COVID-19 pandemic and the stock market: Liquidity, price efficiency, and trading

Abstract

This paper shows that the COVID-19 pandemic is associated with a decrease in liquidity and increases in price efficiency and informed trading before the NYSE closed its trading floor. The closure of the trading floor led to reductions in liquidity, price efficiency, and informed trading on the NYSE, and its subsequent reopening led to increases in these variables. The effects of the pandemic and the trading floor on price efficiency can be explained, at least in part, by their impacts on liquidity and informed trading. The effects on liquidity and price efficiency are fully reversed after the NYSE reopened its trading floor.

1. Introduction

We analyze the effects of the COVID-19 pandemic and the closing and reopening of the NYSE trading floor on various measures of stock market liquidity, price efficiency, and trading in the U.S. stock market. SARS-COV-2 has spread across the globe and killed more than six million people. The U.S. had the first confirmed case of the virus on January 21, 2020. The World Health Organization (WHO) declared a public health emergency over the pandemic on January 30, 2020 and announced the virus's formal name, COVID-19, on February 11, 2020. News related to COVID-19 was the dominant driver of large daily U.S. stock market movements for several months after February 24, 2020.

Baker et al. (2020) report that 18 out of 22 trading days from February 24, 2020 to March 24, 2020 had a change (up or down) in the S&P 500 Index greater than 2.5%, which is higher than any other period in history with the same number of trading days. As the spread of COVID-19 caused massive drops in stock prices and extreme market volatility, the NYSE closed its trading floor on March 23, 2020 when the market, as it turned out, reached near the bottom. The NYSE subsequently began reopening its trading floor on May 26, 2020, allowing floor brokers and market makers to resume their business operations.

The closure of its trading floor has implications for two major players on the NYSE: designated market makers (DMMs) and floor brokers. DMMs have obligations for maintaining fair and orderly markets for their assigned securities. Ordinarily, DMMs operate both manually and electronically to facilitate price discovery during market openings, closings, and periods of substantial trading imbalances or instability. Without the trading floor, DMMs execute all orders electronically and cannot submit pre-opening indications from the trading floor to the Securities Information Processor (SIP) before the market open or during trading halts.

Floor brokers are employees of member firms who execute trades on the exchange floor on behalf of their clients. They act as agents, buying and selling stocks for the public (e.g., institutions, hedge funds, and broker/dealers). During normal times, floor brokers are physically present on the trading floor and actively participate in trading throughout the day, including opening and closing auctions.1 With no trading floor, floor brokers can no longer provide these functions (e.g., they cannot participate in Exchange-facilitated auctions). However, they can still execute trades electronically by routing electronic orders to the Exchange systems.2

Although the NYSE has fewer traders and market makers on the floor today than it did a decade ago, it maintains that humans are still an essential element of its operations. On its website, the NYSE states:

“Though all of our markets operate electronically using cutting edge, ultrafast technology, we believe nothing can take the place of human judgment and accountability. It is this human connection that helps ensure our strength, creating orderly opens and closes, lower volatility, deeper liquidity, and improved prices. For over 200 years, we have maintained a steadfast commitment to stronger, more orderly financial markets. And we intend to keep that tradition going for the next 200.”

The closure of the NYSE's trading floor provides an excellent opportunity to examine the value of the trading floor and human involvement (by DMMs and floor brokers) in improving execution quality and price efficiency.3 Also, as noted above, the disruptions brought by COVID-19 (e.g., rapid declines in share prices and explosions in market volatility) provide an opportunity to explore how these disruptions affected NYSE- and Nasdaq-listed stocks even before the NYSE closed its trading floor. Prior research suggests that financial crises decrease liquidity for at least two reasons. Gorton and Metrick (2010) suggest that liquidity is lower during financial crises because it aggravates adverse selection problems. Nagel (2012) shows that financially-constrained liquidity providers reduce the supply of liquidity during financial crises because they require higher returns.4 Furthermore, our data and research design allow us to explore how the reopening of the NYSE trading floor affects liquidity, price efficiency, and trading on the NYSE and Nasdaq and whether the reopening fully reverses the effect of the pandemic on these metrics.

We show that the COVID-19 pandemic led to an economically significant increase in the bid-ask spread and the price impact of trades and a decrease in the quoted depth for both NYSE-listed and Nasdaq-listed stocks before the NYSE closed its trading floor. The pandemic-led reduction in liquidity for the NYSE stocks is smaller than that for the Nasdaq stocks. One possible interpretation of the latter finding is that the NYSE trading floor mitigated the negative effect of the pandemic on liquidity.

We find a significant increase in price efficiency (i.e., a decrease in variance ratios) in the pandemic period relative to the pre-pandemic period on the NYSE and Nasdaq, and the increase is larger for the NYSE stocks. To the extent that price efficiency increases with liquidity (Chordia et al., 2008), the larger increase in price efficiency on the NYSE could be due, at least in part, to the smaller pandemic-led decrease in liquidity for the NYSE stocks. We also find a significant increase in trading (i.e., the number of trades, total dollar volume, intermarket sweep order trades, and odd-lot trades), order imbalance, and the probability of informed trading (PIN) in the pandemic period relative to the pre-pandemic period on both the NYSE and Nasdaq, and the increase is larger for the NYSE stocks. Because share prices become informationally efficient through informed investors’ trading (Kyle, 1985; Easley et al., 1997), the larger increase in price efficiency on the NYSE could also be due to the larger increase in informed trading on the NYSE.

We also find that the closure of the NYSE trading floor is associated with a decrease in liquidity on the NYSE and Nasdaq. The difference-in-differences (DiD) result shows that the decrease in liquidity for the NYSE stocks is greater than the decrease in liquidity for the Nasdaq stocks, suggesting that the closure of the NYSE trading floor led to a reduction in liquidity for the NYSE stocks after controlling for the market-wide decrease in liquidity. In addition, we find that the reopening of the NYSE trading floor led to an increase in liquidity for the NYSE stocks after controlling for the market-wide increase in liquidity.

When we control for the market-wide decline (increase) in price efficiency, we find that the closure (reopening) of the NYSE trading floor led to a decrease (an increase) in price efficiency for the NYSE stocks. These results could be the results of a decrease (increase) in liquidity for the NYSE stocks associated with the closure (reopening) of its trading floor, given that price efficiency increases with liquidity. The effects of the pandemic on liquidity and price efficiency were fully reversed after the NYSE reopened its trading floor.

We show that the closure (reopening) of the NYSE trading floor led to a decrease (an increase) in trading (e.g., intermarket sweep order trading and odd-lot trading), order imbalance, and PIN for the NYSE stocks after controlling for the market-wide decrease (increase) in these variables. Prior research (e.g., Chakravarty et al., 2012; O'Hara et al., 2014) shows that intermarket sweep orders and odd-lot orders are frequently used in algorithmic trading by institutional investors, market makers, and high-frequency traders who are likely to trade on private information. Hence, the decrease (increase) in price efficiency for the NYSE stocks associated with the closure (reopening) of its trading floor could also be the result of a concurrent decrease (increase) in intermarket sweep order trading and odd-lot trading.

Numerous studies have analyzed the effects of the COVID-19 pandemic on stock markets.5 Foley et al. (2020) show that the pandemic caused a sharp increase in transaction costs across global markets. Baig et al. (2021) show that increases in confirmed cases and deaths due to COVID-19 are associated with a significant increase in illiquidity and volatility. Ozik et al. (2021) show that retail trading mitigated the negative impact of the pandemic on liquidity. Pagano et al. (2021) show that the impact of Robinhood investors on market quality varied with market conditions. Chakrabarty and Pascual (2022) show that stocks with high algorithmic trading did not experience a larger reduction in either competition for liquidity provision or price improvements than stocks with low algorithmic trading during the COVID-19 pandemic.

Other studies examine the effect of the NYSE trading floor closure on market quality. Cox and Woods (2021) show that the closure is associated with a smaller increase in the quoted spread for NYSE stocks than the Nasdaq stocks. Kye and Mizrach (2021) analyze the impact of the NYSE trading floor closure on market quality during the last 30 min of the trading day and show that the closure has limited effects on market quality. Hu and Murphy (2021) show that closing auction market quality generally improved when the NYSE halted floor trading during the COVID-19 pandemic. Brogaard et al. (2021) show that the closure of the NYSE trading floor led to higher effective and quoted spreads and larger pricing errors. Jegadeesh and Wu (2022) find that the price impact of trades for NYSE stocks is greater (smaller) than that for Nasdaq stocks during closing auctions when the NYSE trading floor is closed (open).6

By contrast, our study provides evidence regarding how the pandemic influenced liquidity, price efficiency, trading, order imbalance, and PIN on the NYSE and Nasdaq before the NYSE closed its trading floor. In addition, we explore how the reopening of the NYSE trading floor influenced these variables and whether the effects of the pandemic on these market metrics were partially or fully reversed after the NYSE reopened its trading floor. Prior studies have analyzed the role of DMMs in different markets.7 Our study provides further evidence on the role of traders and DMMs on the floor by comparing liquidity and price efficiency between when the floor is open and when it is closed. More importantly, we contribute to the literature by analyzing liquidity, price efficiency, and informed trading across four distinct subperiods, and show that the pandemic and the closure and reopening of the NYSE trading floor affected price efficiency through the channels of liquidity and informed trading.

The rest of the paper is organized as follows. In Section 2, we explain our research design and sample selection. In Section 3, we analyze how the COVID-19 pandemic and the closure and reopening of the NYSE trading floor affected various measures of liquidity. In Section 4, we examine how price efficiency is related to the pandemic and the closure and reopening of the NYSE trading floor. In Section 5, we explore the effects of the pandemic and the trading floor on trading activities. In Section 6, we investigate whether the effects of the pandemic on liquidity, price efficiency, and trading reversed after the reopening of the NYSE trading floor. In Section 7, we explore whether liquidity and informed trading are channels through which the pandemic and the closure and reopening of the NYSE trading floor led to changes in price efficiency. In Section 8, we examine whether the effects of the pandemic and the closure and reopening of the NYSE trading floor differ between small and large firms. In Section 9, we compare our findings with results of prior research. Concluding remarks are in Section 10.

2. Research design and sample selection

Fig. 1, Fig. 2 show that our study period (January 22, 2020–June 25, 2020) can be divided into four distinct subperiods according to the S&P 500 Index and the CBOE Volatility Index (VIX). The first subperiod (January 22 to February 21) is before the effect of the COVID-19 pandemic manifests in the stock market (via the S&P 500 Index or the VIX). For expositional convenience, we call this period “the pre-COVID period.” The second subperiod (February 22 to March 22) is when the S&P 500 Index plummeted and the VIX exploded. We call this period “the pre-NTF period,” where NTF stands for no trading floor. The third subperiod (March 23 to May 25) is when the NYSE trading floor was closed. We call this period “the NTF period.” The fourth subperiod (May 26 to June 25) is when floor brokers resumed their operations on the floor with a reduced headcount and restrictions in place to enforce social distancing and other safety protocols.8 We call this subperiod “the post-NTF period.” Fig. 1, Fig. 2 show that the pandemic's effects on the S&P 500 Index and the VIX are limited mainly to the pre-NFT period and the NTF period. Hence, we summarize the potential effects of the pandemic and the trading floor for each subperiod as follows.

	COVID-19		Trading floor
	NYSE	Nasdaq	NYSE	Nasdaq
Pre-COVID period	No	No	Yes	No
Pre-NTF period	Yes	Yes	Yes	No
NTF period	Yes	Yes	No	No
Post-NTF period	No	No	Yes	No

Fig. 1.

S&P 500 Index in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of the S&P 500 Index in the pre-COVID (January 22 to February 21), pre-NTF (February 22 to March 22), NTF (March 23 to May 25) and post-NTF (May 26 to June 25) periods, where NTF stands for no trading floor.

Fig. 2.

CBOE Volatility Index (VIX) in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of the VIX in the pre-COVID (January 22 to February 21), pre-NTF (February 22 to March 22), NTF (March 23 to May 25) and post-NTF (May 26 to June 25) periods, where NTF stands for no trading floor.

Note that the difference in a variable (e.g., the effective spread) between the pre-NTF period and the pre-COVID period (i.e., Pre-NTF period – Pre-COVID period) measures the effect of the pandemic on the variable for both the NYSE and Nasdaq stocks. Similarly, the difference between the NTF period and the pre-NTF period (i.e., NTF period – Pre-NTF period) measures the effect of no trading floor (NTF) for the NYSE stocks; the difference between the post-NTF period and the NTF period measures the impacts of the pandemic and the trading floor for the NYSE stocks and the effect of the pandemic for the Nasdaq stocks; and the difference between the NTF period and the pre-COVID period measures the effects of no trading floor and the pandemic for the NYSE stocks and the effect of the pandemic on the Nasdaq stocks.

We use stock attributes in December 2019 to construct a matched sample of NYSE and Nasdaq stocks. For each NYSE stock, we identify all Nasdaq stocks with the same two-digit North American Industry Classification System (NAICS) code. Next, we calculate the composite match score (CMS) for each NYSE stock against each Nasdaq stock with the same NAICS code as C $MS=\sum _{k=1}^4{\left[\frac{X_k^{NYSE}-X_k^{Nasdaq}}{\left\{\frac{X_k^{NYSE}+X_k^{Nasdaq}}{2}\right\}}\right]}^2\text{,}$ where X _k represents share price, dollar volume, return, or volatility, and superscripts NYSE and Nasdaq represent NYSE and Nasdaq stocks. We then select the Nasdaq stock with the lowest CMS for each NYSE stock. If two NYSE stocks are matched to the same Nasdaq stock, we keep the pair with the lower CMS and rematch the other NYSE stock to the remaining Nasdaq stocks.

Divergence in stock attributes for our matched NYSE and Nasdaq stocks becomes more significant as the composite match score increases. To include pairs of matched stocks with similar attributes in our sample, we exclude NYSE and Nasdaq pairs with a CMS greater than three. This filter excludes mega-tech stocks such as Apple from the final sample. Our study sample consists of 1816 matched pairs of NYSE and Nasdaq stocks with similar attributes. The mean and median values of CMS are 0.68 and 0.54, respectively. The mean value of share price, trading volume, stock return, and return volatility for the matched NYSE (Nasdaq) stocks is $45.99 ($46.12), $47.5 million ($46.6 million), 0.0020 (0.0019), and 0.0166 (0.0170), respectively. Across all stock attributes, the difference in the mean value between the NYSE and Nasdaq stocks is not significantly different from zero.9

3. Effects of the pandemic and the trading floor on liquidity

In this section, we explore the effects of the pandemic and the trading floor on various measures of liquidity. We use the following variables as our proxies for liquidity: quoted spread (QSP), effective spread (ESP), value-weighted effective spread (ESP_VW), realized spread (RSP), value-weighted realized spread (RSP_VW), price impact (PIMPACT), value-weighted price impact (PIMPACT_VW), quoted depth (DEPTH), price impact coefficient with an intercept (LAMBDA_1), and price impact coefficient without an intercept (LAMBDA_2). The Appendix provides the definitions of all the variables. The quoted and effective spreads are measures of liquidity and total trading costs; price impacts are measures of adverse selection costs; and quoted depth is a measure of liquidity available at the national bid and offer price (NBBO). The realized spread is a measure of the market maker's revenue (i.e., the difference between the effective spread and the price impact of a trade). We obtain daily values of these variables from the WRDS Intraday Indicator Database (IID). Our final study sample comprises the panel data of 395,888 firm-day observations. Fig. 3, Fig. 4 show the time series patterns of quoted spreads (QSP) and effective spreads (ESP) for the matched NYSE and Nasdaq stocks.10 These figures indicate that our data meet the parallel trends assumption required for the DiD test.

Fig. 3.

Quoted spreads (QSP) for NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of quoted spread for NYSE and Nasdaq stocks in the pre-COVID (January 22, 2020 to February 21, 2020), pre-NTF (February 22, 2020 to March 22, 2020), NTF (March 23, 2020 to May 22, 2020) and post-NTF (May 26, 2020 to June 25, 2020) periods.

Fig. 4.

Effective spreads (ESP) for NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of effective spread for NYSE and Nasdaq stocks in the pre-COVID (January 22, 2020 to February 21, 2020), pre-NTF (February 22, 2020 to March 22, 2020), NTF (March 23, 2020 to May 22, 2020) and post-NTF (May 26, 2020 to June 25, 2020) periods.

3.1. Effects of the pandemic on liquidity

Panel A in Table 1 shows the mean values of each variable in the pre-COVID, pre-NTF, NTF, and post-NTF periods for the matched NYSE and Nasdaq stocks. Panel A also shows the differences in mean values between the pre-NTF and pre-COVID periods (i.e., Pre-NTF – Pre-COVID = ΔP ₁ for the NYSE stocks and ΔP ₂ for the Nasdaq stocks), between the NTF and pre-NTF periods (i.e., NTF – Pre-NTF = ΔC ₁ for the NYSE stocks and ΔC ₂ for the Nasdaq stocks), and between the post-NTF and NTF periods (i.e., Post-NTF – NTF = ΔR ₁ for the NYSE stocks and ΔR ₂ for the Nasdaq stocks).11 Panel B shows the DiD results, i.e., ΔP ₁ – ΔP ₂ [(Pre-NTF – Pre-COVID)_NYSE – (Pre-NTF – Pre-COVID)_Nasdaq], ΔC ₁ – ΔC ₂ [(NTF – Pre-NTF)_NYSE – (NTF – Pre-NTF)_Nasdaq], and ΔR ₁ – ΔR ₂ [(Post-NTF – NTF)_NYSE – (Post-NTF – NTF)_Nasdaq], where the subscripts NYSE and Nasdaq represent NYSE and Nasdaq stocks.

Table 1.

Comparisons of liquidity variables in the pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Comparisons of liquidity variables in the pre-COVID, pre-NTF, NTF, and post-NTF periods
	NYSE stocks							Nasdaq stocks
Variable	Pre-COVID	Pre-NTF	NTF	Post-NTF	Pre-NTF – Pre-COVID (ΔP1)	NTF – Pre-NTF (ΔC1)	Post-NTF – NTF (ΔR1)	Pre-COVID	Pre-NTF	NTF	Post-NTF	Pre-NTF – Pre-COVID (ΔP2)	NTF – Pre-NTF (ΔC2)	Post-NTF – NTF (ΔR2)
QSP (%)	0.4848	0.6091	0.6663	0.4837	0.1243** (14.35)	0.0572** (12.52)	−0.1826** (−23.64)	0.4856	0.6407	0.6566	0.4863	0.1551** (17.39)	0.0159** (8.61)	−0.1703** (−20.56)
ESP (%)	0.2534	0.3296	0.4059	0.2511	0.0762** (21.84)	0.0763** (19.66)	−0.1548** (−35.26)	0.2537	0.3481	0.3623	0.2509	0.0944** (27.63)	0.0142** (9.34)	−0.1114** (−23.25)
ESP_VW (%)	0.3252	0.4401	0.5064	0.3247	0.1149** (20.16)	0.0663** (18.74)	−0.1817** (−33.52)	0.3260	0.4518	0.4668	0.3251	0.1258** (29.35)	0.0150** (8.97)	−0.1417** (−25.79)
RSP (%)	0.1010	0.1114	0.1661	0.1024	0.0104** (9.46)	0.0547** (20.01)	−0.0637** (−24.99)	0.1033	0.1217	0.1296	0.1029	0.0184** (13.89)	0.0079** (7.83)	−0.0267** (−11.64)
RSP_VW (%)	0.1033	0.1293	0.1786	0.1038	0.0260** (14.84)	0.0493** (18.85)	−0.0748** (−26.84)	0.1047	0.1364	0.1450	0.1041	0.0317** (18.93)	0.0086** (8.55)	−0.0409** (−17.76)
PIMPACT (%)	0.1514	0.2192	0.2398	0.1487	0.0658** (24.67)	0.0216** (14.23)	−0.0911** (−36.73)	0.1504	0.2264	0.2327	0.1480	0.0760** (32.82)	0.0063** (8.78)	−0.0847** (−24.72)
PIMPACT_VW (%)	0.2219	0.3108	0.3278	0.2209	0.0889** (27.23)	0.0170** (13.76)	−0.1069** (−39.41)	0.2213	0.3154	0.3218	0.2210	0.0941** (33.15)	0.0064** (7.96)	−0.1008** (−26.03)
DEPTH ($ in thousands)	38.49	31.37	24.18	38.23	−7.124** (−9.48)	−7.190** (−11.69)	14.05** (16.07)	38.33	29.32	27.69	38.12	−9.010** (−11.91)	−1.630** (−7.29)	10.43** (9.57)
LAMBDA _1 × 106	3.772	5.076	6.325	3.808	1.262** (12.64)	1.291** (11.82)	−2.517** (−12.88)	3.682	5.144	5.640	3.734	1.462** (14.86)	0.4960** (7.73)	−1.906** (−8.87)
LAMBDA_2 × 106	3.960	5.307	6.529	4.003	1.296** (13.02)	1.273** (11.35)	−2.526** (−13.83)	3.898	5.281	5.795	3.932	1.383** (13.84)	0.5140** (8.05)	−1.863** (−7.92)

Panel B: Difference-in-differences
Variable	(Pre-NTF – Pre-COVID)NYSE – (Pre-NTF – Pre-COVID)Nasdaq = ΔP1 – ΔP2	(NTF – Pre-NTF)NYSE – (NTF – Pre-NTF)Nasdaq = ΔC1 – ΔC2	(Post-NTF – NTF)NYSE – (Post-NTF – NTF)Nasdaq = ΔR1 – ΔR2
QSP (%)	−0.0308** (−13.53)	0.0413** (14.21)	−0.0123** (−10.06)
ESP (%)	−0.0182** (−10.44)	0.0621** (16.84)	−0.0434** (−14.97)
ESP_VW (%)	−0.0109** (−9.26)	0.0513** (15.95)	−0.0400** (−15.62)
RSP (%)	−0.0080** (−8.85)	0.0468** (14.28)	−0.0370** (−12.85)
RSP_VW (%)	−0.0057** (−7.98)	0.0407** (14.32)	−0.0339** (−13.07)
PIMPACT (%)	−0.0102** (−15.94)	0.0153** (15.82)	−0.0064** (−7.87)
PIMPACT_VW (%)	−0.0052** (−8.36)	0.0106** (14.76)	−0.0061** (−7.59)
DEPTH ($ in thousands)	1.886** (9.36)	−5.560** (−13.59)	3.620** (10.83)
LAMBDA_1 × 106	−0.1996** (−8.53)	0.7950** (12.97)	−0.6110** (−10.71)
LAMBDA_2 × 106	−0.0867** (−6.74)	0.7590** (11.98)	−0.6637** (−11.07)

We define January 22, 2020 to February 21, 2020 as the pre-COVID period, February 22, 2020 to March 22, 2020 as the pre-NTF period, March 23, 2020 to May 25, 2020 as the NTF period, and May 26, 2020 to June 25, 2020 as the post-NTF period, where NTF stands for no trading floor. For each period, we compute the mean value of each variable for our matched NYSE and Nasdaq sample stocks. We use the following variables as our empirical proxies for liquidity: quoted spread (QSP), effective spread (ESP), value-weighted effective spread (ESP_VW), realized spread (RSP), value-weighted realized spread (RSP_VW), price impact (PIMPACT), value-weighted price impact (PIMPACT_VW), quoted depth (DEPTH), price impact coefficient with intercept (LAMBDA_1), and price impact coefficient without intercept (LAMBDA_2). Numbers in parentheses are t-statistics. **Significant at the 1% level.

As noted earlier, the difference in liquidity between the pre-COVID period and the pre-NTF period measures the effect of the pandemic on liquidity before the NYSE closed its trading floor. The results show that the pandemic is accompanied by a significant increase (ΔP ₁ > 0) in the spreads (QSP, ESP, ESP_VW, and RSP) and price impacts (PIMPACT, PIMPACT_VW, LAMBDA_1, and LAMBDA_2) and a significant decrease (ΔP ₁ < 0) in the quoted depth (DEPTH) for the NYSE stocks. These changes are economically significant. For instance, the effective spread (ESP) increases by 0.0762 (a 30% increase) and LAMBDA_1 increases by 1.262 (a 33.5% increase). These results indicate that the pandemic is associated with a decrease in liquidity for the NYSE stocks. The results for the Nasdaq stocks (ΔP ₂) are qualitatively similar to those for the NYSE stocks. The DiD result (i.e., ΔP ₁ – ΔP ₂) in Panel B shows that the decrease in liquidity for the NYSE stocks is smaller than the decrease in liquidity for the Nasdaq stocks.12

To more accurately measure how the pandemic affects liquidity after controlling for stock attributes and the effects of other factors, we estimate the following regression model using the matched NYSE and Nasdaq stocks in the pre-COVID period and the pre-NTF period:

$${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSEx{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}$$

$$+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{;}$$ (1)

where subscripts i and t denote stock i and time t, VAR denotes each liquidity variable, NYSE is a dummy variable equal to one for the NYSE stocks and zero for the Nasdaq stocks, $D^{Pre-NTF}$ is a dummy variable equal to one for the pre-NTF period and zero for the pre-COVID period. PRICE is the stock price, VOLUME denotes the trading volume, RET denotes the stock return, VOLA denotes the return volatility, VIX is the CBOE Volatility Index, and ε denotes the error term. We cluster the standard errors by firm and day. To assess the sensitivity of our results to the model specification, we also estimate equation (1) with firm and day fixed effects.13 We find that the results with and without the fixed effects are qualitatively similar. We provide the results without the fixed effects in the paper and the results with the fixed effects in the Online Appendix.

In equation (1), the coefficient (${\beta }_3$) on $D^{Pre-NTF}$ (which captures the difference in liquidity between the pre-NTF period and the pre-COVID period for the Nasdaq stocks) measures the effect of the pandemic on liquidity for the Nasdaq stocks. Likewise, the coefficient (${\beta }_1$) on $NYSEx{D}^{Pre-NTF}$ measures the differential effect of the pandemic on liquidity for the NYSE stocks relative to the Nasdaq stocks. Panel A in Table 2 shows that the estimates of ${\beta }_3$ are positive and significant in the regression models of the spreads and price impacts, and negative and significant in the regression model of the depth. These results indicate that the pandemic is associated with a decrease in liquidity for the Nasdaq stocks.14 More importantly, the estimates of ${\beta }_1$ are negative and significant in the regression models of the spreads and price impacts, and positive and significant in the regression model of the depth.15 These results indicate that the negative effect of the pandemic on liquidity for the NYSE stocks is smaller than that for the Nasdaq stocks. One possible explanation for this finding is that the NYSE trading floor mitigated the pandemic's negative effect on liquidity, given that the NYSE has the trading floor while Nasdaq did not during the pre-NTF period. Most likely, other differences between the NYSE and Nasdaq may also have contributed to the differential effects of the pandemic on liquidity between the two markets.

Table 2.

Regression results for liquidity measures using pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Regression results using liquidity variables in the pre-COVID and pre-NTF periods

Variable

QSP

ESP

ESP_VW

RSP

RSP_VW

PIMPACT

PIMPACT_VW

DEPTH

LAMBDA_1

LAMBDA_2

NYSE x DPre-NTF

−0.0288** (−7.52)

−0.0174** (−7.28)

−0.0093** (−6.66)

−0.0075** (−8.22)

−0.0051** (−4.76)

−0.0093** (−5.78)

−0.0051** (−3.83)

1.781** (4.03)

−0.2023** (−3.88)

−0.0855** (−3.40)

NYSE

−0.0006 (−0.18)

−0.0002 (−0.16)

−0.0006 (−0.23)

−0.0022 (−0.39)

−0.0010 (−0.16)

0.0020 (0.38)

0.0007 (0.24)

0.1599 (0.92)

0.0873 (1.44)

0.0579 (1.14)

DPre-NTF

0.1548** (5.72)

0.0887** (4.10)

0.1239** (5.01)

0.0174** (7.10)

0.0285** (3.84)

0.0728** (3.17)

0.0919** (3.66)

−8.803** (−2.98)

1.396** (2.97)

1.336** (2.73)

PRICE

−0.0343** (−3.58)

−0.0454** (−7.85)

−0.0713** (−13.73)

−0.0090** (−3.24)

−0.0153** (−3.75)

−0.0393** (−10.59)

−0.0561** (−11.00)

2.223** (2.87)

−3.580** (−17.74)

−3.503** (−18.59)

VOLUME

−0.0794** (−10.70)

−0.0768** (−10.86)

−0.0872** (−10.52)

−0.0483** (−13.76)

−0.0388** (−10.51)

−0.0285** (−7.12)

−0.0484** (−9.17)

17.72** (10.86)

−0.3190** (−2.93)

−0.2583** (−2.75)

RET

−0.0015** (−4.33)

−0.0008** (−3.32)

−0.0001** (−2.74)

−0.0001** (−3.06)

−0.0001** (−2.71)

−0.0011** (−3.33)

−0.0016** (−3.47)

0.0447** (3.03)

−0.0606** (−2.77)

−0.0723** (−2.83)

VOLA

0.0379** (21.51)

0.0291** (22.26)

0.0345** (24.53)

0.0153** (22.49)

0.0139** (22.82)

0.0128** (20.86)

0.0206** (22.47)

−0.0089** (−2.84)

0.0471** (3.06)

0.0341** (2.91)

VIX

0.3769** (9.98)

0.0969** (7.48)

0.1620** (7.80)

0.0348** (3.21)

0.0263** (2.73)

0.1417** (8.38)

0.1736** (10.72)

−8.390** (−5.37)

5.421** (8.89)

5.194** (8.39)

Adjusted R2

0.53

0.52

0.49

0.31

0.25

0.38

0.31

0.18

0.13

0.14

Panel B: Regression results using liquidity variables in the pre-NTF and NTF periods

Variable

QSP

ESP

ESP_VW

RSP

RSP_VW

PIMPACT

PIMPACT_VW

DEPTH

LAMBDA_1

LAMBDA_2

NYSE x DNTF

0.0397** (5.31)

0.0609** (6.49)

0.0526** (5.58)

0.0464** (6.97)

0.0386** (4.96)

0.0143** (3.92)

0.0093** (3.28)

−5.484** (−2.93)

0.7586** (3.59)

0.7260** (2.94)

NYSE

−0.0308** (−4.89)

−0.0163** (−4.18)

−0.0125** (−3.85)

−0.0101** (−3.66)

−0.0078** (−3.62)

−0.0073** (−3.01)

−0.0044** (−2.96)

2.202** (3.02)

−0.0986** (−2.72)

−0.0311* (−2.17)

DNTF

0.0134** (4.14)

0.0128** (3.05)

0.0160** (3.46)

0.0070** (3.51)

0.0074** (3.30)

0.0057** (2.83)

0.0076** (2.86)

−1.569** (−3.62)

0.4667** (3.17)

0.5530** (3.26)

Control variables

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Adjusted R2

0.57

0.55

0.52

0.32

0.27

0.39

0.33

0.15

0.14

0.16

Panel C: Regression results using liquidity variables in the NTF and post-NTF periods

Variable

QSP

ESP

ESP_VW

RSP

RSP_VW

PIMPACT

PIMPACT_VW

DEPTH

LAMBDA_1

LAMBDA_2

NYSE x DPost-NTF

−0.0127** (−4.78)

−0.0458** (−7.45)

−0.0423** (−5.28)

−0.0388** (−6.58)

−0.0356** (−5.54)

−0.0072** (−4.52)

−0.0056** (−3.59)

3.466** (3.38)

−0.6056** (−4.49)

−0.7008** (−4.64)

NYSE

0.0089** (3.04)

0.0421** (3.65)

0.0463** (3.44)

0.0359** (5.18)

0.0325** (4.30)

0.0075** (2.96)

0.0068** (2.77)

−3.381** (−2.75)

0.6284** (3.21)

0.6998** (3.50)

DPost-NTF

−0.1652** (−3.03)

−0.1135** (−2.87)

−0.1381** (−3.31)

−0.0241** (−4.36)

−0.0383** (−4.71)

−0.0811** (−4.37)

−0.0940** (−4.54)

9.681** (3.61)

−1.717** (−3.09)

−1.803** (−2.93)

Control variables

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Adjusted R2

0.56

0.55

0.51

0.34

0.28

0.39

0.31

0.16

0.15

0.16

Panel A provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-COVID and pre-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where subscripts i and t denote stock i and time t, VAR denotes each liquidity variable, NYSE is a dummy variable equal to one for the NYSE stocks and zero for the Nasdaq stocks, D^Pre-NTF is a dummy variable equal to one for the pre-NTF period and zero for the pre-COVID period. PRICE is the stock price, VOLUME denotes the trading volume, RET is the stock return, VOLA is the return volatility, VIX is the CBOE's volatility index, and ε denotes the error term. Panel B provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-NTF and NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^NTF is a dummy variable equal to one for the NTF period and zero for the pre-NTF period. Panel C reports the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the NTF and post-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Post-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Post-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^Post-NTF is a dummy variable equal to one for the post-NTF period and zero for the NTF period. We cluster standard errors by firm and time in the regressions. We use the following variables as our empirical proxies for liquidity: quoted spread (QSP), effective spread (ESP), value-weighted effective spread (ESP_VW), realized spread (RSP), value-weighted realized spread (RSP_VW), price impact (PIMPACT), value-weighted price impact (PIMPACT_VW), quoted depth (DEPTH), price impact coefficient with intercept (LAMBDA_1), and price impact coefficient without intercept (LAMBDA_2). Numbers in parentheses are t-statistics. **Significant at the 1% level. *Significant at the 5% level.

The coefficients (${\beta }_2$) on $\mathrm{N}\mathrm{Y}\mathrm{S}\mathrm{E}$ are not significantly different from zero in all regression models, indicating no difference in liquidity between the NYSE and Nasdaq stocks during the pre-COVID period. The coefficients on the control variables are consistent with the findings of prior research (e.g., Chung et al., 2020). For instance, we observe lower liquidity for stocks with lower prices, smaller trading volume, and higher return volatility.

3.2. Effects on liquidity of the closure of the NYSE trading floor

To examine how the closure of the NYSE trading floor affected liquidity, we compare the above liquidity measures between the pre-NTF period and the NTF period. Panel A in Table 1 shows that the closure of the NYSE trading floor is accompanied by a significant increase (ΔC ₁ > 0) in the spreads and price impacts and a significant decrease (ΔC ₁ < 0) in the quoted depth for the NYSE stocks. These changes are economically significant. For instance, the effective spread increases by 0.0763 (a 23.1% increase) and LAMBDA_1 increases by 1.291 (a 25.4% increase). These results indicate that the closure of the NYSE trading floor is associated with a decrease in liquidity for the NYSE stocks. The results for the Nasdaq stocks are qualitatively similar to those for the NYSE stocks. The DiD result (i.e., ΔC ₁ – ΔC ₂) in Panel B of Table 1 shows that the decrease in liquidity for the NYSE stocks is greater than the decrease in liquidity for the Nasdaq stocks, suggesting that the closure of the NYSE trading floor led to a decrease in liquidity for the NYSE stocks after controlling for the market-wide decrease in liquidity between the pre-NTF period and the NTF period.16

To measure how the absence of the trading floor on the NYSE affects liquidity after controlling for stock attributes and the effects of other factors, we estimate the following regression model using the matched NYSE and Nasdaq stocks in the pre-NTF and NTF periods:

$${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}$$

$$+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$$ (2)

where D ^NTF is a dummy variable equal to one for the NTF period and zero for the pre-NTF period and all other variables are the same as defined for equation (1).

Panel B in Table 2 shows that the coefficients (${\beta }_1)\mathrm{o}\mathrm{n}$ $NYSE\mathrm{x}{D}^{NTF}$ are positive and significant in the regression models of the spreads and price impacts, and negative and significant in the regression model of the depth.17 For instance, the closure of the NYSE trading floor is associated with an increase of 6.09 bps in the mean effective spread of the NYSE stocks.18 The coefficients (${\beta }_3$) on $D^{NTF}$ are qualitatively similar to the estimates of ${\beta }_1$, indicating a contemporaneous decrease in liquidity for the Nasdaq stocks as well. These results suggest that the closure of the NYSE trading floor is associated with a decrease in liquidity for the NYSE stocks after controlling for stock attributes and the market-wide change in liquidity. The coefficients (${\beta }_2$) on $\mathrm{N}\mathrm{Y}\mathrm{S}\mathrm{E}$ are negative and significant in the regression models of the spreads and price impacts and positive and significant in the regression model of the depth, indicating that the NYSE stocks have, on average, higher liquidity than the Nasdaq stocks during the pre-NTF period.

3.3. Effects of the reopening of the NYSE trading floor on liquidity

We compare liquidity measures between the NTF period and the post-NTF period to assess the effect of the reopening of the NYSE trading floor on liquidity. Table 1 shows that the reopening of the NYSE trading floor is accompanied by a significant decrease (ΔR ₁ < 0) in the spreads and price impacts and a significant increase (ΔR ₁ > 0) in the quoted depth for the NYSE stocks. These results suggest that the restoration of the NYSE trading floor is associated with an increase in liquidity for the NYSE stocks. The results for the Nasdaq stocks are qualitatively similar, indicating that the restoration of the NYSE trading floor is also accompanied by an increase in liquidity on the Nasdaq.

The difference in liquidity between the NTF period and the post-NTF period for the NYSE stocks is likely to capture both the effect of the reopening of the NYSE trading floor and the change in the stock market environment between the two periods. By contrast, the difference in liquidity between the NTF period and the post-NTF period for the Nasdaq stocks is likely to capture only the latter effect because Nasdaq had no trading floor during both periods. The DiD result (i.e., ΔR ₁ – ΔR ₂) in Panel B shows that the increase in liquidity for the NYSE stocks is greater than the increase in liquidity for the Nasdaq stocks, suggesting that the reopening of the NYSE trading floor led to an increase in liquidity for the NYSE stocks after controlling for the market-wide increase in liquidity between the NTF period and the post-NTF period.19

We estimate the following regression model using the data in the NTF and the post-NTF periods to measure how the reopening of the NYSE trading floor affects liquidity after controlling for stock attributes and the effect of other factors:

$${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Post-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Post-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}$$

$$+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$$ (3)

where D ^Post-NTF is a dummy variable equal to one for the post-NTF period and zero for the NTF period, and all other variables are the same as previously defined.

Panel C in Table 2 shows that the coefficients (${\beta }_1)$ on $NYSE\mathrm{x}{D}^{Post-NTF}$ are negative and significant in the regression models of the spreads and price impacts, and positive and significant in the regression model of the depth.20 For instance, the reopening of the NYSE trading floor is associated with a decrease of 4.58 bps in the mean effective spread of the NYSE stocks. These results indicate that the restoration of the NYSE trading floor is associated with an increase in liquidity for the NYSE stocks after controlling for the market-wide change in liquidity. The coefficients (${\beta }_3$) on $D^{Post-NTF}$ are qualitatively similar to the estimates of ${\beta }_1$, indicating a contemporaneous increase in liquidity for the Nasdaq stocks due to the change in the stock market environment between the NTF period and the post-NTF period discussed above. The estimates of ${\beta }_2$ are positive and significant in the regression models of the spreads and price impacts and negative and significant in the regression model for the depth, indicating that the NYSE stocks have, on average, lower liquidity than the Nasdaq stocks during the NTF period.

4. Effects of the pandemic and the trading floor on price efficiency

In this section, we explore the effects of the pandemic and the trading floor on price efficiency (In Section 5, we explore possible explanations for these effects.). We use multiple versions of the variance ratio (VR) as empirical proxies for price efficiency: variance ratios based on 15-s/3 x 5-s (VR_1), 1-min/4 × 15-s (VR_2), 5-min/5 x 1-min (VR_3), 15-min/3 x 5-min (VR_4), and 30-min/2 × 15-min (VR_5). The variance ratio is an inverse measure of price efficiency, reflecting non-randomness in price changes. We obtain daily values of these variables from the WRDS Intraday Indicator Database. Fig. 5 shows the time series patterns of VR_1 for the matched NYSE and Nasdaq stocks.21

Fig. 5.

Variance ratios (VR_1) for NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of variance ratio for NYSE and Nasdaq stocks in the pre-COVID (January 22, 2020 to February 21, 2020), pre-NTF (February 22, 2020 to March 22, 2020), NTF (March 23, 2020 to May 22, 2020) and post-NTF (May 26, 2020 to June 25, 2020) periods.

4.1. Effects of the pandemic on price efficiency

To examine how the pandemic affected price efficiency, we replicate Table 1 using the above price efficiency measures and show the results in Table 3 . Panel A shows that the pandemic is accompanied by a significant decrease in all five variance ratios (ΔP ₁ < 0). These changes are economically significant. For instance, VR_1 decreases by 0.0305 (an 8.1% decrease) and VR_3 decreases by 0.0163 (a 5.2% decrease). These results suggest that the pandemic is associated with an increase in price efficiency for the NYSE stocks. The results for the Nasdaq stocks are qualitatively similar. The DiD result (i.e., ΔP ₁ – ΔP ₂) in Panel B shows that the decrease (increase) in variance ratios (price efficiency) for the NYSE stocks is larger than the decrease (increase) in variance ratios (price efficiency) for the Nasdaq stocks.

Table 3.

Comparisons of price efficiency measures in the pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Comparisons of price efficiency measures in the pre-COVID, pre-NTF, NTF, and post-NTF periods
	NYSE stocks							Nasdaq stocks
Variable	Pre-COVID	Pre-NTF	NTF	Post-NTF	Pre-NTF – Pre-COVID (ΔP1)	NTF – Pre-NTF (ΔC1)	Post-NTF – NTF (ΔR1)	Pre-COVID	Pre-NTF	NTF	Post-NTF	Pre-NTF – Pre-COVID (ΔP2)	NTF – Pre-NTF (ΔC2)	Post-NTF – NTF (ΔR2)
VR_1	0.3788	0.3483	0.4115	0.3787	−0.0305** (−27.58)	0.0628** (46.27)	−0.0324** (−32.21)	0.3816	0.3598	0.4071	0.3836	−0.0218** (−17.15)	0.0473** (31.77)	−0.0235** (−26.32)
VR_2	0.3349	0.3159	0.3719	0.3341	−0.0190** (−15.46)	0.0560** (35.61)	−0.0378** (−33.47)	0.3351	0.3264	0.3604	0.3343	−0.0087** (−9.79)	0.0340** (19.81)	−0.0261** (−23.74)
VR_3	0.3154	0.2991	0.3320	0.3149	−0.0163** (−15.34)	0.0329** (22.78)	−0.0171** (−20.88)	0.3153	0.3090	0.3255	0.3160	−0.0063** (−8.96)	0.0165** (12.76)	−0.0095** (−9.91)
VR_4	0.2981	0.2784	0.3092	0.2965	−0.0197** (−15.86)	0.0308** (19.42)	−0.0127** (−16.33)	0.2965	0.2835	0.3015	0.2952	−0.0130** (−12.47)	0.0180** (12.92)	−0.0063** (−7.74)
VR_5	0.2838	0.2646	0.2971	0.2834	−0.0192** (−16.87)	0.0325** (20.86)	−0.0137** (−17.64)	0.2834	0.2750	0.2886	0.2821	−0.0084** (−10.53)	0.0134** (10.98)	−0.0065** (−7.96)

Panel B: Difference-in-differences
Variable	(Pre-NTF – Pre-COVID)NYSE – (Pre-NTF – Pre-COVID)Nasdaq = ΔP1 – ΔP2	(NTF – Pre-NTF)NYSE – (NTF – Pre-NTF)Nasdaq = ΔC1 – ΔC2	(Post-NTF – NTF)NYSE – (Post-NTF – NTF)Nasdaq = ΔR1 – ΔR2
VR_1	−0.0087** (−10.38)	0.0155** (12.04)	−0.0089** (−10.19)
VR_2	−0.0103** (−10.73)	0.0220** (15.19)	−0.0117** (−14.81)
VR_3	−0.0100** (−10.56)	0.0164** (12.13)	−0.0076** (−9.35)
VR_4	−0.0067** (−8.67)	0.0128** (11.27)	−0.0064** (−8.34)
VR_5	−0.0108** (−9.86)	0.0189** (14.92)	−0.0072** (−9.13)

We define January 22, 2020 to February 21, 2020 as the pre-COVID period, February 22, 2020 to March 22, 2020 as the pre-NTF period, March 23, 2020 to May 25, 2020 as the NTF period, and May 26, 2020 to June 25, 2020 as the post-NTF period, where NTF stands for no trading floor. For each period, we compute the mean value of each variable for our matched NYSE and Nasdaq sample stocks. We use multiple versions of variance ratio (VR) as empirical proxies for price efficiency: variance ratios based on 15-s/3 x 5-s (VR_1), 1-min/4 × 15-s (VR_2), 5-min/5 x 1-min (VR_3), 15-min/3 x 5-min (VR_4), and 30-min/2 × 15-min (VR_5). Numbers in parentheses are t-statistics. **Significant at the 1% level.

Panel A in Table 4 provides the results of equation (1) when we use price efficiency as the dependent variable. The estimates of ${\beta }_3$ are negative and significant in all regression models, indicating that the pandemic is associated with an increase in price efficiency on Nasdaq. The estimates of ${\beta }_1$ are negative and significant in all regression models, indicating that the positive effect of the pandemic on price efficiency for the NYSE stocks is greater than that for the Nasdaq stocks. Given the positive relation between price efficiency and liquidity (Chordia et al., 2008), this result could be due, at least in part, to the smaller negative effect of the pandemic on liquidity for the NYSE stocks.

Table 4.

Regression results for price efficiency measures using pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Regression results using price efficiency measures in the pre-COVID and pre-NTF periods
Variable	VR_1	VR_2	VR_3	VR_4	VR_5
NYSE x DPre-NTF	−0.0081** (−5.19)	−0.0096** (−5.72)	−0.0107** (−5.44)	−0.0063** (−4.25)	−0.0092** (−3.78)
NYSE	−0.0030 (−0.77)	−0.0001 (−0.07)	−0.0001 (−0.05)	0.0017 (0.19)	0.0005 (0.19)
DPre-NTF	−0.0194** (−3.38)	−0.0090** (−3.29)	−0.0071** (−2.75)	−0.0138** (−3.18)	−0.0078** (−2.84)
PRICE	0.0248** (13.35)	0.0098** (4.54)	0.0043** (3.24)	0.0032** (3.05)	0.0022** (2.86)
VOLUME	−0.0826** (−23.87)	−0.0732** (−14.99)	−0.0557** (−13.97)	−0.0068** (−3.44)	−0.0064** (−3.26)
RET	0.0002** (3.05)	0.0006** (4.70)	0.0008** (4.57)	0.0003** (3.11)	0.0001** (2.73)
VOLA	0.0044** (24.11)	0.0078** (26.98)	0.0087** (16.17)	0.0042** (11.09)	0.0004** (3.19)
VIX	−0.0259** (−3.41)	−0.0263** (−3.99)	−0.0156** (−3.39)	−0.0338** (−3.59)	−0.0171** (−2.97)
Adjusted R2	0.59	0.41	0.19	0.11	0.08
Panel B: Regression results using price efficiency measures in the pre-NTF and NTF periods
Variable	VR_1	VR_2	VR_3	VR_4	VR_5
NYSE x DNTF	0.0137** (4.48)	0.0202** (5.39)	0.0156** (4.08)	0.0118** (3.52)	0.0175** (4.77)
NYSE	−0.0108** (−3.19)	−0.0095** (−3.30)	−0.0087** (−2.96)	−0.0045** (−2.77)	−0.0097** (−3.04)
DNTF	0.0441** (4.27)	0.0355** (4.00)	0.0147** (3.54)	0.0169** (3.39)	0.0143** (2.78)
Control variables	Yes	Yes	Yes	Yes	Yes
Adjusted R2	0.59	0.43	0.22	0.13	0.10
Panel C: Regression results using price efficiency measures in the NTF and post-NTF periods
Variable	VR_1	VR_2	VR_3	VR_4	VR_5
NYSE x DPost-NTF	−0.0082** (−6.87)	−0.0131** (−7.10)	−0.0068** (−4.76)	−0.0060** (−4.18)	−0.0081** (−5.27)
NYSE	0.0036** (2.72)	0.0129** (3.69)	0.0054** (3.21)	0.0062** (3.61)	0.0087** (3.92)
DPost-NTF	−0.0217** (−3.61)	−0.0246** (−3.87)	−0.0098** (−2.99)	−0.0072** (−2.83)	−0.0062** (−2.88)
Control variables	Yes	Yes	Yes	Yes	Yes
Adjusted R2	0.58	0.45	0.23	0.14	0.09

Panel A provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-COVID and pre-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where subscripts i and t denote stock i and time t, VAR denotes each price efficiency variable, NYSE is a dummy variable equal to one for the NYSE stocks and zero for the Nasdaq stocks, D^Pre-NTF is a dummy variable equal to one for the pre-NTF period and zero for the pre-COVID period. PRICE is the stock price, VOLUME denotes the trading volume, RET is the stock return, VOLA is the return volatility, VIX is the CBOE's volatility index, and ε denotes the error term. Panel B reports the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-NTF and NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_1{NYSE\mathrm{x}D}^{NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^NTF is a dummy variable equal to one for the NTF period and zero for the pre-NTF period. Panel C provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the NTF and post-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Post-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Post-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}$, where D^Post-NTF is a dummy variable equal to one for the post-NTF period and zero for the NTF period. We cluster standard errors by firm and time in the regressions. We use multiple versions of variance ratio (VR) as our empirical proxies for price efficiency variables: variance ratios based on 15-s/3 x 5-s (VR_1), 1-min/4 × 15-s (VR_2), 5-min/5 x 1-min (VR_3), 15-min/3 x 5-min (VR_4), and 30-min/2 × 15-min (VR_5). Numbers in parentheses are t-statistics. **Significant at the 1% level.

Prior research shows that price efficiency increases with liquidity (Chordia et al., 2008) and informed trading (Kyle, 1985; Easley et al., 1997). The pandemic is associated with a decrease in liquidity (as shown in Section 3.1) and an increase in informed trading (as shown in Section 5.1). Hence, whether the pandemic increases or decreases price efficiency would depend on the relative strength of the two opposing effects. Our results suggest that the positive effect of the pandemic on informed trading is greater than the negative effect of the pandemic on liquidity for both the NYSE and Nasdaq stocks.

The results for the control variables show that variance ratios are larger for stocks with higher prices, smaller trading volumes, and higher return volatility and when the VIX is lower, indicating lower price efficiency for these stocks. These results are consistent with Chung et al.’s (2020) findings that autocorrelations in stock returns are larger for stocks with higher prices, smaller trading volumes, and higher return volatility and when the market volatility index is lower.22

4.2. Effects of the closure of the NYSE trading floor on price efficiency

Panel A in Table 3 shows that the closure of the NYSE trading floor is accompanied by a significant increase (ΔC ₁ > 0) in all five variance ratios for the NYSE stocks. For instance, VR_1 and VR_2 increase by 0.0628 (an 18% increase) and 0.0560 (a 17.7% increase), respectively. These results suggest that the closure of the NYSE trading floor is associated with a decrease in price efficiency for the NYSE stocks. The DiD result (i.e., ΔC ₁ – ΔC ₂) in Panel B shows that the decrease in price efficiency for the NYSE stocks is greater than the decrease in price efficiency for the Nasdaq stocks, suggesting that the closure of the NYSE trading floor led to a decrease in price efficiency for the NYSE stocks after controlling for the market-wide decrease in price efficiency between the pre-NTF period and the NTF period.

To examine how the absence of the trading floor on the NYSE affects price efficiency after controlling for stock attributes and the effects of other variables, we estimate equation (2) using price efficiency as the dependent variable. Panel B in Table 4 shows that the estimates of ${\beta }_1$ (0.0137, 0.0202, 0.0156, 0.0118, and 0.0175) are positive and significant in all regression models, indicating that the closure of the NYSE trading floor is associated with a decrease in price efficiency for the NYSE stocks. To the extent that price efficiency increases with liquidity, this result could be explained by the decrease in liquidity on the NYSE associated with the closure of its trading floor.23 This result is consistent with the finding of Brogaard et al. (2021) that the closure of the NYSE trading floor is associated with a 2% increase in pricing errors (which implies a 2% decrease in price efficiency).24 The estimates of ${\beta }_2$ are negative and significant in all regression models, indicating that the NYSE stocks have higher price efficiency than Nasdaq stocks during the pre-NTF period.

4.3. Effects of the reopening of the NYSE trading floor on price efficiency

Panel A in Table 3 shows that the reopening of the NYSE trading floor is accompanied by a significant decrease (ΔR ₁ < 0) in all five variance ratios. The DiD result (i.e., ΔR ₁ – ΔR ₂) in Panel B shows that the decrease in variance ratios for the NYSE stocks is greater than the decrease in variance ratios for the Nasdaq stocks, suggesting that the reopening of the NYSE trading floor led to an increase in price efficiency for the NYSE stocks. Panel C in Table 4 provides the results when we estimate equation (3) using each measure of price efficiency as the dependent variable. The estimates of ${\beta }_1$ are negative and significant in all regression models, indicating that the restoration of the NYSE trading floor is associated with an increase in price efficiency for the NYSE stocks after controlling for other determinants of price efficiency. The estimates of ${\beta }_2$ are positive and significant in all regression models, indicating that the NYSE stocks have, on average, lower price efficiency than the Nasdaq stocks while its trading floor is closed.

5. Effects of the trading floor and the pandemic on trading activities

In this section, we explore how the pandemic and the closure and reopening of the NYSE trading floor affected trading activities to help better understand their effects on price efficiency presented in the previous section. For trading activity variables, we use the number of trades (NTRADE), total dollar volume (DVOL), number of intermarket sweep order trades (NISO), total intermarket sweep order dollar volume (DVISO), number of odd-lot trades (NODDLOT), and total odd-lot dollar volume (DVODDLOT). We obtain daily values of these variables from the WRDS Intraday Indicator Database.

We use intermarket sweep order trading and odd-lot trading as empirical proxies for informed trading. An intermarket sweep order (ISO) is a limit order sent to multiple exchanges simultaneously. Intermarket sweep orders are used mostly in algorithmic trading by institutional investors or market makers.25 Chakravarty et al. (2012) show that ISO trades have a significantly larger information share than non-ISO trades. Odd-lot trades are trades for less than 100 shares in a given security. O'Hara et al. (2014) suggest that odd-lots are frequently used in algorithmic and high-frequency trading. In their study sample, odd-lot trades account for more than 60% in some stocks and contribute 35% of price discovery. The authors interpret these results as evidence that informed traders split orders into odd lots to avoid detection. Fig. 6, Fig. 7, Fig. 8 show the time series patterns of DVOL, DVISO, and DVODDLOT for the matched NYSE and Nasdaq stocks.26 We also use the absolute value of order imbalance (ORDIMB) and the probability of informed trading (PIN) as additional measures of informed trading.

Fig. 6.

Dollar volume (DVOL) for NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of dollar volume for NYSE and Nasdaq stocks in the pre-COVID (January 22, 2020 to February 21, 2020), pre-NTF (February 22, 2020 to March 22, 2020), NTF (March 23, 2020 to May 22, 2020) and post-NTF (May 26, 2020 to June 25, 2020) periods.

Fig. 7.

ISO volume (DVISO) for NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of ISO dollar volume for NYSE and Nasdaq stocks in the pre-COVID (January 22, 2020 to February 21, 2020), pre-NTF (February 22, 2020 to March 22, 2020), NTF (March 23, 2020 to May 22, 2020) and post-NTF (May 26, 2020 to June 25, 2020) periods.

Fig. 8.

Odd lot volume (DVODDLOT) for NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post-NTF periods

The figure shows the values of odd lot dollar volume for NYSE and Nasdaq stocks in the pre-COVID (January 22, 2020 to February 21, 2020), pre-NTF (February 22, 2020 to March 22, 2020), NTF (March 23, 2020 to May 22, 2020) and post-NTF (May 26, 2020 to June 25, 2020) periods.

5.1. Effects of the pandemic on trading activities

To examine how the pandemic affected trading activities and informed trading, we replicate Table 1 using the above trading activity measures, order imbalance, and PIN, and provide the results in Table 5 . Panel A shows that the pandemic is accompanied by a significant increase in all six trading activity measures, order imbalance, and PIN (ΔP ₁ > 0). The DiD result (i.e., ΔP ₁ – ΔP ₂) in Panel B shows that the increase in these variables for the NYSE stocks is larger than that for the Nasdaq stocks. For instance, the pandemic is associated with an additional increase of 462 in the number of ISO trades, a further increase of $5.54 million in the ISO dollar trading volume, an additional increase of 275 in the number of odd-lot trades, and an additional increase of $1.162 million in the odd-lot dollar trading volume for the NYSE stocks relative to the Nasdaq stocks.

Table 5.

Comparisons of trading activity and informed trading measures in the pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Comparisons of trading activity measures in the pre-COVID, pre-NTF, NTF, and post-NTF periods
	NYSE stocks							Nasdaq stocks
Variable	Pre-COVID	Pre-NTF	NTF	Post-NTF	Pre-NTF – Pre-COVID (ΔP1)	NTF – Pre-NTF (ΔC1)	Post-NTF – NTF (ΔR1)	Pre-COVID	Pre-NTF	NTF	Post-NTF	Pre-NTF – Pre-COVID (ΔP2)	NTF – Pre-NTF (ΔC2)	Post-NTF – NTF (ΔR2)
NTRADE	10,018	12,264	9550	10,045	2246** (16.72)	−2714** (−18.67)	495** (13.61)	10,012	11,665	9833	10,069	1653** (11.96)	−1832** (−13.13)	236** (6.12)
DVOL ($ in millions)	70.97	83.78	60.83	71.19	12.81** (13.34)	−22.95** (−16.81)	10.36** (14.52)	68.08	75.35	60.99	68.55	7.270** (9.82)	−14.36** (−9.57)	7.560** (8.47)
NISO	2983	4342	2415	3006	1359** (24.72)	−1927** (−31.58)	591** (16.38)	2957	3.854	2635	2944	897** (12.34)	−1219** (−16.87)	309** (11.21)
DVISO ($ in millions)	12.86	16.72	10.68	12.99	3.861** (18.41)	−6.040** (−17.45)	2.310** (15.47)	12.83	14.65	11.74	12.93	1.816** (11.32)	−2.910** (−9.26)	1.190** (7.28)
NODDLOT	3246	4027	2788	3273	781** (17.79)	−1239** (−21.04)	485** (14.05)	3231	3737	2849	3261	506** (10.65)	−888** (−12.56)	412** (8.65)
DVODDLOT ($ in millions)	8.140	10.99	6.135	8.177	2.853** (15.70)	−4.859** (−19.26)	2042** (18.74)	8.081	9.772	6.947	8.123	1.691** (8.93)	−2.825** (−11.83)	1.176** (7.39)
ORDIMB ($ in millions)	2.849	4.103	2.436	2.860	1.254** (18.14)	−1.667** (−27.73)	0.4236** (9.55)	2.881	3.755	2.786	2.905	0.8740** (14.89)	−0.9690** (−18.38)	0.1191** (5.81)
PIN	0.0571	0.0808	0.0467	0.0576	0.0237** (15.40)	−0.0341** (−21.37)	0.0109** (8.26)	0.0575	0.0718	0.0521	0.0581	0.0143** (11.79)	−0.0197** (−15.49)	0.0060** (6.83)

Panel B: Difference-in-differences
Variable	(Pre-NTF – Pre-COVID)NYSE – (Pre-NTF – Pre-COVID)Nasdaq = ΔP1 – ΔP2	(NTF – Pre-NTF)NYSE – (NTF – Pre-NTF)Nasdaq = ΔC1 – ΔC2	(Post-NTF – NTF)NYSE – (Post-NTF – NTF)Nasdaq = ΔR1 – ΔR2
NTRADE	593** (9.15)	−882** (−10.46)	259** (9.46)
DVOL ($ in millions)	5.540** (7.94)	−8.590** (−12.64)	2.800** (8.62)
NISO	462** (12.71)	−708** (−13.54)	282** (8.21)
DVISO ($ in millions)	2.045** (14.43)	−3.130** (−14.24)	1.120** (10.75)
NODDLOT	275** (8.51)	−351** (−10.68)	73** (6.23)
DVODDLOT ($ in millions)	1.162** (14.73)	−2.034** (−15.38)	0.8660** (12.77)
ORDIMB ($ in millions)	0.3807** (8.15)	−0.6979** (−11.35)	0.3045** (7.31)
PIN	0.0094** (6.99)	−0.0144** (−8.14)	0.0048** (5.22)

We define January 22, 2020 to February 21, 2020 as the pre-COVID period, February 22, 2020 to March 22, 2020 as the pre-NTF period, March 23, 2020 to May 25, 2020 as the NTF period, and May 26, 2020 to June 25, 2020 as the post-NTF period, where NTF stands for no trading floor. For each period, we compute the mean value of each variable for our matched NYSE and Nasdaq sample stocks. We use the following variables as our empirical proxies for trading activities: number of trades (NTRADE), total dollar volume (DVOL), number of intermarket sweep order trades (NISO), total intermarket sweep order dollar volume (DVISO), number of odd-lot trades (NODDLOT), and total odd-lot dollar volume (DVODDLOT). We use the absolute value of order imbalance (ORDIMB) and probability of informed trading (PIN) as measures of informed trading. Numbers in parentheses are t-statistics. **Significant at the 1% level.

Panel A in Table 6 provides the results of equation (1) when we use each trading activity measure, order imbalance, or PIN as the dependent variable. The estimates of ${\beta }_1$ are positive and significant in all regression models, indicating that the positive effect of the pandemic on trading activities and informed trading for the NYSE stocks is greater than that for the Nasdaq stocks. One possible explanation for this finding is that the NYSE trading floor helped increase trading during the pandemic before its closure (i.e., the pre-NTF period). We showed earlier that the pandemic increased price efficiency on the NYSE and Nasdaq, and the increase is larger for the NYSE stocks. Because share prices become informationally efficient through the trading of informed investors, the greater positive effect of the pandemic on price efficiency for the NYSE stocks could be due, at least in part, to the pandemic's greater positive impact on ISO trading, odd-lot trading, order imbalance, and PIN for the NYSE stocks.

Table 6.

Regression results for trading activity measures using pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Regression results using trading activity and informed trading measures in the pre-COVID and pre-NTF periods
Variable	NTRADE	DVOL	NISO	DVISO	NODDLOT	DVODDLOT	ORDIMB	PIN
NYSE x DPre-NTF	577.6** (5.33)	5.683** (6.37)	454.8** (4.84)	1.966** (5.08)	259.1** (3.53)	1.154** (4.47)	0.4011** (5.97)	0.0102** (4.32)
NYSE	6.084 (0.30)	2.607 (0.46)	28.22 (0.57)	0.0230 (0.34)	16.25 (0.86)	0.0612 (0.66)	−0.0381 (−0.46)	−0.0001 (−0.24)
DPre-NTF	1622** (3.72)	7.104** (2.84)	878.9** (4.59)	1.721** (4.13)	515.9** (3.68)	1.542** (3.72)	0.8273** (5.23)	0.0129** (3.64)
PRICE	1087** (11.45)	60.90** (16.08)	−1501** (−16.70)	−2.930** (−7.69)	−766.1** (−11.32)	−0.2538** (−2.73)	−0.2354** (−4.07)	−0.0118** (−14.56)
VOLUME			5637** (21.52)	32.71** (26.47)	6391** (26.51)	14.85** (24.83)	3.923** (26.16)	0.0163** (16.01)
RET	−28.04** (−3.04)	−0.1570** (−2.95)	−8.500** (−2.85)	−0.0137** (−2.90)	−1.160** (−2.79)	−0.0121** (−2.82)	−0.0040* (−2.31)	−0.0001* (−2.47)
VOLA	−235.7** (−10.71)	0.1330** (2.77)	−33.53** (−7.57)	0.2618** (9.57)	3.180** (2.81)	0.2268** (13.58)	0.0468** (11.11)	0.0008** (2.82)
VIX	5999** (16.47)	29.64** (13.07)	1031** (10.99)	0.1145** (2.74)	904.9** (13.53)	0.1212** (2.80)	0.1275* (2.39)	0.0879** (10.97)
Adj. R2	0.11	0.17	0.71	0.63	0.75	0.57	0.51	0.69
Panel B: Regression results using trading activity measures in the pre-NTF and NTF periods
Variable	NTRADE	DVOL	NISO	DVISO	NODDLOT	DVODDLOT	ORDIMB	PIN
NYSE x DNTF	−859.1** (−5.89)	−8.550** (−6.20)	−725.3** (−5.64)	−3.008** (−2.94)	−344.7** (−3.25)	−1.862** (−3.46)	−0.6864** (−6.22)	−0.0137** (−4.65)
NYSE	568.9** (3.45)	8.487** (4.63)	462.3** (5.94)	2.161** (3.63)	269.1** (2.81)	1.201** (3.57)	0.3647** (3.99)	0.0081** (3.63)
DNTF	−1777** (−3.14)	−13.81** (−3.20)	−1224** (−5.03)	−2.856** (−6.38)	−909.3** (−4.89)	−2.846** (−3.33)	−0.9286** (−5.18)	−0.0172** (−4.30)
Control variables	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Adj. R2	0.12	0.17	0.74	0.63	0.76	0.58	0.51	0.73
Panel C: Regression results using trading activity and informed trading measures in the NTF and post-NTF periods
Variable	NTRADE	DVOL	NISO	DVISO	NODDLOT	DVODDLOT	ORDIMB	PIN
NYSE x DPost-NTF	268.9** (3.70)	3.086** (3.56)	272.3** (4.11)	1.214** (3.84)	70.07** (3.59)	0.8320** (3.65)	0.3118** (4.67)	0.0057** (3.63)
NYSE	−274.3** (−3.62)	−0.1920* (−2.28)	−203.6** (−2.90)	−0.9604** (−3.11)	−57.65** (−2.86)	−0.7468** (−2.72)	−0.3386** (−3.88)	−0.0048** (−3.34)
DPost-NTF	217.1** (3.28)	7.410** (2.86)	305.7** (3.05)	1.130** (3.31)	433.9** (4.03)	1.098** (3.53)	0.1054** (2.74)	0.0069** (4.11)
Control variables	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Adj. R2	0.11	0.16	0.72	0.62	0.76	0.57	0.50	0.72

Panel A provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-COVID and pre-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where subscripts i and t denote stock i and time t, VAR denotes each trading activity variable, NYSE is a dummy variable equal to one for the NYSE stocks and zero for the Nasdaq stocks, D^Pre-NTF is a dummy variable equal to one for the pre-NTF period and zero for the pre-COVID period. PRICE is the stock price, VOLUME denotes the trading volume, RET is the stock return, VOLA is the return volatility, VIX is the CBOE's volatility index, and ε denotes the error term. Panel B reports the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-NTF and NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_1{NYSE\mathrm{x}D}^{NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^NTF is a dummy variable equal to one for the NTF period and zero for the pre-NTF period. Panel C provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the NTF and post-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Post-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Post-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^Post-NTF is a dummy variable equal to one for the post-NTF period and zero for the NTF period. We cluster standard errors by firm and time in the regressions. We use the following variables as our empirical proxies for trading activity variables: number of trades (NTRADE), total dollar volume (DVOL), number of intermarket sweep order trades (NISO), total intermarket sweep order dollar volume (DVISO), number of odd-lot trades (NODDLOT), and total odd-lot dollar volume (DVODDLOT). We measure informed trading using absolute value of order imbalance (ORDIMB) and probability of informed trading (PIN). Numbers in parentheses are t-statistics. **Significant at the 1% level. *Significant at the 5% level.

5.2. Effects of the closure of the NYSE trading floor on trading activities

Panel A in Table 5 shows that the closure of the NYSE trading floor is accompanied by a significant decrease (ΔC ₁ < 0) in all six trading activity measures, order imbalance, and PIN for the NYSE stocks. The results for the Nasdaq stocks are qualitatively similar to those for the NYSE stocks. The DiD result (i.e., ΔC ₁ – ΔC ₂) in Panel B shows that the decrease in these variables for the NYSE stocks is greater than the decrease for the Nasdaq stocks. For instance, the closure of the NYSE trading floor is associated with an additional decrease of 708 in the number of ISO trades, a further reduction of $3.13 million in the ISO dollar trading volume, an additional reduction of 351 in the number of odd-lot trades, and an additional decrease of $2.034 million in the odd-lot dollar trading volume for the NYSE stocks, relative to the Nasdaq stocks.

Panel B in Table 6 provides the results of equation (2) for each trading activity variable, order imbalance, and PIN. We find that the estimates of ${\beta }_1$ (i.e., −859.1, −8.550, −725.3, −3.008, −344.7, −1.862, −0.6864, and −0.0137) are negative and significant in all eight regression models and similar in sizes to the corresponding DiD result (i.e., ΔC ₁ – ΔC ₂) in Panel B of Table 5, indicating that the closure of the NYSE trading floor is associated with a decrease in trading, order imbalance, and PIN for the NYSE stocks after controlling for the market-wide change in these variables. To the extent that intermarket sweep orders and odd-lot orders are used by better-informed traders, the decrease in price efficiency for the NYSE stocks associated with the closure of the NYSE's trading floor shown in the previous section could be due to a concurrent reduction in ISO trading, odd-lot trading, order imbalance, and PIN.

5.3. Effects of the reopening of the NYSE trading floor on trading activities

Panel A in Table 5 shows that the reopening of the NYSE trading floor is accompanied by a significant increase (ΔR ₁ > 0) in all six trading activity measures, order imbalance, and PIN for the NYSE stocks. The results for the Nasdaq stocks are qualitatively similar to those for the NYSE stocks (i.e., ΔR ₂ > 0). The DiD result (i.e., ΔR ₁ – ΔR ₂) in Panel B shows that the increase in trading activities, order imbalance, and PIN for the NYSE stocks is greater than the increase in these variables for the Nasdaq stocks.

Panel C in Table 6 shows the results of equation (3) for each trading activity variable, order imbalance, and PIN. The results show that the estimates of ${\beta }_1$ are positive and significant in all regression models, and their magnitudes are comparable to the corresponding DiD values provided in Panel B of Table 5. These results indicate that the restoration of the NYSE trading floor is associated with an increase in trading, order imbalance, and PIN for the NYSE stocks. The increase in price efficiency for the NYSE stocks resulted from the reopening of the NYSE's trading floor shown in the previous section could be due to a concurrent increase in ISO trading, odd-lot trading, order imbalance, and PIN. The estimates of ${\beta }_2$ are negative and significant in all eight regression models, indicating that the NYSE stocks have lower trading activities, order imbalance, and PIN than the Nasdaq stocks during the NTF period.

6. Changes in liquidity, price efficiency, and trading between the pre-pandemic and other periods

In this section, we compare the variables of interest (i.e., liquidity, price efficiency, trading, order imbalance, and PIN) between the pre-COVID period and each of the three subsequent periods (i.e., pre-NTF, NTF, and post-NTF) to assess changes in these variables relative to their values before the pandemic. In particular, comparing these variables between the pre-COVID period and the post-NTF period would inform us whether the effects of the pandemic on these variables are partially or fully reversed after the NYSE reopened its trading floor. For this, we estimate the following regression model using the matched NYSE and Nasdaq stocks in all four periods:

$${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSEx{D}^{Pre-NTF}+{\beta }_{2}NYSEx{D}^{NTF}+{\beta }_{3}NYSEx{D}^{Post-NTF}{+\beta }_{4}NYSE$$

$${+{\beta }_{5}D}^{Pre-NTF}+{\beta }_6{D}^{NTF}+{\beta }_7{D}^{Post-NTF}+{\beta }_8{PRICE}_{i,t}+{\beta }_9{VOLUME}_{i,t}$$

$$+{\beta }_{10}{RET}_{i,t}+{\beta }_{11}{VOLA}_{i,t}+{\beta }_{12}{VIX}_t+{\epsilon }_{i,t}\text{,}$$ (4)

where all variables are the same as previously defined. Panel A in Table 7 shows the results for liquidity variables, Panel B shows the results for price efficiency variables, and Panel C shows the results for trading activity variables, order imbalance, and PIN. To save space, we omit the results for the control variables in Table 7.

Table 7.

Changes in liquidity, price efficiency, and trading between the pre-COVID and other periods.

Panel A: Regression results for liquidity variables
Variable	QSP	ESP	ESP_VW	RSP	RSP_VW	PIMPACT	PIMPACT_VW	DEPTH	LAMBDA_1	LAMBDA_2
NYSE x DPre-NTF	−0.0283** (−4.37)	−0.0175** (−4.18)	−0.0098** (−3.73)	−0.0085** (−5.28)	−0.0063** (−3.93)	−0.0085** (−4.17)	−0.0061** (−3.42)	1.827** (3.54)	−0.2026** (−2.82)	−0.0919** (−2.74)
NYSE x DNTF	0.0131** (3.39)	0.0418** (5.49)	0.0384** (4.63)	0.0364** (5.46)	0.0324** (4.77)	0.0049** (3.32)	0.0046** (3.29)	−3.712** (−3.75)	0.5962** (2.93)	0.6361** (3.27)
NYSE x DPost-NTF	−0.0013 (−0.27)	0.0004 (0.37)	0.0006 (0.22)	0.0021 (0.44)	0.0021 (0.44)	−0.0009 (−0.29)	−0.0012 (−0.47)	−0.0525 (−0.38)	−0.0138 (−0.20)	0.0076 (0.50)
NYSE	−0.0004 (−0.28)	−0.0004 (−0.41)	−0.0007 (−0.31)	−0.0019 (−0.51)	−0.0019 (−0.46)	0.0019 (0.54)	0.0009 (0.39)	0.1678 (0.69)	0.0729 (0.79)	0.0705 (0.56)
DPre-NTF	0.1564** (4.73)	0.0929** (4.53)	0.1257** (5.01)	0.0195** (2.98)	0.0293** (3.20)	0.0745** (4.50)	0.0981** (5.76)	−9.232** (−4.88)	1.509** (2.79)	1.403** (2.86)
DNTF	0.1671** (3.76)	0.1066** (4.66)	0.1373** (3.81)	0.0263** (2.93)	0.0374** (3.28)	0.0792** (5.82)	0.1005** (3.76)	−10.09** (−4.66)	1.863** (3.59)	1.853** (3.32)
DPost-NTF	0.0006 (0.44)	−0.0028 (−0.35)	−0.0007 (−0.34)	−0.0005 (−0.25)	−0.0004 (−0.17)	−0.0025 (−0.47)	−0.0005 (−0.30)	−0.1880 (−0.43)	0.0438 (0.36)	0.0397 (0.65)
Adjusted R2	0.54	0.54	0.50	0.32	0.27	0.39	0.31	0.15	0.14	0.15

Panel B: Regression results for price efficiency variables
Variable	VR_1	VR_2	VR_3	VR_4	VR_5
NYSE x DPre-NTF	−0.0094** (−4.31)	−0.0117** (−4.18)	−0.0094** (−3.84)	−0.0078** (−3.28)	−0.0123** (−5.59)
NYSE x DNTF	0.0053** (3.67)	0.0135** (4.13)	0.0055** (3.68)	0.0057** (3.06)	0.0090** (4.36)
NYSE x DPost-NTF	−0.0025 (−1.30)	−0.0001 (−0.08)	−0.0007 (−0.28)	−0.0005 (−0.26)	0.0009 (0.58)
NYSE	−0.0016 (−1.08)	−0.0002 (−0.15)	0.0001 (0.21)	0.0014 (0.42)	0.0003 (0.35)
DPre-NTF	−0.0231** (−3.74)	−0.0075** (−3.06)	−0.0078** (−2.91)	−0.0128** (−3.85)	−0.0091** (−3.55)
DNTF	0.0257** (5.02)	0.0261** (5.36)	0.0126** (2.76)	0.0067** (2.87)	0.0063** (2.89)
DPost-NTF	−0.0003 (−0.21)	−0.0013 (−0.32)	0.0009 (0.52)	−0.0008 (−0.51)	−0.0018 (−0.69)
Adjusted R2	0.58	0.44	0.21	0.11	0.09

Panel C: Regression results for trading activity and informed trading variables
Variable	NTRADE	DVOL	NISO	DVISO	NODDLOT	DVODDLOT	ORDIMB	PIN
NYSE x DPre-NTF	615.3** (5.38)	5.497** (6.33)	479.4** (5.92)	1.992** (4.93)	286.5** (4.81)	1.341** (5.42)	0.3770** (5.03)	0.0115** (4.25)
NYSE x DNTF	−275.8** (−3.60)	−2.885** (−3.86)	−237.6** (−3.89)	−1.297** (−3.26)	−82.43** (−2.74)	−0.9354** (−3.51)	−0.3115** (−3.79)	−0.0043** (−3.26)
NYSE x DPost-NTF	−26.9 (−0.35)	−0.2640 (−0.43)	29.00 (0.22)	0.0296 (0.28)	−2.914 (−0.44)	−0.0037 (−0.19)	−0.0136 (−0.27)	−0.0001 (−0.36)
NYSE	5.881 (0.28)	2.780 (1.21)	23.91 (0.45)	0.0167 (0.12)	11.41 (0.50)	0.0624 (0.53)	−0.0304 (−0.53)	−0.0005 (−0.51)
DPre-NTF	1603** (4.04)	6.935** (3.27)	868.3** (5.23)	2.048** (3.51)	523.8** (4.96)	1.584** (3.92)	0.8655** (4.89)	0.0110** (5.08)
DNTF	−238.8* (−2.44)	−6.841** (−2.77)	−339.3** (−3.24)	−1.175** (−3.16)	−354.2** (−3.38)	−1.238** (−3.35)	−0.0916* (−2.59)	−0.0054** (−3.64)
DPost-NTF	48.72 (0.62)	0.4042 (0.48)	−11.15 (−0.25)	0.0773 (0.36)	26.55 (0.57)	0.0391 (0.48)	0.0211 (0.42)	0.0007 (0.49)
Adjusted R2	0.12	0.16	0.72	0.64	0.75	0.58	0.49	0.70

This table provides the estimation results of the following regression model using the matched NYSE and Nasdaq stocks in the pre-COVID, pre-NTF, NTF, and post NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE\mathrm{x}{D}^{NTF}+{\beta }_{3}NYSE\mathrm{x}{D}^{Post-NTF}{+\beta }_4{NYSE+{\beta }_{5}D}^{Pre-NTF}+{\beta }_6{D}^{NTF}+{\beta }_7{D}^{Post-NTF}+{\beta }_8{PRICE}_{i,t}+{\beta }_9{VOLUME}_{i,t}+{\beta }_{10}{RET}_{i,t}+{\beta }_{11}{VOLA}_{i,t}+{\beta }_{12}{VIX}_t+{\epsilon }_{i,t}\text{,}$ where subscripts i and t denote stock i and time t, VAR denotes each liquidity variable, NYSE is a dummy variable equal to one for the NYSE stocks and zero for the Nasdaq stocks, D^Pre-NTF is a dummy variable equal to one for the pre-NTF period and zero otherwise, D^NTF is a dummy variable equal to one for the NTF period and zero otherwise, D^Post-NTF is a dummy variable equal to one for the post-NTF period and zero otherwise. PRICE is the stock price, VOLUME denotes the trading volume, RET is the stock return, VOLA is the return volatility, VIX is the CBOE Volatility Index, and ε denotes the error term. We cluster standard errors by firm and time in the regressions. We use the following variables (VAR) as our empirical proxies for liquidity: quoted spread (QSP), effective spread (ESP), value-weighted effective spread (ESP_VW), realized spread (RSP), value-weighted realized spread (RSP_VW), price impact (PIMPACT), value-weighted price impact (PIMPACT_VW), quoted depth (DEPTH), price impact coefficient with intercept (LAMBDA_1), and price impact coefficient without intercept (LAMBDA_2). We use multiple versions of variance ratio (VR) as our empirical proxies for price efficiency measures: variance ratios based on 15-s/3 x 5-s (VR_1), 1-min/4 × 15-s (VR_2), 5-min/5 x 1-min (VR_3), 15-min/3 x 5-min (VR_4), and 30-min/2 × 15-min (VR_5). We use the following variables as our empirical proxies for trading activity variables: number of trades (NTRADE), total dollar volume (DVOL), number of intermarket sweep order trades (NISO), total intermarket sweep order dollar volume (DVISO), number of odd-lot trades (NODDLOT), and total odd-lot dollar volume (DVODDLOT). We use the absolute value of order imbalance (ORDIMB) and probability of informed trading (PIN) as measures as informed trading. To save space, we omit the results for the control variables. Numbers in parentheses are t-statistics. **Significant at the 1% level. *Significant at the 5% level.

6.1. Results for liquidity variables

The difference in liquidity between the pre-NTF period and the pre-COVID period measures the effect of the pandemic on liquidity. Hence, in equation (4), the coefficient (${\beta }_5$) on $D^{Pre-NTF}$ measures the effect of the pandemic on liquidity for the Nasdaq stocks. Likewise, the coefficient (${\beta }_1$) on $NYSE\mathrm{x}{D}^{Pre-NTF}$ measures the differential effect of the pandemic for the NYSE stocks relative to the Nasdaq stocks. As expected, the estimates of ${\beta }_1$ and ${\beta }_5$ in Panel A of Table 7 are similar to the estimates of ${\beta }_1$ and ${\beta }_3$ in Panel A of Table 2.

The coefficients (${\beta }_2$) on NYSE x $D^{NTF}$ in Panel A of Table 7 are positive and significant in the regression models of the spreads and price impacts, and negative and significant in the regression model of the depth.27 These results indicate that the closure of the NYSE trading floor is associated with a decrease in liquidity (relative to its pre-pandemic level) for the NYSE stocks after controlling for market-wide changes in liquidity due to the pandemic and other reasons.

The coefficients (β ₃) on $NYSE\mathrm{x}{D}^{Post-NTF}$ in Panel A of Table 7 are not significantly different from zero in all regression models. Similarly, the coefficients (β ₇) on $D^{Post-NTF}$ are not significantly different from zero in all regression models. Note that β ₃ (β ₇) measures the difference in liquidity between the post-NTF period and the pre-COVID period for the NYSE (Nasdaq) stocks. Hence, these results indicate that the effect of the pandemic on liquidity is completely reversed after the NYSE trading floor is fully restored.

6.2. Results for price efficiency variables

As expected, the estimates of ${\beta }_1$ and ${\beta }_5$ in Panel B of Table 7 are similar to the estimates of ${\beta }_1$ and ${\beta }_3$ in Panel A of Table 4. The coefficients (${\beta }_2$) on NYSE x $D^{NTF}$ in Panel B of Table 7 are positive and significant in all regression models, indicating that the closure of the NYSE trading floor is associated with a decrease in price efficiency (relative to its pre-pandemic level) for the NYSE stocks after controlling for the market-wide change in price efficiency. The coefficients (β ₇) on $D^{Post-NTF}$ in Panel B are not significantly different from zero, indicating no difference in price efficiency on Nasdaq between the post-NTF period and the pre-COVID period. Similarly, the coefficients (β ₃) on $NYSEx{D}^{Post-NTF}$ are not significantly different from zero in all regression models, indicating no difference in price efficiency on the NYSE between the post-NTF period and the pre-COVID period. These results suggest that the effect of the pandemic on price efficiency is fully reversed after the reopening of the NYSE trading floor.

6.3. Results for trading activity variables

As expected, the estimates of ${\beta }_1$ and ${\beta }_5$ in Panel C of Table 7 are similar to the estimates of ${\beta }_1$ and ${\beta }_3$ in Panel A of Table 6. The coefficients (${\beta }_2$) on NYSE x $D^{NTF}$ in Panel C of Table 7 are all negative and significant, indicating that the closure of the NYSE trading floor is associated with a decrease in trading activities, order imbalance, and PIN (relative to their pre-pandemic level) for the NYSE stocks. The coefficients (β ₇) on $D^{Post-NTF}$ and the coefficients (β ₃) on $NYSEx{D}^{Post-NTF}$ in Panel C of Table 7 are insignificant in all regression models, indicating that the reopening of the NYSE trading floor fully reversed the effect of the pandemic on trading activities.

7. Liquidity and informed trading as price efficiency channels

In this section, we explore whether liquidity and informed trading are channels through which the pandemic and the closure and reopening of the NYSE trading floor led to changes in price efficiency. Specifically, we conduct the two-stage least squares (2SLS) regression analysis using each of these three events as an instrumental variable. For space considerations, we report the results using each of the five variance ratios (VR_1 through VR_5) as an inverse measure of price efficiency, the effective spread (ESP) or price impact (PIMPACT) as an inverse measure of liquidity, and the intermarket sweep order dollar volume (DVISO) or the total odd-lot dollar volume (DVODDLOT) as a measure of informed trading.

7.1. The pandemic and the price efficiency channels of liquidity and informed trading

We first estimate the following first-stage regression model using the matched NYSE and Nasdaq stocks in the pre-COVID and pre-NTF periods:

$${LIQUIDITY}_{i,t}or{TRADING}_{i,t}={\beta }_0+{\beta }_{1}NYSEx{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}$$

$$+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$$ (5)

where LIQUIDITY is either the effective spread (ESP) or price impact (PIMPACT), TRADING is either the intermarket sweep order dollar volume (DVISO) or the odd-lot dollar volume (DVODDLOT), and all other variables are the same as previously defined. We then estimate the following second-stage regression model:

$${VR}_{i,t}={\beta }_0+{\beta }_{1L}{\widehat{LIQUIDITY}}_{i,t}+{\beta }_{1T}{\widehat{TRADING}}_{i,t}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}$$

$${+\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$$ (6)

where VR is one of the five variance ratios and $\widehat{\mathrm{L}\mathrm{I}\mathrm{Q}\mathrm{U}\mathrm{I}\mathrm{D}\mathrm{I}\mathrm{T}\mathrm{Y}}\left(\widehat{TRADING}\right)$ is the predicted value of LIQUIDITY (TRADING) from the first-stage regression model in equation (5).28

Panel A in Table 8 reports the estimates of β _1L and β _1T from the second-stage regression model in equation (6) using each of the five variance ratios as the dependent variable.29 The left half of the panel shows the results when we measure liquidity by the effective spread (ESP) and the right half shows the results when we measure liquidity by price impact (PIMPACT). Within each half, we show the results when we measure informed trading by DVISO and DVODDLOT, respectively. The results show that the coefficients (${\beta }_{1L})$ on ${\widehat{LIQUIDITY}}_{i,t}$ are positive and significant and the coefficients (${\beta }_{1T}$) on ${\widehat{TRADING}}_{i,t}$ are negative and significant in all regressions, regardless of whether we measure liquidity by ESP or PIMPACT and informed trading by DVISO or DVODDLOT. Because variance ratios are an inverse measure of price efficiency and both ESP and PIMPACT are an inverse measure of liquidity, the positive ${\beta }_{1L}$ coefficients indicate that price efficiency increases with liquidity. Because DVISO and DVODDLOT are a direct measure of informed trading, the negative ${\beta }_{1T}$ coefficients indicate that price efficiency increases with informed trading.30 Overall, these results support the idea that the pandemic led to an increase in price efficiency through the channels of liquidity and informed trading.

Table 8.

Liquidity and informed trading as price efficiency channels.

Panel A: Results for β1L and β1T from the second-stage regression model using the pre–COVID and pre–NTF periods
Dep. var.	Results for ESP (β1L) and DVISO or DVODDLOT (β1T)				Results for PIMPACT (β1L) and DVISO or DVODDLOT (β1T)
VR_1	ESP	0.3175** (6.12)	ESP	0.3195** (6.07)	PIMPACT	0.4802** (6.28)	PIMPACT	0.4810** (6.18)
	DVISO	−0.0145** (−5.06)	DVODDLOT	−0.0183** (−4.33)	DVISO	−0.0136** (−5.59)	DVODDLOT	−0.0148** (−4.59)
	Adj. R2	0.60	Adj. R2	0.60	Adj. R2	0.59	Adj. R2	0.59
VR_2	ESP	0.3032** (5.51)	ESP	0.3046** (5.76)	PIMPACT	0.4661** (5.54)	PIMPACT	0.4698** (5.76)
	DVISO	−0.0120** (−4.19)	DVODDLOT	−0.0161** (−4.28)	DVISO	−0.0097** (−4.44)	DVODDLOT	−0.0117** (−4.76)
	Adj. R2	0.41	Adj. R2	0.40	Adj. R2	0.41	Adj. R2	0.42
VR_3	ESP	0.2865** (4.39)	ESP	0.2832** (4.60)	PIMPACT	0.4352** (4.43)	PIMPACT	0.4364** (4.36)
	DVISO	−0.0092** (−4.12)	DVODDLOT	−0.0098** (−4.85)	DVISO	−0.0082** (−4.51)	DVODDLOT	−0.0103** (−4.47)
	Adj. R2	0.17	Adj. R2	0.16	Adj. R2	0.17	Adj. R2	0.17
VR_4	ESP	0.1497** (4.47)	ESP	0.1521** (4.09)	PIMPACT	0.3048** (4.16)	PIMPACT	0.3094** (4.28)
	DVISO	−0.0072** (−3.89)	DVISO	−0.0089** (−3.59)	DVISO	−0.0064** (−3.67)	DVODDLOT	−0.0084** (−3.72)
	Adj. R2	0.13	Adj. R2	0.12	Adj. R2	0.13	Adj. R2	0.13
VR_5	ESP	0.0091** (3.45)	ESP	0.0086** (3.77)	PIMPACT	0.1309** (3.98)	PIMPACT	0.1326** (3.77)
	DVISO	−0.0048** (−3.28)	DVODDLOT	−0.0067** (−3.69)	DVISO	−0.0051** (−3.41)	DVODDLOT	−0.0073** (−3.34)
	Adj. R2	0.09	Adj. R2	0.08	Adj. R2	0.08	Adj. R2	0.09

Panel B: Results for β1L and β1T from the second-stage regression model using the pre–NTF and NTF periods
Dep. var.	Results for ESP (β1L) and DVISO or DVODDLOT (β1T)				Results for PIMPACT (β1L) and DVISO or DVODDLOT (β1T)
VR_1	ESP	0.3017** (5.20)	ESP	0.3145** (5.44)	PIMPACT	0.4741** (5.35)	PIMPACT	0.4774** (5.42)
	DVISO	−0.0104** (−4.92)	DVODDLOT	−0.0132** (−4.80)	DVISO	−0.0119** (−4.71)	DVODDLOT	−0.0131** (−4.86)
	Adj. R2	0.58	Adj. R2	0.59	Adj. R2	0.59	Adj. R2	0.58
VR_2	ESP	0.2851** (4.97)	ESP	0.2953** (4.83)	PIMPACT	0.4414** (5.04)	PIMPACT	0.4463** (5.25)
	DVISO	−0.0083** (−4.41)	DVODDLOT	−0.0112** (−4.68)	DVISO	−0.0079** (−4.58)	DVODDLOT	−0.0105** (−4.47)
	Adj. R2	0.43	Adj. R2	0.44	Adj. R2	0.44	Adj. R2	0.43
VR_3	ESP	0.2691** (4.48)	ESP	0.2734** (4.64)	PIMPACT	0.4268** (4.82)	PIMPACT	0.4253** (4.96)
	DVISO	−0.0068** (−4.29)	DVODDLOT	−0.0096** (−4.41)	DVISO	−0.0063** (−4.47)	DVODDLOT	−0.0093** (−4.26)
	Adj. R2	0.22	Adj. R2	0.21	Adj. R2	0.22	Adj. R2	0.22
VR_4	ESP	0.1465** (3.97)	ESP	0.1492** (4.30)	PIMPACT	0.2927** (4.69)	PIMPACT	0.2951** (5.17)
	DVISO	−0.0047** (−3.75)	DVISO	−0.0078** (−4.27)	DVISO	−0.0054** (−4.35)	DVODDLOT	−0.0082** (−4.11)
	Adj. R2	0.14	Adj. R2	0.14	Adj. R2	0.13	Adj. R2	0.13
Dsbr VR_5	ESP	0.0083** (3.32)	ESP	0.0072** (3.26)	PIMPACT	0.1242** (3.84)	PIMPACT	0.1260** (4.40)
	DVISO	−0.0038** (−3.51)	DVODDLOT	−0.0063** (−3.81)	DVISO	−0.0043** (−3.62)	DVODDLOT	−0.0066** (−3.73)
	Adj. R2	0.08	Adj. R2	0.09	Adj. R2	0.09	Adj. R2	0.08
Panel C: Results for β1L and β1T from the second-stage regression model using the NTF and post–NTF periods
Dep. var.	Results for ESP (β1L) and DVISO or DVODDLOT (β1T)				Results for PIMPACT (β1L) and DVISO or DVODDLOT (β1T)
VR_1	ESP	0.3085** (5.50)	ESP	0.3109** (5.93)	PIMPACT	0.4662** (6.24)	PIMPACT	0.4632** (5.72)
	DVISO	−0.0096** (−4.85)	DVODDLOT	−0.0101** (−4.16)	DVISO	−0.0093** (−6.29)	DVODDLOT	−0.0129** (−5.78)
	Adj. R2	0.58	Adj. R2	0.58	Adj. R2	0.57	Adj. R2	0.57
VR_2	ESP	0.2713** (5.04)	ESP	0.2859** (5.61)	PIMPACT	0.4312** (5.21)	PIMPACT	0.4405** (5.45)
	DVISO	−0.0073** (−4.69)	DVODDLOT	−0.0106** (−4.76)	DVISO	−0.0069** (−4.94)	DVODDLOT	−0.0094** (−4.83)
	Adj. R2	0.46	Adj. R2	0.45	Adj. R2	0.45	Adj. R2	0.46
VR_3	ESP	0.2600** (4.66)	ESP	0.2718** (5.18)	PIMPACT	0.4206** (4.85)	PIMPACT	0.4245** (5.01)
	DVISO	−0.0059** (−4.38)	DVODDLOT	−0.0075** (−4.39)	DVISO	−0.0060** (−4.70)	DVODDLOT	−0.0086** (−4.92)
	Adj. R2	0.23	Adj. R2	0.23	Adj. R2	0.24	Adj. R2	0.24
VR_4	ESP	0.1313** (4.20)	ESP	0.1381** (4.78)	PIMPACT	0.2805** (4.40)	PIMPACT	0.2844** (4.78)
	DVISO	−0.0041** (−4.54)	DVISO	−0.0064** (−4.65)	DVISO	−0.0049** (−4.10)	DVODDLOT	−0.0072** (−4.59)
	Adj. R2	0.14	Adj. R2	0.15	Adj. R2	0.14	Adj. R2	0.14
VR_5	ESP	0.0077** (3.84)	ESP	0.0069** (3.41)	PIMPACT	0.1219** (3.62)	PIMPACT	0.1243** (4.25)
	DVISO	−0.0033** (−3.29)	DVODDLOT	−0.0043** (−2.95)	DVISO	−0.0029** (−2.85)	DVODDLOT	−0.0057** (−3.37)
	Adj. R2	0.07	Adj. R2	0.08	Adj. R2	0.08	Adj. R2	0.08

To examine whether COVID-19 led to an increase in price efficiency through the channels of liquidity and informed trading, we estimate the following first-stage regression model using the matched NYSE and Nasdaq stocks in the pre-COVID and pre-NTF periods: ${LIQUIDITY}_{i,t}\mathrm{o}\mathrm{r}{TRADING}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}$+${\beta }_6{RET}_{i,t}$$+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where LIQUIDITY is either the effective spread (ESP) or price impact (PIMPACT), TRADING is either the intermarket sweep order dollar volume (DVISO) or the odd-lot dollar volume (DVODDLOT), and all other variables are the same as previously defined. We then estimate the following second-stage regression model: ${VR}_{i,t}={\beta }_0+{\beta }_{1L}{\widehat{LIQUIDITY}}_{i,t}+{\beta }_{1T}{\widehat{TRADING}}_{i,t}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}{+\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where VR is one of the five variance ratios and $\widehat{LIQUIDITY}\left(\widehat{TRADING}\right)$ is the predicted value of LIQUIDITY (TRADING) from the first-stage regression model. Numbers in parentheses are t-statistics. **Significant at the 1% level.

7.2. The NYSE trading floor closure and the price efficiency channels of liquidity and informed trading

We estimate regression models in equations (5), (6) using the matched NYSE and Nasdaq stocks in the pre-NTF and NTF periods after replacing NYSE x D ^Pre–NTF in equation (5) with NYSE x D ^NTF and D ^Pre–NTF in equations (5), (6) with D ^NTF. Panel B in Table 8 reports the estimates of β _1L and β _1T from the second-stage regression model in equation (6) using each of the five variance ratios as the dependent variable. The results show that the coefficients (${\beta }_{1L})$ on ${\widehat{LIQUIDITY}}_{i,t}$ are positive and significant and the coefficients (${\beta }_{1T}$) on ${\widehat{TRADING}}_{i,t}$ are negative and significant in all regressions. Overall, these results support the idea that the closure of the NYSE trading floor led to a decrease in price efficiency through the channels of liquidity and informed trading.

7.3. The NYSE trading floor reopening and the price efficiency channels of liquidity and informed trading

We next estimate the regression models in equations (5), (6) using the matched NYSE and Nasdaq stocks in the NTF and post-NTF periods after we replace NYSE x D ^Pre–NTF in the regression model in equation (5) with NYSE x D ^Post-NTF and D ^Pre–NTF in the regression models in equations (5), (6) with D ^Post-NTF. Panel C in Table 8 reports the estimates of β _1L and β _1T from the second-stage regression model in equation (6). Again, the results show that the coefficients (${\beta }_{1L})$ on ${\widehat{LIQUIDITY}}_{i,t}$ are positive and significant and the coefficients (${\beta }_{1T}$) on ${\widehat{TRADING}}_{i,t}$ are negative and significant in all regressions, suggesting that the reopening of the NYSE trading floor led to an increase in price efficiency through the channels of liquidity and informed trading.

8. Regression results for large and small firms

In this section, we explore whether the impacts of the pandemic and the trading floor closure/reopening differ between small and large firms. We rank stocks in the NYSE study sample according to the market value of equity (MVE) and group them into three portfolios.31 We use the NYSE stocks in the small (first) and large (third) MVE terciles and their matched Nasdaq stocks in the analysis. Panels A, B, and C in Table 9 show the results when we estimate the regression models in equations (1), (2), (3) for ESP, PIMPACT, VR_3, DVOL, DVISO, DVODDLOT, ORDIMB, and PIN using the stocks in the small MVE tercile. Likewise, Panels D, E, and F show the regression results using the stocks in the large MVE tercile.

Table 9.

Regression results for small and large stocks for liquidity, price efficiency, and trading measures using pre-COVID, pre-NTF, NTF, and post-NTF periods.

Panel A: Regression results for small stocks using variables in the pre-COVID and pre-NTF periods
Variable	ESP	PIMPACT	VR_3	DVOL	DVISO	DVODDLOT	ORDIMB	PIN
NYSE x DPre-NTF	−0.0142** (−4.90)	−0.0068** (−4.12)	−0.0094** (−5.28)	3.557** (3.85)	1.716** (5.19)	1.066** (4.57)	0.3628** (4.96)	0.0081** (4.11)
NYSE	−0.0007 (−0.14)	0.0018 (0.18)	−0.0002 (−0.06)	2.112 (1.05)	0.0235 (0.56)	0.0523 (1.33)	−0.0419 (−0.38)	−0.0002 (−0.31)
DPre-NTF	0.0992** (5.81)	0.0832** (4.93)	−0.0152** (−3.98)	4.627** (4.06)	1.624** (3.95)	1.523** (3.83)	0.8185** (5.68)	0.0113** (3.46)
Adjusted R2	0.48	0.37	0.21	0.19	0.61	0.64	0.47	0.71
Panel B: Regression results for small stocks using variables in the pre-NTF and NTF periods
NYSE x DNTF	0.0741** (7.45)	0.0169** (4.53)	0.0178** (3.81)	−6.454** (−4.79)	−2.085** (−3.47)	−1.713** (−4.31)	−0.5237** (−5.25)	−0.0118** (−5.91)
NYSE	−0.0170** (−4.64)	−0.0062** (−2.90)	−0.0103** (−3.64)	7.573** (3.88)	1.878** (3.92)	1.095** (3.68)	0.3115** (4.33)	0.0075** (5.32)
DNTF	0.0163** (3.84)	0.0070** (2.87)	0.0184** (3.81)	−10.39** (−3.27)	−1.997** (−3.88)	−2.514** (−3.49)	−0.8201** (−5.32)	−0.0146** (−5.44)
Adjusted R2	0.49	0.36	0.23	0.18	0.60	0.62	0.49	0.73
Panel C: Regression results for small stocks using variables in the NTF and post-NTF periods
NYSE x DPost-NTF	−0.0544** (−6.72)	−0.0081** (−4.96)	−0.0083** (−4.54)	1.956** (2.86)	0.8575** (3.54)	0.7081** (4.80)	0.2697** (4.75)	0.0040** (4.24)
NYSE	0.0509** (4.20)	0.0092** (3.56)	0.0075** (2.89)	−0.1817** (−3.43)	−0.8326* (−2.49)	−0.7435** (−2.98)	−0.2883** (−3.24)	−0.0048** (−3.27)
DPost-NTF	−0.1267** (−3.35)	−0.0891** (−3.94)	−0.0109** (−3.32)	5.087** (4.33)	0.9256** (2.71)	1.045** (3.53)	0.0964** (2.92)	0.0052** (3.80)
Adjusted R2	0.49	0.35	0.22	0.17	0.62	0.60	0.49	0.72

Panel D: Regression results for large stocks using variables in the pre-COVID and pre-NTF periods
Variable	ESP	PIMPACT	VR_3	DVOL	DVISO	DVODDLOT	ORDIMB	PIN
NYSE x DPre-NTF	−0.0235** (−7.21)	−0.0154** (−6.45)	−0.0132** (−5.89)	7.349** (6.76)	2.178** (7.30)	1.306** (4.82)	0.4154** (6.98)	0.0134** (5.82)
NYSE	−0.0002 (−0.23)	0.0011 (0.51)	−0.0007 (−0.12)	2.923 (0.67)	0.0460 (0.34)	0.0632 (0.70)	−0.0253 (−0.59)	0.0001 (0.36)
DPre-NTF	0.0897** (4.71)	0.0681** (3.87)	−0.0076** (−3.38)	10.076** (7.47)	2.022** (4.30)	1.897** (2.85)	0.9238** (6.36)	0.0166** (3.77)
Adjusted R2	0.46	0.32	0.23	0.16	0.60	0.67	0.50	0.73
Panel E: Regression results for large stocks using variables in the pre-NTF and NTF periods
NYSE x DNTF	0.0546** (5.96)	0.0147** (4.42)	0.0143** (3.60)	−10.793** (−6.30)	−4.158** (−3.72)	−2.505** (−4.68)	−0.8702** (−7.95)	−0.0161** (−5.92)
NYSE	−0.0198** (−5.76)	−0.0081** (−2.94)	−0.0084** (−2.86)	9.351** (4.64)	2.685**. (4.12)	1.624** (3.83)	0.3843** (−5.78)	0.0117** (5.24)
DNTF	0.0116** (3.29)	0.0051** (2.79)	0.0158** (2.77)	−18.07** (−6.18)	−3.229** (−5.21)	−3.229** (−3.69)	−1.121** (−6.92)	−0.0227** (−6.15)
Adjusted R2	0.47	0.34	0.24	0.15	0.61	0.67	0.52	0.75
Panel F: Regression results for large stocks using variables in the NTF and post-NTF periods
NYSE x DPost-NTF	−0.0367** (−5.73)	−0.0063** (−4.28)	−0.0061** (−4.35)	3.609** (4.72)	1.471** (4.13)	1.038** (5.70)	0.3449** (5.57)	0.0055** (4.71)
NYSE	0.0392** (3.32)	0.0061** (3.14)	0.0058** (2.82)	−0.1508** (−3.16)	−1.373** (−3.27)	−0.8826** (−3.26)	−0.4031** (−4.12)	−0.0069** (−3.90)
DPost-NTF	−0.1006** (−3.01)	−0.0785** (−3.49)	−0.0077** (−3.23)	10.119** (5.84)	1.445** (2.99)	1.352** (3.81)	0.1317** (3.76)	0.0075** (4.73)
Adjusted R2	0.49	0.33	0.22	0.14	0.62	0.66	0.51	0.75

We report the regression results for liquidity, price efficiency, and trading measures using the matched NYSE and Nasdaq small and large stocks separately. Panel A provides the estimation results of the following regression model using the matched NYSE and Nasdaq small stocks in the pre-COVID and pre-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where subscripts i and t denote stock i and time t, VAR denotes each liquidity variable, NYSE is a dummy variable equal to one for the NYSE stocks and zero for the Nasdaq stocks, D^Pre-NTF is a dummy variable equal to one for the pre-NTF period and zero for the pre-COVID period. PRICE is the stock price, VOLUME denotes the trading volume, RET is the stock return, VOLA is the return volatility, VIX is the CBOE's volatility index, and ε denotes the error term. Panel B provides the estimation results of the following regression model using the matched NYSE and Nasdaq small sample stocks in the pre-NTF and NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^NTF is a dummy variable equal to one for the NTF period and zero for the pre-NTF period. Panel C reports the estimation results of the following regression model using the matched NYSE and Nasdaq small sample stocks in the NTF and post-NTF periods: ${VAR}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Post-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Post-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where D^Post-NTF is a dummy variable equal to one for the post-NTF period and zero for the NTF period. We cluster standard errors by firm and time in the regressions. We use the following variables as our empirical proxies: effective spread (ESP) and price impact (PIMPACT) for liquidity, variance ratio based on 5-min/5 x 1-min (VR_3) for price efficiency, total dollar volume (DVOL), total intermarket sweep order dollar volume (DVISO), total odd-lot dollar volume (DVODDLOT) for trading activity, and absolute value of order imbalance (ORDIMB) and probability of informed trading (PIN) for informed trading. We then replicate the above regression models using matched NYSE and Nasdaq large stocks and report the results in Panels D, E, and F. Numbers in parentheses are t-statistics. **Significant at the 1% level. *Significant at the 5% level.

Comparisons of the results in Panel A and Panel D show that the effects of the pandemic on liquidity, price efficiency, and informed trading are directionally the same (i.e., the signs of β ₁ estimates are identical) between small and large stocks. The effects are greater (i.e., larger coefficients in absolute values) in the sample of large stocks, suggesting that liquidity providers and informed traders in large stocks responded more strongly to the pandemic.

Panels B and E show that the effects of the NYSE trading floor closure are directionally the same between small and large stocks. Panels C and F show that the effects of the trading floor reopening are also directionally the same between small and large stocks. We find that the effects on liquidity (ESP) and price efficiency (VR_3) are greater in the sample of small stocks, while the effects on informed trading (DVOL, DVISO, DVODDLOT, ORDIMB, and PIN) are greater in the sample of large stocks.

Panels A, B, and C in Table 10 show the results when we estimate the regression models in equations (5), (6) using ESP or PIMPACT as a measure of liquidity, VR_3 as a measure of price efficiency, and DVISO or DVODDLOT as a measure of informed trading for the stocks in the small MVE tercile. Likewise, Panels D, E, and F show the regression results for the stocks in the large MVE tercile. Comparisons of the results between the two sets of panels show that the effects of liquidity and informed trading on price efficiency are directionally the same between small and large stocks, with greater effects observed in the sample of large stocks.32 The latter result suggests that liquidity and informed trading play a more notable role in large stocks for improving price efficiency.

Table 10.

Liquidity and informed trading as price efficiency channels for small and large stocks.

Panel A: Results for β1L and β1T from the regression model for small stocks using the pre–COVID and pre–NTF periods
Dep. var.	Results for ESP (β1L) and DVISO or DVODDLOT (β1T)				Results for PIMPACT (β1L) and DVISO or DVODDLOT (β1T)
VR_3	ESP	0.2722** (4.21)	ESP	0.2729** (4.13)	PIMPACT	0.4151** (4.57)	PIMPACT	0.4130** (4.28)
	DVISO	−0.0089** (−4.07)	DVODDLOT	−0.0086** (−4.38)	DVISO	−0.0073** (−4.23)	DVODDLOT	−0.0121** (−4.56)
	Adj. R2	0.19	Adj. R2	0.20	Adj. R2	0.18	Adj. R2	0.19
Panel B: Results for β1L and β1T from the regression model for small stocks using the pre–NTF and NTF periods
VR_3	ESP	0.2653** (4.54)	ESP	0.2632** (3.97)	PIMPACT	0.4012** (4.55)	PIMPACT	0.4059** (4.72)
	DVISO	−0.0056** (−3.91)	DVODDLOT	−0.0078** (−4.25)	DVISO	−0.0066** (−3.60)	DVODDLOT	−0.0112** (−4.84)
	Adj. R2	0.20	Adj. R2	0.21	Adj. R2	0.21	Adj. R2	0.20
Panel C: Results for β1L and β1T from the regression model for small stocks using the NTF and post–NTF periods
VR_3	ESP	0.2493** (4.76)	ESP	0.2538** (4.86)	PIMPACT	0.3993** (4.18)	PIMPACT	0.3947** (4.04)
	DVISO	−0.0055** (−4.23)	DVODDLOT	−0.0069** (−3.82)	DVISO	−0.0057** (−3.96)	DVODDLOT	−0.0091** (−4.66)
	Adj. R2	0.25	Adj. R2	0.25	Adj. R2	0.25	Adj. R2	0.25

Panel D: Results for β1L and β1T from the regression model for large stocks using the pre–COVID and pre–NTF periods
Dep. var.	Results for ESP (β1L) and DVISO or DVODDLOT (β1T)				Results for PIMPACT (β1L) and DVISO or DVODDLOT (β1T)
VR_3	ESP	0.2803** (5.23)	ESP	0.2881** (5.07)	PIMPACT	0.4538** (4.93)	PIMPACT	0.4559** (5.09)
	DVISO	−0.0111** (−4.34)	DVODDLOT	−0.0095** (−4.54)	DVISO	−0.0079** (−4.83)	DVODDLOT	−0.0148** (−4.37)
	Adj. R2	0.16	Adj. R2	0.15	Adj. R2	0.17	Adj. R2	0.17
Panel E: Results for β1L and β1T from the regression model for large stocks using the pre–NTF and NTF periods
VR_3	ESP	0.2737** (4.42)	ESP	0.2769** (4.33)	PIMPACT	0.4443** (4.89)	PIMPACT	0.4424** (4.33)
	DVISO	−0.0075** (−4.54)	DVODDLOT	−0.0088** (−4.83)	DVISO	−0.0070** (−4.52)	DVODDLOT	−0.0148** (−4.98)
	Adj. R2	0.19	Adj. R2	0.18	Adj. R2	0.20	Adj. R2	0.21
Panel F: Results for β1L and β1T from the regression model for large stocks using the NTF and post–NTF periods
VR_3	ESP	0.2575** (4.95)	ESP	0.2651** (5.06)	PIMPACT	0.4329** (4.64)	PIMPACT	0.4387** (4.58)
	DVISO	−0.0072** (−4.71)	DVODDLOT	−0.0080** (−4.40)	DVISO	−0.0066** (−4.31)	DVODDLOT	−0.0114** (−4.85)
	Adj. R2	0.22	Adj. R2	0.21	Adj. R2	0.17	Adj. R2	0.23

We examine whether COVID-19 led to an increase in price efficiency through the channels of liquidity and informed trading using small and large stocks separately. We estimate the following first-stage regression model using the matched NYSE and Nasdaq small stocks in the pre-COVID and pre-NTF periods: ${LIQUIDITY}_{i,t}\mathrm{o}\mathrm{r}{TRADING}_{i,t}={\beta }_0+{\beta }_{1}NYSE\mathrm{x}{D}^{Pre-NTF}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}+{\beta }_5{VOLUME}_{i,t}$ + ${\beta }_6{RET}_{i,t}$$+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where LIQUIDITY is either the effective spread (ESP) or price impact (PIMPACT), TRADING is either the intermarket sweep order dollar volume (DVISO) or the odd-lot dollar volume (DVODDLOT), and all other variables are the same as previously defined. We then estimate the following second-stage model: ${VR}_{i,t}={\beta }_0+{\beta }_{1L}{\widehat{LIQUIDITY}}_{i,t}+{\beta }_{1T}{\widehat{TRADING}}_{i,t}+{\beta }_{2}NYSE+{\beta }_3{D}^{Pre-NTF}+{\beta }_4{PRICE}_{i,t}{+\beta }_5{VOLUME}_{i,t}+{\beta }_6{RET}_{i,t}$$+{\beta }_7{VOLA}_{i,t}+{\beta }_8{VIX}_t+{\epsilon }_{i,t}\text{,}$ where VR is the variance ratio based on 5-min/5 x 1-min (VR_3) and $\widehat{LIQUIDITY}\left(\widehat{TRADING}\right)$ is the predicted value of LIQUIDITY (TRADING) from the first-stage regression model. We replicate the regressions for large stocks and report the results in Panels D, E, and F. Numbers in parentheses are t-statistics. **Significant at the 1% level.

9. Discussion of key findings in relation to prior research

In this section, we put our study in perspective by comparing it with prior research. Ozik et al. (2021) and Pagano et al. (2021) investigate the impact of retail investors on stock liquidity during the pandemic lockdown. Chakrabarty and Pascual (2022) study the role of algorithmic traders in liquidity provision during the pandemic. Cox and Woods (2021) analyze the impacts of the pandemic on market fragmentation, algorithmic trading, and hidden liquidity. By contrast, we explore whether the effects of the pandemic on liquidity, price efficiency, and informed trading differ between the NYSE and Nasdaq stocks. We find that the negative impact of the pandemic on liquidity for the NYSE stocks is smaller than that for the Nasdaq stocks. We interpret this finding as evidence that the NYSE trading floor mitigated the negative effect of the pandemic on liquidity, given that the NYSE had the trading floor while Nasdaq did not during the pre-NTF period.

Cox and Woods (2021) report that the COVID-19 pandemic is associated with a more significant increase in the Amihud illiquidity measure for the NYSE stocks than the Nasdaq stocks (see Table 6). This result differs from our finding that the pandemic is associated with a smaller increase in price impacts for the NYSE stocks. A possible explanation for this difference is that the Amihud illiquidity measure is based on daily price changes and trading volume, whereas our estimates of price impact are based on the quote midpoint change associated with each trade.

Kye and Mizrach (2021) analyze the impact of the NYSE trading floor closure on market quality during the last 30 min of the trading day. Hu and Murphy (2021) and Jegadeesh and Wu (2022) examine the effect of the NYSE floor closure on liquidity during closing auctions. By contrast, our study examines the impact of the NYSE floor closure on liquidity, price efficiency, and informed trading during the entire trading day. Cox and Woods (2021) show that the closure of the NYSE trading floor is associated with a smaller increase in the quoted spread for the NYSE stocks than the Nasdaq stocks. To the extent that the increase in the quoted spread for the Nasdaq stocks reflects a market-wide change in liquidity, Cox and Woods's results suggest that the closure of the NYSE trading floor decreased the quoted spread (i.e., increased liquidity) for the NYSE stocks. By contrast, Brogaard et al. (2021) show that the closure of the NYSE trading floor led to higher effective and quoted spreads and larger pricing errors for the NYSE stocks. Our finding that the closure of the NYSE trading floor is associated with a decrease in liquidity and price efficiency on the NYSE is consistent with Brogaard et al. (2021). As expected, we find that the reopening of the trading floor increased liquidity and price efficiency on the NYSE.

Our study differs from prior research in that it shows the pandemic and the closure and reopening of the NYSE trading floor affected price efficiency through their impact on liquidity and informed trading using a unique research design that analyzes liquidity, price efficiency, and informed trading across the four distinct periods: pre-COVID period, pre-NTF period, NTF period, and post-NTF period).

10. Conclusion

The COVID-19 pandemic brought significant disruptions to financial markets across the globe. Market volatility exploded, stock prices plummeted, and liquidity evaporated during the initial months of the pandemic. The NYSE closed its trading floor to protect floor brokers and market makers from the pandemic and subsequently reopened it as the initial shock of the pandemic subsided and health risks associated with floor operations became manageable. In this paper, we explore how the initial shock of the pandemic, the suspension of the NYSE trading floor, and its subsequent restoration influenced liquidity, price efficiency, and trading activities on the NYSE and Nasdaq.

We find that the initial shock of the pandemic led to a significant decrease in liquidity and an increase in price efficiency and informed trading on both the NYSE and Nasdaq before the closure of the NYSE trading floor. The decrease in liquidity is smaller, and the increase in price efficiency and informed trading is larger for the NYSE stocks relative to the Nasdaq stocks. The larger increase in price efficiency on the NYSE can be attributed at least in part to both the smaller decrease in liquidity and the larger increase in informed trading for the NYSE stocks. These results could be due to the positive role of the trading floor in improving liquidity and price efficiency and expediting informed trading. That is, the NYSE trading floor mitigated the negative effect of the pandemic on liquidity while helping to improve price efficiency and expedite informed trading.

The closure of the NYSE trading floor is followed by a larger decrease in liquidity, price efficiency, and informed trading on the NYSE relative to Nasdaq. The decrease in price efficiency may be related, at least in part, to the concurrent decline in liquidity and informed trading. The reopening of the NYSE trading floor is followed by a larger increase in liquidity, price efficiency, and informed trading on the NYSE relative to Nasdaq, reflecting the value of the trading floor in improving liquidity and price efficiency and expediting informed trading. We show that the reopening of the trading floor fully restored liquidity and price efficiency to their pre-pandemic levels, suggesting that the pandemic does not appear to have a permanent effect on these market quality metrics.

Whether trading floor and human involvement add value to asset exchange markets in the age of ultra-high technologies and automated trading has long been debated among market participants, regulators, and scholars. We offer insight on this debate by providing coherent and convincing evidence that trading floor and human involvement improve liquidity and price efficiency. We provide this evidence by looking at how liquidity providers and other market participants responded to the unexpected arrival of the COVID-19 pandemic, the closure of the NYSE trading floor, and the subsequent reopening of the trading floor.

Appendix A.

Variable Definitions

.

Nomenclature

P_k

price of trade k

SHR_k

size (in number of shares) of trade k

Dvol_k

dollar volume of trade k = P _k x SHR _k

BUY_k

a buy order for trade k

SELL_k

a sell order for trade k

B_k

bid price at the time of trade k or quote k

A_k

ask price at the time of trade k or quote k

M_k

bid-ask quote midpoint = (B _k + A _k)/2 at the time of trade k or quote k

BSIZE_k

quoted depth (size) at the bid price at the time of trade k or quote k

ASIZE_k

quoted depth (size) at the ask price at the time of trade k or quote k

D_k

+1 if trade k is a buy and −1 if trade k is a sell

Variable	Definition
Time-Weighted Average Percentage Quoted Spread (QSP) of stock i on day t	QSPi,t=$\sum _{k=1}^N{w}_k\left\{\frac{\left(A_k-B_k\right)}{M_k}\right\}\text{,}$ where $w_k=\frac{\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}k}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{a}\mathrm{y}t}\text{,}$ and N is the total number of quotes of stock i on day t.
Simple Averaged Percentage Effective Spread (ESP) of stock i on day t	${ESP}_{i,t}=\frac{1}{N}\sum _{k=1}^N\left\{\frac{2D_k\left(P_k-M_k\right)}{M_k}\right\}\text{,}$ where N is the total number of trades of stock i on day t.
Value-Weighted Percentage Effective Spread (ESP_VW) of stock i on day t	${{ESP}_{VW}}_{i,t}=\sum _{k=1}^N{w}_k\left\{\frac{2D_k\left(P_k-M_k\right)}{M_k}\right\}\text{,}$ where $w_k=\frac{P_{k}x{SHR}_k}{\sum _{k=1}^N{P}_{k}x{SHR}_k}\text{,}$ and N is the total number of trades of stock i on day t.
Simple Averaged Percent Realized Spread (RSP) of stock i on day t	${RSP}_{i,t}=\frac{1}{N}\sum _{k=1}^N\left\{\frac{2D_k\left(P_k-M_{k+5}\right)}{M_k}\right\}\text{,}$ where Mk+5 is the bid-ask quote midpoint 5 min after the kth trade and N is the total number of trades of stock i on day t.
Value-Weighted Percentage Realized Spread (RSP_VW) of stock i on day t	${RSP\_VW}_{i,t}=\sum _{k=1}^N{w}_k\left\{\frac{2D_k\left(P_k-M_{k+5}\right)}{M_k}\right\}\text{,}$ where $w_k=\frac{P_{k}x{SHR}_k}{\sum _{k=1}^N{P}_{k}x{SHR}_k}\text{,}$Mk+5 is the bid-ask quote midpoint 5 min after the kth trade and N is the total number of trades of stock i on day t.
Simple Averaged Percentage Price Impact (PIMPACT) of stock i on day t	${PIMPACT}_{i,t}=\frac{1}{N}\sum _{k=1}^N\left\{\frac{2D_k\left(M_{k+5}-M_k\right)}{M_k}\right\}\text{,}$ where Mk+5 is the bid-ask quote midpoint 5 min after the kth trade and N is the total number of trades of stock i on day t.
Value-Weighted Percentage Price Impact (PIMPACT_VW) of stock i on day t	${PIMPACT\_VW}_{i,t}=\sum _{k=1}^N{w}_k\left\{\frac{2D_k\left(M_{k+5}-M_k\right)}{M_k}\right\}\text{,}$ where $w_k=\frac{P_{k}x{SHR}_k}{\sum _{k=1}^N{P}_{k}x{SHR}_k}\text{,}$Mk+5 is the bid-ask quote midpoint 5 min after the kth trade and N is the total number of trades of stock i on day t.
Time-Weighted Quoted Depth (DEPTH) of stock i on day t	DEPTHi,t=$\sum _{k=1}^N{w}_k\left({ASIZE}_k+{BSIZE}_k\right)\text{,}$ where wk$=\frac{\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{q}\mathrm{u}\mathrm{o}\mathrm{t}\mathrm{e}k}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{a}\mathrm{y}t}\text{,}$ and N is the total number of quotes of stock i on day t.
Price impact coefficient (λ) with intercept (LAMBDA_1)	The regression coefficient (λ) of the following model: $\mathrm{Ln}\frac{M_{i,t}}{M_{i,t-300}}=\alpha +\lambda *SSqrtDVol+\epsilon \text{,}$ w $\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}SSqrtDVol=Sgn\left({\sum }_{t-300}^{t}BuySHR-{\sum }_{t-300}^{t}SellSHR\right)x$$\sqrt{\left|{\sum }_{t-300}^{t}BuySHR-{\sum }_{t-300}^{t}SellSHR\right|},M_{i,t}=\frac{B_{i,t}+A_{i,t}}{2}$ is the bid-ask midpoint of stock i at second t.
Price impact coefficient (λ) without intercept (LAMBDA_2)	The regression coefficient (λ) of the following model: $\mathrm{Ln}\frac{M_{i,t}}{M_{i,t-300}}=\lambda *SSqrtDVol+\epsilon \text{,}$ w $\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}SSqrtDVol=Sgn\left({\sum }_{t-300}^{t}BuySHR-{\sum }_{t-300}^{t}SellSHR\right)x$$\sqrt{\left|{\sum }_{t-300}^{t}BuySHR-{\sum }_{t-300}^{t}SellSHR\right|},M_{i,t}=\frac{B_{i,t}+A_{i,t}}{2}$ is the bid-ask midpoint of stock i at second t.
Variance ratio based on 15-s/3*5-s (VR_1)	$VR\_1=\left|\frac{VAR\left({Ret}_{15t}\right)}{3VAR\left({Ret}_{5t}\right)}-1\right|\text{,}$ where VAR(Ret15t) is the variance of 15-s log returns.
Variance ratio based on 1-min/4*15-s (VR_2)	$VR\_2=\left|\frac{VAR\left({Ret}_{60t}\right)}{4VAR\left({Ret}_{15t}\right)}-1\right|\text{,}$ where VAR(Ret60t) is the variance of 1-min log returns.
Variance ratio based on 5-min/5*1-min (VR_3)	$VR\_3=\left|\frac{VAR\left({Ret}_{300t}\right)}{5VAR\left({Ret}_{60t}\right)}-1\right|\text{,}$ where VAR(Ret300t) is the variance of 5-min log returns.
Variance ratio based on 15-min/3*5-min (VR_4)	$VR\_4=\left|\frac{VAR\left({Ret}_{900t}\right)}{3VAR\left({Ret}_{300t}\right)}-1\right|\text{,}$ where VAR(Ret900t) is the variance of 15-min log returns.
Variance ratio based on 30-min/2*15-min (VR_5)	$VR\_5=\left|\frac{VAR\left({Ret}_{1800t}\right)}{2VAR\left({Ret}_{900t}\right)}-1\right|\text{,}$ where VAR(Ret1800t) is the variance of 30-min log returns.
NTRADE	Number of trades.
DVOL	Dollar trading volume.
NISO	Number of intermarket sweep order trades.
DVISO	Dollar value of intermarket sweep order trades.
NODDLOT	Number of odd-lot trades.
DVODDLOT	Dollar value of odd-lot trades.
Order imbalance (ORDIMB)	Absolute value of the difference between the dollar value of buyer initiated trades and the dollar value of seller-initiated trades.
Probability of informed trading (PIN)	PINi= αiμi/(αiμi+ 2ϵi), where αi is the probability that an information event has occurred, μi is the arrival rate of informed traders given that an event has occurred, ϵi is the arrival rate of uninformed traders. We estimate PIN using the program provided at WRDS (https://wrds-www.wharton.upenn.edu/pages/support/research-wrds/sample-programs/probability-informed-training-pin/).
PRICE	Price of stock i on day t.
RET	Return of stock i on day t.
VOLUME	Dollar volume of stock i on day t = ${\sum }_{k=1}^N{Price}_k\mathrm{x}{Sharevolume}_k$, where N is the total number of trades of stock i on day t.
VOLA	Standard deviation of stock returns = $\frac{\sum _{\tau =1}^t{\left({Ret}_{i,\tau }-\overline{{Ret}_{i,\tau }}\right)}^2}{t-1}$.

Data availability

Data will be made available on request.