Estimated Benefits of Incremental Suppression of Covid-19 Spread

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1. Introduction

Estimated benefits are necessary in a cost benefit analysis of Covid-19 suppression, thus raising a substantive question: what are the estimated benefits of Covid-19’s *incremental *suppression? This question’s relevance is underscored by the increasingly strong actions taken in late March of 2020 by the US and European governments to suppress Covid-19’s surging spread [1].

In this paper, we estimate the benefits of incremental suppression that result in a hypothetical 10% reduction in Covid-19’s cumulative confirmed cases (CCC) for 14 stock market locations in Asia, Europe, North America, and Australia.^{1} If these estimated benefits turn out to be relatively small, they suggest that incremental suppression should not occur.

First detected in China in early December 2019,^{2} Covid-19 is officially a pandemic as of 03/12/2020 [1]. While Covid-19’s spread has peaked in China by mid-February 2020, it continues to surge in other countries, as exemplified by the US, Italy, Germany, Spain, France and UK, which in descending order had the highest numbers of cumulative confirmed cases (CCC) on 03/31/2020 outside China [1].^{3}

In response to Covid-19’s spread, governments have taken various suppression actions, including national border closures, business and school shutdowns, public event cancelations, limits on social gathering, home isolations, mandatory quarantines, local and international travel restrictions, and reduced service of public transportation [1]. Such actions curb economic activities that accelerate the spread of a viral disease [2].

As Covid-19 is recent, we can only find one study on benefits of suppression. Specifically, [3] (p. 6) estimates that Covid-19’s total cost *sans *suppression in the US exceeds US$13.2 trillion, comprising medical cost, value of lost productivity and fatality cost based on value of statistical life [4]. The total cost estimate for a 78-week suppression period is US$15.8 billion, exceeding those for shorter periods [3] (p. 7). Hence, “it may be optimal to stop [suppression] before a vaccine becomes available” [3] (p. 7).^{4}

Accepting that suppression will likely continue in the summer months of 2020, we propose a stock-market-based approach to estimate the benefit of incremental suppression that will last till no new cases are recorded for 14 days, the projected incubation period of Covid-19.^{5} Since our focus is incremental suppression’s estimated benefits, it differs from [3] ’s focus of whether suppression should end before a vaccine becomes available.

Recognizing Covid-19’s damaging effect on stock prices [5], our approach presumes that a firm’s stock price measures the present value (PV) of future profits [6]. Our approach has two parts. Part 1 explains the benefit calculation based on a stock market index’s (“index’s” for short hereafter) capitalization and CCC elasticity *ε* = percentage change in the index due to 1-perecent change in CCC. Part 2 is a double-log regression, whose estimation yields an index’s CCC elasticity. As the number of cumulative deaths is driven by the number of CCC,^{6} an index’s increase due to a decline in CCC captures the life-saving effect of incremental suppression on an index.^{7}

To develop our approach’s empirics, we conduct a panel data analysis of 14 daily indices for large cap stocks during 01/21/2020-04/03/2020.^{8} These stock markets are chosen based on Covid-19 spread’s geographic variations over time. Our three key findings are as follows. First, an index’s estimated CCC elasticity is small, ranging from −0.010 to −0.057. Second, a hypothetical 10% reduction in CCC caused by incremental suppression is estimated to increase market capitalization by US$0.76 billion for Singapore to US$70 billion for the US. An adjustment to reflect a large cap index’s underrepresentation of a stock market magnifies these benefit estimates. For the US, the adjusted benefit estimate is up to US$100 billion. Finally, we verify that our estimated benefits are empirically reasonable. To the best of our knowledge, these findings are new, chiefly because of our research focus and data recentness.

The rest of this paper proceeds as follows. Section 2 states our benefit formula, regression specification, testable hypotheses, and data construction. Section 3 presents our initial exploration, regression results, estimated benefits, and final checks. Section 4 concludes by recapping our key findings and stating the caveats of our paper.

2. Materials and Methods

2.1. Benefit Formula

Let *I _{k}* denote index

${Y}_{k}={\epsilon}_{k}\times \Delta \mathrm{ln}\left({\text{CCC}}_{k}\right)>0$ . (1)

Let *V _{k}* denote index

$\Delta {V}_{k}={V}_{k}\times {Y}_{k}>0$ , (2)

which is a conservative estimate when *V _{k}* is less than market

2.2. Regression Specification

Applying Equation (1) requires an estimate for *ε _{k}*, which can be obtained from a panel data analysis based on the following double-log regression with random error

$\text{ln}\left({I}_{kt}\right)={\Sigma}_{j}{\alpha}_{k}\mathrm{ln}\left({X}_{kt}\right)+\text{Fixedeffects}+{\mu}_{kt}$ ;^{10} (3)

where *I _{kt}* is market

There are three reasons for our choice of a double-log specification. First,
${\alpha}_{k}=\partial \mathrm{ln}\left({I}_{kt}\right)/\partial \mathrm{ln}\left({X}_{kt}\right)$ is an elasticity, measuring an index’s percentage change due to a 1-percengt change in *X _{kt}* ≡ (1 + number of CCC

Second, it circumvents the problem of population differences because a country with a large population tends to have higher CCC than a country with a small population.

Third, it resolves the scale differences among indices, as exemplified by the US’s S & P 500 index that was below 3000 and Hong Kong’s HSI that was above 20,000 during our chosen sample period of 01/21/2020-04/03/2020, see Section 2.5 below.

We end this section by noting that Equation (3) does not use ln(1 + number of cumulative deaths) as an additional regressor because it is highly correlated (*r* > 0.9) with ln(*X _{kt}*), causing severe multicollinearity that leads to imprecise and counter-intuitive coefficient estimates. Further, Equation (3) does not include government announcements of relief packages because these announcements are driven by Covid-19’s spread severity, which is already captured by ln(

2.3. Testable Hypotheses

Denoting equation (3) as Model 0, we use the *F*-test to test three hypotheses for a better understanding of an index’s CCC responsiveness:

・ *H*_{1}: All markets have the same elasticity, which implies Model 1 with *α _{k}* =

・ *H*_{2}: Fixed effects do not matter, which implies Model 2 that excludes fixed effects.

・ *H*_{3}: Identical elasticity and no fixed effects, which implies Model 3 that restricts *α _{k}* =

2.4. Data Construction

To construct our panel data, we use 14 daily indices for large cap stocks listed in Figure 1 and daily CCC data provided by Johns Hopkins University (JHU). Our sample period is 01/21/2020-04/03/2020, whose beginning date is when JHU first published CCC data and ending date reflects the data available at the time of our writing. The resulting sample contains 727 daily observations, a newly created Covid-19 dataset that differentiates our paper from [3] and studies on prior pandemics such as SARS and Ebola (e.g., [10] and [11]).

3. Results

3.1. Initial Exploration

To presage Covid-19’s damaging effects, Figure 1 portrays the cumulative losses suffered by the 14 chosen markets. China’s loss is noticeably lower than those of other countries, likely because China’s earlier Covid-19 outbreak has already dampened China’s stock market.

For the seven countries most affected by Covid-19 as of 04/03/2020: the US, China, Italy, Germany, Spain, France and UK, Figure 2 shows that their indices tend to decline with CCC. It also highlights that China’s Covid-19 spread peaked in mid-February 2020 when those of the other six countries began to accelerate, painting a time profile that aids our estimation of an index’s CCC elasticity.

Table 1 contains our sample’s descriptive statistics and correlation. While informative, the correlation coefficient of −0.3 does not reveal elasticity *α _{k}*’s size, a task to be accomplished by the regression results reported below.

3.2. Regression Results

Table 2 reports our regression results, leading to the following inferences. First, Model 0’s within *R*^{2} value is 0.85, suggesting Equation (3) reasonably fits the index data. Further, Model 0’s coefficient estimates are all statistically significant (*p*-value < 0.05) and have correct signs. Hence, Model 0 is an empirically plausible representation of the data generating process for the 14 indices.

Second, Model 0’s estimated elasticities range from −0.010 for China to −0.057 for Taiwan. The *α*_{12} estimate for the US is −0.028, implying a 10% decrease in CCC tends to increase the S & P 500 index by 0.28%. The remaining elasticity estimates tell a similar story.

Notes: 1) Cumulative loss = ln(closing index level on 01/20/2020) ? ln(closing index level on 04/03/2020). 2) The 14 market indices are: a) Asia: CSI300 (China), HSI (Hong Kong), TAIEX (Taiwan), STI (Singapore), Nikkei 225 (Japan), KOSPI (South Korea); b) Europe: DAX (Germany), FTSE 100 (UK), CAC 40 (France), IBEX (Spain), FTSE MIB (Italy); c) North America: S & P 500 (US), S & P/TSX (Canada); and d) ASX 200 (Australia).

Figure 1. Cumulative losses by market for the period of 01/21/2020-04/03/2020 that matches the availability of Covid-19 data published by Johns Hopkins University.

Table 1. Descriptive statistics and correlations based on 727 daily observations in the sample period of 01/21/2020-04/03/2020.

Figure 2. Graphic representation of country-specific natural-log values of market index and (1 + number of cumulative confirmed cases).

Finally, the *F*-test results decisively (*p*-value < 0.0001) reject *H*_{1} to *H*_{3}. A close inspection of the elasticity estimates produced by Models 1 to 3 leads to the following remarks. First, Model 1’s estimated elasticity is −0.033, matching the mid-point of the range produced by Model 0. Second, Model 2 yields statistically significant elasticity estimates with wrong signs, implying that it should not be used for our benefit calculation. Third, Model 3’s elasticity estimate is −0.068, much larger in size than Model 0’s. Hence, we decide not to use Model 3 to avoid overstating the benefit estimates.

3.3. Estimated Benefits

To estimate the benefits of a hypothetical 10% decrease in CCC, we use each index’s capitalization on 04/03/2020 as the reference case of no incremental suppression. As market capitalization on 04/03/2020 could have reacted to government announcements of increasingly strong actions, our estimated benefits correspond to additional anti-Covid-19 actions beyond those already announced.

Figure 3 portrays the Δ*V _{k}* estimates based on Model 0’s elasticity estimates reported in Table 2. These Δ

Table 2. Results from a panel data (fixed effects) analysis of large cap index data based on 727 daily observations in the sample period of 01/21/2020-04/03/2020.

Notes: 1) For brevity, this table omits the estimated intercept and fixed effects that are highly statistically significant (*p*-value < 0.01). 2) The CCC elasticities are labelled according to their continental locations: Asia’s elasticities are *α*_{1} to *α*_{6}, Europe’s *α*_{7} to *α*_{11}, North America’s *α*_{12} and *α*_{13}, and Australia’s *α*_{14}. 3) We use robust standard errors clustered by market that are heteroskedasticity-autocorrelation-consistent to determine the coefficient estimates’ statistical significance. 4) Coefficient estimates in bold are statistically significant (*p*-value < 0.05) and have correct signs. Coefficients estimates in *italic* are statistically insignificant (*p*-value > 0.05) and have *wrong* signs. Coefficients estimates in *italic* are statistically significant (*p*-value < 0.05) and have *wrong* signs.

Notes: (1) The benefit calculation is based on equations (1) and (2) in Section 2.1. (2) The elasticity estimates are those reported in Table 2.

Figure 3. Estimated benefits (based on big cap indices’ capitalization) of a hypothetical 10% reduction in the number of cumulative confirmed cases.

3.4. Final Checks

We perform three final checks of the estimated benefits reported in the last section, finding them empirically reasonable.

First, we use the estimated version of Equation (3) to calculate the increase in S & P index’s capitalization under the what-if scenario of no Covid-19 outbreak. This calculation yields Δ*V*_{12} = −*V*_{12} × *a*_{12} × ln(*X*_{12}) = US$8.77 trillion, where *V*_{12} = S & P 500 capitalization on 04/03/2020 = $24.7 trillion, *a*_{12} = *α*_{12 }estimate = −0.0283, and ln(*X*_{12}) = ln(1 + number of CCC in the US on 04/03/2020) = 12.53. The US$8.77 trillion increase is equivalent to a 26% [= 8.87/(8.87 + 24.7)] cumulative loss in total capitalization since 02/21/2020, which is reasonably close to the 29% cumulative loss shown in Figure 1.

Second, we multiply Δ*V*_{12} = US$8.77 trillion by the 1.43 adjustment factor to account for the S & P 500 index’s market underrepresentation. The adjusted Δ*V*_{12} is US$12.54 trillion, comparable to the ~US$13 trillion estimated benefit of suppression inferred from [3]. Thus, our estimated increase in total market capitalization under the scenario of no Covid-19 outbreak resembles the benefit of suppression inferred from an economic cost comparison, notwithstanding that these two numbers are derived from very different methodologies and data sources.

Finally, we re-estimate Equation (3) using the MSCI total market index data which are much less frequently used by financial news media than the big cap stock index data. Except for China with a correlation coefficient of 0.84, the MSCI data are highly correlated (*r* > 0.95) with the large cap index data. Table 3 reports the re-estimation results that are comparable to those reported in Table 2, lending support to our expectation that an index’s CCC elasticity estimate should only be modestly sensitive to the choice between large cap index data and total market index data. A good case in point is that the newly found CCC elasticity estimate for the US is −0.0287, almost identical to the corresponding estimate of −0.0283 in Table 2. Figure 4 portrays the estimated benefits of incremental suppression,

Notes:(1) The benefit calculation is based on Equations (1) and (2) in Section 2.1. (2) The elasticity estimates are those reported in Table 2.

Figure 4. Estimated benefits (based on MSCI total market indices’ capitalization) of a hypothetical 10% reduction in the number of cumulative confirmed cases.

Table 3. Results from a panel data (fixed effects) analysis of MSCI total market index data based on 727 daily observations in the sample period of 01/21/2020-04/03/2020.

Notes: 1) For brevity, this table omits the estimated intercept and fixed effects that are highly statistically significant (*p*-value < 0.01). 2) The CCC elasticities are labelled according to their continental locations: Asia’s elasticities are *α*_{1} to *α*_{6}, Europe’s *α*_{7} to *α*_{11}, North America’s *α*_{12} and *α*_{13}, and Australia’s *α*_{14}. 3) We use robust standard errors clustered by market that are heteroskedasticity-autocorrelation-consistent to determine the coefficient estimates’ statistical significance. 4) Coefficient estimates in bold are statistically significant (*p*-value < 0.05) and have correct signs. Coefficients estimates in *italic* are statistically insignificant (*p*-value > 0.05) and have *wrong* signs. Coefficients estimates in *italic* are statistically significant (*p*-value < 0.05) and have *wrong* signs.

revealing 1) the estimated benefits in this figure are for the most part larger than those in Figure 3; and 2) the US estimated benefit based on total market capitalization is below US$100 billion.

4. Conclusion

This paper proposes a stock-market-based approach to estimate the benefit of a hypothetical 10% reduction in cumulative confirmed cases due to incremental suppression of Covid-19 spread. The resulting estimated benefits for the 14 chosen stock markets range from US$0.76 billion for Singapore to US$70 billion for the US. The adjusted estimate for the US is up to US$100 billion, owing to the S & P 500 index’s 70-80% share of the US total market capitalization. Finally, we verify that our estimated benefits are empirically reasonable.

NOTES

^{1}The US number of CCC on 04/03/2020 is 213,600 [1]. The hypothetical 10% reduction in CCC equals 21,360 confirmed cases, thus easing the highly stressed healthcare system in the US.

^{2}https://www.theguardian.com/world/2020/mar/20/chinese-inquiry-exonerates-coronavirus-whistleblower-doctor-li-wenliang

^{3}Daily Covid-19 updates are available at: https://coronavirus.jhu.edu/map.html.

^{4}A safe and effective vaccine is at least a year away (https://www.theguardian.com/world/2020/apr/03/when-will-a-coronavirus-vaccine-be-ready). In the meantime, Covid-19’s spread will likely subside when a large percentage (e.g., 80%) of the surviving population have developed immunity, reducing the chance of an uninfected person becoming infected (https://time.com/5810454/coronavirus-immunity-reinfection/).

^{5}https://www.npr.org/sections/health-shots/2020/04/01/824903684/the-science-behind-a-14-day-quarantine-after-possible-covid-19-exposure

^{6}This is because confirmation typically precedes death, unless a Covid-19 patient dies before detection, a relatively rare event due to increased Covid-19 testing of symptomatic people and asymptomatic people who have been in an area of a Covid-19 outbreak or had close contact with a confirmed Covid-19 patient.

^{7}To see this point, consider a simple function *y* = *f*(*x*, *z*). If *z* = *g*(*x*), it can be written as *y* = *h*(*x*).

^{8}There are three reasons supporting our index choice. First, these widely available indices are commonly used for measuring market returns. Second, they are highly correlated with the total market indices. Using the US as an illustrative example, the S & P 500 index is highly correlated (*r* > 0.95) with the total market index Wilshire 5000. Finally, using large cap indices results in conservative benefit estimates that mitigate criticisms of overestimation. For the US example, the S & P 500 index’s capitalization is 70% - 80% of the US total market capitalization. To counter the argument that the benefit estimate based on the S & P 500 index is unreasonably low, we adjust the US estimate based on the S & P 500 index’s share of the US total market capitalization.

^{9}We decide not to use a CAPM-based approach (e.g., [5]) that does not readily produce the elasticity estimates necessary for computing D*V _{k}*.

^{10}This regression is spurious when its residuals are non-stationary [7]. Hence, after estimating Equation (3), we used the panel unit root test proposed by [8] to reject the hypothesis that the regression residuals follow a random walk.

^{11}The number of CCC in January 2020 is zero for European countries [1].

^{12}To see this point, consider the simple example of ln(*y*) = *b* ln(1 + *n*) where *n* is a positive integer. As *d*ln(*y*)/*d*ln(*n*) = *b* [*n*/(1 + *n*)], *b* = 0.995 × *d*ln(*y*)/*d*ln(*n*) at *n* = 200.

^{13}When estimating Equation (3), we performed the Hausman test [9] (Chapter 10) to reject the hypothesis that Equation (3) should be based on random effects.

^{14}US$13.2 trillion cost without suppression ? US$15 billion cost with suppression = ~US$13 trillion.

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