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Estimated benefits are necessary for a cost benefit analysis of Covid-19 suppression. We propose a stock-market-based approach to estimate the benefits of incremental suppression of Covid-19’s spread that will last till no new cases are recorded for 14 days, the projected incubation period of Covid-19. This approach’s empirical implementation uses a) total capitalization of 14 market indices for large cap stocks; and b) an index’s estimated elasticity of cumulative confirmed cases (CCC) obtained from a panel data analysis of 727 daily observations in the period of 01/21/2020-04/03/2020. Our estimated benefits of a hypothetical 10% reduction in CCC due to incremental suppression are statistically significant (p-value < 0.05), ranging from US$0.76 billion for Singapore to US$70 billion for the US. As the S & P 500 index’s capitalization is 70% - 80% of the US total market capitalization, the adjusted US benefit estimate is up to US$100 billion. Finally, we verify that these estimated benefits are empirically reasonable.

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 [

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 [^{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 [

As Covid-19 is recent, we can only find one study on benefits of suppression. Specifically, [^{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 [

Recognizing Covid-19’s damaging effect on stock prices [^{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.

Let I_{k} denote index k for k = 1 , ⋯ , 14 . Suppose I_{k}’s elasticity with respect to market k’s CCC is ε k = ∂ ln ( I k ) / ∂ ln ( CCC k ) < 0 . The percentage increase in market k’s capitalization in response to Δln(CCC_{k}) < 0 caused by incremental suppression is:

Y k = ε k × Δ ln ( CCC k ) > 0 . (1)

Let V_{k} denote index k’s capitalization. The dollar increase in V_{k} is:

Δ V k = V k × Y k > 0 , (2)

which is a conservative estimate when V_{k} is less than market k’s total capitalization. For the US example, the S & P 500 index’s capitalization is 70% - 80% of the US total market capitalization. Hence, if DV_{k} is based on the S & P 500 index, its understatement can be as much as 43% [= (1/0.7) − 1].

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 μ_{kt} [^{9}:

ln ( I k t ) = Σ j α k ln ( X k t ) + Fixedeffects + μ k t ;^{10} (3)

where I_{kt} is market k’s index on day t. Whether Equation (3) is empirically plausible is best judged by the regression results reported in Section 3.2 below.

There are three reasons for our choice of a double-log specification. First, α k = ∂ ln ( I k t ) / ∂ ln ( X k t ) is an elasticity, measuring an index’s percentage change due to a 1-percengt change in X_{kt} ≡ (1 + number of CCC_{k} on day t). Justifying X_{kt}’s definition is avoidance of missing data caused by ln(0) being undefined.^{11} Since CCC_{k} is well above 200 for all k by 03/31/2020 [_{k} is numerically identical within two digits to ε_{k}.^{12} We expect α_{k} < 0 because of Covid-19’s damaging effect on stock prices [_{k}, we assume α_{k} is a linear function of binary indicators for market location. The fixed effects are controls for market location, day of week and month of year.^{13}

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(X_{kt}).

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} = α for all 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} = α for all k and excludes fixed effects.

To construct our panel data, we use 14 daily indices for large cap stocks listed in

To presage Covid-19’s damaging effects,

For the seven countries most affected by Covid-19 as of 04/03/2020: the US, China, Italy, Germany, Spain, France and UK,

_{k}’s size, a task to be accomplished by the regression results reported below.

^{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.

Variable [expected market effect] | Mean | Standard deviation | Minimum | Maximum | Correlation coefficient |
---|---|---|---|---|---|

ln(daily stock market index) | 8.95 | 0.80 | 7.28 | 10.25 | 1.00 |

ln(1 + number of cumulative confirmed cases) [−] | 5.21 | 3.47 | 0.00 | 12.53 | −0.30 |

ln(MSCI total market index) | 6.96 | 1.23 | 4.24 | 9.40 | 0.25 |

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.

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.

_{k} estimates based on Model 0’s elasticity estimates reported in _{k} estimates range from US$0.76 billion for Singapore to US$70 billion for the US. Since the S & P 500 index’s capitalization is 70% - 80% of the US total market capitalization, we multiply our US estimate of $70 billion by 1.43 to derive an adjusted estimate of up to US$100 billion, which is far less than the ~US$13 trillion benefit inferred from [^{14} This is understandable because our US benefit estimate is based on incremental suppression, whereas the inferred estimate is based on a comparison of two cost scenarios: without suppression vs. with suppression.

Variable [coefficient] | Model 0: Equation (3) that has varying elasticities (α_{k} ≠ α) and includes fixed effects | Model 1 under H_{1}: Identical elasticity (α_{k} = α) | Model 2 under H_{2}: No fixed effects | Model 3 under H_{3}: Identical elasticity (α_{k} = α) and no fixed effects |
---|---|---|---|---|

R^{2}: within | 0.8531 | 0.8306 | ||

R^{2}: between | 0.0132 | 0.1239 | ||

R^{2}: overall | 0.0168 | 0.0779 | 0.7896 | 0.0882 |

ln(1 + number of cumulative confirmed cases): not country-specific [α] | −0.0332 | −0.0684 | ||

ln(1 + number of cumulative confirmed cases): China [α_{1}] | −0.0102 | −0.0847 | ||

ln(1 + number of cumulative confirmed cases): Hong Kong [α_{2}] | −0.0348 | 0.1912 | ||

ln(1 + number of cumulative confirmed cases): Taiwan [α_{3}] | −0.0573 | 0.0165 | ||

ln(1 + number of cumulative confirmed cases): Japan [α_{4}] | −0.0463 | 0.1232 | ||

ln(1 + number of cumulative confirmed cases): Korea [α_{5}] | −0.0283 | −0.2156 | ||

ln(1 + number of cumulative confirmed cases): Singapore [α_{6}] | −0.0538 | −0.2473 | ||

ln(1 + number of cumulative confirmed cases): Italy [α_{7}] | −0.0334 | 0.0657 | ||

ln(1 + number of cumulative confirmed cases): France [α_{8}] | −0.0385 | −0.0981 | ||

ln(1 + number of cumulative confirmed cases): Germany [α_{9}] | −0.0376 | 0.0072 | ||

ln(1 + number of cumulative confirmed cases): Spain [α_{10}] | −0.0344 | −0.0372 | ||

ln(1 + number of cumulative confirmed cases): UK [α_{11}] | −0.0352 | −0.0736 | ||

ln(1 + number of cumulative confirmed cases): US [α_{12}] | −0.0283 | −0.1591 | ||

ln(1 + number of cumulative confirmed cases): Canada [α_{13}] | −0.0436 | 0.0598 | ||

ln(1 + number of cumulative confirmed cases): Australia [α_{14}] | −0.0526 | −0.0984 | ||

p-value of the F-statistic statistic for testing H_{m} for m = 1, 2, 3 | <0.0001 | <0.0001 | <0.0001 |

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.

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 ΔV_{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

Second, we multiply ΔV_{12} = US$8.77 trillion by the 1.43 adjustment factor to account for the S & P 500 index’s market underrepresentation. The adjusted ΔV_{12} is US$12.54 trillion, comparable to the ~US$13 trillion estimated benefit of suppression inferred from [

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.

Variable [coefficient] | Model 0: Equation (3) that has varying elasticities (α_{k} ≠ α) and includes fixed effects | Model 1 under H_{1}: Identical elasticity (α_{k} = α) | Model 2 under H_{2}: No fixed effects | Model 3 under H_{3}: Identical elasticity (α_{k} = α) and no fixed effects |
---|---|---|---|---|

R^{2}: within | 0.8460 | 0.8008 | ||

R^{2}: between | 0.0019 | 0.3470 | ||

R^{2}: overall | 0.0145 | 0.1046 | 0.8425 | 0.1361 |

ln(1 + number of cumulative confirmed cases): not country-specific [α] | −0.0345 | −0.1308 | ||

ln(1 + number of cumulative confirmed cases): China [α_{1}] | −0.0219 | −0.2539 | ||

ln(1 + number of cumulative confirmed cases): Hong Kong [α_{2}] | −0.0415 | 0.4293 | ||

ln(1 + number of cumulative confirmed cases): Taiwan [α_{3}] | −0.0571 | −0.2965 | ||

ln(1 + number of cumulative confirmed cases): Japan [α_{4}] | −0.0394 | 0.1429 | ||

ln(1 + number of cumulative confirmed cases): Korea [α_{5}] | −0.0325 | −0.1549 | ||

ln(1 + number of cumulative confirmed cases): Singapore [α_{6}] | −0.0674 | 0.1799 | ||

ln(1 + number of cumulative confirmed cases): Italy [α_{7}] | −0.0331 | −0.1952 | ||

ln(1 + number of cumulative confirmed cases): France [α_{8}] | −0.0385 | 0.0239 | ||

ln(1 + number of cumulative confirmed cases): Germany [α_{9}] | −0.0382 | 0.0292 | ||

ln(1 + number of cumulative confirmed cases): Spain [α_{10}] | −0.0337 | −0.1604 | ||

ln(1 + number of cumulative confirmed cases): UK [α_{11}] | −0.0458 | −0.0573 | ||

ln(1 + number of cumulative confirmed cases): US [α_{12}] | −0.0287 | 0.0854 | ||

ln(1 + number of cumulative confirmed cases): Canada [α_{13}] | −0.0539 | 0.0117 | ||

ln(1 + number of cumulative confirmed cases): Australia [α_{14}] | −0.0743 | −0.0924 | ||

p-value of the F-statistic statistic for testing H_{m} for m = 1, 2, 3 | <0.0001 | <0.0001 | <0.0001 |

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

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.

The authors declare no conflicts of interest regarding the publication of this paper.

Woo, C.K., Cao, K.H., Liu, Y.L. and Li, Q.Q. (2020) Estimated Benefits of Incremental Suppression of Covid-19 Spread. Open Access Library Journal, 7: e6645. https://doi.org/10.4236/oalib.1106645