## annext

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---

### Objective and sample
- Objective: Understand what factors explain the difference in output performance recorded in 2020 between the United States and a sample of six European countries.
- Sample: France, Germany, Italy, Poland, Spain, and the United Kingdom.
- Baseline measure: For each country j, percent change in GDP relative to the fourth quarter of 2019:
  - ΔL Y_tj = 100 (Y_tj / Y_2019:Q4_j − 1)  (Equation (1))
- Activity gap with respect to the United States for country j:
  - ΔG Y_tj = ΔL Y_tUSA − ΔL Y_tj  (Equation (2))

### Decomposition approach (overview)
- Overall activity gap vis-à-vis the United States is decomposed into sequential layers to assess contributions from:
  - Underlying trend growth (Layer 1)
  - Sectoral composition of the economy (Layer 2)
  - Behavioral response to the pandemic (Layer 3)
  - Epidemiological developments (Layer 4)
- Decomposition proceeds sequentially: adjust for underlying trend growth, then sectoral composition, then mobility responses (de jure and de facto), and finally epidemiological drivers of mobility.

### Layer 1 — Underlying trend growth
- Data input: Average quarterly growth projections as of the January 2020 World Economic Outlook Update (cutoff vintage around mid-December 2019).
- Finding: By 2020:Q2, differences in underlying growth momentum accounted for most of the activity gap in Poland (which had a higher growth momentum than the US) and a significant fraction in Germany.

### Layer 2 — Sectoral composition and within‑sector differences
- Motivation: Some sectors (for example, contact-intense activities, such as leisure and hospitality) are more affected by social distancing norms.
- Trend-adjusted activity gap after Layer 1 (ω_i_j denotes weight of sector i in country j):
  - ΔG Ỹ_tj = ΔL Ỹ_tUSA − ΔL Ỹ_tj
    = ∑_{i=1}^N ω_i_USA ΔL Ỹ_i,t^USA − ∑_{i=1}^N ω_i_j ΔL Ỹ_i,t^j
    = ∑_{i=1}^N (ω_i_USA − ω_i_j) ΔL Ỹ_i,t^USA + ∑_{i=1}^N ω_i_j (ΔL Ỹ_i,t^USA − ΔL Ỹ_i,t^j)  (Equation (3))
  - First term: contribution of sectoral composition (“sectoral composition” in Figures 5 and 6).
  - Second term: differences in within-sector growth (“within-sector growth difference” in Figures 5 and 6).
- Finding: For some countries, after adjusting for underlying growth, sectoral composition explains part of the gap; remaining within-sector differences remain for further decomposition.

### Layer 3 — Behavioral response to the pandemic (mobility)
- Key variables:
  - De facto mobility: measured from Google mobility metrics (average of retail, workplace, and transport mobility metrics, realigned so 100 = pre-COVID-19 baseline).
  - De jure mobility: containment measures proxied by Oxford Blavatnik’s overall stringency index.
- Step 1 (weekly country-level panel): regress de facto mobility on de jure mobility
  - ΔL M_tj = a + b ΔL R_tj + e_tj  (Equation (4))
  - Residual ΔL(M_tj | R_tj) denotes “additional” de facto mobility (mobility beyond what containment measures imply on average).
- Step 2 (quarterly country-sector panel): regress sectoral activity gaps on de jure mobility and additional de facto mobility
  - ΔL Ỹ_i,t^j = α_i + β̃_i ΔL(M_tj | R_tj) + ρ̃_i ΔL R_tj + ε_i,t^j  (Equation (5))
  - β̃_i and ρ̃_i are sector-specific coefficients.
- Findings:
  - De facto mobility reductions are highly correlated with within-sector activity gaps across time and countries.
  - De jure containment measures and voluntary (additional) de facto mobility are highly colinear.
  - Using results as of 2020:Q2, predicted effects of de jure and de facto mobility explain much of the residual activity gap at the aggregate level for some European countries; residuals after Layers 1–3 are rather small in 2020:Q2.
  - By 2020:Q3 the overall activity gap narrows but the unexplained residual widens, suggesting mobility relaxed faster than output rebounded.

### Layer 4 — Epidemiological developments (infections and fatalities)
- Motivation: Timing and intensity of the pandemic were heterogeneous across countries; for a given number of infections, Europe often experienced more severe outcomes (higher hospitalization and fatality rates).
- Step 1 (weekly country-level panel): regress fatalities on infections (one-week lag on cases)
  - FR_tj = c + d IR_tj + e_tj  (Equation (6))
  - FR_tj and IR_tj denote weekly averages of daily deaths and daily infection cases per million inhabitants; residual FR_tj | IR_tj denotes “additional” fatalities beyond what infections imply on average.
- Step 2: regress the two mobility indicators (de jure mobility and additional de facto mobility) on infection rates and additional fatality rates:
  - ΔL R_tj = α_R + γ_R ΔL(FR_tj | IR_tj) + δ_R IR_tj + ε_tj
  - ΔL(M_tj | R_tj) = α_M|R + γ_M|R ΔL(FR_tj | IR_tj) + δ_M|R IR_tj + ε_tj  (Equation (7))
- Findings:
  - A significant fraction of the 2020:Q2 activity gap in France, Italy, Spain, and the UK can be attributed to the effect that the severity of the pandemic had on mobility (infections and additional fatalities).
  - Layer 4 decomposes mobility contributions into what can be explained by epidemiological developments (labeled “infections” and “additional fatalities”) and what cannot (labeled “de facto mobility, other” and “de jure mobility, other”).
  - The layer does not change the residual magnitude from Layer 3; it reallocates portions of mobility contributions between epidemiological and non-epidemiological drivers.

### Aggregate findings and interpretation
- Accounting for differences in underlying growth, sectoral composition, and drops in de jure and de facto mobility explains the bulk of the activity gap between the United States and some large European economies in 2020.
- Country heterogeneity:
  - The gap is fairly small in some countries (for example, Germany and Poland).
  - For countries with larger activity gaps, stricter voluntary confinements—beyond what containment measures imply—explain most of the gap.
  - A significant part of voluntary mobility reductions reflects that the pandemic was more severe in Europe (higher hospitalizations and fatalities for a given number of infections).
- Residual (unexplained) activity gap after Layers 1–4:
  - Could reflect differences in macroeconomic policies. The set of spending and revenue measures adopted in the United States in 2020 was generally larger than in Europe (reference to Figure 15).
  - Fiscal packages in Europe also included sizable below-the-line measures and state guarantees; overall response was largely effective in preserving income and firms’ liquidity (reference to Figure 16).
  - Fiscal policy lags imply differentiated effects could appear beyond 2020.
  - Could also reflect better adaptability of the US economy to operate under reduced mobility:
    - Allowing coefficients in Equation (5) to vary across countries suggests the elasticity between output and mobility is smaller in the United States than in Europe in relatively large sectors (implying a lower drop in output for a given reduction in mobility).

### Key methodological assumptions and robustness notes
- Mobility data: Google Community Mobility Report, realigned where 100 corresponds to the pre-COVID-19 baseline (median value for each day of the week over January 3 – February 6, 2020); values below 100 indicate percent mobility below normal.
- The de facto mobility metric corresponds to the average of retail, workplace, and transport mobility metrics from Google.
- Identifying assumption in Layer 3 Step 1: containment measures (de jure mobility) cause changes in actual mobility within a given week (used to address multicollinearity).
- Epidemiological timing: daily cases are lagged one week in the fatalities regression to account for the delay between diagnosis and severe manifestations; longer lags did not materially affect results.
- Robustness exercises:
  - Allowing non-linear relationship between de jure and de facto mobility slightly increases the weight of containment measures.
  - Allowing epidemiological factors to affect output directly (not only via mobility) leaves results largely unaffected, suggesting the mobility channel captures most epidemiological effects.

### Teleworkability and preservation of activity; Figures 17–18 (Section 2)
- Teleworkability
  - High teleworkability is identified as a factor that could have facilitated the preservation of economic activity under restrained activity in 2020.
- Figure 17 — Elasticity of Output to de Facto Mobility (Percent)
  - Title: Figure 17. Elasticity of Output to de Facto Mobility (Percent)
  - Sources: IMF staff calculations.
  - Note: IT = information technology.
  - Axis ticks and labels as shown in source: 0 5 10 15 20 25 30 35 40 45
  - Country labels shown in figure extract: GBR, USA, DEU, POL, ITA, ESP, FRA
- Figure 18 — Residual Activity Gap in 2020:Q3 and Teleworkability
  - Title: Figure 18. Residual Activity Gap in 2020:Q3 and Teleworkability (Difference in share of teleworkable jobs with respect to the US, lhs; Layer 3 activity gap residual, percent, rhs)
  - Sources: Dingel and Neiman 2020; and IMF staff calculations.
  - Note: lhs = left-hand scale; rhs = right-hand scale. Country abbreviations are International Organization for Standardization country codes.
  - Variables presented in figure extract:
    - Left-hand metric: Difference in share of teleworkable jobs with respect to the US (label: Teleworkability)
    - Right-hand metric: Layer 3 activity gap residual, percent (label: Residual)
  - Axis ticks and labels as shown in source: -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 (second axis) and -2 0 2 4 6 8 -4 -2 0 2 4 6 8 10 12 (additional axis/grid)
  - Country label examples shown in figure extract: ESP, POL, ITA, DEU, FRA, GBR, USA, Others
  - Sector and component labels appearing in figure extract: Agriculture and fishing; Other industries; Financial and insurance services; Art, entertainment, and recreation; IT and telecoms; Construction; Real estate and renting; Taxes less subsidies; Business services; Trade, transportation, and hospitality; Public service, education, and health; Manufacturing
  - Additional legend note shown: Increasing share of GDP
- Key findings (from the provided text and figures)
  - High teleworkability is identified as a factor that could have facilitated the preservation of economic activity under restrained activity in 2020.
  - Figure 17 conveys an elasticity of output to de facto mobility measured in percent, with country-level comparisons including GBR, USA, DEU, POL, ITA, ESP, FRA.
  - Figure 18 links the residual activity gap in 2020:Q3 with teleworkability, using the difference in share of teleworkable jobs relative to the US (lhs) and a Layer 3 activity gap residual in percent (rhs).

*Italic: Online Annex. Differences in Output Performance between Europe and the United States during COVID-19 (annext - Section 1).*

### Section 1

### annext - Section 1

### Objective and sample
- Objective: Understand what factors explain the difference in output performance recorded in 2020 between the United States and a sample of six European countries.
- Sample: France, Germany, Italy, Poland, Spain, and the United Kingdom.
- Baseline measure: For each country j, percent change in GDP relative to the fourth quarter of 2019:
  - ΔL Y_tj = 100 (Y_tj / Y_2019:Q4_j − 1)  (Equation (1))
- Activity gap with respect to the United States for country j:
  - ΔG Y_tj = ΔL Y_tUSA − ΔL Y_tj  (Equation (2))

### Decomposition approach (overview)
- The overall activity gap vis-à-vis the United States is decomposed into layers to assess contributions from:
  - Underlying trend growth (Layer 1)
  - Sectoral composition of the economy (Layer 2)
  - Behavioral response to the pandemic (Layer 3)
  - Epidemiological developments (Layer 4)
- The decomposition proceeds sequentially: adjust for underlying trend growth, then sectoral composition, then mobility responses (de jure and de facto), and finally epidemiological drivers of mobility.

### Layer 1 — Underlying trend growth
- Uses the average quarterly growth projections as of the January 2020 World Economic Outlook Update (cutoff vintage around mid-December 2019).
- Finding: By 2020:Q2, differences in underlying growth momentum accounted for most of the activity gap in Poland (which had a higher growth momentum than the US) and a significant fraction in Germany.

### Layer 2 — Sectoral composition and within‑sector differences
- Motivation: Some sectors (for example, contact-intense activities, such as leisure and hospitality) are more affected by social distancing norms.
- Algebraic expression for the trend-adjusted activity gap after Layer 1 (ω_i_j denotes weight of sector i in country j):
  - ΔG Ỹ_tj = ΔL Ỹ_tUSA − ΔL Ỹ_tj
    = ∑_{i=1}^N ω_i_USA ΔL Ỹ_i,t^USA − ∑_{i=1}^N ω_i_j ΔL Ỹ_i,t^j
    = ∑_{i=1}^N (ω_i_USA − ω_i_j) ΔL Ỹ_i,t^USA + ∑_{i=1}^N ω_i_j (ΔL Ỹ_i,t^USA − ΔL Ỹ_i,t^j)  (Equation (3))
  - First term: contribution of sectoral composition (“sectoral composition” in Figures 5 and 6).
  - Second term: differences in within-sector growth (“within-sector growth difference” in Figures 5 and 6).
- Finding: For some countries, after adjusting for underlying growth, sectoral composition explains part of the gap; remaining within-sector differences remain for further decomposition.

### Layer 3 — Behavioral response to the pandemic (mobility)
- Key variables:
  - De facto mobility: measured from Google mobility metrics (average of retail, workplace, and transport mobility metrics, realigned so 100 = pre-COVID-19 baseline).
  - De jure mobility: containment measures proxied by Oxford Blavatnik’s overall stringency index.
- Step 1 (weekly country-level panel): regress de facto mobility on de jure mobility
  - ΔL M_tj = a + b ΔL R_tj + e_tj  (Equation (4))
  - Residual ΔL(M_tj | R_tj) denotes “additional” de facto mobility (mobility beyond what containment measures imply on average).
- Step 2 (quarterly country-sector panel): regress sectoral activity gaps on de jure mobility and additional de facto mobility
  - ΔL Ỹ_i,t^j = α_i + β̃_i ΔL(M_tj | R_tj) + ρ̃_i ΔL R_tj + ε_i,t^j  (Equation (5))
  - β̃_i and ρ̃_i are sector-specific coefficients.
- Findings:
  - De facto mobility reductions are highly correlated with within-sector activity gaps across time and countries.
  - De jure containment measures and voluntary (additional) de facto mobility are highly colinear.
  - Using results as of 2020:Q2, predicted effects of de jure and de facto mobility explain much of the residual activity gap at the aggregate level for some European countries; residuals after Layers 1–3 are rather small in 2020:Q2.
  - By 2020:Q3 the overall activity gap narrows but the unexplained residual widens, suggesting mobility relaxed faster than output rebounded.

### Layer 4 — Epidemiological developments (infections and fatalities)
- Motivation: Timing and intensity of the pandemic were heterogeneous across countries; for a given number of infections, Europe often experienced more severe outcomes (higher hospitalization and fatality rates).
- Step 1 (weekly country-level panel): regress fatalities on infections (one-week lag on cases)
  - FR_tj = c + d IR_tj + e_tj  (Equation (6))
  - FR_tj and IR_tj denote weekly averages of daily deaths and daily infection cases per million inhabitants; residual FR_tj | IR_tj denotes “additional” fatalities beyond what infections imply on average.
- Step 2: regress the two mobility indicators (de jure mobility and additional de facto mobility) on infection rates and additional fatality rates:
  - ΔL R_tj = α_R + γ_R ΔL(FR_tj | IR_tj) + δ_R IR_tj + ε_tj
  - ΔL(M_tj | R_tj) = α_M|R + γ_M|R ΔL(FR_tj | IR_tj) + δ_M|R IR_tj + ε_tj  (Equation (7))
- Findings:
  - A significant fraction of the 2020:Q2 activity gap in France, Italy, Spain, and the UK can be attributed to the effect that the severity of the pandemic had on mobility (infections and additional fatalities).
  - Layer 4 decomposes mobility contributions into what can be explained by epidemiological developments (labeled “infections” and “additional fatalities”) and what cannot (labeled “de facto mobility, other” and “de jure mobility, other”).
  - The layer does not change the residual magnitude from Layer 3; it reallocates portions of mobility contributions between epidemiological and non-epidemiological drivers.

### Aggregate findings and interpretation
- Accounting for differences in underlying growth, sectoral composition, and drops in de jure and de facto mobility explains the bulk of the activity gap between the United States and some large European economies in 2020.
- Country heterogeneity:
  - The gap is fairly small in some countries (for example, Germany and Poland).
  - For countries with larger activity gaps, stricter voluntary confinements—beyond what containment measures imply—explain most of the gap.
  - A significant part of voluntary mobility reductions reflects that the pandemic was more severe in Europe (higher hospitalizations and fatalities for a given number of infections).
- Residual (unexplained) activity gap after Layers 1–4:
  - Could reflect differences in macroeconomic policies. The set of spending and revenue measures adopted in the United States in 2020 was generally larger than in Europe (reference to Figure 15).
  - Fiscal packages in Europe also included sizable below-the-line measures and state guarantees; overall response was largely effective in preserving income and firms’ liquidity (reference to Figure 16).
  - Fiscal policy lags imply differentiated effects could appear beyond 2020.
  - Could also reflect better adaptability of the US economy to operate under reduced mobility:
    - Allowing coefficients in Equation (5) to vary across countries suggests the elasticity between output and mobility is smaller in the United States than in Europe in relatively large sectors (implying a lower drop in output for a given reduction in mobility).

### Key methodological assumptions and robustness notes
- Mobility data: Google Community Mobility Report, realigned where 100 corresponds to the pre-COVID-19 baseline (median value for each day of the week over January 3 – February 6, 2020); values below 100 indicate percent mobility below normal.
- The de facto mobility metric corresponds to the average of retail, workplace, and transport mobility metrics from Google.
- Identifying assumption in Layer 3 Step 1: containment measures (de jure mobility) cause changes in actual mobility within a given week (used to address multicollinearity).
- Epidemiological timing: daily cases are lagged one week in the fatalities regression to account for the delay between diagnosis and severe manifestations; longer lags did not materially affect results.
- Robustness exercises:
  - Allowing non-linear relationship between de jure and de facto mobility slightly increases the weight of containment measures.
  - Allowing epidemiological factors to affect output directly (not only via mobility) leaves results largely unaffected, suggesting the mobility channel captures most epidemiological effects.

_Italic: Online Annex. Differences in Output Performance between Europe and the United States during COVID-19 (annext - Section 1)._

### Section 2

### annext - Section 2

### Teleworkability and Preservation of Economic Activity
- One aspect that could have facilitated its ability to preserve economic activity under restrained activity is its high ability to telework (Figure 18).

### Figure 17 — Elasticity of Output to de Facto Mobility
- Title: Figure 17. Elasticity of Output to de Facto Mobility (Percent)
- Sources: IMF staff calculations.
- Note: IT = information technology.
- Axis ticks and labels as shown in source: 0 5 10 15 20 25 30 35 40 45
- Country labels shown in figure extract: GBR, USA, DEU, POL, ITA, ESP, FRA
- Visual grouping indicated in figure: Other (below-the-line) measures; Above-the-line measures

### Figure 18 — Residual Activity Gap in 2020:Q3 and Teleworkability
- Title: Figure 18. Residual Activity Gap in 2020:Q3 and Teleworkability (Difference in share of teleworkable jobs with respect to the US, lhs; Layer 3 activity gap residual, percent, rhs)
- Sources: Dingel and Neiman 2020; and IMF staff calculations.
- Note: lhs = left-hand scale; rhs = right-hand scale. Country abbreviations are International Organization for Standardization country codes.
- Variables presented in figure extract:
  - Left-hand metric: Difference in share of teleworkable jobs with respect to the US (label: Teleworkability)
  - Right-hand metric: Layer 3 activity gap residual, percent (label: Residual)
- Axis ticks and labels as shown in source: -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 (second axis) and -2 0 2 4 6 8 -4 -2 0 2 4 6 8 10 12 (additional axis/grid)
- Country label examples shown in figure extract: ESP, POL, ITA, DEU, FRA, GBR, USA, Others
- Sector and component labels appearing in figure extract: Agriculture and fishing; Other industries; Financial and insurance services; Art, entertainment, and recreation; IT and telecoms; Construction; Real estate and renting; Taxes less subsidies; Business services; Trade, transportation, and hospitality; Public service, education, and health; Manufacturing
- Additional legend note shown: Increasing share of GDP

### Key findings (from the provided text and figures)
- High teleworkability is identified as a factor that could have facilitated the preservation of economic activity under restrained activity in 2020.
- Figure 17 conveys an elasticity of output to de facto mobility measured in percent, with country-level comparisons including GBR, USA, DEU, POL, ITA, ESP, FRA.
- Figure 18 links the residual activity gap in 2020:Q3 with teleworkability, using the difference in share of teleworkable jobs relative to the US (lhs) and a Layer 3 activity gap residual in percent (rhs).

### References (as listed in the source)
- Dingel, Jonathan I., and Brent Neiman. 2020. “How many jobs can be done at home?” Journal of Public Economics, 189.
- Hale, Thomas, Noam Angrist, Emily Cameron-Blake, Laura Hallas, Beatriz Kira, Saptarshi Majumdar, Anna Petherick, Toby Phillips, Helen Tatlow, and Samuel Webster. 2020. Oxford COVID-19 Government Response Tracker, Blavatnik School of Government.

*Source: annext - Section 2 (annext - Section 2, annext.pdf).*

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_Source: https://www.imf.org/-/media/files/publications/reo/eur/2021/april/english/annext.pdf_