## _wp1455 - 0.05 implies that the null can be rejected at a 95% level of confidence.

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---

### C. First-Order Autocorrelations
- Model and estimation
  - Inflation is modeled as a stationary autoregressive AR(p) process; focus on an AR(1) specification (equation (1)).
  - In (1), persistence is the parameter a, with πt quarterly inflation, k a constant, and ε an iid shock to inflation.
  - a can be regarded as the persistence of all previous inflation shocks when (1) is expressed in moving average form.
  - a is estimated by OLS without correction for bias because there is no evidence that quarterly inflation in the sample exhibits a time trend or is a “near-unit root” process in the sense of Andrews and Chen (1994).
- Half-life interpretation and results
  - Half-life is the estimated time taken for half of a shock to the quarterly inflation rate to fade (computed from the estimate of a).
  - Estimates are based on the regression (1) over 2000 Q1 to 2013 Q2.
  - Estimated half-lives and 95 percent confidence intervals (lower interval bounded at zero) are presented in Figure 1 for headline inflation.
  - Half-lives for shocks to headline inflation range from:
    - less than half of one quarter (Canada and New Zealand)
    - to over four quarters (Romania)
  - Latin American countries, including Brazil, are mainly in the upper end of the range but are broadly comparable with their IT peer group.
- Robustness to additional lags
  - Generalizing the AR(1) model to incorporate more lags was found unnecessary for most countries.
  - Partial autocorrelations indicate that the impact of changes in inflation two or more quarters earlier is typically insignificant for the current quarter’s inflation.
  - Specifically, lags of p>1 were statistically significant for only one country for headline inflation out of a total sample size of 33 countries.

### D. Rolling Regressions
- Motivation and method
  - Persistence can vary through time; estimates of persistence can change dramatically based on the sample period, particularly in Latin America and Brazil.
  - To account for time variation, half-lives are estimated using the parameter a from (1) with shorter rolling samples.
  - Rolling regressions use overlapping rolling 8 year samples of quarterly data to balance assessment of time-variation with sufficiently large sample periods.
  - The first sample is Q1 1995 through Q4 2002; the second sample runs Q2 1995 through Q1 2003, and so on. Dates on the charts refer to the end date of each estimation.
- Treatment of nonpositive a and inference
  - When a ≤ 0, the half-life is not defined and is represented by breaks in the time series (some series have large parts not defined, e.g., Norway).
  - When it is not possible to reject the null that a (and the half-life) is zero, the lower 95 percent confidence interval for the half-life is not defined and only the upper interval is shown.
- Empirical findings by country grouping
  - Benchmark cases:
    - Canada and New Zealand show rolling half-lives that are both low and statistically insignificant.
  - Latin America:
    - Experiences vary by country; there is no clear evidence (with one exception) that persistence is declining firmly towards the low levels of Canada or New Zealand.
    - In some cases persistence fell during the early years of IT (e.g., Colombia and Peru).
    - For most countries in the region since 2008:
      - persistence has remained broadly constant and statistically significant (Chile)
      - or increased (Colombia, Guatemala, and Peru)
    - The one exception is Mexico, where persistence is now statistically insignificant following the large sustained decline that followed the [sample period described].

### Inflation persistence: broad patterns and Brazil-specific dynamics (introduction of IT in 2001)
- Broad observations
  - Inflation persistence measured by half-lives fell substantially from a level of "almost 2 quarters" in 2010, but this apparent step-decline is mainly due to the 2002-03 period falling out of the 8-year sample window.
  - Excluding the 2002-03 effect (for example by selecting samples that start in 2004) shows persistence has been more stable.
  - Persistence has increased since 2009 in Brazil.
  - Backward-looking autoregressive approaches can be strongly influenced by historical outliers and less by more recent developments.
- Figures and sample windows referenced
  - Rolling estimates and plots span 2002-Q1 to 2013-Q4 for inflation shock half-lives across countries.
  - Brazil: rolling half-life series compared inflation and GDP from Q4-2002 to Q4-2013 (half-life in quarters).

### E. Output Growth as the driving process
- Proxy and rationale
  - Driving process proxy used: quarterly change in log real GDP (selected because of lack of comparable marginal cost data and uncertainties about output gap measurement).
- Empirical comparisons
  - Scatter plots compare AR(1) coefficients for quarterly change in inflation and GDP using:
    - Full sample starting in Q1 2000.
    - Three 32-quarter sub-samples ending in Q2 2008, Q2 2010, and Q2 2013 (GDP data end two quarters earlier).
  - For all sample periods, the linear correlation between the inflation and GDP AR(1) coefficients was only weakly positive and not statistically significant.
  - Structural models suggest this weak reduced-form relationship could reflect either:
    - A modest impact of the driving process (output growth) on inflation; or
    - Significant idiosyncratic white noise inflation variance.
- Brazil-specific dynamics
  - Rolling estimates of the half-life of quarterly GDP growth have been rising but at a very moderate pace.
  - This contrasts with the large rise and subsequent decline in the inflation half-life.
  - Interpretation: inherited persistence may explain some fluctuations in inflation persistence, but intrinsic persistence (including indexation) and changes in the monetary policy reaction function are likely important.

### III. Forward-looking persistence: concept and rationale
- Limitations of historical estimates
  - Historical-data-based estimates are backward looking and can be slow to pick up changes in persistence.
  - Reducing sample size (rolling estimates) increases weight on recent observations but risks dependence on outliers.
- Use of expectations
  - Alternative: use inflation expectations as a more timely indicator of how long inflation shocks will persist.
  - If expectations are "good" forecasters, measure the effect of changes in actual inflation on those expectations.
  - Survey expectations can provide a leading indicator if they influence price-setters' behavior.

### A. Data (measurement and samples)
- Monthly measures and sample
  - Monthly inflation measure: annual change in the headline consumer price index for each country.
  - Sample period: January 2000 through January 2014.
- Inflation expectations
  - Inflation expectations: predictions for the annual rate of inflation 12 months ahead from surveys (central banks, statistical agencies, private firms).
  - When multiple survey observations exist in a month, the latest available data point is selected.
- Unit-root and cointegration summary
  - Almost all series are stationary; where non-stationary, strong evidence of cointegration between inflation and expectations is reported.
- Statistical summary (Table 2) — selected country statistics (Headline CPI Inflation and 12-Month Expected Inflation — percent unless specified)
  - Brazil (Number of observations 147): Headline CPI Inflation — Mean 6.54; Min 2.96; Max 17.24; Standard deviation 2.93. 12-Month Expected Inflation — Mean 5.36; Min 3.43; Max 12.52; Standard deviation 1.45.
  - Chile (Number of observations 104): Headline CPI Inflation — Mean 3.46; Min -2.29; Max 9.85; Standard deviation 2.57. 12-Month Expected Inflation — Mean 3.21; Min 2.00; Max 6.00; Standard deviation 0.67.
  - Colombia (Number of observations 124): Headline CPI Inflation — Mean 4.32; Min 1.75; Max 7.94; Standard deviation 1.68. 12-Month Expected Inflation — Mean 4.21; Min 2.87; Max 6.10; Standard deviation 0.87.
  - Mexico (Number of observations 170): Headline CPI Inflation — Mean 4.88; Min 2.91; Max 12.32; Standard deviation 1.71. 12-Month Expected Inflation — Mean 4.53; Min 3.42; Max 11.14; Standard deviation 1.52.
  - Peru (Number of observations 143): Headline CPI Inflation — Mean 2.69; Min -1.08; Max 6.75; Standard deviation 1.59. 12-Month Expected Inflation — Mean 2.60; Min 1.63; Max 4.71; Standard deviation 0.58.
  - Czech Republic (Number of observations 170): Headline CPI Inflation — Mean 2.56; Min -0.42; Max 7.55; Standard deviation 1.71. 12-Month Expected Inflation — Mean 2.92; Min 1.40; Max 5.00; Standard deviation 0.83.
  - Israel (Number of observations 170): Headline CPI Inflation — Mean 2.10; Min -2.74; Max 6.94; Standard deviation 2.02. 12-Month Expected Inflation — Mean 2.29; Min 0.30; Max 4.10; Standard deviation 0.64.
  - Poland (Number of observations 170): Headline CPI Inflation — Mean 3.42; Min 0.16; Max 11.64; Standard deviation 2.46. 12-Month Expected Inflation — Mean 3.50; Min 0.20; Max 13.50; Standard deviation 2.76.
  - Turkey (Number of observations 109): Headline CPI Inflation — Mean 8.30; Min 3.99; Max 12.06; Standard deviation 1.81. 12-Month Expected Inflation — Mean 6.83; Min 5.42; Max 8.99; Standard deviation 0.71.
  - Korea (Number of observations 170): Headline CPI Inflation — Mean 2.95; Min 0.85; Max 5.98; Standard deviation 1.04. 12-Month Expected Inflation — Mean 3.55; Min 2.80; Max 4.60; Standard deviation 0.56.
  - Canada (Number of observations 170): Headline CPI Inflation — Mean 2.02; Min -0.95; Max 4.68; Standard deviation 0.97. 12-Month Expected Inflation — Mean 1.94; Min 0.58; Max 2.70; Standard deviation 0.39.
- Unit root and cointegration test p-values (selected entries from Table 3)
  - Brazil: Engle-Granger (Headline Inflation) 0.045; Engle-Granger (Expected Inflation) 0.012; Philips-Perron (Headline Inflation) 0.200; Philips-Perron (Expected Inflation) 0.071.
  - Chile: Engle-Granger (Headline Inflation) 0.023; Engle-Granger (Expected Inflation) 0.005; Philips-Perron (Headline Inflation) 0.247; Philips-Perron (Expected Inflation) 0.098.
  - Colombia: Engle-Granger (Headline Inflation) 0.343; Engle-Granger (Expected Inflation) 0.449; Philips-Perron (Headline Inflation) 0.422; Philips-Perron (Expected Inflation) 0.451; Johansen Test 0.000; Engle-Granger Cointegration 0.31.
  - Mexico: Engle-Granger (Headline Inflation) 0.002; Engle-Granger (Expected Inflation) 0.000; Philips-Perron (Headline Inflation) 0.000; Philips-Perron (Expected Inflation) 0.000.
  - Peru: Engle-Granger (Headline Inflation) 0.036; Engle-Granger (Expected Inflation) 0.152; Philips-Perron (Headline Inflation) 0.034; Philips-Perron (Expected Inflation) 0.044.
  - Czech Republic: Engle-Granger (Headline Inflation) 0.289; Engle-Granger (Expected Inflation) 0.254; Philips-Perron (Headline Inflation) 0.121; Philips-Perron (Expected Inflation) 0.233; Johansen Test 0.010; Engle-Granger Cointegration 0.16.
  - Israel: Engle-Granger (Headline Inflation) 0.050; Engle-Granger (Expected Inflation) 0.002; Philips-Perron (Headline Inflation) 0.046; Philips-Perron (Expected Inflation) 0.000.
  - Poland: Engle-Granger (Headline Inflation) 0.065; Engle-Granger (Expected Inflation) 0.223; Philips-Perron (Headline Inflation) 0.129; Philips-Perron (Expected Inflation) 0.172; Johansen Test 0.000; Engle-Granger Cointegration 0.17.
  - Turkey: Engle-Granger (Headline Inflation) 0.082; Engle-Granger (Expected Inflation) 0.000; Philips-Perron (Headline Inflation) 0.082; Philips-Perron (Expected Inflation) 0.006.
  - Korea: Engle-Granger (Headline Inflation) 0.106; Engle-Granger (Expected Inflation) 0.349; Philips-Perron (Headline Inflation) 0.051; Philips-Perron (Expected Inflation) 0.180; Johansen Test 0.050; Engle-Granger Cointegration 0.47.
  - Canada: Engle-Granger (Headline Inflation) 0.014; Engle-Granger (Expected Inflation) 0.000; Philips-Perron (Headline Inflation) 0.008; Philips-Perron (Expected Inflation) 0.014.

### B. Inflation expectations as forecasters: bias and out-of-sample performance
- In-sample bias tests (regression (3)) — Jan-2000 to Sep-2013 (selected estimates from Table 4)
  - Brazil: Constant α = 1.14**; Coefficient β = 1.00***; Wald test p-value 0.0604.
  - Chile: α = 0.35; β = 1.32***; Wald p-value 0.4690.
  - Colombia: α = -0.18; β = 0.92**; Wald p-value 0.7990.
  - Mexico: α = -0.06; β = 1.08***; Wald p-value 0.8412.
  - Peru: α = 0.31; β = 1.58***; Wald p-value 0.0369.
  - Czech Republic: α = -0.65*; β = 1.38***; Wald p-value 0.0003.
  - Israel: α = -0.17; β = 1.18***; Wald p-value 0.7600.
  - Poland: α = -0.58; β = -0.87*; Wald p-value 0.0001.
  - Turkey: α = 0.81; β = 1.71***; Wald p-value 0.0000.
  - Korea: α = -0.59*; β = 0.93***; Wald p-value 0.1313.
  - Canada: α = 0.13; β = 1.68***; Wald p-value 0.0019.
- In-sample results summary
  - Null hypothesis that expectations are in-sample unbiased (α=0 and β=1) can be rejected at the 5 percent level in 5 out of 11 cases.
  - Brazil: bias is due to persistent underestimation (positive and significant α).
  - In many cases, expectations tend to underestimate the volatility of inflation (β greater than one).
- Out-of-sample performance
  - RMSE comparisons (Figure 5) show survey expectations often have substantially lower RMSEs compared to naive forecasts (random walk, core inflation, inflation target); negative differences indicate better performance for expectations.
  - Forecasting performance compared over full sample and a sample starting January 2004 (to remove Brazil’s early high volatility).

### C. Forward-looking persistence using expectations: specifications and key estimates
- Main specification (4)
  - Endogenous variable: change in expected annual inflation at a rolling 12-month horizon (current month vs previous month).
  - Exogenous variables:
    - Change in actual annual inflation lagged by one month (lag to allow information flow and avoid endogeneity).
    - Change in expected annual inflation lagged by one month (captures slow-moving changes, herd behavior).
  - Coefficient γ1 measures forward-looking persistence (effect of actual inflation change on expected inflation change).
- Asymmetric specification (5)
  - Introduces d1 and d2 dummy variables: d1 = 1 when lagged change in actual inflation is positive; d2 = 1 when lagged change is negative.
  - γ1 interpreted as upward persistence; γ2 as downward persistence.
- Estimation method
  - OLS with Newey-West standard errors for all 11 countries using all available data.
- Table 6 — Effects of actual inflation on expected inflation, Jan-2000 to Jan-2014 (selected coefficients and sample sizes)
  - Brazil: Coefficient on Lagged Inflation Change 0.11*; Coefficient on Lagged Increases 0.18*; Coefficient on Lagged Decreases 0.06; Sample size 146.
  - Chile: 0.14***; 0.16***; 0.12**; 103.
  - Colombia: 0.19***; 0.24***; 0.16***; 123.
  - Mexico: 0.09***; 0.13**; 0.05; 168.
  - Peru: 0.16***; 0.17***; 0.16***; 142.
  - Czech Republic: 0.11***; 0.11*; 0.10**; 168.
  - Israel: 0.02; 0.02; 0.03; 168.
  - Poland: 0.36***; 0.35***; 0.36***; 168.
  - Turkey: 0.13***; 0.14***; 0.12***; 109.
  - Korea: 0.12***; 0.17***; 0.09**; 143.
  - Canada: 0.05**; 0.05*; 0.04; 168.
- Key empirical findings
  - Forward-looking persistence is quite high and statistically significant, particularly among emerging market countries.
  - Example: Poland — on average over the sample period, over ⅓ of any given percentage point change in actual inflation is passed on to expected inflation 12 months ahead (Poland coefficient 0.36***).
  - Persistence is lower among advanced economies.
  - Upward persistence (γ1) is larger and more often statistically significant than downward persistence (γ2) in Brazil and other Latin American countries.
    - A rise in actual inflation passes through to expectations more strongly than a fall reduces expectations.
    - This asymmetry is particularly striking in Brazil.

### Rolling-window evidence and interpretation of persistence dynamics
- Rolling 60-month sample estimates of upward persistence (γ1 from (5))
  - For many countries, a clear falling trend in upward persistence and emerging lack of statistical significance — consistent with policymakers gaining credibility over time (examples: Czech Republic, Poland, Mexico).
  - Brazil is a notable exception: persistence increased and became statistically significant between 2003 and early 2013, contrasting with backward-looking estimates that suggested the opposite over the same period.
- Downward persistence (γ2) behavior
  - In almost all cases, including Brazil, downward persistence does not exhibit a clear trend and is generally not statistically significant.
  - This indicates inflation persistence is typically asymmetric and biased to the upside.
  - Gains in credibility from inflation targeting manifest as reductions in upward persistence.

### IV. Conclusion: implications and interpretations
- Limitations of backward-looking assessments
  - Historical (backward-looking) assessments of inflation persistence can be misleading due to sensitivity to past outliers.
- Advantages of expectations-based measures
  - Using expectations provides a more up-to-date estimate of persistence because the sample period effectively extends into the future and expectations often deliver competitive out-of-sample forecasts.
- Main conclusions about Brazil
  - Backward-looking reduced-form autoregressions suggested a decline in inflation persistence that placed Brazil within the range of its inflation-targeting peers.
  - Forward-looking measures based on expectations show a pick-up in upward inflation persistence in Brazil between 2002 and early 2013.
  - Possible interpretations for rising upward persistence in Brazil:
    - Market participants believed policymakers had become less responsive to rising inflation than to falling inflation (perceived asymmetry in reaction function).
    - Intrinsic persistence could be rising (for example, more prevalent indexation).
  - The reduced-form empirical strategy cannot conclusively identify which interpretation is correct.
  - The increase in upward inflation persistence in Brazil contrasts with many other IT countries (including other emerging markets) where persistence tended to gradually decline — consistent with a gradual buildup of policy credibility and better-anchored expectations.
  - Although upward persistence showed some early signs of falling during the central bank’s rate hiking cycle in 2013, this trend paused and Brazil’s statistically significant inflation persistence continues to stand in sharp contrast to low-persistence benchmark economies such as Canada and New Zealand.

*Source: _wp1455 - introduction of IT in 2001.*

### 0.05 implies that the null can be rejected at a 95% level of confidence.

### _wp1455 - 0.05 implies that the null can be rejected at a 95% level of confidence.

### C. First-Order Autocorrelations
- Model and estimation
  - Inflation is modeled as a stationary autoregressive AR(p) process; focus on an AR(1) specification (equation (1)).
  - In (1), persistence is the parameter a, with πt quarterly inflation, k a constant, and ε an iid shock to inflation.
  - a can be regarded as the persistence of all previous inflation shocks when (1) is expressed in moving average form.
  - a is estimated by OLS without correction for bias because there is no evidence that quarterly inflation in the sample exhibits a time trend or is a “near-unit root” process in the sense of Andrews and Chen (1994).
- Half-life interpretation and results
  - Half-life is the estimated time taken for half of a shock to the quarterly inflation rate to fade (computed from the estimate of a).
  - Estimates are based on the regression (1) over 2000 Q1 to 2013 Q2.
  - Estimated half-lives and 95 percent confidence intervals (lower interval bounded at zero) are presented in Figure 1 for headline inflation.
  - Half-lives for shocks to headline inflation range from:
    - less than half of one quarter (Canada and New Zealand)
    - to over four quarters (Romania)
  - Latin American countries, including Brazil, are mainly in the upper end of the range but are broadly comparable with their IT peer group.
- Robustness to additional lags
  - Generalizing the AR(1) model to incorporate more lags was found unnecessary for most countries.
  - Partial autocorrelations indicate that the impact of changes in inflation two or more quarters earlier is typically insignificant for the current quarter’s inflation.
  - Specifically, lags of p>1 were statistically significant for only one country for headline inflation out of a total sample size of 33 countries.

### D. Rolling Regressions
- Motivation and method
  - Persistence can vary through time; estimates of persistence can change dramatically based on the sample period, particularly in Latin America and Brazil.
  - To account for time variation, half-lives are estimated using the parameter a from (1) with shorter rolling samples.
  - Rolling regressions use overlapping rolling 8 year samples of quarterly data to balance assessment of time-variation with sufficiently large sample periods.
  - The first sample is Q1 1995 through Q4 2002; the second sample runs Q2 1995 through Q1 2003, and so on. Dates on the charts refer to the end date of each estimation.
- Treatment of nonpositive a and inference
  - When a ≤ 0, the half-life is not defined and is represented by breaks in the time series (some series have large parts not defined, e.g., Norway).
  - When it is not possible to reject the null that a (and the half-life) is zero, the lower 95 percent confidence interval for the half-life is not defined and only the upper interval is shown.
- Empirical findings by country grouping
  - Benchmark cases:
    - Canada and New Zealand show rolling half-lives that are both low and statistically insignificant.
  - Latin America:
    - Experiences vary by country; there is no clear evidence (with one exception) that persistence is declining firmly towards the low levels of Canada or New Zealand.
    - In some cases persistence fell during the early years of IT (e.g., Colombia and Peru).
    - For most countries in the region since 2008:
      - persistence has remained broadly constant and statistically significant (Chile)
      - or increased (Colombia, Guatemala, and Peru)
    - The one exception is Mexico, where persistence is now statistically insignificant following the large sustained decline that followed the [sample period described].

*Source: Author’s estimates from the underlying chapter/section content.*

### introduction of IT in 2001.

### _wp1455 - introduction of IT in 2001.

### Inflation persistence: broad patterns and Brazil-specific dynamics
- Inflation persistence measured by half-lives fell substantially from a level of "almost 2 quarters" in 2010, but this apparent step-decline is mainly due to the 2002-03 period falling out of the 8-year sample window.
- Excluding the 2002-03 effect (for example by selecting samples that start in 2004) shows persistence has been more stable.
- Persistence has increased since 2009 in Brazil.
- Backward-looking autoregressive approaches can be strongly influenced by historical outliers and less by more recent developments.
- Figures and sample windows referenced:
  - Rolling estimates and plots span 2002-Q1 to 2013-Q4 for inflation shock half-lives across countries.
  - Brazil: rolling half-life series compared inflation and GDP from Q4-2002 to Q4-2013 (half-life in quarters).

### E. Output Growth as the driving process
- Driving process proxy used: quarterly change in log real GDP (selected because of lack of comparable marginal cost data and uncertainties about output gap measurement).
- Scatter plots compare AR(1) coefficients for quarterly change in inflation and GDP using:
  - Full sample starting in Q1 2000.
  - Three 32-quarter sub-samples ending in Q2 2008, Q2 2010, and Q2 2013 (GDP data end two quarters earlier).
- Empirical finding:
  - For all sample periods, the linear correlation between the inflation and GDP AR(1) coefficients was only weakly positive and not statistically significant.
  - Structural models suggest this weak reduced-form relationship could reflect either:
    - A modest impact of the driving process (output growth) on inflation; or
    - Significant idiosyncratic white noise inflation variance.
- Brazil-specific:
  - Rolling estimates of the half-life of quarterly GDP growth have been rising but at a very moderate pace.
  - This contrasts with the large rise and subsequent decline in the inflation half-life.
  - Interpretation: inherited persistence may explain some fluctuations in inflation persistence, but intrinsic persistence (including indexation) and changes in the monetary policy reaction function are likely important.

### III. Forward-looking persistence: concept and rationale
- Historical-data-based estimates are backward looking and can be slow to pick up changes in persistence.
- Reducing sample size (rolling estimates) increases weight on recent observations but risks dependence on outliers.
- Alternative: use inflation expectations as a more timely indicator of how long inflation shocks will persist.
  - If expectations are "good" forecasters, measure the effect of changes in actual inflation on those expectations.
  - Survey expectations can provide a leading indicator if they influence price-setters' behavior.

### A. Data (measurement and samples)
- Monthly inflation measure: annual change in the headline consumer price index for each country.
- Sample period: January 2000 through January 2014.
- Inflation expectations: predictions for the annual rate of inflation 12 months ahead from surveys (central banks, statistical agencies, private firms).
- When multiple survey observations exist in a month, the latest available data point is selected.
- Unit-root and cointegration summary:
  - Almost all series are stationary; where non-stationary, strong evidence of cointegration between inflation and expectations is reported.
- Statistical summary (Table 2): Headline CPI Inflation and 12-Month Expected Inflation — percent unless specified
  - Brazil (Number of observations 147): Headline CPI Inflation — Mean 6.54; Min 2.96; Max 17.24; Standard deviation 2.93. 12-Month Expected Inflation — Mean 5.36; Min 3.43; Max 12.52; Standard deviation 1.45.
  - Chile (Number of observations 104): Headline CPI Inflation — Mean 3.46; Min -2.29; Max 9.85; Standard deviation 2.57. 12-Month Expected Inflation — Mean 3.21; Min 2.00; Max 6.00; Standard deviation 0.67.
  - Colombia (Number of observations 124): Headline CPI Inflation — Mean 4.32; Min 1.75; Max 7.94; Standard deviation 1.68. 12-Month Expected Inflation — Mean 4.21; Min 2.87; Max 6.10; Standard deviation 0.87.
  - Mexico (Number of observations 170): Headline CPI Inflation — Mean 4.88; Min 2.91; Max 12.32; Standard deviation 1.71. 12-Month Expected Inflation — Mean 4.53; Min 3.42; Max 11.14; Standard deviation 1.52.
  - Peru (Number of observations 143): Headline CPI Inflation — Mean 2.69; Min -1.08; Max 6.75; Standard deviation 1.59. 12-Month Expected Inflation — Mean 2.60; Min 1.63; Max 4.71; Standard deviation 0.58.
  - Czech Republic (Number of observations 170): Headline CPI Inflation — Mean 2.56; Min -0.42; Max 7.55; Standard deviation 1.71. 12-Month Expected Inflation — Mean 2.92; Min 1.40; Max 5.00; Standard deviation 0.83.
  - Israel (Number of observations 170): Headline CPI Inflation — Mean 2.10; Min -2.74; Max 6.94; Standard deviation 2.02. 12-Month Expected Inflation — Mean 2.29; Min 0.30; Max 4.10; Standard deviation 0.64.
  - Poland (Number of observations 170): Headline CPI Inflation — Mean 3.42; Min 0.16; Max 11.64; Standard deviation 2.46. 12-Month Expected Inflation — Mean 3.50; Min 0.20; Max 13.50; Standard deviation 2.76.
  - Turkey (Number of observations 109): Headline CPI Inflation — Mean 8.30; Min 3.99; Max 12.06; Standard deviation 1.81. 12-Month Expected Inflation — Mean 6.83; Min 5.42; Max 8.99; Standard deviation 0.71.
  - Korea (Number of observations 170): Headline CPI Inflation — Mean 2.95; Min 0.85; Max 5.98; Standard deviation 1.04. 12-Month Expected Inflation — Mean 3.55; Min 2.80; Max 4.60; Standard deviation 0.56.
  - Canada (Number of observations 170): Headline CPI Inflation — Mean 2.02; Min -0.95; Max 4.68; Standard deviation 0.97. 12-Month Expected Inflation — Mean 1.94; Min 0.58; Max 2.70; Standard deviation 0.39.
- Unit root and cointegration test p-values (selected entries from Table 3):
  - Brazil: Engle-Granger (Headline Inflation) 0.045; Engle-Granger (Expected Inflation) 0.012; Philips-Perron (Headline Inflation) 0.200; Philips-Perron (Expected Inflation) 0.071.
  - Chile: Engle-Granger (Headline Inflation) 0.023; Engle-Granger (Expected Inflation) 0.005; Philips-Perron (Headline Inflation) 0.247; Philips-Perron (Expected Inflation) 0.098.
  - Colombia: Engle-Granger (Headline Inflation) 0.343; Engle-Granger (Expected Inflation) 0.449; Philips-Perron (Headline Inflation) 0.422; Philips-Perron (Expected Inflation) 0.451; Johansen Test 0.000; Engle-Granger Cointegration 0.31.
  - Mexico: Engle-Granger (Headline Inflation) 0.002; Engle-Granger (Expected Inflation) 0.000; Philips-Perron (Headline Inflation) 0.000; Philips-Perron (Expected Inflation) 0.000.
  - Peru: Engle-Granger (Headline Inflation) 0.036; Engle-Granger (Expected Inflation) 0.152; Philips-Perron (Headline Inflation) 0.034; Philips-Perron (Expected Inflation) 0.044.
  - Czech Republic: Engle-Granger (Headline Inflation) 0.289; Engle-Granger (Expected Inflation) 0.254; Philips-Perron (Headline Inflation) 0.121; Philips-Perron (Expected Inflation) 0.233; Johansen Test 0.010; Engle-Granger Cointegration 0.16.
  - Israel: Engle-Granger (Headline Inflation) 0.050; Engle-Granger (Expected Inflation) 0.002; Philips-Perron (Headline Inflation) 0.046; Philips-Perron (Expected Inflation) 0.000.
  - Poland: Engle-Granger (Headline Inflation) 0.065; Engle-Granger (Expected Inflation) 0.223; Philips-Perron (Headline Inflation) 0.129; Philips-Perron (Expected Inflation) 0.172; Johansen Test 0.000; Engle-Granger Cointegration 0.17.
  - Turkey: Engle-Granger (Headline Inflation) 0.082; Engle-Granger (Expected Inflation) 0.000; Philips-Perron (Headline Inflation) 0.082; Philips-Perron (Expected Inflation) 0.006.
  - Korea: Engle-Granger (Headline Inflation) 0.106; Engle-Granger (Expected Inflation) 0.349; Philips-Perron (Headline Inflation) 0.051; Philips-Perron (Expected Inflation) 0.180; Johansen Test 0.050; Engle-Granger Cointegration 0.47.
  - Canada: Engle-Granger (Headline Inflation) 0.014; Engle-Granger (Expected Inflation) 0.000; Philips-Perron (Headline Inflation) 0.008; Philips-Perron (Expected Inflation) 0.014.

### B. Inflation expectations as forecasters: bias and out-of-sample performance
- In-sample bias test (regression (3)): actual 12-month inflation change regressed on 12-month-ahead predicted change from survey (Newey-West standard errors).
- Table 4: constant α, slope β, and Wald test for α=0 and β=1 — Jan-2000 to Sep-2013 (selected reported estimates)
  - Brazil: Constant α = 1.14**; Coefficient β = 1.00***; Wald test p-value 0.0604.
  - Chile: α = 0.35; β = 1.32***; Wald p-value 0.4690.
  - Colombia: α = -0.18; β = 0.92**; Wald p-value 0.7990.
  - Mexico: α = -0.06; β = 1.08***; Wald p-value 0.8412.
  - Peru: α = 0.31; β = 1.58***; Wald p-value 0.0369.
  - Czech Republic: α = -0.65*; β = 1.38***; Wald p-value 0.0003.
  - Israel: α = -0.17; β = 1.18***; Wald p-value 0.7600.
  - Poland: α = -0.58; β = -0.87*; Wald p-value 0.0001.
  - Turkey: α = 0.81; β = 1.71***; Wald p-value 0.0000.
  - Korea: α = -0.59*; β = 0.93***; Wald p-value 0.1313.
  - Canada: α = 0.13; β = 1.68***; Wald p-value 0.0019.
- In-sample results summary:
  - Null hypothesis that expectations are in-sample unbiased (α=0 and β=1) can be rejected at the 5 percent level in 5 out of 11 cases.
  - Brazil: bias is due to persistent underestimation (positive and significant α).
  - In many cases, expectations tend to underestimate the volatility of inflation (β greater than one).
- Out-of-sample performance:
  - RMSE comparisons (Figure 5) show survey expectations often have substantially lower RMSEs compared to naive forecasts (random walk, core inflation, inflation target); negative differences indicate better performance for expectations.
  - Forecasting performance compared over full sample and a sample starting January 2004 (to remove Brazil’s early high volatility).

### C. Forward-looking persistence using expectations: specifications and key estimates
- Main specification (4):
  - Endogenous variable: change in expected annual inflation at a rolling 12-month horizon (current month vs previous month).
  - Exogenous variables:
    - Change in actual annual inflation lagged by one month (lag to allow information flow and avoid endogeneity).
    - Change in expected annual inflation lagged by one month (captures slow-moving changes, herd behavior).
  - Coefficient γ1 measures forward-looking persistence (effect of actual inflation change on expected inflation change).
- Asymmetric specification (5):
  - Introduces d1 and d2 dummy variables: d1 = 1 when lagged change in actual inflation is positive; d2 = 1 when lagged change is negative.
  - γ1 interpreted as upward persistence; γ2 as downward persistence.
- Estimation method: OLS with Newey-West standard errors for all 11 countries using all available data.
- Table 6: Effects of actual inflation on expected inflation, Jan-2000 to Jan-2014 (selected reported coefficients and sample sizes)
  - Columns reported: Coefficient on Lagged Inflation Change; Coefficients on Lagged Increases (γ1) and Lagged Decreases (γ2); Sample size.
  - Brazil: Coefficient on Lagged Inflation Change 0.11*; Coefficient on Lagged Increases 0.18*; Coefficient on Lagged Decreases 0.06; Sample size 146.
  - Chile: 0.14***; 0.16***; 0.12**; 103.
  - Colombia: 0.19***; 0.24***; 0.16***; 123.
  - Mexico: 0.09***; 0.13**; 0.05; 168.
  - Peru: 0.16***; 0.17***; 0.16***; 142.
  - Czech Republic: 0.11***; 0.11*; 0.10**; 168.
  - Israel: 0.02; 0.02; 0.03; 168.
  - Poland: 0.36***; 0.35***; 0.36***; 168.
  - Turkey: 0.13***; 0.14***; 0.12***; 109.
  - Korea: 0.12***; 0.17***; 0.09**; 143.
  - Canada: 0.05**; 0.05*; 0.04; 168.
- Key empirical findings:
  - Forward-looking persistence is quite high and statistically significant, particularly among emerging market countries.
  - Example: Poland — on average over the sample period, over ⅓ of any given percentage point change in actual inflation is passed on to expected inflation 12 months ahead (Poland coefficient 0.36***).
  - Persistence is lower among advanced economies.
  - Upward persistence (γ1) is larger and more often statistically significant than downward persistence (γ2) in Brazil and other Latin American countries.
    - In particular, a rise in actual inflation passes through to expectations more strongly than a fall reduces expectations.
    - This asymmetry is particularly striking in Brazil.

### Rolling-window evidence and interpretation of persistence dynamics
- Rolling 60-month sample estimates of upward persistence (γ1 from (5)) show:
  - For many countries, a clear falling trend in upward persistence and emerging lack of statistical significance — consistent with policymakers gaining credibility over time (examples: Czech Republic, Poland, Mexico).
  - Brazil is a notable exception: persistence increased and became statistically significant between 2003 and early 2013, contrasting with backward-looking estimates that suggested the opposite over the same period.
- Downward persistence (γ2) behavior:
  - In almost all cases, including Brazil, downward persistence does not exhibit a clear trend and is generally not statistically significant.
  - This indicates inflation persistence is typically asymmetric and biased to the upside.
  - Gains in credibility from inflation targeting manifest as reductions in upward persistence.

### IV. Conclusion: implications and interpretations
- Historical (backward-looking) assessments of inflation persistence can be misleading due to sensitivity to past outliers.
- Using expectations provides a more up-to-date estimate of persistence because the sample period effectively extends into the future and expectations often deliver competitive out-of-sample forecasts.
- Main conclusions about Brazil:
  - Backward-looking reduced-form autoregressions suggested a decline in inflation persistence that placed Brazil within the range of its inflation-targeting peers.
  - Forward-looking measures based on expectations show a pick-up in upward inflation persistence in Brazil between 2002 and early 2013.
  - Possible interpretations for rising upward persistence in Brazil:
    - Market participants believed policymakers had become less responsive to rising inflation than to falling inflation (perceived asymmetry in reaction function).
    - Intrinsic persistence could be rising (for example, more prevalent indexation).
  - The reduced-form empirical strategy cannot conclusively identify which interpretation is correct.
  - The increase in upward inflation persistence in Brazil contrasts with many other IT countries (including other emerging markets) where persistence tended to gradually decline — consistent with a gradual buildup of policy credibility and better-anchored expectations.
  - Although upward persistence showed some early signs of falling during the central bank’s rate hiking cycle in 2013, this trend paused and Brazil’s statistically significant inflation persistence continues to stand in sharp contrast to low-persistence benchmark economies such as Canada and New Zealand.

*Source: _wp1455 - introduction of IT in 2001.*

### REFERENCES

### _wp1455 - REFERENCES

### References

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- Capistrán, Carlos and Manuel Ramos-Francia, 2009, “Inflation Dynamics In Latin America,” Contemporary Economic Policy, vol. 27(3), pp. 349-362.
- Fuhrer, Jeffrey C., 2010, “Inflation Persistence,” Chapter 9 in Handbook of Monetary Economics, Ed. Benjamin M. Friedman and Michael Woodford, Elsevier, pp 423-486.
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- Gürkaynak, Refet S, Andrew T. Levin, and Eric T. Swanson, 2010, “Does Inflation Targeting Anchor Long-Run Inflation Expectations? Evidence from Long-Term Bond Yields in the U.S., U.K., and Sweden,” Journal of the European Economic Association, Volume 8, Issue 6, pp 1208–1242.
- Lucas, Robert, 1976, “Econometric Policy Evaluation: A Critique,” in The Philips Curve and Labor Markets, Carnegie-Rochester Series on Public Policy, Vol. 1, pp. 19-46.
- Mishkin, Frederic S. and Klaus Schmidt-Hebbel, 2007, “Does Inflation Targeting Make a Difference?” in Monetary Policy under Inflation Targeting, Edited by Frederic S. Miskin, Klaus Schmidt-Hebbel, and Norman Loayz, Edition 1, Volume 11, Chapter 9, Central Bank of Chile.
- Roger, Scott, 2010, “Inflation Targeting Turns 20,” Finance and Development, International Monetary Fund, Washington D.C.

*Source: _wp1455 - REFERENCES*

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