## 6.   Long-Term Inflation Expectations Regressed on 2.5% and Exponential Lags of Median Inflation

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### Introduction
- Research question: How does unemployment affect inflation, and why did inflation not fall as much as textbook accelerationist Phillips curves predicted after the Great Recession of 2008-2009?
- Two complementary explanations emphasized:
  - Anchored inflation expectations around the Fed’s 2% PCE target (implying 2.5% for core CPI measures).
  - Labor-market slack is better measured by the short-term unemployment rate (percent unemployed for 26–27 weeks or less) rather than total unemployment.
- Main approach: parsimonious Phillips curve where core inflation depends on a constant (reflecting fixed expected inflation) and the average short-term unemployment over the previous four quarters; fit to data starting in 2000.

### Measuring Core Inflation
- Two core-inflation measures used:
  - CPI excluding food and energy (CPIX).
  - Weighted median inflation (Federal Reserve Bank of Cleveland).
- Empirical properties:
  - Quarterly standard deviation of change in inflation: median = 0.46; CPIX = 0.66.
  - Quarterly innovations in median inflation since 2000 are described as “almost entirely permanent,” while CPIX has a substantial transitory component.
- Finding: R2s for Phillips curves are considerably higher when using the weighted median; median CPI filters out industry-specific relative-price noise better than CPIX.

### Recent Thinking About the Phillips Curve
- Textbook and accelerationist Phillips-curve forms:
  - Expectations-augmented: πt = πet + α(ut − u∗t) + εt, α < 0.
  - Accelerationist (backward-looking): πt = πt−1 + α(ut − u∗t) + εt.
- Missing-deflation puzzle:
  - Accelerationist calibrations predicted inflation well below zero after the recession; actual core inflation remained near pre-2008 levels (CPIX: 2.3% to 1.9% from 2007Q4 to 2014Q2; median: 3.0% to 2.2%).
- Anchored expectations evidence:
  - Fed’s 2% core PCE target implies SPF and core-CPI forecasts anchored at 2.5%.
  - SPF median 10-year CPI forecast nearly constant at 2.5% from ≈2000 onward.
- Short-term unemployment rationale:
  - Long-term unemployed exert less downward pressure on wages; short-term unemployed drive wage and inflation dynamics.
  - Since 2008, short-term unemployment rose less sharply and returned closer to pre-recession levels than total unemployment.

### Explaining Core Inflation Since 2000 (Preferred Specification and Results)
- Preferred parsimonious specification (quarterly, four-lag average of short-term unemployment):
  - Starting form: πt = πe + Σj=1..4 αj(us t−j − us∗ t−j ) + εt.
  - Imposed constant natural rate us∗ and equal coefficients αj → πt = φ + α u s t−1 + εt, where us t−1 is average short-term unemployment over t−4 through t−1 and φ = πe − α us∗.
  - If assume πe = 2.5, then us∗ = (2.5 − φ)/α.
- Empirical results (2000Q1–2014Q2, weighted median inflation unless otherwise noted):
  - Full-sample R2 = 0.81 for weighted median; stability test p-value = 0.594 (no evidence of coefficient change across subperiods).
  - Coefficient on short-term unemployment ≈ -1.0 (a 1 percentage point rise in average short-term unemployment over previous four quarters reduces core inflation by 1 percentage point).
  - Assuming πe = 2.5, implied natural rate of short-term unemployment us∗ = 4.4%.
  - Using CPIX instead of median: full-sample R2 = 0.41; coefficient on short-term unemployment falls from -0.89 (pre-2008) to -0.52 (post-2008).
- Comparisons with more conventional specifications:
  - Replacing short-term with total unemployment (anchored expectations) reduces R2 from 0.81 to 0.55 (weighted median).
  - Using backward-looking expected inflation (average of past four quarters) with short-term or total unemployment yields R2 below 0.50.
  - Pre-2008 accelerationist specifications predict large negative inflation for 2010–2014; the anchored-expectations + short-term unemployment specification does not.
- Forecasting implications for 2008–2014:
  - Pre-2008 Phillips curve with anchored expectations + short-term unemployment produced accurate post-2008 forecasts.
  - Pre-2008 with anchored expectations + total unemployment under-predicts actual inflation from 2010 onward (forecasted inflation 2.1 percentage points below actual in 2011Q3; 1.3 points below at end of sample).
  - Accelerationist specifications (expected inflation = past inflation) produce forecasts predicting inflation below zero by the end of the sample (e.g., -0.6% with short-term slack; -2.1% with total slack), inconsistent with realized median inflation averaging 2.2% over last four quarters.

### Explaining Core Inflation Since 1985 (Extended-Sample Results)
- Extended-sample approach (1985–2014Q2) uses weighted median inflation and SPF long-term expectations πFt:
  - Phillips curve: πt = πFt + α(us t−1 − us∗ t−1) + εt.
  - Natural rate us∗ t−1 estimated by HP filter (smoothing parameter = 16,000); HP series computed using data starting in 1975.
- Estimates and fit:
  - Full-sample (1985–2014Q2): coefficient on short-term unemployment = -0.91; R2 = 0.76.
  - Portion of variation in (π − πF) explained by short-term unemployment: R2 = 0.47.
  - Post-2000 subsample: coefficient = -1.11 (close to preferred post-2000 estimate of -0.98).
  - 1985–1999 subsample: coefficient = -0.61 (standard error = 0.22); test for equal coefficient across subsamples p-value = 0.062 (borderline).
  - Conclusion: a stable expectations-augmented Phillips curve with SPF expectations and short-term unemployment explains inflation reasonably well from 1985 onward, with possible modest coefficient change before 2000.

### The Changing Behavior of Expectations
- Hypothesis: Before 2000, SPF long-term expectations were backward-looking; after ≈2000, expectations became anchored near 2.5%.
- Exponential-lag specification for SPF forecasts (1985–1999):
  - πFt = (1/(1−γ)) * [ (1−γ)πt−1 + γ(1−γ)πt−2 + ... + γ39(1−γ)πt−40 ] + εt, truncated at 40 quarters; γ determines decay.
  - Estimated γ = 0.86 for 1985–1999; R2 = 0.85. With γ = 0.86, sum of first four lags = 0.45; remaining lags sum = 0.55 → supports long lag influence on expectations.
- Mixture specification (anchored + backward-looking):
  - πFt = β·2.5 + (1−β)·[exponential-lag backward-looking term] + εt.
  - Estimates:
    - 1985Q1-1999Q4: β = 0.061 (0.044); γ = 0.874 (0.016); R2 = 0.850.
    - 2000Q1-2014Q2: β = 0.809 (0.082); γ = 0.895 (0.060); R2 = 0.128.
    - Split at 1997Q4 (break date with highest Sup-Wald statistic): 1985Q1-1997Q3: β = 0.064 (0.043); γ = 0.877 (0.017); R2 = 0.741. 1997Q4-2014Q2: β = 0.834 (0.062); γ = 0.876 (0.058); R2 = 0.145.
  - Interpretation: sharp regime shift from predominantly backward-looking expectations to strongly anchored expectations around the late 1990s / ≈2000.

### Conclusion and Policy-Relevant Implications
- A parsimonious Phillips curve with two key features fits recent U.S. core inflation notably well (especially when using weighted median inflation):
  - Labor-market slack measured by short-term unemployment.
  - Expected inflation anchored at a constant level (SPF 10-year forecasts ≈ 2.5% for core CPI, reflecting Fed’s 2% PCE anchor).
- Empirical highlights:
  - Preferred post-2000 coefficient on average short-term unemployment ≈ -1.0; implied short-term natural rate ≈ 4.4% assuming πe = 2.5.
  - Weighted median inflation yields substantially higher R2 (0.81) than CPIX (0.41) for the preferred specification.
  - Extended-sample results (1985–2014Q2) support a stable expectations-augmented Phillips curve with SPF expectations and short-term unemployment (full-sample R2 = 0.76; coefficient on short-term unemployment = -0.91).
- Policy-relevant implications:
  - Anchored expectations reduce the dynamic downward pressure on inflation in a prolonged period of elevated unemployment; with anchored expectations, unemployment influences the level of inflation rather than its continual decline.
  - Monitoring the anchoring of expectations is critical: if expectations become unmoored (e.g., Fed changes its target or realized inflation deviates substantially from the target), the Phillips-curve relationship and forecasts will need to be re-evaluated.
- Note: downward nominal wage rigidity and other mechanisms (oil prices, firm balance-sheet weakness, regional uncertainty) are acknowledged as potential contributors but are not required for the good fit of the proposed Phillips curve in this analysis.

*Source: IMF working paper chapter titled "6.   Long-Term Inflation Expectations Regressed on 2.5% and Exponential Lags of Median Inflation" (content provided from the PDF).*

### References................................................................................................22

### References................................................................................................22

### Figures
- 1.   Weighted Median Inflation vs. CPIX Inflation, 2000-2014................................... 25
- 2.   Long-Term SPF Inflation Expectations vs. 4-Quarter Moving Average of Median 
 Inflation, 1985-2014........................................................................ .......26
- 3.   Short-Term Unemployment vs. Total Unemployment, 1985-2014.......................... .27
- 4.   Core Inflation vs. Fitted Values from Preferred Phillips Curve, 2000Q1-2014Q2......... 28
- 5.   Forecasts for Median Inflation for 2008Q1-2014Q2...........................................29
- 6.   Short-Term   Unemployment and its Trend, 1985-2014......................................... 30
- 7.   Actual and Fitted Values from Phillips Curve with Long-Term Expectations.............. 31

### Tables
- 1.   Preferred Phillips Curve Specifications..........................................................32
- 2.   More Conventional Phillips Curve Specifications, Weighted Median Inflation............33
- 3.   More Conventional Phillips Curve Specifications, CPIX Inflation...........................34
- 4.   Phillips Curve with Long-Term Inflation Expectations......................................... 35
- 5.   Long-Term Inflation Expectations Regressed on Exponential Lags of Median   
      Inflation,      1985Q1-1999Q4.........................................................................      35

*Source: _wp1539 - References................................................................................................22*

### 6.   Long-Term Inflation Expectations Regressed on 2.5% and Exponential Lags of

### 6.   Long-Term Inflation Expectations Regressed on 2.5% and Exponential Lags of Median Inflation

### Introduction
- Research question: How does unemployment affect inflation, and why did inflation not fall as much as textbook accelerationist Phillips curves predicted after the Great Recession of 2008-2009?
- Two complementary explanations emphasized:
  - Anchored inflation expectations around the Fed’s 2% PCE target (implying 2.5% for core CPI measures).
  - Labor-market slack is better measured by the short-term unemployment rate (percent unemployed for 26–27 weeks or less) rather than total unemployment.
- Main approach: parsimonious Phillips curve where core inflation depends on a constant (reflecting fixed expected inflation) and the average short-term unemployment over the previous four quarters; fit to data starting in 2000.

### Measuring Core Inflation
- Two core-inflation measures used:
  - CPI excluding food and energy (CPIX).
  - Weighted median inflation (Federal Reserve Bank of Cleveland).
- Empirical properties reported:
  - Quarterly standard deviation of change in inflation: median = 0.46; CPIX = 0.66.
  - Quarterly innovations in median inflation since 2000 are described as “almost entirely permanent,” while CPIX has a substantial transitory component.
- Finding: R2s for Phillips curves are considerably higher when using the weighted median; median CPI filters out industry-specific relative-price noise better than CPIX.

### Recent Thinking About the Phillips Curve
- Textbook and accelerationist Phillips curve summarized:
  - Expectations-augmented Phillips curve: πt = πet + α(ut − u∗t) + εt, α < 0.
  - Accelerationist form with backward-looking expectations: πt = πt−1 + α(ut − u∗t) + εt.
- Missing-deflation puzzle: accelerationist calibrations predicted inflation well below zero after the recession; actual core inflation remained near pre-2008 levels (CPIX: 2.3% to 1.9% from 2007Q4 to 2014Q2; median: 3.0% to 2.2%).
- Anchored expectations:
  - Fed’s 2% core PCE target implies SPF and core-CPI forecasts anchored at 2.5%.
  - SPF median 10-year CPI forecast nearly constant at 2.5% from ≈2000 onward.
- Short-term unemployment rationale:
  - Long-term unemployed exert less downward pressure on wages; short-term unemployed drive wage and inflation dynamics.
  - Since 2008, short-term unemployment rose less sharply and returned closer to pre-recession levels than total unemployment.

### Explaining Core Inflation Since 2000
- Preferred parsimonious specification (quarterly, four-lag average of short-term unemployment):
  - Start from πt = πe + Σj=1..4 αj(us t−j − us∗ t−j ) + εt.
  - Impose constant natural rate us∗ and equal coefficients αj → reduces to πt = φ + α u s t−1 + εt, where us t−1 is average short-term unemployment over t−4 through t−1 and φ = πe − α us∗.
  - If assume πe = 2.5, then us∗ = (2.5 − φ)/α can be calculated.
- Empirical results (2000Q1–2014Q2, weighted median inflation unless otherwise noted):
  - Full-sample R2 = 0.81 for weighted median; no evidence of coefficient change across subperiods (p-value for stability = 0.59).
  - Coefficient on short-term unemployment ≈ -1.0 (a 1 percentage point rise in average short-term unemployment over previous four quarters reduces core inflation by 1 percentage point).
  - Assuming πe = 2.5%, implied natural rate of short-term unemployment us∗ = 4.4%.
  - Using CPIX instead of median: full-sample R2 falls to 0.41; coefficient on short-term unemployment falls from -0.89 (pre-2008) to -0.52 (post-2008).
- Comparisons with more conventional specifications:
  - Replacing short-term with total unemployment (anchored expectations) reduces R2 from 0.81 to 0.55 (weighted median).
  - Using backward-looking expected inflation (average of past four quarters) with short-term or total unemployment yields R2 below 0.50.
  - Pre-2008 estimated Phillips curves with accelerationist expectations predict large negative inflation (the “missing deflation”) for 2010–2014; the anchored-expectations + short-term unemployment specification does not.
- Forecasting implications (2008–2014 period):
  - Pre-2008 Phillips curve with anchored expectations + short-term unemployment produced accurate post-2008 forecasts.
  - Pre-2008 with anchored expectations + total unemployment under-predicts actual inflation from 2010 onward (forecasted inflation 2.1 percentage points below actual in 2011Q3; 1.3 points below at end of sample).
  - Accelerationist specifications (expected inflation = past inflation) produce forecasts predicting inflation below zero by the end of the sample (e.g., -0.6% with short-term slack; -2.1% with total slack), inconsistent with realized median inflation averaging 2.2% over last four quarters.

### Explaining Core Inflation Since 1985
- Extended-sample approach (1985–2014Q2) uses weighted median inflation and directly includes SPF long-term expectations πFt as the expected-inflation measure:
  - Phillips curve: πt = πFt + α(us t−1 − us∗ t−1) + εt.
  - Natural rate us∗ t−1 estimated by smoothing short-term unemployment with HP filter (smoothing parameter = 16,000); HP series computed using data starting in 1975 to reduce end-point issues.
- Estimates and fit:
  - Full-sample (1985–2014Q2): coefficient on short-term unemployment = -0.91; R2 = 0.76.
  - Portion of variation in (π − πF) explained by short-term unemployment: R2 = 0.47.
  - Post-2000 subsample: coefficient = -1.11 (close to preferred post-2000 estimate of -0.98).
  - 1985–1999 subsample: coefficient = -0.61 (standard error = 0.22); test for equal coefficient across subsamples yields p-value = 0.062 (borderline).
  - Conclusion: a stable expectations-augmented Phillips curve with SPF expectations and short-term unemployment explains inflation reasonably well from 1985 onward, with possible modest coefficient change before 2000.

### The Changing Behavior of Expectations
- Hypothesis: Before 2000, SPF long-term expectations were backward-looking (depend on past inflation); after ≈2000, expectations became anchored near 2.5%.
- Exponential-lag specification for SPF forecasts (1985–1999):
  - πFt = (1/(1−γ)) * [ (1−γ)πt−1 + γ(1−γ)πt−2 + ... + γ39(1−γ)πt−40 ] + εt, truncated at 40 quarters; coefficients constrained to sum to one; γ determines decay rate.
  - Estimated γ = 0.86 for 1985–1999; R2 = 0.85. With γ = 0.86, sum of first four lags = 0.45; remaining lags sum = 0.55 → supports long lag influence on expectations.
- Nested test for mixture of anchored and backward-looking expectations:
  - πFt = β·2.5 + (1−β)·[exponential-lag backward-looking term] + εt.
  - Estimates for 1985–1999: coefficient on 2.5% ≈ 0.06 (statistically indistinguishable from zero).
  - Estimates for 2000–2014Q2: coefficient on 2.5% ≈ 0.81.
  - Sup-Wald test for an unknown break strongly rejects stability; break date with highest statistic = 1997Q4. Splitting at 1997Q4 yields β ≈ 0.06 (pre-break) and β ≈ 0.83 (post-break).
- Interpretation: evidence of a sharp regime shift from backward-looking expectations to strongly anchored expectations around the late 1990s / ≈2000.

### Conclusion
- A parsimonious Phillips curve with two key features fits recent U.S. core inflation notably well (especially when using weighted median inflation):
  - Labor-market slack measured by short-term unemployment.
  - Expected inflation anchored at a constant level (SPF 10-year forecasts ≈ 2.5% for core CPI, reflecting Fed’s 2% PCE anchor).
- Empirical highlights:
  - Preferred post-2000 coefficient on average short-term unemployment ≈ -1.0; implied short-term natural rate ≈ 4.4% assuming πe = 2.5.
  - Weighted median inflation yields substantially higher R2 (0.81) than CPIX (0.41) for the preferred specification.
  - Extended-sample results (1985–2014Q2) support a stable expectations-augmented Phillips curve with SPF expectations and short-term unemployment (full-sample R2 = 0.76; coefficient on short-term unemployment = -0.91).
- Policy-relevant implications:
  - Anchored expectations reduce the dynamic downward pressure on inflation in a prolonged period of elevated unemployment; with anchored expectations, unemployment influences the level of inflation rather than its continual decline.
  - Monitoring the anchoring of expectations is critical: if expectations become unmoored (e.g., Fed changes its target or realized inflation deviates substantially from the target), the Phillips-curve relationship and forecasts will need to be re-evaluated.
- Note: downward nominal wage rigidity and other mechanisms (oil prices, firm balance-sheet weakness, regional uncertainty) are acknowledged as potential contributors but are not required for the good fit of the proposed Phillips curve in this analysis.

*Source: IMF working paper chapter titled "6.   Long-Term Inflation Expectations Regressed on 2.5% and Exponential Lags of Median Inflation" (content provided from the PDF).*

### References

### _wp1539 - References

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- Phillips, A. (1958): “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957,” Economica, 25, 283–299.
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- Stock, J. (2011): “Discussion of Ball and Mazumder, ‘Inflation Dynamics and the Great Recession’,” Brookings Papers on Economic Activity, 387–402.
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- Stock, J. and M. Watson (2010): “Modeling inflation after the crisis,” Proceedings - Economic Policy Symposium - Jackson Hole, 173–220.
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### Figures (titles and sample coverage)
- Figure 1: Weighted Median Inflation vs. CPIX Inflation, 2000-2014 (series labeled Median and CPIX; Inflation (%) on y-axis; quarters from 2000Q1 to 2014Q1 on x-axis).
- Figure 2: Long-Term SPF Inflation Expectations vs. 4-Quarter Moving Average of Median Inflation, 1985-2014 (Inflation (%) from 0 to 5; quarters from 1985Q1 to 2014Q1).
- Figure 3: Short-Term Unemployment vs. Total Unemployment, 1985-2014 (Unemployment (%) from 0 to 12; quarters from 1985Q1 to 2014Q1).
- Figure 4: Core Inflation vs. Fitted Values from Preferred Phillips Curve, 2000Q1-2014Q2 (panels (a)–(d) for Weighted Median Inflation-Quarterly, CPIX Inflation-Quarterly, and 4-Quarter Moving Averages).
- Figure 5: Forecasts for Median Inflation for 2008Q1-2014Q2 (panels (a)–(d) showing Actual Median Inflation and Forecasted Inflation under different expectation/unemployment specifications).
- Figure 6: Short-Term Unemployment and its Trend, 1985-2014 (Short-Term Unemployment (%) with series STU and STU*).
- Figure 7: Actual and Fitted Values from Phillips Curve with Long-Term Expectations (panels (a) π and (b) π − πF for 1985Q1–2014Q1).

### Key empirical results and statistics (from tables)
- Table 1: Preferred Phillips Curve Specification πt = φ + α u_s,t−1 + εt (OLS with robust (HAC) standard errors; stability test reports p-value for Wald test around 2008Q1).
  - (1) Median Inflation, periods:
    - 2000Q1-2007Q4: φ = 6.670 (0.704); α = -0.960 (0.175); R2 = 0.568
    - 2008Q1-2014Q2: φ = 7.177 (0.401); α = -1.053 (0.083); R2 = 0.823
    - 2000Q1-2014Q2: φ = 6.781 (0.332); α = -0.981 (0.076); R2 = 0.809
    - Stability Test p-value: 0.594
  - (2) CPIX Inflation:
    - 2000Q1-2007Q4: φ = 5.879 (0.798); α = -0.891 (0.201); R2 = 0.401
    - 2008Q1-2014Q2: φ = 4.325 (0.841); α = -0.519 (0.174); R2 = 0.266
    - 2000Q1-2014Q2: φ = 4.690 (0.417); α = -0.597 (0.098); R2 = 0.412
    - Stability Test p-value: 0.314

- Table 2: More Conventional Phillips Curve Specifications, Weighted Median Inflation (four model variants reported across same subperiods).
  - Model (1) (same as Table 1 median results): identical φ, α, R2 and Stability Test p-value 0.594.
  - Model (2) πt = φ + α u_t−1 + εt:
    - 2000Q1-2007Q4: φ = 5.542 (0.584); α = -0.567 (0.121); R2 = 0.536
    - 2008Q1-2014Q2: φ = 4.168 (0.668); α = -0.291 (0.095); R2 = 0.334
    - 2000Q1-2014Q2: φ = 4.282 (0.366); α = -0.309 (0.069); R2 = 0.553
    - Stability Test p-value: 0.206
  - Model (3) includes 1/4 lagged average of inflation and u_s,t−1:
    - φ and α reported with R2 = 0.206, 0.238, 0.448; Stability Test p-value: 0.710
  - Model (4) includes 1/4 lagged average and u_t−1:
    - R2 = 0.131, 0.275, 0.401; Stability Test p-value: 0.021

- Table 3: More Conventional Phillips Curve Specifications, CPIX Inflation (four model variants).
  - Model (1) (same as Table 1 CPIX results): Stability Test p-value: 0.314
  - Model (2) πt = φ + α u_t−1 + εt:
    - R2 = 0.357, 0.054, 0.248 across subperiods; Stability Test p-value: 0.024
  - Model (3) with lagged inflation average and u_s,t−1:
    - R2 = -0.020, -0.259, 0.030; Stability Test p-value: 0.864
  - Model (4) with lagged inflation average and u_t−1:
    - R2 = -0.047, -0.223, 0.019; Stability Test p-value: 0.391

- Table 4: Phillips Curve with Long-Term Inflation Expectations πt = πF,t + α(u_s,t−1 − u_s*,t−1) + εt
  - Sample splits and estimates:
    - 1985Q1-1999Q4: α = -0.606 (0.222); R2 = 0.619
    - 2000Q1-2014Q2: α = -1.112 (0.116); R2 = 0.762
    - 1985Q1-2014Q2: α = -0.909 (0.150); R2 = 0.759
    - Stability Test p-value: 0.062

- Table 5: Long-Term Inflation Expectations Regressed on Exponential Lags of Median Inflation, 1985Q1-1999Q4
  - γ = 0.860 (0.015)
  - R2 = 0.846

- Table 6: Long-Term Inflation Expectations Regressed on 2.5% and Exponential Lags of Median Inflation
  - Specification and subperiod estimates:
    - 1985Q1-1999Q4: β = 0.061 (0.044); γ = 0.874 (0.016); R2 = 0.850
    - 2000Q1-2014Q2: β = 0.809 (0.082); γ = 0.895 (0.060); R2 = 0.128
    - 1985Q1-1997Q3: β = 0.064 (0.043); γ = 0.877 (0.017); R2 = 0.741
    - 1997Q4-2014Q2: β = 0.834 (0.062); γ = 0.876 (0.058); R2 = 0.145

### Notes on estimation reported in tables
- OLS with robust (HAC) standard errors is used throughout (standard errors shown in parentheses).
- The stability test reports the p-value for the Wald test of structural stability around 2008Q1 (p-values reported alongside model summaries where applicable).

*Source: _wp1539 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1539.pdf_