## _wp11160 - 1. Statistics of the Distribution of Inflation for Countries with per Capita GDP (PPP base) from US$6000 to 15,000

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---

### Introduction and motivation
- Low inflation is key for macroeconomic stability because high inflation:
  - Lowers domestic savings via deeply negative real interest rates.
  - Reduces capital accumulation due to increased uncertainty.
  - Causes real appreciation of the exchange rate reflecting widened inflation differentials with trade partners.
- Egypt experienced double digit inflation over a couple of years leading to a rapid real appreciation of the Egyptian pound by about 40 percent to the level before the huge devaluation in early 2003.
- Under the pure New Keynesian Phillips Curve (NKPC), disinflation is costless (zero sacrifice ratio) if the central bank credibly commits to a zero output gap in the future.
- Empirical evidence shows inflation has inertia; with inertia the central bank faces a trade-off between disinflation and higher unemployment, making estimation of inflation inertia critical for policy design.
- Main contributions:
  - Empirically estimate inflation inertia in Egypt in the 2000s using the median unbiased estimate of the sum of autoregressive coefficients (Levin et al. (2004), Benati (2008)).
  - Investigate determinants of inflation inertia using cross-country data of over 100 countries estimated by the same method.

### Preliminary discussions and international comparisons
- Recent inflation developments in Egypt:
  - 2003-04 spike mainly reflected pass-through from the huge devaluation of the Egyptian pound in 2003.
  - 2006-07 spike due to an avian flu outbreak and world commodity price increases.
  - 2008 spike caused by world commodity price increases.
  - Expected inflation (Consensus Forecast) after 2007 rose substantially compared to before 2007.
- Distributional evidence for countries with per capita GDP (PPP) from US$6,000 to US$15,000 (annual CPI inflation, percent) — selected figures preserved exactly from Table 1:
  - Average: 12.3, 16.4, 6.6
  - Median: 6.6, 6.4, 5.1
  - Standard deviation: 21.5, 33.6, 6.9
  - Lower quartile: 3.5, 3.1, 2.3
  - Upper quartile: 11.8, 16.8, 8.6
  - Mode in the smoothed histogram 1/: 5.5, 3.5, 2.5
  - Number of observations: 305, 305, 460
  - of which, outliers: 28, 49, 11
  - Note 1/: Eliminating outliers, where outliers are annual inflation either below -5 percent or above 25 percent.
- Transition-matrix evidence for 31 emerging market countries (1980–2009) — selected probabilities from Table 2 (number of observations total: 847):
  - If year t inflation is "0-4 %": probability to stay in "0-4 %" in t+1 = 72.3; probability to move to "4-8 %" = 18.2; observations = 148.
  - If year t inflation is "8-12 %": probability to remain in "8-12 %" in t+1 ≈ one-third and over 70 percent in the "4-12 %" range (summary conclusion reported in the text).
  - If year t inflation is "Over 20 %": probability to remain "Over 20 %" in t+1 = 79.7; observations = 261.
- Conclusion from comparisons: Recent inflation in Egypt is high relative to other countries in comparable income ranges, making disinflation an important policy goal.

### Why inflation inertia matters (theoretical framing)
- Pure NKPC: inflation at t depends on expected future output gaps and current output gap; credible future zero output gap implies costless disinflation.
- Hybrid NKPC (includes lag of inflation): past inflation matters; when θ > 0.5 inflation declines only gradually even with credible future zero output gap, implying a positive sacrifice ratio.
- Therefore, the size of inertia determines disinflation costs and policy trade-offs.

### Measuring inflation inertia — methods used
- Reduced-form autoregressive (AR) models: inertia = sum of AR coefficients; median-unbiased estimation with grid bootstrap used following Andrews and Chen (1994), Benati (2008), Levin et al. (2004).
- Structural approaches referenced: hybrid NKPC with IS and Taylor rule, DSGE methods, and slow-moving trend models (literature overview).
- For Egypt:
  - Monthly headline CPI inflation = first difference of natural logarithm of seasonally adjusted CPI from IFS, January 2000 to June 2010.
  - Number of lags chosen by SIC; SIC-minimizing lag is 1.
  - Chow test indicates structural break around July 2007; sample split into January 2000–June 2007 and July 2007–June 2010.
  - Median-unbiased estimator constructed via Hansen’s (1999) grid bootstrap using 200 grid points and 2000 bootstrap replications at each grid point.

### Inflation inertia in Egypt — estimates and interpretation (Table 3 and related)
- Median-unbiased estimates of AR(1) sum for headline CPI (selected reported numbers preserved exactly):
  - January 2000–June 2007: median-unbiased ≈ 0.51 (reported in table: OLS AROLS Median/unbiased = 0.469; 1/unbiased = 0.51; Lower 90% = 0.10; Upper 90% = 0.32; SIC = 0.625; ICD.W. Adj-R2 = 0.350; additional printed numbers: 0.673, -8.103, -8.021, 2.122, 0.290).
  - July 2007–June 2010: median-unbiased ≈ 0.424 (selected printed entries for August 2007-June 2010 include 0.333, 0.424, 0.070, 0.596, 0.147, 0.741, -6.815, -6.681, 1.998, 0.192).
- Spectral share interpretation:
  - Share of components with frequencies longer than one year about 0.45 in the first sub-period and 0.35 in the second sub-period (textual implication based on spectral analysis).
- Interpretation:
  - Smaller inertia in July 2007–June 2010 reflects larger short-term shocks to inflation (mainly food prices) and larger month-over-month volatility after mid-2007.
- Core inflation (CBE series excluding several food items and administrative prices) — short sample since January 2005:
  - After mid-2007 core inertia larger than headline inertia (intuitive since excluding food raises inertia).
  - In first sub-period headline inertia exceeded core inertia, but difference not statistically significant.
- Summary statistic from Table 4 (some statistics of the distribution of inflation inertia in the 2000s):
  - Egypt: OLS = 0.36, Median Unbiased = 0.48.
  - Cross country estimate: Average = 0.19, Median = 0.20, Median Unbiased = 0.30, Median Unbiased = 0.36.
  - Standard deviation 1/: 0.26, 0.29.
  - Lower quartile: -0.03, 0.06.
  - Upper quartile: 0.37, 0.51.
  - Mode in the smoothed histogram: 0.35, 0.45.
  - Number of samples: 131, 127.
  - Note 1/: Grid bootstrap method for median unbiased estimator.

### Cross-country determinants of inflation inertia — model, data, and key results
- Theoretical calibration (based on Fuhrer (2009) example):
  - Inflation inertia increases as price rigidities (coefficient γ in the NKPC) become larger.
  - Increased volatility of a shock to inflation in the NKPC reduces inflation inertia.
  - Increased volatility of a shock to the output gap increases inflation inertia.
  - Increased persistency in the output gap increases inflation inertia.
- Proxies used in cross-country analysis:
  - Market rigidities proxied by goods market efficiency index (Global Competitiveness Report).
  - Volatility of non-interest government expenditure over GDP as proxy for volatility of demand shock to the output gap.
  - Volatility of terms of trade change as proxy for supply shock to inflation.
  - Per capita GDP (PPP base) as proxy for share of food and energy in CPI; per capita GDP averaged over 1995-99 to avoid endogeneity.
  - Fiscal deficit (average over sample) as proxy for fiscal dominance.
  - Monetary policy framework proxied by inflation-targeting dummy (adopted in 2001) and advanced economy dummy.
  - Measurement error controls: institutions and income level.
- Data and estimation:
  - Quarterly CPI inflation (first difference of log seasonally adjusted CPI) from IFS or INS for about 130 countries spanning Q1 2000 to Q2 2010.
  - Lag length selected by SIC and Chow tests per country.
  - Tobit model used alongside OLS to account for non-linearity and censoring in relation between AR coefficients and spectral shares.
  - Models estimated for full sample (~130 countries) and sub-samples (advanced countries and commodity exporters).
- Main empirical findings (selected preserved coefficients and test statistics from Table 5):
  - Accounting for non-linearity (Tobit) increases explanatory power (higher adjusted R2 / pseudo R2).
  - Volatility of non-interest fiscal expenditure (as a share of GDP) significantly increases inflation inertia; coefficients include 6.089, 6.270, 6.253, 10.147, 12.881, 11.825, 9.348, 5.431, 10.463 with t-statistics (3.09)* **, (3.15)* **, (3.15)* * *, (2.51)*, (1.83), (1.70), (1.31), (1.69), (1.59).
  - Fiscal deficit as a share of GDP affects inflation inertia for the full sample (coefficients include 1.204, 1.373, 1.225 with t-statistics (1.77)*, (1.98)**, (1.74)*); effect insignificant or smaller in advanced economies.
  - Advanced countries dummy is significantly negative: coefficients -0.220, -0.248, -0.223, -0.441 with t-statistics (-2.18)**, (-2.39)**, (-2.11)**, (-2.14)** — advanced countries exhibit lower inflation persistency.
  - Goods market efficiency not significant for full sample but significant for advanced countries in some specifications (coefficients and t-statistics reported in Table 5).
  - ln(GDP) -1 coefficients reported include 0.086, 0.094, 0.087, 0.189, 0.411, 0.469, 0.473, 0.092, 0.339 with t-statistics (2.50)**, (2.68)**, (2.45)**, (2.71)**, (1.22), (1.39), (1.44), (1.65), (2.70)** — suggesting income-related effects and measurement considerations.
  - Reducing targeted inflation (more than one percentage point) coefficients 0.104, 0.263 with t-statistics (1.05), (1.06) — suggestive evidence that reductions in targeted inflation during the sample can bias inertia estimates upward.
  - Number of samples and censored observations vary across specifications (e.g., sample sizes 120, 30, 28; censored observations 25, 64, etc.).
  - Mean squared error (σ for Tobit) and adjusted R2 / pseudo R2 reported across specifications (selected values preserved exactly in Table 5).

### Policy implications (from empirical results)
- Two key implications to reduce inflation inertia (relevant for disinflation and maintaining competitiveness):
  1. Importance of counter-cyclical macroeconomic policies:
     - Positive effect of volatility of demand shocks (proxied by primary fiscal expenditure as a share of GDP) implies that pro-cyclical policy propagates shocks to the output gap, increasing output gap fluctuations and inflation persistency via the Phillips curve.
     - In the extreme case of perfect offsetting of demand shocks, the output gap would stay at zero and inflation would depend only on white-noise supply shocks in the NKPC, producing zero inflation inertia.
  2. Additional benefit of fiscal consolidation to disinflation:
     - Fiscal consolidation reduces inflation not only through lower aggregate demand but also through lower inflation inertia.
     - Persistent large fiscal deficits (fiscal dominance) can cause monetization or unresponsive nominal interest rates, making monetary policy pro-cyclical and increasing inflation persistence.
- Policy prescription summary:
  - Reducing fiscal deficits and implementing more timely counter-cyclical macroeconomic policy are key to reduce inflation inertia and lower the cost of disinflation.
  - Strengthening counter-cyclical monetary policy, establishing a credible nominal anchor (to stabilize inflation expectations), and fiscal consolidation are recommended to lower inflation persistency.
- Caveat:
  - Estimated reduced-form inflation inertia does not identify required change in the present value of the output gap to remove inflation differentials between Egypt and trade partners. Estimating parameters in the hybrid NKPC is necessary to obtain the sacrifice ratio for disinflation and to guide monetary policy during transition periods.

### Conclusions and recommendations for Egypt
- Empirical summary:
  - Inflation inertia for Egypt estimated following Benati (2008): share of components with frequencies longer than one year in Egypt is about 40 percent.
  - Cross-country estimates for about 130 countries indicate Egypt’s inflation inertia is relatively high, around the upper quartile of the sample.
  - Cross-country regression suggests lack of counter-cyclical macroeconomic policy and high fiscal deficit may explain high persistency in Egypt.
- Policy recommendations:
  - Implement more counter-cyclical monetary policy associated with establishing a nominal anchor to stabilize inflation expectations.
  - Maintain committed fiscal consolidation to reduce the deficit by 5 percentage points by FY 2014/15.
- Research suggestion:
  - Estimating parameters in the hybrid NKPC is necessary to determine how much the output gap must decline to achieve disinflation (sacrifice ratio); proposed as future research.

*Source: _wp11160 - 1. Statistics of the Distribution of Inflation for Countries with per Capita GDP (PPP base) from US$6,000 to 15,000 (IMF PDF).*

### 1. Statistics of the Distribution of Inflation for Countries with per Capita GDP (PPP base) from

### _wp11160 - 1. Statistics of the Distribution of Inflation for Countries with per Capita GDP (PPP base) from US$6000 to 15,000

### Main sections (with page references)
- 1. Statistics of the Distribution of Inflation for Countries with per Capita GDP (PPP base) from US$6000 to 15,000 ..............................................................................................................20
- 2. Emerging Market Countries: Transition Matrix, 1980-2009 ...............................................21
- 3. Egypt: Estimated Headlines CPI Inflation (Monthly, Seasonally Adjusted) Intertia, 2000–June 2010 .............................................................................................................................22
- 4. Some Statistics of the Distribution of Inflation Inertia in the 2000s ...................................23
- 5. Determinants of Inflation Inertia by Cross Country Data, 2000–2010 ................................24

### Figures (titles and page cues)
- 1. Expected Inflation (Consensus Forecast) and Actual Inflation (12-month, percent) ............5
- 2. Distribution of Inflation in the 1980s, 90s and 2000s for Countries with per Capita Income from US$6,000 to 15,000 ......................................................................................................6
- 3. Density of Inflation in the 1980s, 90s and 2000s for Countries with per Capita Income from US$6,000 to 15,000 ...............................................................................................................6
- 4. Inflation Distribution Conditional on the Previous Year .......................................................9
- 5. Contribution of Components with Cycles Longer than One Year .......................................10
- 6. Egypt: Monthly Inflation, 2000-2010 ..................................................................................11
- 7. Inflation and its Intertia........................................................................................................12
- 8. Impact of Shocks in the Phillips Curve and Output Gap to AR(1) Coefficient of Inflation..13
- 9. Impact of Shocks in the Phillips Curve and Output Gap to AR(1) Coefficient of Inflation..13
- 10. Midpoint of Inflation Target, 1999-2010 and Path of Midpoint of Inflation Target.........16

### Appendixes
- 1. Coefficient of AR(1) Process of Inflation in an Example in Fuhrer (2009) ........................25
- 2. Why is Inflation Inertia Overestimated when the Inflation Target Has Been Reduced during the Sample Period? ..............................................................................................................26

*Source: _wp11160 - 1. Statistics of the Distribution of Inflation for Countries with per Capita GDP (PPP base) from (IMF PDF).*

### References .............................................................................................................

### _wp11160 - References

### Introduction
- Low inflation is key for macroeconomic stability because high inflation:
  - Lowers domestic savings via deeply negative real interest rates.
  - Reduces capital accumulation due to increased uncertainty.
  - Causes real appreciation of the exchange rate reflecting widened inflation differentials with trade partners.
- Egypt experienced double digit inflation over a couple of years leading to a rapid real appreciation of the Egyptian pound by about 40 percent to the level before the huge devaluation in early 2003.
- If inflation differentials with trade partners diminish, interest rate differentials should become smaller, reducing incentives for carry traders and easing exchange rate pressures.
- Under the pure New Keynesian Phillips Curve (NKPC), disinflation is costless (zero sacrifice ratio) if the central bank credibly commits to a zero output gap in the future.
- Empirical evidence shows inflation has inertia; with inertia the central bank faces a trade-off between disinflation and higher unemployment, making estimation of inflation inertia critical for policy design.
- Main contributions:
  - Empirically estimate inflation inertia in Egypt in the 2000s using the median unbiased estimate of the sum of autoregressive coefficients (Levin et al. (2004), Benati (2008)).
  - Investigate determinants of inflation inertia using cross-country data of over 100 countries estimated by the same method.

### Preliminary discussions
- Recent inflation developments in Egypt:
  - 2003-04 spike mainly reflected pass-through from the huge devaluation of the Egyptian pound in 2003.
  - 2006-07 spike due to an avian flu outbreak and world commodity price increases.
  - 2008 spike caused by world commodity price increases.
  - Expected inflation (Consensus Forecast) after 2007 rose substantially compared to before 2007.
- International comparisons:
  - Table-based analysis of countries with per capita GDP from US$ 6,000 to US$ 15,000 shows average inflation declined to single digits in the 2000s, while median inflation remained in the 5-7 percent range across the 1980s, 1990s, and 2000s.
  - Distributional evidence: share of over 25 percent inflation was about 10 percent in the 1980s, 15 percent in the 1990s, and 2.5 percent in the 2000s.
  - Mode of inflation in the 1990s and 2000s is about 3 percent; density is skewed left.
  - Conclusion: Recent inflation in Egypt is high relative to other countries in comparable income ranges, making disinflation an important policy goal.
- Why inflation inertia matters for disinflation:
  - Pure NKPC: inflation at t depends on expected future output gaps and current output gap; credible future zero output gap implies costless disinflation.
  - Hybrid NKPC (includes lag of inflation) changes implication: past inflation matters; when θ > 0.5 the solution shows inflation declines only gradually even with credible future zero output gap, implying a positive sacrifice ratio.
  - Therefore, size of inertia determines disinflation costs.
- Empirical approaches to measuring inertia:
  - Reduced-form autoregressive (AR) models: inertia = sum of AR coefficients; median-unbiased estimation with grid bootstrap used in literature (Benati 2008; Levin et al. 2004; Capistran and Ramos-Francia 2006).
  - Structural models: time series models with hybrid NKPC, IS and Taylor rule (Dossche and Everaert 2005); DSGE approaches (Rabanal and Rubio-Ramirez 2003); slow-moving trend models (Cogley and Sbordone 2006).
- Transition-matrix evidence for 31 emerging market countries (1980–2009):
  - Conditional probabilities show inertia: if inflation in year t is in 0–4 percent range, probability to stay in that range in t+1 is about 70 percent.
  - When inflation in year t is between 8 and 12 percent, inflation in year t+1 falls in the same 8–12 percent range with about one-third probability and over 70 percent in the 4–12 percent range.
  - Conditional density modes for year t+1 are in or slightly lower than year t; variance of conditional density tends to be smaller when year t inflation is lower, implying greater stability and persistence at lower inflation levels.

### Inflation inertia in Egypt (measurement and results)
- Methodology:
  - Use reduced-form univariate autoregressive (AR(p)) monthly inflation model; inertia defined as sum of AR coefficients.
  - Re-interpret inertia via spectral analysis: share of components with frequencies longer than one year rises non-linearly as AR coefficient approaches one.
  - OLS estimators are downward biased when series are persistent; median-unbiased estimator is used following Andrews and Chen (1994) with confidence intervals from Hansen’s (1999) grid bootstrap using 200 grid points and 2000 bootstrap replications at each grid point.
- Data and sample splits:
  - Monthly headline CPI inflation = first difference of natural logarithm of seasonally adjusted CPI from IFS, spanning January 2000 to June 2010.
  - Number of lags chosen by Schwartz Information Criterion (SIC); SIC-minimizing lag is 1.
  - Chow test indicates structural break around July 2007; sample split into January 2000–June 2007 and July 2007–June 2010.
  - Core inflation (CBE series excluding several food items and administrative prices) also estimated, but core data available only from January 2005 (short sample).
- Estimated inertia (key statistics reported in Table 3):
  - Median-unbiased estimates of AR(1) sum:
    - January 2000–June 2007: about 0.5.
    - July 2007–June 2010: about 0.4.
  - Implications for spectral shares:
    - Share of components with frequencies longer than one year about 0.45 (first sub-period) and 0.35 (second sub-period).
  - Interpretation:
    - Smaller inertia in July 2007–June 2010 reflects larger short-term shocks to inflation (mainly food prices) and larger month-over-month volatility after mid-2007.
  - Core inflation results (short sample): after mid-2007 core inertia is larger than headline inertia (intuitive since excluding food raises inertia), but in the first sub-period headline inertia exceeded core inertia (difference not statistically significant).

### Determinants of inflation inertia — cross-country analysis
- Cross-country estimation:
  - Quarterly CPI inflation (first difference of log seasonally adjusted CPI) from IFS or INS used for about 130 countries spanning Q1 2000 to Q2 2010.
  - Lag length selected by SIC and Chow tests applied for structural breaks per country.
- Cross-country findings:
  - Egypt’s estimated inertia sits well above the median and average and is close to the upper quartile of the cross-country distribution, indicating inflation in Egypt is more persistent than in many other countries.
  - Positive correlation observed between estimated inflation inertia and average inflation over 2000–09 (Figure 7), consistent with hybrid NKPC implications that higher inertia raises disinflation costs and may be associated with higher sustained inflation.
- Cross-country Tobit regression (summary implication):
  - Lack of counter-cyclical macroeconomic policy and high fiscal deficits are associated with higher inflation persistency.
  - Policy implication: more counter-cyclical monetary policy, establishment of a nominal anchor to stabilize inflation expectations, and fiscal consolidation are key to reduce disinflation costs.

### Policy implications and organization of paper
- Policy implications drawn from empirical results:
  - Reducing inflation inertia lowers the costs of disinflation.
  - Strengthening counter-cyclical monetary policy, establishing a credible nominal anchor (to stabilize inflation expectations), and fiscal consolidation are recommended to lower inflation persistency.
- Paper organization:
  - Section II: Preliminary discussions (inflation in Egypt; importance of inertia; literature).
  - Section III: Estimated inflation inertia in Egypt.
  - Section IV: Determinants of inflation inertia using cross-country data.
  - Section V: Policy implications from cross-country regression.
  - Final section: Conclusions.

*Source: _wp11160 - References (IMF PDF content provided)*

### Section II.

### Section II.

### Investigating Determinants of Inflation Inertia―Model
- Calibration based on Fuhrer (2009) example (NKPC and AR(1) output gap) yields:
  - Inflation inertia increases as price rigidities (coefficient of the output gap γ in the NKPC) become larger.
  - Increased volatility of a shock to inflation in the NKPC reduces inflation inertia; increased volatility of a shock to the output gap increases inflation inertia. Both shocks assumed white noise.
  - Increased persistency in the output gap increases inflation inertia.
- Implications for proxies chosen for cross-country analysis:
  - Degree of market rigidities proxied by market efficiency index in the Global Competitiveness Report; increased rigidities in goods and labor markets → higher inflation persistency via larger γ and output gap persistency.
  - Volatility of non-interest government expenditure over GDP: proxy for volatility of demand shock to the output gap; higher volatility → higher inflation persistency.
  - Volatility of terms of trade change: proxy for supply shock to inflation in the NKPC; theoretical sign inconclusive because terms of trade may affect inflation through the output gap in commodity exporters as well as supply shocks.
  - Rep capita GDP (PPP base): proxy for share of food and energy in CPI; higher per capita GDP → lower share of high-volatility items → controls supply-shock variation in NKPC.
  - Fiscal dominance proxied by fiscal deficit as a share of GDP averaged over the sample period; fiscal dominance can make monetary policy pro-cyclical and increase inflation persistence.
  - Monetary policy framework proxied by inflation targeting dummy (adopted in 2001) and advanced economy dummy; frameworks focusing on inflation stabilization may reduce inflation persistency.
  - Measurement errors in CPI: create negatively correlated measurement errors in inflation, biasing autoregressive estimates downward; good institutions and income level used as proxies to control cross-country variation in measurement error.

### The Data and Methodology
- Data sources and sample:
  - Macroeconomic data (terms of trade, fiscal variables, per capita GDP) from IMF WEO database, averaged over 2000 to 2009; per capita GDP averaged over 1995-99 to avoid endogeneity.
  - Volatilities derived from 2000-09 data.
  - Market rigidities proxied by goods market efficiency score averaged over 2007-2009 in the Global Competitiveness Report; labor market efficiency score excluded due to strong correlation with goods market efficiency score.
  - Country group classification follows Spring 2010 WEO.
  - Inflation targeting dummy takes value one when a country adopted inflation targeting in 2001 based on IMF Annual Report on Exchange Rate Arrangement and Exchange Restrictions (oldest available data).
- Estimation approach:
  - Ordinary Least Squares (OLS) may be biased because it cannot incorporate non-linear relation between estimated autoregressive coefficients and the share of long-frequency inflation components from spectrum analysis.
  - Tobit model used in addition to OLS to avoid bias from censoring/non-linearity.
  - Models estimated for full sample (~130 countries) and sub-samples: advanced countries and commodity exporting countries.
  - Rationale for sub-samples: effects of variables (measurement error, fiscal deficit, terms of trade) may differ across country groups (e.g., advanced economies' deep financial markets mitigate fiscal dominance).

### Results
- Main empirical findings (based on Table 5 and Tobit estimates):
  - Accounting for non-linearity increases explanatory power (higher adjusted R2 in Tobit).
  - Volatility of non-interest fiscal expenditure as a share of GDP (proxy for demand-shock volatility) significantly increases inflation inertia; effect insignificant in advanced countries.
  - Fiscal deficit affects inflation inertia for the full sample, but advanced economies appear insulated from this effect.
  - Advanced countries dummy is significantly negative: advanced countries exhibit lower inflation persistency, consistent with well-anchored inflation expectations and the “great moderation.”
  - Goods market inefficiency not significant for full sample but statistically significant for advanced countries, suggesting supply shocks in NKPC matter more for advanced economies.
  - Inflation targeting dummy in developing countries does not appear to reduce inflation persistency. Possible explanation: upward bias in autoregressive estimates when inflation targets were reduced during the sample period among emerging market countries. Adding a dummy for countries that reduced the inflation target during the sample period attenuates the inflation-targeting coefficient in developing-country regressions.

### Policy Implications
- Two key implications to reduce inflation inertia (relevant for disinflation and maintaining competitiveness):
  - Importance of counter-cyclical macroeconomic policies:
    - Positive effect of volatility of demand shocks (proxied by primary fiscal expenditure as a share of GDP) implies that pro-cyclical policy propagates shocks to the output gap, increasing output gap fluctuations and inflation persistency via the Phillips curve.
    - In the extreme case of perfect offsetting of demand shocks, the output gap would stay at zero and inflation would depend only on white-noise supply shocks in the NKPC, producing zero inflation inertia.
  - Additional benefit of fiscal consolidation to disinflation:
    - Fiscal consolidation reduces inflation not only through lower aggregate demand but also through lower inflation inertia.
    - Persistent large fiscal deficits (fiscal dominance) can cause monetization or unresponsive nominal interest rates, making monetary policy pro-cyclical and increasing inflation persistence.
- Policy prescription summary:
  - Reducing fiscal deficits and implementing more timely counter-cyclical macroeconomic policy are key to reduce inflation inertia and lower the cost of disinflation.
  - Inflation inertia reflects inertia in inflation expectations; pro-cyclicality and inflexibility of interest rates increase expected future pro-cyclicality and thus current inflation inertia.

- Caveat:
  - Estimated reduced-form inflation inertia does not identify required change in the present value of the output gap to remove inflation differentials between Egypt and trade partners. Estimating parameters in the hybrid NKPC is necessary to obtain the sacrifice ratio for disinflation and to guide monetary policy during transition periods.

### Conclusions
- Empirical summary:
  - Inflation inertia for Egypt estimated following Benati (2008): share of components with frequencies longer than one year in Egypt is about 40 percent.
  - Cross-country estimates for about 130 countries indicate Egypt’s inflation inertia is relatively high, around the upper quartile of the sample.
  - Cross-country regression suggests lack of counter-cyclical macroeconomic policy and high fiscal deficit may explain high persistency in Egypt.
- Policy recommendations for Egypt:
  - Implement more counter-cyclical monetary policy associated with establishing a nominal anchor to stabilize inflation expectations.
  - Maintain committed fiscal consolidation to reduce the deficit by 5 percentage points by FY 2014/15.
- Research suggestion:
  - Estimating parameters in the hybrid NKPC is necessary to determine how much the output gap must decline to achieve disinflation (sacrifice ratio); this is proposed as future research.

*Source: _wp11160 - Section II.*

### References

### References

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- Hamilton, James D. (1994): Time Series Analysis, Princeton University Press, Princeton, NJ.
- Hansen, Bruce E. (1999): “The Grid Bootstrap and the Autoregressive Model,” Review of Economics and Statistics, 81 (4), 594-607.
- International Monetary Fund (2004): Arab Republic of Egypt, 2004 Article IV Consultation Staff Report, Washington, D.C.
- International Monetary Fund (2007): Arab Republic of Egypt, 2007 Article IV Consultation Staff Report, Washington, D.C.
- International Monetary Fund (2008): Arab Republic of Egypt, 2008 Article IV Consultation Staff Report, Washington, D.C.
- Levin, Andrew T., Fabio M. Natalucci, and Jeremy M. Piger (2004): “The Macroeconomic Effects of Inflation Targeting,” Federal Reserve Bank of St. Louis Review, July/August 2004, 86 (4), 51-80.
- Levin, Andrew T., Fabio M. Natalucci, and Jeremy M. Piger (2004): “Explicit Inflation Objectives and Macroeconomic Outcomes,” European Central Bank Working Paper No. 383.
- Rabanal, Pau and Juan F. Rubio-Ramirez (2003): “Inflation Persistence: How Much Can We Explain?” Federal Reserve Bank of Atlanta Economic Review, Second Quarter 2003, 43-55.
- Rudd, Jeremy and Karl Whelan (2006): “Can Rational Expectations Sticky-Price Models Explain Inflation Dynamics,” American Economic Review, 96 (1), 303-320.
- World Economic Forum (2008, 2009, 2010): The Global Competitiveness Report, 2007-08, 2008-09, 2009-10.

### Key statistics and tables (selected figures preserved exactly)
- Table 1. Statistics of the Distribution of Inflation for Countries with per capita GDP (PPP base) from US$6,000 to 15,000 (Annual CPI inflation, percent):
  - Average: 12.3, 16.4, 6.6
  - Median: 6.6, 6.4, 5.1
  - Standard deviation: 21.5, 33.6, 6.9
  - Lower quartile: 3.5, 3.1, 2.3
  - Upper quartile: 11.8, 16.8, 8.6
  - Mode in the smoothed histogram 1/: 5.5, 3.5, 2.5
  - Number of observations: 305, 305, 460
  - of which, outliers: 28, 49, 11
  - Note 1/: Eliminating outliers, where outliers are annual inflation either below -5 percent or above 25 percent.
- Table 2. Emerging Market Countries: Transition Matrix, 1980-2009 (Percent), number of observations total: 847. Selected cells (rows = inflation in year t, columns = Range of inflation in year t+1):
  - Row "Below 0 %": Below 0 % = 37.5, 0-4 % = 37.5, 4-8 % = 18.8, 8-12 % = 0.0, 12-16 % = 0.0, 16-20 % = 0.0, Over 20 % = 6.3, observations = 16
  - Row "0-4 %": Below 0 % = 4.1, 0-4 % = 72.3, 4-8 % = 18.2, 8-12 % = 4.7, 12-16 % = 0.7, 16-20 % = 0.0, Over 20 % = 0.0, observations = 148
  - Row "Over 20 %": Below 0 % = 0.4, 0-4 % = 0.8, 4-8 % = 2.3, 8-12 % = 2.7, 12-16 % = 5.7, 16-20 % = 8.4, Over 20 % = 79.7, observations = 261
- Table 3. Egypt: Estimated Headline CPI Inflation (Monthly, Seasonally Adjusted) Inertia, 2000-June 2010:
  - January 2000-July 2007: OLS AROLS Median/unbiased = 0.469; 1/unbiased = 0.51; Lower 90% = 0.10; Upper 90% = 0.32; Statistics derived from OLS: SIC = 0.625; ICD.W. Adj-R2 = 0.350; Additional numbers shown: 0.673, -8.103, -8.021, 2.122, 0.290 (as printed).
  - August 2007-June 2010 and Core vs Headline CPI inflation since January 2005 reported similarly with numeric entries preserved as printed (e.g., August 2007-June 2010: 0.333, 0.424, 0.070, 0.596, 0.147, 0.741, -6.815, -6.681, 1.998, 0.192).
  - Headline inflation January 2005-November 2007: 0.485, 0.606, 0.227, 0.744, 0.318, 1.075, -7.620, -7.485, 1.902, 0.248.
- Table 4. Some Statistics of the Distribution of Inflation Inertia in the 2000s:
  - Egypt: OLS = 0.36, Median Unbiased = 0.48.
  - Cross country estimate: Average = 0.19, Median = 0.20, Median Unbiased = 0.30, Median Unbiased = 0.36.
  - Standard deviation 1/: 0.26, 0.29.
  - Lower quartile: -0.03, 0.06.
  - Upper quartile: 0.37, 0.51.
  - Mode in the smoothed histogram: 0.35, 0.45.
  - Number of samples: 131, 127.
  - Note 1/: Grid bootstrap method for median unbiased estiomator.
- Table 5. Determinants of Inflation Inertia by Cross Country Data, 2000-2010 (selected coefficient magnitudes and statistics preserved exactly):
  - Goods market efficiency (from Global Competitiveness Report): coefficients include 0.056, 0.064, 0.065, 0.127, 0.309, 0.437, 0.418, -0.065, -0.133 with t-statistics (0.77), (0.86), (0.87), (0.87), (1.35), (1.81)*, (1.78)*, (-0.50), (-0.53).
  - Volatility of non-interest fiscal expenditure (as a share of GDP): coefficients include 6.089, 6.270, 6.253, 10.147, 12.881, 11.825, 9.348, 5.431, 10.463 with t-statistics (3.09)* **, (3.15)* **, (3.15)* * *, (2.51)*, (1.83), (1.70), (1.31), (1.69), (1.59).
  - Fiscal deficit as a share of GDP: coefficients include 1.204, 1.373, 1.225, 2.116, 1.044, 0.421, -0.252, 2.249, 6.571 with t-statistics (1.77)*, (1.98)**, (1.74)*, (1.48), (0.56), (0.21), (-0.12), (2.04)*, (2.35)**.
  - Advanced countries dummy: coefficients -0.220, -0.248, -0.223, -0.441 with t-statistics (-2.18)**, (-2.39)**, (-2.11)**, (-2.14)**.
  - ln(GDP) -1: coefficients 0.086, 0.094, 0.087, 0.189, 0.411, 0.469, 0.473, 0.092, 0.339 with t-statistics (2.50)**, (2.68)**, (2.45)**, (2.71)**, (1.22), (1.39), (1.44), (1.65), (2.70)**.
  - Reducing targeted inflation (more than one percentage point): 0.104, 0.263 with t-statistics (1.05), (1.06).
  - Number of samples: variously reported as 120, 120, 120, 120, 30, 30, 30, 28, 28.
  - Censored observations: 25, 25, 64, 10, 10, 15.
  - Mean squared error (σ for Tobit): 0.278, 0.277, 0.276, 0.502, 0.286, 0.275, 0.267, 0.255, 0.439.
  - Adjusted R2 (Pseudo R2 for Tobit): 0.112, 0.237, 0.248, 0.103, -0.012, 0.273, 0.310, 0.036, 0.263.
  - Note 1/: Numbers in parenthesis are t-statistics. ***, ** and * indicate significant (both tales) at 1 percent, 5 percent, and 10 percent, respectively.

### Appendix I — Coefficient of (1)AR Process of Inflation in an Example in Fuhrer (2009)
- Model setup (as presented):
  - Equations: y~t = E_t y_{t+1} + γ ε_t + β π_{t+1}~, y~t = ρ y~_{t-1} + u_t~, Var(u_t, ε_t) = [[σ_u^2, 0],[0, σ_ε^2]].
  - Solution expressions presented for π_t~ and Var(u_t).
- Uni-variate AR(1) estimation of inflation:
  - True estimation equation: π_t = α + φ π_{t-1} + e_t.
  - Probability limit of coefficient of lag of inflation (φ̂) given by the formula preserved exactly in the source (multi-term expression showing dependence on ρ, β, γ, σ_u^2, σ_ε^2).
- Key implication (as stated verbatim in the source):
  - "The right hand side of the above equation suggests that inflation inertia, measured by the coefficient in the uni-variate autoregressive process, has positive correlation to ),(ργ and negative correlation to the ratio of the variance of the shock to inflation to that output gap (i.e., 22 u σ σ ε )."

### Appendix II — Why is Inflation Inertia Overestimated when the Inflation Target Has Been Reduced during the Sample Period?
- Data generating process with a change in targeted inflation at time T (notation preserved):
  - For t ≤ T: π_t - π = α(π_{t-1} - π) + ε_t.
  - For t > T: π_t - π* = α*(π_{t-1} - π*) + ε_t, where π and π* are pre- and post-T targets, and 1 > α.
- OLS applied to pooled sample when the true break is ignored leads to the well-known bias formula for the estimated inertia β̂ (full summation formulas preserved in the source).
- Key result (verbatim conclusion from the source):
  - "Therefore, inflation inertia tends to be overestimated when the inflation target has been reduced during the sample period."

*Content derived from the provided "_wp11160 - References" PDF.*

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