## 2.1 Environment (wpiea2024062-print-pdf)

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---

### Model setup, key identities, and propositions
- World with N countries; S internationally produced intermediate goods; each country has representative consumer with preference u_i(C_i, L_i).
- Final good aggregation and prices:
  - D_i = D_i(D_i1, ..., D_iS); D_i = C_i + G_i; Q_i denotes price of final good i.
  - Nominal public consumption eG_i = Q_i G_i given exogenously; private consumption eC_i = Q_i C_i chosen by monetary authority.
- Intermediate goods production (sector s):
  - Y_s = F_s(Z_s L_s, {X_sk}_k=1^S) with Z_s value added–augmented productivity.
  - Labor perfectly mobile across sectors within a country but immobile across countries.
  - Law of One Price for intermediate goods.
- Market clearing:
  - Sum_{i=1}^N D_is + Sum_{k=1}^S X_ks = Y_s, s=1,...,S
  - Sum_{s∈S_i} L_s = L_i, i=1,...,N

Cost minimization and pass-through
- Shephard’s Lemma input shares:
  - ∂log MC_s / ∂log W_s = (W_s L_s) / (MC_s Y_s) = θ_s
  - ∂log MC_s / ∂log P_k = (P_k X_sk) / (MC_s Y_s) = ω_sk
  - θ_s + Σ_k ω_sk = 1
- First-order approximation:
  - d log MC_s ≈ θ_s (d log W_s − d log Z_s) + Σ_k ω_sk d log P_k
- With time-invariant markup:
  - d log P_s = θ_s (d log W_s − d log Z_s) + Σ_k ω_sk d log P_k
- Matrix solution:
  - d log P = [I − Ω]^{−1} Θ (d log W − d log Z)

Labor, nominal output, and link to demand
- Cobb-Douglas implication with perfectly inelastic labor: W_s L_s = (1 − γ_s) eY_s and d log W_s = d log eY_s.
- Nominal output identity:
  - eY = [I − Ω′]^{−1} Ξ′ eD and changes: d log eY = Φ_Y^{−1} [I − Ω′]^{−1} Ξ′ Φ_D d log eD

Propositions (elasticities)
- Proposition 1 (PPI inflation):
  - Under perfectly inelastic labor and conditional on Z and eD:
    - d log P = Φ_D d log eD − Φ_S d log Z
    - Φ_D ≡ [I − Ω]^{−1} Θ Φ_Y^{−1} [I − Ω′]^{−1} Ξ′ Φ_D
    - Φ_S ≡ [I − Ω]^{−1} Θ
- Proposition 2 (CPI inflation):
  - d log CPI = Ξ d log P = Φ_D^{CPI} d log eD − Φ_S^{CPI} d log Z
  - Φ_D^{CPI} ≡ Ξ [I − Ω]^{−1} Θ Φ_Y^{−1} [I − Ω′]^{−1} Ξ′ Φ_D
  - Φ_S^{CPI} ≡ Ξ [I − Ω]^{−1} Θ

Notes on extensions
- Variable markup: add d log μ_s terms.
- Endogenous labor supply: joint wage determination required.

---

### Operationalization: lockdown shocks and Bartik instruments
- Lockdown stringency Λ_s ∈ [0,1] (sector) and Λ_i (country); 1 = full shutdown, 0 = unrestricted.
- Lockdown effects parameterized as:
  - Lockdown reduces sectoral Z by β_S percent and reduces country aggregate demand by β_D percent.
- Sectoral inflation response (general):
  - d log P_s = − Σ_k Φ_S_sk d log Z_k + Σ_i Φ_D_si d log eD_i
- For lockdown shocks:
  - d log P_s = β_S [Σ_k Φ_S_sk d log Λ_k] − β_D [Σ_i Φ_D_si d log Λ_i]
- Bartik instruments:
  - B_S_s ≡ Σ_k Φ_S_sk d log Λ_k (lockdown-supply)
  - B_D_s ≡ − Σ_i Φ_D_si d log Λ_i (lockdown-demand)
  - Empirical equation: d log P_s = β_S B_S_s + β_D B_D_s
- Extensions:
  - Fiscal Bartik: interact Φ_D with d log F_i (fiscal packages).
  - Monetary Bartik: interact Φ_D with d M_i (e.g., 3-month changes in central bank assets).

---

### Data coverage, harmonization, and instrument construction
- PPI inflation data: 1143 production sectors in 53 countries (31 AEs, 22 EMs), period 2019-2022; harmonized to 45 OECD WIOT industries.
- Panel features:
  - Unbalanced, skewed toward manufacturing; services comprise 21 percent of sample.
  - Inflation data winsorized at 1 percent in regressions; robustness to non-winsorized series.
- Monthly country-sector shocks:
  - Lockdown intensity from OxCGRT (index 0 to 1); sector-level lockdown = country stringency × sector ease of work-from-home.
  - Fiscal shock: COVID-19 fiscal stimulus packages (percent of GDP), smoothed with exponential decay half-life of 3 months in baseline.
  - Monetary shock: policy rate changes and central bank balance sheet size; monetary Bartik uses 3-month changes in central bank assets as M_i.
  - Maritime transport cost shocks: Freightos Baltic Container Price Index for 11 routes, interacted with bilateral ad valorem maritime costs (OECD) and aggregated via IO links.
- Bartik construction:
  - Exposure matrices from OECD IOT 2018 across 45 sectors and 64 countries.
  - Primary instruments:
    - Lockdown-supply B_S_s,t = Σ_k Φ_S_sk d log Λ_k
    - Lockdown-demand B_D_s,t = Σ_i Φ_D_si d log Λ_i (with negative sign in definition)
    - Fiscal B_fiscal_s,t = Σ_i Φ_D_si d log F_i
    - Monetary B_monetary_s,t = Σ_i Φ_D_si d M_i
  - Shifts calculated as 3-month changes; four quarterly changes included to capture yearly impact.
- Network and correlation facts:
  - Median sector sources 8 percent of inputs from within sector (92 percent from outside); typical sector transacts with 4–5 other sectors.
  - Correlations: upstream vs downstream exposure between any two sectors = 0.47; lockdown vs monetary = 0.34; lockdown vs fiscal = 0.15; monetary vs fiscal = 0.36.

---

### Baseline regressions and identification
- Local projection baseline:
  - PPI inflation_{s,t+h} = Σ_{l∈{0,3,6,9}} β^S_l B_S_{s,t−l} + Σ_{l∈{0,3,6,9}} β^D_l B_D_{s,t−l} + Σ_{l∈{0,3,6,9}} β^F_l B_fiscal_{s,t−l} + Σ_{l∈{0,3,6,9}} β^M_l B_monetary_{s,t−l} + controls_{s,t} + u_{s,t}
- Regression features:
  - Separate and joint specifications for shocks; full country, sector, and time fixed effects.
  - Controls: lagged inflation, exchange rate depreciation, transport costs, oil price shocks, COVID cases per capita in some specifications.
  - Standard errors clustered at country-sector; Driscoll-Kraay used for autocorrelation.
  - Year-over-year and four-quarter-change specifications reported.

Identification and robustness strategy (simplified setup)
- To avoid endogeneity from local lockdown correlation with local drivers, instruments constructed using only foreign lockdown shocks while controlling for local lockdown.
- Main robustness: foreign-only Bartik yields similar coefficient magnitudes, signs, and significance.

---

### Main empirical findings — key coefficients and magnitudes
- Simplified specification (Table 1):
  - Lockdown supply coefficient: 0.295 (interpretation: full lockdown lowers sector productivity by 29.5 percent; direct PPI impact = 0.295θ where θ is value-added share).
  - Lockdown demand coefficient: −0.355 (interpretation: complete country lockdown depresses aggregate demand by 35.5 percent).
  - Robustness: foreign-shocks-only estimates similar (lockdown-supply = 0.375; lockdown-demand = −0.257).
  - Observations reported: 4838748387 (table note).
- Fiscal shock (Table 2):
  - Contemporaneous fiscal multiplier coefficient: 0.754 ∗∗∗ (0.170) — reading: a $1 increase in fiscal spending increases domestic aggregate demand by almost 75 cents on impact.
  - Quarterly lags (Column 2): Lag 0 = 0.769 ∗∗∗ (0.098); Lag 3 = 0.803 ∗∗∗ (0.147); Lag 6 = 0.794 ∗∗∗ (0.185); Lag 9 = 0.662 ∗∗ (0.265).
  - Observations reported: 4838748387.
- Full specification contemporaneous results (Table 3, Column (1) and selected lags):
  - Lockdown-supply:
    - Lag 0: 0.291 ∗∗∗ (0.041)
    - Lag 3: 0.322 ∗∗∗ (0.048)
    - Lag 6: 0.334 ∗∗∗ (0.047)
    - Lag 9: 0.242 ∗∗∗ (0.058)
  - Lockdown-demand:
    - Lag 0: -0.302 ∗∗∗ (0.050)
    - Lag 3: -0.371 ∗∗∗ (0.034)
    - Lag 6: -0.430 ∗∗∗ (0.037)
    - Lag 9: -0.324 ∗∗∗ (0.077)
  - Fiscal:
    - Lag 0: 0.561 ∗∗∗ (0.113)
    - Lag 3: 0.592 ∗∗∗ (0.148)
    - Lag 6: 0.474 ∗∗ (0.168)
    - Lag 9: 0.345 ∗ (0.204)
  - Monetary:
    - Lag 0: 0.042 ∗∗∗ (0.010)
    - Lag 3: 0.077 ∗∗ (0.032)
    - Lag 6: 0.062 ∗ (0.037)
    - Lag 9: 0.074 (0.050)
  - Other controls:
    - Transport cost: 0.059 ∗∗∗ (0.014)
    - Oil price inflation: 0.517 ∗∗∗ (0.056)
    - FX depreciation: 0.297 ∗∗∗ (0.043)
  - Observations rows in table show concatenated counts (e.g., "48387401774017740177" in the source).
- Robustness table highlights:
  - Shipping cost point estimates ranging from 0.059 to 0.035, significant at 1 percent.
  - Winsorizing and alternative fixed effects do not materially change main coefficients.
  - Monetary contemporaneous coefficients sometimes small or insignificant in variants; lagged monetary effects often more persistent.

---

### Dynamics, decomposition, and network propagation
- Local projection IRFs (summary):
  - Lockdown supply: inflationary via supply disruptions; effects persistent about 10 months.
  - Lockdown demand: deflationary initially; reopening demand surge later drove inflation higher.
  - Fiscal: increases PPI inflation contemporaneously; longer-horizon effects imprecise.
  - Monetary: most persistent impacts among channels.
- Decomposition direct vs indirect (network) effects:
  - ΦS = [I − Ω]−1 Θ = (I + Ω + Ω2 + ...) Θ
  - Direct effect: ΦS,dir = (I + Ω) Θ; Indirect effect: ΦS,ind = ΦS − ΦS,dir
  - For demand: ΦD,dir = Θ Φ−1Y [I − Ω′]−1 Ξ′ ΦD; ΦD,ind = ΦD − ΦD,dir
- Empirical patterns (normalized by standard deviation):
  - Lockdown-supply: direct effect higher on impact but dissipates after ~3 quarters; indirect/network effect builds up, peaks ~2 quarters, remains significant after a year.
  - Lockdown-demand: network effect overwhelmingly dominant — most sectors experience inflationary pressure via higher input costs rather than pure own-demand.
- Regional and foreign-share decompositions:
  - Early supply disruptions originated in Asia and persisted first 6 months of 2020; North America and Europe became significant by March 2020.
  - Reopening in 2021–2022: Europe and North America key contributors; Asia continued some disruptions.
  - Foreign share of supply disruptions:
    - United States: negligible foreign contribution.
    - Taiwan Province of China and Korea: median month foreign share ≈ 10 percent; peaks up to 30 percent (TWN) and 50 percent (KOR).
    - Latin America (except Chile): foreign share < 5 percent in most months.
  - Foreign share of demand disruptions:
    - Substantially higher across regions; Latin America ≈ 20 percent average; Asian manufacturers ≈ 50 percent median month.
  - For most countries, 90 percent of the demand shock operates through higher input costs ("network cost" channel).
- Quantitative contribution totals (conclusion):
  - Pandemic lockdowns contributed 36 percent of global inflation drivers over sample period.
  - Fiscal stimuli contributed 5 percent of global inflation.
  - Demand recovery contributed 15 percent of 2021-2022 global producer inflation.
  - Network effects constitute at least 50 percent of the impact from supply and demand shocks.

---

### Phase-dependent heterogeneity and regional differences
- Phase split (t≤2020m12 vs t>2020m12):
  - Supply disruptions: more severe and longer-lasting in beginning phase than recovery.
  - Demand channel: IRFs nearly identical across phases; recovery demand surge as rapid as initial drop.
    - Interpretation: firms adapt better to rising input costs in recovery than to surging customer demand.
  - Fiscal effects: became much more persistent in recovery phase; policy impacts are state-dependent.
- Asia vs rest of world:
  - Hypotheses for Asia’s lower inflation: (i) slower reopening and quick withdrawal of stimulus; (ii) structural differences reducing shock transmission.
  - Evidence:
    - Slower reopening and faster stimulus withdrawal in Asia during 2021-22 associated with lower inflation.
    - Subsample estimates: lockdown-supply impacts similar in Asia and elsewhere; lockdown-demand, fiscal, and monetary effects smaller and often insignificant in Asia.
  - Conclusion: both slower reopening/faster stimulus withdrawal and structural differences contributed to Asia’s moderate inflation outcomes.

---

### Policy-relevant implications and suggested research avenues
- Key policy points:
  - Reopening-driven demand surges can be dominant drivers of producer inflation; supply disruptions also raise inflation via direct and network channels.
  - Fiscal stimulus has clear contemporaneous inflationary effects; withdrawing stimulus timing matters due to state-dependent persistence.
  - Monetary policy exhibits more persistent impacts on producer inflation than many pandemic-related shocks.
  - Exchange rate depreciation and oil price inflation are robust positive correlates of sectoral PPI inflation; emerging markets show larger sensitivity to FX depreciation.
  - Network propagation is critical: at least 50 percent of supply and demand shock impacts occur through input-output linkages.
- Suggested future research directions:
  - Apply framework to other global shocks (commodity price increases, global energy price movements, cross-border monetary spillovers).
  - Identify country-sector pairs most pivotal for global PPI movements to inform resilience and policy targeting.

*Source: wpiea2024062-print-pdf (IMF working paper excerpt).*

### 2.1   Environment

### 2.1   Environment

### Model setup: agents, goods, and production
- World with N countries; each country has a representative consumer with preference u_i(C_i, L_i) over final good C_i and labor L_i.
- S internationally produced intermediate goods; each country has a final consumption good that aggregates S intermediate goods under CRS technology:
  - D_i = D_i(D_i1, ..., D_iS)
  - D_i = C_i + G_i
  - Q_i denotes price of final good i (consumer price index).
- Nominal public consumption eG_i = Q_i G_i is given exogenously and financed by lump-sum tax; private consumption eC_i = Q_i C_i is chosen by the monetary authority.
- Each intermediate good s ∈ {1, ..., S} (country-sector specific) is produced using domestic value added L_s and intermediate inputs X_sk under CRS:
  - Y_s = F_s(Z_s L_s, {X_sk}_k=1^S)
  - Z_s is value added–augmented productivity in sector s.
- Intermediate goods can be imported; labor is perfectly mobile across sectors within a country but immobile across countries.
- Law of One Price assumed: price of intermediate goods is the same in all countries.
- Market clearing:
  - Sum_{i=1}^N D_is + Sum_{k=1}^S X_ks = Y_s, s=1,...,S
  - Sum_{s∈S_i} L_s = L_i, i=1,...,N
  - S_i denotes set of intermediate goods produced in country i.

### Cost minimization and input shares
- Sector s cost minimization with wage W_s and input prices P_k leads to Shephard’s Lemma conditions:
  - ∂log MC_s / ∂log W_s = (W_s L_s) / (MC_s Y_s) = θ_s (value added share)
  - ∂log MC_s / ∂log P_k = (P_k X_sk) / (MC_s Y_s) = ω_sk (intermediate input share)
  - θ_s + Σ_k ω_sk = 1
- First-order approximation of marginal cost:
  - d log MC_s ≈ θ_s (d log W_s − d log Z_s) + Σ_k ω_sk d log P_k
- Assuming time-invariant markup, price changes equal marginal cost changes:
  - d log P_s = θ_s (d log W_s − d log Z_s) + Σ_k ω_sk d log P_k

### Matrix form and interpretation
- In matrix notation:
  - d log P = Θ (d log W − d log Z) + Ω d log P
  - Solving: d log P = [I − Ω]^{−1} Θ (d log W − d log Z)
- Interpretation:
  - PPI inflation for intermediate goods is a weighted average of changes in value added unit cost (d log W − d log Z) across sectors.
  - Weights involve the Leontief inverse [I − Ω]^{−1} scaled by value added shares.
  - Upstream input producers' costs propagate downstream via these weights.

### Labor and nominal output
- Short-run assumption: labor is perfectly inelastic within each sector: L_s = L_s.
- If production function is Cobb-Douglas in labor, wage bill W_s L_s = (1 − γ_s) eY_s where eY_s = P_s Y_s; with perfectly inelastic labor supply, d log W_s = d log eY_s.
- Nominal output (sales) of sector s:
  - eY_s = Σ_{i=1}^N eD_is + Σ_{k=1}^S eX_ks
  - eY = Ξ′ eD + Ω′ eY ⇒ eY = [I − Ω′]^{−1} Ξ′ eD
  - Changes: d log eY = Φ_Y^{−1} [I − Ω′]^{−1} Ξ′ Φ_D d log eD

### Proposition 1 (PPI inflation)
- Under perfectly inelastic labor supply and conditional on sectoral TFP Z and country demand eD:
  - d log P = Φ_D d log eD − Φ_S d log Z
  - Φ_D ≡ [I − Ω]^{−1} Θ Φ_Y^{−1} [I − Ω′]^{−1} Ξ′ Φ_D captures inflation elasticity to demand shocks.
  - Φ_S ≡ [I − Ω]^{−1} Θ captures inflation elasticity to supply shocks.

### Proposition 2 (CPI inflation)
- Final good is a basket of intermediate goods with shares Ξ, so d log CPI = Ξ d log P.
- Conditional on sectoral TFP Z and country demand eD:
  - d log CPI = Φ_D^{CPI} d log eD − Φ_S^{CPI} d log Z
  - Φ_D^{CPI} ≡ Ξ [I − Ω]^{−1} Θ Φ_Y^{−1} [I − Ω′]^{−1} Ξ′ Φ_D
  - Φ_S^{CPI} ≡ Ξ [I − Ω]^{−1} Θ

### Notes on extensions
- Variable markup case adds d log μ_s terms.
- Endogenous labor supply requires joint determination of wage response via labor demand and supply.

---

### Operationalize theoretical framework: lockdown shocks and Bartik instruments
- Lockdown stringency Λ_s ∈ [0,1] (sector) and Λ_i (country); 1 = full shutdown, 0 = unrestricted.
- Lockdown reduces sectoral value added productivity by β_S percent and reduces country aggregate demand by β_D percent.
- Sectoral inflation response:
  - d log P_s = − Σ_k Φ_S_sk d log Z_k + Σ_i Φ_D_si d log eD_i
  - For lockdown shocks:
    - d log P_s = β_S [Σ_k Φ_S_sk d log Λ_k] − β_D [Σ_i Φ_D_si d log Λ_i]
- Define shift-share (Bartik) instruments:
  - B_S_s ≡ Σ_k Φ_S_sk d log Λ_k (lockdown-supply)
  - B_D_s ≡ − Σ_i Φ_D_si d log Λ_i (lockdown-demand)
  - Empirical equation: d log P_s = β_S B_S_s + β_D B_D_s

- Extend shift-share design to fiscal and monetary shocks by interacting demand exposures Φ_D with fiscal or monetary changes; coefficients to be estimated from data.

---

### 3 Mapping the Model to Data (summary)

### 3.1 Data coverage and harmonization
- PPI inflation data for 1143 production sectors in 53 countries, including 31 advanced economies (AEs) and 22 emerging markets (EMs), for the period 2019-2022.
- Harmonized to 45 industries in the OECD World Input-Output Table (WIOT).
- Panel is unbalanced and skewed towards manufacturing; services comprise 21 percent of the sample.
- Inflation data winsorized at the 1% level for regressions; results robust to non-winsorized series.
- Construction of monthly country-sector level shocks:
  - Lockdown intensity from Oxford COVID-19 Government Response Tracker (index ranges 0 to 1).
  - Sector-level lockdown measure = country-level stringency × sector ease of work-from-home (Dingel and Neiman (2020) using O*NET).
  - Fiscal shock: COVID-19 fiscal stimulus packages from OxCGRT (percent of GDP). For baseline, fiscal packages are smoothed with an exponential decay calibrated so each package has a half-life of 3 months.
  - Monetary policy: uses policy rate changes and changes in central bank balance sheet sizes; monetary Bartik uses 3-month changes in central bank assets as M_i.
  - Maritime transport cost shocks: Freightos Baltic Container Price Index for 11 major maritime routes. Route-sector shocks constructed by interacting route indices with bilateral ad valorem maritime transport costs (OECD Maritime Transport Cost dataset covering 43 importing countries from 218 origins), aggregated via input-output links to sector-time measures.

### Construction of Bartik instruments and exposures
- Exposure (shares) matrices computed from OECD IOT 2018 (pre-pandemic) for 45 sectors and 64 countries to avoid endogeneity.
- Four primary Bartik instruments:
  - Lockdown-supply B_S_s,t = Σ_k Φ_S_sk d log Λ_k
  - Lockdown-demand B_D_s,t = Σ_i Φ_D_si d log Λ_i
  - Fiscal B_fiscal_s,t = Σ_i Φ_D_si d log F_i (fiscal packages)
  - Monetary B_monetary_s,t = Σ_i Φ_D_si d M_i
- Shifts calculated as 3-month changes; four quarterly changes included in regressions to capture yearly impact.
- Network features: median sector sources only 8 percent of its intermediate inputs from within sector (92 percent from outside); network is sparse — majority of sectors transact with 4–5 other sectors.
- Correlations in the data:
  - Correlation between upstream and downstream exposure between any two sector pair: 0.47.
  - Correlation between lockdown and monetary shocks: 0.34.
  - Correlation between lockdown and fiscal shocks: 0.15.
  - Correlation between monetary and fiscal shocks: 0.36.

---

### 4 Baseline Regression
- Local Projection baseline regression (following Jordà (2005)) to study dynamic response of inflation to shocks:
  - PPI inflation_{s,t+h} = Σ_{l∈{0,3,6,9}} β^S_l B_S_{s,t−l} + Σ_{l∈{0,3,6,9}} β^D_l B_D_{s,t−l} + Σ_{l∈{0,3,6,9}} β^F_l B_fiscal_{s,t−l} + Σ_{l∈{0,3,6,9}} β^M_l B_monetary_{s,t−l} + controls_{s,t} + u_{s,t}
- Features of regressions:
  - Subscripts denote sector and time.
  - Regressions run separately for each shock and jointly.
  - Full set of country, sector, and time fixed effects included.
  - Controls may include lagged inflation, exchange rate depreciation, transport costs, and oil price shocks.
  - Standard errors clustered at country-sector level; Driscoll-Kraay standard errors used to address autocorrelation.
  - For each shock, specifications report year-over-year changes (β_l same for all l) and variants where the four quarterly changes have different coefficients to capture within-year response timing.

*Source: wpiea2024062-print-pdf - 2.1   Environment*

### 4.1   Simplified Setup

### 4.1   Simplified Setup

### Simplified specification and identification
- Specification: sub-specification of equation (16) including the two Bartik instruments related to lockdown, B^S_{s,t−l} and B^D_{s,t−l} with l=0, and country, time, and sector fixed effects. Initial focus on contemporaneous inflationary impact with h=0.
- Identification concern: local lockdown may correlate with other local inflation drivers because diagonal elements of the input-output matrix tend to be large. To address this, instruments constructed using only foreign lockdown shocks while controlling for local lockdown.

### Main findings (simplified specification, Table 1)
- Lockdown supply coefficient: 0.295.
  - Interpretation (Proposition 1): elasticity of value-added productivity due to lockdown. Complete lockdown lowers sector productivity by 29.5 percent.
  - Inflationary translation examples:
    - If sector is 100% value added and uses no intermediate inputs, full lockdown increases PPI inflation by 29.5 percent.
    - If fraction θ of sales comes from value added, direct inflationary impact = 0.295θ.
- Lockdown demand coefficient: −0.355.
  - Interpretation (Proposition 1): elasticity of aggregate demand to lockdown changes. Complete country lockdown depresses aggregate demand by about 35.5 percent.
  - Inflationary translation example: if country spending accounts for 50 percent of a sector’s revenue, direct-impact sectoral deflation = 35.5×0.5=17.8 percent (plus second-round input-output effects).
- Robustness: using only foreign lockdown shocks (Acemoglu et al. (2016) approach) yields coefficients similar in magnitude, sign, and significance; within-sector lockdown control only significant at the 10 percent level.

### Fiscal stimulus (simplified specification, Table 2)
- Specification: regress PPI inflation at country-sector-month on Bartik fiscal instrument, full set of country, time, sector fixed effects, include 12 monthly lags of fiscal shock, assume disbursement calibrated to have half time of 3 months.
- Contemporaneous fiscal multiplier coefficient: 0.754.
  - Reading: a $1 increase in fiscal spending increases domestic aggregate demand by almost 75 cents on impact.
  - Translation to inflation (example): For a country accounting for 50 percent of a sector’s revenue and sector value added share 40%: direct inflationary impact = 0.754×0.5×0.4=0.15, or 15 percent (plus second-round input-output effects).
- Dynamics: most inflationary impact occurs on announcement month and some from one or two months prior. The 11-month lag coefficient is also significant, suggesting changes in fiscal stimuli (not just levels) matter; withdrawing stimulus from high levels would make inflation converge back down.

---

### 4.2   Full Specification — contemporaneous results (h=0, Table 3)
- Full specification: equation (16) including all shocks and controls; every column includes country, sector, and time fixed effects; winsorize sectoral inflation at 1 percent.
- Column (1) contemporaneous coefficients and interpretations:
  - Lockdown supply coefficient: 0.291.
    - Example: full lockdown of a major supplier that accounts for 50% of input costs leads to 0.291×0.5 = 14.5% PPI inflation in affected sector.
  - Lockdown demand coefficient: −0.302.
    - Example: sector selling entirely to domestic market with value-added share 50% experiences deflationary impact = 0.302×0.5 = 15%.
  - Fiscal contemporaneous coefficient: 0.561.
    - Example: fiscal stimulus equal to 10% of GDP raises each industry’s PPI inflation by 5.6%.
  - Monetary contemporaneous coefficient: 0.042.
    - Interpretation: doubling central bank assets raises PPI inflation by about 4%.
- Robustness to controls: results robust to including lagged inflation, currency depreciation, maritime transport inflation, and oil price shocks.
- Dynamics (local projections, Figure 3):
  - Lockdown: increases inflation via supply disruptions but can produce deflation via demand; effects persistent for about 10 months.
  - Fiscal: tends to increase inflation, but effects at longer horizons estimated imprecisely; after half a year effect not distinguishable from zero in this specification.
  - Monetary: most persistent impacts on producer inflation among the four channels, though longer-horizon effects less statistically significant.

### Controls and additional robustness checks
- Maritime transport costs:
  - Constructed by interacting route-specific monthly maritime freight costs (Freightos Baltic Container Price Index) with sector-specific exposure from OECD Maritime Transport Cost dataset.
  - Inclusion does not materially change main coefficients.
  - Point estimates for shipping cost impact on PPI inflation range from 0.059 to 0.035 and are statistically significant at the 1 percent level.
  - Interpretation example: coefficient 0.035 implies transport cost inflation of 10 percent on 100 percent of inputs would increase PPI inflation by 0.35 percent.
- Oil price shock:
  - Constructed by interacting global oil price changes with sector exposure to oil shocks derived from input-output table.
  - Including oil shock mitigates size of main effects but direction and statistical significance remain intact.
- COVID cases per capita: included as potential control to address concern that domestic infections drive inflation changes correlated with trading partners’ infections.
- Table 4 robustness:
  - Winsorizing PPI inflation at 1 percent does not materially impact results; where differences occur, lockdown-demand and lockdown-supply shocks have larger impacts, implying winsorizing is conservative.
  - Alternative fixed effects: dropping time fixed effects or using country-sector fixed effects instead of separate country, sector, time fixed effects yields no large differences.
- Acknowledged omitted factors not included due to data limitations:
  - Labor market tightness, time-varying market power, role of inventories or storage. Unless systematically correlated with pre-pandemic trade shares, these omissions likely increase noise rather than bias.

---

### 4.3   Relative contributions of inflation drivers (2020–2022)
- Method: predicted PPI inflation decomposed by subgroups (contemporaneous and lags): lockdown-supply, lockdown-demand, fiscal, monetary, and other controls; variable contributions aggregated by weighted mean across sectors with weights proportional to sectoral output.
- Main result: model explains inflation dynamics well globally and for major countries (United States, Germany, China, India).
- Largest contributor: lockdown/reopening effects on demand.
  - Early pandemic: demand-driven downward pressure on prices dominated supply-driven upward pressure, producing overall deflationary force.
  - Accommodative monetary policy early in pandemic played significant role preventing deflation.
  - Later period: reopening triggered a surge in demand that drove inflation higher, overwhelming supply normalization effects.
  - Monetary renormalization had some inflationary effect but relatively small compared to demand recovery.

---

### 4.4   Phase-dependent (beginning vs recovery) impulse responses
- Approach: local projection regressions allowing coefficients to differ between first 12 months of global pandemic (t≤2020m12) and recovery period (t>2020m12); include full fixed effects and controls (lagged inflation, exchange rate depreciation, maritime transport cost inflation).
- Key findings (Figure 6 IRFs):
  - Supply disruptions (lockdown-supply): inflationary impact more severe and longer-lasting in the beginning phase than in recovery.
  - Demand channel (lockdown-demand): IRFs almost identical for the two phases; recovery through demand is as rapid as initial drop.
    - Interpretation: firms better able to adapt to rising input costs in recovery (e.g., switching inputs) but less able to adapt to surging customer demand.
  - Fiscal measures: inflationary impact became much more persistent in the recovery phase.
    - Interpretation: early fiscal packages supported businesses/workers without long-lasting inflationary impact; once economy recovered, additional fiscal stimulus can lead to very persistent inflation.
- Policy implication: fiscal policy impacts are state-dependent; overstimulating during recovery risks persistent inflation.

*Source: Excerpt from "4.1 Simplified Setup" and subsequent sections in the provided IMF content unit.*

### 4.5   The Role of Network in Propagating Shocks

### 4.5   The Role of Network in Propagating Shocks

### Decomposition of direct versus network effects
- Lockdown-supply Bartik instrument constructed by multiplying the lockdown exposure matrix ΦS with the vector of lockdown "shifts" Λ.
- Exposure matrix decomposition:
  - ΦS = [I − Ω]−1 Θ = (I + Ω + Ω2 + ...) Θ = (I + Ω) Θ |{direct} + (Σi=2 Ωi) Θ |{indirect}
  - Direct effect defined as shocks originating in that industry or in the direct suppliers.
  - Indirect effect defined as shocks transmitted from an industry at least two steps away in the production chain.
- Direct and indirect lockdown-supply Bartik instruments:
  - BS,dir s,t = Σk ΦS,dir sk dlogΛk, where ΦS,dir = (I + Ω) Θ.
  - BS,ind s,t = Σk ΦS,ind sk dlogΛk, where ΦS,ind = ΦS − ΦS,dir.
- Demand-side decomposition:
  - ΦD = [I − Ω]−1 Θ Φ−1Y [I − Ω′]−1 Ξ′ ΦD.
  - For inflationary pressure, the component Θ Φ−1Y [I − Ω′]−1 Ξ′ ΦD is assigned to the "direct effect" (captures how higher demand for a sector’s output, directly or through the supply chain, puts upward pressure on that sector’s marginal cost).
  - The remainder is the "network effect" of demand (how that cost pressure propagates through the network).
- Direct and indirect lockdown-demand Bartik instruments:
  - BD,dir s,t = Σk ΦD,dir sk dlogΛk, where ΦD,dir = Θ Φ−1Y [I − Ω′]−1 Ξ′ ΦD.
  - BD,ind s,t = Σk ΦD,ind sk dlogΛk, where ΦD,ind = ΦD − ΦD,dir.

### Results: direct versus network strength and dynamics
- Regression approach:
  - Run a regression analogous to baseline (16) allowing coefficients to differ for direct and network variables by shock type.
  - Normalize each shock by its standard deviation so coefficients capture relative strength of direct versus network effects.
- Lockdown-supply shock:
  - Direct effect is higher on impact but less persistent.
  - Indirect (network) effect builds up over time, takes longer to converge to zero, and reaches a peak in about two quarters.
  - Direct effect dissipates after three quarters; indirect effect remains significant after a year.
- Lockdown-demand shock:
  - Network effect is overwhelmingly dominant — most sectors experience inflationary pressure via higher input costs rather than direct pressure on their own labor cost.

### Unpacking lockdown shocks (regional decomposition and foreign share)
- Decomposition by input of origin (Panel (a) of Figure 8; demand mirror in Panel (b)):
  - Supply disruptions initially emerged in Asia, persisting through the first 6 months of 2020.
  - By March 2020, North America and Europe became significant contributors with comparable magnitudes.
  - Minor surge at the close of 2020 and onset of 2021 driven primarily by Europe’s second wave of lockdowns.
  - During 2021-2022, easing of supply disruptions largely attributable to reopenings in Europe and North America; Asia continued to experience ongoing lockdowns.
  - Between Europe and North America, Europe contributed more to the reopening force.
- Foreign share of supply disruptions (Figure 9):
  - United States: negligible foreign contribution to its supply disruptions.
  - Taiwan Province of China and Korea (median month): 10 percent of supply disruptions originate from abroad; peaks up to 30 percent for Taiwan Province of China and 50 percent for Korea in the sample.
  - Latin American countries (except Chile): foreign share is less than 5 percent in most months.
- Foreign share on the demand side (Panel (b) of Figure 9):
  - Foreign share substantially higher across all regions.
  - Latin American countries: average foreign share close to 20 percent.
  - United States: similar higher foreign share pattern as on demand side.
  - Asian manufacturers: foreign share around 50 percent in a median month.
- Channels for demand-driven inflation:
  - "Pure Demand": increased demand within a specific sector raises that sector’s prices directly.
  - "Network Cost": surge in demand inflates prices of intermediate goods, affecting sectors via elevated input costs.
- Share of demand effect operating through network cost (Figure 10):
  - For the majority of countries, 90 percent of the demand shock manifests through higher input costs.
  - Network propagation is large, highlighting importance of incorporating input-output network in analyses of global shocks.

### Inflation in Asia: hypotheses and evidence
- Two hypotheses for Asia’s comparatively lower inflation:
  - (i) Slower re-opening and quick withdrawal of large stimulus packages.
  - (ii) Structural differences in the effects of shocks.
- Evidence supporting hypothesis (i):
  - Figure 1: Asian countries did not have the same rapid reopening observed elsewhere.
  - Figure 5: China and India show smaller inflationary impact from lockdown-demand in 2021 and 2022 relative to Germany and the USA.
  - Figure 12 scatter: during 2021-22, Asian countries typically experienced a slower pace of reopening alongside rapid withdrawal of stimulus packages, both leading to lower inflation.
- Evidence supporting hypothesis (ii):
  - Subsample estimates for Asia (Figures 13 and 14):
    - Lockdown-supply shocks had similar impacts and timing in Asia and the rest of the world.
    - Lockdown-demand shocks resulted in smaller effects in Asia (smaller demand coefficient).
    - Fiscal and monetary interventions had smaller magnitudes and were not statistically significant in Asia, unlike for the full sample.
  - Possible explanations for structural differences (not identified definitively by the methodology):
    - Smaller proportion of services in GDP among Asian countries (services may have driven inflation elsewhere during reopening).
    - Potential policies regulating prices in key sectors in Asia.
  - Conclusion: both (i) more gradual reopening and faster withdrawal of large stimulus packages and (ii) structurally smaller inflation response to shocks contributed to Asia’s moderate inflation; substantial global heterogeneity exists in inflation responses to supply-chain shocks.

### Key quantitative findings and contributions (from conclusion)
- Pandemic lockdowns contributed 36 percent of global inflation drivers over the sample period.
- Fiscal stimuli contributed 5 percent of global inflation.
- Demand recovery was the primary driver of 2021 producer inflation, contributing 15 percent of 2021-2022 global inflation.
- Network effects constitute at least 50 percent of the impact from supply and demand shocks.

### Broader implications and avenues for future research
- The paper merges Bartik-style shift-share design with local projection methods to estimate time-varying effects of production shocks on producer inflation using pre-shock input-use patterns.
- Using sectoral PPIs and input-output linkages for 53 countries, the framework identifies significant roles for both supply and demand channels and for network propagation.
- Suggested future research:
  - Study impacts of other global shocks (e.g., commodity price increases following Russia’s war in Ukraine, global energy price movements, global spillovers from monetary policy along trade routes).
  - Identify which country-sector pairs are most important for determining global movements in producer prices to inform policymakers about systemically important sectors and supply links and to build resilience to shocks.

*Source: IMF working paper chapter "4.5   The Role of Network in Propagating Shocks" (wpiea2024062-print-pdf).*

### References

### wpiea2024062-print-pdf - References

### Key literature themes
- Supply chain disruptions and production networks
  - Works examining macroeconomic effects of supply chain disruptions: "Firms, failures, and fluctuations: the macroeconomics of supply chain disruptions" (Daron Acemoglu and Alireza Tahbaz-Salehi, 2020); "Supply chain disruptions: Evidence from the great east japan earthquake" (Vasco M Carvalho et al., 2021); "Global supply chains in the pandemic" (Barthélémy Bonadio et al., 2021); "The aggregate effects of global and local supply chain disruptions: 2020–2022" (George A Alessandria et al., 2023); "Covid-19 supply chain disruptions" (Matthias Meier and Eugenio Pinto, 2022); and related empirical and theoretical contributions (e.g., Baqaee and Farhi; La’O and Tahbaz-Salehi).
- Shift-share/Bartik instruments and identification
  - Foundational and methodological references: "Shift-share designs: Theory and inference" (Rodrigo Adao, Michal Kolesár, and Eduardo Morales, 2019); "Quasi-experimental shift-share research designs" (Kirill Borusyak, Peter Hull, and Xavier Jaravel, 2022); empirical examinations and applications (Timothy J Bartik, David Card, Daniel A Broxterman and William D Larson, Jaeger et al., Goldsmith-Pinkham et al.).
- Inflation dynamics, Phillips curve, and pandemic-era drivers
  - Studies on inflation surges, Phillips curve nonlinearities, and pandemic-era inflation: Benigno and Eggertsson (2023); Guerrieri et al. (2022); Harding, Lindé, and Trabandt (2023); Di Giovanni et al. (2023); Leigh, Laurence Ball, and Mishra (2022); and evidence on shipping costs and inflation (Yan Carrière-Swallow et al., 2023).
- Fiscal and monetary policy transmission, heterogeneity, and multipliers
  - Fiscal policy measurement and multipliers: Auerbach and Gorodnichenko (2012); Ramey and Zubairy (2018); Riera-Crichton, Vegh, and Vuletin (2015); Tagkalakis (2008); Bartik/Bartik-instrument literature on identification (Goldsmith-Pinkham et al., 2020). Monetary policy transmission heterogeneity (Pragyan Deb et al., 2023) and supply-side effects of monetary policy (Baqaee, Farhi, and Sangani, 2021).
- Methods for impulse responses and local projections
  - Òscar Jordà (2005, 2023) on local projections and impulse response inference; related methodological work (e.g., Jaravel on product innovations; Elliott and Golub on networks and fragility).

### Empirical findings reported in Appendix A — Main Tables
- Table 1: Contemporaneous Inflationary Effects of Lockdown Shocks
  - Dependent variable: Sectoral PPI Inflation (y/y)
  - Column headings: All shocks | Foreign shocks only
  - Lockdown supply shock:
    - All shocks: 0.295 ∗∗∗ (0.028)
    - Foreign shocks only: 0.375 ∗∗ (0.131)
  - Lockdown demand shock:
    - All shocks: -0.355 ∗∗∗ (0.036)
    - Foreign shocks only: -0.257 ∗∗∗ (0.070)
  - Within-sector lockdown shock:
    - Foreign shocks only column: 0.054 ∗ (0.032)
  - Controls included:
    - Time effects: Yes
    - Industry effects: Yes
    - Country effects: Yes
  - Observations: 4838748387
  - Notes:
    - Panel regression (16) with contemporaneous effects (h=0).
    - Lockdown supply and demand shocks are Bartik instruments defined in section 3.1.
    - Inflation and shocks measured as one-year changes; observations at monthly frequency.
    - First column uses Bartik instruments summing lockdown shocks in all countries and sectors; second column includes only foreign shocks and controls for within-sector lockdown shock separately (as in Acemoglu et al., 2016).
    - Driscoll-Kraay standard errors reported in parentheses.
    - Significance: ∗ p<0.10, ∗∗ p<0.05, ∗∗∗ p<0.01

- Table 2: Contemporaneous Inflationary Effects of Fiscal Shock
  - Dependent variable: Sectoral PPI Inflation (y/y)
  - Columns: (1) | (2)
  - Fiscal shock, annual change:
    - Column (1): 0.754 ∗∗∗ (0.170)
  - Fiscal shock, quarterly change — Lag 0:
    - Column (2): 0.769 ∗∗∗ (0.098)
  - Fiscal shock, quarterly change — Lag 3:
    - Column (2): 0.803 ∗∗∗ (0.147)
  - Fiscal shock, quarterly change — Lag 6:
    - Column (2): 0.794 ∗∗∗ (0.185)
  - Fiscal shock, quarterly change — Lag 9:
    - Column (2): 0.662 ∗∗ (0.265)
  - Controls included:
    - Time effects: Yes
    - Industry effects: Yes
    - Country effects: Yes
  - Observations: 4838748387
  - Notes:
    - Panel regression (16) with contemporaneous effects of fiscal shocks only (h=0).
    - Fiscal shock is the Bartik instrument defined in (source text).

*Source: wpiea2024062-print-pdf - References*

### section 3.1. The first column measures year-over-year changes in fiscal shock, while the second

### wpiea2024062-print-pdf - section 3.1. The first column measures year-over-year changes in fiscal shock, while the second

### Regression specification and data notes
- Dependent variable: Sectoral PPI Inflation (y/y).
- Supply, demand, fiscal, and monetary shocks are included as 4 quarterly changes. Inflation, transport cost, oil inflation, and exchange rate depreciation are measured as year-over-year changes. Observations are at the monthly frequency.
- Driscoll-Kraay standard errors reported in parentheses.
- Significance notation: ∗ p<0.10, ∗∗ p<0.05, ∗∗∗ p<0.01.

### Table 3 — Full specification: Inflationary Effects of All Shocks (coefficients and standard errors)
- Columns: (1) (2) (3) (4)
- Lockdown-supply
  - Lag 0: 0.291 ∗∗∗ (0.041); 0.326 ∗∗∗ (0.037); 0.325 ∗∗∗ (0.036); 0.088 ∗∗ (0.030)
  - Lag 3: 0.322 ∗∗∗ (0.048); 0.355 ∗∗∗ (0.058); 0.353 ∗∗∗ (0.059); 0.166 ∗∗∗ (0.032)
  - Lag 6: 0.334 ∗∗∗ (0.047); 0.359 ∗∗∗ (0.051); 0.357 ∗∗∗ (0.053); 0.174 ∗∗∗ (0.023)
  - Lag 9: 0.242 ∗∗∗ (0.058); 0.267 ∗∗∗ (0.053); 0.264 ∗∗∗ (0.055); 0.112 ∗∗∗ (0.027)
- Lockdown-demand
  - Lag 0: -0.302 ∗∗∗ (0.050); -0.368 ∗∗∗ (0.035); -0.369 ∗∗∗ (0.035); -0.165 ∗∗∗ (0.034)
  - Lag 3: -0.371 ∗∗∗ (0.034); -0.429 ∗∗∗ (0.057); -0.431 ∗∗∗ (0.058); -0.274 ∗∗∗ (0.033)
  - Lag 6: -0.430 ∗∗∗ (0.037); -0.473 ∗∗∗ (0.048); -0.474 ∗∗∗ (0.050); -0.319 ∗∗∗ (0.031)
  - Lag 9: -0.324 ∗∗∗ (0.077); -0.354 ∗∗∗ (0.047); -0.352 ∗∗∗ (0.047); -0.220 ∗∗∗ (0.028)
- Fiscal
  - Lag 0: 0.561 ∗∗∗ (0.113); 0.578 ∗∗∗ (0.150); 0.585 ∗∗∗ (0.149); 0.656 ∗∗∗ (0.135)
  - Lag 3: 0.592 ∗∗∗ (0.148); 0.479 ∗∗ (0.198); 0.482 ∗∗ (0.196); 0.588 ∗∗∗ (0.173)
  - Lag 6: 0.474 ∗∗ (0.168); 0.459 ∗∗∗ (0.134); 0.462 ∗∗∗ (0.116); 0.540 ∗∗∗ (0.123)
  - Lag 9: 0.345 ∗ (0.204); 0.269 ∗∗ (0.110); 0.261 ∗∗ (0.101); 0.319 ∗∗ (0.127)
- Monetary
  - Lag 0: 0.042 ∗∗∗ (0.010); 0.025 (0.022); 0.026 (0.022); 0.003 (0.021)
  - Lag 3: 0.077 ∗∗ (0.032); 0.057 ∗∗∗ (0.013); 0.057 ∗∗∗ (0.013); 0.044 ∗∗ (0.015)
  - Lag 6: 0.062 ∗ (0.037); 0.040 ∗∗∗ (0.008); 0.040 ∗∗∗ (0.009); 0.027 ∗∗ (0.012)
  - Lag 9: 0.074 (0.050); 0.042 ∗∗ (0.017); 0.042 ∗∗ (0.017); 0.043 ∗∗ (0.022)
- Other controls (selected)
  - Transport cost: 0.059 ∗∗∗ (0.014); 0.035 ∗∗∗ (0.010)
  - Oil price inflation: 0.517 ∗∗∗ (0.056)
  - FX depreciation: 0.297 ∗∗∗ (0.043); 0.288 ∗∗∗ (0.042); 0.303 ∗∗∗ (0.038)
  - FX depreciation * EM dummy: 0.079 ∗∗ (0.033); 0.093 ∗∗ (0.036); 0.068 ∗∗ (0.030)
  - Lagged inflation: 0.160 (0.165); 0.161 (0.165); 0.164 (0.132)
- Fixed effects: Full fixed effects included in all columns.
- Observations: 4838; 740; 1774; 01774; 017740177? (presented as "48387401774017740177" in source table cell)

### Table 4 — Robustness exercises: Inflationary Effects of All Shocks (coefficients and standard errors)
- Columns: (1) (2) (3) (4) (5)
- Lockdown-supply
  - Lag 0: 0.088 ∗∗ (0.030); 0.084 ∗∗ (0.031); 0.173 ∗∗∗ (0.045); 0.129 ∗∗ (0.049); 0.086 ∗∗ (0.040)
  - Lag 3: 0.166 ∗∗∗ (0.032); 0.161 ∗∗∗ (0.033); 0.266 ∗∗∗ (0.052); 0.177 ∗∗∗ (0.046); 0.171 ∗∗∗ (0.051)
  - Lag 6: 0.174 ∗∗∗ (0.023); 0.169 ∗∗∗ (0.025); 0.253 ∗∗∗ (0.050); 0.087 ∗∗ (0.032); 0.186 ∗∗∗ (0.048)
  - Lag 9: 0.112 ∗∗∗ (0.027); 0.109 ∗∗∗ (0.030); 0.170 ∗∗∗ (0.035); 0.061 (0.046); 0.126 ∗∗∗ (0.026)
- Lockdown-demand
  - Lag 0: -0.165 ∗∗∗ (0.034); -0.159 ∗∗∗ (0.032); -0.284 ∗∗∗ (0.053); -0.209 ∗∗∗ (0.038); -0.156 ∗∗∗ (0.034)
  - Lag 3: -0.274 ∗∗∗ (0.033); -0.265 ∗∗∗ (0.032); -0.427 ∗∗∗ (0.050); -0.266 ∗∗∗ (0.042); -0.273 ∗∗∗ (0.046)
  - Lag 6: -0.319 ∗∗∗ (0.031); -0.309 ∗∗∗ (0.033); -0.478 ∗∗∗ (0.061); -0.186 ∗∗∗ (0.030); -0.326 ∗∗∗ (0.049)
  - Lag 9: -0.220 ∗∗∗ (0.028); -0.212 ∗∗∗ (0.026); -0.344 ∗∗∗ (0.061); -0.122 ∗∗∗ (0.025); -0.230 ∗∗∗ (0.041)
- Fiscal
  - Lag 0: 0.656 ∗∗∗ (0.135); 0.637 ∗∗∗ (0.139); 0.818 ∗∗∗ (0.216); 0.504 ∗∗∗ (0.140); 0.609 ∗∗∗ (0.155)
  - Lag 3: 0.588 ∗∗∗ (0.173); 0.575 ∗∗ (0.177); 0.770 ∗∗ (0.282); 0.424 (0.272); 0.569 ∗∗ (0.200)
  - Lag 6: 0.540 ∗∗∗ (0.123); 0.526 ∗∗∗ (0.131); 0.741 ∗∗ (0.245); 0.615 ∗∗∗ (0.154); 0.542 ∗∗∗ (0.158)
  - Lag 9: 0.319 ∗∗ (0.127); 0.320 ∗∗ (0.126); 0.485 ∗∗ (0.198); -0.118 (0.179); 0.352 ∗∗ (0.136)
- Monetary
  - Lag 0: 0.003 (0.021); 0.010 (0.020); 0.008 (0.034); 0.040 ∗ (0.023); 0.002 (0.023)
  - Lag 3: 0.044 ∗∗ (0.015); 0.047 ∗∗ (0.016); 0.071 ∗∗ (0.028); 0.090 ∗∗ (0.035); 0.045 ∗∗ (0.015)
  - Lag 6: 0.027 ∗∗ (0.012); 0.028 ∗∗ (0.011); 0.052 ∗∗ (0.017); 0.068 ∗ (0.038); 0.028 ∗∗ (0.013)
  - Lag 9: 0.043 ∗∗ (0.022); 0.042 ∗∗ (0.021); 0.091 ∗∗ (0.044); 0.066 (0.042); 0.044 ∗∗ (0.021)
- Other controls (selected)
  - Transport cost: 0.035 ∗∗∗ (0.010); 0.032 ∗∗∗ (0.010); 0.049 ∗∗ (0.020); 0.078 ∗∗ (0.033); 0.025 ∗∗ (0.011)
  - Oil price inflation: 0.517 ∗∗∗ (0.056); 0.517 ∗∗∗ (0.056); 0.665 ∗∗∗ (0.077); 0.517 ∗∗∗ (0.060); 0.520 ∗∗∗ (0.068)
  - FX depreciation: 0.303 ∗∗∗ (0.038); 0.259 ∗∗∗ (0.037); 0.326 ∗∗∗ (0.057); 0.288 ∗∗∗ (0.026); 0.297 ∗∗∗ (0.039)
  - FX depreciation * EM dummy: 0.068 ∗∗ (0.030); 0.114 ∗∗ (0.035); 0.279 ∗∗∗ (0.067); 0.085 ∗ (0.047); 0.073 ∗∗ (0.028)
  - Lagged inflation: 0.164 (0.132); 0.162 (0.132); 0.181 (0.176); 0.157 (0.127); 0.040 (0.145)
- Specification differences across columns
  - Covid Cases per Capita: No; Yes; No; No; No
  - Winsorized 1 percent: Yes; Yes; No; Yes; Yes
  - Time FE: Yes; Yes; Yes; No; Yes
  - Country Sector FE: Yes; Yes; Yes; Yes; No
  - Country-Sector FE: No; No; No; No; Yes
- Observations row presented as: 40177 40177 40177 40177 40177 (source shows "4017740177401774017740177" contiguous in table)

### Main interpretive findings (from figures and notes)
- Lockdown-supply shocks increase PPI inflation contemporaneously and for several months (effects strong and lasting for about 10 months, per local projection IRFs).
- Lockdown-demand shocks decrease PPI inflation contemporaneously and over subsequent months.
- Fiscal stimuli increase PPI inflation contemporaneously; effects at longer horizons are estimated imprecisely.
- Monetary shocks have more persistent impacts on inflation than lockdown or fiscal channels.
- Lockdown reopening is identified as a dominant driver of high inflation in the recovery from the pandemic (global and major-nation decompositions).
- The inflationary impact of lockdown via supply channels becomes unimportant in the recovery phase (2021 and later), while fiscal stimuli play a larger role in that phase.
- Network effects amplify transmission:
  - Demand shocks largely operate through indirect network (“cost”) channels rather than “pure demand”; source states "90 percent of demand shock is via the “cost” channel."
- Cross-country patterns:
  - East Asia lockdowns important at onset, later dominated by reopening in Europe and US.
  - US and LAC less vulnerable to foreign supply disruptions than “Asian manufacturers” (e.g., TWN and KOR).
  - Countries are 4-5 times more prone to foreign demand shocks than supply shocks.
  - LAC: about 20-30 percent of demand shock is spillover from foreign lockdown/reopening policies.
- Regional patterns:
  - Figures show lockdown stringency by region (index 0 to 1), COVID-19 fiscal stimulus by region (share of GDP), and evolution of trade costs by route (Baltic Container Price Index).

### Policy-relevant points distilled from results
- Supply-side lock-down disruptions and subsequent reopening materially increased PPI inflation through direct sectoral effects and network propagation; reopening dynamics can be a major inflation driver.
- Demand contractions from lockdowns exert deflationary pressure, but network cost-channel transmission of demand increases can raise PPI inflation substantially.
- Fiscal stimulus has a clear contemporaneous inflationary effect; persistence at longer horizons is less precise, implying careful calibration of stimulus withdrawal timing is important.
- Monetary shocks show persistent inflation effects, suggesting central banks’ actions have durable impacts relative to pandemic-related shocks.
- Exchange rate depreciation and oil price inflation are robust positive correlates of sectoral PPI inflation across specifications.
- Emerging markets exhibit larger sensitivity to FX depreciation (FX depreciation * EM dummy coefficients positive and significant in multiple specifications), indicating exchange rate management and external vulnerability matter for inflation outcomes.

*Source: wpiea2024062-print-pdf - section 3.1. The first column measures year-over-year changes in fiscal shock, while the second*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024062-print-pdf.pdf_