Assessing the impact of COVID-19 on major industries in Japan: A dynamic conditional correlation approach

Abstract

This study assesses the impact of the novel coronavirus disease (COVID-19) cases on the Japanese stock market. As of October 30, 2020, the cumulative number of cases in Japan has reached over one hundred thousand. COVID-19 has significantly affected both the lifestyle and the economy in Japan. First, this study develops composite stock indices by industry sector and prefecture, taking into consideration the effects of the increase in infections on industries and firms in the core prefectures. Second, this study investigates the dynamic conditional correlations between the composite stock index returns and the increment in COVID-19 cases using dynamic conditional correlation multivariate GARCH models. Finally, it can contribute to financial research in terms of coexistence of regional business economies with COVID-19.

1. Introduction

The novel coronavirus disease (COVID-19; caused by the SARS-CoV-2 virus) has caused an unprecedented pandemic. Globally, approximately 40 million people have been infected with COVID-19 as of October 17, 2020, with more than 1.1 million fatalities, according to the latest data by Johns Hopkins University (JHU, 2020). It has caused great confusion in every country.

In the field of public health, infections are categorized into three types: endemic, epidemic, and pandemic, with the degree of severity increasing in that order. Finally, a pandemic has a similar meaning to an epidemic, but it refers to those infections that have the most severe effects on a global scale (Vynnycky and White, 2010). On March 11, 2020, the World Health Organization (WHO) declared COVID-19 a global pandemic (WHO, 2020). Additionally, in terms of risk management in the field of finance, the pandemic, same as the global financial crisis (2007–2009), belongs to the category of “systemic risks.” It is therefore recognized that COVID-19 should be subject to systemic risk management.

In Japan, a mass outbreak of COVID-19 took place among the 3711 passengers and crew of the cruise ship, Diamond Princess, in February 2020. A total of 712 patients were confirmed positive for the virus and the threat of COVID-19 became a serious concern (NIID, 2020).

As measures against COVID-19, the Japanese government has implemented trial and error style of policies up until now, although the contents of these policies have been questioned. For example, at a press conference on May 4, although former Prime Minister Shinzo Abe indicated that the anti-influenza drug Avigan would receive regulatory approval, it is yet to be approved as of the end of October 2020. Considering that vaccines have not yet been developed for past pandemic diseases, such as the Severe Acute Respiratory Syndrome (SARS; outbreak in 2002) and the Middle East Respiratory Syndrome (outbreak in 2012), the delay in regulatory approval for Avigan is expected.

Examining the chain of events up until now, on April 7, 2020, former Prime Minister Abe officially issued a “declaration of a state of emergency” and expressed that “the Japanese economy is facing its greatest crisis since the end of the Second World War.” Additionally, on May 4, the declaration was extended for an additional month along with commentary that “it is necessary to prepare for a fight that extends for some period of time.” However, on May 14, the declaration was lifted in 39 prefectures, and the occasion was marked as “a day to start to return to a new everyday life.” On May 25, the declaration was wholly lifted with the assertion that “the strength of the Japanese model has been shown” (source: June 13, Nihon Keizai Shimbun). Additionally, the “Novel Coronavirus Expert Meeting” was also abolished on June 24. However, thereafter, a second wave of infection, originating from “entertainment and social activities that happen in the evening in bars and clubs” of Shinjuku Ward in Tokyo, have been rapidly increasing the number of infected persons in a wide range of age groups (Fig. 1 ). On July 10, the infections hit a record high.

Fig. 1.

Cumulative cases by prefecture as of 10:00 AM, October 16, 2020. Notes: A prefecture colored in black is Tokyo. In addition, from north to south, prefectures in brown are Saitama, Kanagawa, Aichi, Osaka, and Fukuoka, and ones in pink are Hokkaido, Chiba, Kyoto, Hyogo, and Okinawa.

Evaluating the policies taken by the government at the present time, when the prospects for the resolution of the COVID-19 crisis do not look positive, is not the goal of this study. Yet the effect of COVID-19 on the financial economy may be even greater than the effect of the global financial crisis. From a global perspective, for example, as of November 6, 2020, the operating profit for Toyota, which has production and sales locations worldwide, is expected to decrease by 46% for the fiscal year ending March 31, 2021. This is also true for other automobile manufacturers. The effects on the automobile industry, which includes many subsidiaries, sub-subsidiaries, and affiliates are significant.

In contrast, in the domestic economy, 616 instances of COVID-19-related bankruptcies, 534 legal liquidations, and 82 suspensions of business have been identified. The rank by industry is as follows: “restaurants and dining” (88 cases), “hotels and inns” (59 cases), “apparel and general retail” (44 cases), “construction” (37 cases), “food wholesalers” (36 cases), “apparel wholesalers” (25 cases), and so on (source: Teikoku Databank Corporate, 2020 as of 4:00 PM, October 16). With the end of the COVID-19 crisis nowhere in sight, the effects are increasingly extending into the long term.

Additionally, in the food wholesale industry, there are concerns regarding the increase of COVID-19 infections in distribution centers, which are controlled by avoiding the three conditions for transmission, or “Three C's,” closed spaces (closed spaces with poor ventilation), crowded places (where many people congregate), and close-contact settings (such as close conversations in which individuals are close enough to touch each other). The construction industry has been affected by the closure of job sites and delays in obtaining construction materials caused by disruption in distribution and the supply chain. The food production industry has been affected by school closures and the suspension of events, causing many firms to go bankrupt.

Accordingly, this study analyzes the variations of sector stock index by prefecture as a proxy of regional firm economies. In another perspective, following the increase in COVID-19 infections, financial researchers worldwide have grown concerned about the effects of COVID-19 on the financial economy. These researchers have put together special COVID-19-related reports in academic journals, and many are calling for social contributions (Goodell, 2020).

In Section 2, a literature review of existing research is conducted. In Section 3, the analysis approach and data used in the study are examined. In Section 4, the analysis results are shown and discussed, and Section 5 shows the conclusion.

2. Literature review

In finance, existing research related to pandemics is almost unknown. This is because although pandemics are a type of macro stress that severely impact the economy, pandemics that had a global effect on the financial economy like COVID-19 have not occurred in the past. Research on pandemics as infectious diseases has taken place for many years, and Vynnycky and White (2010) is the basic text for mathematical modeling. Also, Kiss et al. (2018) elucidate a mathematical model for infections based on the propagation of a virus from person to person through a complex network.

Though not regarded as pandemic research, a small number of studies using infectious disease models do exist, such as Kanno (2015), in which we examine a succession of bankruptcies in the Japanese banking system following the global financial crisis by applying a Susceptible-Infected-Recovered Dead (SIRD) model. The SIRD model adds a “dead” state to a Susceptible-Infected-Recovered model, a typical mathematical model used for infectious diseases.

In contrast, since March 2020, COVID-19 and financial market related articles were published in line with the COVID-19 outbreak. In terms of stock markets, Goodell and Huynh (2020) analyzed the abnormal returns of 49 industrial sectors from December 9, 2019–February 28, 2020. Shehzad et al. (2020) employed the asymmetric power GARCH model and found that COVID-19 substantially harms United States’ (US) and Japan's market returns. Mazur et al. (2021) investigated the US stock market performance during the crash of March 2020, triggered by COVID-19. Akhtaruzzaman et al. (2021) showed that dynamic conditional correlations between Chinese and G7 stock returns, financial and nonfinancial alike, increased significantly during the COVID-19 period. Zaremba et al. (2020) demonstrated that non-pharmaceutical interventions significantly increase equity market volatility. Ashraf (2020) examined the stock markets’ response to the COVID-19 pandemic using daily COVID-19 confirmed cases and deaths and stock market returns data from 64 countries over the period January 22, 2020 to April 17, 2020. Okorie and Lin (2021) investigated the fractal contagion effect of the COVID-19 pandemic on the stock markets.

Also, in terms of market analysis using news analytics tool, Cepoi (2020) offered novel empirical evidence on the relationship between COVID-19 related news and stock market returns across the top six countries most affected by the pandemic and showed the COVID-19 news-related variables from the RavenPack analytics tool. Haroon and Rizvi (2020) analyzed the relationship between sentiment generated by coronavirus-related news and volatility of equity markets using the same tool. Shi and Ho (2020) examined the impact of public news sentiment on volatility states of firm-level returns using the same tool.

3. Analysis approach and data

This study analyzes the impact of COVID-19 on regional stock index returns as proxies of regional firm economies using the dynamic conditional correlations.

3.1. Analysis approach

Composite stock index. We compose prefectural stock index using the stock prices of firms composed of the Tokyo Stock Price Index (TOPIX). At present, TOPIX is used as a representative stock index to express economic movements in Japan as a whole. TOPIX includes all domestic common stocks listed in the First Section of the Tokyo Stock Exchange. It is assigned a market capitalization of 100 as of January 4, 1968, to which all subsequent market capitalizations are indexed (Tokyo Stock Exchange, 2020).

Additionally, the 33 Tokyo Stock Exchange Sector Indices are stock indices that divide this index into 33 different industry sectors (see Table A.8). By rearranging firm stock prices applicable to a sector and a prefecture, it is possible to develop stock indices arranged both “by prefecture” and “by industry.”

Today, the majority of stock indices worldwide are weighted by market capitalization such as TOPIX, the S&P 500 Index, and the NASDAQ Composite Index of the United States. Weighting by market capitalization means that the total amount of a listed stock's market capitalization (a number that represents the firm value and is obtained by multiplying the stock price by the number of listed shares) is calculated by dividing the total market capitalization of the index at a certain point in time. This is compared to the value at a past point in time so that it expresses how much the market capitalization has increased or decreased at the time of calculation, thereby expressing the change in the price of the stock as an asset.

The calculation formula of composite prefectural index ${\mathrm{Index}}_{i,j,t}$ for prefecture $i$ and sector $j$ at time $t$ is as follows:

$${\mathrm{Index}}_{i,j,t}=\frac{{\sum }_{k\in K_{i,j}}{l}_{k,t}{P}_{k,t}}{{\sum }_{k\in K_{i,j}}{l}_{k,0}{P}_{k,0}}\times {\mathrm{SV}}_{i,j,0}$$ (1)

where $l_{k,t}$ and $P_{k,t}$ are the adjusted number of shares issued1 and the stock price for firm $k$ belonging to prefecture $i$ and sector $j$ at time $t$, respectively. $K_{i,j}$ is a set for firms belonging to prefecture $i$ and sector $j$. ${\mathrm{SV}}_{i,j,0}$ is a standard value for the index related to prefecture $i$ and sector $j$ at time 0.

Dynamic conditional correlation. To calculate dynamic conditional correlation (DCC), we introduce the multivariate GARCH model proposed by Engle (2002). The model is a dynamic multivariate regression model, in which the conditional variances and covariances of the errors follow an autoregressive moving average structure. The DCC multivariate GARCH model uses a nonlinear combination of univariate GARCH models with time-varying cross-equation weights to model the conditional covariance matrix of the errors.

In the DCC multivariate GARCH model, DCC is defined as follows:

$${\rho }_{\mathrm{ij},t}=\frac{h_{\mathrm{ij},t}}{\sqrt{h_{\mathrm{ii},t}{h}_{\mathrm{jj},t}}}$$ (2)

where the diagonal elements of a time-varying conditional covariance matrix of the disturbances, $h_{\mathrm{ii},t}$ and $h_{\mathrm{jj},t}$, follow univariate GARCH processes, $h_{\mathrm{ij},t}$ are the off-diagonal elements of the matrix, and hence ${\rho }_{\mathrm{ij},t}$ follows the dynamic process.

In DCC GARCH model, the conditional variance ${\sigma }_{k,t}^2$ ($k=1,\dots ,m$; $m$: the number of dependent variables) evolves according to a univariate GARCH model of the form

$${\sigma }_{k,t}^2=exp({\gamma }_k{z}_{k,t})+\sum _{l=1}^{p_k}{\alpha }_l{\epsilon }_{k,t-l}^2+\sum _{l=1}^{q_k}{\beta }_l{\sigma }_{k,t-l}^2$$ (3)

where for each series $k$, ${\gamma }_k$ is a $1\times p$ vector of parameters, $z_k$ is a $p\times 1$ vector of independent variables including a constant term, ${\epsilon }_k$ is a standardized disturbance with mean zero and variance one, the ${\alpha }_l^{\prime }$ are ARCH parameters, and the ${\beta }_l^{\prime }$ are GARCH parameters. $p_k$ and $q_k$ are the number of lags for the ARCH term and the GARCH term, respectively.

Using Stata 14, we estimate DCC GARCH models. To this end, $p_k$ for the ARCH term, $q_k$ for the GARCH term, suppression of the constant term in the mean equation, and the assumed distribution such as Gaussian distribution or $t$-distribution for the errors need to be set. Additionally, in terms of the optimization algorithm in the multivariate regression model, Berndt–Hall–Hall–Hausman algorithm is adopted. Tolerance parameters are set to defaults: 1e$-$6 in coefficients vector, 1e$-$5 in Hessian scaled gradient; 1e$-$7 in log-normal likelihood (Gould et al., 2010)). To reduce the calculation burden, 5–9 sectors are grouped in addition to the daily increment of COVID-19 cases as the dependent variables in a model.

3.2. Data

Stock data. This study needs daily data enough to calculate dynamic conditional correlations. To this end, Pronexus Inc.'s eol database has been used to obtain the stock market prices and shares issued for the relevant firms. There are 2169 firms that make up TOPIX.

Most of the listed firms’ headquarters are concentrated in Tokyo. Only Tokyo has firm headquarters for every industry, which makes it possible to examine the relationship between the stock return movement and the increment in COVID-19 cases (i.e., number of patients admitted to the hospital, etc.). The First Section of the Tokyo Stock Exchange is primarily composed of large firms, and firms in industries such as manufacturing do not necessarily have their employees concentrated at their headquarters. However, this is one of the few promising methods that can be used in understanding the relationship between the increase in COVID-19 cases and regional business economies.

The objects of analysis in this case are industries with a large number of firms that have been driven to bankruptcy or suspension by the effects of COVID-19, specifically “hotels and inns” (included in the “service industry,” which is one of the 33 sector indices), “restaurants and dining” (included in the “retail business” sector index), “apparel and general retail” (covered by the “textile goods” and “retail industry” sector indices, respectively), as well as “transportation equipment” and the “air transport industry,” which have experienced major reductions in demand. The industries that are subject to analysis do not necessarily align perfectly with the division of the 33 TOPIX sector indices, but they do allow a general understanding to be obtained. In contrast, as an industry that is expected to contribute to resolving the increase in COVID-19 cases, “pharmaceutical firms” (the “medical products” sector index), which develop vaccines and provide testing equipment and are expected to see improved performance, are also considered. The summary statistics are shown in Table 1 . By using square-root-t method and assuming 250 business days in a year, annualizing the standard deviation of stock market returns results in a 27% volatile figure.

Table 1.

Summary statistics pertaining to daily returns for the period from January 6, 2020 to October 16, 2020.

Variable	Obs.	25%	Median	75%	Max	Mean	S.D.
Stock market returns	2169	$-0.014$	$-0.000$	0.013	9.527	$0.000$	0.017
TSE Sector index returns	33	$-0.009$	$-0.000$	0.010	0.113	$-0.000$	0.018

Note: Abbreviations: Obs., observations; S.D., standard deviation. 25% and 75% indicate the first quartile and the third quartile, respectively.

COVID-19 data. In terms of COVID-19 related statistics in Japan, it became possible to collect COVID-19-related data with any degree of accuracy in a compiled form beginning from mid-March. At first, figures were publicly reported according to infection statuses reported from each prefecture based on Article 12 of the Infectious Disease Act and scrutinized by the Ministry of Health, Labor, and Welfare. Since May 8, the reporting method was changed to public reports that compile numbers independently reported by each prefecture. Thus, the data for new COVID-19 cases by prefecture since mid-March are necessary to be put together. The data are publicly available at the site of a firm of J.A.G JAPAN Corp. (J.A.G JAPAN, 2020).

Fig. 2 reveals the number by day of the week pertaining to the new COVID-19 cases by prefecture. Because of the large variation in the number of the tested people by day of the week, the weekly moving average number is instead used to smooth the case curves. Additionally, to conduct correlation analysis, the increments of new COVID-19 cases are calculated corresponding to the daily stock index returns. It is impossible to calculate the daily change rates corresponding to the day without any new cases.

Fig. 2.

New COVID-19 cases by prefecture. Notes: Prefecture No; 1: Hokkaido; 11: Saitama; 12: Chiba; 13: Tokyo; 14: Kanagawa; 23: Aichi; 26: Kyoto; 27: Osaka; 28: Hyogo; 40: Fukuoka.

In terms of large cumulative COVID-19 cases (Fig. 1), we focus on the 10 prefectures, that is, Hokkaido, Saitama, Chiba, Tokyo, Kanagawa, Aichi, Kyoto, Osaka, Hyogo, and Fukuoka,2 and analyze the effect of COVID-19 on regional business economies.

In Hokkaido, initially, infections were concentrated among Chinese tourists, but soon after several clusters, mass outbreaks of patients occurred in Sapporo City which houses the entertainment districts. The number of cases in Tokyo and the three surrounding prefectures (Saitama, Chiba, and Kanagawa) is likewise conspicuous and, needless to say, represents the center of the Japanese economy. Osaka is likewise the commercial and industrial heart of the Kansai region, and large corporations are more concentrated here than in the neighboring prefectures. Additionally, Osaka has many entertainment districts that allow for socialization and contact between people, resulting in a large number of hospitalizations and so on. Kyoto is the most prosperous city among Japanese sightseeing cities. Hyogo is also famous for Kobe City as an international city. Fukuoka has the largest commercial area in Kyushu region.

4. Analysis results and discussion

This section presents the empirical analysis results. Table 2 indicates summary statistics for daily stock index returns by prefecture and industry. Approximately 39% of these, or 854 firms, are headquartered in Tokyo, the second is Osaka with 206, and the third is Aichi with 107. The mean value of composite index returns nationwide is $-$0.052%, whereas the mean value of the index returns for 10 selected prefectures (i.e., 192 sectors) is $-$0.066%. This difference shows that the effect on prefectures with more cases is larger than on the others.

Table 2.

Summary statistics for daily stock indices returns by prefecture and sector.

Pref	1	1	1	1	1	1	1	1	11	11	11	11	11	11	11	11	11	11	11	11	11	11	11	11
Sec	1	2	20	21	22	27	28	29	2	6	10	12	13	14	16	17	18	19	20	21	23	28	29	33
Obs.	1	1	2	3	2	1	7	1	1	2	3	1	4	1	4	5	2	1	2	1	1	8	1	1
Med	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	0.00	0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	0.00
Max	0.08	0.09	0.10	0.07	0.07	0.11	0.06	0.07	0.09	0.12	0.07	0.10	0.04	0.12	0.09	0.07	0.10	0.16	0.09	0.21	0.15	0.06	0.07	0.15
Mean	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	0.00
S.D.	0.03	0.03	0.03	0.02	0.02	0.03	0.01	0.02	0.03	0.03	0.02	0.02	0.01	0.04	0.03	0.02	0.03	0.02	0.03	0.04	0.03	0.01	0.03	0.03
Pref	12	12	12	12	12	12	12	12	12	12	13	13	13	13	13	13	13	13	13	13	13	13	13	13
Sec	2	5	16	17	20	21	23	28	29	33	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Obs.	2	2	1	2	1	2	2	7	3	1	3	5	5	8	63	19	13	19	8	77	21	4	16	11
Med	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.01	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00
Max	0.13	0.08	0.09	0.08	0.10	0.07	0.08	0.08	0.07	0.08	0.06	0.06	0.09	0.06	0.07	0.09	0.09	0.06	0.10	0.06	0.06	0.08	0.09	0.12
Mean	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00
S.D.	0.03	0.03	0.02	0.02	0.02	0.02	0.03	0.02	0.02	0.03	0.02	0.01	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.03	0.03
Pref	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	14	14	14	14	14
Sec	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	1	2	5	6	7
Obs.	14	57	76	17	27	18	161	7	16	8	3	11	19	78	12	21	8	24	5	1	2	3	3	2
Med	$-$0.00	$-$0.00	0.00	0.00	0.00	0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00
Max	0.09	0.07	0.07	0.08	0.06	0.06	0.09	0.08	0.06	0.09	0.10	0.07	0.06	0.06	0.06	0.08	0.07	0.05	0.11	0.07	0.12	0.10	0.09	0.13
Mean	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00
S.D.	0.02	0.02	0.02	0.02	0.02	0.01	0.02	0.02	0.02	0.03	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.03	0.03	0.03
Pref	14	14	14	14	14	14	14	14	14	14	14	14	14	14	14	14	23	23	23	23	23	23	23	23
Sec	8	10	13	14	15	16	17	18	19	20	21	23	26	27	28	33	2	5	6	7	8	10	12	13
Obs.	1	4	8	1	2	11	15	3	1	1	4	4	2	5	11	1	3	4	2	7	2	1	1	13
Med	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	0.00	$-$0.01	$-$0.00
Max	0.07	0.08	0.09	0.09	0.12	0.07	0.07	0.07	0.08	0.07	0.09	0.11	0.09	0.07	0.05	0.22	0.09	0.07	0.07	0.08	0.04	0.10	0.11	0.09
Mean	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00
S.D.	0.02	0.02	0.03	0.03	0.03	0.02	0.02	0.03	0.02	0.02	0.02	0.02	0.03	0.02	0.02	0.07	0.02	0.02	0.02	0.02	0.01	0.02	0.03	0.02
Pref	23	23	23	23	23	23	23	23	23	23	23	23	23	23	23	26	26	26	26	26	26	26	26	26
Sec	14	15	16	17	18	19	20	21	22	23	26	27	28	29	33	2	6	8	10	11	13	16	17	18
Obs.	2	1	12	4	3	1	6	11	2	2	3	9	14	3	1	1	2	2	3	1	1	3	13	2
Med	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00
Max	0.09	0.13	0.10	0.08	0.07	0.13	0.07	0.06	0.09	0.09	0.11	0.09	0.06	0.09	0.10	0.09	0.09	0.06	0.07	0.11	0.12	0.07	0.07	0.13
Mean	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00
S.D.	0.03	0.02	0.02	0.02	0.02	0.03	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.03	0.03	0.03	0.02	0.02	0.03	0.03	0.03	0.02	0.02
Pref	26	26	26	26	26	26	26	26	26	26	27	27	27	27	27	27	27	27	27	27	27	27	27	27
Sec	19	20	21	23	26	27	28	29	32	33	2	5	6	7	8	9	10	11	12	13	14	15	16	17
Obs.	2	2	2	1	1	1	2	1	1	2	7	14	4	5	11	2	34	1	1	7	1	3	2	15
Med	0.00	0.00	$-$0.00	0.00	0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	0.00
Max	0.06	0.10	0.09	0.17	0.10	0.08	0.06	0.08	0.09	0.06	0.06	0.09	0.07	0.08	0.06	0.09	0.07	0.08	0.10	0.08	0.08	0.10	0.06	0.08
Mean	0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	0.00
S.D.	0.02	0.03	0.03	0.06	0.03	0.02	0.02	0.02	0.03	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.03	0.02	0.02	0.02	0.02	0.02
Pref	27	27	27	27	27	27	27	27	27	27	27	27	27	28	28	28	28	28	28	28	28	28	28	28
Sec	18	19	20	21	22	23	26	27	28	29	30	31	33	2	4	5	6	7	8	10	11	12	13	14
Obs.	3	11	1	2	2	7	4	33	22	2	2	1	9	5	1	1	2	1	2	7	2	4	3	5
Med	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00
Max	0.08	0.07	0.07	0.05	0.07	0.09	0.08	0.06	0.05	0.10	0.09	0.10	0.07	0.07	0.14	0.10	0.09	0.11	0.11	0.06	0.07	0.09	0.10	0.09
Mean	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	$-$0.00	0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.01	$-$0.00	$-$0.00	$-$0.00
S.D.	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.03	0.02	0.03	0.02	0.02	0.03	0.02	0.03	0.02	0.03	0.02	0.09	0.02	0.03	0.03
Pref	28	28	28	28	28	28	28	28	28	28	40	40	40	40	40	40	40	40	40	40	40	40	40	40
Sec	15	16	17	19	21	23	26	27	28	33	2	3	5	7	17	20	21	22	23	27	28	29	32	33
Obs.	2	8	5	1	2	2	2	5	5	1	3	1	2	2	3	2	4	2	2	6	6	2	1	1
Med	0.00	$-$0.00	0.00	$-$0.01	0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	$-$0.00	0.00	0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00
Max	0.11	0.09	0.09	0.16	0.09	0.11	0.11	0.07	0.07	0.11	0.06	0.09	0.09	0.10	0.11	0.16	0.09	0.11	0.09	0.06	0.09	0.08	0.08	0.15
Mean	0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	$-$0.00	0.00	$-$0.00	0.00	$-$0.00
S.D.	0.02	0.02	0.02	0.04	0.03	0.02	0.02	0.04	0.02	0.03	0.02	0.02	0.02	0.02	0.03	0.03	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.04

Notes: Abbreviations: Pref, prefecture; Obs., observations; Med, median; S.D., standard deviation. Pref Number: 1: Hokkaido; 11: Saitama; 12: Chiba; 13: Tokyo; 14: Kanagawa; 23: Aichi; 26: Kyoto; 27: Osaka; 28: Hyogo; 40: Fukuoka. Refer to Table A.8 pertaining to Sector Number. Total number of observations is 1476.

Table 3, Table 4, Table 5, Table 6, Table 7 denote the optimization results of DCC multivariate models. Sector names in the Tables are referred to “Short name” column in Table A.8. The brute-force optimization trials are conducted in terms of $p=1,2$ for the ARCH term, $q=0,1$ for the GARCH term, suppressing the constant term in the mean equation, and the assumed distribution for the errors (i.e., Gaussian distribution or t-distribution) in Eq. (3). In case of high volatile increment in cases, $t$-distribution is apt to be fitted and GARCH models are not necessarily optimized (i.e., $q=0$). For example, the models for Tokyo are GARCH(2,1) (i.e., $(p,q)=(2,1)$) are obtained, whereas the models for Osaka are ARCH(2) (i.e., $(p,q)=(2,0)$) are obtained.

Table 3.

Estimation results of DCC multivariate GARCH models (1/5).

Hokkaido (8 sectors)			Saitama (16 sectors)						Chiba (10 sectors)
Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000
	Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$
FAF			Foods			PrecInstr			Foods			Services
cons	0.001	0.196	arch			arch			arch			arch
FAF			L1.	0.427***	0.001	L1.	0.304***	0.009	L1.	0.058	0.495	L1.	0.071	0.447
arch			L2.	0.023	0.633	L2.	0.02	0.782	cons	0.001***	0	cons	0.001***	0
L1.	0.509***	0.002	cons	0***	0	cons	0***	0	Const			LandTrans
L2.	0.161	0.276	Metal			OtherP			arch			arch
cons	0***	0	arch			arch			L1.	0.12	0.334	L1.	0.196	0.297
Foods			L1.	0.052	0.52	L1.	0.263	0.193	cons	0.001***	0	cons	0.001***	0
cons	0.001	0.574	L2.	0.054	0.348	L2.	0.459*	0.051	Machinery			RetailT
Foods			cons	0.001***	0	cons	0***	0	arch			arch
arch			Chemicals			InfoCom			L1.	0.059	0.585	L1.	0.797***	0
L1.	0.108	0.38	arch			arch			cons	0.001***	0	cons	0***	0
L2.	0.181	0.142	L1.	0.267	0.104	L1.	0.034	0.715	EleAppli			Banks
cons	0.001***	0	L2.	0.232*	0.061	L2.	0.085	0.456	arch			arch
InfoCom			cons	0***	0	cons	0.001***	0	L1.	0.053	0.454	L1.	0.282	0.159
cons	0.005**	0.044	Rubber			Services			cons	0.001***	0	cons	0.001***	0
InfoCom			arch			arch			InfoCom			RealEstate
arch			L1.	0.669***	0.002	L1.	0.063	0.438	arch			arch
L1.	0.023	0.766	L2.	0.14	0.103	L2.	0.072	0.351	L1.	0.032	0.401	L1.	0.113	0.418
L2.	0.116	0.344	cons	0***	0	cons	0.001***	0	cons	0.001***	0	cons	0.001***	0
cons	0.001***	0	TransEquip			LandTrans			CaIncr			CaIncr
Services			arch			arch			arch			arch
cons	0.003	.	L1.	0.263*	0.06	L1.	0.347**	0.015	L1.	0.707*	0.069	L1.	0.428	0.118
Services			L2.	0.151	0.278	L2.	0.037	0.652	cons	1.943***	0.003	cons	2.288***	0
arch			cons	0.000***	0	cons	0.001***	0
L1.	0.043	.	IronSteel			RetailT
L2.	0.087	.	arch			arch
cons	0***	0	L1.	0.369**	0.028	L1.	0.093	0.443
EPGas			L2.	0.015	0.784	L2.	0.145	0.239
cons	0.001	0.225	cons	0***	0	cons	0***	0
EPGas			Machinery			Banks
arch			arch			arch
L1.	0.239	0.105	L1.	0.12*	0.086	L1.	0.02	0.701
L2.	0.27*	0.091	L2.	0.008	0.908	L2.	0.365**	0.023
cons	0***	0.004	cons	0***	0	cons	0***	0
WholeT			EleAppli			RealEstate
cons	0.002*	0.069	arch			arch
WholeT			L1.	0.034	0.652	L1.	0.047***	0
arch			L2.	0.062	0.158	L2.	0.108	0.227
L1.	0.672***	0	cons	0.001***	0	cons	0.001***	0
L2.	0.005	0.335	CaIncr			CaIncr
cons	0***	0	arch			arch
RetailT			L1.	0.206	0.14	L1.	0.187	0.172
cons	0.002**	0.038	L2.	0.12	0.494	L2.	0.103	0.505
RetailT			cons	2.754***	0	cons	2.911***	0
arch
L1.	0.052	0.504
L2.	0.127	0.114
cons	0***	0
Banks
cons	0.002	0.119
Banks
arch
L1.	0.403**	0.026
L2.	0.047	0.733
cons	0***	0
CaIncr
cons	0.1	0.416
CaIncr
arch
L1.	0.324	0.134
L2.	0.465**	0.024
cons	0.955***	0.003

***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. L1 and L2 are a first-order lag and a second-order lag, respectively. Sector name refers to “Short name” in Table A.8. CaIncr: cases increment; cons: constant.

Table 4.

Estimation results of DCC multivariate GARCH models (2/5).

Tokyo (33 sectors)
Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000
	Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$
FAF			PulpPaper			EleAppli			AirTrans			CaIncr
arch			arch			arch			arch			arch
L1.	0.111	0.356	L1.	0.106	0.293	L1.	0.022	0.666	L1.	0.123	0.303	L1.	0.358	.
L2.	0.033	0.837	L2.	0.041	0.54	L2.	0.037	0.501	L2.	0.04	0.721	L2.	0.203***	0
garch			garch			garch			garch			garch
L1.	0.058	0.851	L1.	1.53***	0	L1.	0.084	0.787	L1.	0.662***	0.008	L1.	1.272	.
cons	0.001***	0	cons	0	0.442	cons	0.001***	0	cons	0.003***	0	cons	4.586	.
Foods			Chemicals			PrecInstr			WhHaTrans
arch			arch			arch			arch
L1.	0.027	0.718	L1.	0.107	0.111	L1.	0.027	0.497	L1.	0.318*	0.094
L2.	0.274	0.107	L2.	0.056	0.318	L2.	0.021	0.626	L2.	0.152	0.219
garch			garch			garch			garch
L1.	0.486*	0.074	L1.	1.213***	0.01	L1.	0.331	.	L1.	0.633**	0.03
cons	0	0.204	cons	0	0.479	cons	0***	0	cons	0	0.16
Mining			Pharma			OtherP			WholTrade
arch			arch			arch			arch
L1.	0.089	0.294	L1.	0.178	0.496	L1.	0.013	0.947	L1.	0.271**	0.031
L2.	0.003	0.962	L2.	0.168	0.414	L2.	0.029	0.836	L2.	0.277*	0.066
garch			garch			garch			garch
L1.	0.787***	0	L1.	0.237	0.467	L1.	0.806	0.108	L1.	0.122	0.717
cons	0.002***	0	cons	0*	0.091	cons	0	0.466	cons	0***	0.01
OilCoal			Rubber			InfoCom			RetailT
arch			arch			arch			arch
L1.	0.077**	0.034	L1.	0.151	0.113	L1.	0.025	0.442	L1.	0.068	0.446
L2.	0.114***	0	L2.	0.023	0.723	L2.	0.1***	0	L2.	0.206	0.178
garch			garch			garch			garch
L1.	0.258	0.18	L1.	0.35	0.421	L1.	0.751***	0	L1.	0.375	0.218
cons	0***	0	cons	0	0.116	cons	0***	0	cons	0	0.126
Const			TransEquip			Services			Banks
arch			arch			arch			arch
L1.	0.498**	0.024	L1.	0.056	0.268	L1.	0.303**	0.05	L1.	0.214	0.187
L2.	0.065	0.491	L2.	0.093	0.323	L2.	0.079	0.46	L2.	0.015	0.904
garch			garch			garch			garch
L1.	0.363*	0.063	L1.	0.47*	0.073	L1.	0.071	0.838	L1.	0.326	0.278
cons	0***	0.008	cons	0.001***	0	cons	0.001***	0	cons	0*	0.063
Metal			IronSteel			EPGas			SecComFut
arch			arch			arch			arch
L1.	0.404**	0.021	L1.	0.188**	0.045	L1.	0.988***	0.004	L1.	0.126	0.315
L2.	0.029	0.845	L2.	0.004	0.977	L2.	0.115***	0	L2.	0.245	0.304
garch			garch			garch			garch
L1.	0.213	0.406	L1.	0.075	0.851	L1.	0.072	0.163	L1.	0.589	0.251
cons	0**	0.012	cons	0.001**	0.046	cons	0***	0	cons	0	0.489
GlassCera			NonMetals			LandTrans			Insurance
arch			arch			arch			arch
L1.	0.26**	0.026	L1.	0.121	0.152	L1.	0.186	0.344	L1.	0.012	0.926
L2.	0.066	0.52	L2.	0.025	0.696	L2.	0.823**	0.02	L2.	0.018	0.905
garch			garch			garch			garch
L1.	0.191	0.592	L1.	0.764***	0	L1.	0.097	0.39	L1.	0.436	0.34
cons	0**	0.011	cons	0.001***	0	cons	0***	0.001	cons	0.001**	0.013
TextAppa			Machinery			MarineTrans			OtherFB
arch			arch			arch			arch
L1.	0.105	0.413	L1.	0.079	0.109	L1.	0.011	0.928	L1.	0.157	0.162
L2.	0.077	0.541	L2.	0.287***	0.001	L2.	0.278	0.263	L2.	0.262**	0.023
garch			garch			garch			garch
L1.	0.015	0.955	L1.	0.574	0.22	L1.	0.426	0.322	L1.	0.562***	0
cons	0.001***	0	cons	0.001**	0.011	cons	0.001	0.185	cons	0.001***	0
CaIncr			CaIncr			CaIncr			RealEstate
arch			arch			arch			arch
L1.	0.173	.	L1.	0.148	.	L1.	0.685	0.42	L1.	0.199*	0.092
L2.	0.113***	0	L2.	0.104***	0	L2.	0.17	0.682	L2.	0.053	0.839
garch			garch			garch			garch
L1.	1.045	.	L1.	1.037	.	L1.	0.76	0.164	L1.	0.659	0.37
cons	0.522	.	cons	0.325	.	cons	31.185	.	cons	0	0.654

***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. L1 and L2 are a first-order lag and a second-order lag, respectively. Sector name refers to “Short name” in Table A.8. CaIncr, cases increment; cons, constant.

Table 5.

Estimation results of DCC multivariate GARCH models (3/5).

Kanagawa (21 sectors)									Aichi (23 sectors)
Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000
	Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$
FAF			TransEquip			InfoCom			Foods			IronSteel			EPGas
cons	0***	0	arch			arch			arch			arch			arch
Foods			L1.	0.266**	0.021	L1.	0.03	0.424	L1.	0.298	0.159	L1.	0.084	0.406	L1.	0.484**	0.029
cons	0.001***	0	L2.	0.071***	0	L2.	0.067***	0	L2.	0.036	0.783	L2.	0.033	0.692	L2.	0.142	0.481
Const			cons	0.001***	0	cons	0***	0	garch			cons	0.002***	0.001	cons	0***	0.002
cons	0.001***	0	IronSteel			Services			L1.	0.454*	0.085	NonMetals			LandTrans
Metal			arch			arch			cons	0.001***	0	arch			arch
cons	0.001***	0	L1.	0.416***	0.001	L1.	0.303**	0.026	Const			L1.	0.662**	0.044	L1.	0.105	0.549
GlassCera			L2.	0.053	0.597	L2.	0.291*	0.06	arch			L2.	0.207	0.407	L2.	0.441*	0.077
cons	0.001***	0	cons	0.001***	0	cons	0***	0	L1.	0.254	0.21	cons	0***	0	cons	0***	0.003
TextAppa			NonMetals			LandTrans			L2.	0.059	0.601	Machinery			WhHaTrans
cons	0.001***	0	arch			arch			garch			arch			arch
Chemicals			L1.	0.252*	0.062	L1.	0.175**	0.028	L1.	0.709***	0	L1.	0.182	0.215	L1.	0.161	0.386
cons	0***	0	L2.	0.007	0.853	L2.	0.362***	0.003	cons	0.001***	0	L2.	0.078***	0	L2.	0.322*	0.077
CaIncr			cons	0.001***	0	cons	0***	0	Metal			cons	0.001***	0	cons	0***	0
cons	10.709***	0	Machinery			WhHaTrans			arch			EleAppli			WholeT
			arch			arch			L1.	0.297	0.221	arch			arch
			L1.	0.087	0.262	L1.	0.085***	0	L2.	0.135	0.358	L1.	0.148***	0.001	L1.	0.399***	0.003
			L2.	0.054	0.321	L2.	0.144	0.314	garch			L2.	0.02	0.857	L2.	0.037	0.534
			cons	0***	0	cons	0.001***	0	L1.	0.685***	0	cons	0.001***	0	cons	0***	0
			EleAppli			WholeT			cons	0.001***	0	PrecInstr			RetailT
			arch			arch			GlassCera			arch			arch
			L1.	0.295*	0.096	L1.	0.025	0.709	arch			L1.	0.092	0.699	L1.	0.179	0.133
			L2.	0.009	0.897	L2.	0.229**	0.045	L1.	0.015	0.832	L2.	0.031	0.846	L2.	0.008	0.918
			cons	0***	0	cons	0***	0	L2.	0.117*	0.097	cons	0.001***	0	cons	0***	0
			PrecInstr			RetailT			garch			OtherP			Banks
			arch			arch			L1.	0.24	0.345	arch			arch
			L1.	0.016	0.633	L1.	0.168	0.113	cons	0.001***	0	L1.	1.125**	0.034	L1.	0.141	0.14
			L2.	0.309**	0.018	L2.	0.162	0.2	TextAppa			L2.	0.025	0.743	L2.	0.23	0.147
			cons	0***	0	cons	0***	0	arch			cons	0.001***	0	cons	0***	0
			OtherP			RealEstate			L1.	0.449*	0.073	InfoCom			RealEstate
			arch			arch			L2.	0.287	0.146	arch			arch
			L1.	0.19**	0.039	L1.	0.23**	0.037	garch			L1.	0.043	0.755	L1.	0.095	0.264
			L2.	0.108	0.41	L2.	0.274**	0.029	L1.	0.722*	0.065	L2.	0.299	0.195	L2.	0.052	0.514
			cons	0***	0	cons	0.003***	0	cons	0	0.414	cons	0.001***	0	cons	0.001***	0
			CaIncr			CaIncr			Chemicals			Services			CaIncr
			arch			arch			arch			arch			arch
			L1.	0.217*	0.054	L1.	0.272**	0.042	L1.	0.208	0.422	L1.	0.107	0.272	L1.	0.596***	0
			L2.	0.198**	0.039	L2.	0.17*	0.066	L2.	0.243	0.303	L2.	0.105	0.504	L2.	0.418***	0.005
			cons	5.503***	0	cons	5.476***	0	garch			cons	0.001***	0	cons	0.599***	0
									L1.	0.416**	0.044	CaIncr
									cons	0**	0.041	arch
									Rubber			L1.	1.513***	0.001
									arch			L2.	1.042**	0.015
									L1.	0.098	0.573	cons	0.721*	0.098
									L2.	0.057	0.649
									garch
									L1.	0.638***	0.001
									cons	0.004***	0
									TransEquip
									arch
									L1.	0.021	0.814
									L2.	0.041	0.382
									garch
									L1.	0.278	0.39
									cons	0.001***	0
									CaIncr
									arch
									L1.	1.164***	0.006
									L2.	1.046**	0.013
									garch
									L1.	0.089	0.345
									cons	0.429	0.119

***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. L1 and L2 are a first-order lag and a second-order lag, respectively. Sector name refers to “Short name” in Table A.8. CaIncr, cases increment; cons, constant.

Table 6.

Estimation results of DCC multivariate GARCH models (4/5).

Kyoto (19 sectors)						Osaka (27 sectors)
Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000
	Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$
Foods			PrecInstr			Foods			TransEquip			EPGas
arch			arch			arch			arch			arch
L1.	0.427***	0.001	L1.	0.304***	0.009	L1.	0.119	0.144	L1.	0.19*	0.056	L1.	0.429**	0.037
L2.	0.023	0.633	L2.	0.02	0.782	L2.	0.165**	0.043	L2.	0.466**	0.02	L2.	0.301**	0.027
cons	0***	0	cons	0***	0	cons	0***	0	cons	0***	0	cons	0***	0.001
Metal			OtherP			Const			IronSteel			LandTrans
arch			arch			arch			arch			arch
L1.	0.052	0.520	L1.	0.263	0.193	L1.	0.085	0.366	L1.	0.197	0.222	L1.	0.292**	0.028
L2.	0.054	0.348	L2.	0.459*	0.051	L2.	0.034	0.613	L2.	0.073	0.6	L2.	0.62***	0.001
cons	0.001***	0	cons	0***	0	cons	0***	0	cons	0.001***	0	cons	0***	0
Chemicals			InfoCom			Metal			NonMetals			WhHaTrans
arch			arch			arch			arch			arch
L1.	0.267	0.104	L1.	0.034	0.715	L1.	0.257	0.191	L1.	0.085	0.325	L1.	0.214*	0.053
L2.	0.232*	0.061	L2.	0.085	0.456	L2.	0.1	0.213	L2.	0.012	0.835	L2.	0.044**	0.041
cons	0***	0	cons	0.001***	0	cons	0***	0	cons	0.001***	0	cons	0***	0
Rubber			Services			GlassCera			Machinery			WholeT
arch			arch			arch			arch			arch
L1.	0.669***	0.002	L1.	0.063	0.438	L1.	0.507***	0.005	L1.	0.255	0.113	L1.	0.38**	0.012
L2.	0.14	0.103	L2.	0.072	0.351	L2.	0.012	0.859	L2.	0.182	0.272	L2.	0.182	0.131
cons	0***	0	cons	0.001***	0	cons	0***	0	cons	0***	0.005	cons	0***	0
TransEquip			LandTrans			TextAppa			EleAppli			RetailT
arch			arch			arch			arch			arch
L1.	0.263*	0.06	L1.	0.347**	0.015	L1.	0.158*	0.09	L1.	0.042	0.631	L1.	0.052	0.578
L2.	0.151	0.278	L2.	0.037	0.652	L2.	0.08	0.342	L2.	0.116	0.523	L2.	0.138	0.198
cons	0***	0	cons	0.001***	0	cons	0***	0	cons	0***	0	cons	0***	0
IronSteel			RetailT			PulpPaper			PrecInstr			Banks
arch			arch			arch			arch			arch
L1.	0.369**	0.028	L1.	0.093	0.443	L1.	0.128	0.286	L1.	0.257**	0.018	L1.	0.208	0.233
L2.	0.015	0.784	L2.	0.145	0.239	L2.	0.123	0.369	L2.	0.066	0.282	L2.	0.126**	0.019
cons	0***	0	cons	0***	0	cons	0***	0	cons	0***	0	cons	0.001***	0
Machinery			Banks			Chemicals			OtherP			SecComFut
arch			arch			arch			arch			arch
L1.	0.12*	0.086	L1.	0.02	0.701	L1.	0.544***	0.006	L1.	0.072	0.386	L1.	0.061***	0
L2.	0.008	0.908	L2.	0.365**	0.023	L2.	0.112	0.36	L2.	0.021	0.785	L2.	0.01	0.759
cons	0***	0	cons	0***	0	cons	0***	0	cons	0***	0	cons	0.001***	0
EleAppli			RealEstate			Pharma			InfoCom			Insurance
arch			arch			arch			arch			arch
L1.	0.034	0.652	L1.	0.047***	0	L1.	0.147	0.244	L1.	0.105	0.516	L1.	0.156	0.264
L2.	0.062	0.158	L2.	0.108	0.227	L2.	0.283**	0.049	L2.	0.051	0.682	L2.	0.189	0.141
cons	0.001***	0	cons	0.001***	0	cons	0***	0	cons	0***	0	cons	0.001***	0
CaIncr			CaIncr			Rubber			Services			RealEstate
arch			arch			arch			arch			arch
L1.	0.206	0.14	L1.	0.187	0.172	L1.	0.107	0.494	L1.	0.066	0.573	L1.	0.001	0.987
L2.	0.12	0.494	L2.	0.103	0.505	L2.	0.315*	0.079	L2.	0.042	0.502	L2.	0.177	0.102
cons	2.754***	0	cons	2.911***	0	cons	0.001***	0	cons	0***	0	cons	0***	0
						CaIncr			CaIncr			CaIncr
						arch			arch			arch
						L1.	0.615***	0.005	L1.	0.736***	0.005	L1.	0.789***	0.006
						L2.	0.859***	0.006	L2.	0.809***	0.009	L2.	0.922***	0.003
						cons	0.949*	0.093	cons	0.755	0.163	cons	0.519	0.159

***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. L1 and L2 are a first-order lag and a second-order lag, respectively. Sector name refers to “Short name” in Table A.8. CaIncr, cases increment; cons, constant.

Table 7.

Estimation results of DCC multivariate GARCH models (5/5).

Hyogo (21 sectors)									Fukuoka (14 sectors)
t(3), Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000			t(3), Pr $>$ chi2 = 0.000			Gaussian, Pr $>$ chi2 = 0.000
	Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$		Coef.	$P>|z|$	Coef.	$P>|z|$
Foods			Pharma			OtherP			Foods			PrecInstr
arch			arch			arch			arch			arch
L1.	0.229	0.11	L1.	0.134	0.7	L1.	0.128	0.458	L1.	0.83**	0.012	L1.	0.304***	0.009
L2.	0.264*	0.082	L2.	0.183***	0	L2.	0.047	0.79	L2.	0.053	0.66	L2.	0.02	0.782
cons	0***	0	cons	0.001***	0	cons	0.001***	0	cons	0.001***	0	cons	0***	0
OilCoal			Rubber			Services			Metal			OtherProd
arch			arch			arch			arch			arch
L1.	0.513	0.103	L1.	0.156	0.44	L1.	0.203	0.203	L1.	0.025	0.858	L1.	0.263	0.193
L2.	0.031	0.892	L2.	0.111	0.636	L2.	0.013	0.909	L2.	0.066	0.301	L2.	0.459*	0.051
cons	0.001***	0	cons	0.001***	0	cons	0.001***	0	cons	0.002***	0	cons	0***	0
Const			TransEquip			LandTrans			Chemicals			InfoCom
arch			arch			arch			arch			arch
L1.	0.563**	0.045	L1.	0	0.999	L1.	0.249	0.172	L1.	0.587*	0.057	L1.	0.034	0.715
L2.	1.123***	0.005	L2.	0.013	0.957	L2.	0.216	0.257	L2.	0.041	0.826	L2.	0.085	0.456
cons	0**	0.029	cons	0.002***	0	cons	0***	0	cons	0***	0	cons	0.001***	0
Metal			IronSteel			WhHaTrans			Rubber			Services
arch			arch			arch			arch			arch
L1.	0.011	0.94	L1.	0.304*	0.087	L1.	0.127	0.276	L1.	0.887**	0.024	L1.	0.063	0.438
L2.	0.319	0.101	L2.	0.157***	0	L2.	0.192**	0.05	L2.	0.245	0.148	L2.	0.072	0.351
cons	0.001***	0	cons	0.001***	0	cons	0***	0	cons	0.001***	0	cons	0.001***	0
GlassCera			NonMetals			WholeTrade			TransEquip			LandTrans
arch			arch			arch			arch			arch
L1.	0.449*	0.074	L1.	0.061***	0	L1.	1.712***	0	L1.	0.364	0.159	L1.	0.347**	0.015
L2.	0.477*	0.1	L2.	0.025	0.735	L2.	0.001	0.249	L2.	0.026	0.897	L2.	0.037	0.652
cons	0.001***	0.001	cons	0.001***	0	cons	0***	0	cons	0***	0	cons	0.001***	0
TextAppa			Machinery			RetailTrade			IronSteel			RetailT
arch			arch			arch			arch			arch
L1.	0.036	0.829	L1.	0.091	0.61	L1.	0.12	0.347	L1.	0.666*	0.051	L1.	0.093	0.443
L2.	0.233	0.332	L2.	0.169	0.27	L2.	0.035	0.724	L2.	0.036	0.639	L2.	0.145	0.239
cons	0.002***	0	cons	0.001***	0	cons	0***	0	cons	0.001***	0	cons	0***	0
Chemicals			EleAppli			RealEstate			Machinery			Banks
arch			arch			arch			arch			arch
L1.	0.014	0.901	L1.	0.06	0.678	L1.	0.572***	0.008	L1.	0.208	0.155	L1.	0.02	0.701
L2.	0.123	0.39	L2.	0.01	0.934	L2.	0.005	0.956	L2.	0.046	0.767	L2.	0.365**	0.023
cons	0.001***	0	cons	0.001***	0	cons	0.001***	0	cons	0.001***	0	cons	0***	0
CaIncr			CaIncr			CaIncr			EleAppli			RealEstate
arch			arch			arch			arch			arch
L1.	0.737	0.118	L1.	1.017**	0.049	L1.	0.184	0.165	L1.	0.011	0.898	L1.	0.047***	0
L2.	0.557	0.311	L2.	0.427	0.432	L2.	0.121	0.434	L2.	0.214***	0	L2.	0.108	0.227
cons	4.46**	0.033	cons	3.893*	0.052	cons	2.784***	0	cons	0.001***	0	cons	0.001***	0
									CaIncr			CaIncr
									arch			arch
									L1.	1.203*	0.057	L1.	0.187	0.172
									L2.	1.105	0.185	L2.	0.103	0.505
									cons	2.683	0.196	cons	2.911***	0

***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. L1 and L2 are a first-order lag and a second-order lag, respectively. Sector name refers to “Short name” in Table A.8. CaIncr, cases increment; cons, constant.

In terms of robustness check, the header in Table 3, Table 4, Table 5, Table 6, Table 7 reports the assumed distribution for the errors and the Wald test for the goodness of fit of a model against the null hypothesis that all the coefficients in the mean equations are zero, where the null hypothesis is rejected at the 5% level. Additionally, Table 3, Table 4, Table 5, Table 6, Table 7 show the statistical significance for the coefficients on the variables of the models.

Fig. 3 indicates the DCCs between the daily return of prefectural stock index and the daily increment of COVID-19 cases in 10 prefectures. As shown in these panels, the DCCs were negative in almost all sectors and prefectures for the period and the variations were volatile in many sectors and prefectures. Hence, prefecture industries with positive DCCs and some noticeable sectors with negative DCCs are examined as follows:

Fig. 3.

Dynamic conditional correlation between prefectural stock index and the increment of COVID-19 cases.

In Hokkaido, only retail trade industry had slightly positive DCCs from August, 2020 to September, 2020. Regarding the retail industry in Hokkaido, large-scale supermarkets and furniture stores such as Nitori Holdings and Aeon Hokkaido were able to operate even under the declaration of a state of emergency. These firms actually had more customers than usual and their stock prices increased. In Chiba, the DCCs for foods and retail trade industries were positive in a consistent manner. This results from the government's declaration of a state of emergency which thereby increases time spent at home. In Saitama, the DCCs for transportation industry as well as information and communication industry were positive. The former is due to the increasing products sale by mail-order. The latter resulted from the increase for remote work and students’ staying at home.

In Tokyo, the DCCs for information and communication industry as well as electric power and gas industry were positive because of remote work and staying at home. Precision instrument industry's increase reflected the increasing demands in home electrical appliances by remote work and medical equipment by COVID-19 cases. Regarding the pharmaceutical industry in Tokyo, contrary to expectations, the correlation coefficient was negative. The number of COVID-19 cases reached a peak during Golden week (i.e., from the end of April to the beginning of May) and thereafter decreased (Fig. 3), owing to new business styles such as remote work, staggered working hours, online meeting, and suspensions of various types of shops and restaurants.

In Kanagawa, the DCCs for the information and communication industry were positive. In Aichi, the DCCs for foods and warehousing and harbor transportation industries were positive. In contrast, the DCCs for transportation equipment and rubber products industries as well as iron and steel and machinery industries were negative. Because Toyota motors is located in Aichi, its performance reflects the related industries. In Kyoto, foods, iron and steel, land transportation, and information and communication had positive DCCs; especially, land transportation, including SG holdings with a home delivery subsidiary: Sagawa Express, which had a high business demand.

In Osaka, electric appliance, transportation equipment, and information and communication industries had positive DCCs, reflecting the increased demand by remote work and staying at home. By contrast, for the textile production industry, the DCCs were consistently negative, because the number of COVID-19 cases peaked in the middle of the declaration of a state of emergency and hereafter decreased sharply (Fig. 3). However, firms such as Shikibo and Kurabo Industries were fortunate to significantly benefit from the unique increase in demand for masks. Shikibo published test results showing that textile materials treated with their anti-viral processing, called “Flutect,” were effective against COVID-19, thereby gathering the interest of individual investors. Kurabo Industries has responded to government requests not only for masks but also for the production of materials such as medical gowns. In Hyogo, pharmaceutical industry's positive correlation coefficient was as expected. Additionally, foods, nonferrous metals, electric appliances, services, wholesale trade, retail trade is mentioned as industries of positive DCCs. In Fukuoka, foods, iron and steel, land transportation, and information and communication industries had positive DCCs.

5. Conclusion

This study contributed to analyzing the dynamic conditional correlations of COVID-19 cases on the Japanese stock market. First, we developed stock index by prefecture and sector using the data for all domestic common stocks listed in the First Section of the Tokyo Stock Exchange. This stock index represents the regional economic circumstances by sector. Second, investigating the dynamic correlation between the stock index returns as a proxy of performance of firms with their headquarters in major prefectures and the daily increment of COVID-19 cases using DCC multivariate GARCH models, contributes to financial research related to pandemics by allowing the visualization of the effects of COVID-19 on regional firms’ economies.

The financial related data for this study are limited to those of the daily stock market, because it hasn’t been long since the outbreak of COVID-19. Thus, for future studies, the use of corporate financial data, macroeconomic data, and other market data such as credit default swaps is recommended.

Appendix A. TOPIX sector indices list

TOPIX Sector Indices (33 Sectors) are listed in Table A.8 .

Table A.8.

TOPIX sector indices (33 sectors).

Sector No	Sector name	Short name
1	Fishery, Agriculture &Forestry	FAF
2	Foods	Foods
3	Mining	Mining
4	Oil and Coal Products	OilCoal
5	Construction	Const
6	Metal Products	Metal
7	Glass and Ceramics Products	GlassCera
8	Textiles and Apparels	TextAppa
9	Pulp and Paper	PulpPaper
10	Chemicals	Chemicals
11	Pharmaceutical	Pharma
12	Rubber Products	Rubber
13	Transportation Equipment	TransEquip
14	Iron and Steel	IronSteel
15	Nonferrous Metals	NonMetals
16	Machinery	Machinery
17	Electric Appliances	EleAppli
18	Precision Instruments	PrecInstr
19	Other Products	OtherP
20	Information &Communication	InfoCom
21	Services	Services
22	Electric Power and Gas	EPGas
23	Land Transportation	LandTrans
24	Marine Transportation	MarineTrans
25	Air Transportation	AirTrans
26	Warehousing and Harbor Transportation	WaHaTrans
27	Wholesale Trade	WholeTrade
28	Retail Trade	RetailTrade
29	Banks	Banks
30	Securities and Commodities Futures	SecComFut
31	Insurance	Insurance
32	Other Financing Business	OtherFB
33	Real Estate	RealEstate