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### I. Introduction — motivation and high-level findings
- Motivation:
  - The COVID-19 pandemic had unusual sectoral effects that renewed interest in propagation and amplification of localized shocks in the aggregate economy.
  - Containment measures restricted activity in high-contact sectors; shocks rapidly spilled over to other industries, aggregate demand, domestically and across countries via trade linkages.
- Research focus:
  - Empirically quantify the extent to which shocks originating in certain sectors spill over and affect other sectors, both domestically and abroad.
  - Compare historical shocks (supply-side and demand-side) with the COVID-19 shocks to assess the size of spillovers relative to direct impacts.
- Key qualitative findings:
  - For supply shocks, total spillover effects from supplier and client sectors are almost twice as large, on average, than effects from shocks originating within a sector.
  - For demand shocks, spillover effects are up to seven times larger than own effects.
  - A sector’s share in a country’s GVA remains persistently lower after negative supply shocks, especially when originating in the same sector.
  - During COVID-19 the downturn was more severe and widespread across industries than during the Global Financial Crisis and other recent recessions, and more concentrated and lasting in high-contact sectors (accommodation and food services, transportation, brick-and-mortar retail).
  - Combining actual COVID-19 shocks by country and sector with historical-estimate results suggests almost half of the impact on a given sector can be attributed to spillovers from other sectors, predominantly from domestic suppliers.
  - The decline in real GVA due to spillovers relative to own shocks is larger for low-contact sectors.

### II. Methodology and data
- Shock decomposition and construction:
  - Own shocks: shocks originating in the focal sector.
  - Network (spillover) shocks: Upstream domestic (UpD), Upstream foreign (UpF), Downstream domestic (DnD), Downstream foreign (DnF).
  - Network shock formulas (as provided):
    - DnD_s,c,t = sum_a_{s,c,j,c,0} OwnShock_{j,c,t} for j ≠ s
    - UpD_s,c,t = sum_â_{s,c,j,c,0} OwnShock_{j,c,t} for j ≠ s
    - DnF_s,c,t = sum_sum_a_{s,c,j,g,0} OwnShock_{j,g,t} for g ≠ c j
    - UpF_s,c,t = sum_sum_â_{s,c,j,g,0} OwnShock_{j,g,t} for g ≠ c j
  - Definitions of a_{s,c,j,k,t} and â_{s,c,j,k,t} given as shares of focal sector total sales.
- Types of shocks:
  - Supply shock (TFP): ΔlogTFP_{s,c,t} = Δlog rGVA_{s,c,t} − α_{s,c,t} Δlog L_{s,c,t} − (1−α_{s,c,t}) Δlog K_{s,c,t}.
    - rGVA_{s,c,t}: real gross value added.
    - L_{s,c,t}: total hours worked.
    - K_{s,c,t}: real fixed capital stock.
    - α_{s,c,t}: sectoral labor share of value added (2-year moving average).
    - Caveat: TFP shocks reflect changes in efficiency, but also capacity utilization or measurement error.
  - Demand shock (government purchases): year-on-year percentage change in government purchases from each sector, constructed by weighting change in real total government spending by sector sales to public administration/government consumption.
    - Government spending shock not derived for public administration, education, and health sectors.
- Data:
  - Historical shocks use WIOD (World Input-Output Database).
  - WIOD coverage: up to 43 countries and 56 sectors over 1995-2014.
  - Use 2013 release for supply-side analysis; combine 2013 and 2016 releases for government spending shocks.
  - COVID-19 construction uses input-output data year 2014 (WIOD last available period).
- Empirical specification:
  - Local projections estimated as:
    - Δ^h Y_{s,c,t} = β_{Own,h} OwnShock_{s,c,t} + Σ_J β_{J,h} Shock_{s,c,t}^J + Γ_{s,c,t} + ε_{s,c,t}^h
    - Shock variables divided by their own standard deviation for comparability.
  - Data treatment:
    - Cap values of cumulative growth in real GVA larger than 0.5^h (smaller than −0.5^h) at 0.5^h (−0.5^h) to mitigate outliers.
    - Timing choice for TFP shocks excludes mechanical contemporaneous effect of own TFP shocks on sectoral GVA.

### III. Historical empirical results — magnitudes and persistence
- General findings:
  - Network effects are sizable relative to own effects for both TFP and government spending shocks.
  - For productivity (TFP) shocks: total spillover effects are almost two times larger than own effects, on average.
  - For government spending shocks: spillover effects are broadly the same size as for the supply shock, while own effects are smaller.
- Key summary statements from Appendix B:
  - The relative size of the spillover effects, compared with the own effect for the government spending shock, is about seven times larger than for the productivity shock.
  - Spillover effects are persistent for both types of shocks, especially productivity shocks, remaining sizable up to five years after the shock.
  - TFP changes tend to have much larger estimated downstream effects.
  - No evidence in the global sample of a dominant role for upstream effects in response to demand shocks (contrasting some U.S.-focused studies).
- Recovery and persistence (two-step approach):
  - A sector does not recover, on average, from a productivity shock originating in its own sector: the sector’s share of GVA remains 5 percent lower up to five years after the shock.
  - Government spending shocks and shocks originating in other sectors do not statistically significantly affect a sector’s size on average, although productivity network effects may be large and long-lived.
- Selected regression magnitudes (representative coefficients, every shock divided by its standard deviation; standard errors in parentheses):
  - Demand-side shocks — Panel B (Own and Total Network Shock):
    - h=1: Own Shock: 0.003* (0.002); Total Network Shock: 0.008*** (0.001); Number of Observations: 16,438; R^2: 0.113
    - h=2: Own Shock: 0.006** (0.003); Total Network Shock: 0.008*** (0.002); Number of Observations: 16,438; R^2: 0.154
    - h=3: Own Shock: 0.006 (0.004); Total Network Shock: 0.010*** (0.003); Number of Observations: 16,438; R^2: 0.183
    - h=4: Own Shock: 0.008 (0.005); Total Network Shock: 0.014*** (0.004); Number of Observations: 16,438; R^2: 0.208
    - h=5: Own Shock: 0.007 (0.006); Total Network Shock: 0.014*** (0.005); Number of Observations: 16,438; R^2: 0.228
  - Supply-side TFP shocks — Panel B (Own and Total Network Shock):
    - h=0: Own Shock: 0.001 (0.001); Total Network Shock: 0.002 (0.001); Number of Observations: 22,972; R^2: 0.109
    - h=1: Own Shock: 0.003* (0.001); Total Network Shock: 0.006*** (0.002); Number of Observations: 21,738; R^2: 0.172
    - h=2: Own Shock: 0.001 (0.002); Total Network Shock: 0.009*** (0.003); Number of Observations: 20,504; R^2: 0.187
    - h=3: Own Shock: –0.001 (0.003); Total Network Shock: 0.010** (0.004); Number of Observations: 19,270; R^2: 0.208
    - h=4: Own Shock: –0.001 (0.005); Total Network Shock: 0.009 (0.006); Number of Observations: 18,036; R^2: 0.230

### IV. COVID-19 analysis — approach and quantitative back-of-the-envelope results
- Approach:
  - Differentiate supply and demand dimensions of the pandemic shock across sector groups by contact intensity.
  - Measure changes in TFP and total hours worked between 2019Q4 and 2020H1.
  - Assign change in TFP and a fraction of change in hours to supply component; remaining fraction of hours change to demand component.
  - Split of hours into supply/demand based on sector “teleworkability” and essentiality from Shibata (2020) classification (assumed constant across countries).
  - Derive network shocks using input-output tables for 2014 (WIOD) and obtain own and network effects by multiplying shocks by estimated coefficients.
- Calibration and formulas (Appendix C):
  - TFP proxy: ΔlogTFP_{s,c} = ΔlogGVA_{s,c} − ΔlogL_{s,c}.
  - Share of activity affected by COVID-19 restrictions:
    - α_{s,c} = (1 − share of telework_{s,c}) × (1 − share of essential_{s,c}).
  - Final effect on sectoral real GVA:
    - Effect_{s,c}^J = β_{SUP,J,1} (ΔlogTFP_{s,c}^J + α_s ΔlogL_{s,c}^J) + β_{DEM,J,0} (1 − α_s) ΔlogL_{s,c}^J
      - β_{SUP,J,1}: supply-side coefficients from historical TFP shocks (Table B1, Panel A).
      - β_{DEM,J,0}: demand-side coefficients from historical government spending shocks (Table B2, Panel A).
      - J ∈ {Own, UpD, UpF, DnD, DnF}.
- Key quantitative findings:
  - Sectoral spillovers have been significant during the current crisis, with a relative contribution of network shocks to the decline in GVA in the first year of the pandemic of about 40 percent, on average.
  - Foreign spillovers played a more limited role relative to domestic spillovers.
  - Own effect is larger for high-contact sectors; relative importance of spillovers is larger for low-contact sectors.
  - The absolute size of spillovers is likely more modest in low-contact than high-contact sectors because the contraction in GVA was less severe for low-contact sectors.
  - The relative size of sectoral spillovers compared with own effects is smaller for COVID-19 than for past productivity and government spending shocks, because the pandemic originated in sectors more peripheral to production networks (predominantly services).
- Timing and interpretation:
  - Effects reported are relative contributions to the total GVA drop, owing to standardization of coefficients.
  - Timing convention implies results should be interpreted as occurring in the aftermath of the initial COVID-19 shock.
- Sample and classifications:
  - Sample for Figure 8: up to 34 countries (24 advanced and 10 emerging markets) over 1995–2014.
  - Sector groupings:
    - High-contact, affected sectors: wholesale and retail trade, hotels and restaurants, entertainment and personal services, transportation, education, health, and construction.
    - Low-contact sectors: all other sectors.

### V. Policy implications and conclusions
- Historical sector-level analysis:
  - Shows sizable and persistent sectoral spillovers from both supply and demand shocks across a broad sample of countries.
  - Negative sectoral productivity shocks can have persistent effects, leading to long-lasting declines in affected sectors (example: sector’s share remains 5 percent lower up to five years after an own productivity shock).
- COVID-19-specific implications:
  - Sectoral spillovers meaningfully amplified the shock, even if the relative size of spillovers was smaller than for past shocks due to the peripheral sectoral origin.
  - The lack of recovery of sectors after past negative productivity shocks highlights potential for permanent declines in the sectors most affected by COVID-19.
- Policy recommendations:
  - Targeted support to firms in hard-hit sectors can have outsized effects in mitigating output losses early in a crisis by limiting sectoral spillovers.
  - Policies that facilitate reallocation of capital and workers to other sectors may yield high returns, given historical incomplete recovery of sectors after large negative shocks.
  - Policy design should consider amplification and transmission effects in sectoral contexts (for example, transitions to a low-carbon economy or sector-specific public investment).
  - Further research is needed on propagation of other types of shocks, especially those from sector-specific policy changes, to help prepare for negative spillovers and leverage positive ones.

*Source: wpiea2021204-print-pdf - References (appendices and annex tables)*

### References ___________________________________________________________ 19

### wpiea2021204-print-pdf - References ___________________________________________________________ 19

### I. Introduction
- Motivation
  - The COVID-19 pandemic had unusual sectoral effects that renewed interest in propagation and amplification of localized shocks in the aggregate economy.
  - Containment measures restricted activity in high-contact sectors; shocks rapidly spilled over to other industries, aggregate demand, domestically and across countries via trade linkages.
- Research focus
  - Empirically quantify the extent to which shocks originating in certain sectors spill over and affect other sectors, both domestically and abroad.
  - Compare historical shocks (supply-side and demand-side) with the COVID-19 shocks to assess the size of spillovers relative to direct impacts.
- Key qualitative findings (from the introduction)
  - For supply shocks, total spillover effects from supplier and client sectors are almost twice as large, on average, than effects from shocks originating within a sector.
  - For demand shocks, spillover effects are up to seven times larger than own effects.
  - A sector’s share in a country’s GVA remains persistently lower after negative supply shocks, especially when originating in the same sector.
  - During COVID-19 the downturn was more severe and widespread across industries than during the Global Financial Crisis and other recent recessions, and more concentrated and lasting in high-contact sectors (accommodation and food services, transportation, brick-and-mortar retail).
  - Combining actual COVID-19 shocks by country and sector with historical-estimate results suggests almost half of the impact on a given sector can be attributed to spillovers from other sectors, predominantly from domestic suppliers.
  - The decline in real GVA due to spillovers relative to own shocks is larger for low-contact sectors.

### II. Contribution to literature
- Methodological lineage
  - Builds on Acemoglu and others (2016) and Acemoglu, Akcigit, and Kerr (AKK).
  - Extends AKK by:
    - Considering a large number of countries rather than US-only.
    - Constructing foreign network shocks using inter-country input-output linkages.
    - Deriving quantitative implications from past shocks for the COVID-19 crisis.
- Related literature
  - Macro effects of sectoral/microeconomic shocks and network amplification (references include Foerster, Sarte, and Watson, 2011; Di Giovanni, Levchenko, and Méjean, 2014; Baqaee and Farhi, 2019).
  - Analyses of COVID-19 economic shock anatomy and transmission (Baqaee and Farhi, 2020 and 2021; Bekaert, Engstrom, and Ermolov, 2020; Bonadio and others, 2020; Cerdeiro and Komaromi, 2020, among others).

### II. Historical sectoral shocks and their economic effects — Methodology (A)
- Shock decomposition and classification
  - Own shocks: shocks originating in the focal sector.
  - Network (spillover) shocks: shocks originating in other sectors, classified as:
    - Upstream domestic (UpD): originating in customer sectors that travel upstream to focal sector.
    - Upstream foreign (UpF): upstream shocks originating in customer sectors in other countries.
    - Downstream domestic (DnD): originating in supplier sectors that travel downstream to the focal sector.
    - Downstream foreign (DnF): downstream shocks originating in supplier sectors in other countries.
- Construction of network shocks from input-output tables (formulas as provided)
  - DnD_s,c,t = sum_a_{s,c,j,c,0} OwnShock_{j,c,t} for j ≠ s
  - UpD_s,c,t = sum_â_{s,c,j,c,0} OwnShock_{j,c,t} for j ≠ s
  - DnF_s,c,t = sum_sum_a_{s,c,j,g,0} OwnShock_{j,g,t} for g ≠ c j
  - UpF_s,c,t = sum_sum_â_{s,c,j,g,0} OwnShock_{j,g,t} for g ≠ c j
  - Definitions:
    - a_{s,c,j,k,t} = [sales (j,k)→(s,c),t] / sales_{s,c,t} : sales from sector j in country k to focal sector s in country c as share of focal sector total sales.
    - â_{s,c,j,k,t} = [sales (s,c)→(j,k),t] / sales_{s,c,t} : sales of focal sector s in country c to sector j in country k as share of focal sector total sales.
- Types of sector-level shocks analyzed
  - Supply shock: year-on-year percentage change in sectoral TFP.
    - Constructed as ΔlogTFP_{s,c,t} = Δlog rGVA_{s,c,t} − α_{s,c,t} Δlog L_{s,c,t} − (1−α_{s,c,t}) Δlog K_{s,c,t}, where:
      - rGVA_{s,c,t} is real gross value added;
      - L_{s,c,t} is total hours worked;
      - K_{s,c,t} is real fixed capital stock;
      - α_{s,c,t} is sectoral labor share of value added (calculated as a 2-year moving average).
    - Caveat: TFP shocks as in (5) reflect changes in efficiency, but also capacity utilization or measurement error in factors.
  - Demand shock: year-on-year percentage change in government purchases from each sector.
    - Built by weighting change in real total government spending in country c at year t by sector s sales in country c and year t−1 going to public administration or government consumption in final demand, as a share of sectoral output in t−1.
    - Total real government spending in country c at time t is the sum of government consumption and total inputs of the public administration sector in country c at time t.
    - Government spending shock is not derived for public administration, education, and health sectors.

### II. Historical sectoral shocks and their economic effects — Data (B)
- Data sources and coverage
  - Historical shocks built using World Input-Output Database (WIOD).
  - WIOD provides input-output tables for up to 43 countries and 56 sectors over the period 1995-2014.
  - WIOD includes employment, capital stocks, gross output and value added.
  - Use the 2013 release for supply-side shock analysis (contains real variables for TFP construction per (5)).
  - Combine 2013 and 2016 releases to maximize sample coverage for government spending shocks.
  - Appendix A provides details on country and sector coverage for each exercise.

### II. Historical sectoral shocks and their economic effects — Empirical specification and key results (C)
- Estimation framework
  - Local projections (Jordà, 2005) estimated as:
    - Δ^h Y_{s,c,t} = β_{Own,h} OwnShock_{s,c,t} + Σ_J β_{J,h} Shock_{s,c,t}^J + Γ_{s,c,t} + ε_{s,c,t}^h
      - Δ^h Y_{s,c,t} is cumulative growth in real GVA of sector s in country c between:
        - t−1 and t+ h for government spending shocks;
        - t and t+ h for TFP shocks.
      - Shock_{s,c,t}^Own measures own shocks; Shock_{s,c,t}^J are network shocks (J ∈ {DnD, DnF, UpD, UpF}) or TotalNwk = sum of the four network shocks.
      - Γ_{s,c,t} is a set of sector, country, and time fixed effects.
      - Each shock variable in (6) is divided by its own standard deviation to make coefficients comparable.
  - Data treatment notes:
    - Cap values of cumulative growth in real GVA larger than 0.5^h (smaller than −0.5^h) at 0.5^h (−0.5^h) to mitigate outliers.
    - Timing choice for TFP shocks excludes sizable and largely mechanical contemporaneous effect of own TFP shocks on sectoral GVA.
- Empirical findings (historical shocks)
  - Network effects are sizable relative to own effects for both TFP and government spending shocks.
  - For productivity (TFP) shocks:
    - Total spillover effects are almost two times larger than own effects, on average.
    - Reference: Figure 2, Panel 1, and Table B1, Panel B, in Appendix B.
  - For government spending shocks:
    - Spillover effects are broadly the same size as for the supply shock, while own effects are smaller.
    - Reference: Figure 2, Panel 2, and Table B2, Panel B, in Appendix B.

### III. COVID-19 analysis (summary of approach and key comparative findings)
- Focus and approach
  - Differentiate supply and demand dimensions of the pandemic shock across sector groups by contact intensity.
  - Document differential cumulative value-added growth performance across sector groups.
  - Combine actual COVID-19 shocks by country and sector with historical-estimate results to quantify importance of spillovers.
- Key comparative findings
  - The COVID-19 downturn was more severe and widespread across industries than the GFC and other recent recessions, but more concentrated and lasting in high-contact sectors (examples: accommodation and food services, transportation, brick-and-mortar retail).
  - Estimated spillovers during COVID-19:
    - Almost half of the impact to a given sector can be attributed to spillovers from shocks originating in other sectors, predominantly from shocks to domestic suppliers.
    - Spillovers estimated for COVID-19 are somewhat smaller than for historical shocks, consistent with the pandemic shock emanating from sectors less central to production networks.

*Source: wpiea2021204-print-pdf - References ___________________________________________________________ 19*

### Appendix B). As  a  result, the  relative size  of the spillover effects, compared with the own

### wpiea2021204-print-pdf - Appendix B). As  a  result, the  relative size  of the spillover effects, compared with the own

### Key results on spillovers and shock amplification
- The relative size of the spillover effects, compared with the own effect for the government spending shock, is about seven times larger than for the productivity shock.
- Spillover effects are persistent for both types of shocks, but especially productivity shocks, remaining sizable up to five years after the shock hits.
- Shocks not only affect activity in sectors in which they originate but can also have large impacts on connected sectors and generate amplification effects in the case of simultaneous shocks.
- TFP (total factor productivity) changes tend to have much larger estimated downstream effects, consistent with literature showing supplier productivity shocks lead to price changes that affect downstream quantities.
- The authors do not find evidence in their global sample of a dominant role for upstream effects in response to demand shocks that previous U.S.-focused studies found.

### Historical negative sectoral shocks: recovery and persistence
- Method: two-step approach
  - Step 1: Estimate percent change in sector s share of country c GVA from t−1 to t as a function of lags of negative TFP or government spending shocks (own and Total Network), with country-time, sector-time, and country-sector fixed effects (equation (7)).
  - Step 2: Estimate dynamic panel model to recover autocorrelation structure of shocks for own and total network shocks with analogous fixed effects (equation (8)).
  - Combine (7) and (8) to construct impulse response functions for cumulative growth rate in GVA shares.
- Findings on recovery:
  - A sector does not recover, on average, from a productivity shock originating in its own sector: the sector’s share of GVA remains 5 percent lower up to five years after the shock.
  - Government spending shocks and shocks originating in other sectors do not statistically significantly affect a sector’s size on average, although productivity network effects may be large and long-lived.
- Data handling note: changes in GVA shares larger than 0.5 (smaller than -0.5) are capped at 0.5 (-0.5).
- Regression details: estimated coefficients for intermediate regressions (7) and (8) reported in Table B3 in Appendix B.

### Sectoral dimension of the COVID-19 shock: supply and demand components
- The COVID-19 crisis combined a massive initial supply shock with a large decline in demand, with propagation through production networks.
- Supply-side:
  - Lockdowns reduced effective productive capacity and required reorganization of production, lowering productivity.
  - Initial sectoral supply shocks spilled over to affect supply in other sectors through production links.
- Demand-side:
  - Demand fell due to reduced mobility and higher precautionary savings amid uncertainty.
  - Propagation from supply to demand was amplified by liquidity-constrained households and firms, causing layoffs and further declines in private spending.
- U.S. case evidence:
  - Quantities purchased initially fell across the board; price changes were relatively muted.
  - Statistical decompositions suggest supply shocks accounted for about two-thirds of the decrease in employment and output in the United States in the second quarter of 2020, with large demand shocks in food services, accommodation, and tourism sectors.

### Quantifying sectoral spillovers during COVID-19 (back-of-the-envelope exercise)
- Approach:
  - Measure changes in TFP and total hours worked between 2019Q4 and 2020H1.
  - Assign change in TFP and a fraction of change in hours to the supply component; remaining fraction of hours change assigned to demand component.
  - Split of hours into supply/demand based on sector “teleworkability” and essentiality (Shibata (2020) classification).
  - Derive network shocks using input-output tables for 2014 (WIOD).
  - Obtain own and network effects on GVA by multiplying shocks by corresponding estimated coefficients.
- Key quantitative findings:
  - Sectoral spillovers have been significant during the current crisis, with a relative contribution of network shocks to the decline in GVA in the first year of the pandemic of about 40 percent, on average.
  - Foreign spillovers played a more limited role relative to domestic spillovers, consistent with other studies.
  - Own effect is larger for high-contact sectors; relative importance of spillovers is larger for low-contact sectors.
  - The absolute size of spillovers is likely more modest in low-contact than high-contact sectors because the contraction in GVA was less severe for low-contact sectors.
  - The relative size of sectoral spillovers compared with own effects is smaller for COVID-19 than for past productivity and government spending shocks, because the pandemic originated in sectors more peripheral to production networks (predominantly services).
- Timing and interpretation:
  - The average effects reported are relative contributions to the total GVA drop, owing to standardization of coefficients.
  - The timing convention implies results should be interpreted as occurring in the aftermath of the initial COVID-19 shock.

### Sample and data notes
- Sample for Figure 8: up to 34 countries (24 advanced and 10 emerging markets) over 1995–2014.
- Input-output data year used: 2014 (last available in the WIOD dataset).
- Sector groupings:
  - High-contact, affected sectors: wholesale and retail trade, hotels and restaurants, entertainment and personal services, transportation, education, health, and construction.
  - Low-contact sectors: all other sectors.

### Policy implications and conclusions
- Historical sector-level analysis shows sizable and persistent sectoral spillovers from both supply and demand shocks across a broad sample of countries.
- Negative sectoral productivity shocks can have persistent effects, leading to long-lasting declines in affected sectors.
- For the COVID-19 crisis:
  - Sectoral spillovers meaningfully amplified the shock, even if the relative size of spillovers was smaller than for past shocks due to the peripheral sectoral origin.
  - The lack of recovery of sectors after past negative productivity shocks highlights the potential for permanent declines in the sectors most affected by COVID-19.
- Policy recommendations and implications:
  - Targeted support to firms in hard-hit sectors can have outsized effects in mitigating output losses early in a crisis by limiting sectoral spillovers.
  - Policies that facilitate reallocation of capital and workers to other sectors may yield high returns, given historical incomplete recovery of sectors after large negative shocks.
  - Policy design should consider amplification and transmission effects in sectoral contexts (for example, transitions to a low-carbon economy or sector-specific public investment).
  - Further research is needed on propagation of other types of shocks, especially those from sector-specific policy changes, to help prepare for negative spillovers and leverage positive ones.

*Source: Authors’ calculations and text from the IMF content unit provided.*

### References

### wpiea2021204-print-pdf - References (Appendices A–C and Annex Tables)

### Appendix A. Data coverage — sectors and countries
- Table A1. Sectors Considered in the Analysis of Productivity and Government Spending Shocks (sectors listed exactly as in source)
  - Agriculture, Hunting, Forestry and Fishing
  - Mining a nd Quarrying
  - Food, Beverages a nd Tobacco
  - Textiles, wea ring a pparel a nd lea ther products
  - Wood a nd Products of Wood and Cork
  - Pulp, Pa per, Pa per, Printing a nd Publishing
  - Coke, Refined Petroleum; Chemicals a nd Chemical Products
  - Rubber and Pla stics
  - Other Non-Metallic Mineral
  - Ba sic Metals a nd Fa bricated Metal
  - Electrica l a nd Optical Equipment
  - Tra nsport Equipment
  - Ma chinery, Not Elsewhere Cla ssified; Manufacturing, Not Elsewhere Classified; Recycling
  - Electricity, Ga s a nd Water Supply
  - Construction
  - Sa le, Ma intenance a nd Repair of Motor Vehicles and Motorcycles; Retail Sa le of Fuel
  - Reta il Tra de, Except of Motor Vehicles a nd Motorcycles; Repair of Household Goods
  - Wholesa le trade, except of motor vehicles a nd motorcycles
  - Hotels a nd Restaurants
  - La nd transport a nd transport via pipelines
  - Wa ter Tra nsport
  - Air Tra nsport
  - Other Supporting a nd Auxilia ry Tra nsport Activities; Activities of Travel Agencies
  - Post a nd Telecommunications
  - Fina ncial Intermediation
  - Rea l Esta te Activities
  - Public Admin a nd Defense; Compulsory Social Security*
  - Education*
  - Hea lth a nd Social Work*
  - Priva te Households with Employed Persons
  - Other Business Activities
  - Other Community, Social a nd Personal Services
  - Notes: Reclassification of the sectors in the 2013 and 2016 releases of WIOD data. Stars denote sectors excluded from the analysis of government spending shocks.

- Table A2. Country Coverage
  - Spillovers from past TFP a nd government spending shocks (list of economies exactly as in source)
    - Austra lia ; Austria; Belgium; Bra zil; Bulgaria ; Canada; China; Croatia*; Cyprus; Czech Republic; Denmark; Estonia; Finla nd; Fra nce; Germany; Greece; Hungary; India; Indonesia; Ireland; Italy; Ja pan; Korea; Latvia; Lithuania; Luxembourg; Malta; Mexico; Netherlands; Norway*; Poland; Portugal; Romania; Russia; Slovak Republic; Slovenia; Spain; Sweden; Switzerland*; Ta iwa n Province of China; Turkey; United Kingdom; United States
  - COVID-19 spillovers (list of economies exactly as in source)
    - Austra lia ; Austria; Belgium; Bra zil; Canada; China; Czech Republic; Denmark; Finla nd; France; Germany; Greece; Hungary; India ; Indonesia; Ireland; Italy; Ja pan; Korea; Mexico; Netherlands; Norway; Poland; Portugal; Romania; Russia ; Slovak Republic; Spain; Sweden; Switzerland; Taiwan Province of China ; Turkey; United Kingdom; United States
  - Notes: Sta rs denote countries included in the a nalysis of government spending shocks only.

### Appendix B. Additional results — key regression outputs and panels
- Table B2. Effects of Demand-Side Government Spending Shocks (Panel A. Own and Spillover Effects; Panel B. Own and Total Spillover Effects)
  - Panel A — Own and Spillover Effects: cumulative growth of real GVA at horizons h=1 to h=5 (coefficients with standard errors in parentheses)
    - h=1 (column (1))
      - Own Shock: 0.003* (0.002)
      - Upstream Domestic Shock: 0.003** (0.001)
      - Upstream Foreign Shock: 0.000 (0.002)
      - Downstream Domestic Shock: 0.006*** (0.001)
      - Downstream Foreign Shock: 0.005*** (0.002)
      - Number of Observations: 16,438
      - R^2: 0.114
    - h=2 (column (2))
      - Own Shock: 0.006** (0.003)
      - Upstream Domestic Shock: 0.003 (0.002)
      - Upstream Foreign Shock: –0.001 (0.003)
      - Downstream Domestic Shock: 0.005** (0.002)
      - Downstream Foreign Shock: 0.004 (0.003)
      - Number of Observations: 16,438
      - R^2: 0.154
    - h=3 (column (3))
      - Own Shock: 0.006 (0.004)
      - Upstream Domestic Shock: 0.004 (0.003)
      - Upstream Foreign Shock: 0.000 (0.003)
      - Downstream Domestic Shock: 0.008*** (0.003)
      - Downstream Foreign Shock: 0.003 (0.003)
      - Number of Observations: 16,438
      - R^2: 0.183
    - h=4 (column (4))
      - Own Shock: 0.008 (0.005)
      - Upstream Domestic Shock: 0.003 (0.004)
      - Upstream Foreign Shock: 0.001 (0.005)
      - Downstream Domestic Shock: 0.011*** (0.004)
      - Downstream Foreign Shock: 0.008* (0.005)
      - Number of Observations: 16,438
      - R^2: 0.208
    - h=5 (column (5))
      - Own Shock: 0.007 (0.006)
      - Upstream Domestic Shock: 0.004 (0.005)
      - Upstream Foreign Shock: 0.000 (0.005)
      - Downstream Domestic Shock: 0.010** (0.005)
      - Downstream Foreign Shock: 0.010* (0.006)
      - Number of Observations: 16,438
      - R^2: 0.229
  - Panel B — Own and Total Spillover Effects
    - h=1 to h=5 (coefficients with standard errors)
      - h=1: Own Shock: 0.003* (0.002); Total Network Shock: 0.008*** (0.001); Number of Observations: 16,438; R^2: 0.113
      - h=2: Own Shock: 0.006** (0.003); Total Network Shock: 0.008*** (0.002); Number of Observations: 16,438; R^2: 0.154
      - h=3: Own Shock: 0.006 (0.004); Total Network Shock: 0.010*** (0.003); Number of Observations: 16,438; R^2: 0.183
      - h=4: Own Shock: 0.008 (0.005); Total Network Shock: 0.014*** (0.004); Number of Observations: 16,438; R^2: 0.208
      - h=5: Own Shock: 0.007 (0.006); Total Network Shock: 0.014*** (0.005); Number of Observations: 16,438; R^2: 0.228

- Annex Table 2.3.1. Spillovers from Supply-Side TFP Shock (Panel A. Own and Spillover Effects; Panel B. Own and Total Spillover Effects)
  - Panel A — Own and Spillover Effects (h=0 to h=4)
    - h=0 (column (1))
      - Own Shock: 0.001 (0.001)
      - Upstream Domestic Shock: 0.000 (0.001)
      - Upstream Foreign Shock: –0.001 (0.002)
      - Downstream Domestic Shock: 0.002 (0.002)
      - Downstream Foreign Shock: 0.004** (0.001)
      - Number of Observations: 22,972
      - R^2: 0.110
    - h=1 (column (2))
      - Own Shock: 0.002 (0.001)
      - Upstream Domestic Shock: 0.001 (0.003)
      - Upstream Foreign Shock: 0.000 (0.002)
      - Downstream Domestic Shock: 0.006** (0.003)
      - Downstream Foreign Shock: 0.004* (0.002)
      - Number of Observations: 21,738
      - R^2: 0.173
    - h=2 (column (3))
      - Own Shock: –0.001 (0.002)
      - Upstream Domestic Shock: 0.004 (0.005)
      - Upstream Foreign Shock: 0.000 (0.003)
      - Downstream Domestic Shock: 0.006 (0.005)
      - Downstream Foreign Shock: 0.006** (0.003)
      - Number of Observations: 20,504
      - R^2: 0.187
    - h=3 (column (4))
      - Own Shock: –0.001 (0.003)
      - Upstream Domestic Shock: 0.004 (0.008)
      - Upstream Foreign Shock: 0.001 (0.004)
      - Downstream Domestic Shock: 0.008 (0.007)
      - Downstream Foreign Shock: 0.005 (0.004)
      - Number of Observations: 19,270
      - R^2: 0.208
    - h=4 (column (5))
      - Own Shock: –0.001 (0.005)
      - Upstream Domestic Shock: 0.005 (0.010)
      - Upstream Foreign Shock: 0.001 (0.005)
      - Downstream Domestic Shock: 0.004 (0.010)
      - Downstream Foreign Shock: 0.002 (0.006)
      - Number of Observations: 18,036
      - R^2: 0.230
  - Panel B — Own and Total Spillover Effects (h=0 to h=4)
    - h=0: Own Shock: 0.001 (0.001); Total Network Shock: 0.002 (0.001); Number of Observations: 22,972; R^2: 0.109
    - h=1: Own Shock: 0.003* (0.001); Total Network Shock: 0.006*** (0.002); Number of Observations: 21,738; R^2: 0.172
    - h=2: Own Shock: 0.001 (0.002); Total Network Shock: 0.009*** (0.003); Number of Observations: 20,504; R^2: 0.187
    - h=3: Own Shock: –0.001 (0.003); Total Network Shock: 0.010** (0.004); Number of Observations: 19,270; R^2: 0.208
    - h=4: Own Shock: –0.001 (0.005); Total Network Shock: 0.009 (0.006); Number of Observations: 18,036; R^2: 0.230
  - Source and estimation notes (verbatim):
    - Source: IMF staff calculations.
    - Note: The dependent variables are cumulative growth of real GVA at horizon h after a shock. Shocks are changes in sectoral TFP originated in Own sector or in other sectors in the production network, as described in the text. Total Network Shock is the sum of the four types of network shocks. Every shock is divided by its standard deviation. Regressions are estimated separately for each horizon. The sample covers 29 advanced and 11 emerging economies over 1995–2009 (see Annex Table 2.1.2). All regressions include country, sector, and year fixed effects. Standard errors are clustered at the country-sector level. * p<0.1; ** p<0.05; *** p<0.01.

- Annex Table 2.3.2. Spillovers from Demand-Side Government Spending Shock (Panel A and B)
  - Source and estimation notes (verbatim):
    - Source: IMF staff calculations.
    - Note: The dependent variables are cumulative growth of real GVA at horizon h after a shock. Shocks are changes in sectoral government spending originated in Own sector or in other sectors in the production network, as described in the text. Total Network Shock is the sum of the four types of network shocks. Every shock is divided by its standard deviation. Regressions are estimated separately for each horizon. The sample covers 31 advanced and 12 emerging economies over 1995–2014 (see Annex Table 2.1.2). All regressions include country, sector, and year fixed effects. Standard errors are clustered at the country-sector level. * p<0.1; ** p<0.05; *** p<0.01.

- Table B3. Intermediate Steps in the Estimation of Sector Recovery
  - Estimation details (verbatim):
    - Source: Authors.
    - Note: Odd columns report estimates of equation (7); the dependent variable is the percent change in the share of GVA of sector 푠 in total GVA in country 푐 from time 푡−1 to 푡. Even columns report estimates of equation (8); the dependent variable is the contemporaneous shock in sector 푠, country 푐, at time 푡. Columns are grouped by the type of shock considered (TFP and government spending) and source of shock (own sector versus total network shock). Regressors are 푆ℎ표푐푘
푠,푐,푡−ℎ
퐽
, with ℎ being the time lag and 퐽 the type of shock considered in each pair of columns. All regressions are estimated for negative contemporanoues shocks only. They all include a set of country-time, sector-time, and country-sector fixed effects. Standard errors, in parentheses, are clustered at the country-sector level. * p<0.1, ** p<0.05, *** p<0.01.

### Appendix C. Construction of the COVID-19 shocks — methodology and formulas
- Calibration window and data sources
  - COVID-19 shocks to TFP (Δlog푇퐹푃
푠,푐
) and total hours worked (Δlog퐿
푠,푐
) are calibrated for each sector 푠 in country 푐 by considering changes between 2019Q4 and 2020H1.
  - Total sectoral hours worked are derived from mean weekly hours worked and employment levels from ILOSTAT.
  - Changes in sectoral GVA are from the OECD’s Quarterly National Accounts statistics.
  - Missing data are extrapolated using sector and country income group averages.
  - Footnote verbatim: "This effectively assumes unchanged capital."

- TFP proxy and decomposition
  - Changes in TFP are proxied by changes in labor productivity, calculated as:
    - Δlog푇퐹푃
푠,푐
=Δlog퐺푉퐴
푠,푐
−Δlog퐿
푠,푐
  - The change in TFP is treated as a supply-side shock.

- Partition of hours worked into supply and demand components
  - The change in hours worked Δlog퐿
푠,푐
 is partitioned into a supply component and a demand component according to the share of activities in a sector expected to be affected by COVID-19 containment measures.
  - Definition of the share of activity affected by COVID-19 restrictions:
    - 훼
푠,푐
=
(
1−share of telework
s,c
)
×
(
1−share of essential
s,c
)
  - Shares of telework and essentiality are based on the classification of sectors in the United States provided in Shibata (2020) and are assumed constant across countries.
  - Interpretation: sectors with low 훼
푠
 (e.g., essential sectors or highly teleworkable sectors) attribute most observed change in hours to demand factors; sectors with high 훼
푠
 (e.g., hospitality, construction) attribute most observed change in hours to supply factors.
  - Figure C1 in the source shows values of 훼
푠
 (shares reflect degree of teleworkability and essentiality; assumed the same across countries).

- Construction of own and network shocks
  - Sectoral supply and demand shocks derived via this methodology for each sector and country are "own shocks" (terminology from Section II.A).
  - Network shocks to productivity and labor are built by applying formulas (1)-(4) based on input-output tables for the year 2014 (WIOD dataset, last available period).

- Recovery of effects on sectoral real GVA (final aggregation formula)
  - The effect of shocks on sectoral real GVA is recovered as:
    - Effect
푠,푐
퐽
=훽
푆푈푃,퐽,1
(Δlog푇퐹푃
푠,푐
퐽
+훼
푠
Δlog퐿
푠,푐
퐽
)+훽
퐷퐸푀,퐽,0
(
1−훼
푠
)
Δlog퐿
푠,푐
퐽
  - Where:
    - 훽
푆푈푃,퐽,1
 are the supply-side coefficients estimated for historical TFP shocks (Table B1, Panel A).
    - 훽
퐷퐸푀,퐽,0
 are the demand-side coefficients estimated for historical government spending shocks (Table B2, Panel A).
    - J = Own, UpD, UpF, DnD, DnF (types of shocks).
  - Notes on estimation: Every shock is divided by its standard deviation in regressions; regressions include country, sector, and year fixed effects; standard errors clustered at the country-sector level.

*Italic: Source: wpiea2021204-print-pdf - References (appendices and annex tables)

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021204-print-pdf.pdf_