ECONOMIC REPORT OF THE PRESIDENT

inflation up to 2007 and then expectations from the Federal Open
Market Committee onward. Measuring inflation by the core CPI (that
is, excluding food and energy), Figure 2-x depicts the goodness-of-fit
(known as R²) over rolling 20-year periods. During the 1990s, this relationship
was robust, averaging an R 2 of 0.46 (meaning that movements
in the unemployment rate accounted for 46 percent of the variation in
inflation). Over an estimation period that includes the past 20 years,
however, the R² is only slightly above zero (meaning that this model
explains almost none of the recent variation in inflation).
The deterioration in fit in this Phillips curve relationship results in
dramatically less precise estimates for the NAIRU, as shown in Figure
2-xi, which shows the band associated with a 50-percent probability that
the true estimate lies within.1 An increased goodness-of-fit corresponds
to a thinner confidence band, implying less uncertainty over the true
value of the NAIRU. Since 2011 though, uncertainty surrounding the
true NAIRU has risen: A mere 50-percent confidence band in 2014
ranges from –4.3 to 6.1, providing little certainty over the current rate of
unemployment that will keep inflation stable. Moreover this is only one
model of the NAIRU, other models show similar increases in uncertainty
over time and the total uncertainty is even larger than shown by any
Percent
8.0
Figure 2-xiv
NAIRU from Trailing 20-Year Price-Price Phillips Curve
Rolling Regression, 1978–2015
π t – π te = α + βu t + ε t
6.0
2015
4.0
2.0
0.0
1978 1983 1988 1993 1998 2003 2008 2013
Note: NAIRU is the unemployment rate that keeps inflation stable. It is calculated as α/β. Dashed line
represents result from regression over entire sample period. Shaded area indicates a 50 percent
confidence band around the point estimate, calculated using a method discussed in Staiger, Stock, and
Watson (1997) for analyzing the ratio of the means of two dependent normal random variables.
Confidence bands since 2012 include implausible negative values.
Source: Bureau of Labor Statistics; Federal Reserve Board, Haver Analytics; CEA calculations.
1 Confidence band calculated using a method discussed in Staiger, Stock, and Watson
(1997), which extends upon a technique introduced in Fieller (1954). A 50 percent band is
used—as opposed to a one-sigma band—because increasingly higher levels of confidence
produce confidence bands that approach unboundedness starting after 2010.
The Year in Review and the Years Ahead | 115