services and prices of food and beverages, both expressed relative to core pce prices ; and and are the weights of energy and food in total consumption. the core inflation forecasting equation is where is expected long - run inflation ; denotes the level of resource utilization ; controls for the effect of changes in the relative price of core imported goods ; 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, is approximated using the unemployment rate less the congressional budget office ’ s ( cbo ) historical series for the long - run natural rate, while is proxied using the median forecasts of long - run pce or cpi inflation reported in the survey of professional forecasters, with a constant adjustment of 50 basis points prior to 2007 to put the cpi forecasts on a pce basis. ( prior to 1991 : q4, this series is based on the long - run inflation expectations reported in the hoey survey. ) the relative import price term,, is defined as the annualized growth rate of the price index for core imported goods, less the lagged four - quarter change in core pce inflation, all multiplied by the share of nominal core imported goods in nominal gdp. to decompose recent movements in inflation into its various components, the series used in the inflation model – for which data are available only through 2015 : q2 in most cases – are first extended through the end of 2015. in the case of inflation, the extensions are consistent with the medians of fomc participants ’ projections for total and core pce inflation in 2015 that were reported at the press conference following the september fomc meeting. 35 similarly, over the second half of 2015 is defined to be consistent with the median of fomc projections for the 2015 : q4 unemployment rate, less the cbo ’ s estimates of the historical path of the long - run natural rate ; the cbo ’ s 2015 estimate is almost identical to the median of fomc participants ’ most recent projections of the normal longer - run level of the unemployment rate. for changes in the prices of consumer energy and core imports, the 2015 : h2 extrapolations are based on regressions of these two series on current and lagged changes in, respectively, crude oil prices and exchange rates. this approach predicts that energy prices should decline at annual rates of about 6 percent in 2015 : q3

as an expectations - augmented phillips curve. 21 total inflation in turn reflects movements in core inflation, combined with changes in the prices of food and energy. an important feature of this model of inflation dynamics is that the overall effect that variations in resource utilization, import prices, and other factors will have on inflation depends crucially on whether these influences also affect long - run inflation expectations. figure 6 illustrates this point with a stylized example of the inflation consequences of a gradual increase in the level of import prices – perhaps occurring in response to stronger real activity abroad or a fall in the exchange value of the dollar – that causes the rate of change of import prices to be elevated for a time. 22 first, consider the situation shown in panel a, in which households ’ and firms ’ expectations of inflation are not solidly anchored, but instead adjust in response to the rates of inflation that are actually observed. 23 such conditions – which arguably prevailed in the united states from the 1970s to the mid - 1990s – could plausibly arise if the central bank has, in the past, allowed significant and persistent movements in inflation to occur. in this case, the temporary rise in the rate of change of import prices results in a permanent increase in inflation. this shift occurs because the initial increase in inflation generated by a period of rising import prices leads households and firms to revise up their expectations of future inflation. a permanent rise in inflation would also result from a sustained rise in the level of oil prices or a temporary increase in resource utilization. by contrast, suppose that inflation expectations are instead well anchored, perhaps because the central bank has been successful over time in keeping inflation near some specified target and has made it clear to the public that it intends to continue to do so. then the response of inflation to a temporary increase in the rate of change of import prices or any other transitory shock will resemble the pattern shown in panel b. in this case, inflation will deviate from its longer - term level only as long as import prices are rising. but once they level out, inflation will fall back to its previous trend in the absence of other disturbances. 24 a key implication of these two examples is that the presence of well - anchored inflation expectations greatly enhances a central bank ’ s ability to pursue both of its objectives – namely, price stability and full employment. because temporary shifts in the rate of change of import prices or other transitory shocks have no permanent influence on expectations, they have only a transitory effect on inflation. as