## CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE - ONLINE ANNEX

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### Distribution of the Global Inflation Surge
- European countries (AEs and EMDEs) were relatively more affected by the inflation surge; other AEs (mostly in Asia) and Asian EMDEs witnessed notably lower inflation.
- Dynamics were highly synchronized across countries with more than 50 countries (out of 80 AEs and EMDEs) witnessing inflation rises of more than 5 percent relative to 2019.
- Energy inflation peaked at close to 40 percent in advanced economies while economies in Asia were much less affected.
- Raw correlation between sector energy-dependence and price flexibility: .43.

### Energy Price Shocks: Magnitude and Composition (2020–2023)
- Energy shocks during 2020–2023 were extraordinarily large relative to prior decades, evidenced by the long right tail of the distribution of energy price changes.
- Large energy shocks were not primarily driven by oil; oil fluctuations were broadly in line with historical oil price fluctuations. Larger drivers were gas prices and coal.
- Regional year-on-year energy price inflation shows notable heterogeneity across regions (Asia EMs, Euro Area, Asia AEs, Other AEs, Other EMs).

### Energy Price Passthrough: Methodology
- Baseline local projections estimated for h = 0, 1, 2, ..., 12 with:
  - Dependent variable: CPI inflation, π_{j,t+h}^{CPI}.
  - Key coefficients: β_h (baseline passthrough of lagged energy price inflation π^{energy}_{j,t-1}); γ_h (change in passthrough since Covid; PPP t dummy = 1 for years 2020 onward and 0 for 2010–19).
  - Controls X_{j,t-1}: 4 lags of CPI inflation and 4 lags of the output gap.
- Non-linear specification includes quadratic and cubic terms in lagged energy inflation.
- Local projections IV specification instruments energy inflation with the oil supply news shock from Kaenzig (2021) for AEs; IV not used for EMDEs due to weak instruments.

### Energy Price Passthrough: Main Findings
- No evidence for a systematic strengthening of the passthrough post-Covid; non-linearities matter (peak responses slightly larger at higher energy inflation levels).
- Non-linear marginal effects in AEs:
  - At 1 percent energy inflation: a 1 percentage point increase in energy inflation → ~.05 percentage points peak CPI inflation.
  - At 20 percent energy inflation: a 1 percentage point increase → ~.08 percentage points peak CPI inflation, and the response is more persistent.
- IV-LP results for AEs: pre-Covid and post-Covid passthrough estimates are comparable.
- Average passthrough of energy inflation into CPI inflation: .06 percentage points per 1 percentage point of energy inflation.

### Sectoral Passthrough: Heterogeneity by Energy Dependence and Price Flexibility
- Specification tests interaction of energy inflation with sectoral characteristics c_{i,j} (sectoral energy dependence P^energy_{i,j} or sectoral price flexibility δ_i).
- Sectoral energy dependence computed as total direct plus indirect energy share in total inputs using OECD input-output tables (Leontief inverse for indirect share).
- Sectoral price flexibility based on measures from Rubbo (2023) for the US; assumed identical for non-US sectors.
- Empirical magnitudes:
  - A sector with a 1 standard deviation (9 percentage point) higher energy dependence has .027 percentage points higher sectoral inflation when energy inflation rises by 1 percentage point.
  - In 2022Q1 US energy price inflation = 33.4 percent:
    - Comparing least to most energy-dependent US sector: most connected sectors estimated to have had 2.71 percentage points higher sectoral inflation.
    - Going from least (professional and scientific services) to most price flexible sector (agriculture) implies 3.4 percentage points higher sectoral inflation for the most price flexible sector when US energy inflation was 33.4 percent in 2022Q1.
  - Average passthrough into CPI: .06 percentage points per 1 percentage point energy inflation.

### Phillips Curve Estimation: Specification and Results
- Country-by-country bivariate Phillips curve regressions run separately:
  - Pre-Covid sample: 2010Q1–2019Q4; post-Covid sample: 2020Q3–2024Q1.
  - Specification: π_{i,t}^s = α_i^{pre/post} + β_i^{pre/post} û_{i,t} + ε_{i,t}, with π_{i,t}^s ∈ {core, goods, services, wage inflation} and û_{i,t} = unemployment gap estimated via univariate HP-filter.
- Findings:
  - Cross-country distribution of Δ_i β = β_i^{post} − β_i^{pre} and Δ_i α = α_i^{post} − α_i^{pre} show the Phillips curve has shifted and steepened near-universally.
  - Shifting and steepening stronger for goods than services in AEs.
  - In EMs, patterns are weaker: evidence for an upwards shift but no evidence for steepening (coefficients statistically insignificant and magnitudes close to zero for core, goods, and services inflation).
- Richer Phillips curve (Equation (6)) includes controls: two lags of inflation measures, lagged energy inflation, lagged import price inflation, one-year ahead inflation expectations (robust to 5-year ahead expectations); results broadly consistent.
- Robustness:
  - Using output gap as slack confirms qualitative results; output gap standard deviation larger than unemployment gap (AEs: 2.05 percent vs. .91 percent; EMs: 2.50 percent vs. .99 percent), producing smaller magnitudes.
  - Euro area specification with time fixed effects (OLS and IV) supports shifting and steepening in AEs.

### Analytical Details on Inflation Decompositions and Shock Identification
- Headline inflation shocks: difference between headline and core inflation regressed on energy inflation to identify energy component (fitted value) and non-energy component (residual).
- Phillips curve specification (Equation (8)): dependent variable = deviation of core inflation from 5-year inflation expectations; regressors include economic slack, slack × Covid dummy, lagged inflation, import prices, and headline inflation shocks.
- Estimation approach:
  - Equations (7) and (8) estimated as pooled regressions separately for other AEs and for EMDEs.
  - Robustness: IV specification instrumenting inflation expectations and unemployment gap with their lags yields comparable results.
  - Croatia dropped due to Eurozone accession timing.
  - Shifting of the Phillips curve cannot be separately identified when post-Covid change in the constant is co-linear with time fixed effects.
- Measurement choices:
  - Core inflation: median inflation measure from Dao et al. (2024) where available; otherwise headline excluding food and energy.
  - Labor market tightness: vacancy-unemployment ratio in AEs; unemployment gap via HP-filter in EMs.
  - For AEs, import prices largely driven by energy (about ¾ of import prices explained by energy during 2021-2022), thus excluded from AE specification.
  - For the US, a monthly specification estimated.
- Data transformation: quarterly results converted to 12-month moving averages in relevant charts.

### Findings on Phillips Curve and Inflation Shocks
- Pre-Covid Phillips curve was flat; substantial steepening post-Covid documented (point estimates for change in slope larger but with larger confidence bands).
- Headline inflation shocks (especially energy) were a major driver of headline inflation spikes in some EM regions.
- Heterogeneity in EMs:
  - Eastern Europe: headline inflation peaked at about 16 percentage points (12-month moving average); core inflation rose only about 2 percentage points higher than core inflation in LAC.
  - LAC: headline inflation peaked at around 10 percentage points (12-month moving average).
  - Inflation expectations in both LAC and Eastern Europe remained stable despite large headline shocks.
  - Real wage growth in Eastern Europe picked up recently, but passthrough to higher inflation limited because the unemployment gap has not tightened yet.

### Comparison of Historical Inflation Episodes
- Episode identification algorithm:
  1. Select country-year pairs where average annual inflation rises by at least 2pp, i.e., Π_T – Π_T-1 ≥ 2 percent.
  2. Drop episodes in low-income, non-market economies.
  3. Drop episodes where post-shock inflation remains low, i.e., Π_T ˂ 3 percent.
  4. Drop episodes where pre-shock inflation is too high, i.e., average(Π_T-1, Π_T-2) > 25 percent.
  5. Drop episodes where the inflation is a reversion to recent high inflation, i.e., max(Π_T-2, Π_T-3) > Π_T.
- Dataset extension: by extending Ari et al. (2023) to include post-pandemic periods, over 200 inflation episodes identified.

### Deviation from Taylor-rule-implied Tightening
- Taylor rule used: f^L_T_t = f^* + φ_π (π_t − π^*) − φ_u (u_t − u^*), with calibration φ_π = 1.5 and φ_Y = 1; using Okun’s law, φ_u = 2 φ_Y.
- Tightening deviation computed as observed short-term interest rate tightening from its pre-episode average minus Taylor-rule-implied tightening.
- Comparative findings:
  - Post-2020 tightening relative to Taylor-rule-implied tightening lies between resolved and unresolved 1970s episodes.
  - For 1970s unresolved, 1970s resolved, and post-2020 sets, the Taylor rule suggests stronger tightening during the first two years than the data show (likely due to lagged policy response).
  - Deviation between actual policy rate changes and Taylor-rule suggestions smaller for resolved 1970s episodes and post-2020 than for unresolved 1970s episodes.
  - In resolved 1970s episodes, policy rate changes in subsequent periods became more pronounced than Taylor rule suggested, likely to anchor inflation expectations.
- Pre-shock inflation volatility: pre-2020 volatility significantly lower than in the 1970s. Sample sizes: 1970s unresolved = 12 episodes; 1970s resolved = 13 episodes (1973–79); post-2020 = 125 episodes centered on 2021 and 2022.

### Monetary Policy Transmission: VAR Analysis
- Country-specific small-scale structural VARs with time-varying parameters and stochastic volatility estimated for selected AEs (US, euro area, UK) and EMs (India, Brazil, Mexico).
- Model variables (five per model):
  - Real GDP, consumer prices, short-term policy rates, and two transmission-channel variables (AEs: 10-year sovereign bond yield and unemployment rate; EMs: terms of trade and nominal effective exchange rate).
- Data and transformations:
  - Quarterly data through 2024Q2; sample start dates vary by country.
  - Real GDP and consumer prices expressed as annualized q-on-q growth rates; interest rates, unemployment rates, terms of trade indices, and NEER expressed as first differences.
  - For AEs, shadow rate used near the effective lower bound.
- Identification and normalization:
  - Sign restrictions imposed for four quarters to identify monetary policy, aggregate supply, and aggregate demand shocks.
  - Impulse responses normalized so peak policy rate response = 100 basis points; transmission measured as impulse responses of output and consumer prices.
- Tightening period dating: Blinder (2023) chronology for the US; periods with policy rate increases for at least two quarters for other countries.
- Empirical results:
  - US (latest tightening 2022Q1-2023Q3): stronger short-term responses of output and consumer prices than 1970s–1980s average, but 1970s–80s responses statistically significant for longer horizons; responses similar to 1990–2019 average. Cumulative responses indicate transmission of latest tightening similar to historical average.
  - Cross-country since 1990: some variation over time, but no strong evidence of systematic and significant differences in response magnitudes when comparing the latest episode to 1990s–2019 average.
  - Quantitative comparison: Ramey (2016) reports median peak impact of a normalized 100 basis points monetary policy shock to US output of -1.6 percent (interquartile range -0.7 percent to -2.1 percent); this study’s average peak response for the US since 1990 is -0.9 percent.

### Global Dynamic Network Model: Structure and Calibration
- Model: 11-sector, 2-country model calibrated to the U.S. and rest of the world using OECD ICIO production network data.
- Production uses three factors: fixed capital, variable labor, and an intermediate bundle combined via a CES production function with elasticity = 0.5.
- Intermediate bundle: products from all 11 sectors aggregated with a CES aggregator.
- Sectoral and preference parameters:
  - Sectoral bundle elasticity (household consumption bundle) = 0.8.
  - Elasticity between U.S. variety and rest-of-world variety = 1.5.
  - Production function elasticity for substitution between different types of goods = 0.1.
  - Calvo-style price adjustment with sector-varying degrees of sluggishness; Phillips Curve slopes from Rubbo (2023) (originally Pasten, Schoenle and Weber (2020)).
  - Labor supply: aggregate wages sticky; sectoral labor supply with constant elasticity of transformation = 0.76.
- Households: Ricardian (Blanchard-Yaari OLG with GHH preferences and habit formation) and hand-to-mouth.
- Sectoral inflation expectations deviate from rational expectations per:
  π_{s,t,t+1}^e = ρ_e π_{s,t−1,t}^e + ρ_l π_{s,,t−1} + (1−ρ_e−ρ_l) E_t π_{s,t+1}, entering all Phillips Curve equations when firms set prices.

### Non-linear Phillips Curve and Sectoral Supply Constraints
- Supply constraints modeled as exogenous, time-varying maximum workforce limits per sector (occasionally binding).
  - Constraints rarely bind in normal times; can bind in crises or high demand, curtailing firm labor demand at prevailing wages.
  - Binding constraints lower labor demand relative to no-constraint case and increase steepness of the aggregate Phillips Curve when demand continues to rise.
- Illustrative dynamics:
  - When demand low: employment in every sector below maximum and sensitive to small demand changes.
  - When demand high: some sectors hit supply constraints; further demand raises prices instead of employment, producing higher inflation and less output for given demand increase.

### Shock Extraction Methodology and Identification of Labor Constraints
- Target sample: 2020Q1-2023Q4; observables: sectoral value added, sectoral value-added deflators, import prices, aggregate CPI inflation, interest rates for US and rest of world.
- Estimation: model linearized; shocks estimated via Kalman filter in a just-identified manner; number of shocks equals number of observables; conditioned so initial conditions impact small.
- Labor constraint identification:
  - Define “labor wedge” as shadow price between marginal product of labor and prevailing market wage (estimated via smoother); treated as exogenous shock.
  - Identification assumptions:
    (i) labor productivity shocks must be positive and labor wedge zero; or
    (ii) labor wedge positive and labor productivity shocks zero.
  - Iterative procedure: if estimated shocks violate assumptions, switch active shock and re-run Kalman filter until convergence.

### Counterfactuals and Treatment of Labor Wedges
- Counterfactuals reuse Kalman filter with adjusted observables (e.g., earlier tightening via adjusted interest rates).
- Labor wedges re-estimated given new interest rate profile while keeping labor quantity same as baseline; if re-estimated wedges negative, set wedge to zero and re-estimate labor quantity, iterating until no negative wedges remain.
- Special counterfactuals treat observed positive labor wedges as exogenous observables (do not react endogenously):
  - When wedge treated as indicative of labor constraint: positive demand counterfactual does not raise quantity of labor in that sector; labor wedge increased to maintain labor at estimated-data quantity.
  - When wedge treated as typical shock: quantity of labor rises in a positive demand counterfactual while wedge remains at estimated value.
- Wherever labor wedge positive in counterfactuals, corresponding labor level imposed as an occasionally binding constraint.

### Decomposition and Sectoral Contributions to CPI in Counterfactuals
- CPI decomposition in counterfactual where rest of world tightens three quarters later:
  - Compute contributions from sectoral value-added deflators/costs and sector-specific expectations using full input-output linkages; real exchange rate effects shown separately.
  - Excess contribution computed by subtracting observed indirect effect from counterfactual indirect contribution assuming equal deflator rises in all sectors; bars sum to zero.
  - Time series labels: 2022:Q3, 22:Q4, 23:Q1, 23:Q2, 23:Q3, 23:Q4.
  - Sector grouping: Food and energy; Manufacturing; Services; Real exchange rate.

### Inflation Drivers and Impulse Response Scenarios
- US model-based inflation drivers (percent, year-over-year) simulated via 1000-period bootstrap to replicate 2020Q1–2023Q4; five-year ahead inflation expectations at steady state; slack = deviation of GDP from steady state.
- Negative Capacity Constraint scenario: negative labor constraint shock in agriculture, mining, and energy sectors with no change in aggregate demand isolates interaction of constraint and demand.
  - Policy rules in experiment:
    - “Targets stickiest sectors’ inflation” (targets five sectors with steepest Phillips curves).
    - “Inflation forecast targeting” (targets four-quarter moving average of future CPI inflation).
    - “Flexible prices” (no nominal rigidities).
    - “50/50 CPI and constrained sectors” (targets CPI and sectoral inflation in agriculture, mining, energy).
  - Taylor parameters: Taylor parameter = 3; persistence parameter = 0.5; neither GDP nor output gap targeted.
  - Key takeaway: inflation rises for one period and moderates slowly because price level adjustment can maintain a labor constraint without continuous further price increases.
  - Policy targeting food and energy can create persistent inflation only because targeted upstream sectors’ inflations have different persistence than non-targeted sectors.

### Sectoral Price Dispersion and Monetary Policy Rule Comparisons
- Sectoral price dispersion (percent, sectoral prices relative to CPI) in scenarios:
  - Flexible prices: constrained upstream sectors (agriculture, mining, energy) show short-lived price increases; other sectors move marginally; initial price dispersion lower because downstream pass-through reduces dispersion.
  - Sticky prices: relative prices deviate more from flexible benchmark, especially for service sectors with sticksier prices; flexible upstream sectors raise prices quickly while sticky downstream sectors do not, increasing initial dispersion.
  - Policy rule targeting upstream constrained sectors: initial relative price movements of targeted sectors close to flexible benchmark; inflation momentum in other sectors builds over time, creating cyclical dynamics and resource misallocation.
- Comparison of four monetary policy rules (including AIT):
  - Targeting the inflation of the stickiest sectors delivers the most effective single-sector-targeting strategy for CPI stabilization.
  - Volatilities under targeting stickiest sectors similar to AIT; AIT slightly outperforms as weight on GDP volatility increases.
  - Both stickiest-sector targeting and AIT outperform inflation forecast targeting and 50/50 on CPI and constrained sectors.
- Numerical/graphical markers preserved from figures: axis ticks include ranges –1.0 to 3.0 and 0,5,10,15,20; weight on GDP volatility axis from 0.0 to 1.0 (0.1 increments); vertical values from –0.7 to 0.0.

### Findings and Policy Implications
- Sticky prices increase initial sectoral price dispersion relative to flexible-price benchmark, particularly for service sectors.
- Monetary policy rules that explicitly account for sectoral price stickiness can materially improve CPI stabilization.
- Rules narrowly targeting constrained upstream sectors risk inducing inflation momentum and volatility in non-targeted sectors, causing larger cyclical fluctuations and resource misallocation.
- AIT provides robustness as the policymaker places greater weight on reducing GDP volatility; targeting stickiest sectors approximates AIT performance for CPI stabilization.
- Consideration of both CPI and GDP volatilities and their trade-offs important when selecting policy frameworks.

*Source: CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE - ONLINE ANNEX (International Monetary Fund | April 2024).*

### CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE -

### CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE - ONLINE ANNEX

### Distribution of the Global Inflation Surge
- European countries (AEs and EMDEs) were relatively more affected by the inflation surge; other AEs (mostly in Asia) and Asian EMDEs witnessed notably lower inflation (Panels 1–2).
- Dynamics were highly synchronized across countries with more than 50 countries (out of 80 AEs and EMDEs) witnessing inflation rises of more than 5 percent relative to 2019 (Panels 3–4).
- Energy inflation peaked at close to 40 percent in advanced economies while economies in Asia were much less affected (Panel 4).
- Raw correlation between sector energy-dependence and price flexibility (using cross-country data) is .43, indicating overlap but also independent variation between these characteristics.

### Energy Price Shocks: Magnitude and Composition (2020–2023)
- Energy shocks during 2020–2023 were extraordinarily large relative to prior decades, evidenced by the long right tail of the distribution of energy price changes (Online Annex Figure 2.2.2, Panel 1).
- These large energy shocks were not primarily driven by oil; oil fluctuations were broadly in line with historical oil price fluctuations (Panel 2). The larger drivers were gas prices (Panel 3) and coal.
- Regional year-on-year energy price inflation (Panel 4) shows notable heterogeneity across regions (Asia EMs, Euro Area, Asia AEs, Other AEs, Other EMs).

### Energy Price Passthrough: Methodology
- Baseline local projections specification estimated (forall h = 0, 1, 2, ..., 12):
  - Dependent variable: CPI inflation, π_{j,t+h}^{CPI}.
  - Key coefficients:
    - β_h captures baseline passthrough of lagged energy price inflation π^{energy}_{j,t-1} into CPI inflation.
    - γ_h measures any change in passthrough since Covid; PPP t dummy equals one for years 2020 onward and zero for 2010–19.
  - Controls X_{j,t-1} include 4 lags of CPI inflation and of the output gap.
- Non-linear specification includes quadratic and cubic terms in lagged energy inflation (Equation (2)), following prior work (similar to Dao et al., 2024).
- Local projections IV specification instruments energy inflation with the oil supply news shock from Kaenzig (2021) to address endogeneity concerns (IV-LP for AEs; IV not used for EMDEs due to weak instruments).

### Energy Price Passthrough: Main Findings
- No evidence for a systematic strengthening of the passthrough post-Covid; peak responses slightly larger at higher levels of energy inflation, indicating non-linearities matter.
- When energy inflation is 1 percent:
  - A one percentage point increase in energy inflation leads to a peak rise in CPI inflation of about .05 percentage points in AEs.
- When energy inflation is 20 percent:
  - A one percentage point increase in energy inflation triggers about .08 percentage points of CPI inflation at the peak in AEs, and the response is more persistent.
- IV-LP results for AEs show pre-Covid and post-Covid passthrough estimates are comparable.

### Sectoral Passthrough: Heterogeneity by Energy Dependence and Price Flexibility
- Specification (3) tests interaction of energy inflation with sectoral characteristics c_{i,j} (either sectoral energy dependence P^energy_{i,j} or sectoral price flexibility δ_i).
- Sectoral energy dependence computed as total direct plus indirect energy share in total inputs using OECD input-output tables (Leontief inverse used for indirect share).
- Sectoral price flexibility based on measures from Rubbo (2023) for the US; assumed identical for non-US sectors.
- Empirical results (Online Annex Figure 2.2.6):
  - Passthrough of energy inflation into sectoral inflation is stronger in sectors with higher energy dependence and in sectors with more flexible prices.
  - Quantitatively: a sector with a 1 standard deviation (9 percentage point) higher energy dependence has .027 percentage points higher sectoral inflation when energy inflation rises by 1 percentage point.
  - Average passthrough of energy inflation into CPI inflation is about .06 percentage points for 1 percentage point of energy inflation.
  - In 2022Q1, US energy price inflation was 33.4 percent:
    - Comparing least to most energy-dependent sector in the US, the most connected sectors are estimated to have had 2.71 percentage points higher sectoral inflation.
    - Going from least (professional and scientific services) to most price flexible sector (agriculture) implies 3.4 percentage points higher sectoral inflation for the most price flexible sector when US energy inflation was 33.4 percent in 2022Q1.

### Phillips Curve Estimation: Specification and Results
- Country-by-country bivariate Phillips curve regressions run separately for pre-Covid (2010Q1–2019Q4) and post-Covid (2020Q3–2024Q1):
  - Pre-Covid: π_{i,t}^s = α_i^{pre} + β_i^{pre} û_{i,t} + ε_{i,t}
  - Post-Covid: π_{i,t}^s = α_i^{post} + β_i^{post} û_{i,t} + ε_{i,t}
  - π_{i,t}^s covers inflation measures in {core, goods, services, wage inflation}. û_{i,t} is the unemployment gap estimated using a univariate HP-filter.
- Findings:
  - Cross-country distribution of differences Δ_i β = β_i^{post} − β_i^{pre} and Δ_i α = α_i^{post} − α_i^{pre} show the Phillips curve has shifted and steepened near-universally around the globe (Figure 2.6, Panels 2 and 3 in main chapter).
  - Shifting and steepening confirmed and stronger for goods than for services in AEs.
  - In EMs, patterns are weaker overall: evidence for an upwards shift in the Phillips curve but no evidence for steepening (coefficients statistically insignificant and magnitudes close to zero for core, goods, and services inflation).
- Richer Phillips curve specification (Equation (6)) adds controls and interacts slack with COVID dummy:
  - Controls include two lags of inflation measures, lagged energy inflation, lagged import price inflation, and one-year ahead inflation expectations (results robust to using 5-year ahead expectations).
  - Estimates from Equation (6) (Online Annex Figure 2.2.7) broadly consistent with main findings: shifting and steepening in AEs (stronger for goods), weaker patterns in EMs.
- Robustness checks:
  - Using output gap as measure of slack (multiplying output gap by −1 for comparability) confirms qualitative results; magnitudes smaller because output gap has larger standard deviation than unemployment gap (2.05 percent vs. .91 percent in AEs; 2.50 percent vs. .99 percent in EMs).
  - Euro area specification with time fixed effects (absorbing Euro-area-wide supply shocks and monetary policy variation) implemented with OLS and IV; findings remain supportive of shifting and steepening in AEs.

### Key Quantitative Figures and Parameters
- Sample: 80 AEs and EMDEs (more than 50 countries experienced inflation rises > 5 percent relative to 2019).
- Correlation between energy-dependence and price flexibility: .43.
- Average passthrough of energy inflation into CPI inflation: .06 percentage points per 1 percentage point of energy inflation.
- Sectoral impact: 1 standard deviation in sectoral energy dependence = 9 percentage point increase → .027 percentage points higher sectoral inflation per 1 percentage point energy inflation.
- US energy price inflation in 2022Q1: 33.4 percent.
  - Max sectoral difference due to energy dependence: 2.71 percentage points.
  - Max sectoral difference due to price flexibility (least to most flexible): 3.4 percentage points.
- Non-linear marginal effects in AEs:
  - At 1 percent energy inflation, a 1 percentage point increase → ~.05 percentage points peak CPI inflation.
  - At 20 percent energy inflation, a 1 percentage point increase → ~.08 percentage points peak CPI inflation.
- Output gap standard deviations: AEs = 2.05 percent; EMs = 2.50 percent.
- Unemployment gap standard deviations: AEs = .91 percent; EMs = .99 percent.

*Source: CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE - ONLINE ANNEX (International Monetary Fund | April 2024).*

### Annex Figure 2.2.7, panels 5 and 6) are broadly consistent with our earlier estimates, suggesting a

### ch2onlineannexes - Annex Figure 2.2.7, panels 5 and 6) are broadly consistent with our earlier estimates, suggesting a

### Analytical Details on Inflation Decompositions
- Key empirical framework:
  - Equation (7): headline inflation shocks constructed as the difference between headline and core inflation; these shocks are regressed on energy inflation to identify an energy component (fitted value from regression (7)) and a non-energy component (residual from equation (7)).
  - Equation (8): Phillips curve specification with dependent variable = deviation of core inflation from 5-year inflation expectations; regressors include economic slack, interaction of slack with a Covid dummy, lagged inflation, import prices, and headline inflation shocks; allows labor market tightness to affect core inflation directly.
- Estimation details and robustness:
  - Equations (7) and (8) are estimated as pooled regressions separately for other AEs and for EMDEs to match earlier Phillips curve estimation.
  - A robustness check re-estimates equation (7) using an instrumental variables specification instrumenting inflation expectations and the unemployment gap with their lags; results are comparable.
  - Croatia is dropped from the sample because it only joined the Eurozone in 2023.
  - The shifting of the Phillips curve cannot be identified separately when the post-Covid change in the constant becomes co-linear with the time fixed effect.
- Measurement choices:
  - Core inflation: median inflation measure from Dao et al. (2024) where available; otherwise headline inflation excluding food and energy.
  - Labor market tightness: vacancy-unemployment ratio in AEs (following Barnichon and Hale Shapiro, 2024); unemployment gap estimated via a univariate HP-filter for EMs where vacancy data are scarce.
  - For AEs, import prices are primarily driven by energy (about ¾ of import prices explained by energy during the 2021-2022 inflation surge); import prices are therefore excluded from the AE specification.
  - For the US, a monthly specification is estimated to ensure sufficient observations.
- Data transformation:
  - All charts with results from inflation decompositions convert quarterly data to 12-month moving averages.

### Findings on Phillips Curve and Inflation Shocks
- Empirical evidence:
  - Pre-Covid Phillips curve is flat; substantial steepening of the Phillips curve post-Covid is documented (point estimates for change in slope are somewhat larger but with larger confidence bands).
  - Headline inflation shocks (especially energy) were a major driver of headline inflation spikes in some EM regions (see heterogeneity discussion below).
- Heterogeneity across Emerging Markets (summary of Online Annex Figure 2.2.8):
  - Eastern Europe: headline inflation peaked at about 16 percentage points (12-month moving average); core inflation rose only about 2 percentage points higher than core inflation in LAC.
  - LAC: headline inflation peaked at around 10 percentage points (12-month moving average).
  - Inflation expectations in both LAC and Eastern Europe remained stable with minimal movements despite large headline shocks.
  - Real wage growth in Eastern Europe picked up recently, but passthrough to higher inflation has been limited because the unemployment gap has not tightened yet.

### Further details on the comparison of historical inflation episodes
- Episode identification algorithm (following Ari et al., 2023):
  1. Select country-year pairs where average annual inflation rises by at least 2pp, i.e., Π_T – Π_T-1 ≥ 2 percent.
  2. Drop episodes in low-income, non-market economies.
  3. Drop episodes where post-shock inflation remains low, i.e., Π_T ˂ 3 percent.
  4. Drop episodes where pre-shock inflation is too high, i.e., average(Π_T-1, Π_T-2) > 25 percent.
  5. Drop episodes where the inflation is a reversion to recent high inflation, i.e., max(Π_T-2, Π_T-3) > Π_T.
- Dataset extension and sample:
  - By extending Ari et al. (2023) to include post-pandemic periods, a total of over 200 inflation episodes are identified.

### Deviation from Taylor-rule-implied Tightening
- Taylor-rule formulation used:
  - f^L_T_t = f^* + φ_π (π_t − π^*) − φ_u (u_t − u^*).
  - Calibration: φ_π = 1.5 and φ_Y = 1; using Okun’s law, φ_u = 2 φ_Y.
- Computation of deviations:
  - Tightening between post-inflation-episode t and the average of the last two pre-episode years computed as the difference between the period t Taylor-rule and the average implied interest rate for the two pre-episode years (formula provided in text).
  - Differential ∆ defined as observed short-term interest rate tightening from its pre-episode average minus the Taylor-rule-implied tightening (explicit expression provided).
- Comparative findings (Online Annex Figure 2.2.9 and related text):
  - Post-2020 tightening relative to Taylor-rule-implied tightening lies between resolved and unresolved 1970s episodes.
  - For all three sets (1970s unresolved, 1970s resolved, post-2020), the Taylor rule suggests stronger tightening during the first two years than the data show (likely due to lagged policy response).
  - The deviation between actual policy rate changes and Taylor-rule suggestions is smaller for resolved 1970s episodes and for the post-2020 period than for unresolved 1970s episodes.
  - In resolved 1970s episodes, policy rate changes in subsequent periods became more pronounced than suggested by the Taylor rule, likely to anchor inflation expectations.
- Pre-shock inflation volatility (Online Annex Figure 2.2.10):
  - Pre-2020 inflation volatility was significantly lower compared to the 1970s (volatility proxied by variance of inflation between t − 5 and t − 1 normalized by its mean over the same period).
  - Sample sizes noted: 1970s unresolved includes 12 inflation shock episodes; 1970s resolved includes 13 inflation shock episodes (1973–79); post-2020 encompasses 125 inflation episodes centered around 2021 and 2022.

### Monetary policy transmission: VAR Analysis
- Model and data:
  - Country-specific small-scale structural VARs with time-varying parameters and stochastic volatility estimated for selected AEs (US, euro area, UK) and EMs (India, Brazil, Mexico).
  - Each model includes five variables: real GDP, consumer prices, short-term policy rates, and two additional transmission-channel variables (AEs: 10-year sovereign bond yield and unemployment rate; EMs: terms of trade and nominal effective exchange rate).
  - For AEs, a shadow rate estimate is used as proxy for the short-term policy rate when the effective lower bound is approached.
  - Quarterly data used for the longest available samples through 2024Q2; sample start dates vary by country (e.g., 1960Q1 for US and UK, 1970Q1 for euro area, 1997Q1 for India, Brazil, Mexico).
  - Variables: real GDP and consumer prices expressed as annualized q-on-q growth rates; interest rates, unemployment rates, terms of trade indices, and NEER expressed as first differences.
- Identification:
  - Standard sign restrictions imposed for four quarters to identify monetary policy shocks, aggregate supply shocks, and aggregate demand shocks (Online Annex Table 2.3.1 shows restrictions).
  - Normalization: impulse responses to a standardized contractionary monetary policy shock normalized so peak policy rate response corresponds to an increase of 100 basis points.
  - Transmission measured as impulse responses of output and consumer prices to the standardized shock, derived from average parameter values estimated during each tightening period.
- Tightening period dating:
  - Tightening periods set using Blinder (2023) chronology for the US and periods with policy rate increases for at least two quarters in other countries (Online Annex Table 2.3.2 lists dates of most recent tightening cycles).
- Empirical results:
  - US impulse responses (Online Annex Figure 2.3.1):
    - Latest tightening cycle (2022Q1-2023Q3) shows stronger short-term responses of output and consumer prices than 1970s–1980s average but 1970s–80s responses are statistically significant for longer horizons.
    - Responses in the latest tightening episode are similar to the average for 1990–2019.
    - Cumulative responses indicate transmission to output and consumer prices of the latest tightening cycle appears similar to the historical average.
  - Cross-country comparison since 1990 (Online Annex Figure 2.3.2):
    - Some variation over time in transmission for each country, but no strong evidence of a systematic and significant difference in response magnitudes when comparing the latest episode to the average transmission observed between the 1990s and 2019.
  - Quantitative comparison note:
    - Ramey (2016) reports median peak impact of a normalized 100 basis points monetary policy shock to US output of -1.6 percent (interquartile range -0.7 percent to -2.1 percent); the study’s average peak response for the US since 1990 is -0.9 percent.

### Global Dynamic Network Model (overview)
- Model structure and calibration:
  - 11-sector, 2-country model calibrated to the U.S. and the rest of the world using OECD ICIO production network data.
  - Production uses three factors: fixed capital, variable labor, and an intermediate bundle; combined with a CES production function with elasticity = 0.5.
  - Intermediate bundle composed of products from all 11 sectors with a CES aggregator.
- Purpose:
  - To analyze network propagation of shocks across sectors and countries (model description continues beyond excerpt).

*Source: ch2onlineannexes - Annex Figure 2.2.7, panels 5 and 6) are broadly consistent with our earlier estimates, suggesting a — Online Annex, World Economic Outlook, International Monetary Fund | April 2024 / October 2024.*

### conclusions are also qualitatively similar to those of available studies for specific countries. For instance, Barrett a

### CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE - ONLINE ANNEX

### Summary of empirical comparisons
- Conclusions are qualitatively similar to available studies for specific countries: Barrett and Platzer (2024) find evidence that the transmission of the latest tightening shock in the US, beyond the very short run, was broadly in line with historical pre-pandemic averages. Lane (2024) finds no significant evidence of changes in the transmission in the euro area.
- Analysis is conducted across 11 sectors: Agriculture, Mining and Energy, Manufacturing, Construction, Wholesale & retail, IT & Telecommunications, Finance and Insurance, Real Estate, Professional, Scientific & Technical, Education, Health & Government Services, and Arts, Entertainment & Recreation.

### Model structure and key parameters
- Production: 2-nest CES production structure across sectors and within-sector (U.S. variety and rest-of-world variety) with the following elasticities:
  - Sectoral bundle elasticity: 0.8 (household consumption bundle)
  - Elasticity between U.S. variety and rest-of-world variety: 1.5
  - Production function elasticity for substitution between different types of goods in production (captures difficulty substituting energy with manufactured goods): 0.1
- Price adjustment: Calvo (1983) style sluggish price adjustment with sector-varying degrees of sluggishness; Phillips Curve slopes obtained from Rubbo (2023) originally from Pasten, Schoenle and Weber (2020).
- Labor supply: Aggregate wages are sticky; labor supply differentiated by sector with a constant elasticity of transformation of 0.76.
- Households: Two types
  - Ricardian households: Blanchard (1985)-Yaari (1965) overlapping generations, Greenwood–Hercowitz–Huffman (1988) preferences with habit formation, access financial markets.
  - Hand-to-mouth households: consume labor income.
- Sectoral inflation expectations deviate from rational expectations according to:
  π_{s,t,t+1}^e = ρ_e π_{s,t−1,t}^e + ρ_l π_{s,,t−1} + (1−ρ_e−ρ_l) E_t π_{s,t+1}
  - π_{s,,t} is inflation in sector s at time t.
  - π_{s,t,t+1}^e is inflation expectations in sector s formed at t for t+1.
  - E_t π_{s,t+1} are model-consistent rational expectations formed in period t.
- Expectations: These sectoral expectation deviations enter all Phillips Curve equations when firms set prices; other agents form expectations in a model-consistent manner.

### Non-linear Phillips Curve and sectoral supply constraints
- Supply constraints are modeled as exogenous, time-varying maximum workforce limits per sector (occasionally binding). Constraints:
  - Rarely bind in normal times.
  - Can bind in crisis times or when demand is sufficiently high; when binding, firm labor demand at prevailing wage is curtailed to the employment limit.
  - Binding constraints lower labor demand relative to no-constraint case and increase the steepness of the aggregate Phillips Curve when demand continues to rise.
- Illustrative setup: supply constraints imposed arbitrarily in ascending fashion across the 11 sectors (horizontal lines = maximum employment). Employment responses to varying aggregate demand (monetary policy shock size on x-axis) show:
  - When demand is low, employment in every sector is below maximum and sensitive to small demand changes.
  - When demand is high, some sectors hit supply constraints; further demand raises prices instead of employment, producing higher inflation and less output for a given demand increase.

### Shock extraction methodology
- Target sample: 2020Q1-2023Q4.
- Observables: sectoral value added, sectoral value-added deflators, import prices, aggregate CPI inflation, interest rates for US and rest of world (data from Federal Reserve Economic Data, OECD, Eurostat).
- Estimation approach:
  - Quasi-non-linear shock estimation: model linearized, shocks estimated via Kalman filter in a just-identified manner.
  - Number of shocks matches number of observables; Kalman filter conditioned so impact of initial conditions is small.
- Identification of labor constraints:
  - Define a “labor wedge” between marginal product of labor and prevailing market wage (estimated using the smoother) representing the shadow price of labor constraint; treated as exogenous shock to identify level of labor constraint.
  - Identification assumptions: (i) labor productivity shocks must be positive and labor wedge zero; or (ii) labor wedge is positive and labor productivity shocks are zero. The model does not allow both positive labor wedges and positive productivity shocks in the same period and sector.
  - Iterative procedure: if estimated shocks violate assumptions, the active shock is switched and Kalman filter re-run until convergence.

### Stylized identification examples
- Case 1 (data left of initial supply curve): observed price and quantity imply supply must decrease; two explanations:
  - Impose a constraint at observed quantity (positive shadow value of constraint).
  - Assume productivity decrease (orange case).
  - Identification imposes: productivity shocks are never negative and are zero whenever labor wedges are positive, leading to attributing required supply decreases to imposed supply bottlenecks when applicable.
- Case 2 (data right of initial supply curve): observed data implies supply increase; options:
  - Impose constraint at observed quantity (would imply negative shadow value — inconsistent with maximum labor limit).
  - Assume productivity increase — identified as positive productivity shock.

### Counterfactual construction and treatment of labor wedges
- Counterfactuals reuse the Kalman filter with adjusted observables per scenario (e.g., earlier tightening: interest rate adjusted to match assumed earlier tightening).
- Labor wedges re-estimated given new interest rate profile while keeping quantity of labor the same as baseline estimation; re-estimated labor wedges can be negative — in such cases wedge set to zero and quantity of labor re-estimated, iterating until no negative wedges remain.
- Special dotted-line counterfactuals (in Figure 2.13): treat observed positive labor wedges as exogenously given observables (do not react endogenously). Concretely:
  - When labor wedge treated as indicative of a labor constraint, a positive demand counterfactual does not raise quantity of labor in that sector; labor wedge increased to maintain labor at estimated-data quantity.
  - When labor wedge treated as a typical shock, quantity of labor would rise in a positive demand counterfactual while the labor wedge remains at the estimated value.
- In counterfactuals, wherever labor wedge is positive, the corresponding level of labor is imposed as an occasionally binding constraint.

### Decomposition and sectoral contributions to CPI in counterfactuals
- Online Annex Figure 2.4.3: shows excess total (direct and indirect) contribution of sectoral prices to CPI changes in counterfactual where rest of world tightens three quarters later.
  - Computation: decompose CPI changes into contributions from changes in sectoral value-added deflators/costs and sector-specific expectations using full set of input-output linkages; real exchange rate affects prices of foreign goods shown with a separate bar.
  - Excess contribution computed by subtracting observed indirect effect from counterfactual indirect contribution assuming equal deflator rises in all sectors. Because this is an excess contribution, the bars sum to zero.
  - Time series labels shown: 2022:Q3, 22:Q4, 23:Q1, 23:Q2, 23:Q3, 23:Q4.
  - Sector grouping in figure: Food and energy; Manufacturing; Services; Real exchange rate.

### Inflation drivers and impulse responses
- Online Annex Figure 2.4.4: Inflation drivers in the United States from model data (percent, year-over-year) estimated following Dao and others (2024) with parameters from simulation of 1000 periods bootstrapped to replicate 2020:Q1 to 2023:Q4 sample. Five year ahead inflation expectations assumed at steady state; slack is deviation of GDP from steady state.
  - Headline components shown: Energy; Other; Headline: Energy; Headline: Other; Residual; Pass-through; Pass-through Energy; Expectations; Slack.
- Online Annex Figure 2.4.5: Effect of Negative Capacity Constraint (percent deviation from steady state, quarter-over-quarter, annualized) — scenario: negative labor constraint shock in agriculture, mining, and energy sectors without changes in aggregate demand (isolates interaction of constraint and demand).
  - Policy rules: Taylor rules identical except for inflation measure targeted.
    - “Targets stickiest sectors’ inflation” targets the five sectors with the steepest Phillips curves.
    - “Inflation forecast targeting” targets the four-quarter moving average of future CPI inflation.
    - “Flexible prices” scenario: relative prices in a scenario without nominal rigidities in any sector market.
    - “50/50 CPI and constrained sectors” targets CPI inflation and sectoral inflation in agriculture, mining, and energy.
  - Taylor parameters used: Taylor parameter = 3; persistence parameter = 0.5; neither GDP nor output gap targeted.
  - Key takeaway: inflation rises for only one period and then moderates slowly. Explanation: price rises are needed to maintain a labor constraint at a certain level, leading to a temporary surge in sectoral inflation; to maintain the labor constraint thereafter, no further price rises are needed — the elevated price level suffices. This creates a temporary surge followed by moderation.
  - Note: policy rule targeting food and energy prices can create persistent inflation in face of capacity constraint shocks only because sectoral inflations of sticky-price sectors (targeted less) have more persistence than those of flexible-price sectors (targeted more).

*Source: IMF staff calculations and model descriptions in CHAPTER 2 THE GREAT TIGHTENING: INSIGHTS FROM THE RECENT INFLATION EPISODE - ONLINE ANNEX*

### 3. GDP

### 3. GDP

### Sectoral Price Dispersion
- Online Annex Figure 2.4.6. depicts sectoral price dispersion (Percent, sectoral prices relative to CPI).
- Scenario: same as in Figure 2.15. Overall Taylor parameter on inflation is 3 with policy inertia of 0.5. Other rules are the same as Figure 2.15.
- Observed sectoral patterns:
  - When all prices are flexible:
    - Agriculture, mining, and energy (sectors facing supply constraints) exhibit short-lived price increases.
    - Prices of other sectors move marginally.
    - Initial price dispersion under flexible prices is lower because downstream sectors can pass on higher costs, reducing dispersion from the average price level.
  - Under sticky prices:
    - Relative prices deviate more from the flexible-price benchmark, especially for service sectors which tend to have stickier prices than goods sectors.
    - More flexible upstream sectors are able to quickly raise prices while sticky downstream sectors are not, raising initial price dispersion.
  - When the policy rule targets short-run inflation in agriculture and energy (targeted upstream sectors):
    - Initial relative price movements of these targeted sectors are close to the flexible-price benchmark.
    - Inflation momentum in other sectors builds over time, which the policy rule does not respond to as strongly because inflation in the targeted upstream sectors is low or negative.
    - This creates cyclical dynamics and larger gyrations with resource misallocation across sectors, as in Figure 2.15 in the main chapter.

### Comparison of Monetary Policy Rules and Volatility
- Online Annex Figure 2.4.7. compares volatility of CPI and GDP responses under four monetary policy rules in Figure 2.15, including AIT (Average Inflation Targeting).
- Presentation: Each line represents a linear combination of CPI and GDP volatilities with opposite signs. When the weight on GDP volatility is zero, the y-intercept corresponds to the negative sum of squared deviations of CPI from its steady state.
- Interpretation rule: A higher line indicates lower volatility in either CPI or GDP, suggesting the corresponding rule is more effective at stabilizing the economy.
- Rules compared (labels as in figure):
  - Targeting stickiest sectors’ inflation
  - Inflation forecast targeting
  - 50/50 on CPI and constrained sectors
  - AIT
- Key comparative results:
  - Targeting the inflation of the stickiest sectors delivers the most effective strategy for CPI stabilization.
  - Volatilities under targeting the stickiest sectors are quantitatively similar to those under AIT, with AIT slightly outperforming as the weight on GDP volatility increases.
  - Both of these rules (targeting stickiest sectors and AIT) clearly surpass the other two rules (inflation forecast targeting and 50/50 on CPI and constrained sectors).

### Mechanisms and Dynamics Highlighted
- Upstream vs downstream flexibility:
  - Upstream (agriculture, mining, energy) can be more flexible and respond quickly to supply shocks; downstream (services, some manufacturing) often have stickier prices, amplifying initial dispersion when prices are sticky.
- Policy targeting trade-offs:
  - Focusing policy on stabilizing upstream constrained sectors can suppress initial price responses in those sectors but permit inflation momentum to accumulate elsewhere, inducing cyclical dynamics and resource misallocation.
- Numeric and graphical markers preserved from figures:
  - Axis tick values shown in figures include ranges from –1.0 to 3.0 and 0,5,10,15,20 (as presented in Online Annex Figure 2.4.6.), and weight on GDP volatility axis from 0.0 to 1.0 with intermediate ticks (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) and vertical values from –0.7 to 0.0 (as presented in Online Annex Figure 2.4.7.).

### Findings and Implications for Monetary Policy
- Findings:
  - Sticky prices increase initial sectoral price dispersion relative to the flexible-price benchmark, particularly for service sectors.
  - Targeting stickiest sectors’ inflation is the most effective single-sector-targeting rule for CPI stabilization and approximates the performance of AIT.
  - AIT slightly outperforms stickiest-sector targeting as the policymaker places greater weight on reducing GDP volatility.
- Policy implications:
  - Monetary policy rules that explicitly account for sectoral price stickiness can materially improve CPI stabilization.
  - Rules narrowly targeting constrained upstream sectors risk inducing inflation momentum and volatility in non-targeted sectors, causing larger cyclical fluctuations and resource misallocation.
  - Consideration of both CPI and GDP volatilities (and their trade-offs) is important when selecting policy frameworks; AIT provides robustness as the weight on GDP volatility increases.

*International Monetary Fund | April 2024*

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_Source: https://www.imf.org/-/media/files/publications/weo/2024/october/english/ch2onlineannexes.pdf_