## wp18241

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### 2.1    Inflation Performance in Emerging Markets
- Summary findings
  - Following a period of disinflation during the 1990s and early 2000s, inflation in emerging markets remained relatively low and stable since the mid-2000s.
  - The weighted average of headline CPI inflation for the 19 emerging markets in the sample declined dramatically—by more than a 100 percentage points from 1995 to 2004—and leveled off at about five percent thereafter, which is about three percentage points higher than the weighted average of advanced economies.
  - Median headline inflation declined from about 20 percent to about five percent since 2004.
  - Core CPI inflation, producer price inflation (PPI), and GDP deflators exhibit similar patterns: declined until the mid-2000s and remained low and stable thereafter.
  - The 19 countries in the sample constitute 80 percent of the GDP of all emerging market and developing economies.

- Measures and sample
  - Inflation measures: Headline CPI; Core CPI (excludes food and energy); Producer prices (PPI); GDP deflators.
  - Sample: 19 emerging markets selected based on availability of longer-term inflation forecasts and a minimum population of two million. Countries: Argentina, Brazil, Bulgaria, Chile, China, Colombia, Hungary, India, Indonesia, Malaysia, Mexico, Peru, Philippines, Poland, Romania, Russia, South Africa, Thailand, and Turkey.
  - Time focus: post-disinflation period starting in the mid-2000s.

- Cross-country heterogeneity
  - Late 1990s: about half of the countries experienced inflation rates above 10 percent.
  - Since 2004: share with inflation exceeding 10 percent declined to about one country out of 10.
  - For 10 percent of the sample, volatility and persistence are about two to three times higher than for the median country (latest observation covering 2016–2018).
  - Notable heterogeneity in levels, volatility, and persistence of headline and core inflation.

- Volatility and persistence
  - Since 2004, inflation volatility in emerging markets has been stable or declining.
  - Decline in inflation volatility is not driven by exchange rate behavior; no clear evidence of a decline in volatility of exchange rate movements since the late 1990s.
  - Volatility computed as the standard deviation of detrended inflation using three-year windows.
  - Inflation persistence declined gradually during the sample period but remains somewhat above the level in advanced economies.
  - Persistence measured following Stock and Watson (2007, 2010): decomposing π_t into permanent ζ_t and transitory η_t where ζ_t = ζ_{t−1} + ϵ_t; persistence measure is the estimated standard deviation of the shock to the permanent component.
  - Two factors implying greater expected volatility/persistence in emerging markets: higher share of consumption attributable to food and other commodities; less developed monetary policy institutions and frameworks.
  - Despite these factors, since 2004 volatility in emerging markets has been comparable to advanced economies.

- Interpretation and policy context
  - Lower and more stable inflation since the mid-2000s could reflect strengthened domestic macroeconomic frameworks (e.g., adoption of inflation targeting and fiscal rules) and offsetting external forces (China’s integration into world trade, weaker global demand after the global financial crisis, benign external financial conditions).
  - Institutional changes in the 19 countries:
    - Number of inflation targeters increased from zero in 1995 to 15 in 2017.
    - Number of countries with some type of fiscal rule rose from 2 to 14 in 2007; fell to 11 by 2011 (Argentina, India, and Russia suspended rules); rose to 12 when Russia implemented a new fiscal rule in 2013.
  - The subsequent empirical analysis aims to quantify domestic and global contributions to inflation since the mid-2000s.

### 3.1    An Augmented Phillips Curve Framework
- Empirical strategy (estimated hybrid New‑Keynesian Phillips curve, augmented for external factors)
  - Specification: π_i,t = γ_b π_i,t−1 + γ_f π^e_i,t + β Ygap_i,t + θ Z^*_i,t + η_i + ε_i,t
    - π: core inflation or headline inflation.
    - π^e: three-year-ahead inflation expectations (Consensus Economics; quarterly from 2014; South Africa: Bureau for Economic Research).
    - Ygap: domestic output gap (HP-filtered real GDP).
    - Z^*: import-weighted foreign output gap; indicator for external price pressure (lagged); lag of energy and food price inflation (energy and food not included in core specs).
    - Foreign output gap: ∆Y^*_gap_i,t = Σ_{j≠i} ω_{ij,t} Ygap_j,t (ω lagged one year; measured annually; import shares).
    - External price pressure: ∆P^*_i,t = ∆mPPI_i,t + ∆neer_i,t − ∆P_i,t where ∆mPPI_i,t = Σ_{j≠i} ω_{ij,t} ∆PPI_j,t and ∆neer_i,t = Σ_{j≠i} ω_{ij,t} (∆e_i,t − ∆e_j,t).
  - Estimation methods: median regressions (baseline), robust regressions, constrained regressions (sum of coefficients on past inflation and expectations = 1).
  - Country fixed effects included; variance inflation factor well below 10 for all explanatory variables.
  - Potential endogeneity acknowledged; lags-based estimators such as GMM not used due to data structure.

- Estimation results (selected quantitative findings)
  - Explanatory power: variables account for 52 percent of variation of core inflation and 44 percent of variation of headline inflation.
  - Inflation expectations (three-year-ahead):
    - Core regressions: coefficient ranges between 0.5 and 0.6 (table examples: 0.587***, 0.631***, 0.566***).
    - Headline regressions: coefficient ranges between 0.4 and 0.5 (table examples: 0.396***, 0.303***, 0.564***).
  - Persistence (lagged inflation coefficients):
    - Core: 0.494***, 0.500***, 0.434***.
    - Headline: 0.422***, 0.481***, 0.436***.
  - Output gap coefficients (economic magnitude):
    - Core: 0.159***, 0.168***, 0.103.
    - Headline: 0.188**, 0.182***, 0.110.
    - A one percentage point increase in the output gap is associated with an increase in core/headline inflation by 0.2 percentage points (text).
  - External factors:
    - Lag of external price pressure (core): 0.018***, 0.018***, 0.032***.
    - Lag of external price pressure (headline): 0.005, −0.001, 0.020.
    - Lag of food price inflation (headline): 0.013***, 0.018***, 0.025***.
    - Lag of energy price inflation (headline): 0.000, −0.001, −0.001 (not significant).
    - Foreign output gap coefficients: not statistically significant (examples: 0.021, 0.060, 0.070 for core; 0.117, 0.085, 0.169 for headline).
    - Economic magnitudes: one percentage point increase in external price pressure increases core inflation by 0.02 to 0.03 percentage points; one percentage point increase in lagged food price inflation increases headline inflation by 0.01 to 0.02 percentage points.
  - Sample and fit:
    - Countries: 18 (core regressions) and 19 (headline regressions).
    - Observations: 633 (core) and 668 (headline).
    - R-squared: 0.525 (core median regression); pseudo R-squared for robust regressions shown (0.445 for core robust).
    - Significance notation: *** p <0.01, ** p <0.05, * p <0.1.
  - Constrained regressions (sum of past inflation and expected inflation = 1): Wald tests cannot reject sum = one for median and robust regressions.

### 3.2    Contributions to inflation deviations from “target”
- Method
  - Country-specific contributions computed accounting for persistence: C^x_{i,t} = C^x_{i,t−1} γ_b + (φ^x x_{i,t}).
  - Contribution of inflation expectations re-expressed as deviation from either explicit target (announced under inflation targeting) or implicit target (moving average of 10-year-ahead inflation expectations).
  - Analysis done across four subperiods: 04Q1–08Q2; 08Q3–09Q4; 10Q1–14Q2; 14Q3–18Q1.

- Key findings (quantitative and qualitative)
  - Largest contributor to deviations of core inflation from target is inflation expectations; on average, expectations exceeded the inflation target for the sampled emerging markets.
  - Domestic cyclical conditions played a smaller role: booms raised inflation above target; global financial crisis downturns lowered inflation below target.
  - External price pressure: largest external contributor but economically small and on average deflationary.
    - Average annual contribution of external price pressure: −0.05 percentage point over the sample period.
    - Average contribution of longer-term inflation expectations: 0.5 percentage point.
  - Foreign slack (foreign output gap) contribution is economically insignificant.
  - Overall deviation of inflation from target declined gradually during 2004–14 by 0.7 percentage point (text).

- Common driver / time fixed effects analysis
  - Two-step approach: include time fixed effects in specification without external variables; regress time fixed effects on cross-country averages of domestic determinants to obtain predicted values and residuals.
  - Findings:
    - Common component captures commodity-induced inflation surge during 2008.
    - For other subperiods, common component’s contribution to inflation deviations from target is small.
    - Estimated time fixed effects correlate with domestic explanatory variables, reducing concern about neglected external forces.
    - Residual provides negligible average contribution to inflation during the post-global financial crisis period.
  - Interpretation: limited average impact of global factors on inflation deviations; fluctuations in longer-term inflation expectations interpreted as mostly domestic in origin.

- Cross-country heterogeneity
  - Chile and Poland: small contributions of inflation expectations from the target (consistent with mature monetary frameworks).
  - Russia and Thailand: large deviations of inflation expectations from target.
  - External price developments exerted downward pressure on domestic prices for three‑fourths of economies in the sample (magnitude small).
  - Cyclical factors’ impact limited on average when averaged over 2004–18.

### 3.3    Contributions to inflation variation (variance-style decomposition)
- Method
  - Contribution of variable x to variation: C_var,x_i = (1/T Σ_t |C^x_{i,t}|) / Σ_{x∈X} (1/T Σ_t |C^x_{i,t}|).
  - Contribution of inflation expectations C_var,π^e expressed in terms of deviations from the target.

- Key quantitative findings
  - Inflation expectations are the largest contributing explanatory factor for four-fifths of sample countries, explaining, on average, 20 percent of the variation in inflation.
  - Heterogeneity across countries: share attributable to inflation expectations ranges from 2 percent to 35 percent.
  - External price movements explain, on average, 8 percent of inflation deviations.
  - Foreign output gap contribution is negligible in all decomposition results.

- Domestic versus global grouping (average shares)
  - Domestic subset (inflation expectations and output gap):
    - Explain between 52 percent and 77 percent of core inflation dynamics.
    - Explain between 32 percent and 55 percent of headline inflation dynamics.
  - Global subset (foreign output gap, external price pressure, commodity price inflation):
    - Explain between 3 percent and 5 percent of core inflation dynamics.
    - Explain between 3 percent and 11 percent of headline inflation dynamics.
  - Robustness caveat: inflation expectations can reflect both domestic and global influences; similar results obtained when purging expectations of external factors.

### 3.4    Robustness Exercises
- General limitations and extreme assumption
  - Acknowledged unexplained variation: "45 percent of the variation in inflation remains unexplained."
  - If all residual attributed to uncaptured foreign factors, average contribution of foreign factors to inflation variation would be:
    - 26 percent for core inflation.
    - 44 percent for headline inflation.
  - Even under this extreme assumption, these are "still less than or comparable to the average contribution of domestic factors (68 percent for core inflation and 44 percent for headline inflation)."

- Time fixed effects specifications (Table 2 summaries)
  - Time fixed effects specification: average contribution of foreign factors to inflation is 11 percent for both core and headline inflation.
  - Time fixed effects plus external price pressure: average contribution of foreign factors to inflation variation is 17 percent for core inflation and 14 percent for headline inflation.
  - Two-stage orthogonalization (regressing inflation expectations on foreign price pressure, foreign output gap, and fixed effects, then using residuals): coefficients on external price pressure and foreign output gap are "marginally significant" in the first stage; second stage results similar to baseline, implying inflation expectations are mostly driven by domestic factors.

- Weighted commodity inflation interaction (Column (5) of Table 2)
  - Coefficient for food price inflation remains significant and larger in magnitude; average weight of food in CPI baskets of the 19 sample countries: 32.9 percent.
  - Coefficient for energy inflation remains insignificant; average weight of energy in CPI baskets: 9.6 percent.
  - Selected median-regression coefficients (reported):
    - Inflation expectations 3 years ahead: 0.832*** (Core, Col 1); 0.327*** (Headline, Col 2); 0.862*** (Core, Col 3); 0.353*** (Headline, Col 4); 0.354*** (Headline weighted, Col 5).
    - Lag of inflation: 0.444***, 0.488***, 0.435***, 0.490***, 0.417***.
    - Output gap: 0.172***, 0.230***, 0.138***, 0.225***, 0.167**.
    - Lag of external price pressure: 0.016***, 0.018***, 0.006 (where reported).
    - Lag of weighted food price inflation (Col 5): 0.045***.
    - Lag of weighted energy price inflation (Col 5): 0.016 (insignificant).
    - Countries: 19 where reported; Observations: 634, 669, 634, 669, 668; R-squared: 0.561, 0.494, 0.568, 0.498, 0.445.

- Extensions: trade openness, GVCs, China component (Table 3 summaries)
  - Extended specification includes trade openness or GVC participation and interactions with external variables.
  - Main finding: "There is no significant evidence that deeper trade integration has a significant effect on domestic inflation."
  - When significant, coefficients on trade openness and GVC participation are positive but "relatively small" and not consistent across inflation measures.
  - Trade openness * foreign output gap significant in one specification for headline inflation, but magnitude small.
  - China decomposition (Columns (5) and (6) of Table 3):
    - External price pressure from China: -0.004 (Core), -0.002 (Headline) — not significant.
    - External price pressure excluding China: 0.018*** (Core), 0.007 (Headline).
    - Interpretation: external price pressure from China does not have significant impact on core or headline inflation dynamics, while non-Chinese external price pressures remain significant for core inflation.
  - Selected coefficients (reported):
    - Inflation expectations 3 years ahead across Columns (1)–(6): 0.643***, 0.406***, 0.632***, 0.378***, 0.551***, 0.399***.
    - Lag of inflation: 0.479***, 0.422***, 0.479***, 0.427***, 0.502***, 0.426***.
    - Output gap: 0.154***, 0.223***, 0.173***, 0.194**, 0.163***, 0.206***.
    - Trade openness: 0.015* (Core), 0.026 (Headline) where reported.
    - GVC participation: 0.060** (Core), -0.033 (Headline) where reported.
    - External price pressure excl. China: 0.018*** (Core), 0.007 (Headline).
    - External price pressure from China: -0.004, -0.002.
    - Countries: 18 or 19 where reported; Observations: 624, 659, 633, 668, 627, 662; R-squared: 0.524, 0.453, 0.526, 0.446, 0.523, 0.446.

- Inflation expectation horizons (Table 4 summaries)
  - Baseline uses three-year-ahead expectations; robustness uses horizons up to seven years ahead.
  - Core inflation: coefficient on expected inflation for horizons three to seven years ahead range from 0.56 to 0.64 (reported robustness).
    - Reported examples: 0.637*** (4-year), 0.614*** (5-year), 0.585*** (6-year), 0.560*** (7-year).
  - Headline inflation: inflation expectations become insignificant for horizons of six years ahead and beyond.
    - Reported headline examples: 0.397** (4-year), 0.448* (5-year), 0.256 (6-year), -0.066 (7-year).
  - Lag of inflation and output gap remain generally positive and significant for core across horizons; headline shows more variability.

- Robustness exercise conclusions (summarized)
  - Domestic factors account for the lion’s share of inflation dynamics in emerging markets.
  - Fluctuations in longer-term inflation expectations (linked to domestic developments) are the main driver of average deviations of inflation from target and inflation variability.
  - Contribution of global variables is not always statistically significant and is substantially smaller than domestic factors in economic terms.
  - Robustness tests confirm the impact of global factors is marginal compared to domestic factors and that inflation expectations largely reflect evolution of domestic variables.

*Source: wp18241; https://www.imf.org/-/media/files/publications/wp/2018/wp18241.pdf*

### 2.1    Inflation Performance in Emerging Markets   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .4

### 2.1    Inflation Performance in Emerging Markets

### Summary findings
- Following a period of disinflation during the 1990s and early 2000s, inflation in emerging markets remained relatively low and stable since the mid-2000s.
- The weighted average of headline CPI inflation for the 19 emerging markets in the sample declined dramatically—by more than a 100 percentage points from 1995 to 2004—and leveled off at about five percent thereafter, which is about three percentage points higher than the weighted average of advanced economies.
- Median headline inflation declined from about 20 percent to about five percent since 2004.
- Core CPI inflation, producer price inflation (PPI), and GDP deflators exhibit similar patterns: declined until the mid-2000s and remained low and stable thereafter.
- The 19 countries in the sample constitute 80 percent of the GDP of all emerging market and developing economies.

### Measures and trends in the sample
- Inflation measures discussed:
  - Headline CPI (headline inflation)
  - Core CPI (core inflation, excludes food and energy)
  - Producer prices (PPI)
  - GDP deflators
- Time coverage and sample:
  - Post-disinflation period marked starting in the mid-2000s; figures and analysis focus on changes since that break.
  - Sample of 19 emerging markets selected based on availability of longer-term inflation forecasts and a minimum population of two million. The sample includes: Argentina, Brazil, Bulgaria, Chile, China, Colombia, Hungary, India, Indonesia, Malaysia, Mexico, Peru, Philippines, Poland, Romania, Russia, South Africa, Thailand, and Turkey.

### Cross-country heterogeneity
- Share of countries with double-digit inflation:
  - In the late 1990s, about half of the countries in the sample experienced inflation rates above 10 percent.
  - Since 2004, the share declined significantly; still, one country out of 10 emerging markets experienced inflation rates exceeding 10 percent.
- Distributional evidence:
  - For 10 percent of the sample, volatility and persistence are about two to three times higher than for the median country (latest observation covering 2016–2018).
  - There is notable cross-country heterogeneity in levels, volatility, and persistence of both headline and core inflation.

### Volatility and persistence
- Inflation volatility:
  - Since 2004, inflation volatility in emerging markets has been stable or declining.
  - The decline in inflation volatility is not driven by exchange rate behavior; there is no clear evidence of a decline in the volatility of exchange rate movements since the late 1990s.
  - For volatility, the distributional plots use three-year windows; volatility is computed as the standard deviation of detrended inflation.
- Inflation persistence:
  - Inflation persistence declined gradually during the sample period, though it remains somewhat above the level in advanced economies.
  - Persistence is measured following Stock and Watson (2007) and Stock and Watson (2010): decomposing inflation, π_t, into permanent component ζ_t and transitory component η_t where ζ_t = ζ_{t−1} + ϵ_t; persistence measure is the estimated standard deviation of the shock to the permanent component of inflation.
  - Two factors implying greater expected volatility/persistence in emerging markets:
    - A higher share of consumption attributable to food and other commodities (more volatile prices).
    - Monetary policy institutions and frameworks could be less developed, reducing effectiveness and increasing persistence.
- Despite these factors, since 2004 volatility in emerging markets has been comparable to that in advanced economies.

### Interpretation and policy context
- Lower and more stable inflation since the mid-2000s could reflect:
  - Strengthened domestic macroeconomic frameworks (e.g., adoption of inflation targeting and fiscal rules).
  - Offsetting external forces (e.g., China’s integration into world trade, weaker global demand after the global financial crisis, benign external financial conditions) that may have produced disinflationary pressures.
- Institutional changes noted over the last two decades among the 19 countries:
  - Number of inflation targeters increased from zero in 1995 to 15 in 2017.
  - Number of countries with some type of fiscal rule rose from 2 to 14 in 2007; fell to 11 by 2011 (Argentina, India, and Russia suspended rules); rose to 12 when Russia implemented a new fiscal rule in 2013.
- Broader relevance:
  - The text frames the subsequent empirical analysis (Section 3) to quantify the contributions of domestic and global factors to inflation since the start of the post-disinflation period in the mid-2000s.

*Source: wp18241 - 2.1    Inflation Performance in Emerging Markets; https://www.imf.org/-/media/files/publications/wp/2018/wp18241.pdf*

### 3.1    An Augmented Phillips Curve Framework

### 3.1    An Augmented Phillips Curve Framework

### 3.1.1 Empirical strategy
- Estimated specification (hybrid New-Keynesian Phillips curve, augmented for external factors):
  - π_i,t = γ_b π_i,t−1 + γ_f π^e_i,t + β Ygap_i,t + θ Z^*_i,t + η_i + ε_i,t
  - π is core inflation or headline inflation.
  - π^e denotes three-year-ahead inflation expectations (Consensus Economics; quarterly from 2014; South Africa: Bureau for Economic Research, quarterly for full sample). Expectations are based on headline inflation forecasts.
  - Ygap is domestic output gap (HP-filtered real GDP).
  - Z^* includes: import-weighted foreign output gap, an indicator for external price pressure (lagged), and lag of energy and food price inflation (energy and food not included in core inflation specs).
  - Foreign output gap: ∆Y^*_gap_i,t = Σ_{j≠i} ω_{ij,t} Ygap_j,t (ω are lagged one year, measured annually, import shares).
  - External price pressure: ∆P^*_i,t = ∆mPPI_i,t + ∆neer_i,t − ∆P_i,t, where ∆mPPI_i,t = Σ_{j≠i} ω_{ij,t} ∆PPI_j,t and ∆neer_i,t = Σ_{j≠i} ω_{ij,t} (∆e_i,t − ∆e_j,t).
  - Estimation methods: median regressions (baseline), robust regressions, constrained regressions (sum of coefficients on past inflation and expectations = 1).
- Data and estimation notes:
  - Country fixed effects included.
  - Variance inflation factor well below 10 for all explanatory variables.
  - Potential endogeneity acknowledged; data structure prevents use of lags-based estimators such as GMM.

### 3.1.2 Estimation results (summary of Table 1 and text)
- Overall explanatory power:
  - The explanatory variables account for 52 percent of the variation of core inflation and 44 percent of the variation of headline inflation.
- Inflation expectations:
  - Coefficient on three-year-ahead inflation expectations:
    - Core inflation regressions: ranges between 0.5 and 0.6 (table: 0.587***, 0.631***, 0.566***).
    - Headline inflation regressions: ranges between 0.4 and 0.5 (table: 0.396***, 0.303***, 0.564***).
- Persistence (lagged inflation):
  - Lag of core/headline inflation coefficients in table: 0.494***, 0.500***, 0.434*** (core) and 0.422***, 0.481***, 0.436*** (headline).
- Domestic cyclical conditions:
  - Output gap coefficients (table): core: 0.159***, 0.168***, 0.103; headline: 0.188**, 0.182***, 0.110.
  - Economic magnitude: a one percentage point increase in the output gap is associated with an increase in the core/headline inflation rate by 0.2 percentage points (text description).
- External factors:
  - Lag of external price pressure (table): 0.018***, 0.018***, 0.032*** for core; 0.005, −0.001, 0.020 for headline.
  - Lag of food price inflation (headline specifications): 0.013***, 0.018***, 0.025***.
  - Lag of energy price inflation (headline specifications): 0.000, −0.001, −0.001 (not significant).
  - Foreign output gap coefficients (table): not statistically significant (values shown: 0.021, 0.060, 0.070 for core; 0.117, 0.085, 0.169 for headline).
  - Economic magnitudes: a one percentage point increase in the external price pressure variable is associated with an increase of 0.02 to 0.03 percentage points in the core inflation rate; a one percentage point increase in lag of food price inflation is associated with an increase of 0.01 to 0.02 percentage points in the headline inflation rate.
- Sample and fit (from Table 1):
  - Countries: 18 (core regressions) and 19 (headline regressions).
  - Observations: 633 (core) and 668 (headline).
  - R-squared reported: 0.525 (core median regression); pseudo R-squared for robust regressions shown (0.445 for core robust).
  - Robust standard errors in parentheses; significance: *** p <0.01, ** p <0.05, * p <0.1.
- Robustness/constraints:
  - Constrained regressions force sum of coefficients on past inflation and expected inflation to equal one; Wald tests cannot reject sum = one for median and robust regressions.

### 3.2 Contributions to inflation deviations from “target”
- Method:
  - Compute country-specific contributions C^x_{i,t} accounting for inflation persistence: C^x_{i,t} = C^x_{i,t−1} γ_b + (φ^x x_{i,t}).
  - Contribution of inflation expectations re-expressed as deviation from either an explicit target (announced under inflation targeting) or an implicit target (moving average of 10-year-ahead inflation expectations).
- Key findings (across four subperiods: 04Q1–08Q2; 08Q3–09Q4; 10Q1–14Q2; 14Q3–18Q1):
  - Largest contributor to deviations of core inflation from target is inflation expectations (on average, expectations exceeded the inflation target for the sampled emerging markets).
  - Domestic cyclical conditions played a smaller role: booms raised inflation above target; global financial crisis downturns lowered inflation below target.
  - External price pressure was the largest external contributor but economically small and on average deflationary:
    - Average annual contribution of external price pressure: −0.05 percentage point over the sample period.
    - Average contribution of longer-term inflation expectations: 0.5 percentage point.
  - Foreign slack (foreign output gap) contribution is economically insignificant.
  - Overall deviation of inflation from target declined gradually during 2004–14 by 0.7 percentage point (text).
- Common driver analysis (time fixed effects approach):
  - Two-step approach: include time fixed effects in specification without external variables; regress time fixed effects on cross-country averages of domestic determinants to obtain predicted values and residuals (the “true” residual).
  - Results:
    - Common component captures commodity-induced inflation surge during 2008.
    - For other subperiods, the common component’s contribution to inflation deviations from target is small.
    - Estimated time fixed effects correlate with domestic explanatory variables, reducing concern about neglected external forces.
    - Residual provides negligible average contribution to inflation during the post-global financial crisis period.
  - Interpretation: limited average impact of global factors on inflation deviations; fluctuations in longer-term inflation expectations are central and interpreted as of domestic origin.
- Cross-country heterogeneity (country-level contributions):
  - Examples:
    - Chile and Poland: small contributions of inflation expectations from the target (consistent with mature monetary frameworks).
    - Russia and Thailand: large deviations of inflation expectations from target.
  - External price developments exerted downward pressure on domestic prices for three-fourths of economies in the sample (magnitude small).
  - Cyclical factors’ impact is limited on average when averaged over 2004–18.

### 3.3 Contributions to inflation variation (variance-style decomposition)
- Method:
  - Contribution of each variable x to variation: C_var,x_i = (1/T Σ_t |C^x_{i,t}|) / Σ_{x∈X} (1/T Σ_t |C^x_{i,t}|).
  - For this exercise, contribution of inflation expectations C_var,π^e is expressed in terms of deviations from the target.
- Key findings:
  - Inflation expectations are the largest contributing explanatory factor for four-fifths of sample countries, explaining, on average, 20 percent of the variation in inflation.
  - Substantial heterogeneity across countries: share attributable to inflation expectations ranges from 2 percent to 35 percent.
  - External price movements explain, on average, 8 percent of inflation deviations.
  - Foreign output gap contribution is negligible in all decomposition results.
- Domestic versus global grouping (S_n subsets):
  - Domestic subset: inflation expectations and output gap.
  - Global subset: foreign output gap, external price pressure, and commodity price inflation.
  - Results (average shares of variation explained):
    - Domestic contributions explain between 52 percent and 77 percent of core inflation dynamics.
    - Domestic contributions explain between 32 percent and 55 percent of headline inflation dynamics.
    - Foreign factors explain between 3 percent and 5 percent of core inflation dynamics.
    - Foreign factors explain between 3 percent and 11 percent of headline inflation dynamics.
  - Robustness note: labeling of contributions as domestic vs global has caveats because inflation expectations can reflect both domestic and global influences; authors report similar results when purging inflation expectations of external factors.

*Source: wp18241 - 3.1 An Augmented Phillips Curve Framework (authors’ calculations, tables, and figures as presented in the source document).*

### 3.4    Robustness Exercises

### 3.4    Robustness Exercises

### Global Factors
- Limitations noted:
  - "45 percent of the variation in inflation remains unexplained."
  - Variables categorized as domestic (foreign) could contain foreign (domestic) elements; endogeneity from omitted variables; three-years ahead inflation expectations might not represent long-term expectations.
- Extreme assumption: if all residual is due to uncaptured foreign factors, average contribution of foreign factors to inflation variation would be:
  - 26 percent for core inflation
  - 44 percent for headline inflation
  - These are "still less than or comparable to the average contribution of domestic factors (68 percent for core inflation and 44 percent for headline inflation)."
- Time fixed effects specification (Columns (1) and (2) of Table 2):
  - Average contribution of foreign factors to inflation: 11 percent for both core and headline inflation.
- Time fixed effects plus external price pressure (Columns (3) and (4) of Table 2):
  - External price pressures remain significant.
  - Average contribution of foreign factors to inflation variation: 17 percent for core inflation and 14 percent for headline inflation.
- Two-stage orthogonalization robustness check:
  - Regression of inflation expectations on foreign price pressure, foreign output gap, and country and time fixed effects yields coefficients on external price pressure and foreign output gap that are "marginally significant" in the first stage.
  - Second stage replaces inflation expectations with the residual orthogonal to foreign factors; results are similar to baseline, "ensuring that inflation expectations are mostly driven by domestic factors."
- Weighted commodity inflation interaction (drawing on Choi et al. (2018); Column (5) of Table 2):
  - Coefficient for food price inflation remains significant and becomes larger in magnitude; average weight of food in CPI baskets of the 19 sample countries: 32.9 percent.
  - Coefficient for energy inflation remains insignificant; average weight of energy in CPI baskets: 9.6 percent.
- Table 2 median-regression highlights (selected coefficients and statistics as reported):
  - Inflation expectations 3 years ahead: 0.832*** (Core, Col 1); 0.327*** (Headline, Col 2); 0.862*** (Core, Col 3); 0.353*** (Headline, Col 4); 0.354*** (Headline weighted, Col 5).
  - Lag of core/headline inflation: 0.444***, 0.488***, 0.435***, 0.490***, 0.417***.
  - Output gap: 0.172***, 0.230***, 0.138***, 0.225***, 0.167**.
  - Lag of external price pressure: 0.016***, 0.018***, 0.006 (where reported).
  - Lag of weighted food price inflation (Col 5): 0.045***.
  - Lag of weighted energy price inflation (Col 5): 0.016 (insignificant).
  - Countries: 19 (where reported); Observations: 634, 669, 634, 669, 668; R-squared: 0.561, 0.494, 0.568, 0.498, 0.445.

### Extensions (Trade openness, GVCs, China component)
- Extended specification (equation (9)) includes trade openness or participation in GVCs and interactions with external variables.
- Main findings:
  - "There is no significant evidence that deeper trade integration has a significant effect on domestic inflation."
  - When significant, coefficients on trade openness and GVC participation are positive but "relatively small" and not consistent across inflation measures.
  - Trade openness * foreign output gap significant in Column (2) for headline inflation, suggesting foreign cyclical movements impact inflation more when economy is more open, but "magnitude of the effect is small."
- China decomposition:
  - External price pressure decomposed into Chinese and non-Chinese components.
  - Results (Columns (5) and (6) of Table 3):
    - External price pressure from China: -0.004 (Core), -0.002 (Headline) — not significant.
    - External price pressure excl. China: 0.018*** (Core), 0.007 (Headline).
  - Interpretation: "External price pressure from China does not have any significant impact on core or headline inflation dynamics, while non-Chinese external price pressures remain a significant determinant in the specification for core inflation."
- Selected coefficients and statistics from Table 3 (median-regression as reported):
  - Inflation expectations 3 years ahead: 0.643***, 0.406***, 0.632***, 0.378***, 0.551***, 0.399*** (across Columns (1)–(6)).
  - Lag of core/headline inflation: 0.479***, 0.422***, 0.479***, 0.427***, 0.502***, 0.426***.
  - Output gap: 0.154***, 0.223***, 0.173***, 0.194**, 0.163***, 0.206***.
  - Lag of external price pressure reported as 0.009, 0.011, -0.001, 0.029 (varying by specification).
  - Trade openness: 0.015* (Core), 0.026 (Headline) where reported.
  - GVC participation: 0.060** (Core), -0.033 (Headline) where reported.
  - External price pressure excl. China: 0.018*** (Core), 0.007 (Headline).
  - External price pressure from China: -0.004, -0.002.
  - Countries: 18 or 19 where reported; Observations: 624, 659, 633, 668, 627, 662; R-squared: 0.524, 0.453, 0.526, 0.446, 0.523, 0.446.

### Inflation Expectation Horizons
- Baseline uses three-year-ahead inflation expectations; robustness tests use horizons up to seven years ahead.
- Core inflation results are robust to horizon changes:
  - Coefficient on expected inflation for horizons three to seven years ahead range from 0.56 to 0.64 (reported as "(the coefficient on expected inflation for horizons three to seven years ahead range from 0.56 to 0.64)").
- Headline inflation:
  - Inflation expectations become insignificant for horizons of six years ahead and beyond, reflecting higher volatility of headline inflation relative to core inflation.
- Interpretation note: potential reverse causality from current inflation to inflation expectations at shorter horizons; decrease in estimated coefficients as horizon lengthens is consistent with this concern, but "the small magnitude of the differences suggests the effect is limited in economic terms."
- Selected coefficients and statistics from Table 4 (median-regression as reported):
  - Core inflation, inflation expectations n years ahead: 0.637*** (4-year), 0.614*** (5-year), 0.585*** (6-year), 0.560*** (7-year).
  - Headline inflation, inflation expectations n years ahead: 0.397** (4-year), 0.448* (5-year), 0.256 (6-year), -0.066 (7-year).
  - Lag of core/headline inflation ranges: 0.502*** to 0.549*** for core; 0.459*** to 0.537*** for headline across horizons.
  - Output gap coefficients and lag of external price pressure remain positive and significant for core across horizons; headline shows more variability and lower significance.
  - Countries: 18 or 19 where reported; Observations vary: 577, 603, 576, 576, 612, 638, 611, 610; R-squared: 0.514, 0.519, 0.513, 0.511, 0.446, 0.439, 0.442, 0.443.

### Robustness exercise conclusions (summarized findings)
- Domestic factors account for the lion’s share of inflation dynamics in emerging markets; fluctuations in longer-term inflation expectations (linked to domestic developments) are the main driver of average deviations of inflation from target and inflation variability.
- Contribution of global variables is not always statistically significant and is substantially smaller than domestic factors in economic terms.
- Robustness tests confirm:
  - The impact of global factors is marginal compared to domestic factors.
  - Inflation expectations reflect evolution of domestic variables rather than global developments.

*Source: 3.4 Robustness Exercises, wp18241*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18241.pdf_