## wpiea2020218-print-pdf - 0.2 standard deviations, while a one-standard deviation decline in daily deaths per million is

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### Mobility and drivers of mobility change
- A one-standard deviation decline in daily cases per million is associated with an increase in mobility of 0.2 standard deviations, while a one-standard deviation decline in daily deaths per million is associated with an increase in mobility of only 0.05 standard deviations.
- Shapley decomposition (Table 1) — at a one-week horizon the model explains about 67 percent of overall variability in mobility:
  - Lagged Mobility: 27.08 percent variation explained
  - Reopening: 30.68 percent variation explained
    - School: 2.91
    - Retail: 6.70
    - Industry: 1.92
    - Services: 6.49
    - Travel: 1.67
    - Public/Events: 4.21
    - Overall Reopen Period: 6.75
  - Infections: 16.62 percent variation explained
    - Cases: 6.91
    - Deaths: 9.70
  - Time Trend: 25.61
  - Overall Variation Explained: 67.3
- Interpretation:
  - Reopening policies account for the bulk of explained variation in mobility (about 31 percent).
  - Lagged infections or voluntary social distancing explain a much smaller fraction (16 percent).
  - Government actions have both direct (restricting movement) and indirect (signaling safety) effects.

### Sectoral identification and robustness checks
- Sectoral disaggregation (Equation (3) → differenced Equation (4)) isolates sectoral reopening effects by removing time-varying unobservables.
- Two-sector analysis (retail and workplace, with workplace measured by services + industry) findings:
  - A sectoral easing action of one unit leads to a statistically significant increase in sectoral mobility of about 2-4 percentage points (left panel, Figure 10).
  - Sectoral job postings (right panel, Figure 10): a sectoral easing action of one unit leads to a statistically significant increase in sectoral job postings index of about 0.15 percentage points after approximately four days.
  - The employment response is lower than mobility, indicating sluggishness in labor market indicators.
- Robustness checks:
  - Controlling for sectoral heterogeneity, testing rates, self-reported mask usage, and self-reported non-household social contacts yields similar baseline findings (results referenced in Figures 15 and Annex Figure 16, noting reduced sample sizes where applicable).

### Effect of reopenings on subsequent infections (aggregate)
- Using an aggregate reopening index (R_it), a unit easing is associated with:
  - Cases: about 4 percent increase in daily cases after two weeks and close to 8 percent after one month.
  - Deaths: daily deaths increase by about 2 percent one month after each unit of easing.
- Shapley decomposition for infections (3-week horizon, Table 2):
  - Overall Variation Explained: Cases 45.05; Deaths 80.69
  - Lagged Mobility: Cases 2.39; Deaths 10.66
  - Reopening: Cases 24.50; Deaths 20.27
    - School: Cases 1.58; Deaths 1.69
    - Retail: Cases 1.59; Deaths 4.77
    - Industry: Cases 4.04; Deaths 1.79
    - Services: Cases 0.97; Deaths 2.45
    - Travel: Cases 2.01; Deaths 1.01
    - Public/Events: Cases 3.36; Deaths 3.11
    - Overall Reopen Period: Cases 10.93; Deaths 5.42
  - Infections (lagged): Cases 71.11; Deaths 55.89
    - Cases (lagged): Cases 59.63; Deaths 22.74
    - Deaths (lagged): Cases 11.58; Deaths 33.14
  - Time Trend: Cases 1.86; Deaths 13.16
- Interpretation:
  - Reopening measures explain about 20-24 percent of variability in subsequent infections.
  - The dynamics of the epidemic itself (lagged infections and country-specific trends) explain a larger fraction (around 69-73 percent).
  - Lagged mobility accounts for a small share (3-10 percent).

### Heterogeneity: speed, timing, and sequencing of reopenings
- Speed and timing (Equation (5)):
  - Fast reopeners (effective-to-actual days open metric above median) exhibit significantly higher daily cases per unit of easing: almost 10-15 percent higher relative to slow reopeners.
  - Countries that opened later along the infection curve (early vs. late defined by reduction in daily deaths relative to peak before first reopening action) had 5-7 percent higher daily cases per unit of easing relative to those that opened earlier.
  - No statistically significant differential in mobility per unit of easing between fast vs. slow or early vs. late reopeners, but fast/early reopeners experience a longer period of increased average mobility.
  - Predicted paths (Figure 13): alternative reopening strategies produce marked differences in infections trajectories but only minor differences in mobility pick-up.
  - Policy implication: gradual and prudent reopening (slower and later) can substantially reduce reinfection risk with only a modest additional economic cost from delayed full reopening.
- Sequencing of sectoral reopenings:
  - Method: for each sector j, construct sequencing terciles of the sum of other sectors' reopenings (early EO_jit = bottom tercile, middle MO_jit, late LO_jit), then interact sectoral reopening with sequencing to estimate ζ_j^E, ζ_j^M, ζ_j^L.
  - Key results (Figure 14):
    - The effect of a sectoral reopening step is larger when sequenced toward the end of the overall reopening plan.
    - Example: one-unit easing in services has little effect on infections if sequenced early or middle, but a positive and statistically significant effect if sequenced late.
    - Amplification effects differ across sectors: retail and events show relatively larger increases in daily cases when opened late compared with opening other sectors (e.g., schools) at similar stages.
    - Suggestion: sequencing retail to open early and schools later carries lower risk than the opposite strategy.
    - Exception: international travel shows lower and insignificant amplification when opened later; possible explanation is negligible importation effect when community transmission is already high.
  - Caveats: sectoral sequencing results are preliminary; more granular transmission data and consideration of equity and other factors are required.

### Robustness to testing and other non-pharmaceutical interventions
- Controlling for daily tests per-capita (smaller sample) yields similar average and differential reopening effects (Figure 15).
- Additional controls for self-reported mask usage and self-reported number of non-household social contacts (smaller sample from Imperial College survey countries) do not materially change baseline findings.

### Conclusions and policy takeaways
- Reopening measures supported a recovery in economic activity but were associated with an uptick in infections through end-August; the infection uptick translated into a smaller increase in fatalities than earlier lockdown-period estimates, likely reflecting younger infected demographics and improved medical care.
- The reinfection risk increases disproportionately under certain reopening strategies:
  - Faster and earlier reopening is associated with substantially higher subsequent infections per unit of easing.
  - Sequencing matters: reopening sectors late (when many others are already open) amplifies infection risk, with retail and events posing relatively larger amplification risks than schools.
- Policy implications:
  - Gradual, slower, and later reopening strategies can materially reduce infection amplification with only modest additional economic cost from delayed full reopening.
  - Sectoral sequencing can be used to mitigate amplification risk (e.g., prioritize sequencing that opens lower-amplification sectors earlier).
  - Continued attention to population behavior (mask usage, social distancing) and targeted containment measures remains crucial as activity resumes.
- Remaining limits: results are subject to data limitations (testing, survey coverage) and require more granular transmission data for definitive sequencing guidance.

*Source: wpiea2020218-print-pdf (IMF working paper).*

### 0.2 standard deviations, while a one-standard deviation decline in daily deaths per million is

### wpiea2020218-print-pdf - 0.2 standard deviations, while a one-standard deviation decline in daily deaths per million is

### Mobility and drivers of mobility change
- A one-standard deviation decline in daily cases per million is associated with an increase in mobility of 0.2 standard deviations, while a one-standard deviation decline in daily deaths per million is associated with an increase in mobility of only 0.05 standard deviations.
- Shapley decomposition (Table 1) — at a one-week horizon the model explains about 67 percent of overall variability in mobility:
  - Lagged Mobility: 27.08 percent variation explained
  - Reopening: 30.68 percent variation explained
    - School: 2.91
    - Retail: 6.70
    - Industry: 1.92
    - Services: 6.49
    - Travel: 1.67
    - Public/Events: 4.21
    - Overall Reopen Period: 6.75
  - Infections: 16.62 percent variation explained
    - Cases: 6.91
    - Deaths: 9.70
  - Time Trend: 25.61
  - Overall Variation Explained: 67.3
- Interpretation: reopening policies account for the bulk of explained variation in mobility (about 31 percent), while lagged infections or voluntary social distancing explain a much smaller fraction (16 percent). Government actions have both direct (restricting movement) and indirect (signaling safety) effects.

### Sectoral identification and robustness checks
- Sectoral disaggregation (Equation (3) → differenced Equation (4)) isolates sectoral reopening effects by removing time-varying unobservables.
- Two-sector analysis (retail and workplace, with workplace measured by services + industry) findings:
  - A sectoral easing action of one unit leads to a statistically significant increase in sectoral mobility of about 2-4 percentage points (left panel, Figure 10).
  - Sectoral job postings (right panel, Figure 10): a sectoral easing action of one unit leads to a statistically significant increase in sectoral job postings index of about 0.15 percentage points after approximately four days. The employment response is lower than mobility, indicating sluggishness in labor market indicators.
- Robustness: controlling for sectoral heterogeneity, testing rates, self-reported mask usage, and self-reported non-household social contacts yields similar baseline findings (results referenced in Figures 15 and Annex Figure 16, noting reduced sample sizes where applicable).

### Effect of reopenings on subsequent infections (aggregate)
- Using an aggregate reopening index (R_it), a unit easing is associated with:
  - Cases: about 4 percent increase in daily cases after two weeks and close to 8 percent after one month.
  - Deaths: daily deaths increase by about 2 percent one month after each unit of easing.
- Shapley decomposition for infections (3-week horizon, Table 2):
  - Overall Variation Explained: Cases 45.05; Deaths 80.69
  - Lagged Mobility: Cases 2.39; Deaths 10.66
  - Reopening: Cases 24.50; Deaths 20.27
    - School: Cases 1.58; Deaths 1.69
    - Retail: Cases 1.59; Deaths 4.77
    - Industry: Cases 4.04; Deaths 1.79
    - Services: Cases 0.97; Deaths 2.45
    - Travel: Cases 2.01; Deaths 1.01
    - Public/Events: Cases 3.36; Deaths 3.11
    - Overall Reopen Period: Cases 10.93; Deaths 5.42
  - Infections (lagged): Cases 71.11; Deaths 55.89
    - Cases (lagged): Cases 59.63; Deaths 22.74
    - Deaths (lagged): Cases 11.58; Deaths 33.14
  - Time Trend: Cases 1.86; Deaths 13.16
- Interpretation: reopening measures explain a sizable share (about 20-24 percent) of variability in subsequent infections, but the dynamics of the epidemic itself (lagged infections and country-specific trends) explain a larger fraction (around 69-73 percent). Lagged mobility accounts for a small share (3-10 percent).

### Heterogeneity: speed, timing, and sequencing of reopenings
- Speed and timing (Equation (5)):
  - Countries classified as fast reopeners (effective-to-actual days open metric above median) exhibit significantly higher daily cases per unit of easing: almost 10-15 percent higher relative to slow reopeners.
  - Countries that opened later along the infection curve (early vs. late defined by reduction in daily deaths relative to peak before first reopening action) had 5-7 percent higher daily cases per unit of easing relative to those that opened earlier.
  - No statistically significant differential in mobility per unit of easing between fast vs. slow or early vs. late reopeners — but fast/early reopeners experience a longer period of increased average mobility.
  - Predicted paths (Figure 13): alternative reopening strategies produce marked differences in infections trajectories but only minor differences in mobility pick-up.
  - Policy implication: gradual and prudent reopening (slower and later) can substantially reduce reinfection risk with only a modest additional economic cost from delayed full reopening.
- Sequencing of sectoral reopenings:
  - Method: for each sector j, construct sequencing terciles of the sum of other sectors' reopenings (early EO_jit = bottom tercile, middle MO_jit, late LO_jit), then interact sectoral reopening with sequencing to estimate ζ_j^E, ζ_j^M, ζ_j^L.
  - Key results (Figure 14):
    - The effect of a sectoral reopening step is larger when sequenced toward the end of the overall reopening plan.
    - Example: one-unit easing in services has little effect on infections if sequenced early or middle, but a positive and statistically significant effect if sequenced late.
    - Amplification effects differ across sectors: retail and events show relatively larger increases in daily cases when opened late compared with opening other sectors (e.g., schools) at similar stages.
    - Suggestion: sequencing retail to open early and schools later carries lower risk than the opposite strategy.
    - Exception: international travel shows lower and insignificant amplification when opened later; possible explanation is negligible importation effect when community transmission is already high.
  - Caveats: sectoral sequencing results are preliminary; more granular transmission data and consideration of equity and other factors are required.

### Robustness to testing and other non-pharmaceutical interventions
- Controlling for daily tests per-capita (smaller sample) yields similar average and differential reopening effects (Figure 15).
- Additional controls for self-reported mask usage and self-reported number of non-household social contacts (smaller sample from Imperial College survey countries) do not materially change baseline findings.

### Conclusions and policy takeaways
- Reopening measures supported a recovery in economic activity but were associated with an uptick in infections through end-August; the infection uptick translated into a smaller increase in fatalities than earlier lockdown-period estimates, likely reflecting younger infected demographics and improved medical care.
- The reinfection risk increases disproportionately under certain reopening strategies:
  - Faster and earlier reopening is associated with substantially higher subsequent infections per unit of easing.
  - Sequencing matters: reopening sectors late (when many others are already open) amplifies infection risk, with retail and events posing relatively larger amplification risks than schools.
- Policy implications:
  - Gradual, slower, and later reopening strategies can materially reduce infection amplification with only modest additional economic cost from delayed full reopening.
  - Sectoral sequencing can be used to mitigate amplification risk (e.g., prioritize sequencing that opens lower-amplification sectors earlier).
  - Continued attention to population behavior (mask usage, social distancing) and targeted containment measures remains crucial as activity resumes.
- Remaining limits: results are subject to data limitations (testing, survey coverage) and require more granular transmission data for definitive sequencing guidance.

*Source: wpiea2020218-print-pdf (IMF working paper).*

### REFERENCES

### REFERENCES

### Key Citations
- Adda, Jérôme, 2016, “Economic activity and the spread of viral diseases: Evidence from high frequency data,” The Quarterly Journal of Economics, Vol. 131, No. 2, pp. 891–941.
- Caselli, Francesca, Francesco Grigoli, Weicheng Lian, and Damiano Sandri, 2020, “The Great Lockdown: Dissecting the Economic Effects,” World Economic Outlook.
- Cheng, Wei, Patrick Carlin, Joanna Carroll, Sumedha Gupta, Felipe Lozano Rojas, Laura Montenovo, Thuy D Nguyen, Ian M Schmutte, Olga Scrivner, Kosali I Simon, and others, 2020, “Back to Business and (Re) employing Workers? Labor Market Activity During State COVID-19 Reopenings,” NBER Working Paper.
- Egert, Balazs, Yvan Guillemette, and David Turner, 2020, “Walking the tightrope: avoiding a lockdown while containing the virus,” OECD Working Paper.
- Glaeser, Edward L, Ginger Zhe Jin, Benjamin T Leyden, and Michael Luca, 2020, “Learning from Deregulation: The Asymmetric Impact of Lockdown and Reopening on Risky Behavior During COVID-19,” NBER Working Paper.
- Gupta, Sumedha, Kosali Simon, and Coady Wing, 2020, “Mandated and voluntary social distancing during the COVID-19 epidemic,” Brookings Papers on Economic Activity.
- Hale, Thomas, Anna Petherick, Toby Phillips, and Samuel Webster, 2020, “Variation in government responses to COVID-19,” Blavatnik school of government working paper, Vol. 31.
- Han, Emeline, Melisa Mei Jin Tan, Eva Turk, Devi Sridhar, Gabriel M Leung, Kenji Shibuya, Nima Asgari, Juhwan Oh, Alberto L García-Basteiro, Johanna Hanefeld, and others, 2020, “Lessons learnt from easing COVID-19 restrictions: an analysis of countries and regions in Asia Pacific and Europe,” The Lancet.
- Henderson, J Vernon, Tim Squires, Adam Storeygard, and David Weil, 2018, “The global distribution of economic activity: nature, history, and the role of trade,” The Quarterly Journal of Economics, Vol. 133, No. 1, pp. 357–406.
- Jinjarak, Yothin, Rashad Ahmed, Sameer Nair-Desai, Weining Xin, and Joshua Aizenman, 2020, “Accounting for Global COVID-19 Diffusion Patterns, January-April 2020,” Techn. rep., National Bureau of Economic Research.
- Jones, Sarah P., 2020, “Imperial College London YouGov Covid 19 Behaviour Tracker,” Covid Data Hub.
- Jordà, Òscar, 2005, “Estimation and inference of impulse responses by local projections,” American economic review, Vol. 95, No. 1, pp. 161–182.
- Levinson, Meira, Muge Cevik, and Marc Lipsitch, 2020, “Reopening Primary Schools during the Pandemic,” The New England journal of medicine, Vol. 383, No. 10.
- Stage, Helena B, Joseph Shingleton, Sanmitra Ghosh, Francesca Scarabel, Lorenzo Pellis, and Thomas Finnie, 2020, “Shut and re-open: the role of schools in the spread of COVID-19 in Europe,” arXiv preprint arXiv:2006.14158.
- WHO, 2020, “Public health considerations while resuming international travel, 30 July 2020,”

### Appendix — Figure: Robustness to Testing, Masks and Social Distancing
- Figure 16(a): plots effect of reopening on the (log of) seven day moving average of cases and deaths as in (2).
- Figure 16(b): plots effect of reopening on the (log of) seven day moving average of cases and deaths, after controlling for testing rate, self-reported masks usage and self-reported social interactions.
- Note: Results in both figures are from a reduced (comparable) sample of countries for which survey responses on masks and social distancing are available.

### Appendix — Table 3: Baseline Effects of Reopening on Mobility (Index with 100 as normal)
- Horizon (Days): 0 7 14 21 28
- Reopening: 1.228 ∗∗∗; 0.784 ∗∗∗; 0.503 ∗∗; -0.045; -0.163 (standard errors: (0.168)(0.254)(0.246)(0.259)(0.233))
- Cases (Lagged): 0.002; -0.005; -0.001; 0.000; -0.017 (standard errors: (0.009)(0.017)(0.017)(0.016)(0.017))
- Deaths (Lagged): -0.100; -0.257 ∗∗; -0.393 ∗∗∗; -0.391 ∗∗∗; -0.320 ∗∗ (standard errors: (0.077)(0.130)(0.138)(0.144)(0.147))
- Mobility (Lagged): 0.440 ∗∗∗; 0.280 ∗∗∗; 0.199 ∗∗∗; 0.125 ∗∗∗; 0.092 ∗∗∗ (standard errors: (0.031)(0.044)(0.038)(0.038)(0.035))
- Reopen Period Dummy: 0.554; 0.114; 2.757 ∗∗∗; 3.523 ∗∗∗; 2.260 ∗∗ (standard errors: (0.770)(1.003)(0.960)(1.147)(0.992))
- Infection Time Trend: 2.686; 1.995; 1.269; 1.673; 1.805 (standard errors: (1.967)(1.590)(1.573)(1.566)(1.567))
- Observations: 20751 92117 70161 81466 (as presented: 20751921177016181466)
- r2: 0.863 0.809 0.782 0.718 0.657
- Specification: panel fixed effects with country and time fixed effects. Standard errors robust to arbitrary heteroscedasticity and time series auto-correlation. * at 10%; ** at 5%; *** at 1%.

### Appendix — Table 4: Baseline Effects of Reopening on Daily Cases (log of 7 day m.a.)
- Horizon (Days): 14 21 28 35 42
- Reopening: 0.031 ∗; 0.063 ∗∗∗; 0.084 ∗∗∗; 0.089 ∗∗∗; 0.071 ∗∗∗ (standard errors: (0.019)(0.023)(0.026)(0.028)(0.027))
- Cases (Lagged): 0.737 ∗∗∗; 0.573 ∗∗∗; 0.373 ∗∗∗; 0.200 ∗∗∗; 0.043 (standard errors: (0.061)(0.064)(0.064)(0.062)(0.062))
- Deaths (Lagged): -0.058; -0.058; -0.032; -0.043; -0.058 (standard errors: (0.077)(0.090)(0.095)(0.098)(0.100))
- Mobility (Lagged): 0.008 ∗∗∗; 0.010 ∗∗∗; 0.011 ∗∗∗; 0.012 ∗∗∗; 0.013 ∗∗∗ (standard errors: (0.002)(0.003)(0.003)(0.003)(0.003))
- Reopen Period Dummy: -0.281 ∗∗∗; -0.369 ∗∗∗; -0.419 ∗∗∗; -0.402 ∗∗∗; -0.343 ∗∗∗ (standard errors: (0.090)(0.118)(0.127)(0.120)(0.101))
- Infection Time Trend: 0.016; 0.049; 0.009; 0.026; -0.121 ∗ (standard errors: (0.051)(0.062)(0.071)(0.065)(0.069))
- Observations: 20682 20682 20682 20692 2002 (as presented: 20682068206820692002)
- r2: 0.655 0.464 0.370 0.389 0.445
- Specification: panel fixed effects with country and time fixed effects. Standard errors robust to arbitrary heteroscedasticity and time series auto-correlation. * at 10%; ** at 5%; *** at 1%.

### Appendix — Table 5: Baseline Effects of Reopening on Daily Deaths (log of 7 day m.a)
- Horizon (Days): 14 21 28 35 42
- Reopening: 0.018 ∗; 0.016 ∗; 0.021 ∗∗∗; 0.017 ∗; 0.014 (standard errors: (0.010)(0.009)(0.008)(0.009)(0.010))
- Cases (Lagged): 0.141 ∗∗∗; 0.126 ∗∗∗; 0.095 ∗∗∗; 0.089 ∗∗∗; 0.076 ∗∗∗ (standard errors: (0.030)(0.025)(0.022)(0.021)(0.024))
- Deaths (Lagged): 0.526 ∗∗∗; 0.453 ∗∗∗; 0.405 ∗∗∗; 0.305 ∗∗∗; 0.243 ∗∗∗ (standard errors: (0.055)(0.045)(0.038)(0.039)(0.042))
- Mobility (Lagged): 0.000; 0.000; 0.001; 0.001; 0.002 ∗ (standard errors: (0.001)(0.001)(0.001)(0.001)(0.001))
- Reopen Period Dummy: -0.064 ∗∗; -0.085 ∗∗; -0.118 ∗∗∗; -0.072 ∗; -0.007 (standard errors: (0.031)(0.035)(0.039)(0.039)(0.039))
- Infection Time Trend: -0.004; 0.005; -0.004; 0.018; -0.028 (standard errors: (0.012)(0.014)(0.019)(0.022)(0.028))
- Observations: 20682 20682 20682 20692 2002 (as presented: 20682068206820692002)
- r2: 0.837 0.803 0.758 0.618 0.465
- Specification: panel fixed effects with country and time fixed effects. Standard errors robust to arbitrary heteroscedasticity and time series auto-correlation. * at 10%; ** at 5%; *** at 1%.

*Source: wpiea2020218-print-pdf - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020218-print-pdf.pdf_