Explaining Inflation During the Great Contraction Robert G. Murphy Department of Economics Boston College Chestnut Hill, MA 02467 murphyro@bc.edu January 4, 2013 ODE Advisor Session, American Economic Association Meetings, San Diego, CA
Overview 1. Document failure of Phillips curve models to accurately explain recent inflation experience in the United States. 2. Illustrate time-varying slope of the Phillips curve. 3. Explore reasons why the slope might vary over time and explicitly account for this time variation. 4. Focus on implications of the sticky-price and stickyinformation approaches to price adjustment. 5. Introduce proxies for the inflation environment and uncertainty about regional economic conditions.
Findings 1. Phillips curve can explain recent behavior of inflation when modified to account for implications of sticky-information approach. 2. Unlike Ball and Mazumder (BPEA 2011), no need to rely on anchored expectations. 3. Able to account for recent behavior of inflation using traditional core measures rather than median inflation: The consumer price index (CPI) less food and energy; The price index for personal consumption expenditures (PCE) less food and energy.
Standard Phillips Curve Model (Gordon, 1983; Fuhrer, 1995; Staiger et al, 1997) (1) π t = π e n t + β u t u t + ε t (2) π t e = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ] (3) n π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β u t u t + ε t where term,. ε t u t u t n is assumed to be uncorrelated with the error
Alternative Measures of Gap Variable (a) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β[u t u t n ] where β < 0. (b) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β[y t y t n ] where β > 0.
Table 1: Phillips Curve Estimates for Sample Period 1960:1 to 2007:4 (a) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β[u t u t n ] (b) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β[y t y t n ] (a) Unemployment Gap (b) GDP Gap Inflation Measure Total CPI Core CPI Total CPI Core CPI Coefficient for β -0.530 (0.095) -0.498 (0.081) 0.282 (0.048) 0.235 (0.042) RM 1.711 1.465 1.696 1.483 p -value for H 0 : coefficients on lagged inflation sum to one 0.607 0.854 0.891 0.971 Inflation Measure Total PCE Core PCE Total PCE Core PCE Coefficient for β -0.384 (0.071) -0.311 (0.052) 0.199 (0.36) 0.143 (0.027) RM 1.285 0.936 1.281 0.950 p -value for H 0 : coefficients on lagged inflation sum to one 0.666 0.754 0.900 0.744
Figure 1: Natural Rate of Unemployment, 1960:1-2020:4 Percent of Potential Labor Force 5 5.5 6 6.5 1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1 Long-Term Natural Rate Short-Term Natural Rate Source: Congressional Budget Office
Figure 2: Dynamic Predictions of Inflation for 2008:1-2012:2 Using 1960:1-2007:4 Sample Period 4-Quarter Moving Average (A) Total CPI Inflation Quarterly Percent Change at Annual Rate -10-5 0 5 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap Prediction LT Unemployment Gap Prediction GDP Gap Prediction
(B) Total PCE Inflation Quarterly Percent Change at Annual Rate -6-4 -2 0 2 4 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 qdate Actual Inflation ST Unemployment Gap Prediction LT Unemployment Gap Prediction GDP Gap Prediction
Figure 3: Dynamic Predictions of Inflation for 2008:1-2012:2 Using 1960:1-2007:4 Sample Period 4-Quarter Moving Average (A) Core CPI Inflation Quarterly Percent Change at Annual Rate -10-5 0 5 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap Prediction LT Unemployment Gap Prediction GDP Gap Prediction
(B) Core PCE Inflation Quarterly Percent Change at Annual Rate -4-2 0 2 4 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap Prediction LT Unemployment Gap Prediction GDP Gap Prediction
Figure 5: Dynamic Predictions of Inflation for 2011:1-2012:4 Using 1960:1-2010:4 Sample Period 4-Quarter Moving Average (A) Core CPI Quarterly Percent Change at Annual Rate -2-1 0 1 2 3 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap Prediction LT Unemployment Gap Prediction GDP Gap Prediction
(B) Core PCE Quarterly Percent Change at Annual Rate -1 0 1 2 3 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap Prediction LT Unemployment Gap Prediction GDP Gap Prediction
Figure 6: Time-Varying Slope Coefficient For Core CPI Inflation 40-Quarter Rolling Samples Centered at Date Shown (A) Short-term Unemployment Gap Coefficient on Gap Variable -2-1.5-1 -.5 0.5 1965q1 1970q1 1975q1 1980q1 1985q1 1990q1 1995q1 2000q1 2005q1
(B) GDP Gap Coefficient on Gap Variable -.2 0.2.4.6.8 1965q1 1970q1 1975q1 1980q1 1985q1 1990q1 1995q1 2000q1 2005q1
Figure 7: Time-Varying Slope Coefficient For Core PCE Inflation 40-Quarter Rolling Samples Centered at Dates Shown (A) Short-term Unemployment Gap Coefficient on Gap Variable -1.5-1 -.5 0.5 1965q1 1970q1 1975q1 1980q1 1985q1 1990q1 1995q1 2000q1 2005q1
(B) GDP Gap Coefficient on Gap Variable -.2 0.2.4.6 1965q1 1970q1 1975q1 1980q1 1985q1 1990q1 1995q1 2000q1 2005q1
Table 2: Phillips Curve Estimates for Core Inflation Sample Periods: 1960:1 to 1984:4 and 1985:1 to 2007:4 (a) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β[u t u t n ] (b) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β[y t y t n ] (a) Unemployment Gap Sample Period 1960:1-1984:4 (b) GDP Gap Inflation Measure Core CPI Core PCE Core CPI Core PCE Coefficient for β -0.555 (0.121) -0.353 (0.072) 0.250 (0.061) 0.153 (0.037) RM 1.956 1.169 1.992 1.203 p -value for H 0 : coefficients on lagged inflation sum to one 0.895 0.811 0.950 0.829 Sample Period 1985:1-2007:4 (a) Unemployment Gap (b) GDP Gap Inflation Measure Core CPI Core PCE Core CPI Core PCE Coefficient for β -0.254 (0.069) -0.128 (0.073) 0.155 (0.038) 0.093 (0.041) RM 0.542 0.572 0.535 0.565 p -value for H 0 : coefficients on lagged inflation sum to one 0.666 0.583 0.889 0.731
Figure 10: Dynamic Predictions of Inflation for 2008:1-2012:2 Using 1985:1-2007:4 Sample Period 4-Quarter Moving Average (A) Core CPI Inflation Quarterly Percent Change at Annual Rate -4-2 0 2 4 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap GDP Gap
(B) Core PCE Inflation Quarterly Percent Change at Annual Rate -2-1 0 1 2 3 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation ST Unemployment Gap GDP Gap
Alternative Specifications for Phillips Curve (4) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β 0 [u t u n t ] + β 1 π t [u t u n t ]+ β 2 σ π t [u t u n t ]+ β 3 σ y t [u t u n t ] where the slope coefficient varies with the inflation environment (π t,σ π t ) and/or regional dispersion in economic conditions (σ y t ): Sticky Price Model: (e.g., Ball, Mankiw, and Romer, BPEA 1988) β 1 < 0, β 2 < 0, β 3 = 0. Sticky Information Model: (e.g., Mankiw and Reis, QJE 2002) β 1 < 0, β 2 < 0, β 3 < 0.
Figure 12: Measures of the Inflation Environment Mean and Standard Deviation of Inflation, Rolling 40-Quarter Samples Centered at Date Shown Core CPI Inflation Percent 0 2 4 6 8 1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 Mean of Inflation Standard Deviation of Inflation
Core PCE Inflation Percent 0 2 4 6 8 1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 Mean of Inflation Standard Deviation of Inflation Note: Data are 4-quarter moving average of the respective series.
Figure 11: Regional Dispersion of Economic Conditions Standard Deviation of State Personal Income Growth Around National Average Percent 0 2 4 6 8 1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 Note: Data are 4-quarter moving average of quarterly standard deviation. Growth rate of personal income is computed as percent change over same quarter a year ago.
Table 3: Phillips Curve Estimates with Level and Variance of Inflation Sample Periods: 1960:1 to 2007:4 and 1960:1 to 2012:2 (a) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β 0 [u t u t n ] (b) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β 0 [u t u t n ]+ β 1 π t [u t u t n ]+ β 2 σ t π [u t u t n ] Sample Period 1960:1-2007:4 Inflation Measure Core CPI Core PCE β 0 β 1 β 2 RM p -value for H 0 :β 1 = β 2 = 0 Equation (a) Equation (b) Equation (a) Equation (b) -0.498 0.222-0.311 0.048 (0.081) (0.245) (0.052) (0.189) -0.349-0.066 (0.106) (0.070) 0.441-0.031 (0.193) (0.224) 1.465 1.422 0.936 0.928 0.001 0.079 Sample Period 1960:1 to 2012:2 Inflation Measure Core CPI Core PCE β 0 β 1 β 2 RM p -value for H 0 :β 1 = β 2 = 0 Equation (a) Equation (b) Equation (a) Equation (b) -0.328 0.342-0.208 0.137 (0.066) (0.141) (0.042) (0.093) -0.360-0.057 (0.102) (0.068) 0.425-0.100 (0.186) (0.181) 1.465 1.381 0.944 0.911 0.000 0.000
Table 4: Phillips Curve Estimates with Dispersion of Regional Income Growth Sample Periods: 1960:1 to 2007:4 and 1960:1 to 2012:2 (c) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β 0 [u t u t n ]+ β 3 σ t y [u t u t n ] (d) π t = 0.25[π t 1 + π t 2 + π t 3 + π t 4 ]+ β 0 [u t u t n ]+ β 1 π t [u t u t n ]+ β 2 σ t π [u t u t n ]+ β 3 σ t y [u t u t n ] Sample Period 1960:1-2007:4 Inflation Measure Core CPI Core PCE β 0 β 1 β 2 β 3 RM p -value for H 0 :β 1 = β 2 = 0 Equation (c) Equation (d) Equation (c) Equation (d) 0.584 0.649 0.429 0.264 (0.240) (0.261) (0.152) (0.185) -0.238 0.013 (0.106) (0.069) 0.488 0.186 (0.187) (0.216) -0.330-0.346-0.226-0.293 (0.069) (0.089) (0.044) (0.061) 1.389 1.371 0.879 0.877 0.035 0.253 Sample Period 1960:1 to 2012:2 Inflation Measure Core CPI Core PCE β 0 β 1 β 2 β 3 RM p -value for H 0 :β 1 = β 2 = 0 Note: π is the inflation rate, Equation (c) Equation (d) Equation (c) Equation (d) 0.653 0.783 0.432 0.432 (0.167) (0.173) (0.108) (0.108) -0.251 0.026 (0.102) (0.067) 0.470 0.035 (0.180) (0.174) -0.347-0.344-0.226-0.277 (0.055) (0.084) (0.035) (0.058) 1.347 1.331 0.865 0.866 0.034 0.541 is the unemployment rate, * is the CBO estimate of the short-
Figure 13: Dynamic Predictions of Inflation for 2008:1-2012:2 Using 1960:1-2007:4 Sample Period Including Interaction Terms for Inflation Environment Core CPI Inflation Quarterly Percent Change at Annual Rate -4-2 0 2 4 6 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation Predicted Inflation Two-standard-error Confidence Bands
Core PCE Inflation Quarterly Percent Change at Annual Rate -1 0 1 2 3 4 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation Two-standard-error Confidence Bands Predicted Inflation
Figure 14: Dynamic Predictions of Inflation for 2008:1-2012:2 Using 1960:1-2007:4 Sample Period Including Interaction Term for Regional Dispersion of Income Growth Core CPI Inflation Quarterly Percent Change at Annual Rate -4-2 0 2 4 6 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation Predicted Inflation Two-standard-error Confidence Bands
Core PCE Inflation Quarterly Percent Change at Annual Rate 0 1 2 3 4 2000q1 2002q1 2004q1 2006q1 2008q1 2010q1 2012q1 Actual Inflation Two-standard-error Confidence Bands Predicted Inflation
Summary 1. Standard Phillips curve models predict ongoing shortfall in economic activity should have led to deflation. 2. Evidence suggests slope of Phillips curve has varied over time and is probably lower today than several decades ago. 3. Account explicitly for reasons why slope may vary by focusing on implications of the sticky-price and stickyinformation approaches to price adjustment. 4. Find that a modified Phillips curve which includes a proxy for the uncertainty of regional economic conditions can explain the recent behavior of inflation.
Future Work 1. Document whether underprediction of inflation has happened in other countries. 2. Explore formal models linking implications of the sticky-information approach to the slope of the Phillips curve. 3. Develop and test other proxies for uncertainty about regional economic conditions.