Short-term headline-core inflation dynamics.
Mehra, Yash P. ; Reilly, Devin
Many analysts contend that the Federal Reserve under Chairmen Alan
Greenspan and Ben Bernanke has conducted monetary policy that focuses on
core rather than headline inflation. The measure of core inflation used
excludes food and energy prices. (1) The main argument in favor of using
core inflation to implement monetary policy is that core inflation
approximates the permanent or trend component of inflation much better
than does headline inflation, the latter being influenced more by
transitory movements in food and energy prices. The empirical evidence
favorable to the use of core inflation in policy is recently reviewed in
Mishkin (2007b). This empirical evidence consists of examining
short-term dynamics between headline and core inflation measures,
indicating that, in samples that start after the early 1980s, headline
inflation has reverted more strongly toward core inflation than core
inflation has moved toward headline inflation. However, the research
reviewed also shows that the evidence indicating the reversion of
headline inflation to core inflation is quite weak in samples that start
in the 1960s, suggesting that headline-core inflation dynamics may not
be stable over time. (2)
In this article we re-examine the short-term dynamics between
headline and core measures of inflation over a longer sample period of
1959-2007. We offer new evidence that headline-core inflation dynamics
have indeed changed during this sample period and that this change in
dynamics may be due to a change in the conduct of monetary policy in
1979. (3) In particular, we examine such dynamics over three
sub-periods: 1959:1-1979:1, 1979:2-2001:2, and 1985:1-2007:2. We
consider the sub-sample 1985:1-2007:2, as it spans a period of
relatively low and stable inflation. We consider both the consumer price
index (CPI) and the personal consumption expenditure (PCE) deflator. The
data used is biannual because the structural vector autoregression (VAR)
model employed uses the Livingston survey data on the public's
expectations of headline CPI inflation, which is available twice a year.
However, the basic results on the change in short-term headline-core
inflation dynamics are robust to using quarterly data and to including
additional determinants of inflation in bivariable headline-core
inflation regressions.
The empirical evidence presented here indicates headline and core
measures of inflation are co-integrated, suggesting long-run
co-movement. However, the ways these two variables adjust to each other
in the short run and generate co-movement have changed across these
sub-periods. In the pre-1979 sample period, when a positive gap opens up
with headline inflation rising above core inflation, the gap is
eliminated mainly as a result of headline inflation not reverting and
core inflation moving toward headline inflation. This result suggests
headline inflation is better than core inflation in assessing the
permanent component of inflation. In post-1979 sample periods, however,
the positive gap is eliminated as a result of headline inflation
reverting more strongly toward core inflation than core inflation moving
toward headline inflation. This suggests core inflation would be better
than headline inflation in assessing the permanent component of
inflation.
Recent research suggests a monetary policy explanation of this
change in short-term headline-core inflation dynamics. We focus on a
version of monetary policy explanation suggested by the recent work of
Leduc, Sill, and Stark (2007), which attributes the persistently high
inflation of the 1970s to a weak monetary policy response to surprise
increases in the public's expectations of inflation. In particular,
using a structural VAR that includes a direct survey measure of expected
(headline CPI) inflation, Leduc, Sill, and Stark show that prior to
1979, the Federal Reserve accommodated exogenous movements in expected
inflation seen in the result that the short-term real interest rate did
not increase in response to such movements, which then led to persistent
increases in actual inflation. Such Federal Reserve behavior, however,
is absent post-1979, leading to a decline in the persistence of
inflation. We illustrate that such a change in Federal Reserve behavior
is also capable of generating the change in headline-core inflation
dynamics documented above.
In particular, when we consider a variant of the structural VAR
model that includes expected headline inflation, actual headline
inflation, actual core inflation, and a short-term nominal interest
rate, we find that a change in the interest rate response to exogenous
movements in expected headline inflation can explain the change in
actual headline-core inflation dynamics. Thus, prior to 1979, when the
Federal Reserve accommodated exogenous movements in expected headline
inflation, a surprise increase in expected headline inflation (say, due
to higher energy and food prices) was not reversed, leading to
persistent increases in actual headline inflation with core inflation
moving toward headline inflation. A surprise increase in expected
headline inflation thus generates co-movement between actual headline
and core inflation measures. Since such Federal Reserve accommodation of
shocks to expected headline inflation is absent post-1979, surprise
increases in expected headline inflation are reversed, with actual
headline inflation inverting to core inflation. In the most recent
sample period, 1985:1-2007:2, surprise increases in expected headline
inflation have no significant effect on core inflation, whereas surprise
increases in core inflation do lead to increases in headline inflation,
generating co-movement between headline and core CPI inflation measures.
Since movements in food and energy prices are likely significant sources
of movements in the public's expectations of headline inflation,
this empirical work implies that change in headline-core inflation
dynamics may be due to the Federal Reserve having convinced the public
it would no longer accommodate food and energy inflation.
The rest of the paper is organized as follows. Section 1 presents
the main empirical results on the nature of the change in headline-core
inflation dynamics across three sub-periods spanning the sample of
1959-2007. Section 2 presents and discusses results from recent research
including a structural VAR model, suggesting a monetary policy
explanation of the change in headline-core inflation dynamics documented
in Section 1. Section 3 contains concluding observations.
1. EMPIRICAL RESULTS ON HEADLINE-CORE INFLATION DYNAMICS
In this section we present the econometric work consistent with
change in short-term headline-core inflation dynamics. Figure 1, which
charts headline and core measures of PCE and CPI inflation, provides a
look at the behavior of these two measures of inflation during the
sample period of 1959-2007. Two observations are noteworthy. The first
is that headline and core measures of CPI and PCE inflation co-move over
the sample period. The lower graph in each panel of Figure 1 charts the
"core deviation," measured as the gap between headline and
core inflation rates. This series is mean stationary, consistent with
co-movement. The second point to note is that, although Figure 1 shows
that headline and core measures of inflation co-move in the long run, it
is not clear from the figure how this co-movement arises. This
co-movement may be a result of one series adjusting to the other, or
both series adjusting to each other. We formally investigate such
dynamics in this section.
[FIGURE 1 OMITTED]
One approach to headline-core inflation dynamics uses the
co-integration-error-correction methodology popularized by Granger
(1986) and Engle and Granger (1987), among others. Under this approach,
one examines short-term inflation dynamics under the premise that
headline and core inflation series may be nonstationary but
co-integrated, indicating the presence of a long-run relationship
between these two measures. Using short-term error-correction equations,
one can then estimate how these two series adjust if headline inflation
moves above or below its long-run value implied by the co-integrating
regression. Another approach treats the inflation series as being mean
stationary in levels, especially during shorter sample periods. (4) One
infers short-term headline-core dynamics by examining the near-term
responses of headline and core inflation measures to a core deviation.
We employ both of these approaches.
Unit Roots, Co-integration, and Short-Term Dynamics
To investigate whether there exists a long-run co-integrating
relationship between headline and core measures of inflation, we first
examine the unit root properties of these two series. Table 1 presents
test results for determining whether headline ([[pi].sub.t.sup.H]) and
core ([[pi].sub.t.sup.C]) inflation measures have unit roots. The test
used is the t-statistic, implemented by estimating the augmented
Dickey-Fuller (1979) regression of the form
[X.sub.t] = [m.sub.0] + [rho][X.sub.[t-1]] + [k.summation over
(s=1)] [m.sub.1s][DELTA][X.sub.[t-s]] + [[epsilon].sub.t], (1)
Table 1 Unit Root Tests
Augmented Dickey-Fuller Regressions Biannual Data from 1959:1-2007:2
Levels:
[[PI].sub.t.sup.H] = [m.sub.0] + [rho][[PI].sub.[t-1].sup.H]
+ [[SIGMA].sub.[s=1].sup.k][DELTA][[PI].sub.[t-s].sup.H]
[[PI].sub.t.sup.C] = [m.sub.0] + [rho][[PI].sub.[t-1].sup.C]
+ [[SIGMA].sub.[s=1].sup.k][DELTA][[PI].sub.[t-s].sup.C]
CPI
[^.[rho]] [t.sub.[^.[rho]]] k
Headline 0.8362 -2.3982 4
Core 0.8510 -2.4537 1
Levels:
[[PI].sub.t.sup.H] = [m.sub.0] + [rho][[PI].sub.[t-1].sup.H]
+ [[SIGMA].sub.[s=1].sup.k][DELTA][[PI].sub.[t-s].sup.H]
[[PI].sub.t.sup.C] = [m.sub.0] + [rho][[PI].sub.[t-1].sup.C]
+ [[SIGMA].sub.[s=1].sup.k][DELTA][[PI].sub.[t-s].sup.C]
PCE
[^.[rho]] [t.sub.[^.[rho]]] k
Headline 0.8896 -1.9427 4
Core 0.9092 -2.1164 0
First Differences:
[DELTA][[PI].sub.t.sup.H] = [m.sub.0] +
[rho]([DELTA][[PI].sub.[t-1].sup.H]) +
[[SIGMA].sub.[s=1].sup.k][DELTA]
([DELTA][[PI].sub.[t-s].sup.H]) [DELTA][[PI].sub.t.sup.C]
= [m.sub.0] + [rho]([DELTA].sub.[t-1].sup.C])
+ [[SIGMA].sub.[s=1].sup.k][DELTA]
([DELTA][[PI].sub.[t-s].sup.C])
CPI
[^.[rho]] [t.sub.[^.[rho]]] k
Headline -0.4085 -6.0378 3
Core -0.4239 -8.7399 1
First Differences:
[DELTA][[PI].sub.t.sup.H] = [m.sub.0] +
[rho]([DELTA][[PI].sub.[t-1].sup.H]) +
[[SIGMA].sub.[s=1].sup.k][DELTA]
([DELTA][[PI].sub.[t-s].sup.H]) [DELTA][[PI].sub.t.sup.C]
= [m.sub.0] + [rho]([DELTA].sub.[t-1].sup.C])
+ [[SIGMA].sub.[s=1].sup.k][DELTA]
([DELTA][[PI].sub.[t-s].sup.C])
PCE
[^.[rho]] [t.sub.[^.[rho]]] k
Headline -0.4590 -6.5147 3
Core -0.0851 -10.6229 0
Notes: [[PI].sup.H] and [[PI].sup.C] are headline and core inflation,
respectively, in levels, while [DELTA][[PI].sup.H] and
[DELTA][[PI].sup.C] are first differences of headline and core
inflation. [^.[rho]] and the t-statistic, [t.sub.[^.[rho]]], for [rho]
= 1 are from the augmented Dickey-Fuller regressions. The series has a
unit root if [rho] = 1. The 5 percent critical value is -2.9. The
number of lagged first differences (k) is chosen using the Akaike
Information Criterion.
where [X.sub.t] is the pertinent variable, [epsilon] is the
disturbance term, and k is the number of lagged first differences to
make [epsilon] serially uncorrelated. If [rho] = 1, [X.sub.t] has a unit
root. The null hypothesis [rho] = 1 is tested using the t-statistic. As
can be seen, the t-statistic reported in Table 1 is small for levels of
inflation series but large for first differences of these series,
suggesting that inflation is nonstationary in levels but stationary in
first differences over 1959:1-2007:2. If headline and core inflation
measures are nonstationary in levels, there may exist a long-run
co-integrating relationship between them. We use a two-step
Engle-Granger (1987) procedure to test for the presence of a long-run
relationship. In step one of this procedure, we estimate by ordinary
least squares (OLS) the regression of the form
[[pi].sub.t.sup.H] = [a.sub.0] + [a.sub.1][[pi].sub.t.sup.C] +
[[mu].sub.t], (2)
where [[mu].sub.t] is the disturbance term. In step two, we
investigate the presence of a unit root in the residuals of regression
(2) using the augmented Dickey-Fuller test implemented by estimating
regression of the form
[[~.u].sub.t] = [delta][[~.u].sub.[t-1]] + [k.summation over
(s=1)][b.sub.1s][DELTA][[~.u].sub.[t-s]], (3)
where [~.u] is the residual. If [delta] = 1, then there does not
exist a long-run relationship between headline and core measures of
inflation. The null hypothesis, [delta] = 1, is tested using the
t-statistic. Table 2, Panel A presents the pertinent t-statistic, which
is large for both PCE and CPI inflation measures, leading to the
rejection of the null hypothesis. These test results suggest headline
and core measures of inflation are indeed co-integrated.
Table 2 Co-integration Tests
Panel A: Engle-Granger Test
[[^.[alpha]].sub.0] [[^.[[alpha].sub.1]
CPI 0.1790 0.9714
PCE -0.0111 1.0408
Panel B: Johansen Test
[[lambda].sub.1] [[lambda].sub.2]
CPI 0.2617 0.0852
PCE 0.2554 0.0584
Panel C: Fully Modified OLS Estimates
[[alpha].sub.0] [[alpha].sub.1]
CPI 0.0837 0.9956
PCE -0.0144 1.0427
Panel A: Engle-Granger Test
[^.[delta]] [[^.t].sub.[delta]] k
CPI 0.2924 -4.4380 3
PCE 0.3101 -4.7694 3
Panel B: Johansen Test
Co-integrating Vector LR
CPI (-1.3725, 1.4368) 28.8223 **
PCE (-1.8244, 1.9375) 28.0137 **
Panel C: Fully Modified OLS Estimates
[s.sub.1] [s.sub.2]
CPI 0.9326 0.8841
PCE 0.3521 0.2481
Notes: Biannual data from 1959:1-2007:2. * 10 percent significance, **
5 percent significance. For the Engle-Granger (1987) test,
[[^.[alpha]].sub.0], [[^.[alpha]].sub.1] [^.[delta]] and the
t-statistic for [delta] = 1 in Panel A are from two regressions of the
form [[PI].sub.t.sup.H] = [[alpha].sub.0] + [[alpha].sub.1]
[[PI].sub.t.sup.C] + [u.sub.t] and [[~.u].sub.t] =
[delta][[~.u].sub.[t-1]] +
[[SIGMA].sub.[s=1].sup.k][b.sub.s][DELTA][[~.u].sub.[t-s]]. Headline
and core measures are not co-integrated if the residual series,
[[~.u].sub.t], has a unit root, i.e., if [delta] = 1. For the Johansen
(1988) test, the table shows the two eigenvalues, [[lambda].sub.1] and
[[lambda].sub.2], used in evaluating Johansen's likelihood function,
the estimated co-integrating vectors, and the likelihood ratio
statistic, LR, for testing the null hypothesis of no co-integration.
The LR is calculated as -T 1n(1 - [[lambda].sub.1]), where T is the
number of total observations. Critical values for LR are reported under
the heading Case 1 in Hamilton (1994, 768, Table B.1 1). Panel C shows
results from a fully modified OLS regression of the form
[[PI].sub.t.sup.H] = [[alpha].sub.0] + [[alpha].sub.1]
[[PI].sub.t.sup.C] + [u.sub.t]. The statistic [s.sub.1] is the
Significance level of the test hypothesis [[alpha].sub.1] = 1, while
[s.sub.2] is the significance level of the test of the hypothesis
[[alpha].sub.0] = 0 and [[alpha].sub.1] = 1. See notes from Table 1 for
variable definitions.
The Engle-Granger test is implemented above by assuming a
particular normalization, regressing headline inflation on core
inflation, and examining the presence of a unit root in the residuals of
(2). For robustness with respect to normalization, we also implement the
likelihood test of co-integration as in Johansen (1988). Table 2, Panel
B reports the likelihood test results and estimated co-integrating
vectors. The likelihood ratio statistic that tests the null hypothesis
of no co-integrating vector against the alternative of one
co-integrating vector is large, leading to the rejection of the null
hypothesis.
In order to be able to carry out tests of hypotheses on parameters
of the estimated co-integrating vectors, we re-estimate the
co-integrating relationship (2) using a fully modified OLS estimator as
in Phillips and Hansen (1990) because standard OLS estimates, though
consistent, do not have the asymptotic normal distribution. The
estimates are reported in Table 2, Panel C. As can be seen, the
estimated long-run coefficient, [[~.a].sub.1], is positive and
statistically different from zero, suggesting the presence of a positive
relationship between headline and core inflation measures. The estimated
long-run coefficient, [[~.a].sub.1], is not different from unity,
suggesting the headline measure of inflation moves one-for-one with the
core measure in the long run. The significance level of the statistic
that tests the null hypothesis [a.sub.0] = 0, [a.sub.1] = 1 is .88 using
CPI and .25 using PCE. These significance levels are large, leading to
an acceptance of the null hypothesis.
Having established above that headline and core measures of
inflation co-move in the long run, we now investigate the sources of
this co-movement by estimating short-term error-correction equations of
the form given in (4) and (5):
[DELTA][[pi].sub.t.sup.H] = [b.sub.0] +
[[lambda].sub.h][[mu].sub.[t-1]] + [k.summation over (s=1)]
[DELTA][[pi].sub.[t-s].sup.H] + [[upsilon].sub.t], and (4.1)
[DELTA][[pi].sub.t.sup.c] = [b.sub.0] +
[[lambda].sub.c][[mu].sub.[t-1]] + [k.summation over (s=1)]
[DELTA][[pi].sub.[t-s].sup.C] + [[upsilon].sub.t]. (4.2)
Under the assumptions [a.sub.0] = 0, [a.sub.1] = 1, we can re-write
(4) as (5):
[DELTA][[pi].sub.t.sup.H] = [b.sub.0] +
[[lambda].sub.h][([[pi].sup.H] - [[pi].sup.C]).sub.[t-1]] + [k.summation
over (s=1)] [DELTA][[pi].sub.[t-s].sup.H] + [[upsilon].sub.t], and (5.1)
[DELTA][[pi].sub.t.sup.C] = [b.sub.0] +
[[lambda].sub.c][([[pi].sup.H] - [[pi].sup.C]).sub.[t-1]] + [k.summation
over (s=1)] [DELTA][[pi].sub.[t-s].sup.C] + [[upsilon].sub.t]. (5.2)
Regressions (4) and (5) capture short-term dynamics between
headline and core inflation measures, and the coefficients
[[lambda].sub.h] and [[lambda].sub.c] indicate how headline inflation
and core inflation adjust if a gap emerges between headline and core
inflation rates. If [[lambda].sub.h] = 0 and [[lambda].sub.c] > 0,
headline and core inflation stay together mainly by core inflation
moving toward headline inflation. If [[lambda].sub.h] < 0 and
[[lambda].sub.c] = 0, headline and core inflation stay together mainly
by headline inflation moving toward core inflation. If [[lambda].sub.h]
< 0 and [[lambda].sub.c] > 0, both series adjust, with headline
inflation moving toward core inflation and core inflation moving toward
headline inflation. The relative magnitudes of these adjustment
coefficients convey information about which series adjusts more in
response to a core deviation.
Table 3, Panel A, presents estimates of short-term error-correction
(adjustment) coefficients, providing information about the ways these
two series adjust over three sub-samples considered. Focusing first on
the adjustment coefficient, [[^.[lambda]].sub.h], that appears in
headline inflation regressions, this estimated coefficient is positive
and not statistically different from zero in the pre-1979 sample period,
but is negative and statistically different from zero in the recent
sample period, 1985:1-2007:2. This result holds for headline CPI as well
as for headline PCE inflation. These estimates of the adjustment
coefficient, [[^.[Lambda]].sub.h], suggest that if headline inflation is
above core inflation, headline inflation inverts toward core inflation
in the recent sample period but not in the pre-1979 sample period.
Focusing now on the adjustment coefficient, [[^.[lambda]].sub.c], that
appears in core inflation equations, we see that results differ for CPI
and PCE inflation measures. In core PCE inflation equations, the
estimated coefficient is positive, large, and statistically significant
in the pre-1979 sample period but it becomes small and not statistically
different from zero in the recent sample period, 1985:1-2007:2,
suggesting that if headline inflation is above core inflation, core
inflation moves toward headline inflation in the pre-1979 sample period
but not in the recent sample period, 1985:1-2007:2. For CPI inflation,
the adjustment coefficient, [[^.[lambda]].sub.c], that appears in the
core inflation equation does decline significantly from .91 in the
pre-1979 sample period to .19 in the recent sample period. However, it
remains statistically significant in the recent sample period,
suggesting the CPI measure of core inflation has also moved somewhat
toward headline inflation. Together, these short-term adjustment
coefficients suggest that, whereas in the pre-1979 sample period
headline and core measures of inflation stayed together as a result of
core inflation moving toward headline inflation, in the recent sample
period they have stayed together more as a result of headline inflation
moving toward core inflation than core inflation moving toward headline
inflation. In order to check robustness, discussed in detail later in
this article, we re-estimate short-term adjustment equations (5)
augmented to include two additional lags of other economic determinants
of inflation such as changes in a short-term nominal interest rate and
changes in the unemployment rate. Table 3, Panel B, presents the
short-term adjustment coefficients from these short-term augmented
regressions. We can see estimates of short-term adjustment coefficients
yield qualitatively similar results about change in headline-core
inflation dynamics. (5)
Table 3 Short-Term Headline-Core Inflation Dynamics
Panel A: Bivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h]([[PI].sub.[t-1].sup.h] -
[[PI].sub.[t-1].sup.C]) + [[SIGMA].sub.[s=1].sup.2]
[DELTA][[PI].sub.[t-s].sup.H] + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.c] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2][DELTA][[PI].sub.[t-s].sup.C] +
[[upsilon].sub.t]
CPI
[[lambda].sub.h] [[bar.R].sup.2]
1959:1-1979:1 0.3551 -0.027
1979:2-2001:2 -0.2208 0.144
1985:1-2007:2 -0.7319 ** 0.365
Panel B: Multivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h] ([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.H]
+ [DELTA][[PI].sub.[t-s].sup.C] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.C] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.C]
+ [DELTA][[PI].sub.[t-s].sup.H] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
1959:1-1979:1 0.4745 0.251
1979:2-2001:2 -0.0881 0.322
1985:1-2007:2 -0.6471 * 0.351
Panel A: Bivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h]([[PI].sub.[t-1].sup.h] -
[[PI].sub.[t-1].sup.C]) + [[SIGMA].sub.[s=1].sup.2]
[DELTA][[PI].sub.[t-s].sup.H] + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.c] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2][DELTA][[PI].sub.[t-s].sup.C] +
[[upsilon].sub.t]
CPI
[[lambda].sub.c] [[bar.R].sup.2]
1959:1-1979:1 0.9141 ** 0.433
1979:2-2001:2 0.2917 0.136
1985:1-2007:2 0.1943 ** 0.264
Panel B: Multivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h] ([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.H]
+ [DELTA][[PI].sub.[t-s].sup.C] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.C] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.C]
+ [DELTA][[PI].sub.[t-s].sup.H] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
1959:1-1979:1 1.0793 ** 0.520
1979:2-2001:2 0.6665 ** 0.601
1985:1-2007:2 0.2701 ** 0.465
Panel A: Bivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h]([[PI].sub.[t-1].sup.h] -
[[PI].sub.[t-1].sup.C]) + [[SIGMA].sub.[s=1].sup.2]
[DELTA][[PI].sub.[t-s].sup.H] + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.c] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2][DELTA][[PI].sub.[t-s].sup.C] +
[[upsilon].sub.t]
PCE
[[lambda].sub.h] [[bar.R].sup.2]
1959:1-1979:1 0.4011 -0.042
1979:2-2001:2 -0.8139 ** 0.200
1985:1-2007:2 -0.6168 ** 0.328
Panel B: Multivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h] ([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.H]
+ [DELTA][[PI].sub.[t-s].sup.C] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.C] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.C]
+ [DELTA][[PI].sub.[t-s].sup.H] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
1959:1-1979:1 0.2213 0.147
1979:2-2001:2 -0.2972 0.260
1985:1-2007:2 -0.5400 0.261
Panel A: Bivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h]([[PI].sub.[t-1].sup.h] -
[[PI].sub.[t-1].sup.C]) + [[SIGMA].sub.[s=1].sup.2]
[DELTA][[PI].sub.[t-s].sup.H] + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.c] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2][DELTA][[PI].sub.[t-s].sup.C] +
[[upsilon].sub.t]
PCE
[[lambda].sub.c] [[bar.R].sup.2]
1959:1-1979:1 0.7734 ** 0.406
1979:2-2001:2 -0.0483 0.107
1985:1-2007:2 0.0763 0.203
Panel B: Multivariable Adjustment Regressions
[DELTA][[PI].sub.t.sup.H] = [[beta].sub.0] +
[[lambda].sub.h] ([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.H]
+ [DELTA][[PI].sub.[t-s].sup.C] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
[DELTA][[PI].sub.t.sup.C] = [[beta].sub.0] +
[[lambda].sub.c]([[PI].sub.[t-1].sup.H] -
[[PI].sub.[t-1].sup.C]) +
[[SIGMA].sub.[s=1].sup.2]([DELTA][[PI].sub.[t-s].sup.C]
+ [DELTA][[PI].sub.[t-s].sup.H] + [DELTA][sr.sub.[t-s]]
+ [DELTA][ur.sub.[t-s]]) + [[upsilon].sub.t]
1959:1-1979:1 0.6770 * 0.354
1979:2-2001:2 0.4519 * 0.335
1985:1-2007:2 0.4158 ** 0.280
Notes: * 10 percent .significance, ** 5 percent significance. The
coefficients [[lambda].sub.h] and [[lambda].sub.c] are estimated using
OLS; [DELTA][sr.sub.t] is the first difference in die short-term
nominal rate, defined as the three-month Treasury-hill rate: [DELTA]ur
is the first difference in the unemployment rate. See notes from Table
1 for the. definitions of other variables.
Stationarity and Mean Reversion
We also examine short-term headline-core dynamics by focusing on
the influence of core deviation on the longer-horizon behavior of
inflation, assuming headline and core inflation measures are likely mean
stationary in shorter sample periods. If headline inflation is above
core inflation and if adjustment occurs mainly as a result of headline
inflation moving toward core inflation, we should expect headline
inflation to decline in the near term. With that in mind, we examine the
behavior of inflation over various forecast horizons as in(6.1)and(6.2):
(6)
[[pi].sub.[t+f].sup.H] - [[pi].sub.t.sup.H] = [b.sub.0f] +
[[lambda].sub.hf][([[pi].sup.H] - [[pi].sup.C]).sub.t] + [k.summation
over (s=1)][b.sub.1f][[pi].sub.[t-s].sup.H] + [[mu].sub.[t+f]], and
(6.1)
[[pi].sub.[t+f].sup.C] - [[pi].sub.t.sup.C] = [c.sub.0f] +
[[lambda].sub.cf][([[pi].sup.H] - [[pi].sup.C]).sub.t] + [k.summation
over (s=1)][c.sub.1f][[pi].sub.[t-s].sup.C] + [[mu].sub.[t+f]], (6.2)
where [[pi].sub.[t+f].sup.H] is the f-periods-ahead headline
inflation rate, [[pi].sub.t.sup.H] is the current-period headline
inflation rate, [[pi].sub.t.sup.C] is the current-period core inflation
rate, [[pi].sub.[t+f].sup.H] - [[pi.C] is the contemporaneous core
deviation, f is the forecast horizon, and [[mu].sub.[t+f]] is a
mean-zero random disturbance term. Regressions (6.1) and (6.2) relate
the change in inflation over the next f (six-month) periods to the
contemporaneous gap between headline and core inflation rates. If the
coefficients, [[lambda].sub.hf], in (6.1) are generally negative and the
coefficients, [[lambda].sub.cf], in (6.2) are zero, then core deviation
is eliminated primarily as a result of headline inflation inverting to
core inflation. In contrast, if the coefficients, [[lambda].sub.hf], in
(6.1) are zero and the coefficients, [[lambda].sub.cf], in (6.2) are
positive, core deviation is eliminated mainly as a result of core
inflation moving toward headline inflation.
Table 4 presents estimates of the coefficients from regressions
given in (6.1) and (6.2). The estimates are presented for forecast
horizons of one to four periods in the future. Panel A presents
estimates using CPI and Panel B uses PCE. Since results derived using
CPI are broadly similar to those derived using PCE inflation, we focus
on estimates derived using CPI. As can be seen in the pre-1979 sample
period, estimated coefficients [[^.[lambda]].sub.hf], f = 1, 2, ..., 4
are zero and [[^.[lambda]].sub.cf], f = 1, 2, ..., 4 are positive,
confirming that the series have stayed together mainly as a result of
core inflation moving toward headline inflation. In the most recent
sample period, 1985:1-2007:2, however, estimated coefficients
[[^.[lambda]].sub.hf], f = 1,2, ..., 4 are negative and
[[^.[lambda]].sub.cf], f = 1, 2, ..., 4 are positive, suggesting that
both series are adjusting to each other. However, relative magnitudes of
the estimated adjustment coefficients suggest headline inflation has
moved more toward core inflation than core inflation has moved toward
headline inflation.
Table 4 Short-Term Headline-Core Inflation Dynamics
Long-Horizon Behavior of Inflation
[[PI].sub.[t+f].sup.H] - [[PI].sub.t.sup.H] =
[b.sub.[0, f]] + [[lambda].sub.hf]
([[PI].sub.t.sup.H] - [[PI].sub.t.sup.C]) +
[[SIGMA].sub.[s=1].sup.2][[PI].sub.[t-s].sup.H] +
[[mu].sub.[t+f]]
[[PI].sub.[t+f].sup.C] - [[PI].sub.t.sup.C] =
[b.sub.[0, f]] + [[lambda].sub.cf]
([[PI].sub.t.sup.H] - [[PI].sub.t.sup.C]) +
[[SIGMA].sub.[s=1].sup.2][[PI].sub.[t-s].sup.C] +
[[mu].sub.[t+f]005D
Panel A: CPI
1959:1-1979:1
[[^.[lambda]].sub.hf] [[^.[lambda]].sub.cf]
(t - value) (t - value)
f = 1 0.2922 (1.4712) 0.9476 (5.1898)
f = 2 0.1799 (0.6308) 1.0523 (4.0652)
f = 3 0.2708 (0.8540) 0.9571 (3.2132)
f = 4 -0.4165 (-1.1036) 0.5683 (1.5071)
Panel B: PCE
1959:1-1979:1
[[^.[lambda]].sub.hf] [[^.[lambda]].sub.cf]
(t - value) (t - value)
f = 1 0.1621 (0.6311) 0.7294 (4.3905)
f = 2 -0.0373 (-0.1061) 0.7377 (2.7125)
f = 3 -0.1051 (-0.2686) 0.5343 (1.6707)
f = 4 -0.9059 (-2.1481) 0.2232 (0.6207)
[[PI].sub.[t+f].sup.H] - [[PI].sub.t.sup.H] =
[b.sub.[0, f]] + [[lambda].sub.hf]
([[PI].sub.t.sup.H] - [[PI].sub.t.sup.C]) +
[[SIGMA].sub.[s=1].sup.2][[PI].sub.[t-s].sup.H] +
[[mu].sub.[t+f]]
[[PI].sub.[t+f].sup.C] - [[PI].sub.t.sup.C] =
[b.sub.[0, f]] + [[lambda].sub.cf]
([[PI].sub.t.sup.H] - [[PI].sub.t.sup.C]) +
[[SIGMA].sub.[s=1].sup.2][[PI].sub.[t-s].sup.C] +
[[mu].sub.[t+f]]
Panel A: CPI
1979: 2-2001:2
[[^.[lambda]].sub.hf] [[^.[lambda]].sub.cf]
(t - value) (t - value)
f = 1 -0.7230 (-2.3898) 0.1660 (0.6635)
f = 2 -0.8962 (-3.5360) 0.2796 (1.1604)
f = 3 -0.6554 (-2.4870) 0.1431 (0.5892)
f = 4 -1.2379 (-3.9101) -0.1730 (-0.6615)
Panel B: PCE
1979:2-2001:2
[[^.[lambda]].sub.hf] [[^.[lambda]].sub.cf]
(t - value) (t - value)
f = 1 -0.9177 (-3.9444) -0.1905 (-1.1215)
f = 2 -1.2218 (-5.5721) -0.0874 (-0.5304)
f = 3 -0.8718 (-4.0458) -0.0183 (-0.0981)
f = 4 -1.5878 (-7.2154) -0.6071 (-3.1880)
[[PI].sub.[t+f].sup.H] - [[PI].sub.t.sup.H] =
[b.sub.[0, f]] + [[lambda].sub.hf]
([[PI].sub.t.sup.H] - [[PI].sub.t.sup.C]) +
[[SIGMA].sub.[s=1].sup.2][[PI].sub.[t-s].sup.H] +
[[mu].sub.[t+f]]
[[PI].sub.[t+f].sup.C] - [[PI].sub.t.sup.C] =
[b.sub.[0, f]] + [[lambda].sub.cf]
([[PI].sub.t.sup.H] - [[PI].sub.t.sup.C]) +
[[SIGMA].sub.[s=1].sup.2][[PI].sub.[t-s].sup.C] +
[[mu].sub.[t+f]]
Panel A: CPI
1985:1-2007:2
[[^.[lambda]].sub.hf] [[^.[lambda]].sub.cf]
(t - value) (t - value)
f = 1 -0.7101 (-4.9165) 0.1858 (3.7078)
f = 2 -0.9658 (-5.9644) 0.1906 (2.5528)
f = 3 -0.8059 (-4.9527) 0.1478 (1.7234)
f = 4 -1.0563 (-6.2716) 0.0934 (3.6687)
Panel B: PCE
1985:1-2007:2
[[^.[lambda]].sub.hf] [[^.[lambda]].sub.cf]
(t - value) (t - value)
f = 1 -0.7550 (-4.5498) 0.0684 (0.6118)
f = 2 -0.9640 (-4.9353) 0.2006 (1.6302)
f = 3 -0.8452 (-4.4408) 0.1519 (1.2177)
f = 4 -1.1517 (-5.4391) -0.0300 (-0.1976)
Notes: f is the number of periods in the forecasting horizon.
Regressions are estimated including levels of lagged inflation. All
regressions are estimated using OLS. See notes from Table 1 for
variable definitions.
Robustness: Multivariate System, Data Frequency, and Sample Breaks
The change in short-term headline-core inflation dynamics
summarized above are derived using a bivariable framework, biannual
data, and three sub-periods generated by breaking the sample in 1979 and
1984. Here, we present some additional evidence indicating inference
that the nature of change in headline-core inflation dynamics remains
robust to several changes in specification. The first change in
specification expands the regressions given in (5.1) and (5.2) to
include other possible determinants of inflation such as changes in a
short-term nominal interest (capturing the possible influence of
monetary policy actions) and changes in the unemployment rate (as a
proxy for the influence of the state of the economy). We focus on the
sign and statistical significance of the short-term adjustment
coefficients in these expanded regressions. As already noted, estimates
from these multivariate regressions (Table 3, Panel B) yield
qualitatively similar inferences about the nature of the change in
short-term headline-core inflation dynamics to those derived using
bivariable regressions.
Rather than focus on three sub-periods, we estimate the short-term
adjustment coefficients from the multivariate versions of regressions
given in (5.1) and (5.2) using rolling regressions over a 19-year
window. (7) We estimate those regressions using biannual as well as
quarterly data. Since the results using biannual data are qualitatively
similar to those derived using quarterly data and, since the results
also appear robust to the use of CPI or PCE inflation, we focus on
estimates derived using biannual data and CPI inflation. Panel A in
Figure 2 charts estimates of the short-term adjustment coefficient,
[[lambda].sub.h], from headline inflation regressions, and Panel B
charts estimates of the short-term adjustment coefficient,
[[lambda].sub.c], from core inflation regressions, with 95 percent
confidence bands. In samples that begin in the 1960s or early 1970s, the
short-term adjustment coefficient, [[lambda].sub.h], is usually positive
but statistically indifferent from zero whereas the short-term
adjustment coefficient, [[lambda].sub.c], is positive and statistically
different from zero, suggesting headline inflation does not revert, but
rather core inflation moves toward headline inflation. In contrast, in
samples that begin in the early 1980s, the short-term adjustment
coefficient, [[lambda].sub.h], is instead negative and statistically
significant whereas the short-term adjustment coefficient,
[[lambda].sub.c], is positive but not always statistically different
from zero. This suggests that the gap between headline and core CPI
inflation is eliminated as a result of headline inflation inverting
toward core inflation rather than core inflation moving toward headline
inflation. These results are qualitatively similar to those derived
using bivariable regressins estimated across three chosen sample
periods.
[FIGURE 2 OMITTED]
2. DISCUSSION OF RESULTS
What explains the change in the short-term headline-core inflation
dynamics documented above? Recent research suggests a monetary policy
explanation. Mishkin (2007a) provides evidence that in recent years
inflation persistence has declined and inflation has become less
responsive to changes in unemployment and other shocks. He attributes
this change in inflation dynamics to the anchoring of inflation
expectations as a result of better conduct of monetary policy. In a
recent paper, Leduc, Sill, and Stark (2007) attribute the persistently
high inflation of the 1970s to a weak monetary policy response to
surprise increases in the public's expectations of inflation. In
particular, using a structural VAR that includes a direct survey measure
of expected (headline CPI) inflation, Leduc, Sill, and Stark show that,
prior to 1979, the Federal Reserve accommodated exogenous movements in
expected inflation, seen in the result that the short-term real interest
rate did not increase in response to such movements, which then led to
persistent increases in actual inflation. Such behavior, however, is
absent post-1979. We argue below that such change in the Federal
Reserve's accommodation of expected headline inflation is also
capable of generating the change in actual headline-core inflation
dynamics documented above. We demonstrate this by using a variant of the
structural VAR model that includes actual headline and core inflation
measures. (8)
To explain further, consider a four-variable VAR that contains a
direct survey measure of the public's expectations of headline
inflation, represented by the median Livingston survey forecast of the
eight-month-ahead headline CPI inflation rate ([[pi].sub.t.sup.eH]). The
other variables included in the VAR are actual headline CPI inflation
([[pi].sub.t.sup.H]), actual core CPI inflation ([[pi].sub.t.sup.C]),
and a short-term nominal interest rate ([sr.sub.t]). Following Leduc,
Sill, and Stark (2007), we define and measure variables in such a way
that survey participants making forecasts do not observe contemporaneous
values of other VAR variables, thereby helping to identify exogenous
movements in expected headline inflation. (9) Using a recursive
identification scheme {[[pi].sub.t.sup.eH], [[pi].sub.t.sup.H],
[[pi].sub.t.sup.C], [sr.sub.t]} in which expected inflation is ordered
first and the short nominal interest rate is last, we examine and
compare the impulse responses of actual headline and core inflation
measures to surprise increases in expected headline inflation (and core
inflation itself).
Figure 3 shows the responses of VAR variables to a one-time
surprise increase in expected headline inflation for three sample
periods: 1959:1-1979:1 (Panel A), 1979:2-2001:2 (Panel B), and
1985:1-2007:2 (Panel C). Figure 4 shows the responses to a one-time
increase in core inflation. In these figures, and those that follow, the
solid line indicates the point estimate, while the darker and lighter
shaded regions represent 68 percent and 90 percent confidence bands,
respectively.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Focusing on Figure 3, we highlight two observations. First, the
effects of a surprise increase in expected headline inflation on actual
headline and core measures of inflation have changed over time. In the
pre-1979 sample period, a surprise increase in expected headline
inflation is not reversed and leads to a persistent increase in actual
headline and core inflation measures. However, in post-1979 sample
periods, such effects have become weaker. In fact, in the most recent
sample period, 1985:1-2007:2, a surprise increase in expected headline
inflation is reversed and has no significant effect on actual headline
and core inflation measures (compare responses in Panels A and C). These
results suggest that, in the pre-1979 sample period, shocks to expected
headline inflation can generate co-movement between headline and core
measures of inflation and that this co-movement arises as a result of
headline inflation not reverting to core inflation and core inflation
moving toward headline inflation. In contrast, in the recent sample
period, 1985:1-2007:2, a surprise increase in expected headline
inflation does not generate co-movement between actual headline and core
inflation measures because they are not affected by movements in
expected headline inflation. As discussed below, a surprise increase in
core inflation, however, can generate co-movement between headline and
core measures of inflation in the most recent sample period.
Second, the interest rate responses shown in Figure 3 suggest
monetary policy may be at the source of the above-noted change in the
response of actual headline inflation to expected headline inflation
shocks. If we focus on the nominal interest rate response shown in Panel
A, we see that the nominal interest rate does increase in response to a
surprise increase in expected headline inflation, but that this increase
in the nominal interest rate approximates the increase in expected
headline inflation leaving the real interest essentially unchanged. (10)
The behavior of the real interest rate in response to surprise increases
in expected headline inflation suggests that the Federal Reserve
followed an accommodative monetary policy. However, in the sample period
1979:2-2001:2, the real interest rate rises sharply in response to a
surprise increase in expected headline inflation, suggesting that the
Federal Reserve did not accommodate shocks to expected headline
inflation. In the most recent sample period, 1985:1-2007:2, there is no
significant response of the real interest rate to an expected inflation
shock, because a surprise increase in expected headline inflation is
reversed, having no significant effect on actual headline and core
inflation measures.
Focusing on Figure 4, we see that it is only in the most recent
sample period, 1985:1-2007:2, in which a surprise increase in core
inflation leads to an increase in expected and actual headline
inflation, generating co-movement between headline and core measures of
inflation. This co-movement is generated as a result of headline
inflation moving toward core inflation. Furthermore, the real interest
rate does rise significantly in response to a surprise increase in core
inflation, suggesting that in conducting monetary policy the Federal
Reserve appears to be focused on the core measure of inflation. In
contrast, in the pre-1979 sample period, a surprise increase in core
inflation does not lead to an increase in headline inflation and there
is no significant response of the nominal interest rate. (11)
Together, the responses depicted in Figures 3 and 4 imply that,
before 1979, headline and core inflation measures co-move mainly as a
result of core inflation moving toward headline inflation, because the
Federal Reserve accommodated surprise increases in the public's
expectations of headline inflation. A surprise increase in core
inflation is simply reversed and does not lead to higher expected or
actual headline inflation. Since 1979, however, the Federal Reserve has
not accommodated increases in the public's expectations of headline
inflation, and hence co-movement has mainly arisen as a result of
headline inflation moving toward core inflation.
Food and Energy Inflation
Since the measure of core inflation used here is derived excluding
food and energy inflation from headline inflation, and since food and
energy prices are likely to be a significant source of movements in
expected headline inflation, the results discussed above imply that
change in monetary policy response to expected headline inflation may
reflect change in monetary policy response to movements in expected food
and energy prices. Since we do not have any direct survey data on the
public's expectations of food and energy price inflation, we
provide some preliminary evidence on this issue by examining responses
to movements in actual food and energy inflation. With that in mind, we
consider another variant of the structural VAR model that includes
expected headline inflation, actual core inflation, the food and energy
component of headline CPI inflation, and the short-term nominal interest
rate. We continue to assume the baseline identification ordering
{[[pi].sub.t.sup.eH], [[pi].sub.t.sup.C], ([[pi].sub.t.sup.H] -
[[pi].sub.t.sup.C]), [sr.sub.t]} in which expected headline inflation is
exogenous but food and energy price inflation is not. Food and energy
inflation is measured as the gap between headline and core inflation
rates.
Figure 5 shows responses to a surprise increase in the food and
energy component of headline inflation over three sample periods:
1959:1-1979:1 (Panel A), 1979:2-2001:2 (Panel B), and 1985:1-2007:2
(Panel C). In the pre-1979 sample period a surprise temporary increase
in food and energy prices has a significant effect on expected headline
inflation, leading to a persistent increase in expected (and hence
actual) headline inflation. Core inflation is also persistently higher
in response to a surprise increase in food and energy inflation. These
responses suggest that a surprise increase in food and energy inflation
can generate co-movement between headline and core measures of
inflation, with core inflation moving toward headline inflation.
However, in post-1979 sample periods the positive response of expected
headline inflation to a surprise increase in food and energy inflation
weakens considerably. More interestingly, in the most recent sample
period, 1985:1-2007:2, a surprise increase in food and energy inflation
has no significant effect on expected headline inflation, suggesting
that the public believes increases in food and energy prices are
unlikely to lead to a persistent increase in headline inflation (compare
responses across Panels A through C). (12)
[FIGURE 5 OMITTED]
The response of the real interest rate to a surprise increase in
food and energy prices implicit in Panels A through C suggests a
monetary policy explanation of the decline in the influence of food and
energy prices on expected headline inflation. In the pre-1979 period,
the real interest rate does not change much because the rise in nominal
interest rate matches the rise in expected headline inflation,
suggesting an accommodative stance of monetary policy. However, in the
sample period 1979:2-2001:2, the real interest rate rises significantly
in response to a surprise increase in food and energy prices, suggesting
that the Federal Reserve did not accommodate increases in food and
energy prices. Hence, the decline in the influence of food and energy
inflation on expected headline inflation since 1979 may be due to the
Federal Reserve no longer accommodating shocks to food and energy
prices.
In the most recent sample period, 1985:1-2007:2, however, there is
no significant response of the nominal (or real) interest rate to a
surprise increase in food and energy prices, because a surprise increase
in food and energy inflation has no significant effect on expected
headline inflation. One plausible explanation of the absence of any
significant effect of movements in food and energy inflation on expected
headline inflation is that past Federal Reserve behavior has convinced
the public that it would not accommodate food and energy inflation. As a
result, surprise increases in food and energy inflation have no
significant effect on expected headline inflation, suggesting the
Federal Reserve has become credible.
But do shocks to food and energy inflation matter for expected
headline inflation? The results of the variance decomposition of
expected headline inflation presented in Table 5 are consistent with the
decline in the influence of food and energy inflation on expected
headline inflation since 1979. In the pre-1979 sample period, shocks to
the food and energy component of inflation account for about 35 percent
of the variability of expected headline inflation at a two-year horizon,
whereas in the recent sample period, 1985:1-2007:2, they account for
less than 4 percent of the variability of expected headline inflation at
the same two-year horizon.
Table 5 Variance Decomposition of Expected Headline CPI Inflation
Panel A: 1959:1-1979:1
Ordering: [[PI].sup.eH], [[PI].sup.C], [[PI].sup.H] - [[PI].sup.C], SR
Steps [[PI].sup.eH] [[PI].sup.C] [[PI].sup.H] - [[PI].sup.C] SR
1 100.000 0.000 0.000 0.000
2 83.939 0.979 11.621 3.461
3 56.768 3.739 32.307 7.186
4 49.345 4.427 35.859 10.370
6 45.326 7.700 36.358 10.616
8 44.895 10.508 35.244 9.353
Panel B: 1979:2-2001:2
1 100.000 0.000 0.000 0.000
2 75.964 12.141 7.771 4.125
3 62.899 22.970 10.382 3.749
4 55.940 29.473 10.809 3.777
6 49.066 35.928 10.363 4.644
8 45.673 39.126 9.858 5.343
Panel C: 1985:1-2007:2
1 100.000 0.000 0.000 0.000
2 66.457 27.758 0.081 5.704
3 55.816 35.223 2.653 6.309
4 50.830 39.187 3.676 6.307
6 49.452 41.004 3.676 5.867
8 49.412 41.533 3.659 5.394
Notes: Entries are in percentage terms, with the exception of those
under the column labeled "Steps." Those entries refer to n-step-ahead
forecasts for which decomposition is done. [[PI].sup.eH] is expected
headline inflation, as measured by the Livingston Survey. See notes
from Tables 1 and 3 for the definitions of the other variables.
3. CONCLUDING OBSERVATIONS
This article investigates empirically short-term dynamics between
headline and core measures of CPI and PCE inflation over three sample
periods: 1959:1--1979:1, 1979:2-2001:2, and 1985:1-2007:2. Headline and
core inflation measures are co-integrated, suggesting long-run
co-movement. However, the ways in which these two variables adjust to
each other in the short run and generate co-movement have changed across
these sample periods. In the pre-1979 sample period, when a positive gap
opens up with headline inflation rising above core inflation, the gap is
eliminated mainly as a result of headline inflation not reverting and
core inflation moving toward headline inflation. These dynamics suggest
headline inflation would be better than core inflation in assessing the
permanent component of inflation. In post-1979 sample periods, however,
the positive gap is eliminated as a result of headline inflation
reverting more strongly toward core inflation than core inflation moving
toward headline inflation, suggesting core inflation would be better
than headline inflation in assessing the permanent component of
inflation. Although short-term headline-core inflation dynamics are
investigated using biannual data, the basic result on change in
inflation dynamics is robust to the use of quarterly data and includes
additional economic determinants of inflation in the bivariable
headline-core inflation regressions. The results are also not sensitive
to the precise breakup of the sample in 1979 and 1984.
Recent research suggests a monetary policy explanation of change in
inflation dynamics. We focus on a version suggested in Leduc, Sill, and
Stark (2007) that attributes the decline in the persistence of actual
headline inflation to a change in the accommodative stance of monetary
policy in 1979. We illustrate that such a change in monetary policy
response to exogenous shocks to the public's expectations of
headline inflation can generate the change in headline-core inflation
dynamics documented above. Before 1979, the Federal Reserve accommodated
shocks to expected headline inflation: A surprise increase in expected
headline inflation is not reversed, leading to a persistent increase in
actual headline inflation and co-movement arising as a result of core
inflation moving toward headline inflation. Since 1979 that has not been
the case: A surprise increase in expected headline inflation is reversed
and co-movement arises mainly as a result of headline inflation moving
toward core inflation.
Since food and energy prices are likely a significant determinant
of expected headline inflation, the results imply that the change in
headline-core inflation dynamics may simply be due to the Federal
Reserve no longer accommodating food and energy inflation. In the most
recent sample period, a surprise increase in food and energy inflation
has no significant effect on the public's expectations of headline
inflation. This result suggests that past Federal Reserve behavior has
convinced the public that it would no longer accommodate food and energy
inflation.
In previous research, analysts have often found that the empirical
evidence indicating that core inflation is better than headline
inflation at gauging the trend component of inflation is not robust
across sample periods. The empirical work in this article explains this
lack of robustness; namely, headline-core inflation dynamics changed
with a change in the conduct of monetary policy in 1979. Hence, in
sample periods beginning in the 1960s and ending in the 1980s or 1990s,
the hypothesis that the trend component of inflation is best gauged by
focusing only on core inflation may or may not be found consistent with
the data.
REFERENCES
Bernanke, Ben S. 2007. "Inflation Expectations and Inflation
Forecasting." Remarks at the Monetary Economics Workshop of the
NBER Summer Institute, Cambridge, Massachusetts.
Blinder, Alan S., and Ricardo Reis. 2005. "Understanding the
Greenspan Standard." Proceedings of Jackson Hole Symposium, Federal
Reserve Bank of Kansas City.
Clark, Todd E. 2001. "Comparing Measures of Core
Inflation." Federal Reserve Bank of Kansas City Economic Review:
5-31
Cogley, Timothy. 2002. "A Simple Adaptive Measure of Core
Inflation." Journal of Money, Credit and Banking 34 (February):
94-113.
Crone, Theodore M., N. Neil K. Khettry, Loretta J. Mester, and
Jason Novak. 2008. "Core Measures as Predictors of Total
Inflation." Federal Reserve Bank of Philadelphia Working Paper
08-9.
Dickey, D. A., and W. A. Fuller. 1979. "Distribution of the
Estimator for Autoregressive Time Series with a Unit Root." Journal
of the American Statistical Association 74: 427-31.
Engle, Robert F., and C. W. J. Granger. 1987. "Co-Integration
and Error-Correction: Representation, Estimation and Testing."
Econometrica (March): 251-76.
Granger, C. W. J. 1986. "Development in the Study of
Cointegrated Economic Variables." Oxford Bulletin of Economics and
Statistics 48: 213-28.
Hamilton, J. D. 1994. Time Series Analysis. Princeton, N.J.:
Princeton University Press.
Johansen, S. 1988. "Statistical Analysis of Cointegrating
Vectors." Journal of Economic Dynamics and Control 12: 231-54.
Kiley, Michael T. 2008. "Estimating the Common Trend Rate of
Inflation for Consumer Prices and Consumer Prices Excluding Food and
Energy Prices." Finance and Economics Discussion Series, Division
of Research and Statistics and Monetary Affairs, Federal Reserve Board,
Washington, D.C.
Leduc, Sylvain, Keith Sill, and Tom Stark. 2007.
"Self-Fulfilling Expectations and the Inflation of the 1970s:
Evidence from the Livingston Survey." Journal of Monetary
Economics: 433-59.
Lubik, Thomas, and Paolo Surico. 2006. "The Lucas-Critique and
the Stability of Empirical Models." Federal Reserve Bank of
Richmond Working Paper 6.
Mehra, Yash P., and Brian D. Minton. 2007. "A Taylor Rule and
the Greenspan Era." Federal Reserve Bank of Richmond Economic
Quarterly 93 (Summer): 229-50.
Mehra, Yash P., and Christopher Herrington. 2008. "On Sources
of Movements in Inflation Expectations: A Few Insights from a VAR
Model." Federal Reserve Bank of Richmond Economic Quarterly 94
(Spring): 121-46.
Mishkin, Frederick S. 2007a. "Inflation Dynamics."
Working Paper 13147. Cambridge, Mass.: National Bureau of Economic
Research (June).
Mishkin, Frederick S. 2007b. "Headline Versus Core Inflation
in the Conduct of Monetary Policy." Speech at the Business Cycles,
International Transmission and Macroeconomic Policies Conference,
Montreal, Canada, October 20.
Phillips, Peter, and Bruce E. Hansen. 1990. "Statistical
Inference in Instrumental Variables Regression with I(1)
Processes." Review of Economic Studies 57 (January): 99-125.
Rich, Robert, and Charles Steindel. 2005. "A Review of Core
Inflation and an Evaluation of its Measures." Federal Reserve Bank
of New York Staff Report 236.
Webb, Roy. 1995. "Forecasts of Inflation from VAR
Models." Journal of Forecasting (May): 267-86.
(1) The evidence suggesting the Federal Reserve under Chairman
Greenspan focused on a core measure of inflation appears in Blinder and
Reis (2005), Mehra and Minton (2007), and Mishkin (2007b).
(2) See also Clark (2001), Blinder and Reis (2005), Rich and
Steindel (2005), and Kiley (2008). These analysts use different
empirical methodologies to come to the same conclusion that core
inflation is better than headline inflation in gauging the trend in
inflation if we focus on the samples that start in the early 1980s. For
example, Kiley (2008) uses statistical models to extract directly the
trend component of inflation and argues that, in the 1970s and early
1980s, core as well as headline inflation contains information about the
trend; however, in the recent data, the trend is best gauged by focusing
on core inflation. The evidence in Clark (2001), Blinder and Reis
(2005), Rich and Steindel (2005), and Crone et al. (2008) is based on
comparing the relative forecast performance of core and headline
measures; only in recent data is core inflation the better predictor of
future headline inflation.
(3) The evidence indicating that inflation dynamics have changed
since 1979 appears in Bernanke (2007); Leduc, Sill, and Stark (2007);
and Mishkin (2007a).
(4) Many analysts have noted the low power of unit root tests in
detecting nonstationarity in series, arguing that inflation may not have
a unit root when some more attractive alternative hypotheses are
considered. For example, Webb (1995) argues that it is possible to
reject the hypothesis of a unit root in inflation when the alternative
hypothesis allows for the presence of breaks in monetary policy regimes.
As noted in the main text of this article, we also examine short-term
headline-core inflation dynamics, treating inflation as being stationary
within each sub-period.
(5) The adjusted R-squared statistics provided in Table 3 appear
reasonable given that short-term adjustment equations are estimated
using first-differences of inflation measures.
(6) In previous research, analysts have focused only on equation
(4.1), examining inversion in headline inflation. See, for example,
Clark (2001), Cogley (2002), and Rich and Steindel (2005)
(7) In the multivariable versions of (5.1) and (5.2), we include
changes in a short-term nominal interest rate and changes in the
unemployment rate, besides including lags of headline and core inflation
rates.
(8) For an empirical demonstration of the impact of change in
policy on the stability of empirical models (the so-called Lucas
critique), see Lubik and Surico (2006).
(9) For further details see Leduc, Sill, and Stark (2007) and Mehra
and Herrington (2008).
(10) We infer the response of the real interest rate to a shock by
comparing the responses of the nominal interest rate and expected
headline inflation. Thus, the expected real interest rate response is
simply the short-term nominal interest rate response minus the expected
headline inflation response.
(11) However, in the pre-1979 sample period, a surprise increase in
core inflation is reversed and leads to a decline (not increase) in
expected and actual headline inflation. Even though the nominal interest
rate does not increase in response to a positive shock to core
inflation, the expected real interest rate does increase because of a
decline in expected headline inflation. These responses suggest that the
Federal Reserve was not as accommodative to shocks to core inflation as
it was to shocks to expected headline inflation. As noted by several
analysts, the Federal Reserve may have believed that shocks to food and
energy prices are likely temporary and would not lead to persistent
increases in headline inflation.
(12) In the recent sample period. 1985:1-2007:2, a surprise
increase in food and energy prices does feed into core inflation.
Yash P. Mehra and Devin Reilly
Thomas Lubik, Roy Webb, and Nadezhda Malysheva provided valuable
comments on this article. The views expressed in this article do not
necessarily reflect those of the Federal Reserve Bank of Richmond or the
Federal Reserve System. E-mails: yash.mehra@rich.frb.org;
devin.reilly@rich.frb.org.
