Pandemic or panic A firmlevel study on the psychological and industrial impacts of COVID19 on the
Pandemic or panic? A firm-level study on the psychological and industrial impacts of COVID-19 on the Chinese stock market
This study thoroughly investigates the relationship between coronavirus disease 2019 (COVID-19) and daily stock price fluctuations. Using several types of COVID-19 patients as indicators, we explore whether stock prices are significantly affected by the impact of COVID-19. In addition, we take the Chinese stock market as an example and pay special attention to the psychological and industrial impacts of COVID-19 on financial markets. This study makes two contributions to the literature. First, from a theoretical perspective, we show a new quantitative relationship between psychological reactions to the pandemic and stock prices. Furthermore, by pointing out a specific functional expression of the impulse response, we delineate the mechanism of shocks to the stock market. To the best of our knowledge, this is the first time that the impulse of shocks to financial markets has been theoretically calculated. Second, this study empirically estimates the marginal effect of the COVID-19 pandemic on the fluctuation of stock market returns. In addition, by controlling for stock fundamentals, we estimate the diverse reactions of the industrial sector to stock price fluctuations caused by the pandemic. The results confirmed that the COVID-19 pandemic caused panic in the stock market, which not only caused stock prices to fall but also increased the volatility of daily returns. For the shock impulse, we identified the cumulative level of the pandemic variable and its differential increment. As the empirical results show,
Introduction
On November 26, 2021, the newly emerged SARS-CoV-2 variant (B. 1. 1. 529) was officially named "Omicron" by the World Health Organization (WHO), shocking the global stock market. This day was supposed to be the "Black Friday" shopping day in the United States and many other countries. This is because the panic caused a global stock market crash.
This "Black Friday" is a crash of the US stock market that began on February 26, 2020, when the daily infection rate of Coronavirus infection 2019 (COVID-19) began to increase in many regions around the world. Remember. In February 2020, as the number of COVID-19 infected people began to increase in many regions around the world, the US stock market had plummeted, and on June 26, 2020, in the United States and other areas. This scenario was repeated in response to the rapid rise in the recent infection rate. The closely relationship between the stock market performance and the progress of COVID-19 pandemic is attracting attention not only in social policies but also in academic and industry.
In recent decades, several pandemics (H1N1, SARS, Ebola hemorrhage, etc.) occurred, but nothing had a wide, global and huge impact like COVID-19. Therefore, analyzing the economic and financial impact of COVID-19 is a unique contribution to understanding its essential mechanisms and complex relationships. Furthermore, in China, the COVID-19 trends are almost converged, but in many other regions the COVID-19 trend continues to spread, so COVID-19 is a research sample of Chinese stock markets. Studying shocks on financial markets due to the epidemic can also have suggestive results for other local stock markets.
In December 2019, Wuhan became the epicenter of viral pneumonia generated in China, and later called COVID-19 by WHO. To prevent further expansion of infection, the Chinese government took isolation measures in multiple ministries and cities, including Wuju and Shanghai on January 23, 2020. Later, the WHO classified this event into an international public health emergency. Footnote 1 COVID-19 has already threatened hundreds of thousands of residents and has hit China and the world's economy. Restaurants are closed and companies are shrinking. In addition, the growing interest in the spread of pandemics quickly spread to the stock market and had a negative effect. For example, in China, the Shanghai General Index dropped 7. 7 % and the Shenzhen comprehensive index dropped by 8. 5 % due to the pandemic on February 3, after the spring holiday of 2020. To deal with this, the Chinese Securities Director Management Committee (certificate) has stopped selling all securities. Footnote 2
In February, as COVID-19 continued to evolve, the Chinese government introduced several prevention and control measures. However, delaying the return to work and tightening traffic restrictions in China may have a cyclical impact on economic growth. For example, many consumer retail and transportation industries have been heavily affected by the pandemic. According to a report cited by Standard & Poor's Global Ratings, a 10% drop in personal consumption would reduce China's overall gross domestic product (GDP) growth rate by about 1. 2%. Footnote 3 On the other hand, the Spring Festival (Chinese New Year) is the largest population movement in China every year, which may accelerate the spread of COVID-19 and make it more difficult to control. On the other hand, the Spring Festival is also associated with the peak of consumption in that year. However, in 2020, the pandemic dealt a severe blow to the service industry, which was ready to receive tourists, including hotels, transportation, catering, entertainment, and retail. All of these industries suffered heavy losses.
The economic effects of COVID-19 are directly and indirectly affected by restrictions on population mobility. According to data released by the Ministry of Transport of the People's Republic of China, the total traffic volume on the first day of the Lunar New Year in 2020 was down 28. 8% year-on-year. Footnote 4 The number of travelers during the Spring Festival also fell sharply: from 415 million in 2019 to only 152 million in 2020. Footnote 5 The Chinese government suspended domestic group travel and closed nearly 20% of domestic routes due to the sharp decline in passenger numbers. In addition, domestic consumption, one of the most important drivers of the Chinese economy, inevitably suffered a huge loss. According to the China Cuisine Association, 78% of catering enterprises during the Spring Festival in 2020 lost 100% of their revenue compared to 2019. The hospitality and catering industry's sales revenue in the first quarter of 2019 was RMB 423. 4 billion, but it is expected to lose about RMB 210 billion in the first quarter of 2020. Footnote 6
China's stock market has been hit hard in this way. On the first trading day after the Chinese New Year in 2020, the Shanghai Stock Exchange Index fell 8. 5%, with over 3, 000 stocks falling. Similarly, in March 2003, when SARS-CoV cases surged, the Hong Kong Stock Exchange fell about 10%, while the MSCI China Index fell 8. 6%. They rose 14. 7% in one month and 30. 9% in three months. Footnote 8 In 2016, when the Zika virus spread in Brazil, the MSCI Brazil Index fell about 3%. However, one month later it rose 14. 8% and three months later it rose 35. 4%. Footnote 9 In 2018, when the Ebola virus spread in the Congo, the MSCI World Index fell 7% in one month. Footnote 10 Similar events and trends in history show that the impact of major pandemics on stock markets is complex. Comparing COVID-19 and SARS, we can see that the economic cycles and external environments are completely different. Around 2003, China's trade growth with the world was very strong. In 2001, after China joined the World Trade Organization (WTO), the growth rate of total foreign trade rose from 21. 8% in 2002 to 37. 1% in 2003, but fell from 9. 6% in 2018 to 3. 4% in 2019. Therefore, after the SARS epidemic in 2003, the economy recovered quickly. Footnote 11 In 2003, China's investment and industrial growth rates temporarily declined in the second quarter and then turned to an upward trend. The recovery of trade and industry was very strong. Footnote 12
In recent years, the "Black Swan" phenomenon has occurred frequently. Each time, the international stock market, the foreign exchange market, and various product markets react immediately. For example, on June 24, 2016, a referendum was held in the UK to ask the EU member, and the EU withdrawal won with a 51. 9 % vote rate. After the results of the results, the British pound fell more than 10 % a day, plunging to the lowest level in the past 31 years. Footnote 14 On December 5, 2016, a referendum was held in Italy to revise the constitution, and it was rejected, and the country's Prime Minister Matteo Renzi resigned. On that day, the euro fell 1. 4 %, a low since March 2015, and over 2 % in Italy for the first time. Footnote 15
Over the past few decades, China has experienced the Black Swan incident many times in financial markets. The toxic powdered milk, toxic capsules, an ineffective vaccine, and the crisis over financial scams have led to significant losses not only in stock market investors but also in the corresponding food and pharmaceuticals. These events have caused many shor t-term fluctuations to the financial markets, but many domestic investors do not yet know how to identify uncertainties under certain market conditions and how to deal with them. The Black Swan event panicks the world. However, if the general public responds excessively to these events, the entire capital market will be damaged. Therefore, appropriate policy intervention, such as a policy to prevent market liquidity, is required. Many companies are accelerating product innovation and changing business models and organizational management models to cope with the adverse effects of COVID-19 pandemic. Corporate social responsibilities (CSR) are also being studied (Bae et al.) In addition, both the central government and the local government are actively introducing various measures to stabilize growth, and pandemic economic growth. It is expected to make up for the loss. < SPAN> In recent years, the "Black Swan" phenomenon has occurred frequently. Each time, the international stock market, the foreign exchange market, and various product markets react immediately. For example, on June 24, 2016, a referendum was held in the UK to ask the EU member, and the EU withdrawal won with a 51. 9 % vote rate. After the results of the results, the British pound fell more than 10 % a day, plunging to the lowest level in the past 31 years. Footnote 14 On December 5, 2016, a referendum was held in Italy to revise the constitution, and it was rejected, and the country's Prime Minister Matteo Renzi resigned. On that day, the euro fell 1. 4 %, a low since March 2015, and over 2 % in Italy for the first time. Footnote 15
Over the past few decades, China has experienced the Black Swan incident many times in financial markets. The toxic powdered milk, toxic capsules, an ineffective vaccine, and the crisis over financial scams have led to significant losses not only in stock market investors but also in the corresponding food and pharmaceuticals. These events have caused many shor t-term fluctuations to the financial markets, but many domestic investors do not yet know how to identify uncertainties under certain market conditions and how to deal with them. The Black Swan event panicks the world. However, if the general public responds excessively to these events, the entire capital market will be damaged. Therefore, appropriate policy intervention, such as a policy to prevent market liquidity, is required. Many companies are accelerating product innovation and changing business models and organizational management models to cope with the adverse effects of COVID-19 pandemic. Corporate social responsibilities (CSR) are also being studied (Bae et al.) In addition, both the central government and the local government are actively introducing various measures to stabilize growth, and pandemic economic growth. It is expected to make up for the loss. In recent years, the "Black Swan" phenomenon has occurred frequently. Each time, the international stock market, the foreign exchange market, and various product markets react immediately. For example, on June 24, 2016, a referendum was held in the UK to ask the EU member, and the EU withdrawal won with a 51. 9 % vote rate. After the results of the results, the British pound fell more than 10 % a day, plunging to the lowest level in the past 31 years. Footnote 14 On December 5, 2016, a referendum was held in Italy to revise the constitution, and it was rejected, and the country's Prime Minister Matteo Renzi resigned. On that day, the euro fell 1. 4 %, a low since March 2015, and over 2 % in Italy for the first time. Footnote 15
Over the past few decades, China has experienced the Black Swan incident many times in financial markets. The toxic powdered milk, toxic capsules, an ineffective vaccine, and the crisis over financial scams have led to significant losses not only in stock market investors but also in the corresponding food and pharmaceuticals. These events have caused many shor t-term fluctuations to the financial markets, but many domestic investors do not yet know how to identify uncertainties under certain market conditions and how to deal with them. The Black Swan event panicks the world. However, if the general public responds excessively to these events, the entire capital market will be damaged. Therefore, appropriate policy intervention, such as a policy to prevent market liquidity, is required. Many companies are accelerating product innovation and changing business models and organizational management models to cope with the adverse effects of COVID-19 pandemic. Corporate social responsibilities (CSR) are also being studied (Bae et al.) In addition, both the central government and the local government are actively introducing various measures to stabilize growth, and pandemic economic growth. It is expected to make up for the loss.
While various kinds of economic shocks, especially shocks to the stock market, are well known, the COVID-19 pandemic has had a huge and widespread impact, bringing several new challenges. As we have seen, the response of each industry to the pandemic is diverse, and the mechanism of transmission of such shocks remains mysterious. When psychological effects are added to this mechanism, the relationship becomes even more difficult to understand. Without a doubt, the COVID-19 pandemic is a disaster, and new insights are needed to understand many things that we thought were already almost known. In this study, we therefore dig deeper into the specific mechanisms by which the pandemic affects stock prices and volatility.
Do psychological issues arising from COVID-19 affect the stock market? At present, this is unclear. Will news about the fight of medical workers against COVID-19, as well as recovery and mortality rates, affect stock market performance? This is also unclear. Of particular note is whether the number of suspected COVID-19 infections, together with quarantine activities, will affect investor behavior in the stock market. At present, there is little evidence in the literature to answer this question.
In this study, we take China as an example to analyze in depth the impact of the COVID-19 outbreak on the stock market. This is a very difficult problem to tackle, because everything is intertwined at that time. Therefore, we must isolate the impact of the COVID-19 pandemic from other possible influencing factors. In this study, we thoroughly investigate the relationship between COVID-19 and daily stock price fluctuations. We use different types of COVID-19 patients as indicators to explore whether stock prices are significantly affected by COVID-19. In addition, we use a sample of the Chinese stock market to pay special attention to the psychological and industrial impacts of COVID-19 on financial markets.
Literature review
Shocks to the stock market
This study makes two contributions to the literature. First, it is a theoretical contribution in the sense that it shows a new quantitative relationship between psychological reactions to the pandemic and stock prices. In addition, it depicts the mechanism of shocks to the stock market by pointing out a specific functional expression of the impulse reaction. To the best of our knowledge, this is also the first time that the impulse of shocks to financial markets has been theoretically calculated. Second, this study empirically estimates the marginal effect of the COVID-19 pandemic on the fluctuation of stock market returns. By controlling for stock fundamentals, this study estimates the impact of the diverse responses of industries to the pandemic on stock volatility as well. Finally, this study provides important policy implications regarding stock market volatility and the resumption of industrial activities.
Black Swan events and the financial market
This paper is structured as follows. Section 3 describes a new theoretical framework linking the psychological and industrial effects of COVID-19. Section 4 presents the data of the study. Section 5 presents an empirical discussion using factors used as variables that may affect daily returns of stock market prices according to the theory. In Section 6, we discuss some important issues regarding the empirical methodology and the corresponding results. Finally, in Section 7, we draw our conclusions.
The literature on stock market volatility is vast (Barsky and Long 1993; Barlevy and Veronesi 2003; Engle et al.). One of the most important drivers of volatility is shocks to the stock market. The literature also examines shocks to other financial markets, such as aggregate shocks (Hahn et al. 2020), exports (Amiti and Weinstein 2011; Caliendo et al. 2017; Kim et al. 2018; Kong and Prinz 2020), dual-earner couples (Crawford et al. 2019), personal financial assets (Bleakley and Ferrie 2016), and exchange rates (Eichenbaum and Evans 1995). Moreover, this line of research also targets information shocks (Hung et al. 2015; Berger et al.). Even investment banking careers have been linked to stock market shocks (Oyer 2008).
Some scholars have discovered that uncertainty shocks are consumed, invested, productivity, and volatility in the stock market regarding shocks related to the Black Swan event (Baudry and Portier 2004; Berger et al. 2015; basu and bundick 2017). The reaction of financial and financial policy on the stock market has been discussed (Hassett and MetCalf 1999; Muelle 2001; Rigobon and Sack 2003; Christiano et al. 2005; Fratzscher and RIETH 2019). In addition, the reaction of the stock market to political shocks is also an important factor (Kaustia and Torstila 2011; Wagner et al.) The existence of wealthy shocks in the stock market (Gormley et al.) It turned out that both 2011) and credit shocks (Khan and Thomas 2013) are important. In addition, FORBES and RIGONBON (2002) indicates that financial transmission will significantly increase the inte r-market link after shocks and financial crisis in one country. Finally, it is known that social movements also affect the stock return (King and Soule 2007).
In order to further investigate the reaction of the stock market to the Black Swan event, research is being conducted to explore the effects of these events consisting of economic events, social events, terrorism, and natural disasters.
Other common types of influential shocks
First, a study that investigates stock prices to major international terrorism, has shown that most of them have a gentle or negative effect on the stock price in the long term. The stock market recovers quickly, although there is a major impact in the short term. The only event that had a significant impact was 9. 11 (Nikkinen et al. 2008; bronrn and derwall 2010; Hanabusa 2010; Liargovas and Repousis 2010; Zopiatis et al. 2017). KAROLYI and MARTELL (2005) indicate that more advanced countries are related to a greater negative stock price response.
In addition, scholars discuss the impact of natural disasters on the stock market. Baker and Bloom (2013) is investigating the impact of natural disasters, terrorism, and unexpected political shocks on economic growth. They have found that financial markets are not developed and the labor markets have the largest influence. Some researchers do not recognize a significant impact on market returns (WORTHINGTON 2008) and show negative returns only on the day of the event (Caporale et al.) And natural disasters that cause severe economics. Some researchers have a negative stock price response (YAMORI and KOBAYASHI 2002; Wang and Kutan 2013; TAVOR and TEITLER-REGEV 2019). Worthtington and Valadkhani (2004) analyzes natural disasters in various genres and has revealed that the effects of natural disasters have different impacts on the Australian stock market.
The shock of COVID-19 to the economy and the financial markets
In addition, major news around the world is a factor that affects the stock market. Students who analyze the reactions of the stock market to the world news believe that the main news of war, politics, monetary policy, and sudden public scandals will affect stock prices (Zhou and Zhao 2013) ) The difference in total return may be due to various types of news (Cutler et al. 1989). Stock prices can also be influenced by stock trading activities. Robinson and Bangwayo-Skeete (2017) indicates that stock prices in markets where transactions are not active do not respond to most of the major news. In this series of documents, major events in the stock market, such as the relevance of Poison Pill and stock market reactions, are being studied (Rhee and Fiss 2014; DoroBantu et al.).
In addition, energy accidents that cause fluctuations in the stock market are being considered. From 1907 to 2007, the stock market generally did not seem to have responded significantly to major energy accidents (Sovacool et al. 2008). SCHOLTENS and BOERSEN (2011) have concluded that stock prices did not have significant reactions to environmental accidents of energy companies that occurred between 1907 and 2007, and support Sovacool and others.
COVID-19 pandemic is developing very rapidly, and academic understanding of the complex impact on economic and financial markets is progressing.
The term “COVID-19 shock” has now been formally proposed in finance academic circles (Caballero and Simsek 2021). The pandemic has caused shocks to technology, finance, the economy, and government policies (Gu et al. Satif et al. (2021) described the possible impact of COVID-19 on bilateral trade. It has shown a negative trend in labor supply and demand, hitting the service industry and raising further discussions on security and unemployment prevention in all sectors (Ceylan et al.)
We can also see whether the COVID-19 pandemic has changed the relationship between oil prices and stock returns by observing it. Preliminary insights have been gained from the impact of the pandemic on financial markets, namely stock returns. Inspired by the cash flow hypothesis, an increase in production costs leads to an increase in oil prices, so that cash flow dividends decrease and, as a result, stock returns also decrease. Zhang et al. (2021) demonstrated that COVID-19 reduced the impact of oil prices on stock returns by about 89. 5%.
Researchers have studied the impact of COVID-19 on financial markets from several perspectives (Gu et al. 2020, Heyden and Heyden 2020, Apostolakis et al. al. 2021, Liu et al. 2021, Nigmonov and Shams 2021). Existing literature shows that COVID-19 affects stock markets. Some indicate that the total number of infected people and deaths has a negative impact on stock market returns (Al-Awadhi et al. 2020; Ashraf 2020a; Zhang et al. 2021), while others indicate a larger long-term impact on the most affected countries (Sharma et al. 2021). However, the impact on China's stock market is shown to be short-term as government policies are implemented (Hu et al.). The short-term reaction of global stock markets during the COVID-19 pandemic has also been examined (Heyden and Heyden 2020; Rahman et al.). COVID-19 hits solar energy stock prices in both the short and long term, but the impact is less significant in non-OECD countries (Wei et al.).
Research gap
Theoretically, investors are likely to overreact and adopt a conservative approach to investment decisions due to COVID-19 (Shear et al.). Huber et al. (2021) show that increased risk aversion during the pandemic may lead to reduced investment despite lower risk in experimental assets. However, Angrisani et al. (2020) believe that the increase in risk premia during the pandemic is due to changes in beliefs and not to changes in market participants' risk appetite. As the disease has caused a sustained decline across the world, some scholars have analyzed the sentiment of panic and constructed a global COVID-19 fear index to use as an indicator for investment decisions (Haroon and Rizvi 2020; Papadamou et al.). The sustained decline in global markets leads to financial risk spillovers that devastate the entire financial system through negative returns, increased uncertainty, and increased volatility (Ashraf 2020b; Goodell and Goutte 2020; Sharif et al.). Spillover effects during the COVID-19 pandemic have been examined, including spillovers between financial technology stocks and other financial assets (Lan et al. 2021) and volatility spillovers between European stock markets (Aslam et al. 2021; Youssef et al. 2021).
Finally, the absence of management in the study of financial crises is unusual (Starkey 2015). Indeed, crisis management is an important part of business management (Pearson 2010; Bundy et al. 2017), especially during the global financial crisis (DesJardine et al.). Here, we attempt to add to the existing scholarship on this issue.
Theoretical framework
To the best of our knowledge, very few studies have been conducted on pandemic-induced shocks to financial markets, and most of them are empirical. Therefore, the theoretical mechanism of why and how a pandemic causes a shock in the stock market remains unclear. Therefore, this study contributes to this literature by revealing the hidden mechanism of the shock and by applying it empirically to financial markets, taking the Chinese stock market as an example. Unlike the existing literature on similar topics, this study also makes a great theoretical contribution by depicting the impact mechanism of the pandemic shock on the stock market through a detailed mathematical model. Moreover, the empirical part of this study employs comprehensive examination and regression.
Here, we classify influential factors into three categories. The first is fundamentals, which include the macroeconomic situation and the basic business conditions of listed companies. The macroeconomic situation reflects the overall business performance of listed companies and determines the further development of listed companies. The macroeconomic situation is closely related to listed companies and their corresponding stock prices. The basic business conditions of listed companies include financial status, profitability, market share, management system, etc.
The second is psychological factors, which are mainly reflected in stock price fluctuations. If people feel panicked, they will have a negative attitude toward the stock market and stock prices will fall. However, if it turns out that it was an overreaction to the pandemic or the recovery rate increases, confidence in the stock market will be restored and stock prices will recover.
The third category is industry factors. From our perspective, different industries have different impacts on stock price fluctuations. Theoretically, after the outbreak of COVID-19, there was an urgent need for medical supplies, which led to an increase in stock prices in health-related industries. On the other hand, the reason why stock prices in entertainment-related industries fell was because the opportunities to go to movie theaters, clubs, theme parks, etc. were drastically reduced.
So, we introduce the following equation:P = f(Fund, Psy, Ind).$$
Here, P is the firm-level stock price, f(-) is a function whose details are not yet known, Fund is the firm-level fundamentals, Psy is the psychology factor, and Ind is the industry factor. We assume that all these functions are continuous and twice differentiable.
By differentiating this function with respect to time, we get the following result:
Since our main research interest is the rate of change of firm-level stock prices, we divide both sides of the equation by P:Here, GP
is the growth rate or rate of change of firm-level stock prices.< \bullet >The right-hand side of the equation shows that firm-level fundamentals do not change much in the short term and are not reflected in public company reports. Therefore, for simplicity, we substitute (1) into (2).
= 0\). For Psy and Ind, however, things are more complicated. From the facts during the pandemic, we assume that: Psy = Psy(Epi).Ind = Ind(Epi).$$.
Here, the EPI represents a COVID-19 pandemic. When these two equations are differently different from time, it becomes as follows:(EPI) \ Mathop \ Limits^
When the equation (6) and the equation (7) are assigned to the equation (3), and the terms are sorted, the following is as follows.
Here, the logarithm on both sides of the ceremony can be obtained:
Thus, this formula has a very close meaning in empiricality. However, many related functions are still unknown and cannot be applied directly to empirical analysis.<<\mathop P\limits^< \bullet >Furthermore, ⓐ (y = ⓐln (ⓐfrac)<\prime>& gt; & gt;) ⊖) ⊖)
(EPI) Differences. )<\partial Y> <<\partial Ind^<\prime >Get.<(EPI) & gt; & gt;. $k is obtained.
This formula is the second floor derivative to Y's Indies, and the following relationship can be obtained:(EPI)
Here, we will integrate both sides of the formula (10):Here c1
Is an integral constant.
When the formula (11) and the formula (12) are combined, it will be as follows:<<\ln (Psy^<\prime >(EPI) & gt; & gt; = \ Frac<\prime >(EPI) + Ind^<(EPI). $ $
This formula is the second floor derivative to Y's Indies, and the following relationship can be obtained:(Epi)). \\.
This formula is the second floor derivative to Y's Indies, and the following relationship can be obtained:(Epi). \\ psy
In order to determine the key function of PSY (EPI), it is necessary to integrate the formula (16) on both sides as follows:<\prime\prime>(EPI)) & gt; & gt;<\prime\prime>(EPI) + Ind^
Here, we will integrate both sides of the formula (10):Here c2And C3
Is the integral constant in these steps. When the formula (18) is assigned to the equation (17), it becomes as follows:
After some complicated derivation (see Mathematical Appendix for details), the following will be obtained:
Equation (20) provides a new perspective to draw a quantitative relationship between stock prices and pandemic. If the specific function of PSY and India is a secondary format, it is reasonable to assume that the secondary condition of the typical secondary function is linear, so the secondary term is constant.
When both sides of the formula (20) are differented, they are as follows.
Next, if the logarithm is taken on both sides of the equation (21), the following will be as follows.
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