Effectiveness of Government Policies in Response to the COVID-19 Outbreak

This paper assesses the quantitative impact of government interventions on deaths related to the COVID-19 outbreak. Using daily data for 32 countries and relying on the stringency of the conducted policies, we find that the greater the strength of government interventions at an early stage, the more effective these are in slowing down or reversing the growth rate of deaths. School closures have a significant impact on reducing the growth rate of deaths which is less effective compared to the case where a number of policy interventions are combined together. These results can be informative for governments in responding to future COVID-19 outbreaks or other pandemics not least because there is a possibility of further waves of COVID-19 infections and deaths as governments progressively relax their interventions.


Introduction
As evident by the tremendous media attention, the COVID-19 pandemic has triggered severe social and economic costs. The Financial Times, for instance, has a dedicated website 1 which provides free access to its analysis. At the time of writing, there were around 23.4 million confirmed cases of COVID-19 infections and 0.80 million deaths. 2 Lessons learned from previous pandemics imply a huge impact on economic activity. Barro et al. (2020) use data for 43 countries to find that the 'Spanish flu' of the 1918-1920 period generated real per capita GDP declines of 6% for countries on average. Using data stretching back to the 14th century for France, Germany, Italy, the Netherlands, Spain, and the UK, Jordà et al. (2020) show that pandemics depress the real rate of interest for years after a pandemic, perhaps as many as 40 years (wars do not have such effects).
To bring down COVID-19-related infections and deaths in the pandemic thus far, governments have responded with a number of interventions. Among others, Cowling et al. (2020) show that non-pharmaceutical interventions (including border restrictions, quarantine and isolation, distancing, and changes in population behavior) were associated with reduced transmission of COVID-19 in Hong Kong. Using data for Germany, Hartl et al. (2020a, b) find a reduction in the growth rate of COVID-19, seven days after the implementation of containment policies on 13 March 2020 and again eight days after the implementation of further measures on 22 March 2020. Chen and Qiu (2020) rely on a dynamic panel epidemiological model of nine countries to show that interventions like mask wearing and centralized quarantine can replace the costly, in economic terms, national lockdown without significantly heightening the epidemic peak. Basu et al. (2020) use panel data analysis for the case of England to find that greater stringency is associated with stronger social distancing; nevertheless, the poor still distance less than the rich. Hsiang et al. (2020) use panel regression analysis to find that interventions prevented or delayed around 530 million  infections across six countries (China, South Korea, Iran, Italy, France, and the United States). Chudik et al. (2020) rely on an epidemiological model for a number of Chinese provinces and ten countries to find that it takes about 21 days from infection to recovery (or death) rather than the 14 days typically assumed in designing quarantine policies.
As the first wave of the COVID-19 outbreak appears to be easing in many countries around the globe, it is extremely crucial to provide an initial quantitative assessment of the impact that ongoing government interventions have had on controlling the pandemic. As noted by a recent communication news article in Nature (Gibney, 2020), "working out the effectiveness of the measures implemented worldwide to limit the coronavirus's spread is now one of scientists' most pressing questions". The pressing issue of the efficacy of government interventions could be further addressed by the following questions: First, can a prompt and strict government response curb the mortality curve of the epidemic? Second, does the severity of interventions affect (and by how much) the subsequent evolution of the growth rate of deaths? Third, under uncontrolled pandemic conditions, can the shift to harsher measures lower (and by how much) the growth rate of deaths? Providing this information should be vital to governments as they attempt to design strategies to return to a 'new normal' and, at the same time, prevent further waves of the COVID-19 outbreak.
This paper attempts to address these critical questions in a quantitative manner. To do so, we first define two critical concepts: (i) the strength of the policies and (ii) the early stage implementation of these policies. In particular, we define the policy strength of any certain day as the average value of the Government Response Tracker index (developed by the University of Oxford) for the preceding 14 days (Lauer et al. 2020, estimate that the incubation period of the virus is 14 days). Early stage refers to any day that precedes or is equal to the first observed day in which the number of confirmed deaths is at least five (both definitions are further discussed in section 5). Considering these concepts, we form three hypotheses of interest.
"Speed is of the essence" is our first hypothesis. That is, if COVID-19 policy measures are effective, then the strength of these measures taken at an early stage should be related positively to the probability of attaining a statistically insignificant trend in deaths attributable to COVID-19. "Stringency matters" is our second hypothesis. Upon realization of a positive significant trend in deaths, and under the assumption that the COVID-19 related policy measures taken at an early stage have been effective, then the strength of these measures should still inversely affect the trend slope shaped by the COVID-19 deaths. "Speed of adjustment matters" is our third hypothesis. As countries that initially responded with "low strength" policy measures progressively increase the strength of their response, a significant reduction in the trend slope should take place after a certain breakpoint in time. Thus, for countries with a break in the trend slope, if COVID-19 policy measures are effective then the difference in the This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=3602004 strength of the policy measures (between the break time and the early stage) should be related inversely to the difference of the slopes in the observed trends (after and before the break).
To examine these hypotheses, we use daily data on COVID-19 related deaths for 32 countries. We rely on the Perron and Yabu (2009a) statistical test to endogenously determine a break on the linear trend of the logarithm of deaths per country. We also estimate the slope of this trend based on the work of Perron and Yabu (2009b). 3 We then assess the impact of government interventions on the trend slope shaped by the daily number of deaths. Our results suggest that a unit increase in the strength of the overall policy measures (school closures) at an early stage raises the probability of attaining an insignificant trend in deaths by 1.1% (0.7%). We also find that a unit increase in the overall policy measures (school closures) at an early stage lowers the growth rate of deaths by 0.2% (0.1%). Finally, governments that initially respond with "low strength" policy measures but progressively increase the strength of their response, succeed in slowing down or reversing the growth rate of deaths after a certain breakpoint in time. In particular, a unit increase in the adjustment of the overall policy (school closures) between the breakpoint in time and the early stage lowers the difference in the growth rate of deaths (observed after and before the breakpoint) by 0.3% (0.1%). Therefore, we find that the greater the strength of government interventions at an early stage, the more effective these are in slowing down or reversing the growth rate of deaths. Additionally, the evidence suggests that school closures alone, have a significant impact -albeit, one which is less powerful in reducing the growth rate of deaths than that achieved by pooling together a number of government interventions. Overall, governments can use some of the results of this paper to respond to future COVID-19 outbreaks or to other pandemics not least because further waves of COVID-19 infections and deaths are likely to emerge as policymakers progressively relax their interventions; indeed, August 2020 saw a further rise in confirmed COVID-19 cases. 4 The paper proceeds as follows: section 2 discusses the data; section 3 provides the theoretical motivation; section 4 describes the methodology; section 5 presents the empirical strategy and model estimates; section 6 presents robustness checks and, section 7 concludes. 5

Data
We focus on 32 countries that have been affected by the pandemic crisis and use daily data on the total number of confirmed deaths attributed to COVID-19. Our sample covers the January 1 st , 2020 to April 30 th , 2020 period. The accuracy of official confirmed cases of COVID-19related infections is limited by how effectively a country is testing people to confirm cases and accurately reporting results. Countries have, in fact, approached COVID-19 testing in different ways. For example, Germany and South Korea have been much more aggressive in testing and confirming infections than other countries. 5,6 With this in mind, we focus on deaths related to COVID-19. The raw data on the daily deaths for all countries of our sample come from the European Centre for Disease Prevention and Control (ECDC). 7,8 Figure 1 reports the data. From Figure 1, daily deaths in China reached a peak in mid-February before dropping again (isolated blue surface in the purple area). Daily deaths in Italy reached a peak in late March 2020. Daily deaths in Spain, France and the UK reached a peak in early April 2020.

Theoretical motivation
The rationale for the structure of the estimated specifications in Section 5 can be deployed by linking the framework of a reduced-form econometric model, commonly implemented in economics to assess the impact of various conducted policies on target variables, and a typical epidemiological model. The use of reduced-form econometric specifications in epidemiology is not new. These specifications may prove quite informative when the purpose of the analysis is not to describe the mechanism of disease transmission, but rather to evaluate the impact of disease-related interventions on the number of cases or deaths (Hsiang et al. 2020). The main advantage of reduced-form econometric modeling is that it permits sufficient inference on the 8 total effectiveness of policy interventions without the need to provide input for essential epidemiological parameters that may be uncertain or even unknown.
Along the same lines, Hsiang et al. (2020) rely on a typical Susceptible-Infected-Recovered (SIR) model to focus on the initial phase of the outbreak where the susceptible individuals in the limit approximate the population and the infections increase exponentially. Hsiang et al. (2020) show that the initial system of equations is reduced to a simple first-order differential equation, which describes the change of infections in the beginning of the outbreak. The general solution for the number of infections at time t ( () It ) is: where (0) I is the number of infections at the start of the process, e is the Naperian base and g is the growth rate of infections at each unit of time. By calculating the natural logarithm for the ratio of the general solution over two sequential points in time (e.g. 2 t and 1 t ), it is easily shown that the growth rate of infections is equal to the difference of two principal parameters of the SIR model: where is the transmission rate of the disease and is the recovery rate. In the absence of vaccination and other government interventions (e.g. social distancing measures which affect or health system investments that affect ), the growth rate remains time-invariant. Under the realistic hypothesis that the very short-run investments on the health system do not alter , the growth rate of infections becomes time-dependent only when disease anti-contagion policies are implemented to the susceptible population. In other words, the growth rate of infections may be expressed as a function of the time-varying anti-contagion policies.
Assuming a typical linear functional form, the growth rate of infections can be described by the following reduced form econometric specification: where 0 is the growth rate of infections in the absence of social distancing policies, 1 is the expected impact of these policies on the growth rate of infections, () Pt is a measure of stringency for the conducted social distancing policies at time t and () ut is a normally distributed stochastic process with constant mean and constant variance. 9 Equation (3) describes the infection process for a disease and reveals that social distancing policies have a contemporaneous effect on the growth rate of the process. An emerging issue is whether the same process can be applied to model the growth rate of the resulting deaths. As there is a time distance between infection and death, the number of deaths at time t ( () Dt ) is proportional to the number of infections at an earlier time th . Hence, following Amaro et al. (2020), the number of deaths at time t can be defined as: where is the proportion of the infected individuals that finally die from the disease and h is the time horizon that separates infection from death. Given equation (4), it can be shown that the growth rate of deaths at time t is equal to the growth of infections at time th : In the presence of social distancing policies, equations (3) and (5) indicate that these may affect the growth rate of infections instantly (through the transmission parameter ), and impact the growth of deaths only after h time horizons. Thus, the reduced form econometric specification is: where 0 is the growth rate of deaths in the absence of anti-contagion policies, 1 is the average impact of the anti-contagion policies on the growth of deaths and () zt is the error term. Equation (6) signals that the growth rate of deaths at time t depends on the anticontagion policies implemented h time horizons in the past. As such, econometric specifications which ignore this structure can lead to misleading inferences.

Methodology
Epidemic curves consist of time-series observations showing the number of cases or deaths.
The epidemiological stylized facts along with the respective theoretical underpinnings suggest that the level of an epidemic curve increases exponentially with time, while the log-level of the curve is approximately a linear function of time (Ma, 2020). Hence, since our focus is on the log-level of deaths, the linear testing frameworks of Perron and Yabu (2009a,b) come as a natural choice. In particular, Perron and Yabu (2009a) test for a break in the slope of a trend function of a series without prior information on whether the noise component is integrated This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=3602004 of order one or a stationary process. For an autoregressive error component of order one, we assume the following data-generated process for the variable t y : 12 where =1,..., tT , t e is an i.i.d. process with zero mean and variance 2 , and t x and w are ( × r 1) vectors containing the deterministic components of the series depending on the adopted specification and the unknown parameters, respectively. It is also assumed that 0 u is a finite scalar with a being in the range of -( 1, 1], allowing this way the error component to be either stationary or integrated of order one. For our purpose, the specification of interest is model II (break in the trend) in Perron and Yabu (2009a). Therefore, T is the break date at some 1 ( , ) k 01 and I( ) is an inidcator function) and Hence, we focus our interest on testing the hypothesis Rw g where R is a full rank matrix and g is a ( × q 1) vector of q restrictions; in this case, we focus on the significance of the 2 b coefficient. When = a 1, its approximation through OLS and the use of quasi-feasible generalized least squares (FGLS) to obtain estimates for w leads to a Wald statistic 1 () F Wk that no longer has a chi-square limit distribution. Hence, Perron and Yabu (2009a) propose a superconsistent estimate of a through the following truncation: For the case of an unknown break, Perron and Yabu (2009a) propose the following FMS Exp W statistic estimated for all permissible break dates: where 11 = ( ; 1-) K k k for 0 with 1 k being the break fraction in the sample and a trimming parameter. The problem with the limit distribution of FMS Exp W statistic is that it differs for the cases of an integrated of order one or a stationary process. Consequently, Perron and Yabu (2009a) identify the limit distributions and provide asymptotic critical values for different levels of the trimming parameter . Although the limit distributions are different for the two cases above, the critical values for the respective quantiles are quite similar. Hence, Perron and Yabu (2009a) propose to use the larger critical value.
Once the break in trend is identified, Perron and Yabu (2009b) propose an approach to estimate and test the significance of the linear trend in a series t y . The approach is again robust to the presence of an integrated or stationary error component. In particular, assuming that in equation (7)

Empirical strategy and findings
To assess the overall effectiveness of the conducted policies in response to the COVID-19 outbreak, we follow the empirical strategy deployed in Figure 3 Table 1. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=3602004 For the latter group of countries, the Perron and Yabu (2009a) test identifies endogenously the break date ( * t ) at which the structural change in trend takes place (see column 2 of Table   1). Unsurprisingly, the date of the break occurs much earlier in China (the origin of the virus).
The date of the break in Italy precedes the ones in Spain, France, the US, Germany and the UK. 17 For countries like South Korea or Greece, we do not detect a trend in deaths; these are countries that have reported deaths of a similar magnitude on daily basis for the investigated sample.
Once the significant break date * t has been identified, we proceed by estimating the coefficient of trend component on the series through the method of Perron and Yabu (2009b).
For the first group of countries, the slope estimation (  Table 1). Thus, for both groups of countries, we obtain estimates for the average growth rate of deaths (along with their statistical significance) without allowing the identified structural change in the trend to affect the magnitude of the coefficients. Notice, from column 4 of Table 1 that, among those 19 countries with a break in the trend of deaths, Spain records the highest average growth rate of deaths (that is, 30.6% per day) followed by the US (that is, 23.4% per day). After the break, the same 19 countries experience an average growth rate of deaths, which either slows down significantly or turns negative. 17 For the UK, the structural break in the trend of deaths comes later than for other European countries including Italy, France, Spain and the Netherlands. Richard Horton (Editor of medical journal The Lancet) has been very critical of the UK's response to the crisis. For instance, Horton told the Science Select Committee of UK MPs in late March 2020 that the government's scientific advisers failed to take into account early warnings of the seriousness of the epidemic in China; see: https://cutt.ly/YyqHwA4.  (Perron and Yabu, 2009a) and slope estimates (Perron and Yabu, 2009b  For column 1, ***, ** and * denote a statistically significant break in trend at the 0.01, 0.05, and 0.10 level, respectively. For columns 3, 4, and 5, ***, ** and * refer to the statistical significance of the estimated slope. Focusing on the significance of the slope estimates (see columns 3 and 4 of Table 1) for all countries, we move on to investigate within a binary choice framework the validity of the first hypothesis. Thus, for each country i (i =1,…, 32) we define the dichotomous variable i D which takes the value of one (1) if a non-significant slope coeffient is estimated and zero (0) if the coefficient is significant. 18 In this case, i D takes the value of 1 for 13 countries and the value of 0 for 19 countries.
Moreover, for each observation t of the sample T , we define the strength ( t S ) of the overall policies (implemented to control the spread of COVID-19) as the average value of the OxCGRT index over the period t 1 to t 14 . 19 We further define the concept of early stage policies at time t , when t is less than or equal to t (t ≤t ). Thus, for each country i , we build the early stage strength of the overall policies at time t (start of i ETS ), denoted by t i S . Hence, the first hypothesis is examined by the following simple probit specification: where 0 and 1 are parameters to be estimated and i u is the error term assuming the usual properties (an i.i.d. normally distributed process). In this specification, a statistically significant and positive value for the coefficient 1 would indicate that the strength of the policy measures at an early stage ( t i S ) is related positively to the probability of attaining an insignificant slope for the series of deaths. The estimates of equation (10) 20 are shown in Table 2 below. The symbol *** implies that the estimate is significant at the 0.01 significance level. The specification is estimated by the Maximum Likelihood estimation approach using robust standard errors (s.e.). The Hosmer and Lemeshow (1989) HL statistic fails to reject the null hypothesis that the observed and expected proportions are the same across all constructed groups, implying a good model fit. Finally, the LM test for heteroscedasticity as illustrated in Davidson and MacKinnon (2004) fails to reject the null hypothesis of no heteroscedasticity.
In terms of the first hypothesis (that is, speed is of the essence), the relevant coefficient 1 is positive and significant at the 0.01 significance level. This finding implies that the higher 19 The strength is calculated for the observations that belong to the , interval. 20 The motivation for using equation (10) relates to the epidemiological model reported in section 3. In particular, if, at the early stage of an outbreak, anti-contagion policies are implemented, then the transmission rate parameter ( ) as well as the growth rate of infections and the growth rate of deaths should all be influenced negatively. Hence, we expect for countries that have implemented harsh anti-contagion policies, the transmission rate to decrease in magnitude and, therefore, the slope of deaths (average growth rate) not to be statistically different from zero. On the other hand, consider the case where such policies are not implemented and/or stringency is low. Then, the transmission rate will increase in magnitude and, therefore, the slope of deaths (average growth rate) will be positive and statistically different from zero. the strength of the policy measures at an early stage, the higher the probability of attaining an insignificant trend slope for the observed deaths. In more detail, the associated marginal effect to the estimated coefficient (that is, 0.011) suggests that for every unit increase in the strength of the OxCGRT index, the probability of attaining an insignificant trend component on the death series increases by 1.1%. Figure 4   To examine the validity of the second hypothesis (that is, stringency matters) our focus turns to those 20 countries with a statistically significant positive trend coefficient (see columns 3 and 4 of Table 1). 21 To do so, we construct the j C variable by assigning to each country j ( = ,..., ), only if this slope is positive and statistically significant. Thus, the second hypothesis is examined by the following specification: where 0 and 1 are parameters to be estimated and j u is the error term. A negative value for the coefficient 1 would indicate that the higher the strength of the policies at an early stage, the lower the growth rate of deaths for the subsequent period. The estimates of equation (11) 22 are reported in Table 3. The symbol *** implies that the estimate is significant at the 0.01 significance level. The specification is estimated by OLS using the Newey and West general covariance estimator for the reported standard errors (s.e.). The p-value associated to the White's test for heteroscedasticity implies no heteroscedasticity. Similarly, the p-value of the Breusch and Godfrey (B.G.) test for serial correlation suggests no serial correlation. Finally, the p-value for the Jarque-Bera test provides evidence in failing to reject the null hypothesis, implying normality for the error term. The diagnostic tests suggest no evidence of specification error.
With reference to the second hypothesis, the relevant coefficient 1 is negative and significant. The estimated coefficient (-0.002) suggests that for every unit increase in the strength of the index at an early stage, the slope of the trend component reduces by 0.2%. In the case of the UK, given the strength of the country's measures at t , the predicted daily average growth rate of deaths is 19.4% (that is, 0.216-0.002*11; this compares with an actual value of 21.6% from column 4 of Table 1). For Italy, the respective prediction is 14.8% (this compares with an actual value of 21.2% from column 4 of Table 1). Overall, our findings provide support to the validity of the second hypothesis.
For the third hypothesis (that is, speed of adjustment matters), attention is paid to those 19 countries with a significant break in trend (see column 1 of where 0 and 1 are parameters and m u is the error term. A negative value for 1 would indicate an inverse relationship between the adjustment in the strength of policies (over the time distance from t to * t ), and the change in the slopes before and after * t . The estimates of equation (12) 23 are reported in Table 4. With reference to the third hypothesis (speed of adjustment matters), the 1 coefficient is negative and significant. Consequently, an increase in the strength of measures (between t and * unit increase in the strength of the index between t and * t , the slope in the period after * t reduces by 0.3% (compared to the respective slope for the period before * t ). In the case of the UK, for instance, where the change in the strength of measures is 58.4 units, the predicted change in the daily growth rate of deaths is -21.4% (that is, -0.039-0.003*58.4; this compares with an actual value of -21.5% from column 6 of Table 1). The respective prediction for Italy is -17.9% (this compares with an actual value of -22.1% from column 6 of Table 1).
Overall, by exploiting the trend signals of the death series for 32 countries and relying on the stringency of the conducted policies, we find that government interventions are effective in slowing down or reversing the growth rate of deaths. The studies of Flaxman et al. (2020) and Hsiang et al. (2020) hospitalizations,deaths) are subject to all kinds of under-reporting. Raftery et al. (2020) discuss in detail specific limitations and cautions regarding COVID-19 data (cases, hospitalizations, emergency department visits, deaths, excess deaths) and what the implications are for decision making. Indeed, decision makers can make better choices when they have better understanding of the strengths and limitations of these data. Raftery et al. (2020) note that the number of confirmed COVID-19 cases is "likely to be a substantial underestimate of the prevalence of the disease in a population given that most people with COVID-19 are asymptomatic, and even among those who are symptomatic, not all are tested." They also note that COVID-19 deaths "are affected by the accuracy of cause-of-death determinations and reflect the state of the outbreak several weeks previously because of the long course of COVID-19 infection." They view excess deaths as the best mortality indicator of the COVID-19 outbreak, but also note that because of the possibility of death misclassification, excess deaths represent a mix of confirmed COVID-19 deaths and deaths from other causes.

Robustness checks
Thus, the presence of measurement errors raises the issue of whether one can be sufficiently confident that the empirical results reported above are reliable to inform decision making. Since our empirical setting focuses on the inherent trend signal of the deaths attributed to COVID-19, our analysis could be potentially misleading if the employed dataset fails to reveal the true trajectory of the trend. To address this concern, and following Raftery et al. (2020) who note that "compared with the other data reviewed here, excess deaths are the best indicator of the mortality impacts of the pandemic", we look at the excess mortality data compiled by The Financial Times (FT). 24 The FT dataset provides weekly data on excess mortality for a number of countries. 25 Excess mortality refers to the difference between the observed number of deaths (attributed to all causes) in the weeks of January 2019 to April 2020 and the median value for the same periods between 2015 and 2019. Excess mortality data are presented in Figure 5. The dataset is discussed at https://www.ft.com/content/a26fbf7e-48f8-11ea-aeb3-955839e06441 and provided at https://github.com/Financial-Times/coronavirus-excess-mortality-data. For presentation purposes, missing observations are interpolated through the quadratic-match average method. Again, for presentation purposes, excess deaths are plotted since 2019. Doing so allow us to see how excess mortality has evolved prior to and during the COVID-19 outbreak. 25 The data for Indonesia and Turkey refer only to Istanbul and Jakarta, respectively, and thus are excluded.
We focus on 17 countries that are common to the FT excess mortality dataset and our sample; 12 of these countries exhibit positive excess mortality from mid-March 2020 onwards.
Although not all of these excess deaths are necessarily attributable to the COVID-19 disease, we may argue with reasonable confidence that excess deaths adequately capture the trend signal of the true COVID-19 deaths. 26 To validate our analysis, we calculate the correlation coefficient between the number of COVID-19 deaths reported by the ECDC dataset and the excess mortality figures reported by the FT dataset. The correlation coefficients for each country are reported in Figure 6. 27

Figure 6. Correlation coefficient between COVID-19 deaths and excess mortality
We can reasonably expect that COVID-19 deaths from the ECDC dataset would exhibit a high degree of linear association with excess mortality FT data for all countries with a significant positive trend, as reported in Table 1. These are 12 countries in total. Conversely, 26 The literature on excess mortality is currently emerging. For instance, Vandoros (2020; see also references therein) hints to the possibility that some people might have died from COVID-19 without being diagnosed. He also points to spillover effects on other causes such as patients postponing their hospital appointments because of fear of contacting the virus in hospitals. the COVID-19 deaths from the ECDC dataset would arguably exhibit a lower degree of linear association with the excess mortality FT data, for all countries with an insignificant trend (as reported in Table 1). These are 5 countries in total. From Figure 6, the correlation coefficients for the 12 countries (exhibiting a significant trend) range between 0.70 and 0.97 (the average correlation coefficient value for these 12 countries is 0.90). The correlation coefficients for the remaining 5 countries (exhibiting an insignificant trend) are considerably lower (the average correlation coefficient value for these 5 countries is 0.19). Given these findings, we argue that despite the existence of errors in the measurement of the reported deaths of the ECDC dataset, the dataset is still capable of correctly signaling the true trajectory of the trend. Therefore, our analysis is sufficiently reliable to inform decision making.
We move on and turn our attention to school closures. Rather than using the aggregate stringency index of government interventions, we repeat our analysis by focusing on the 'school closures' component of the OxCGRT index. Consequently, we look at the strength of the school closure policy defined as the average value of the 'school closures' sub-index for the preceding 14-days of the time points of interest (that is; t and * t ). School closures have been the focus of media attention. 28 The Guardian, for instance, notes that there is very little evidence that school closures are effective in combating COVID-19. Viner et al. (2020) provide a comprehensive review (see also references therein) of the impact of school closures during coronavirus outbreaks around the world. They make the point that "the evidence to support national closure of schools to combat COVID-19 is very weak and data from influenza outbreaks suggest that school closures could have relatively small effects on a virus with COVID-19's high transmissibility and apparent low clinical effect on school children" (Viner et al. 2020;pp. 402-403). Viner et al. (2020) also flag the economic costs of school closures.
Indeed, from previous virus outbreaks, school closure costs are estimated between 0.2% and 1% of UK national gross domestic product per annum for school closures of 12-13 weeks and up to 3% of GDP for an 8-week school closure in the US. Ferguson et al. (2020) use an epidemiological model to find that school closures alone would prevent only 2-4% of deaths, much less than other social distancing interventions.
Using the school closures sub-index in our specifications instead of the aggregate stringecy index, we estimate 1 at 0.034 in equation (10), 1 at -0.001 in equation (11) and of the results of this paper to respond to future COVID-19 outbreaks or other pandemics. This is important not least because there is a possibility of further waves of COVID-19 infections and deaths as governments progressively relax their interventions. In fact, a sustainable exit strategy may not be very straightforward. As noted by Anderson et al. (2020), the implementation of social distancing measures has been politically challenging but technically simple. On the other hand, easing social distancing measures will most likely involve a process of trial and error, especially if there is evidence of further COVID-19 outbreaks emerging.