An empirical investigation of COVID-19 effects on herding behaviour in USA and UK stock markets using a quantile regression approach

This study investigates the effects of the COVID-19 pandemic on herding behaviour among investors in two well-developed markets. Utilizing daily prices of stock indexes from the period of December 5, 2017 to February 28, 2022 for USA and January 9, 2018 to February 28, 2022 for UK, we test for herding behaviour using the quantile regression approach in addition to the OLS model. We found no evidence of herding before the COVID-19 pandemic in both bullish and bearish markets for USA and UK. However, herding incidence was discovered in the USA and UK bullish market during the COVID-19 period. In the bearish market, herding behaviour was only found during the COVID-19 period in USA. The study provides policymakers and investors with information to draw significant measures in their investment portfolio management during crises and pandemics.


Introduction
The world is currently hit by the COVID-19 pandemic, leading to a significant distortion in economic activities. This global crisis has impacted financial markets in many ways (Goodell 2020), even though it is complicated to estimate its impact on economic and social life activities. The COVID-19 pandemic has infected over 624 million people and killed about 6.55 million individuals as of October 24, 2022(WHO 2022. In addition to the loss of lives, the pandemic has affected the performance of public and private sector businesses, declining the economic growth rate of most countries worldwide (Verma et al. 2021). The impact of the pandemic has forced governments across different countries to implement unprecedented interventions to slow the spread of the virus, including closing international borders, instituting national and regional quarantine, and enacting lockdown measures. A study conducted in the USA indicated that the effectiveness of these non-pharmaceutical interventions rapidly affected the labour market negatively; however, the implementation of economic support measures to reduce the negative impact of these interventions became effective shortly but partially eased unemployment in the country (Dergiades et al. 2022). This problem has made the situation a "black swan" following the negative impact of the pandemic on daily human activities and the poor performances of economies worldwide (Yarovaya et al. 2021).
Almost all countries in the world are fighting the COVID-19 disease. However, the expectancy of an ending COVID-19 pandemic is unpredictable as the virus mutates. This undesirable crisis has generated global fear and economic shock to financial activities worldwide. The COVID-19 pandemic has significantly increased US dollar volatility prices, resulting in the broad selling of financial stocks and the generation of a severe and vicious cycle (Chang et al. 2020). According to Ali et al. (2020), countries like the United States of America (USA), United Kingdom (UK), Germany, and South Korea experienced a massive increase in stock market volatility between December 2019 to March 2020, and afterward, due to the pandemic. Economic sectors such as the healthcare system, agriculture, information technology stocks and natural gas have earned very encouraging returns, unlike equity prices for over 1,450 Standard and Poor performing firms in real estate, hospitality management, petroleum and entertainment at the early stages of the pandemic (Mazur et al. 2021). It is interesting to wonder if COVID-19 has a significant effect on herding behaviour, influencing the performance of stock prices in financial markets.
Globally, the behaviour of investors has been widely studied (Alhaj-Yaseen and Ladd 2019; Cakan et al. 2019;Chang et al. 2000;Christie & Huang 1995;Weisberg 2013), especially following current financial market anomalies and resulting volatility and market spill-overs across various financial markets. Due to market stress periods and their impact on stock market movements, one fascinating area that has attracted international research is the assessment of herd behaviour. Herd behaviour is experienced when many act in the same direction at a given period. Nofsinger and Sias (1999) have defined the term as having a group of investors transacting in the same way, in the same direction for a given period (long or short). In financial markets, herd behaviour is observed when investors transact in the same direction or deny their own information and views and are influenced by collective behaviour, despite the possibility of being misled by this group.
This paper investigates the behaviour of investors before and during the COVID-19 pandemic in the USA and UK financial stock markets under different market periods or conditions: bullish, bearish, and normal market periods. Literature has proved that herding is expected not to occur in well-established markets, unlike emerging markets where the presence of inexperienced agents, speculative trading, weak regulations and low liquidity are common and plausible explanations to influence overreaction and herd behaviour (Chang et al. 2000;Pochea et al. 2017).

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Journal of Economics and Finance (2023) 47:517-540 Significant studies on herding have also shown that investors tend to herd during market stress periods which can lead to market volatility (Angela- Maria et al. 2015;Bogdan et al. 2022;Clements et al. 2017;Jirasakuldech and Emekter 2021). During periods categorised by increasing market volatility, herding becomes very persistent. In view of this, a positive relationship could be derived between pandemics and market volatility. In analysing volatility levels in the USA, it was observed that the volatility measured in the early months of 2020 was more than those experienced in October 1987, December 2008, or the ending periods of 1929, attributing the effect to many reasons including, but not restricted to behavioural and policy reactions to the COVID-19 pandemic (Baker et al. 2020). Therefore, an increase in market volatility is experienced during pandemics and financial crises (Diamandis 2008;Ferreruela and Mallor 2021).
This study uses the quantile regression model to comprehensively study investors behaviour in the USA and UK stock markets. The quantile regression model is a robust approach that produces estimates conditioned on the median and can easily account for outliers (Yu et al. 2003). In quantile regression, curves represent the relationship between dependent and independent variables at specified quantiles. Hence, a modified herding behaviour detector as suggested by Chang et al. (2000) is illustrated on several quantiles. The approach provides a more detailed result of investors behaviour as it thoroughly examines the whole market return distribution. Unfortunately, the ordinary least square (OLS) regression model can be limited in explaining investors behaviour as it produces a single model, which may not provide very good information about investors behaviour at some locations of the market distribution.
Several studies have been conducted in recent times where the Cross Sectional Standard Deviation (CSSD) and Cross Sectional Absolute Deviation (CSAD) approaches have been widely used to detect herding behaviour among investors (Duygun et al. 2021;Espinosa-Méndez and Arias 2021b;Ferreruela and Mallor 2021;Susana et al. 2020). In Europe, Espinosa-Méndez and Arias (2021a) investigated whether the COVID-19 pandemic affected capital markets in France, Germany, Italy, United Kingdom and Spain. Results revealed a strong indication that the COVID-19 pandemic potentially drives herding behaviour. The pandemic influenced agents with less information to follow the decision of agents with more information due to fear and uncertainty. Similar results were evident in Australia (Espinosa-Méndez and Arias 2021b) and India (Dhall and Singh 2020), confirming how crises and pandemics cause investors to react or follow the decisions of other investors.
Furthermore, the COVID-19 pandemic offers an exclusive opportunity to explore the behaviour of investors in cryptocurrency and energy sector markets. For instance, Yarovaya et al. (2021) examined whether the COVID-19 pandemic amplifies herding behaviour in four most traded cryptocurrency markets (USD, EUR, JPY and KRW). Their findings showed that herding was experienced on bullish and bearish market days; however, herding did not get stronger during the COVID-19 pandemic periods. On the contrary, in energy stocks, Chang et al. (2020) documented that herding is more likely to occur during extremely low oil price returns. The study attributed the effect to investors unwisely selling their assets as a result of panic in taking risks during the COVID-19 pandemic, creating a vicious cycle.
The ongoing literature on COVID-19 impact on investors' behaviour has been studied across financial stocks, cryptocurrencies and energy stocks. However, there have been limited studies focusing on the COVID-19 effects on well-established markets such as the USA and UK.
Herding impacts financial markets in diverse ways. Typically, the behaviour of investors causes the value of assets to move away from economic principles, therefore making the value of assets biasedly priced. This has primarily been observed to be the cause of financial bubbles throughout economic and financial history. Some of these phenomena are equity bubbles such as The Dutch Tulip Mania in 1634, Japan's Bubble Economy in 1980s, The Dot-com Bubble in the Late 1990s, The Debt of the Roaring Twenties, which caused the Great Depression, and The US Housing Bubble that led to the Great Recession, making the study of this behaviour very significant. The behaviour of investors cannot be determined based on mere theoretical evidence, hence, there is a need for an empirical analysis of this behaviour. This effect is critical in financial decision-making as it establishes behavioural patterns and trends which can tell a particular market's direction.
The remainder of this study is structured as follows: the second section outlines the methodologies and model estimation techniques used to detect herding behaviour. The third section presents the data description and preliminary analysis of the study. The fourth and fifth sections present the main empirical results and discuss possible reasons for herding behaviour in the selected markets, respectively. The conclusion section summarizes the study and provides some suggestions for future research. Christie and Huang (1995) proposed the CSSD model, which best detects herding behaviour if a low dispersion value occurs at the extreme ends of a particular financial market period. This behaviour is typical when investors reject their beliefs and follow market consensus. The CSSD model is widely used in various studies to detect herding behaviour in financial markets. However, the model becomes severely biased in determining herding behaviour when datasets contain outliers (Jirasakuldech and Emekter 2021). Hence, Chang et al. (2000) proposed the CSAD model, which is more robust in detecting herding behaviour at any moment in the financial market. Chang et al. (2000) explain that rational asset pricing models predict a linear relationship between market returns and CSAD. In extreme market conditions, the dispersion between the individual returns and market is expected to decrease or increase at a decreasing rate when investors follow market consensus (Pochea et al. 2017). This implies that the linear relationship between market returns and dispersion no longer holds when investors reject their views and follow aggregate market behaviours. Therefore, the relationship between market returns and CSAD becomes non-linear during significant market movement in market consensus. Hence, the CSAD model proposed to detect herding behaviour during such market movements is expressed as:

Detecting herding behaviour
where and i are parameters of the CSAD model, t represents the error term, | | R m,t | | represent the absolute market return term and R 2 m,t is the square of the market return which detects herding. A negative and statistically significant 2 indicates evidence of herding behaviour. This means that the cross-sectional dispersion of returns increases but at a decreasing rate if 1 is positive and statistically significant.

Herding behaviour in asymmetric market condition
One key factor influencing the future stock market trend is investors emotional state. According to Shiller (2000), investors' confidence drives prices of stocks upward, especially in bullish or up market conditions, influencing other investors to follow the trend. Similar behaviour is observed in bearish or declining markets when fear and lack of confidence push other investors to follow market trends. The up-and-down trend exhibited by investors in financial markets is likely to display asymmetric behaviour during such market movements. To investigate whether herding behaviour is present in asymmetric market conditions, the CSAD model is modified as: such that: A negative and statistically significant 3 and 4 would indicate the presence of herding in up and down markets, respectively.

Herding behaviour before and during COVID-19 period
To examine the impact of COVID-19 on the possible herding behaviour among investors in the USA and UK stock markets, the CSAD model has been specifically modified to include a COVID-19 dummy. The COVID-19 dummy represents when COVID-19 cases were reported in the countries used for this study. The specified model is expressed as: such that: (1) 1 During COVID − 19 periods 0 Before the COVID − 19 outbreak A negative and statistically significant parameter for 3 and 4 would show that investors exhibit herding during the COVID-19 periods and before the COVID-19 outbreak, respectively.

COVID-19 impact and asymmetric effect on herding behaviour
Existing studies (Chang et al. 2000;Christie and Huang 1995;McQueen et al. 1996) have revealed that herding can be experienced during market stress. In this study, circumstances such as asymmetric conditions in financial stock markets and the COVID-19 pandemic, which are possible causes of market spillovers, are considered together. Thus, a model is developed to determine herding behaviour in asymmetric (up and down) market conditions before and during COVID-19. Unlike other studies such as Duygun et al. (2021), Espinosa-Méndez and Arias (2021a), and Espinosa-Méndez and Arias (2021b), where asymmetric effect and COVID-19 were assessed independently, this study jointly determines whether the two proposed information causes investors to herd. The possible COVID-19 impact on investors behaviour in asymmetric market conditions is represented as follows: where conditions expressed in Eqs. 3 and 5 still hold for Eq. 6. A negative and statistically significant parameter for 5 and 7 indicates that investors exhibit herding in up and down markets, respectively, during COVID-19 periods. Also, a negative and statistically significant parameter for 6 and 8 would show that investors herd in up-and-down markets, respectively, before the COVID-19 outbreak in the various countries under study.

Quantile regression model
The quantile regression model is a statistical method usually used in extreme value analysis, and it expresses a dependent variable as a function of explanatory variables (Schaumburg 2012;Yu et al. 2003). This model evaluates the conditional median and other quantiles of explanatory variables (Koenker and Hallock 2001). The quantile regression model estimates the relationship between dependent and explanatory variables by illustrating the model on several quantiles. The approach is more robust to outliers as it considers all data points that may be observed highly away from the model when the ordinary least square (OLS) approach is used.
Quantile regression is a very useful tool in risk modelling as it provides significant insight into empirical analysis in finance. Most studies in finance focus on detecting (6) herding behaviour on the extremes of market distribution. However, some studies on herding may fail to determine the actual behaviour of investors since there is a possibility of detecting herding in other regions when the entire market distribution is investigated. As a result, the quantile regression approach is sufficient in identifying herding behaviour since the model can account for herding incidence at any moment of the market return distribution. The quantile regression model is given as: where y i and x i are the dependent variable and vector of explanatory variables, respectively, and * is a vector of the quantile regression parameters that explain the explanatory variables. In other to minimize the weighted deviations from the conditional quantile, we estimate: where the relationship between the dependent variable y i and explanatory variable x i is characterized by different estimates of the th quantile, is a weighted factor or a check function such that for any ∈ (0, 1) , the check function is explained as: The quantile regression model is used in this study to thoroughly examine the relationship between dispersion measure and market return. For instance, in the estimation of COVID-19 effects on herding in asymmetric behaviour of market returns using quantile ( ) regression, the CSAD t and market returns in Eq. 6 can be expressed in quantiles as: In this study, herding behaviour was estimated at 5%, 25%, 50%, 75% and 95% quantiles. A negative and statistically significant parameter 5, , 6, , 7, and 8, would indicate the presence of herding at the th quantile.

Data
The data used to detect herding behaviour was compiled from the Wall Street Journal and Market Watch websites. The data comprised the daily closing prices of stock indexes in two leading financial stock markets worldwide: S&P 500, Dow Jones Industrial Average and Nasdaq Composite for the USA (Fig. 1), and FTSE 100, FTSE 250 and FTSE AIM UK 50 for the UK (Fig. 1). With the first COVID-19 case reported on January 20, 2020 for the USA and January 31, 2020 for the UK, data spans from December 5, 2017 to February 28, 2022, and January 9, 2018 to February 28, 2022 for USA and UK, respectively. All missing observations in the extracted data were deleted. Hence, an equal number of observations were used before and during the COVID-19 periods for the two countries ( Fig. 1). A total of 1065 observations each were used for all market indexes in the USA and UK. The daily returns of stocks are derived as follows: where R i,t is the returns for stock i on day t , P t is the closing price for stock i on day t and P t−1 is the closing stock price for the previous day before day t . It can be observed in both USA and UK markets that all indexes showed an upward trend, although prices fluctuated with time before the COVID-19 outbreak. However, a sudden downward trend was experienced in all market indexes after the outbreak of the COVID-19 pandemic. Prices began to trend upward after the sudden fall due to the pandemic (Fig. 1). The CSAD method is a modified version of the CSSD, which measures the individual daily stock return dispersion around the average stock market return. The CSAD is an alternative method that detects herding in the entire distribution of the market return. The method is described as a measure of return dispersion and is calculated as: where R i,t is the observed return for stock i on day t , R m,t is the equally-weighted average market return of the portfolio on day t and N is the number of all market indexes in the portfolio.

Descriptive statistics
The descriptive statistics for the average market return and CSAD measure for USA and UK are displayed in Table 1. In the USA market, the highest average market returns (9.180) and CSAD measure (1.587) were observed during the COVID-19 period. However, the lowest average market returns (-13.252) and CSAD measure (0.000) were observed during and before the COVID-19 outbreak, respectively. Also, in the UK market, the highest average market returns (8.280) and CSAD measure (3.212) were observed during the COVID-19 period. Similarly, the lowest average market returns (-9.815) and CSAD measure (0.000) were observed during the COVID-19 period. However, a CSAD measure (0.000) was seen before the COVID-19 outbreak. The lowest and highest market returns obtained in the USA and UK indicate higher market returns fluctuations that reveal price volatility during the COVID-19 event. Moreover, the mean and standard deviation estimates for average market return in both markets under study were higher during the COVID-19 period. This clearly shows a significant variation during the COVID-19 periods for the USA and UK markets, attributing the variation to the effect of the unexpected event (COVID-19 pandemic). This effect is explained by Chiang and Zheng (2010), which describes that the large trading range reported by the mean and standard deviation shows that a market depicts unusual cross-sectional variation resulting from unforeseen events, which is a significant cause of high market volatility. Figure 2 shows the daily average market returns for the USA and UK stock markets with their respective CSAD plots.

Main empirical results
The regression results for USA and UK stock markets, as explained in Eq. 1, are shown in Table 2 1 . As explained in the literature, a negative and statistically significant estimate of 2 indicates herding. Therefore, evidence of herding is experienced in the USA market as 2 is consistent with literature. Even though 2 for UK market was negative, herding was not present since the 2 estimate was statistically insignificant.
Results in Table 3 indicate whether herding behaviour exists in the USA and UK market during bullish ( 3 ) and bearish ( 4 ) market periods 2 . A negative and statistically significant estimate for 3 was achieved for USA and UK stock markets. Similarly, a negative and statistically significant estimate for 4 was only achieved for USA market. The empirical results imply that, investors in USA's market exhibit herding in bullish and bearish market conditions. However, investors in the UK exhibit herding during bullish market periods only. Table 4 reports the effect of COVID-19 on investors actions in the USA and UK markets 3 . Results showed no evidence of herding before the outbreak of COVID-19  Chang et al. (2000) in Eq. 1. Numbers in parenthesis are t-statistics based on Newey and West (1986)  for both USA and UK markets. However, herding was discovered only in the USA market during the COVID-19 outbreak, as 3 is negative and statistically significant. The estimated regression coefficients for Eq. 4 are shown in Table 5. The model was developed to critically assess whether investors herd during asymmetric market conditions considering the effect of the COVID-19 pandemic. Results revealed herding behaviour in the bullish market during COVID-19 periods ( 5 is negative and statistically significant), confirming results achieved for herding in the bullish market (Table 3) during the COVID-19 pandemic (Table 4) for USA, signifying investors emotional response to the pandemic. In addition, herding is experienced in the bearish market of USA during the COVID-19 period ( 7 is negative and statistically significant). In UK, the study only revealed evidence of herding in the bullish market during COVID-19 periods.
The quantile regression analysis provides a more comprehensive study of the conditional distribution of CSAD and market returns. The results from the Quantile regression investigate the presence of herding behaviour under different market trends in the incidence of global market stress (COVID-19). Table 6 represents the outcome of the two stock markets considered. Using the quantile regression to obtain quantile estimates for investors behaviour, evidence of herding is detected in the bullish market during COVID-19 periods at the extreme lower tail ( = 5%) of the return distribution for UK. A similar effect was experienced in the median quantile ( = 50%) and extreme upper tail ( = 95%) of the market return distribution for USA. However, herding prevalence was not present in 5%, 25% and 75% quantiles for USA, and 25%, 50%, 75% and 95% quantiles for UK in the bullish market during the COVID-19 pandemic. In the bearish market and during COVID-19 outbreak, herding was only present in the median percentile ( = 50%) for USA. There was no sign of herding in the bearish market before or during the COVID-19 pandemic for UK. Similarly, in the USA, there was no evidence of herding before the COVID-19 outbreak in bullish and bearish market conditions.  Chang et al. (2000) in Eq. 4. Numbers in parenthesis are t-statistics based on Newey and West (1986) Chang et al. (2000) in Equation 6. Numbers in parenthesis are t-statistics based on Newey and West (1986) Table 6 Quantile results of herding behaviour in asymmetric market condition before and during COVID-19 periods in USA and UK stock markets This table presents the regression results of the modified model suggested by Chang et al. (2000) in Eq. 11. Numbers in parenthesis are t-statistics based on Newey and West (1986)

Herding behaviour
Results from the full sample in Table 2 suggest evidence of herding in the USA stock market. However, the UK stock market showed no indication of herding. The behaviour exhibited by investors in the UK is consistent with previous studies such as (Blasco and Ferreruela 2008;Chang et al. 2000), which provide similar results on the absence of herding in well-developed markets. In well-developed markets, investors have more efficient information in making decisions that do not result in herding. Conversely, to UK results, there was a need to further examine the possible causes of herding behaviour in the USA. In so doing, the study assessed investors behaviour considering the effects of the COVID-19 pandemic in asymmetric market conditions to identify the reason for herding in the USA.

Herding behaviour in asymmetric market conditions before the COVID-19 pandemic
The existence of herding in up and down market trends are usually caused by overenthusiasm and overreaction by investors. In practical terms, investors in a particular market purchase stocks when the market shows an upward trends and sell stocks when the market follows a downward trend. In this study, there was no sign of herding behaviour in up and down market trends before the COVID-19 outbreak (Tables 4, 5 and 6). This results is consistent with research findings of Bogdan et al. (2022) which showed no evidence of herding prior to the COVID-19 pandemic in developed markets. This effect can be attributed to investors taking decisions based on their knowledge and understanding of asset pricing which do not conform to decisions made by other investors in markets free from disturbances. This makes herding extremely difficult to detect, especially in developed market.

Herding behaviour in asymmetric market condition during the COVID-19 pandemic
Existing studies have associated causative factors of herding to confidence, greed and fear expressed by investors in their decision-making in financial stock markets (Duygun et al. 2021;Pochea et al. 2017;Statman et al. 2006). Previous studies such as Hirshleifer et al. (2006) have explained that the behaviour of investors to accept greater exposure to systematic risk or acquire higher average risk-adjusted returns by extensively exploiting information is to earn higher profits. During events that hinder financial and economic stability, investors abandon their personal information and are influenced by financial news and actions of other investors to commit to investment resources and associated aims accessible to them based on their understanding of risk and returns (Talwar et al. 2021). However, this behaviour may be unintentional as investors may trade on the basis of having similar information, which could result in herding behaviour.
Typically, investors panic and sell stocks with the perception that they will not perform well during crises and pandemics. Nevertheless, investors also purchase specific stocks due to their higher demand during unexpected events such as the COVID-19 pandemic. In this study, herding was observed among investors in bullish and bearish markets, and during the COVID-19 pandemic (Tables 3, 4, 5 and 6). The behaviour of investors in USA and UK financial markets during the COVID-19 pandemic is consistent with the research findings of Duygun et al. (2021), which detected herding among investors during the Global Financial Crises in USA and Eurozone equity market. The presence of herding behaviour in the bullish market can be attributed to major stocks such as consumer staples, information technology, healthcare and pharmaceutical products experiencing significant demand during the COVID-19 outbreak. Social distancing protocols and stay-at-home measures implemented in most countries caused food stocks and manufacturing industries to increase in value because of high consumer demand for food products for storage due to an unknown ending date for restrictions during the pandemic. Similarly, information technology products were essential since most workers across the globe worked from home due to the closure of industries and organizations. Healthcare and pharmaceutical products were also in high demand throughout the pandemic. Healthcare workers were classified as "frontline workers" who needed sanitizers (alcohol), personal protective clothes, vaccines and drugs to control the COVID-19 disease as well as other existing diseases. The rise in demand for these products may influence investors to divert more capital into such products since the goal of every investor is to earn huge profits.
Investors in the USA market were uncertain about what the prices of stocks may hold in the subsequent days due to the COVID-19 disease, implying their exuberance of not bearing risk as prices of stocks were increasing or declining in the financial market. The behaviour exhibited by investors in the bearish market might be due to a significant decline in the demand for entertainment, real estate, consumer discretionary, transportation services, and some energy stocks (Nundy et al. 2021). The entertainment industry experienced a heavy loss due to restrictions imposed on them due to the pandemic. Real estate and consumer discretionary products became unwanted since people valued products that could prevent them from contracting the COVID-19 disease and sustain them throughout the pandemic. Lockdown measures also restricted people from travelling, making transportation services and some energy products experience massive losses. These actions posed a significant threat to industries within the entertainment, real estate, consumer discretionary, transportation services and energy sectors. Investors sold their investments because they feared these products may decrease in value in the stock market and were unwilling to suffer losses during the COVID-19 pandemic.

Quantile regression estimates
The variation in the estimates between the two techniques is that the OLS approach focuses on the mean as a measure of location, whereas the quantile regression can compute a family of regression curves, which offers a comprehensive view of the conditional distribution between CSAD and market returns (Alexander 2008;. This aids in detecting the effect of the pandemic (COVID-19) on herding behaviour that may exist at different conditions within the quantile distribution between CSAD and market returns. Figure 3 shows the quantile regression model plot for COVID-19 effects on investors behaviour in asymmetric conditions. A deviation of the estimated relationship between CSAD and market returns from the confidence boundary, as illustrated in Fig. 3 explains the importance of quantile regression in assessing herding behaviour. Hence, this can assist in discovering the specific regions within the return distribution where herding was prevalent.

Conclusion
This research empirically examines the behaviour of investors in the USA and UK financial stock markets in asymmetric market conditions during and before the COVID-19 outbreak. Data used to discover herding was from December 5, 2017 to February 28, 2022, and January 9, 2018 to February 28, 2022 for USA and UK, respectively. First, we implement the model Chang et al. (2000) suggested to find herding behaviour among investors. Herding is only discovered in the USA. However, we further investigate the behaviour of investors by considering asymmetric market conditions and COVID-19 periods. The modification of the CSAD model additionally detected herding in the UK market.
Our study uses the quantile regression analysis in addition to the OLS to observe a complete analysis of herding behaviour. The approach improves on some statistical issues associated with implementing the OLS approach. The study found no evidence of herding before the COVID-19 pandemic for both USA and UK. However, herding incidence was observed during the COVID-19 period. Herding is discovered at the median quantile and extreme upper tails in the bullish market of USA during the COVID-19 period. In the bearish market of USA, herding behaviour was only found at the median quantile during the COVID-19 periods. There was no evidence of herding in the bearish market of UK during the COVID-19 period. However, herding was only discovered in the bullish market at the extreme lower tails during the COVID-19 pandemic for UK.
The consequences of this research findings are of great importance to investors and market regulators as they face challenges that may hinder market efficiency. The existence of herding behaviour in stock markets can cause financial instability and limit the possibility of varied decisions. Regarding the fact that herding behaviour can cause security prices to move away from market equilibrium values which can further fuel price fluctuations in stock exchange (Bouri et al. 2021;Demirer et al. 2015;Nofsinger and Sias 1999), the research findings of this study provide challenges for investors and policymakers in their efforts to monitor investor sentiment and alleviate mis-valuations which may occur in financial markets. From asset pricing point of view, this research provides information about investment sentiment, which could help predict volatility levels and the valuation of derivative contracts. Moreover, investors behavior regarding uncertainty in infectious diseases can be Fig. 3 Quantile plots for COVID-19 effects on herding distribution under asymmetric market conditions. The red horizontal line shows the OLS regression model, the black line with dots is the estimated quantile relationship between CSAD and market returns before and during COVID-19 periods in different market conditions, whiles the red dashed line shows a 95% confidence boundary for the OLS regression model used to study price determination in financial markets and this can help formulate strategies to exterminate downside risk in investors investment portfolios.
To the best of our knowledge, no study has been performed to compare investors actions during and before the COVID-19 outbreak in developed countries (USA and UK financial stock market). Although the study detected herding among investors during market stress periods such as the COVID-19 pandemic, further investigation may be required to identify the type of herding exhibited by investors during the COVID-19 periods. Hence, future studies may focus on whether herding exhibited by investors in developed markets is spurious or intentional during the COVID-19 pandemic.

Appendix
Tables 7,8,9  Chang et al. (2000) in Eq. 1. Numbers in parenthesis are t-statistics based on Newey and West (1986) consistent standard errors. Bold estimates are clear indication of herding. The estimates are statistically significant at 1%, 5% and 10%, represented by ***, ** and *, respectively  Table 8 Quantile results of herding behaviour in asymmetric market condition in USA and UK stock markets This table presents the quantile regression results of the modified model suggested by Chang et al. (2000) in Eq. 2. Numbers in parenthesis are t-statistics based on Newey and West (1986) consistent standard errors. Bold estimates are clear indication of herding. The estimates are statistically significant at 1%, 5% and 10%, represented by ***, ** and *, respectively Quantiles  Table 9 Quantile results of herding behaviour for before and during COVID-19 periods This table presents the quantile regression results of the modified model suggested by Chang et al. (2000) in Eq. 4. Numbers in parenthesis are t-statistics based on Newey and West (1986) consistent standard errors. Bold estimates are clear indication of herding. The estimates are statistically significant at 1%, 5% and 10%, represented by ***, ** and *, respectively Quantiles