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The Estimated Inflation Model and Inflation Decomposition Procedure
The inflation model used in the decomposition procedure includes two equations--an identity for the change in the price index for total personal consumption expenditures (PCE) and a simple reduced-form forecasting equation for core PCE inflation. The identity is \\pi_t= \\pi_t^c+\\omega_t^e \\mathit{RPIE}_t+\\omega_t^f \\mathit{RPIF}_t,
where \\pi_t and \\pi_t^c denote growth rates (expressed as annualized log differences) of total and core PCE prices, respectively; \\mathit{RPIE}_t and \\mathit{RPIF}_t are annualized growth rates for prices of consumer energy goods and services and prices of food and beverages, both expressed relative to core PCE prices; and \\omega_t^e and \\omega_t^f are the weights of energy and food in total consumption. The core inflation forecasting equation is
\\pi_t^c= \\mathrm{.41} \\pi_t^e + \\mathrm{.36} \\pi_{t-1}^c+ \\mathrm{.23} \\pi_{t-2}^c - \\mathrm{.08} \\mathit{SLACK}_t+\\mathrm{.57} \\mathit{RPIM}_t+\\epsilon_t,
where \\pi_t^e is expected long-run inflation; \\mathit{SLACK}_t denotes the level of resource utilization; \\mathit{RPIM}_t controls for the effect of changes in the relative price of core imported goods; \\epsilon_t is a white-noise error term; and the coefficients are ordinary least squares estimates obtained using data from 1990:Q1 to 2014:Q4.
For estimation purposes, \\mathit{SLACK}_t is approximated using the unemployment rate less the Congressional Budget Office's (CBO) historical series for the long-run natural rate,