The economic damage of COVID-19 on regional economies: an application of a spatial computable general equilibrium model to South Korea.

We developed a spatial computable general equilibrium model of South Korea to assess the spatial spillover effects of the COVID-19 pandemic on South Korea's regional economic growth patterns. The model measures a wide range of economic losses, including human health costs at the city and county level, through an analysis of regional producers' profit maximization on the supply side and regional households' utility maximization on the demand side. The model's findings showed that if the level of spatial interaction decreases by 10% as a result of social distancing policies, the national gross domestic product drops by 0.815-0.864%. This loss in economic growth can be further decomposed into 0.729% loss in agglomeration effect, 0.080-0.130% loss in health effect associated with medical treatment and premature mortality, and 0.005% loss in labor effect. The results of the models and simulations shed light on not only the epidemiological effects of social distancing interventions, but also their resultant economic consequences. This ex-ante evaluation of social distancing measures' effects can serve as a guide for future policy decisions made at both the national and regional level, providing policymakers with the tools for tailored solutions that address both regional economic circumstances and the spatial distribution of COVID-19 cases.

Introduction

In March of 2020, the World Health Organization (WHO) declared the coronavirus (COVID-19) a worldwide pandemic, leading to the start of a public health emergency which has had severe impacts on human mortality rates, economic activity, international trade, income disparity, education and labor markets, government expenditures, and production networks. While every country has been affected, the distribution and size of these impacts is related to countries’ spatial economic networks and industrial structures. In one example, countries affiliated with the European Bank for Reconstruction and Development (EBRD) are predicted to exhibit greater economic resilience during the crisis, in comparison with other advanced-economy nations and emerging-market nations (EBRD 2020). Specifically, regions whose economies rely more heavily on retail, transportation and storage, and accommodation and food services are expected to suffer more from economic downturns. Countries’ paths to economic recovery have also been affected by social distancing (SD) interventions, which while being effective in controlling the spread of COVID-19, have also led to high social and economic costs and political fatigue over the long-term. As a political tool, social distancing has had both positive and negative repercussions, suppressing the diffusion of COVID-19 in communities on the one hand, but also preventing potential regional economic growth that could form through agglomeration and network effects.

This paper explores two main research questions: how does social distancing affect national economic growth, and what are the impacts of COVID-19 and the measures taken to limit its spread on regions’ economic growth and their interregional disparity? To address these questions, we assess the spillover effects of spatial interactions on regional incomes and the social costs of COVID-19 within an agglomeration economy by developing a spatial computable general equilibrium (SCGE) model of South Korea. Through a multi-sectoral economic equilibrium structure, the model captures the impacts of different spatial economic policies on resource allocation and captures a range of economic losses in cities and counties, such as those associated with human health, by analyzing the profit maximization of regional producers on the supply side and the utility maximization of regional households on the demand side. The SCGE model was applied to examine how spatial interaction levels, or social distancing (SD), have affected the economic behavior of regional consumers and producers, and how this has in turn affected the spatial distribution of economic activities. For this study’s dataset, South Korea was spatially disaggregated into 228 regions (cities and counties), with 2020 set as the benchmark year, and an extended multiregional input–output (IO) table of 16 regions was developed in order to provide the SCGE model with a reference. Section 2 of this paper reviews the spread of COVID-19 in South Korea, and Sect. 3 explores the effects of SD intervention on spatial interactions, regional economics, and spatial growth patterns using counterfactual simulations of the SCGE model. In the final section, we discuss how these findings could be used to guide national, urban, and rural policymakers as they balance the prevention of COVID-19’s spread with the protection of regional economic growth, and also give suggestions for future research directions.

The spread of COVID-19 in South Korea

Figure 1 illustrates the number of confirmed cases and average amount of mobility per week in 2019 and 2020, and the table at the bottom demonstrates the levels of SD interventions in South Korea shown in Table 1. The mobility data were estimated using mobile phone data by counting in cases where people visited areas other than their own residence and stayed for more than 30 min. Since the first case of COVID-19 in South Korea was confirmed on January 20, 2020, the transmission pattern of cases during 2020 consisted of three main waves. The first wave took place from February to March, the second wave in August, and the third wave took place in November. During the first wave, the main source of COVID-19 transmission was linked to outbreaks occurring within religious gatherings in Daegu, the nation’s fourth-largest city in southeastern South Korea. Accordingly, the government then implemented SD rules to limit personal mobility levels and the size of public gatherings. In May 2020, the government then eased SD requirements in response to the slowdown of COVID-19’s spread, as the number of new cases had declined. As public life moved toward normalcy in June and July, personal mobility levels recovered to near 2019 levels, though this recovery was abruptly halted by the second wave of sporadic group infections occurring in the Seoul Metropolitan area (SMA) in August. The government then returned to the reinforcement of SD protocols across the country, limiting businesses’ opening hours and prohibiting gatherings of more than 50 people. The number of newly confirmed cases per week was lower than the peak rate of the first wave, and subsequently dropped during September and October. However, unlike the tail end of the first wave, small herd infections continued to occur within the greater SMA until mid-November, and without any significant ceasing of cases, a third wave was declared in late November, when the number of confirmed cases soared again due to seasonal disease spread patterns and public fatigue with social distancing. Consequently, the government once again imposed stricter restrictions in the SMA, where COVID-19 infections were more prevalent than in the rest of Korea. However, despite this significant decrease in personal mobility, the transmission of COVID-19 continued through asymptomatic individuals, and the number of newly confirmed cases during the third wave was larger than that during the first wave period.

Fig. 1

Confirmed cases and mobility in 2019 and 2020.

Source: Central Disease Control Headquarters and Statistics Korea

Table 1

Social distancing interventions in South Korea

	Level 1	Level 1.5	Level 2	Level 2.5	Level 3
	Preventive measures	Local transmission		Nationwide community transmission
	Distancing in daily life	Beginning of local circulation	Rapid spread of local transmission, beginning of nationwide community transmission	Nationwide community transmission intensifies	Nationwide massive community transmission
Core indicators (Weekly average of daily local transmission cases)	(SMA) Below 100 (Mountain and Island Area) Below 10 (Rest of Korea) Below 30	(SMA) 100 or more (Mountain and Island Area) 10 or more (Rest of Korea) 30 or more	If one of the following three conditions are met: ① Case numbers 2 × or more of the criteria for level 1.5 ② Local transmission in 2 or more regions ③ More than 300 new cases nationwide	400–500 or more new cases per day or a rapid surge in the number of cases (such as doubling)	800–1000 or more new cases per day or a rapid surge in the number of cases (such as doubling)
Supplementary indicators	① Weekly average of number of cases aged 60 or above ② Hospital bed capacity to treat severe/critical cases ③ Epidemiological investigation capacity ④ Basic reproduction number ⑤ Cluster infection situation ⑥ Percentage of cases with transmission chain under investigation ⑦ Percentage of cases confirmed while under home quarantine
Major disease control and prevention measures	Infection prevention and control measures mandatory for high-risk activities and facilities	(Region with high circulation) Stronger measures to prevent spread including limiting the number of people allowed inside publicly used facilities (Other region) Maintain level 1 measures but local governments may place other measures as deemed appropriate based on circumstances	(Region with high circulation) Ban gathering/assembly/event with 100 or more people; Ban gathering in nightlife venues; takeout/delivery only for restaurants past 9 pm; mask wearing mandatory indoors (Other region) Level 1.5 core measures to be implemented; local governments may place other measures as deemed appropriate based on circumstances	Nationwide ban on gathering/assembly/event with 50 or more people; ban gathering in singing rooms; major publicly used facilities may not operate past 9 pm * Regions with lower risk may implement other measures as deemed appropriate by the local government based on the circumstances	Nationwide ban on gathering/assembly/event of 10 or more people; Publicly used facilities other than essential facilities must suspend operation * Local governments may not implement lower measures
Nightlife venues	Restrictions on the number of people		Operation not allowed
Restaurants and cafes	Restrictions on the number of people		To-go and delivery only for cafes To-go and deliver only for restaurants after 9 pm
Indoor gyms	Restrictions on the number of people	No eating and drinking	No operations after 9 pm	Operation not allowed
Sports games	50%	30%	10%	No spectators	No games
Religious facilities	Seat between seats	≤ 30%	≤ 20%	≤ 20, no-contact	1-peron video only
		No eating and drinking
At work	Adequate ratio of remote working recommended (ex. 1/5)	Increase the ratio of remote working recommended (ex. 1/3)		Remote working for 1/3 of employees recommended	Mandatory remote working except for essential workers
Schools	UP to 2/3 students recommended	Up to 2/3 students only	Up to 1/3 students recommended	1/3 of students only	Online

Source Press Release by Korea Disease Control and Prevention Agency press release (November 11, 2020) and COVID-19 Central Disaster and Safety Countermeasure Headquarters (November 1, 2020)

The Local Indicator of Spatial Association (LISA) index, or Moran’s index (Anselin 1995), is used to identify spatial autocorrelations between regional cases, with the index being positive if the weighted average value of the surrounding regions is similar to that of a particular region.1 The LISA analysis reveals that the number of confirmed cases correlated significantly in the cities of Seoul and Daegu and their surrounding counties, while the territorial size of the number of confirmed cases per population for the Daegu cluster was larger than that of the SMA. The concentration of confirmed cases in the SMA was expected due to the area’s large population size, but the spatial autocorrelation within the SMA was not highly statistically significant with regard to population size. Meanwhile, the country’s eastern mountainous areas displayed clear clusters in the number of deceased individuals per confirmed cases, which can be explained by the area’s high proportion of elderly residents and relatively weaker medical infrastructure when compared to that of the rest of the country (Fig. 2).

Fig. 2

LISA analysis of confirmed cases of COVID-19

As of January 21, 2021, South Korea’s cumulative number of confirmed cases was ranked as 87th out of the 236 countries monitored by WHO, with the cumulative number of confirmed cases per million measuring at 1434, far below the world average of 12,165, which can be mainly attributed to the country’s higher levels of mask-wearing compliance. At the start of the first wave, the government did not close borders, but as the spread of COVID-19 worldwide grew over time, public authorities chose to forgo national lockdowns and instead implemented a 3 T (testing, tracing, treatment) strategy. The plan consists of (1) expanding test capabilities; (2) tracing confirmed individuals’ routes through data gathered from mobile phones, credit card usage, and surveillance camera in public space footage; and (3) separating confirmed patients with mild symptoms and severe symptoms, with an ICT technology-based testing management system of drive-through and walk-through. In addition to this 3 T strategy, five levels of social distancing policies were implemented according to the weekly average of daily transmission cases, with the government placing a limitation on the number of people using public indoor facilities in specific areas at Level 1.5, and suspending the operation of publicly used facilities nationwide at Level 3 (see Table 1).

Review of the economic impacts of the COVID-19 pandemic

Quantitative methods to measure the economic impacts of COVID-19 epidemic can be classified into general equilibrium analysis (Maliszewska et al. 2020; Porsse et al. 2020; Cui et al. 2021), and partial equilibrium analysis (Sansa 2020; Sharif et al. 2020; Laborde et al. 2020; Pradesha et al. 2020). The computable general equilibrium (CGE) model is an analytical method based on general equilibrium theory which measures the economy-wide impact of policy shocks on the national or regional economy. Maliszewska et al. (2020) applied a global standard CGE model to varying lockdown duration scenarios, and found that a short-run lockdown would result in a global GDP contraction of 2.5%, and contraction of 4% for a long-run lockdown. They designed four impact channels to transmit the shock throughout the economy, including: the direct impact of a reduction in employment; the increase in costs of international transactions; the drop in travel demands; and the decline in demands for services that require proximity between people. The results revealed that developing countries would incur greater economic damage than industrialized countries with more service-oriented sectors. Porsse et al. (2020) addressed the economic impacts of the COVID-19 outbreak on the Brazilian economy using a dynamic interregional CGE model, looking specifically at two major shocks, consisting of a negative shock of labor supply due to increased rates of morbidity and mortality, and a temporary shutdown of nonessential economic activities due to social isolation practices. The model predicted that the national GDP growth rate in 2020 could reduce by 0.48–3.78% during a three-month shutdown, and by 7.64–10.90% within six months of a shutdown. Cui et al. (2021) evaluated the impact mechanisms of the pandemic on the output of transport sectors based on a decomposition analysis of the CGE model. The simulation suggested that the passenger transport sector’s output would decrease by a greater margin than that of the freight transport sector. In total, the output of the waterway passenger transportation sector declined the most (11.44%), followed by the road passenger transportation sector (8.96%), aviation passenger transportation sector (5.26%), and railway passenger transportation sector (3.08%) in 2020. Additionally, Guan et al. (2020) used an extended, adaptive regional IO model to quantify the short-run supply-chain effects of containment strategies on national and industrial production patterns. They found that the supply-chain loss caused by COVID-19 lockdowns would vary depending on the number of countries imposing restrictions, and was more sensitive to the duration of the lockdown than its degree of severity.

Meanwhile, in terms of partial equilibrium analysis studies, Sharif et al. (2020) analyzed the time–frequency relationship between the COVID-19 outbreak, oil price levels, and the US stock market, with the use of a Granger causality test. The findings revealed that COVID-19 had strong short-term impacts on the US stock market and oil price levels, which was lower than those caused by geopolitical risk and economic uncertainty. Regarding the impact of the epidemic on income and employment inequality, Hirvonen et al.’s (2020) pre-pandemic wealth index and Laborde et al.’s (2020) IFPRI’s global model showed that the COVID-19 pandemic reduced incomes for low-income households in Africa and South Asia. Béland et al. (2020) examined the short-term consequences of the COVID-19 pandemic on US employment and wage levels, and showed that the spreading of COVID-19 increased the unemployment rate and decreased the labor force participation rate, but had no significant impact on wages. Specifically, the negative impacts on the labor market would be more concentrated on workers who were younger and less-educated, as well as those who identified as male and Hispanic. On the other hand, analysis from Fana et al. (2020) determined that the individuals that were most vulnerable to COVID-19-related economic repercussions consisted of female, non-native, self-employed, temporary, low-education, and low-wage workers.

Within the context of COVID-19 economic studies, in comparison with other analytical methods, general equilibrium analysis methods, such as the CGE model, are expected to provide the most comprehensive analysis of the pandemic’s potential impact on the behavior of economic agents, including households, firms, and governments, as the model’s built-in structure is able to capture the various linkages of industrial sectors and markets. In contrast with partial equilibrium analysis models which only ascertain the effects from a single sector, the CGE model is able to fully map out the interdependencies of different agents’ supply and demand levels within the economy. As the model can calculate the simultaneous determination of prices and quantities in multiple inter-connected markets, it is able to capture disruptions in the production and consumption patterns caused by natural disasters and resultant policy shocks. By tracing the effects through layers of economic relationships, the CGE model more accurately reveals the wider economic impact of policies, uncovering not only their direct effects, but their indirect or unintended effects as well. In one case-study, Deloitte (2020) stated that COVID-19 could affect the global economy via three main channels: by directly affecting production potentials (supply), by disrupting supply chains and commodity and service flows (supply), and by generating a financial impact on firms and markets (demand). For this study, we developed a CGE model that could identify the direct and indirect effects of COVID-19’s spread on economic behaviors, which could then be used to evaluate the efficiency and effectiveness of various policy choices.

Method

This SCGE model was developed with the theoretical foundation of new economic geography and new economic growth, and takes into account changes in (1) regional productivities within an agglomeration economy (increasing returns to scale), (2) industrial and residential relocations from long-distance economies and reductions in transportation costs, and (3) consumer preferences for a variety of goods. The SCGE model is designed to determine the optimal price and quantity of each commodity and service within a simultaneous system, specifying the various functional links and sectoral interactions between the supply and demand levels in a production-consumption structure. When producers and households attempt to reach their respective economic goals of profit maximization and utility maximization, the balance identity between the demand and supply of each input factor and commodity market is endogenously solved for in order to obtain the price. In other words, following traditional economic theory, the quantity is determined by the behavioral optimization of the economic agents, which consists of firms and households. As a multiregional approach, the SCGE model classifies South Korea into 228 regions of cities and counties to have two types of economic agents such as producers (firms) and consumers (households). The model comprises of six blocks of (1) spatial interaction (accessibility), (2) price equilibrium, (3) supply of producers and regional trade, (4) labor mobility, (5) demand of consumers on the real-side economy, and (6) the spatial distribution of COVID-19 infections and confirmed cases (see Fig. 3).

Fig. 3

Model structure

Nearly any given SD intervention affects the level of spatial interactions, as measured by “spatial accessibility,” which can be interpreted as a growth or market potential with economic mass. The accessibility level in this paper is calculated by a gravity-typed function of economic activities of all destinations and travel time (cost) between any pair within the transportation network (Kim et al. 2004). Meanwhile, regional labor demand is used as a proxy variable for interaction opportunities at any given destination, and the minimum travel time (or cost) matrix among the regions is derived from the network assignment stage of Transportation Planning Modeling with EMME/2. For any given SD intervention, there is a resultant decrease in spatial interactions or an increase in travel time, implying an overall reduction in accessibility. Several empirical studies have demonstrated that the SD measure affects travel times, especially in the area of public transport which is one of the most disrupted sectors of the COVID-19 pandemic. Kamga et al. (2021) analyzed the impact of the COVID-19 pandemic on public transportation operations using the New York City subway Line 1 as an example. Five scenarios of physical distancing are simulated and analyzed in this paper: 3 ft, 4 ft, 5 ft, 5.4 ft, and 6 ft of separation between passengers. They found the evidence for differences in the additional passenger waiting time caused by the 5 different social distancing measures, indicating that the number of trains must be increased to shorten the waiting time. The key finding is that, by decreasing the minimum distance from 6 to 5.4 ft, the number of additional trains required to serve the transit demand will decrease by 42% and more resources are saved. In addition, Gkiotsalitis and Cats (2022) investigated the impact of different distancing policies on operational costs, passenger-related costs and vehicle occupancy levels, computing the optimal service frequencies of the Washington DC metro lines under different distancing policies (no distancing, 1-m distancing, 1.5-m distancing, 2-m distancing). They also found that different subway lines and different SD measures had significantly different effects on total travel time and passenger waiting time.

The average cost-pricing rule is applied to price-level determination by clearing the excess demand in labor, capital, and commodity markets under the Walrasian equilibrium condition (Gottinger 1998). The SCGE includes two major price types: free on board (FOB) on the supply side and cost, insurance, and freight (CIF) on the demand side. The FOB price, which is the output value at which firms produce their commodities, is composed of the primary factor payments and the marginal costs of the intermediate inputs. The CIF price is the market price which consumers pay for commodities and services, and is defined as the sum of the FOB price at the origin (production area) and the transportation cost from the origin to destination (market area), which is determined by the travel time and transportation cost per unit of time (tariff).

Within the commodity market, each regional producer is assumed to offer a single representative commodity, maximizing profit under the two-level Cobb–Douglas production of output. At the upper level, the regional output is determined by the Cobb–Douglas production function of the value added and intermediate demand. Using technologies for substitution between the pooled commodities and factors of production, the producer chooses the quantities of intermediate demand or value added under the fixed share of the output and an elasticity of substitution equal to unity. The lower level is composed of a calibration of (1) value added with technologies for substitution between labor and capital and (2) the intermediate demands among the 228 regional commodities. The value added is estimated with two private paid-factor inputs of the labor and capital stock, and one external-factor input taken from the level of spatial interaction in order to take agglomeration economic effects into consideration. As previously mentioned, accessibility increases with spatial interactions, which in turn generates the positive externality of agglomeration economies, affecting productivity and increasing the value of the shift parameter in the production function. The signs of the linear and quadratic terms of the spatial interaction variable in the value-added equation are positive and negative, respectively. In graphical terms, the value-added factor can be displayed as an inverted U for spatial interaction: the marginal benefit of the interaction to the value-added term increases steeply at the early stage, at a diminishing rate in the middle stage, and decreases in the late stage (Kim et al. 2014). The regional producer maximizes output values using the Cobb–Douglas intermediate demand function, which is a function of the 228 regional commodities. Under the first-order condition, inter-regional trade increases with the input coefficient, the production output of the destination, and the output price, but decreases with the CIF price, which is determined by travel time, the transportation cost per unit of time, and FOB price. Producers are typically willing to purchase more commodities to obtain the lowest CIF price if the quality of competing commodities is homogeneous.

The labor demand by region is derived from the producer’s value-added maximization, in which the marginal revenue of each factor input is equal to its factor input price. The regional wage consists of a wage-distortion term and an average wage rate derived by balancing total labor demand with supply under a neoclassical labor market closure rule (Iqbal and Siddiqui 2001). Each regional labor input is assumed to be homogeneous and mobile across regions, and multiregional migration between origin and destination depends on the economic differences in the gross regional product (GRP) per capita and the population sizes of any two given regions. With the budget constraint where regional income consists of wages and capital return, the regional consumer maximizes the Cobb–Douglas type utility, and consumption expenditure by regional commodity is calibrated with a linear function of total household income.

The number of confirmed cases of COVID-19 was specified as a function of spatial interactions, the share of total area consisting of residential and commercial land, and population size.2 The elasticity of the spatial interaction of confirmed cases was estimated to be 0.3099, meaning that if the level of the spatial interaction rises by 1%, the number of confirmed cases would increase by 0.3099%. The number of deceased patients was determined by the number of confirmed cases, the population’s aging rate, and the number of medical doctors. For this model, the medical cost of COVID-19 was calculated by multiplying the number of confirmed cases by the per-capita cost, or $6710 (USD). On average, patients were reported to stay in the hospital for an average of 20.7 days in 2020. Therefore, when calculating the impact on human health, the value of COVID-19-related premature deaths was calculated by taking into account the number of deaths and the Value of a Statistical Life (VSL) figure, which ranges from $63,636 to $381,818 in COVID-19 reports (Table 2).3

Table 2

Economic impacts of the COVID-19 pandemic

Method	Subject	Author	Region	Main findings
CGE model	GDP	Maliszewska et al. (2020), Porsse et al. (2020), Cui et al. (2021)	Global	Decline in global GDP
IO model	Global supply chains	Guan et al. (2020)	Global, China, Europe, USA	Supply chain losses depend on the strictness and duration of the lockdown
Social accounting matrix	Poverty	Laborde et al. (2020) Pradesha et al. (2020)	Global, Africa, Asia	Slowdown of global economy and increase of the number of poor people
Linear model	Financial effects	Sansa (2020), Sharif et al. (2020)	USA, China	Strong short-term impacts on stock market and oil prices
Qualitative analysis	Trade	Keynes and Bown (2020), WTO (2020)	Global	Decline in total trade volumes
	Household incomes	Hirvonen et al. (2020), Abate et al. (2020)	Ethiopian	Strong income declines for poor households
	Food supply	Hobbs (2020), Rizou et al. (2020)	Canada, USA	Change in consumption patterns, labor shortages, and disruptions to transportation networks
	Labor market	Fana et al. (2020), Béland et al. (2020)	Germany, Spain, Italy	Increase in unemployment and labor force participation rates

In order to develop a SCGE model, a benchmark dataset is necessary in order to create the internally consistent structures of the economic relations between the economic agents, while also providing the initial values for the model. For this purpose, we calibrated an extended multiregional IO table, tracking the monetary and commodity flows of each sector in terms of their respective receipts and expenditures. There are two types of parameters in the SCGE model: structural coefficients and behavioral parameters. The former consists of non-elasticity parameters derived from benchmark and cross-sectional survey data, including input coefficients and consumption propensities. The latter are estimated with econometric models that incorporate historical data, including the elasticities of accessibility in the production function. Each shift parameter is adjusted so that the SCGE model can reproduce the extended IO model at the base run. The SCGE model is composed of 9024 equations and endogenous variables, which can capture a unique solution of the variables under convexity. Exogenous variables make up a travel-time matrix, and the lagged population size and the consumer price index are treated as the numeraire for the model. The numerical specifications of the model foundation is shown in Table 3.4

Table 3

Specification of major equations

Major equations in CGE model
(1) Spatial interaction (Accessibility)	ACC_i=∑_jL_jDISTijα
(2) Price equilibrium	PVA_i∗VA_i=PX_i∗X_i-∑jTR_ji∗PCIF_ji PCIF_ij=PX_i+CIF_ij∗DIST_ij WCPI=∑iXIO_i∗PX_i
(3) Supply of producers and regional trade	X_i=XTR_ji,VA_i VA=VAL_i,K_i,ACC_i TR_ij=TRPCIF_ij,X_j,PX_j L_i=LWA_i,VA_i,PVA_i K_i=KRA_i,VA_i,PVA_i LD=∑iL_i KD=∑iK_i
(4) Labor mobility	POP_i=NaturalGrowthofPOP_i+∑jMIG_ji-∑jMIG_ij lnMIG_ij=8.29+0.31∗lnL_iPOP_i+0.55∗lnL_jPOP_j+1.97∗lnVA_iPOP_i-0.25∗lnVA_iPOP_i^2-0.47∗lnVA_jPOP_j+0.03∗lnVA_jPOP_j^2-0.93∗lnDIST_ij
(5) Demand of consumers	U_i=UFR_ji FR_ji=FRPCIF_ij,VA_j,PVA_j X_i=∑jTR_ij+FR_ij+DK_i
(6) Spatial distribution of COVID-19 infections and confirmed cases	lnCONFI_i=CONFIP_i+1.15932∗lnPOP_i∗1,000,000+0.30990∗lnACC_i+0.71214∗LANDUSE_i lnDEATH_i=DEATHP_i+0.42718∗lnCONFI_i+1.81069∗AGEING_i-0.05615∗DOCTOR_i
Endogenous variables
ACC_i: Accessibility of region i CONFI_i: Number of confirmed cases of region i DEATH_i: Deceased number of COVID 19 FR_ij: Final demand of region j for commodity produced at region i K_i: Capital (stock) demand of region i KD: Total capital (stock) demand L_i: Labor demand of region i LD: Total labor demand MIG_ij: Number of migrants from region i to region j PCIF_ij: CIF price of region j for commodity produced at region i POP_i: Population size of region i PVA_i: Price of value added of region i PX_i: Production price of region i RA_i: Capital return rate of region i TR_ij: Intermediate demand of region j for commodity produced at region i U_i: Utility level of region i VA_i: Value added of region i WA_i: Wage rate of region i WCPI: Price index X_i: Output of region i
Exogenous variables and parameters
AGEING_i: Population ageing index of region i DIST_ij: Travel time from region i to region j DK_i: External demand of region i DOCTOR_i: Number of doctors of region i LANDUSE_i: Share of total area occupied by residential and commercial land uses of region i CONFIP_i: Constant parameter of confirmed case equation DEATHP_i: Constant parameter of deceased case equation CIF_ij: Tariff rate of region j for commodity produced at region i XIO_i: Regional weight value of price index α: Mobility-resistance parameter

: Accessibility of region i

: Number of confirmed cases of region i

: Deceased number of COVID 19

: Final demand of region j for commodity produced at region i

: Capital (stock) demand of region i

: Total capital (stock) demand

: Labor demand of region i

: Total labor demand

: Number of migrants from region i to region j

: CIF price of region j for commodity produced at region i

: Population size of region i

: Price of value added of region i

: Production price of region i

: Capital return rate of region i

: Intermediate demand of region j for commodity produced at region i

: Utility level of region i

: Value added of region i

: Wage rate of region i

: Price index

: Output of region i

: Population ageing index of region i

: Travel time from region i to region j

: External demand of region i

: Number of doctors of region i

: Share of total area occupied by residential and commercial land uses of region i

: Constant parameter of confirmed case equation

: Constant parameter of deceased case equation

: Tariff rate of region j for commodity produced at region i

: Regional weight value of price index

: Mobility-resistance parameter

Due to the non-stochastic properties of the SCGE model, the model’s reliability as a policy assessment tool has been assessed through (1) the comparison of simulation results with actual values and (2) the assessment of the stability or robustness of results through a sensitivity analysis of changes in the key parameter values (Bandara and Coxhead 1999; De Maio et al. 1999). For this study, the latter method was selected due to our focus on counterfactual analysis, and our lack of the time-series data that is necessary for comparative studies. The results from the sensitivity analysis find that the GDP and regional average wages would reduce by 0.23–0.34% and 0.10–0.15%, respectively, if the elasticity of spatial accessibility for the value added function increases by 5% in the model, thereby implying that the model is not sensitive to elasticity values and is suitable for counterfactual analysis.

Results

Overall, SD interventions generate both direct and indirect economic impacts. As an example of a direct impact, restrictions on indoor public events and social gatherings can lead to fewer spatial interactions between economic agents, implying increases in travel time. This then affects the number of confirmed cases of COVID-19, as well as the transaction volumes for goods, services, and factor inputs, which are understood as indirect effects. These direct and indirect impacts are spatially distributed across regions, having spillover effects on adjacent regions around an area hit by COVID-19, as well as the functionally linked industrial sectors where economic agents pay the economic costs (negative benefits). The SCGE model captures this spatial distribution of indirect economic impacts at the city and county levels, which is where policymakers implement strategies to mitigate economic costs, primarily through the provision of relief packages and fiscal stimulus.

This section analyzes the economic impacts of spatial interactions to take into account the effects of SD interventions on regional economies, applying the SCGE model to a baseline scenario, and then giving four additional alternative scenarios. The baseline scenario represents a reference case where there is no outbreak of COVID-19 within an existing policy framework. Overall, the only differences between the baseline and alternative scenarios exist within the changes in travel time (cost) between cities and counties, meaning that the four other scenarios are only distinguished by differing levels of spatial interactions, which can also be seen as a measure of accessibility. After simulating all of the counterfactual scenarios, each simulation’s results were compared with those of the baseline scenario. As discussed previously, the level of spatial interactions has both positive and negative impacts on economic growth. Generally, the level of spatial interactions improve regional incomes at an increasing rate until the optimal point or point of inflection. In contrast, the spatial interactions also induce negative outcomes, mainly taking place in the form of labor force losses and increased social costs, such as medical treatment-related expenses and death measured in terms of the statistical value of a human life. These results imply that a net change in the regional income depends on the gap between the elasticity values (speeds) of spatial interactions for both productivities and costs. This economic damage can then be decomposed into a series of net changes taking form in (1) an agglomeration-loss effect originating from a weakened agglomeration economy, (2) a health-loss effect associated with the medical expenses of confirmed cases and the VSL due to lives lost to COVID-19,5 and (3) a labor productivity-loss effect caused by a reaction between components (1) and (2), such as a reduction in the labor force due to individuals who cannot work due to a COVID-19 diagnosis. The agglomeration-loss effect increases with travel time (cost), while the health-loss and the labor productivity-loss effects decrease alongside it. As a result, the economic damage caused by travel time changes is expected to be inconclusive overall (Fig. 4).

Fig. 4

Decomposition of GDP changes into three components

Table 4 displays the results of a simulation of Korea’s gross economic performance for each counterfactual scenario in terms of their respective simulated GDP to the level under the baseline case. All economic values are derived from the optimization of the economic behavior of regional producers and consumers. As shown in Table 4, if the travel time (cost) increases by 10% from the baseline, the GDP would decrease by an estimated 0.815–0.864%. For a 10% decrease in the spatial interaction level, the agglomeration-loss effect and the health-loss effect are estimated as 0.729% of the GDP (a partial effect of component 1) and 0.080–0.130% (a partial effect of component 2) compared with the baseline level estimates. Summing the two partial effects of components (1) and (2), the net GDP decrease amounted to 0.809–0.859% of the baseline. The difference between these partial-sum effects and the economic damage, 0.005%, stems from the labor productivity-loss effect that is generated from workers that cannot work due to self-isolation measures and medical treatment.

Table 4

Impacts of a 10% reduction in spatial interaction level on national GDP (unit: %)

	5%	10%	15%	20%
Total effect	− 0.517 to − 0.467	− 0.864 to − 0.815	− 1.185 to − 1.136	− 1.486 to − 1.437
Agglomeration-loss effect	− 0.381	− 0.729	− 1.052	− 1.354
Health-loss effect	− 0.131 to − 0.081	− 0.130 to − 0.080	-0.128 to − 0.080	− 0.127 to − 0.079
Labor productivity-loss effect	− 0.005	− 0.005	− 0.005	− 0.004

The value is a share of the GDP at the baseline

Generally, the economic damages varied spatially in accordance with interregional connectivity and regional assets, as shown in Table 5, where 228 cities and counties are aggregated into five regional economic areas (REAs): Seoul, Central, South-West, South-East, and Busan (See Fig. 5).6 If the spatial interaction level reduces by 10% compared with the baseline as shown in Table 5, the economic damage could be most serious in the South-East REA including the city of Daegu7; the GRP could decrease by 2.022–2.313% much higher than the national average (0.815–0.864%). The Seoul REA had the second highest level of economic damage (0.861–0.894%), followed by Busan (0.779–0.788%) and the South-West REA (0.329–0.336%).

Table 5

Impacts of a 10% reduction in spatial interaction level on regional GRP (unit: %)

	Seoul	Central	South-West	South-East	Busan	Total
Total effect	− 0.894 to − 0.861	− 0.194 to − 0.178	− 0.336 to − 0.329	− 2.313 to − 2.022	− 0.788 to − 0.779	− 0.864 to − 0.815
Agglomeration-loss effect	− 0.798	− 0.147	− 0.313	− 1.558	− 0.761	− 0.729
Health-loss effect	− 0.092 to − 0.058	− 0.044 to − 0.028	− 0.023 to − 0.015	− 0.737 to − 0.446	− 0.026 to − 0.017	− 0.130 to − 0.080
Labor productivity-loss effect	− 0.005	− 0.002	− 0.001	− 0.019	− 0.001	− 0.005

The value is a share of the GRP at the baseline

Fig. 5

Classification of five regional economic areas

Our simulation results in Table 6 show that the Busan REA would receive the highest share of agglomeration loss (96.57%), which was much larger than the national average (84.43%); with the values for the other regions being 92.91% for the South-West REA, 89.26% for the Seoul REA, 75.89% for the Central REA, and 67.34% for the South-East REA. The shares of the agglomeration-loss effect of Busan REA and South-West REA were high in Table 6, since the numbers of confirmed cases remained relatively low in two regions. In particular, the Busan REA’s proportion (96.57%) was much higher than the national average (84.43%) because of its significant contribution to national economic growth. The share of the health-loss effect in the South-East REA, as expected, reached to 31.86%, the highest among the five REAs, mainly due to the spatial concentration of confirmed cases around Daegu. For Seoul REA, a portion of agglomeration-loss effect was 89.26% due to its densely populated area and productive industrial specialization in spite of the high confirmed cases. This table implies that the relative magnitude of sub-impact components could be determined by the spread of COVID-19 in the region and the degree of economic interaction. It means that national government-mandated SD measures in the Busan and South-West REAs need to be eased in a sense that the health-loss effects were quite small compared with the agglomeration-loss effects.

Table 6

Share of impacts of a 10% reduction in spatial interaction level on regional GRP (unit: %)

	Seoul	Central	South-West	South-East	Busan	Total
Agglomeration-loss effect	89.26	75.89	92.91	67.34	96.57	84.43
Health-loss effect	10.24	22.91	6.74	31.86	3.30	15.02
Labor productivity-loss effect	0.51	1.20	0.35	0.80	0.13	0.54

The value is a share of the total effect

It would be meaningful to examine how these economic outcomes are distributed across cities and counties under the spatiotemporal conceptual framework of LISA. As explained previously, LISA reveals spatial changes within the hot spots of economic effects that take place in response to SD interventions. A “hot spot” is defined as an occurrence of local spatial agglomeration and clustering, and is shown as HH (high relative damage with adjacent regions with high relative damages) in Fig. 6. The hot spots of the economic damage and the agglomeration-loss effect can be seen in the Seoul and South-East REAs (including Daegu), with strong positive complementary, rather than competitive, relationships existing between the counties and their adjacent regions. Hot spots related to health-loss effects were concentrated in Daegu, while hot spots related to labor productivity-loss effects tended to be located in eastern coastal and mountainous areas. These results imply that the government should prioritize locally tailored plans when implementing COVID-19 recovery, adaptation, and response tools, including the creation of context-sensitive SD protocols and quarantine measures.8

Fig. 6

Geographical distribution of impacts of spatial interactions on GRP (unit: %). HH: high relative damage with adjacent regions with high relative damages. LH: low relative damage with adjacent regions with high relative damages. LL: low relative damage with adjacent regions with low relative damages. HL: high relative damage with adjacent regions with low relative damages

Conclusions

In this paper, SD policy measures implemented to mitigate the spread of COVID-19 are indirectly evaluated through a general equilibrium framework that incorporates factor mobility and institutional rigidities into the real side of regional markets. If spatial interactions are regulated such that travel time (cost) increases by 10%, the national GDP could drop by an estimated 0.815–0.864%. This outcome can be additionally decomposed into a 0.729% agglomeration-loss effect, a 0.080–0.130% health-loss effect, and a 0.005% labor productivity-loss effect.

Further research could apply the SCGE model to the calibration of economic losses resulting from the various outbreaks which took place in 2020. By estimating the degree to which each type of SD measure (self-isolation, school closures, public events banned, and complete lockdowns) affects the travel behavior of consumers and producers and changes travel time and cost, it would then be possible to calculate the overall effect of SD measures on the efficiency and welfare of national and regional economies. Another possible line of inquiry could involve the integration of the SCGE model with a model of disease-generated health costs, which would make it possible to measure the impacts of COVID-19 on medical service costs, in addition to the subsequent loss of labor input according to population cohort. By continuing to expand on this current study, future models would make it possible to identify the best policies which would ensure countries and regions' long-term economic sustainability, even as they mitigate the spread of COVID-19. Together with the above points, the SCGE model can be operated for examining how universal and selective economic relief strategies affect economic activities of regional economies as well as small- and medium-sized enterprises such as food and beverage establishments, and other service-oriented businesses. Through capturing spillover and feedback effects of the SD intervention on the economic agents and local markets, the government could assess positive and negative outcomes of each subsidy policy in terms of regional inequality, industrial sustainability, and economic resilience. Finally, while the SD reduces industrial productivities due to the increases in economic distances and travel costs, it could have a positive effect on the accessibility through the reduction in the travel time. It is worthwhile to examine reactions of economic agents to changes in the travel time as well as the travel cost, and the net effect of the SD on the productivity could be estimated with implementing an integrated system of the transportation demand model with the SCGE model.