The economic downturn during the COVID-19 pandemic has resulted in a significant decline in the stock market. Some of the previous studies have examined the impacts of COVID-19 epidemic on the downside risks of stock market. One of the main conclusions is that, in general, the occurrence of COVID-19 caused a direct and significant drop in stock prices (Baker, Bloom, Davis, Kost & Sammon et al. (2020) , Al-Awadhi, Al-Saifi, Al-Awadhi & Alhamadi (2020), Ramelli & Wagner (2020) , Zhang, Hu & Ji (2020) ). While from the perspective of volatility risk, COVID-19 will significantly increase the volatility of the stock market (Baek, Mohanty & Mina (2020) , Onali (2020) , Papadamou, Fassas, Kenourgios & Dimitriou (2020) ). Different from the existing literature, this paper focuses on stock market crash risk. Mazur, Dang & Vega (2020) and Ziemba (2020) study the US stock market crash during the Covid-19 period. However, they treat the crash risk as the extreme downside volatility.
In our paper, following Chen, Hong & Stein (2001) and Kräussl, Lehnert & Senulytė (2016) , we measure the crash risk by using the conditional skewness of the market return. It is a better way to simultaneously capture the asymmetry and negative extremes of the crash risk (Kim, Li & Zhang (2011) , Kim, Li & Zhang (2011b) , Wen, Xu, Ouyang & Kou (2019) ). And then, we conduct an empirical analysis to consider the impacts of the economic policy uncertainty on the crash risk of the US stock market.
In fact, in the early days of the epidemic, the US stock market has experienced a plunge. From Figure 1 , we can see that the stock market has suffered a severe impact from COVID-19. The S&P 500 Index plummeted by one-third in a short period: from 3380 points on February 14, 2020, to 2,237 points on March 23, 2020. Our subsequent empirical results further confirm this intuitive conclusion that COVID-19 negatively affects stock market crash risk. We find that the severity of the epidemic, proxied by the growth rate of the daily new confirmed cases, does have a significant negative impact on the conditional skewness of the market return, i.e., the crash risk of stock market. It is also consistent with Liu, Duc Huynh & Dai (2020)'s work on the Chinese market, who find that the epidemic increases the crash risk of stock market.
However, we have noticed that although the number of daily confirmed cases in the United States continued to rise in the following period, stock prices gradually returned to the level before the epidemic, and it even hit a new high in the past three years. It shows that the severity of the epidemic alone is not enough to explain the stock crash. 2 0 1 7 -0 1 -1 0 2 0 1 7 -0 4 -0 6 2 0 1 7 -0 7 -0 3 2 0 1 7 -0 9 -2 7 2 0 1 7 -1 2 -2 1 2 0 1 8 -0 3 -2 1 2 0 1 8 -0 6 -1 5 2 0 1 8 -0 9 -1 1 2 0 1 8 -1 2 -0 6 2 0 1 9 -0 3 -0 6 2 0 1 9 -0 5 -3 1 2 0 1 9 -0 8 -2 6 2 0 1 9 -1 1 -1 9 2 0 2 0 -0 2 -1 8 2 0 2 0 -0 5 -1 3 2 0 2 0 -0 8 -0 7
Daily New Confirmed Cases (Left Axis) S&P 500 (Right Axis)
We argue that one of the reasons for this situation is the reduction of uncertainty in economic policies, which is believed to have a wide-ranging impact on economic and financial activities (Gulen & Ion (2016) , Brogaard & Detzel (2015) , Dai, Xiong & Zhou (2020) , Wen, Zhao, Zhang & Hu (2019) ). As we can see from Figure 2 , during the epidemic, economic policy uncertainty (EPU) and stock prices show the opposite trend. In the early stages of the epidemic, as the uncertainty caused by COVID-19 rose sharply, stock prices have also suffered a crash. However, with the successive government measures designed to deal with the epidemic, economic policy uncertainty has gradually decreased, which is what we believe a fundamental reason for the stock market rebound. In other words, we believe that the reduction of economic policy uncertainty during the epidemic will help reduce the crash risk of stock market. Our findings also support this hypothesis. We find that the conditional skewness reacts negatively to the change rate of economic policy uncertainty, indicating that the reduction of economic policy uncertainty can effectively reduce the crash risk of stock market. We further find that this effect only exists during the epidemic, and it is not significant during regular periods. It may mean that the stability of economic policies plays a more critical role in reducing the extremely negative impact of major crisis events. 2 0 1 7 -0 1 -1 0 2 0 1 7 -0 4 -0 6 2 0 1 7 -0 7 -0 3 2 0 1 7 -0 9 -2 7 2 0 1 7 -1 2 -2 1 2 0 1 8 -0 3 -2 1 2 0 1 8 -0 6 -1 5 2 0 1 8 -0 9 -1 1 2 0 1 8 -1 2 -0 6 2 0 1 9 -0 3 -0 6 2 0 1 9 -0 5 -3 1 2 0 1 9 -0 8 -2 6 2 0 1 9 -1 1 -1 9 2 0 2 0 -0 2 -1 8 2 0 2 0 -0 5 -1 3 2 0 2 0 -0 8 -0 7 
This paper adds to the extant literature in several ways. First, unlike existing research related to COVID-19, which mainly involves stock market returns and volatility, we focus our attention on the stock market crash risk. Return and volatility are the first and second moments of return distributions, respectively, and we use conditional skewness to measure the crash risk, thus paying attention to the third moment of stock market returns. Second, we confirm the conclusion that COVID-19
will increase the crash risk in the US stock market, which is initially drawn by Liu, Duc Huynh & Dai (2020) in the Chinese stock market. We further find that the increase in the number of confirmed cases can only explain the worsening crash risk of stock market in the early stages of the epidemic. However, it cannot explain why in the middle and late stages, when the number of cases continues to increase, the crash risk will decrease instead. Therefore, the third contribution of our study is that we find that the stability of economic policies can provide a specific explanation for this puzzle. Our findings show that high economic policy uncertainty will increase the crash risk of the US stock market. In contrast, low uncertainty of economic policies can help reduce the likelihood of stock market crashes, especially during the extreme crisis of the COVID-19 global pandemic. More importantly, this paper has important policy implications. Just as our findings show the importance of economic policy stability in reducing the crash risk, we suggest that when facing major crisis events, policymakers should introduce event-response policies as soon as possible. It is helpful to reduce the adverse effects of economic policy uncertainty.
To measure the severity of the COVID-19 pandemic, we use the logarithmic growth rate of daily confirmed cases (rCases) in the US as the proxy. The initial dataset is from Our World in Data (https://ourworldindata.org/coronavirus). We also set a dummy variable, D_epid, to divide the whole sample into two periods: beforeand after-the epidemic. We set the value of this dummy is one after January 21, 2020, the date when the first case of COVID-19 in the United States is confirmed, and zero otherwise.
We use three economic policy uncertainty related indices based on daily newspaper coverage in the United States in our paper, all of which are proposed by Baker, Bloom & Davis (2016) 
Where t r is the logarithmic return of the S&P 500 index, retrieved from Yahoo Finance (https://finance.yahoo.com/), and t h is a classical GARCH(1,1) structure.
There are two residual forms in the model: the residual t  and the standardized residual t  .
1 t I  represents the information set at the time t. t s is the conditional skewness process and it is the key part in our model. In addition to the constant term, it consists of two parts: the autoregressive part and the lagged return shocks part. León, Rubio & Serna (2005) and also Kräussl, Lehnert & Senulytė (2016) , both of them use the Gram-Charlier series expansion to estimate the model. We will follow their works, and the difference is we truncate at the third moment. Table 1 gives the estimation results of the GARCH-S model. In general, most of the coefficients are significant, suggesting that the model can fit the data well. We focus on the conditional skewness process. As expected, the coefficient of the shock to skewness is positive and significant (0.0361 with a z-statistic 7.2590) and the coefficient of lagged skewness is also positive and significant (0.1544 with a z-statistic 5027.295). The structure of the conditional skewness is very similar to that in the variance case, indicating that the skewness is autocorrelated and persistent.
All the data in our paper is daily, and the sample period is from January 2017 to
August 2020. Table 2 shows the descriptive statistics of the variables we used, and all variables are stationary. Notes: (1) ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The z-statistics are presented in the brackets.
(2) Due to the high non-linearity of the likelihood function, we use the starting values of parameters estimated from the simple GARCH (1,1) model. 
We use the simple time series model to conduct our empirical analysis. The dependent variable is the stock market crash risk, measured by conditional skewness estimated from the GARCH-S model. We have two main explanatory variables. The first is the logarithmic growth rate of daily confirmed cases, rCases, and the logarithmic change rate of the Economic Policy Uncertainty Index for the United States, rEPU. The alternative variables for rEPU will be used in the robustness checks. The primary model is specified as:
where p and q will be determined by the AIC or SC information criterion.
In order to examine the potentially different roles that EPU may play during the epidemic, we add the interaction term of D_epid and rEPU in our model:
We start our empirical analysis by only considering the explanatory variable rCases, and the results are shown in Table 3 . As we expected, all the coefficient of 1 t rCases  is negative and significant at 1% level, indicating the severity of the epidemic has a direct negative impact on the crash risk of the US stock market. This finding is also consistent with Liu, Duc Huynh & Dai (2020)'s work in the Chinese stock market. Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets.
We further consider the role of economic policy uncertainty in affecting the crash risk in this section. We first only add the explanatory variable rEPU into our model, and the results are reported in Table 4 . We can see that all the coefficients of t rEPU except that in column (4) is negative and significant at 5% level. It is consistent with our exception that increased economic policy uncertainty will increase the possibility of a stock market crash. In other words, improving the stability of economic policies will help prevent a stock market crash.
When considering the influence of rCases and rEPU at the same time, we use the Akaike information criterion (AIC) and Schwarz criterion (SC) to determine the lag length of the variables. The results are shown in Table 5 . Although the optimal lag lengths obtained according to different criteria are different, the conclusion that the severity of COVID-19 and EPU have negative influences on the crash risk of stock market is still holding. In terms of explanatory power, when the variables rCases and rEPU are added into the model simultaneously, its explanatory power has been significantly improved. For example, comparing the results in the first column of Table 5 with the results in the second column of Table 3 , we can see that after adding rEPU, the adj-R 2 increases from 0.0497 to 0.0504. While comparing the results from the second column of Table 5 with that in the first column of Table 3 , the Adj-R 2 has increased from 0.0479 to 0.0502.
The effects of EPU on stock market crash risk Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets. Notes: *** , ** , * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets. The optimal lag length in column (1) is determined by the AIC criterion, while the SC criterion determines the optimal lag length in column (2).
Finally, we consider whether the impact of EPU on crash risk is different during the epidemic. We know that when a crisis event occurs, the government usually needs to formulate a series of policies to alleviate the negative impact of the crisis.
Therefore, economic policy uncertainty during the COVID-19 crisis may play a different role from the normal period.
The relevant results are given in Table 6 . We can see that the coefficients of the interaction terms are negative and significant at the 5% level, while the coefficients of rEPU are not significant anymore. More accurately, take the results from column (1) for example, the coefficient of rEPU during the before-epidemic period is -0.0062 with t-statistics -1.5967 (not significant at 10% level). While during the epidemic period, the coefficient of rEPU is -0.0408 with t-statistics=-2.8666. It indicates that in a regular period, changes in economic policy uncertainty do not significantly affect the risk of stock market crashes. Moreover, during the epidemic, the increase in uncertainty caused by COVID-19 will increase the stock market crash risk. The timely formulation of response policies can reduce this uncertainty, thereby helping to prevent the possibility of extreme risks in the stock market. Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively.
The t-statistics are presented in the brackets. We set the lag length of each variable based on the previous results in Table 5 .
There are two alternative measures about EPU: rEMU and rEMV-ID,
representing the equity market uncertainties for the normal time and the pandemic period. In this section, we use these two variables to redo our empirical analysis. The results are reported in Table 7 and Table 8 , respectively. In general, the results are robust. Notes: *** , ** , * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets.
Robustness results from EMV_ID 
This paper has examined the role of economic policy uncertainty in affecting the stock market crash. we use the conditional skewness from the GARCH-S model as the proxy for crash risk. Our findings shed new light that COVID-19 will increase the crash risk of the US stock market. Second, we find that the increase in economic policy uncertainty has the risk of triggering a stock market crash. However, further evidence suggests that this effect of EPU is significant only during the epidemic. It reminds us that proactive policies should be implemented in time during crisis events to reduce the economic policy uncertainty, which is very important to prevent the stock market from crashing effectively. Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets.