## _wp13124

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### Introduction
- Context:
  - Despite persistently-high unemployment following the Great Recession, inflation in the United States remained remarkably stable.
  - The paper assesses changing determinants of inflation by fitting a standard open-economy Phillips curve to U.S. data while allowing key parameters to vary over time.
- Main finding (overview):
  - The observed stability of inflation after the crisis reflects the interaction of three factors:
    - inflation expectations have become better anchored and to a lower level;
    - the slope of the Phillips curve has flattened;
    - the importance of import-price inflation has increased.

### Model and estimation
- Model specification:
  - A standard unemployment-based Phillips curve with time-varying slope and time-varying import-price weight.
  - Variables (as defined in the source): headline CPI inflation; inflation expectations; unemployment rate; NAIRU (Non-Accelerating-Inflation Rate of Unemployment) over the medium term; import-price inflation (relative-price of imports deviation from average); cost-push shock.
  - Inflation expectations, the unemployment gap, and the NAIRU evolve via constrained random-walk specifications; short-run inflation expectations are a time-varying weight on long-run expectations and lagged year-over-year CPI inflation.
- Data:
  - Quarterly, seasonally adjusted.
  - Sample period: 1961Q1 to 2012Q2.
  - Relative price of imports: import-price deflator relative to the GDP deflator.
  - Long-run inflation expectations sourced from the Federal Reserve Bank Board.
  - All inflation rates are annualized.
- Estimation method:
  - Non-linear (extended) Kalman filter with state constraints and smoothing (forward and backward recursions adjusted when inequality constraints bind).
  - Measurement matrix uses the Jacobian to linearize the non-linear measurement function.
  - Two-step estimation:
    - Step 1: 10-year rolling regressions with non-linear least squares (parameters and NAIRU constant in each rolling window) to obtain initial shock-variance estimates.
    - Step 2: Constrained maximum likelihood estimation, restricting shock variances not to exceed those from rolling regressions.
  - Identification and robustness:
    - The model calibrates two versions differing in the assumed flexibility of the NAIRU (one relatively stable, one relatively flexible) to address the signal-to-noise identification issue between unemployment-gap and NAIRU shocks.

### Results
- Fit and qualitative behavior:
  - A traditional Phillips curve fits U.S. inflation reasonably well over the sample, including after the Great Recession, except for a handful of episodes with particularly large inflation spikes.
  - Filtered and smoothed estimates are qualitatively similar across NAIRU specifications.
- Evolution of expectations and parameters:
  - Long-run inflation expectations:
    - Became unanchored during the 1970s.
    - Became more backward-looking and volatile in that period.
    - Began drifting downward as the Federal Reserve moved toward inflation targeting in the early 1980s and settled at a lower level (around 2 percent) by about 2000.
  - Short-run expectations:
    - Short-run inflation expectations have become more stable (the time-varying weight on long-run expectations increased) and remained remarkably stable in the several years following the Great Recession.
  - Phillips curve slope:
    - The slope of the Phillips curve has flattened over time.
    - At the end of sample (mid-2012), the slope is roughly half the magnitude it was in the 1970s.
    - The flattening is similar across NAIRU specifications, though the level of the slope is higher when a more flexible NAIRU is assumed.
  - Import-price inflation:
    - The importance of import-price inflation increased over time, consistent with rising import penetration and globalization.
- Decomposition and counterfactuals:
  - Predicted inflation following the Great Recession:
    - Using estimated parameters and given long-run expectations, unemployment rate, and import-price inflation, the Phillips curve explains inflation since the Great Recession well.
    - Short-run inflation expectations had a negligible effect on inflation in the post-crisis period.
    - Downward pressure from high unemployment (mid-2009 to end of sample) was largely offset by higher import prices.
  - Counterfactual using 1973-recession parameters:
    - The model predicts deflation of around 1 percent per year by the end of 2011 under parameter values following the 1973 recession, driven by a large negative contribution from inflation expectations.

### Conclusions and policy implications
- Summary conclusions:
  - A traditional Phillips curve with time-varying parameters describes U.S. inflation dynamics reasonably well across the sample and after the Great Recession.
  - Three key contributors to post-crisis inflation stability:
    - better-anchored and lower long-run inflation expectations;
    - a flatter Phillips curve slope;
    - a greater role for import-price inflation.
- Policy takeaways:
  - A flatter Phillips curve helped avoid deflation since the Great Recession but reduces the effectiveness of policy if inflation rises significantly (i.e., it is a double-edged sword).
  - Policymakers should not take anchored expectations for granted and should act to ensure long-run inflation expectations remain firmly anchored.
  - Further research into structural reasons for the observed flattening of the Phillips curve is warranted.

*Source: Working Paper “The Great Recession and the Inflation Puzzle,” Troy Matheson and Emil Stavrev, WP/13/124 (May 2013).*

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