revenues to government expenditures	0.25	[1]
$\frac{X^S}{Y}$	Stable ratio of consumption of health goods to non-oil production	0.056	[1]
$\frac{R^{\mathit{oil}}}{G}$	Stable ratio of oil revenues to government expenditures	0.81	[1]
$\frac{X^{\mathit{sg}}}{G}$	Stable ratio of government health expenditures to government expenditures	0.071	[1]
${\delta }^k$	Physical capital depreciation rate	0.028	[2]
$\omega$	size of the crisis	0.05–0.1–0.15	[3]
${\rho }_z$	AR(1) parameter, persistence of health disaster risk	0.4–0.6–0.8	[3]

[1] Model calculations; [2] Data average; [3] Yang et al. (2020)

To estimate other indicators, first the distribution, prior mean values and standard deviation were determined. The prior distribution for each parameter was chosen based on the characteristics of that parameter and the characteristics of the desired distribution. For example, if a parameter falls between zero and one, it is appropriate to use the beta distribution for it. For parameters with a range from zero to infinity, gamma distribution was used. In the next phase, they were estimated by using the Bayesian method. The results of the Bayesian estimation of the indicators are presented in Table 2.

Table 2.

Estimating model indicators

Parameters	Prior mean	Prior distribution	References	Posterior mean	HPD interval	Standard deviation
$\beta$	0.96	Beta	[1]	0.973	0.948–0.993	0.018
$\alpha$	0.412	Beta	[2]	0.749	0.602–0.881	0.1
${\psi }_s$	0.302	Gamma	[3]	0.221	0.152–0.294	0.05
$\upsilon$	5.46	Gamma	[4]	3.675	2.44–4.984	1.00
oop	0.6	Beta	[3]	0.642	0.462–0.817	0.1
${\delta }^s$	0.08	Beta	[5]	0.096	0.076–0.117	0.01
$\varphi$	0.27	Beta	[5]	0.281	0.188–0.377	0.05
${\rho }_A$	0.75	Beta	[6]	0.55	0.48–0.619	0.1
${\rho }_{R^{\mathit{oil}}}$	0.798	Beta	[3]	0.735	0.664–0.802	0.1
${\rho }_G$	0.8	Beta	[6]	0.748	0.618–0.871	0.1
${\rho }_{X^{\mathit{sg}}}$	0.35	Beta	[3]	0.296	0147–0.446	0.1
${\epsilon }_t^A$	0.07	Invg	[3]	0.053	0.0431–0.0652	0.01
${\epsilon }_t^z$	0.07	Invg	[3]	0.07	0.051–0.09	0.01
${\epsilon }_t^{R^{\mathit{oil}}}$	0.07	Invg	[3]	0.072	0.061–0.083	0.01
${\epsilon }_t^G$	0.07	Invg	[3]	0.0396	0.034–0.044	0.01
${\epsilon }_t^{X^{\mathit{sg}}}$	0.07	Invg	[3]	0.056	0.045–0.068	0.01

[1] Bahrami and Aslani (2011); [2] Rahmani, Samadi, and Bakhshi Dastjerdi (2021); [3] Research Assumption; [4] Yagihashi and Du (2015); [5] Yang et al. (2020); [6] Hosseini and Asgharpur (2021)

Prior distribution and posterior distribution of estimation of model indices have been reported in Fig. 2.

Fig. 2.

Prior and posterior distributions of model indicators in Bayesian estimation Source: Current Research

Brooks and Gelman (1998) diagnostic test and Monte Carlo Markov Chain (MCMC) suggests that the index estimation is fitting and reliable. This test has three indicators, interval, m2 and m3; which respectively represents the interval, second-order moment (variance) and third-order moment of the parameters. Considering the results of this test, it can be concluded that the length of total sequence interval and mean length of the within sequence intervals of all parameters have converged (Fig. 3). Therefore, the results of Bayesian estimation have good accuracy.

Fig. 3.

The MCMC outcomes (multivariate convergence diagnostic) Source: Current Research

Testing impulse-response functions of macroeconomic variables

Impulse-response functions depict the dynamic behavior of the model variables over time in the event of a shock, as much as a standard deviation, to a variable affected by this impulse. In what follows, the impulse-response functions of the macroeconomic variables to health shock will be investigated with the real business cycle approach.

Impulse-response after health disaster risk shock

Figure 4 demonstrates how the increased risk of a pandemic outbreak can affect Iran’s macroeconomic variables. In this figure, impulse-response functions, following z shock, are shown by a continuous black line in accordance with the base scenario ${\rho }_z$= 0.6. The increased risk of health disaster as much as a standard deviation smoothly deteriorates the health status. To improve the status, hours quarantine and health expenditures are increased, which means increased health investment. Since the sum of working hours, leisure hours, and quarantine hours are proportional, when additional hours are assigned to quarantine, working hours will decrease, and then the marginal productivity of physical capital would fall; which is due to the complementarity of labor and capital in the production function of Cobb Douglas. In the end, labor income and capital income will decrease. Therefore, total output, consumption and physical investment would suffer a considerable fluctuation. This arises from the household’s optimal choice when it comes to this impulse. These events, in general, cause a decline in the quality of life of the household. Over time, the lack of physical capital would increase physical investment and work hours, and eventually, it would be restored to its past stable level.

Fig. 4.

Effect of 1 standard deviation increase in health disaster risk at different levels of risk persistence Source: Current Research

As it is known, as a result of household optimization, economic recession becomes more severe. In other words, when faced with a negative health shock, the household reduces its hours of employment and consumption, and on the other hand, increases the hours of quarantine, which means a more severe economic recession. Figure 4 also indicates how an economy responds to the persistence of health disaster risk under different circumstances. In an optimistic scenario ${\rho }_z$ = 0.4 the dynamics of variables, following the health shock, is similar to the base scenario, but the only difference is its less intensity. In the pessimistic scenario ${\rho }_z$ = 0.8, the degree of variable dynamics is more intense than in the other two scenarios.

In Fig. 5, impulse-response functions, following z shock, are depicted by a continuous black line according to the base scenario $\omega$ = 0.1 and in situations where the persistence of the risk is flat. In an optimistic scenario $\omega$ = 0.05, the dynamics of variables following the health shock is similar to the base scenario, but the only difference is its less intensity. In the pessimistic scenario $\omega$=0.15, the degree of the variable dynamics is much more intense than in the other two scenarios.

Fig. 5.

Effect of 1 standard deviation increase in health disaster risk at different disaster sizes Source: Current Research

Conclusion and recommendations

Evidence and results of studies suggest the profound effects of such pandemics as COVID-19 on countries’ economy. In most studies, epidemiological models were used to predict the outbreak of a disease, but they have a critical drawback: they fail to consider the interaction between economic decisions and contamination levels (Eichenbaum et al. 2021). Therefore, the motivation behind the present research was to understand the intensity of health shock in Iran’s oil economy by using a DSGE model. DSGE models can demonstrate precise interactions between market decision-makers in the framework of general equilibrium. In addition, in these models, market decision makers are optimized within a stochastic environment. Since the duration of the virus outbreak and its effect on the economy are not clear, using these models is more appropriate (Yang et al. 2020). The results indicate that the increased risk of health disaster as much as a standard deviation can lessen work hours, and hence the marginal productivity of physical capital. In the end, labor income and capital income would also decrease, and hence physical investment and total consumption would suffer a considerable loss. Among these variables, consumption has accepted the most effect and, compared to other variables, converges more slowly to the value of its steady state. This is due to the decrease in the permanent income of the household during the period of the outbreak of the disease due to the reduction of wealth or the use of loans. Gradually, by draining the initial effect of the health shock, working hours and household income increases; But because of the decline in wealth, the household allocates a larger proportion of this increase in income to wealth or savings. On the other hand, because consumption decisions are highly dependent on current income and wealth, and investment decisions have been made in the past, thus investment, working hours and production, converges to value of their steady state faster than consumption.

It should be noted that the innovations of the present study compared to the model used in Grossman (2000), Vasilev (2017) and Yang et al. (2020) are: 1- separating health expenditure into private and public health expenditure; 2- adding an oil block to the model; 3- using Bayesian method to estimate the model. The findings of the present research are in line with the above studies.

Given the results of the present study and that countries like Iran are devoid of the essential power and financial skill to curb the outbreak of the disease, one effective way to combat the conditions is social distancing. Moreover, social distance involves the closure of educational centers, factories, shops, transportation systems, quarantine, and the like (Asoyan et al. 2020; Eichenbaum et al. 2021; Yang et al. 2020). Given the significance of public vaccination as an essential way to improve health status and quality of life, it is recommended that the government pave the path for the thriving of businesses and socio-economic activities as early as possible by employing specific policies such as budget allocation for vaccine manufacturing companies or importers (International Monetary Fund 2021).

As a suggestion for future studies, if the structure of the model changes according to the new Keynesian assumptions, and such topics as market imperfection and price stickiness are embedded, then we can analyze the role of monetary policies in health crisis management. Furthermore, with the role of government expanding in the economy, we can study the impact of the government’s fiscal policies on the fluctuations of macroeconomic variables, following the encounter with the outbreak of a pandemic disease. On the other hand, it is suggested that the effect of a pandemic outbreak be evaluated in different regimes and according to Markov Switching models.

Key messages

1. Health shock and its economic impact suffer a research gap when using dynamic stochastic general equilibrium models.

2. Health expenditures are divided into two parts-private and public.

3. In most similar studies, the parameter calibration method is used for simulation purposes, but the present study utilized a Bayesian method for estimating parameters.

Appendix 1

First-order condition

$$\begin{array}{cc}{C}_t:& {\lambda }_t=\frac{1}{C_t}\end{array}$$ 23

$$\begin{array}{cc}{K}_{t+1}:& {\lambda }_t=\beta E_t{\lambda }_{t+1}\left[r_{t+1}^k+\left(1-{\delta }^k\right)\right]\end{array}$$ 24

$$\begin{array}{cc}{H}_t^w:& {\lambda }_t=\frac{{\psi }_n}{w_t}\end{array}$$ 25

$$H_t^q:{\lambda }_t={\mu }_t.\left(1,-,\varnothing \right).{\left(X_t^s\right)}^{\varnothing }.{(w_t.H_t^q)}^{-\varnothing }$$ 26

$$\begin{array}{cc}{X}_t^s:& {\lambda }_t.oo{p}_t={\mu }_t.\left(\varphi \right){\left(X_t^s\right)}^{\varphi -1}.{\left(w_t.H_t^q\right)}^{1-\varphi }\end{array}$$ 27

$$\begin{array}{cc}{S}_{t+1}:& {\mu }_t=\beta \left\{\frac{{\psi }_s}{S_{t+1}^v}+{\mu }_{t+1}.\left(1-{\delta }^s\right)\right\}\end{array}$$ 28

$$\underset{n\to \infty }{\mathit{lim}}{\beta }^t{\lambda }_t{K}_{t+1}=0$$ 29

$$\underset{n\to \infty }{\mathit{lim}}{\beta }^t{\mu }_t{S}_{t+1}=0$$ 30

${\lambda }_t$ Lagrange multiplier in the household budget constraint, and ${\mu }_t$ is the Lagrange multiplier of the health capital transition equation. The first equation under first-order condition was obtained by optimizing the ultimate utility of consumption with regard to the price of wealth shadow. The second equation is the Euler's equation that depicts the optimal allocation of physical capital in two consecutive periods. Next, work hours are singled out in such a way that the final benefit of a work should be equal to the final cost of doing a work. In Eq. 4, quarantine hours are designated in such a way that the health gain of an extra hour of quarantine can be offset by the cost of utility. Health expenses are determined in such a way that the health gain of an additional unit of health expenses is offset by the utility cost. The last optimal condition is the between-time health allocation, in which a household equalizes the marginal benefits to the marginal cost of good health. The transversality conditions are normal conditions without a Ponzi scheme for a physical capital and the rejection of an explosive path for health capital.

Appendix 2

Log-linearized system

$$\overline{S}.{\widehat{S}}_{t+1}-\overline{\mathit{IS}}.{\widehat{\mathit{IS}}}_t-\left(1,-,{\delta }^s\right)\overline{S}{\widehat{S}}_t+\omega .\overline{z}.{\widehat{z}}_t=0$$ 31

$${\widehat{I}}_t^S-\mathrm{\varnothing }.{\widehat{X}}_t^s-\left(1-\mathrm{\varnothing }\right){\widehat{w}}_t-\left(1-\mathrm{\varnothing }\right){\widehat{H}}_t^q=0$$ 32

$${\overline{X}}^s.{\widehat{X}}_t^s-{\overline{X}}^{\mathit{sp}}.{\widehat{X}}_t^{\mathit{sp}}-{\overline{X}}^{\mathit{sg}}.{\widehat{X}}_t^{\mathit{sg}}=0$$ 33

$${\widehat{X}}_t^{\mathit{sg}}-{\widehat{X}}_t^s=0$$ 34

$${\widehat{K}}_{t+1}={\delta }^k.{\widehat{I}}_t^k+\left(1-{\delta }^k\right).{\widehat{K}}_t$$ 35

$${\widehat{w}}_t-{\widehat{C}}_t=0$$ 36

$${\widehat{C}}_t-\beta \left[{\overline{r}}^k+\left(1-{\delta }^k\right)\right]\left({\widehat{C}}_{t+1}\right)+\beta \left({\overline{r}}^k.{\widehat{r}}_{t+1}^k\right)=0$$ 37

$${\widehat{w}}_t+{\widehat{H}}_t^q-{\widehat{X}}_t^s=0$$ 38

$$\left(\frac{1}{\overline{C}}\right)\left(\frac{{\mathit{oop}}_t}{\varnothing }\right){\left(\frac{\varnothing }{\left(1,-,\varnothing \right).{\mathit{oop}}_t}\right)}^{1-\varnothing }\left[\frac{1}{\beta },\left({\widehat{C}}_t\right),-,\left(1,-,{\delta }^s\right),{\widehat{C}}_{t+1}\right]-\left(\frac{{\psi }_s}{{\overline{S}}^v}\right)v({\widehat{S}}_{t+1})=0$$ 39

$${\widehat{Y}}_t-{\widehat{A}}_t-\alpha .{\widehat{K}}_t-\left(1-\alpha \right){\widehat{H}}_t^w-\left(1-\alpha \right){\widehat{S}}_t^w=0$$ 40

$${\widehat{r}}_t^k+{\widehat{K}}_t-{\widehat{w}}_t-{\widehat{H}}_t^w=0$$ 41

$${\widehat{G}}_t+\left(\frac{{\overline{X}}^{\mathit{sg}}}{\overline{G}}\right){\widehat{X}}_t^{\mathit{sg}}-\left(\frac{\overline{T}}{\overline{G}}\right){\widehat{T}}_t-\left(\frac{{\overline{R}}^{\mathit{oil}}}{\overline{G}}\right){\widehat{R}}_t^{\mathit{oil}}=0$$ 42

$${\widehat{A}}_t={\rho }_A.{\widehat{A}}_{t-1}+{\epsilon }_t^A$$ 43

$${\widehat{z}}_t={\rho }_z.{\widehat{z}}_{t-1}+{\epsilon }_t^z$$ 44

$${\widehat{R}}_t^{\mathit{oil}}={\rho }_{R^{\mathit{oil}}}.{\widehat{R}}_{t-1}^{\mathit{oil}}+{\epsilon }_t^{R^{\mathit{oil}}}$$ 45

$${\widehat{G}}_t={\rho }_G.{\widehat{G}}_{t-1}+{\epsilon }_t^G$$ 46

$${\widehat{X}}_t^{\mathit{sg}}={\rho }_{X^{\mathit{sg}}}.{\widehat{X}}_{t-1}^{\mathit{sg}}+{\epsilon }_t^{X^{\mathit{sg}}}$$ 47

$${\widehat{Y}}_t+\left(\frac{{\overline{R}}^{\mathit{oil}}}{\overline{Y}}\right){\widehat{R}}_t^{\mathit{oil}}-\left(\frac{\overline{C}}{\overline{Y}}\right){\widehat{C}}_t-\left(\frac{{\overline{X}}^s}{\overline{Y}}\right){\widehat{X}}_t^s-\left(\frac{{\overline{I}}^k}{\overline{Y}}\right){\widehat{I}}_t^k-\left(\frac{\overline{G}}{\overline{Y}}\right){\widehat{G}}_t-\left(\frac{\overline{w}{\overline{H}}^q}{\overline{Y}}\right)\left({\widehat{w}}_t+{\widehat{H}}_t^q\right)=0$$ 48

Author contributions

AB wrote the main manuscript text and also prepared figures 1–5. All authors reviewed the manuscript.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.