## wp18280 - 2.1    Data

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### Data sources and coverage
- Inflation expectations: survey-based inflation forecasts from professional forecasters reported by Consensus Economics for horizons between three and seven years ahead.
- Horizon choice: focusing on horizons three years ahead and beyond "to ensure that beliefs about inflation in the long term are captured—rather than the effect of transitory shocks and the response of monetary policy."
- Frequency and availability:
  - Consensus Economics long-term inflation surveys are available at biannual frequency up to 2013 and quarterly thereafter.
  - Data covers 24 advanced and 21 emerging economies; the panel is unbalanced with surveys starting between 1989 and the early-1990s for most countries, but only since 2009 in a few cases.
  - Early Consensus Economics’ surveys only report mean forecasts; dispersion of responses available since 2005, or later in some cases.
- Moments used for each period t and forecast horizon h:
  - (i) Mean forecast: π^e,h_t = 1/T ∑_{t=1}^T π^e,h_{j,t}.
  - (ii) Dispersion: σ_t(π^e,h_j) = standard deviation across individual forecasts.
  - One-year-ahead horizon corresponds to forecasts for the current calendar year; two-year-ahead to the following calendar year; seven years ahead is the longest available.
- Inflation-target construction:
  - For inflation-targeting regimes, inflation targets for current year and up to seven years ahead retrieved from published central bank inflation reports.
  - Single announced target assumed to apply to current year and all subsequent years.
  - When only current-year and long-term targets are given without an explicit path, the long-term target is assumed to correspond to the inflation target three years after the last explicit short-term target.
  - For non-inflation-targeting economies, the inflation target at all horizons is set to the mean inflation forecast for the longest-term horizon, π^e,7+_t.
- Data limitations:
  - Long-term forecast dispersion is missing in early surveys; data availability is unbalanced across countries and time.
  - Commodity terms-of-trade index (used elsewhere) constructed from changes in international prices of 46 commodities weighted by net-export-to-GDP ratios (details appear elsewhere).

### Anchoring metrics constructed (context)
- Four complementary anchoring metrics computed for horizons h = 3,...,7:
  - Metric #1: root-mean-square deviation of mean inflation forecast at horizon h from the inflation target over period ω: √(1/T ∑_{t=1}^T (π^e,h_t − π^*_t)^2).
  - Metric #2: standard deviation of the mean inflation forecast at horizon h over period ω: √(1/(T−1) ∑_{t=1}^T (π^e,h_t − π^e,h)^2).
  - Metric #3: average over period ω of the standard deviation across individual forecasters at horizon h: 1/T ∑_{t=1}^T [√(1/(J−1) ∑_{j=1}^J (π^e,h_{j,t} − π^e,h_t)^2)].
  - Metric #4: sensitivity of h-year-ahead mean inflation forecasts to changes in short-term mean forecasts, β_h, from country-specific regressions over period ω: ∆π^e,h_t = α + β_h ∆π^e,1_t + ε_t.
- Computability and minimum-sample requirements:
  - Metrics #1 and #3 can be computed for each survey period t.
  - Metrics #2 and #4 require minimum numbers of surveys; analysis sets minima at 4 and 10, respectively.
- Treatment: metrics are complementary; no single metric fully captures anchoring.

*italics: wp18280 - 2.1    Data*

### A Summary Anchoring Index — construction and patterns
- Correlation across metrics: correlation between country rankings across any two anchoring measures based on three-year-ahead forecasts ranges from 0.56 to 0.87.
- Focus: anchoring index constructed from three-year-ahead inflation forecasts (longer horizons used in robustness checks).
- Standardization and aggregation:
  - For each metric m and horizon h, compute standardized measure z_{m,h,i,ω} = (x_{m,h,i,ω} − ̄x_{m,h}) / σ(x_{m,h}), where ̄x_{m,h} and σ(x_{m,h}) are the average and standard deviation of metric m (horizon h) across all countries and periods between 1989 and 2017.
  - Observations for each standardized metric are centered at zero with standard deviation one.
  - Anchoring index for horizon h = minus the simple average of the four standardized metrics z_{m,h,i,ω}; higher index ⇒ better anchoring.
- Aggregate evolution (three-year-ahead index, balanced panel, 1998–2017):
  - Extent of anchoring increased substantially over the sample period.
  - Upper decile broadly stable at about 0.5.
  - Bottom decile increased from about −1.5 in 1998–2003 to above zero at end of sample (2012–17).
  - Median increased from slightly below zero to about 0.3 over the sample period.
- Advanced vs. emerging economies:
  - Most improvement occurred among emerging economies, primarily up to mid-2000s; subsequent gains subdued.
  - Median anchoring in advanced economies relatively stable over two decades; interquartile range narrowed during 2000s due to improvements at the lower quartile.
  - Substantial cross-country heterogeneity among emerging economies:
    - Examples in source: Chile and Poland had anchoring higher than the advanced-economy average.
    - Examples in source: Argentina, Ukraine, and Russia had substantially lower index values (Argentina’s value is −1.5; visualization vertical axis minimum set to −0.5 in figure).

### Empirical correlates of anchoring (selected reported statistics)
- Relationship with actual inflation performance:
  - Strong nonlinear relationship between anchoring index and percent of time actual inflation is above its target (Figure 5, panel [a]).
  - Regression reported: Slope = .016; t-stat = 6.84; Slope ^2 = 0; t-stat ^2 = -9.82; R2 = .186.
- Exchange rate regime:
  - No evidence of significant association between anchoring and exchange rate regime (Ilzetzki et al., 2017 classification) (Figure 5, panel [b]).
  - Regression reported: Slope = .0028; t-stat = .58; R2 = 0.
- Central bank transparency:
  - Anchoring related to central bank policy transparency (Dinçer and Eichengreen, 2014).
  - Regression reported: Slope = .1006; t-stat = 17.88; R2 = .289.
- Inflation-targeting regime maturity:
  - Adoption and greater age of an IT regime associated with better-anchored expectations.
  - Regression reported: Slope = .042; t-stat = 10; R2 = .11.
- Fiscal sustainability and fiscal rules:
  - Anchoring positively related to market perception of public debt sustainability proxied by sovereign CDS spreads.
  - Regression reported for Log CDS Spread (Sovereign Debt (bps)): Slope = -.1246; t-stat = -8.85; R2 = .139.
  - Anchoring related to presence and duration of fiscal rules: number of years with fiscal rule: Slope = .0234; t-stat = 9.609999999999999; R2 = .11.

### Terms-of-trade shocks — motivation and facts
- Theory: well-anchored inflation expectations imply inflationary shocks have only temporary effects and inflation exhibits low persistence.
- Empirical proxy for external shock:
  - Country-specific commodity terms-of-trade index (Gruss, 2014): ∆ctot_{i,t} = sum_{c=1}^{C} ∆P_{c,t} · Ω_{i,c,t}, with P_{c,t} log real price of commodity c (c = 1,...,46) and Ω_{i,c,t} time-varying lagged weights.
  - Weights: Ω_{i,c,t} = (1/3) sum_{s=1}^{3} (x_{i,c,τ−s} − m_{i,c,τ−s}) / GDP_{i,τ−s}, where x = exports, m = imports, GDP in US dollars at year τ.
  - Interpretation: a one percentage point change in the commodity terms-of-trade index ≈ change in aggregate disposable income equivalent to one percentage point of GDP.
  - For interpretation, ∆ctot reversed so that positive change denotes a deterioration in terms of trade.
- Distributional facts for sample (Figure 6):
  - Distributions for advanced and emerging economies similar, centered around zero.
  - Standard deviation: advanced economies = 0.48; emerging economies = 0.44.
- Transmission channels:
  - Direct channel: international commodity price changes affect domestic consumer prices (ambiguous sign depending on net-exporter/importer status and consumption weights).
  - Indirect income channel: negative terms-of-trade shock lowers disposable income → reduces demand → downward pressure on consumer prices (unambiguous sign).
  - Exchange-rate channel (when exchange rate can adjust): deterioration triggers depreciation → inflationary impact on domestic-currency consumer prices (unambiguous sign).
- Empirical focus:
  - Condition responses on exchange rate regime; focus on floats (flexible regimes) where exchange-rate propagation channel is present.
  - Hypothesis: inflationary effect of a negative terms-of-trade shock that triggers depreciation is smaller and fades quicker when inflation expectations are better anchored; test whether cumulative CPI response depends on pre-shock anchoring.

### Source attribution
*Source: Authors’ calculations, as presented in the PDF chapter titled "2.3    A Summary Anchoring Index".*

### 3.2    Empirical Approach and Main Results

### Empirical strategy and estimation details
- Estimation method: local projection method of Jordà (2005) to estimate cumulative CPI response over 12 months to a change in country-specific commodity terms of trade index in panel setting.
- Baseline specification: equation (7) estimated by ordinary least squares for h = 1,...,12.
- Controls and fixed effects:
  - μi = country fixed effects; νt = time fixed effects.
  - J = 12 lags of the change in consumer prices (∆p).
  - anchor = average value of the inflation expectations anchoring index over a rolling six-year window.
  - flex = dummy = 0 for fixed exchange rate regimes and = 1 otherwise (Ilzetzki et al., 2017 classification).
- Standard errors:
  - Country-based cluster-robust standard errors (following Jordà et al., 2015).
  - Driscoll and Kraay (1998) used in robustness exercises.
- Sample:
  - Data for 31 economies at monthly frequency over 1999m1–2017m12.
  - Exclusions: euro area countries (no independent monetary authority), Venezuela (hyperinflation during sample), and Ukraine (civil war effects).
- Interpretation:
  - Dependent variable: cumulative change in log CPI between t−1 and t+h; estimated βh = cumulative impact of an innovation in terms of trade on CPI.
  - Conditional cumulative effect of ∆ctot on CPI: δ(pi,t+h−1 − pi,t−1)/δ∆ctot i,t = βh3 + βh4 flex i,t + βh5 anchor i,t + βh6 flex i,t × anchor i,t, for h = 1,...,12.
  - Estimated βh6 is negative for all h = 1,...,12 and statistically significant at the 99 percent confidence level, implying that for floats, better-anchored inflation expectations are associated with a smaller increase in consumer prices following a negative terms-of-trade shock.

### Main findings — exchange rate regime heterogeneity
- Flexible vs fixed regimes:
  - Negative terms-of-trade shock leads to a significant increase in consumer prices in economies with flexible exchange rate regimes.
  - Response of consumer prices for pegs (flex = 0) is statistically indistinguishable from zero.
- Reported figure context:
  - Cumulative response corresponds to a negative terms-of-trade shock of 1 percent.
  - Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

### Role of anchoring among floats — level of prices (selected quantitative results)
- Anchoring distribution among floats:
  - Standard deviation of anchoring = 0.68 for 1998–2017 and = 0.27 for 2012–2017.
- CPI level response to a negative terms-of-trade shock (drop in disposable income of one percent of GDP) for floats:
  - Weakly anchored (anchor = 25th percentile): CPI increases by 0.35 percentage point after six months and 0.55 percentage point one year after the shock.
  - Strongly anchored (anchor = 75th percentile): cumulative response of consumer prices is indistinguishable from zero.
  - Difference between weakly and strongly anchored responses is statistically significant at the 95 percent confidence level.
- Marginal effects at six-month horizon:
  - Marginal effect at anchor = 25th percentile ≈ 0.38 percent.
  - Marginal effect at anchor = 10th percentile ≈ 0.93 percent (anchoring index ≈ −0.75).
  - Marginal effect at anchor = 95th percentile = [−0.17] percent (negative effect reflecting weaker domestic demand dominating).

### Role of anchoring — inflation rate persistence (selected quantitative results)
- Redefinition: dependent variable = month-on-month inflation rate (∆p_i,t+h−1 annualized) for h = 1,...,12.
- Reported dynamics (Figure 11):
  - Poorly anchored expectations:
    - Inflation rate increases by about 1.10 percentage points three months after the shock.
    - Month-on-month inflation rate remains more than 0.60 percentage point above pre-shock level even 12 months after the shock.
  - Strongly anchored expectations:
    - Inflation increases somewhat (response after two months ≈ 0.32 percentage points, significant at the 95 percent confidence level).
    - Inflation returns quickly to pre-shock level; response not statistically different from zero three months after the shock.

### Exchange rate depreciation and pass-through
- Alternative dependent variables: natural logarithm of nominal bilateral exchange rate (local currency per U.S. dollar) and import-weighted nominal effective exchange rate (NEER).
- NEER definition: ∆neer_i,t = Σ_{j=1, j≠i}^J ωij,t (∆e_i,t − ∆e_j,t), where e_i,t is log bilateral exchange rate (local currency per U.S. dollar) and ωij,t are import shares lagged one year.
- Findings:
  - Depreciation magnitude following terms-of-trade shocks is not significantly related to anchoring extent.
  - Exchange rate response somewhat larger for weakly-anchored countries than for well-anchored ones, but differences generally not statistically significant.
  - Marginal effect after 6 months: does not differ significantly for different anchoring values (Figure 14, panel [a]).
  - NEER results: depreciation may be somewhat larger when expectations are poorly anchored (Figures 13 and 14, panel [b]); differences statistically significant for a few horizons only.
- Interpretation:
  - Weak significance of anchoring on exchange rate response, combined with strong significance for consumer prices, suggests:
    - Exchange rate tends to depreciate more when expectations are poorly anchored.
    - Pass-through from a given currency depreciation triggered by a terms-of-trade shock appears larger when inflation expectations are poorly anchored.

### Selected reported coefficients and statistics (Tables A.2 and A.3)
- Table A.2 (Cumulative Response of Consumer Prices) — sample: Countries = 31; Observations = 6,214; R-squared rises from 0.569 to 0.775 across horizons:
  - ∆ctotXflex coefficients (h = 1..12): 0.023, 0.077, 0.149**, 0.190***, 0.247***, 0.294***, 0.340***, 0.395***, 0.441***, 0.471***, 0.533***, 0.624***.
  - ∆ctotXanchorXflex coefficients (h = 1..12): -0.160***, -0.310***, -0.475***, -0.559***, -0.649***, -0.810***, -0.949***, -1.016***, -1.154***, -1.385***, -1.535***, -1.638***.
  - Notes: All regressions include 12 lags of ∆p and country and time fixed effects. Country-based cluster-robust standard errors in parentheses. ∆ctot reversed so that positive change denotes a deterioration in the terms of trade. ***p <0.01, **p <0.05, *p <0.1.
- Table A.3 (Response of Consumer Price Inflation) — sample: Countries = 31; Observations = 6,214; R-squared ranges from 0.569 to 0.477 across horizons:
  - ∆ctotXflex coefficients (h = 1..12): 0.277, 0.652**, 0.860**, 0.491*, 0.684**, 0.558, 0.563, 0.660*, 0.543, 0.359, 0.743**, 1.092**.
  - ∆ctotXanchorXflex coefficients (h = 1..12): -1.924***, -1.799***, -1.979**, -1.001**, -1.081, -1.941**, -1.665**, -0.803, -1.654***, -2.771***, -1.803**, -1.232**.
  - Notes: Same regression controls and significance conventions as Table A.2.

### 3.4    Robustness

### Robustness checks and outcomes
- Overview: robustness tests for CPI response differences between strongly and weakly anchored expectations; baseline in panel (a) of Figure 15; panels (b)–(f) present alternative specifications.
- Alternative exchange rate classifications:
  - Panel (b): includes observations of free falling exchange rates (very high inflation, over 40 percent per year) within Ilzetzki et al. (2017) classification.
  - Panel (c): uses updated Shambaugh (2004) classification.
  - Finding: results under both alternative classifications are very similar to baseline.
- Standard error correction:
  - Panel (d): Driscoll and Kraay (1998) standard errors (account for cross-sectional dependence) instead of clustering by country.
  - Finding: confidence intervals wider under Driscoll and Kraay (1998), but null that responses under strongly and weakly anchored expectations are equal can still be rejected at the 95 percent confidence level.
- Anchoring index composition:
  - Concern: Metric #4 could be higher if inflation is inherently more persistent, biasing anchoring index.
  - Panel (e): results when Metric #4 is excluded from anchoring index.
  - Finding: main result holds when Metric #4 excluded.
- Expectation horizon:
  - Baseline uses three-year-ahead expectations.
  - Panel (f): uses five-year-ahead expectations.
  - Finding: main result holds when using five-year-ahead expectations.

### Key quantitative implications (from Conclusions and estimations)
- Index construction: survey-based long-term inflation forecasts used to construct anchoring index for 45 advanced and emerging economies starting in 1989.
- Cross-country evolution: anchoring improved significantly over past two decades, especially among emerging economies, but substantial heterogeneity persists.
- Main empirical result (terms-of-trade shock → consumer prices, conditional on flexible exchange rates):
  - When anchoring at 25th percentile (poorly anchored), a negative terms-of-trade shock of 1 percent (deterioration equivalent to drop in aggregate disposable income of one percent of GDP) leads to persistent increase in consumer price inflation: annualized month-on-month inflation rate remains more than 0.6 percentage point above pre-shock level one year after the shock.
  - When anchoring at 75th percentile (strongly anchored), response of inflation much smaller—about 0.3 percent after two months—and returns to pre-shock level by three months after the shock.
- Policy implication: poorly anchored expectations make temporary shocks to inflation have more durable effects on consumer price dynamics and require a stronger policy reaction to bring inflation under control.

*Source: wp18280 - 3.4 Robustness (Authors’ calculations).*

### 2.1    Data  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 

### wp18280 - 2.1    Data

### Overview of data sources and coverage
- Inflation expectations are measured using survey-based inflation forecasts from professional forecasters reported by Consensus Economics for horizons between three and seven years ahead.
- Focusing on horizons three years ahead and beyond is intended "to ensure that beliefs about inflation in the long term are captured—rather than the effect of transitory shocks and the response of monetary policy."
- Consensus Economics long-term inflation surveys are available at biannual frequency up to 2013 and quarterly thereafter.
- The data covers 24 advanced and 21 emerging economies but is unbalanced, with surveys starting between 1989 and the early-1990s for most countries, but only since 2009 in a few cases.
- Early Consensus Economics’ surveys only report mean forecasts; the dispersion of responses is only available since 2005, or even later in a few cases.

### Inflation expectations: moments used
- For each period t in which there is a survey and forecast horizon h, two moments of the distribution of responses by individual forecasters j are used:
  - (i) the average of individual inflation forecasts, π^e,h_t = 1/T ∑_{t=1}^T π^e,h_{j,t};
  - (ii) the standard deviation across individual forecasts, σ_t(π^e,h_j).
- The one-year-ahead horizon in any given Consensus survey corresponds to forecasts for the current calendar year; the two-year-ahead horizon corresponds to the following calendar year; and so forth.
- The horizon of seven years ahead and beyond is the longest available.

### Inflation target construction
- For inflation-targeting regimes, inflation targets at each point in time for the current year and up to seven years ahead are retrieved from published central bank inflation reports.
- When a single target is announced, it is assumed to refer to the objective for the current year as well as for all subsequent years.
- When a target is announced for the current year and the long term but without an explicit path for intermediate targets, the assumption is that the long-term target corresponds to the inflation target three years after the last explicit short-term target.
- For economies that do not follow inflation-targeting regimes, the inflation target at all horizons is set to the mean inflation forecast for the longest-term horizon, π^e,7+_t.

### Data limitations and sample notes
- Data availability is unbalanced across countries and time; long-term forecast dispersion is missing in early surveys.
- Annex Figure A.1 and Table A.1 summarize data availability (not reproduced here).
- The commodity terms-of-trade index used elsewhere in the study is constructed from the change in the international price of 46 commodities weighted by the ratio of net exports of each commodity to GDP (description appears elsewhere in the source).

### Link to anchoring metrics (context for subsequent analysis)
- The paper constructs four complementary anchoring metrics using the Consensus long-term forecasts (computed for horizons h = 3,...,7):
  - Metric #1 — root-mean-square deviation of mean inflation forecast at horizon h from the inflation target over period ω: √(1/T ∑_{t=1}^T (π^e,h_t − π^*_t)^2).
  - Metric #2 — standard deviation of the mean inflation forecast at horizon h over period ω: √(1/(T−1) ∑_{t=1}^T (π^e,h_t − π^e,h)^2).
  - Metric #3 — average over period ω of the standard deviation across individual forecasters at horizon h: 1/T ∑_{t=1}^T [√(1/(J−1) ∑_{j=1}^J (π^e,h_{j,t} − π^e,h_t)^2)].
  - Metric #4 — sensitivity of h-year-ahead mean inflation forecasts to changes in short-term mean forecasts, β_h, from country-specific regressions over period ω: ∆π^e,h_t = α + β_h ∆π^e,1_t + ε_t.
- Metrics #1 and #3 can be computed for each period t with a survey; Metrics #2 and #4 require a minimum number of surveys. In the analysis that follows, minimum numbers are set at 4 and 10, respectively.
- The four metrics are treated as complementary; no single metric fully captures anchoring and each has advantages and shortcomings, including data coverage.

_italics: wp18280 - 2.1    Data_

### 2.3    A Summary Anchoring Index

### 2.3    A Summary Anchoring Index

### Overview
- The four anchoring metrics convey a consistent picture: the correlation between the relative ranking of countries across any two of the anchoring measures based on three-year-ahead inflation forecasts ranges from 0.56 to 0.87.
- The analysis focuses on the anchoring index constructed from three-year ahead inflation forecasts (with longer horizons considered in robustness exercises in section 3.4).
- Sample and timing references: metrics averaged across all countries and periods between 1989 and 2017; evolution shown for a balanced sample of economies with data available since 1998 using six-year rolling windows.

### Construction of the anchoring index
- For each metric m based on h-years ahead inflation expectations x_{m,h,i,ω} (i denotes countries; ω denotes periods/rolling windows):
  - Construct standardized measure z_{m,h,i,ω} = (x_{m,h,i,ω} − ̄x_{m,h}) / σ(x_{m,h}), where ̄x_{m,h} and σ(x_{m,h}) are the average and standard deviation of metric m (at horizon h) across all countries and periods between 1989 and 2017.
  - Observations for each standardized metric are centered at zero with standard deviation one.
  - The anchoring index for horizon h is minus the simple average of the four standardized metrics (z_{m,h,i,ω}), so that a higher (lower) value of the index corresponds to a better (worse) anchoring of inflation expectations.

### Evolution and cross-country patterns (1998–2017)
- Aggregate evolution (three-year-ahead index, balanced panel):
  - The extent of anchoring increased substantially over the sample period.
  - Upper decile of the distribution remained broadly stable at a value of about 0.5.
  - Bottom decile increased from about −1.5 in the first subperiod (1998–2003) to above zero at the end of the sample (2012–17).
  - Median across countries increased from slightly below zero to about 0.3 over the sample period.
- Advanced vs. emerging economies:
  - The lion’s share of improvement occurred among emerging economies, primarily up to the mid-2000s; subsequent gains were subdued.
  - Median anchoring across advanced economies was relatively stable over the past two decades; interquartile range narrowed during the 2000s due to improvements at the lower quartile.
  - Cross-country heterogeneity is substantial, especially among emerging economies.
    - Some emerging economies (example labels in source: Chile and Poland) had anchoring higher than the advanced-economy average.
    - Others (example labels in source: Argentina, Ukraine, and Russia) had substantially lower index values (Argentina’s value is −1.5; vertical axis minimum was set to −0.5 in the figure for visualization).

### Empirical relationships and correlates of anchoring
- Relationship with actual inflation performance:
  - Evidence points to a strong nonlinear relationship between the anchoring index and the percent of time that actual inflation is above its target (Figure 5, panel [a]).
  - The highest anchoring levels are observed when actual inflation was higher than the target only half of the time.
  - Regression/statistics reported for panel (a): Slope = .016; t-stat = 6.84; Slope ^2 = 0; t-stat ^2 = -9.82; R2 = .186.
- Exchange rate regime:
  - No evidence of a significant association between anchoring and the exchange rate regime as measured by Ilzetzki et al. (2017) de facto regime classification (Figure 5, panel [b]).
  - Regression/statistics reported for panel (b): Slope = .0028; t-stat = .58; R2 = 0.
- Central bank transparency:
  - The extent of anchoring appears related to central bank policy transparency (Dinçer and Eichengreen, 2014).
  - Regression/statistics reported for panel (c): Slope = .1006; t-stat = 17.88; R2 = .289.
- Inflation-targeting regime maturity:
  - Adopting an inflation targeting (IT) regime is closely associated with increased transparency and better-anchored expectations.
  - Evidence shows inflation expectations are better-anchored in countries that adopted an IT regime and with greater age of the regime.
  - Regression/statistics reported for panel (d): Slope = .042; t-stat = 10; R2 = .11.
- Fiscal sustainability and fiscal rules:
  - Anchoring is positively related to market perception about public debt sustainability proxied by sovereign CDS spreads.
  - Regression/statistics reported for panel (e) (fiscal sustainability / Log CDS Spread, Sovereign Debt (bps)): Slope = -.1246; t-stat = -8.85; R2 = .139.
  - The extent of anchoring is also related to whether a fiscal rule is in place and, in particular, to how long a fiscal rule has been in place.
  - Regression/statistics reported for panel (f) (number of years with fiscal rule): Slope = .0234; t-stat = 9.609999999999999; R2 = .11.
- Summary: findings support coherence of the anchoring index; determinants such as central bank transparency, maturity of IT regimes, fiscal sustainability, and fiscal rules are associated with higher anchoring, while exchange rate regime shows no robust association.

### Terms-of-trade shocks and inflation persistence (motivation for subsequent analysis)
- Theory: well-anchored inflation expectations imply inflationary shocks should have only temporary effects and inflation should exhibit low persistence.
- Empirical approach:
  - Focus on consumer price responses to external terms-of-trade shocks proxied by changes in a country-specific commodity terms of trade index (Gruss, 2014).
  - Define ∆ctot_{i,t} = sum_{c=1}^{C} ∆P_{c,t} · Ω_{i,c,t}, where P_{c,t} is log real price of commodity c in period t (c = 1,...,46) and Ω_{i,c,t} are time-varying, lagged weights.
  - Weights computed as Ω_{i,c,t} = (1/3) sum_{s=1}^{3} (x_{i,c,τ−s} − m_{i,c,τ−s}) / GDP_{i,τ−s}, with x (exports), m (imports), and GDP in US dollars at year τ.
  - A one percentage point change in the commodity terms-of-trade index can be interpreted as a change in aggregate disposable income equivalent to one percentage point of GDP.
  - For interpretation, variations in ctot have been reversed so that a positive change denotes a deterioration in the terms of trade.
- Distributional facts for estimation sample (Figure 6):
  - Distributions for both advanced and emerging economies are very similar, centered around zero.
  - Standard deviation for advanced economies is 0.48; for emerging economies is 0.44.
- Channels by which terms-of-trade shocks affect consumer prices:
  - Direct channel: change in international commodity prices affects domestic consumer prices (ambiguous sign depending on net exporter/importer status and consumption weights).
  - Indirect income channel: a negative terms-of-trade shock lowers aggregate disposable income, reducing aggregate demand and putting downward pressure on consumer prices (unambiguous sign).
  - Exchange-rate channel (present when exchange rate can adjust): a deterioration in terms of trade triggers depreciation, which has an unambiguous inflationary impact on domestic-currency consumer prices.
- Empirical focus for subsequent analysis:
  - Condition responses on the exchange rate regime and focus on the effect of anchoring within floats (relatively flexible exchange rate regimes) where the exchange-rate propagation channel is present.
  - Hypothesis to be tested: the inflationary effect of a negative terms-of-trade shock that triggers depreciation is smaller and fades quicker when inflation expectations are better anchored; test whether cumulative response of consumer prices after a terms-of-trade shock depends on pre-shock anchoring.

*Source: Authors’ calculations, as presented in the PDF chapter titled "2.3    A Summary Anchoring Index".*

### 3.2    Empirical Approach and Main Results

### 3.2    Empirical Approach and Main Results

### Empirical strategy and estimation
- Method: local projection method of Jordà (2005) to estimate the cumulative response of the consumer price index over 12 months to a change in the country-specific commodity terms of trade index in a panel setting.
- Baseline specification: equation (7) (see source) estimated by ordinary least squares for each h = 1,...,12.
- Fixed effects and controls:
  - μi are country fixed effects; νt are time fixed effects.
  - J = 12 lags of the change in consumer prices (∆p) are included.
  - anchor: average value of the inflation expectations anchoring index over a rolling six-year window.
  - flex: dummy = 0 for fixed exchange rate regimes and = 1 otherwise (Ilzetzki et al., 2017 classification).
- Standard errors: country-based cluster-robust standard errors (following Jordà et al., 2015). Driscoll and Kraay (1998) used in robustness exercises.
- Sample: data for 31 economies at monthly frequency over 1999m1–2017m12.
- Exclusions: euro area countries (no independent monetary authority), Venezuela (hyperinflation during sample), and Ukraine (civil war effects).

### Key estimation details and interpretation
- Dependent variable in baseline: cumulative change in log CPI between t−1 and t+h; estimated βh is the cumulative impact of an innovation in the terms of trade on CPI.
- Conditional cumulative effect of a change in ∆ctot on CPI given in equation (8):
  - δ(pi,t+h−1 − pi,t−1)/δ∆ctot i,t = βh3 + βh4 flex i,t + βh5 anchor i,t + βh6 flex i,t × anchor i,t, for h = 1,...,12.
- The estimated coefficient βh6 is negative for all h = 1,...,12 and statistically significant at the 99 percent confidence level, implying that, for floats, better-anchored inflation expectations are associated with a smaller increase in consumer prices following a negative terms-of-trade shock.

### Main findings — exchange rate regime heterogeneity
- Flexible vs fixed regimes:
  - A negative terms-of-trade shock leads to a significant increase in consumer prices in economies with flexible exchange rate regimes.
  - The response of consumer prices for pegs (flex = 0) is statistically indistinguishable from zero.
- Figure summary (as reported):
  - The cumulative response shown corresponds to a negative terms-of-trade shock of 1 percent.
  - Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

### Role of anchoring among floats — level of prices
- Distribution of anchoring among floats:
  - Anchoring displays substantial variability across countries and periods (panels for 1998–2017 and 2012–2017).
  - Standard deviation of anchoring: 0.68 for 1998–2017 and 0.27 for 2012–2017.
- CPI level response for floats to a negative terms-of-trade shock associated with a drop in disposable income of one percent of GDP:
  - Under weakly anchored expectations (anchor = 25th percentile): CPI increases by 0.35 percentage point after six months and 0.55 percentage point one year after the shock.
  - Under strongly anchored expectations (anchor = 75th percentile): cumulative response of consumer prices is indistinguishable from zero.
  - The difference between weakly and strongly anchored responses is statistically significant at the 95 percent confidence level.
- Marginal effect at specific anchoring percentiles (6-month horizon):
  - Marginal effect at anchor = 25th percentile ≈ 0.38 percent.
  - Marginal effect at anchor = 10th percentile ≈ 0.93 percent (anchoring index ≈ −0.75).
  - Marginal effect at anchor = 95th percentile = [−0.17] percent (negative effect reflecting weaker domestic demand dominating).

### Role of anchoring — inflation rate persistence
- Redefinition: dependent variable redefined as month-on-month inflation rate (∆p i,t+h−1 annualized) for h = 1,...,12.
- Reported results (Figure 11):
  - Under poorly anchored expectations:
    - Inflation rate increases by about 1.10 percentage points three months after the shock.
    - Month-on-month inflation rate remains more than 0.60 percentage point above its pre-shock level even 12 months after the shock.
  - Under strongly anchored expectations:
    - Inflation increases somewhat (response after two months ≈ 0.32 percentage points, statistically significant at the 95 percent confidence level).
    - Inflation rate returns quickly to pre-shock level; response is not statistically different from zero three months after the shock.

### Exchange rate depreciation and pass-through
- Question: Is higher inflation persistence when expectations are poorly anchored driven by larger currency depreciation or larger exchange rate pass-through?
- Alternative dependent variables: natural logarithm of the nominal bilateral exchange rate (local currency per U.S. dollar) and the import-weighted nominal effective exchange rate (NEER).
- NEER definition used:
  - ∆neer i,t = Σ_{j=1, j≠i}^J ωij,t (∆e i,t − ∆e j,t), where e i,t is log bilateral exchange rate (local currency per U.S. dollar), and ωij,t are import shares from IMF Direction of Trade Statistics lagged one year.
- Nominal exchange rate results:
  - Depreciation magnitude following terms-of-trade shocks is not significantly related to the extent of anchoring.
  - Response of the exchange rate is somewhat larger for weakly-anchored countries than for well-anchored countries, but the difference is generally not statistically significant.
  - Marginal effect after 6 months: does not differ significantly for different anchoring values (Figure 14, panel [a]).
- Nominal effective exchange rate results:
  - Depreciation may be somewhat larger when expectations are poorly anchored (Figures 13 and 14, panel [b]).
  - Differences are only statistically significant for a few horizons.
- Interpretation:
  - Weak significance of anchoring on exchange rate response, together with strong significance for consumer prices, suggests two mechanisms:
    - The exchange rate appears to depreciate by more when expectations are poorly anchored.
    - The pass-through rate from a given currency depreciation triggered by a terms-of-trade shock seems to be larger when inflation expectations are poorly anchored.

*Source: wp18280 - 3.2    Empirical Approach and Main Results*

### 3.4    Robustness

### 3.4 Robustness

### Robustness tests — overview
- The section presents robustness tests to the main findings on the response of the CPI based on equation (7) when inflation expectations are strongly and weakly anchored.  
- Baseline results are reported in panel (a) of Figure 15 for convenience; panels (b)–(f) present alternative specifications and checks.

### Alternative exchange rate classifications (Figure 15, panels b and c)
- Panel (b): Uses Ilzetzki et al. (2017) classification but includes observations of free falling exchange rates (regimes with very high inflation, over 40 percent per year) that are often lumped with ordinary flexible regimes.
- Panel (c): Uses the updated exchange rate classification of Shambaugh (2004).
- Finding: The results under both alternative exchange rate classifications are very similar to the baseline results.

### Standard error correction (Figure 15, panel d)
- Panel (d): Standard errors corrected using the Driscoll and Kraay (1998) procedure (which accounts for cross-sectional dependence) instead of clustering by country.
- Finding: Confidence intervals are wider under Driscoll and Kraay (1998) standard errors, but the null that the responses of consumer prices under strongly and weakly anchored expectations are equal can still be rejected at the 95 percent confidence level.

### Anchoring index composition (Figure 15, panel e)
- Concern: Metric #4 (sensitivity of long-term expectations to inflation surprises) could be higher if inflation is inherently more persistent, potentially biasing the anchoring index.
- Panel (e): Presents results when Metric #4 is excluded from the anchoring index.
- Finding: The main result holds when Metric #4 is excluded.

### Expectation horizon (Figure 15, panel f)
- Baseline: Anchoring index based on three-year ahead inflation expectations.
- Panel (f): Uses five-year ahead inflation expectations instead.
- Finding: The main result holds when using five-year ahead inflation expectations.

### Key quantitative findings and implications (from Conclusions and estimations)
- Index construction: Survey-based long-term inflation forecasts used to construct an anchoring index for 45 advanced and emerging economies starting in 1989.
- Cross-country evolution: The extent of anchoring of inflation expectations improved significantly over the past two decades, especially among emerging economies, but substantial heterogeneity persists.
- Main empirical result (terms-of-trade shock → consumer prices, conditional on flexible exchange rates):
  - When anchoring is at the 25th percentile (poorly anchored), a negative terms-of-trade shock of 1 percent (deterioration in the commodity terms-of-trade index equivalent to a drop of aggregate disposable income of one percent of GDP) leads to a significant and persistent increase in consumer price inflation: the annualized month-on-month inflation rate remains more than 0.6 percentage point above its pre-shock level one year after the shock.
  - When anchoring is at the 75th percentile (strongly anchored), the response of inflation is much smaller—about 0.3 percent after two months—and returns to its pre-shock level only three months after the shock.
- Policy implication: Poorly anchored expectations make temporary shocks to inflation have more durable effects on consumer price dynamics and require a stronger policy reaction to bring inflation under control.

### Supporting estimation evidence (selected quantitative elements from tables)
- Table A.2 (Cumulative Response of Consumer Prices): regression results include:
  - ∆ctotXflex coefficients (cumulative response coefficients rise over horizons, with values including 0.023, 0.077, 0.149**, 0.190***, 0.247***, 0.294***, 0.340***, 0.395***, 0.441***, 0.471***, 0.533***, 0.624*** for h=1..12).
  - ∆ctotXanchorXflex coefficients (negative and statistically significant across horizons: -0.160***, -0.310***, -0.475***, -0.559***, -0.649***, -0.810***, -0.949***, -1.016***, -1.154***, -1.385***, -1.535***, -1.638*** for h=1..12).
  - Sample: Countries = 31; Observations = 6,214; R-squared rises from 0.569 to 0.775 across horizons.
  - Notes: All regressions include 12 lags of the change in consumer prices, and country and time fixed effects. Country-based cluster-robust standard errors in parentheses. ∆ctot is reversed so that a positive change denotes a deterioration in the terms of trade. ***p <0.01, **p <0.05, *p <0.1.
- Table A.3 (Response of Consumer Price Inflation): selected coefficients include:
  - ∆ctotXflex coefficients (e.g., 0.277, 0.652**, 0.860**, 0.491*, 0.684**, 0.558, 0.563, 0.660*, 0.543, 0.359, 0.743**, 1.092** for h=1..12).
  - ∆ctotXanchorXflex coefficients (large negative and often statistically significant: -1.924***, -1.799***, -1.979**, -1.001**, -1.081, -1.941**, -1.665**, -0.803, -1.654***, -2.771***, -1.803**, -1.232** for h=1..12).
  - Sample: Countries = 31; Observations = 6,214; R-squared ranges from 0.569 to 0.477 across horizons.
  - Notes: Same regression controls and significance conventions as Table A.2.

*Source: Authors’ calculations.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18280.pdf_