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NBE WO~G
PAPER SERIES
THE TIME-VARYING NAIRU AND ITS
IMPLICATIONS FOR ECONOMIC POLICY
Robert J. Gordon
Working Paper 5735
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
August 1996
This research is supported by the National Science Foundation. I am grateful to Tomonori Ishikawa
for research assistance and to Mark Watson for helpful discussions. This paper is part of NBER’s
research program in Economic Fluctuations and Growth. Any opinions expressed are those of the
author and not those of the National Bureau of Economic Research.
O 1996 by Robert J. Gordon. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that fill credit, including 0 notice,
is given to the source.
NBER Working Paper 5735
August 1996
THE TIME-VARYING NAIRU AND ITS
IMPLICATIONS FOR ECONOMIC POLICY
ABSTRACT
This paper estimates the NAIRU (standing for the ~on-~ccelerating
unemployment)
Inflation Rate of
as a parameter that varies over time. The NAIRU is the unemployment
is consistent with a constant rate of inflation.
rate that
Its value is determined in an econometric model in
which the inflation rate depends on its own past values (“inertia”), demand shocks proxied by the
difference between the actual unemployment
rate and the estimated NAIRU, and a set of supply
shock variables.
The estimated NAIRU for the U.S. economy differs somewhat for alternative measures of
the inflation rate. The NAIRU estimated for the GDP deflator varies over the past forty years within
the narrow range of 5.7 to 6.4 percent; its estimated value for the most recent quarter(1996:Q1)
5.7 percent. In that quarter a lower NAIRU of 5.3 percent is obtained for the chain-weighted
deflator. Recent research claiming that there is a three-percentage-point
is
PCE
range of uncertainty about
the NAIRU is rejected as inconsistent with the behavior of the American economy in the late 1980s
and early 1990s.
Robert J. Gordon
Department of Economics
Northwestern University
Evanston, IL 60208-2600
and NBER
[email protected]. nwu.edu
The relationship
monetary
policy.
between inflation
and unemployment
is central to the conduct
of
More than 35 years ago Paul Samuelson and Robert Solow (1960) coined
the term “Phillips curve” at the 1959 AEA meetings, reacting promptly
to the publication
of
Phillips’s seminal (1958) article.
A few years later Milton Friedman
“natural rate of unemployment,”
which more recently has come to be known by the familiar
acronym
“NAIRU,” standing for the ~on-&ccelerating
(1968) coined the term
~nflation Bate of ~nemployment.
at any given time there exists a unique NAIRU, then the Phillips curve tradeoff
at that unemployment
rate. The Fed cannot make the actual unemployment
the NAIRU in the long run, but it can maintain
setting the actual unemployment
rate of inflation,
a stable rate of inflation
rate equal to the NAIRU.
the Fed desires to reduce the inflation
is vertical
rate differ from
if it succeeds in
If instead of maintaining
rate toward
If
a stable
zero or some other
target, then it needs to keep the actual unemployment
rate above the NAIRU.
whether
the Fed needs to know the value of
the goal is steady inflation
or lower inflation,
Either way,
the NAIRU.
The NAIRU is not carved in stone.
In Friedman’s
is “ground out” by the set of ‘Walrasian” macroeconomic
the structure
change.
and institutions
of product
There is a perception
if so the NAIRU has doubtless
exhibited
pronounced
(1968) interpretation,
the NAIRU
relations in the economy,
including
and labor markets, and any of these relations
can
that much about the economy has changed in the 1990s, and
changed
as well.
cycles over the postwar
Indeed,
period,
as we shall see, the NAIRU has
albeit within a surprisingly
narrow
range.
The Fed acts as if it already accepts the fact that the NMRU
adapted
policy procedures
that implicitly incorporate
new information
can move and has
to update previous
The Time-Varying
estimates of the NAIRU.
around
Whereas in early 1994 it implicitly believed that the NAIRU was
6.0 percent and sharply raised short-term
that the actual unemployment
not accelerate in response
to an average unemployment
dynamic simulations
of regression
rate. 2 Because these simulations
without
any appreciable
drift, I had submitted
were capable
of
sample
the accuracy of such
post-sample
simulations
as evidence that the NAIRU was still 6.0 percent.
acceleration
of inflation
that occurred in 1988-89,
6.0 percent for a period of three years, is consistent
and I
equations
rate accurately for many years after the end of the regression
e.g., 1987-94,
did
rate well below 6.0 percent.1
to assume that the NAIRU was 6.0 percent,
by running
the value of the inflation
tracking the inflation
period,
repeatedly
for most of 1995
interest rates to drift down slightly when inflation
For many years it was reasonable
that predict
interest rates when it correctly predicted
rate was about to fall below 6.0 percent,
and early 1996 it allowed short-term
tested that assumption
NAIRU, Page 2
when the unemployment
The substantial
rate fell below
with the view that the NAIRU was at
6.0 percent or above as recently as 1988-89.
1. Even though the actual unemployment rate averaged 5.6 percent in the 21 months ending
in May, 1996, below the Fed’s previous NAIRU estimate of 6.0 percent, the inflation rate did not
accelerate. Indeed, one key measure of inflation, the personal consumption deflator (on the new
chain-weighted basis) decelerated. The implicit price deflator for personal consumption expenditures
on the new chain-weighted basis rose 2.7 percent in 1992, 2.6 percent in 1993, 2.4 percent in 1994,
2.4 percent in 1995, and only 1.9 percent in the four quarters ending in 1996:Q1.
2. The inflation equation was developed in a series of papers, including Gordon (1970,
1975, 1977a, and 1982b).
King-Watson (1994) have called this approach the “Gordon-Solow
model,” citing the first of my papers and Solow’s 1969 book. In order to determine whether the
inflation relationship has changed, I have maintained unchanged the set of variables, lag lengths, and
other features of the equation introduced in Gordon (1982b) and Gordon-King (1982). The most
recent assessments of the performance of this equation are contiined in Gordon (1990a, 1994).
The Time-Varying
However,
reduced
numerous
factors have changed
the NAIRU, and indeed
since 1988-89
in a way that may have
the absence of an acceleration
of inflation
suggests that the NAIRU may well have fallen below 6.0 percent.
and their penetration
in the labor force continues
under intense pressure from consumers
The rest of the industrial
to decline.
and foreign competitors
world has experienced
as arguing that the economy
at all” (Stevenson,
Manufacturers
have been
to restrain price increases.
and there is ample
Business executives are quoted
has changed drastically in the last ten years.
John F. Welch Jr. recently stated that ‘There is no inflation
in 1995-96
Labor unions are weak
a sluggish recovery,
foreign capacity to provide supplies to U. S. manufacturers.
NAIRU, Page 3
General Electric’s
. . . there is no pricing power
1996).
The “Quiescence” of Phillips Curve Research
Has the NAIRU declined?
Surprisingly,
macroeconomists
If so, from what level a decade ago to what level today?
have thus far provided
be taken “off the shelf’ by policymakers
little research
has been conducted
no answer to this question
who need to know the answer.
on the U. S. inflation
contrast to feverish research activity in the 1960s and 1970s.
on the “quiescence” of the field.
One explanation
process is so stable, and the models developed
have been no behavioral
economists”
relation,
mysteries to solve.
have continued
process
For remarkably
in the past decade,
King-Watson
in
(1994) comment
of this void is that the U. S. inflation
in the early 1980s work so well, that there
In the words of King and Watson,
to view the Phillips curve as an essentially
once the original econometric
that can
“Keynesian
intact structural
models of the 1960s were amended
“to represent
The Time-Varying
supply shocks and build in a zero long-run
been accomplished
research,
(as in Gordon,
except periodically
remarkable
tradeoff” (1994, p. 160).
NAIRU, Page 4
Once this task had
1977), there was no further agenda warranting
checking
that the relation
remained
continued
stable, and indeed
“the
feature of the Phillips curve in the post war period was its stability” (Watson-
King, 1994, p. 160).
In this interpretation,
macroeconomics
has split into two camps.
from the Keynesians are the “neoclassical and monetarist
Sargent 1978) dismissed
the long-run
negative
between
models of the late 1960s contrasted
1970s.
new breed
tradeoff
and did not notice,
of post-1975
and included
Phillips
supply-shock
negative or positive correlation
the economy
neoclassical
of taking
economists
business-cycle
that incorporated
a vertical
long-run
the model to generate
depending
of a
either a
on whether
or supply shocks.
as the variable
to be determined
of aggregate
nor explained.
in the model (whether
variety), the determination
in the data of the
the resurrection
to real theories
equations
by the
much less take seriously,
variables that allowed
behavior of inflation was neither explored
by the set of behavioral
predicted
to empirical work on
between inflation and unemployment,
inflation
turned
and unemployment
stopped paying attention
curve estimates
was subjected to demand
Instead
inflation
failure on a grand scale,” since
with the distinctly positive correlation
At that point neoclassical economists
the Phillips correlation
economists, ” They (notably Lucas-
the Phillips curve as “econometric
correlation
Across the street
by their
fluctuations
models,
in which
the
While real output was determined
of the Lucas “surprise” or real-
of the price levei was left unspecified.
Implicitly,
The Time-Varying
the price level was left as a residual, i.e., as the level of nominal
NAIRU, Page 5
GDP (in turn often equal
to the money supply plus a stochastic error term) divided by whatever level of real GDP was
determined
by the model.
Phillips curve approach,
This treatment
was the diametric
to that implied in the
the inflation
rate,
while the growth rate of real GDP is implicitly a residual equal to the rate of nominal
GDP
growth
in which an equation
opposite
is specified to determine
minus the rate of inflation.
Agenda for this Paper
The NAIRU is defined
as the unemployment
under a specified set of conditions.
It is meaningful
the inflation
process.
the inflation
process that incorporated
rate consistent
with steady inflation
only within a well-specified
This paper begins by describing
and resurrected
the mainstream
“triangle model” of
the Phillips curve from what Lucas
and Sargent (1978) had called the “wreckage” of the early and mid 1970s.
NAIRU in terms of this model and examine
We define the
both what the model includes
shocks and rate of change effects) and what it excludes
model of
(e.g., supply
(any explicit role for expectations
or wages).
Then, instead of simply assuming a value for the NAIRU and testing the validity of
that assumed
econometric
intituitively
value in dynamic
technique
post-sample
that allows a time-varying
NAIRU
this paper
adapts
an explicit
to be esti~ted.
We show
why some previous authors, notably Staiger et. al. (1996), have found estimates
of the NAIRU to be highly imprecise,
of ambiguity
simulations,
which
surrounds
and we propose a simple criterion
the topic.
to clear the cloud
We emerge with a set of alternative
NAIRU
The Time-Varying
estimates for the 1955-96
on which inflation
period which differ only moderately
measure, specification,
NAIRU, Page 6
from each other depending
and sample period is used.
As we shall see, the most interesting
for the current period relate to the contrasting
differences
among the proposed
behavior of alternative
NAIRU series
price indexes, and we
suggest that the Fed needs to decide which inflation
index it is trying to stabilize, e.g., the
GDP deflator, the deflator for Personal Consumption
Expenditures
Price Index.
After we identify the alternative
NAIRU series, we then use preferred
of the inflation equation to compute dynamic simulations
on the assumption
concludes
of alternative
by examining
(PCE), or the Consumer
of the inflation rate in future years
paths for the actual unemployment
implications
versions
rate.
The paper
for the past, current, and future conduct
of monetary
policy.
Several important
entirely concerned
quite different
topics lie outside of the research agenda in this paper.
with the inflation
behavior
of inflation
estimates the time-varying
process developed
process in the United States and does not treat the
and unemployment
in Europe
in my previous
work; it does not develop
Second,
it
of monetary
lagged responses
policy
such a model from scratch.
rate should be the Fed’s target but does not inquire into
the methods by which the Fed should attempt to accomplish
subsequent
or Japan.
NAIRU within the context of the “triangle” model of the inflation
Third, it asks which unemployment
the channels
First, it is
that
of output,
To preview the main conclusions,
link changes
that goal, i.e., it does not study
in the short-term
income, employment,
interest
rate to
and unemployment.
at any given time there is a NAIRU for the U. S,
The Time-Varying
economy.
Our alternative
NAIRU estimates differ moderately
the exact fevel of the 1996 NAIRU, depending
regarding
to be used. The alternative
substantially
since 1988-89,
unemployment
opening
up the opportunity
rate than was feasible then.
marginally better explanation
Further,
among among
primarily
estimates all support the conclusion
NAIRU, Page 7
themselves
on the inflation
index
that the NAIRU has declined
for the Fed to maintain
the time-varying
a lower
NAIRU provides
a
of inflation behavior in the 1990s than the previously assumed
fixed NAIRU of 6.0 percent.
The “Triangle” Model of Inflation
between the rate
The “Phillips curve” has become a generic term for any relationship
of change of a nominal price or wage and the fevel of a real indicator
demand
in the economy,
relation was amended
emerged
such as the unemployment
by incorporating
was an interpretation
of inflation
Long ago, the simple Phillips
supply shocks and a zero long-run
the dependence
inertia, demand,
In this framework
tradeoff.3
of the inflation
lower-case
letters
What
rate on a tripartite
a general specification
designate
first
set
and supply.
for the rate of price change (p,) is:
(1)
Pt = a(L)p~.l + b(L)D~ + c(L)z~ + et.
Here
of
of the Phillips curve that I have called the “triangle” model
— a label summarizing
of basic determinants:
rate.
of the intensity
differences
of logarithms,
upper-case
letters
3. Schultze (1975) and Gordon (1975) introduced explicit variables to isolate the effect of
food and energy prices and price controls on the U. S. inflation rate.
The Time-Varying
designate logarithms
of levels, L is a polynomial
demand
so that D,=O indicates the absence of excess demand), z, is a vector of
(normalized
supply shock variables (normalized
et is a serially uncorrelated
of basic determinants,
demand
in the lag operator,
NAIRU, Page 8
D, is an index of excess
so that Zt =0 indicates an absence of supply shocks), and
error term.
The “triangle” rubric is associated with the three sets
respectively “inertia” (i.e., the influence of the lagged inflation
terms),
(the D, terms), and supply (the z, terms).
If the sum of coefficients
“natural rate” of the demand
While the estimated
on lagged inflation equals uni~
variable (Wt ) consistent
sum of coefficients
with a constant
on lagged inflation
(see Tables 1-3 below), that sum must be constrained
(Z ~ = 1), then there is a
rate of inflation.
is usually roughly equal to unity
to be erectly
natural rate of the demand variable to be calculated from (1).
unity for a meaningful
Among the demand variables
that have been entered as proxies for D~ are the “output gap” (log ratio of actual to natural
or potential
real GDP), the “unemployment
rate of unemployment
gap” (difference between the actual and natural
— or NAIRU), and the rate of capacity utilization.
As written in (1) the model is incomplete,
exogenous,
since there are two endogenous
even if the supply shock variables (z,) are
variables, the inflation rate (PI) and the demand
variable (D~). The model can be closed with one or more equations
process.
“output
The simplest
approach
gap,” treats as exogenous
defines D, as the log output
the growth
rate of nominal
specifying the demand
ratio (R, = /n&l ~,
)) or
GDP in excess of natural
output growth (“excess nominal GDP growth”), and closes the model with a second equation
which is simply an identity
relating the change in the output
gap to inflation
and excess
The Time-Varying
nominal GDP growth.
textbooks,
This identity, used in one form or another in many macroeconomics
states that the change in the output gap equals the growth rate in nominal
(x,) relative to natural output growth
R, - R,.l
The model consisting
exogenous
exogenous
NAIRU, Page 9
demand
= xt-y*t
(y’,), minus the inflation
rate:
-pt.
(2)
of (1) and (2) has two equations
shock
variable
is excess
in two unknowns,
nominal
GDP
growth
& and p,.
Interpretations
(xi - y*, ), the
in previous time periods.
of the NAIRU
In this paper we are interested
that is consistent
in estimating
with steady inflation.
to (1) with the unemployment
the NAIRU, i.e., the unemployment
The equations
gap substituted
estimated
the unemployment
and the time-varying
for Dt:
gap is the difference
NAIRU
@t-U~t ).
rate
in this paper are identical
(3)
Pt = a(L)pt.l + b(L) Wt-wt ) + c(L)zt + et,
exogenous,
The
supply shock variable is the vector Z1, an d the lagged elements pf.l and &.l are
predetermined
where
GDP
between
If excess nominal
the actual unemployment
GDP growth
the model can be closed by adding two equations,
and the other of which is an “Okun’s Law” equation
relating
rate
is again taken as
one of which is (2) above,
the unemployment
gap to
The Time-Varying
the output
gap.4
The NAIRU,
unemployment
inflation.
standard
or alternatively
rate which
The structure
the “natural rate of unemployment,”
is consistent
of (3) suggests
version is the “no-supply-shock”
consistent
with steady inflation
emerges from the estimation
with
wo
steady
(nonaccelerating
alternative
concepts
steady inflation
NAIRU, that is, the unemployment
The
rate which is
of (3) with the z, “supply shock” variables included
to control
For example, if the inflation rate has been steady in the
rate is the “no-supply-shock
in the absence of supply shocks.
increase sharply in response
that
or decelerating)
of the NAIRU.
recent past, but then suddenly exhibits a “spike” that is entirely explained
unemployment
is simply
in the absence of supply shocks. This is the NAIRU that
for the influence of supply shocks.
the current
NAIRU, Page 10
by the Zj variables,
NAIRU” that is compatible
An alternative
unqualified
to an adverse supply shock by the estimated
with
NAIRU would
amount
of the
shock [c(L)zJ divided by the sum of the b coefficients.
focus
By taking excess nominal GDP growth as exogenous,
the triangle model allows us to
on
of building
determinants
the
inflation
of aggregate
macroeconomics
the determination
process
without
demand.
the distraction
Admittedly,
this simplification
of the
sweeps two-thirds
under the rug, And it ignores channels by which inflation
of nominal GDP, which may cause econometric
a model
of
feeds back into
bias in inflation equations
4. Using the symbols in the text, an Okun’s law equation that closes the model would be:
U, - ~,
= O(L)& + c,.
Empirically the sum of the 8 coefficients has been around -0.5 for most of the postwar period,
although in the 1990-95 subinterval that sum has been close to -1.0.
The Time-Varying
in which
nominal
proposition,
GDP
appears
directly
in the presence of contemporaneous
and of supply shocks that are imperfectly
equation
coefficient
(1) that use nominal
on nominal
is biased toward
measured,
the smaller
zero,
The more
the bias.5
unemployment
by finding
estimates of the triangle-type
accurately
In their
equation
Alternatively,
using the
the influence
consideration
of the
Granger-causes
on the unemployment
of supply
shocks
endogeneity
support
inflation,
is
of the
the inclusion
of
but they do not
variable in the presence
supply shocks.G
In general, supply shocks create an omitted variable problem in the traditional
curve specification
inflation
(D~) variable will yield a
like (2), King-Watson
that unemployment
the issue of bias in the coefficient
measured
measured,
GDP
gap as a proxy for the demand variable will yield a coefficient
rate in an inflation
of imperfectly
As a general
feedback from inflation to nominal
GDP as a proxy for the demand
unemployment
consider
variable.
GDP which is biased away from zero.
output gap or unemployment
which
an an explanatory
NAIRU, Page 11
that includes only lagged inflation
and the unemployment
Phillips
gap.’
One
5. Formal measures of the bias are developed in Gordon (1990b, Table 1, p. 1121).
6. “More specifically, in a reduced form vector autoregression, past unemployment is
important for predicting current inflation but past inflation contains little information about current
unemployment” (King-Watson, 1994, p. 161).
7. While early work on the Phillips curve focussed on wage behavior, and required a “markup” equation to relate inflation to wage changes, it has proven more useful since the mid-1970s to
estimate a reduced-form equation in which inflation is directly related to unemployment, thus
eliminating the need to be concerned with the two-way links between wages and prices. A complete
set of wage equations for both the U. S, and for Germany, estimated with the same specification as
in this paper, can be found in Franz-Gordon (1993). That paper determined that the U. S. wage
NAIRU for 1990 was 6.2 percent, almost exactly the same as estimated in this paper for the GDP
deflator by the time-varying approach described below.
The Tim~Varying
expects inflation
extraneous
to be negatively related to unemployment,
positive
correlation
between
inflation
but if supply shocks create an
and unemployment
variables are inclu&d to proxy for the influence of supply shock,
unemployment
unreliable
will be biased toward zero, and the resulting
predictions
NAIRU, Page 12
and
no e~licit
then the coefficient
equation
on
is likely to produce
in periods when supply shocks are absent.
Rate of Change Effects
In previous
research I have found that wage and price change depend
on both the
level and change in the demand variable, i.e., the output gap or unemployment
gap.a The
role of the change effect is automatically
allowed
to enter as long as the gap variable is
entered with more than one lag. For instance, if the gap variable is entered as the current
value and one lagged value and the coefficients are estimated as -0.5 and +0.3, respectively,
then this is identically
equal to an equation
of the gap are entered
separately,
in which the current level and current change
with respective coefficients
of -0.2 and -0.3.
In light of
the high statistical significance of the change effect in the results discussed below, time-series
equations
that do not allow for the change
effect (either by entering
it directly
allowing the level of the gap to enter with one or more lags) are misspecified.
effect is particularly
important
in explaining
a result that I have found previously
macroeconomic
price behavior
or by
The change
in the 1930s,
and that Romer (1996) has recently substantiated.
8. I first noted the importance of the rate-of-change effect in Gordon (1977a, pp. 270-1).
The Time-Varying
Missing Eiements:
Expectations
The original
unemployment.
Phillips
bter,
article
and Wages
was about
the relation
These are issues of substantive
adaptive
above has no expectations
Much attention
is deliberate.
to the interpretation
lags in the formation
price and wage inertia
is compatible
with rational
can be delayed by wage and price contracts,
level.
promptly
the
and rationally
formation
upward
movement
explained.
be~een
yet everyone
contracts,
form
about the aggregate
price
the dynamics
delivery lags, or anything
of
else.
The relationship
of prices to wages
markup equation
of the type
Labor’s share in national income exhibits a strong
the mid-1960s
The Fed’s goal is to control
Price
is the omission of wages in the triangle
on wages was a mistake.
literature.
issues.
can
terms in (1) and (3) is to capture
has changed over time and is not well described by a constant
used in the eariy Phillips-curve
and
based on full information
formation,
of price
and by the time needed for cost
~bie,
as the omission of expectations
The earlier fixation
in the late
The speed
are two total] y different
input-output
related to expectation
As important
model.
through
The role of the lagged inflation
inertia, whether
and no wages.
was diverted
expectations.
adjustment
expectations
Phillips
Since then we have learned that
of expectations.
and the speed of expectation
to percolate
and
of the lagged effect of prices on wages as
adjustment
increases
wage changes
significance.
The omission of expectations
reflecting
between
expected inflation was added and we had the “expectational
curve. ” But the triangle model as summarized
1960s and early 1970s
NAIRU, Page 13
and early 1970s that has not been adequately
inflation,
not wage growth,
and models
with
The TimeVarying
NAIRU, Page 14
separate wage growth and price markup equations
do not perform as well as equations
(1) and (2) above in which wages are implicitly
solved out and only a reduced
estimated.
By treating the relationship
change to unemployment,
Samuelson
of inflation
the triangle approach
to unemployment,
returns
form of a relationship
implications
of the original
quadrant.
The earliest credit for ignoring
between the unemployment
wages is
the Phiilips curve in the
rate and price changes, not wage changes.
of the Triangie Model
Whether
the unemployment
like (1) or (3) determining
gap or some other demand variable enters an equation
the inflation rate, this equation,
GDP is exogenous
excess growth
To control
of nominal
together with the assumption
that
as in (2), generates several clear implications.
In the long run inflation
phenomenon.”
equivalent
rather than of wage
to the framework
claimed by Irving Fisher (1926), whose neglected article discovered
1.
form is
and Solow article (1960) that coined the term “Phillips curve” and plotted U. S.
data on the inflation-unemployment
nominal
like
inflation,
is “always and everywhere
policy needs a nominal
GDP itself.
Targeting
an excess nominal
anchor,
the no-supply-shock
most plausibly
NAIRU,
level of “natural” or “potentiai” real GDP, will lead to accelerating
decade like the 1970s when supply shocks are significant,
GDP
serially correlated,
the
or the
inflation
in a
and positive
(i.e., adverse).
2.
inflation;
There
is no special connection
between
the growth
in the money supply and
any effect of money growth on inflation is shared by an identical effect of velocity
The Time-Varying
growth
NAIRU, Page 15
on inflation.
3.
In the short run, fluctuations
loops on a diagram plotting
in excess nominal
inflation against the unemployment
inertia, i.e., the role of the lagged dependent
of the inflation
4.
unemployment
gap.
and unemployment
shocks
can cause a positive
The observation
(3) in slowing the response
gap.
between
inflation
and
that the Phillips curve correlation
between
inflation
correlation
was positive rather than negative in the 1970s is consistent
triangle model, due to its explicit treatment
5. The triangle model is resolutely
by the finite Phillips curve adjustment
GDP growth.
With excess nominal
unemployment
gaps are determined
incorporate
lead to clockwise
gap. The loops come from
variable in equation
rate to a change in the unemployment
Supply
GDP growth
the implication
man that “unemployment
Keynesian.
Prices are prevented
(b) from mimicking
GDP growth
as a residual.
that King-Watson
treated
changes in nominal
as exogenous,
However,
the output
in oil prices) raises the inflation
GDP growth,
and
the triangle model does not
(1994) attribute
by aggregate demand
by inertia and
to their “Keynesian” straw
disturbances.”
Instead, ktb
demand and supply shocks influence both the inflation rate and the unemployment
any given level of excess nominal
with the
of supply shocks like the rise in oil prices.
coefficient
is dominated
the
rate. For
an adverse supply shock (e.g., an increase
rate, reduces the output gap, and raises the unemployment
gap.
What
theoretical
story is consistent
with the mainstream
triangle
implicitly are price setters and demand takers. Although the Patinkin-Clower
model?
Agents
disequilibrium
The TimeVarying
framework,
as developed
by Barre-Grossman
(1976) and others,
setting, it is the right model of quantity determination
macroeconomists
curves by constraints
while forgetting
of price
Agents are pushed off notional
that spill over from rationed
tend to brush off the disequilibrium
of price determination,
has no model
given whatever sources of inertia and
finite Phillips slopes prevent prices from clearing markets.
supply and demand
NAIRU, Page 16
framework
markets.
Today’s
because it has no theory
that it has the right theory of output determination.
Validation of the Triangle Modei
The triangle
econometrics
model may be unique in that its textbook
and theory came after that.
The textbooks
version came first, and the
were published
equations were set out in 1976.9 The econometric
version, developed
validated
experienced
in 1981-87
percentage
corresponded
parameters
through
when
loss in output
associated
almost
exactly
estimated
through
1987 in post-sample
of inflation
the sacrifice
to what
with
ratio
the deceleration
had been predicted
the end of 1980.10
dynamic simulations
observed in 1987-90
and the deceleration
Versions
in 1978; the basic
in the late 1970s, was
by the economy
of inflation
in advance
(i.e., the
that occurred)
on the basis of
of the equation
estimated
tracked quite precisely the acceleration
of inflation that occurred in 1990-93.
9. See Gordon (1977b), a paper presented at the AEA meetings in October, 1976.
A
diagrammatic version originated in a classroom handout that Rudiger Dornbusch developed at the
Chicago Business School in early 1975. Both my version and that of Dornbusch combined a Phillips
curve, long-run neutrality, a nominal GDP identity like (2), and a role for exogenous supply shocks.
10.
econometric
deviation of
was reduced
Gordon-King (1982, Table 5, line 3) computed a sacrifice ratio of 6.2 from their
version of the triangle model. Using the data avaiiable at the time, the cumulative
actuai from potential output during the period 1980-87 was 26.2 percent and inflation
by 4.1 percentage points from 1979-80 to 1985-86, for an actual sacrifice ratio of 6.4.
The Time-Varying
The positive
performance
of the triangle
model
NAIRU, Page 17
stands in sharp contrast
shambles in which the Phillips curve literature found itself in the mid-1970s.
of departure
for Lucas’s new classical revolution
A central point
was the failure of the 1960s Phillips curve.
In the language of Lucas and Sargent (1978, pp. 49-50), “that these predictions
incorrect,
and that the doctrine on which they were based is fundamentally
simple matters of fact . . . the task which faces contemporary
[is] that of sorting through
the wreackage.
. . of that remarkable
Sargent wrote those lines; it has survived and thrived,
Barro (1978) and others to valididate
Estimating
aground
a
macroeconomics
textbook.
force)
event called the
while empirical attempts
by Robert
proposition
inertia.
a time series for the NAIRU has been published
My NAIRU series increases
from the 1950s
by using a demographic
when in the late 1980s (Gordon,
reversal of the 1980s (notably a reduced
the NAIRU
accordingly,
I found
other than its empirical performance,
to 6.0 percent
intellectual
in my
to the 1970s,
adjustment
to the
rate to reflect the rising share of teenagers and females in the labor force
had reduced
justification
of inflation
Perry’s (1970) innovation
during that era. However,
the demographic
of the business cycle
the new classical policy ineffectiveness
on the bedrock
two decades
George
unemployment
flawed, are now
Time-varying NAIRU
For almost
following
students
were wildly
The triangle model was in print in its present form before Lucas and
Keynesian Revolution.”
failed, running
to the
for the entire period
after 1978.
1990) I tested to see whether
share of teenagers
that it had
not.
in the labor
Without
any
I arbitrarily set the textbook NAIRU equal
The NAIRU series that combines
the
The Time-Varying
demographic
adjustment
6.0 percent thereafter
the relative
through
is henceforth
performance
1978 with an assumption
NAIRU, Page 18
that the NAIRU is conswnt
at
called the “textbook NAIRU series.” This paper assesses
of the textbook
NAIRU series and an alternative
(’W’) NAIRU series that bases changes in the NAIRU on time-varying
time-varying
parameter
estimates.
Form of the Inflation Equation
The estimation
of the TV-NAIRU combines the above inflation equation
here, with an explicit specification
p,
=
(3), repeated
of the TV-NAIRU:
a(~)p,.1 + b(L)(u,-@, ) +
c(L)z,
+ e,,
(3)
w,= UN,.,+ Et.
(4)
In (3) the error term ●, is iid with a mean of zero and a standard
the standard
deviation
o, = O, then ~t
is constant.
E, each quarter.
UNt to vary each time period,
then the TV-NAIRU
standard
variation
“stochastic time-varying
Gaussian
maximum
previously
applied
likelihood
The following
would be free to jump up and down
equation.
regression
by Hamilton
(1994).
using a very different
(1995) and Staiger, Stock, and Watson
are the key elements
The model
of the inflation
The sample period is 1955:2-1996:1,
(3)-(4) is a
model” that can be estimated
as described
to the issue of the NAIRU,
King, Stock, and Watson
previous papers.
methods
When
When a= # O, the model allows the
in the inflation
parameter
of o..
If no limit were placed on the ability of
NAIRU to vary by an amount
and soak up all the residual
deviation
version
using
It was
of (3), by
(1996).
equation
or 164 quarters.
(3), as developed
All right-hand-side
in
The Tim~Varying
variables are allowed to enter with unconstrained
to be identical to those in Gordon
to unity, inflation
NAIRU ~, - ~,
changes
distributed
lags.
NAIRU, Page 19
Lag lengths are chosen
(1990).11 Note that with a sum of a(L) coefficients
remains constant
in a steady state with the unemployment
equal
rate at the
=0) and with supply shocks absent (z,= O). Supply shock variables include
in the relative
price of imports,
the change
in the relative
price of food and
energy, 12and the change in the real effective foreign exchange rate.13 Dummy variables are
included
for the “on” and “off’ effects of the Nixon price controls.
These dummy variables,
and indeed all the other variables, are defined exactly the same as in all my papers starting
with (1982 b).
Also included
is the difference
between productivity
growth and its trend,
reflecting
the fact that, while most of any cyclical increase or decrease in productivity
is
reflected
in a movement
to
in profits
in the same direction,
a small fraction
remains
11. The only smoothing structure imposed on the lag distributions involves the lagged
dependent variable, where 24 lagged terms enter. Rather than estimating 24 unconstrained
coefficients, the lagged dependent variable is entered as a series of four-quarter moving averages of
rates of change, e.g., the first variable is a four-quarter average of lags t-1 to t-4, the next t-5 through
t-9, etc. The coefficients on the individual moving averages are unconstrained. Exclusion tests
indicate that the moving averages representing lags 13 through 24 enter with a significance level of
between 1 and 2 percent in the two equations displayed in Table 1 for the sample periods 1955-96
and are thus highly significant.
12. The food-energy effect is defined as the difference of the rate of change of the chainweighted consumption deflator minus the rate of change of the chain-weighted consumption deflator
net of food and energy. Chain-weighted deflators are available back to 1959 and are linked to the
implicit deflator prior to 1959.
13. An additional supply shock variable, the change in sensitive raw materials prices, BCD
series 99, was tested and found to be insignificant, with a t-ratio below 1.
footnote 7).
See Gordon (1994,
The TimeVarying
influence
the inflation
rate in the opposite
Data on Unemployment
Figure
1 displays
direction.14
and infiation
the actual unemployment
difference between the actual unemployment
unemployment
1969-70
business cycles, with short back-to-back
that barely nudged
the actual unemployment
More excess demand followed in 1973-74,
1973-74,
Another
followed
cycle occurred
the U. S. National
the context
nominal
NAIRU is the textbook
recessions
gap tells
in 1957-58
by the mild
rate above the NAIRU.
in the late 1980s, with excess demand
gap during 1991-93
comparable
and another
GDP growth,
period of
price indexes from which we will calculate three
The chain-weighted
GDP deflator
(the basic deflator concept in
Income and Product Accounts since early 1996) is convenient
of the triangle
to
late 1994 and early 1996.
Figure 2 compares three alternative
NAIRU series.
The
followed by the severe recessions of 1974-75 and
by a positive unemployment
mild excess demand between
alternative
rate and the textbook
NAIRU.
and then a long period of excess demand in the 1960s followed
recession
1981-82.
rate and the textbook
gap (separately dispiayed below in Figure 4). The unemployment
a familiar story of poswar
and 1960-61,
NAiRU, Page 20
model,
since it makes the definition
and the inflation
rate in equation
linking
output
(2) above hold exactly.
could be made that it makes more sense for the Fed to stabilize consumer
to use in
growth,
A case
prices than GDP
14. The productivity deviation variable was first introduced in exactly the same form in my
(1970) paper. The productivity deviation is defined as the log ratio of actual nonfarm private output
per hour to a Ioglinear piecewise trend running through 1950:Q2, 1954:Q4, 1963:Q3, 1972:Q2,
1978:Q3, 1987:Q3, and 1994:Q3.
The 1987-94 growth rate of this trend is 1.07 percent per
annum.
The Tim~Varying
NAIRU, Page 21
prices, and for this reason we compute alternative NAIRU series for the chain-weighted
deflator,
also shown in Figure 2. For reference is shown a third series, the inflation
CPI-U-X 1.15 All three series show the mme basic cycles of acceleration
the inflation
(1974-75
rate, although
and 1979-81)
than the GDP deflator,
there are notable
the consumption
differences.
and in 1980-81
they rise further.
rate of
and deceleration
In both supply-shock
deflator and CPI inflation
PCE
in
episodes
rates accelerate earlier
On average consumer
price
inflation was more rapid than GDP inflation from 1987 to 1994, and this is the counterpart
of the fact that the real wage grew less rapidly in terms of consumer
product
prices.
consumer
The opposite
price inflation
smoothness
completely
occurred
was slower than inflation
Alternative Time-Varying
As indicated
phenomenon
during
prices than in terms of
1955-60
and 1965-73,
when
in the GDP deflator.
NAIRU Series
above, the model (3)-(4) requires that an assumption
of the computed
TV-NAIRU
series.
An assumption
be imposed on the
of a, = O implies
constant NAIRU wries of 6.0 percent, as shown by the horizontal
3. At the other extreme an assumption
a
line in Figure
of aC = 0.4 implies a highly variable NAIRU series,
as shown by the line with the long dashes in Figure 3. In between are series with assumed
standard
deviations
the standard
of 0.1 and 0.2.
deviation
This problem
Which of these and other possible assumptions
about
should we make?
is analogous
to the choice of a smoothness
parameter
for the Hodrick-
15. This hybrid series is equal to the CPI before 1967 and aher 1982, while between 1967
and 1982 substitutes the current rental-equivalence approach for owner-occuped housing in place
of the official CPI pre-1983 treatment that is universally regarded as erroneous.
The Time-Varying
Prescott
filter so often used to detrend
deviation
variables.
may not be the same for every variable or topic.
paraphraw
Milton Friedman,
of the economy,
The most sensible standard
If the NAIRU is viewed,
as “ground out” by the macroeconomic
then it should shift slowly.
NAIRU incorporated
inflation
time-series
into equation
NAIRU, Page 22
structure
to
and behavior
This is especially true, since the concept of the
(3) is the unemployment
rate consistent
with steady
in the absence of supply shocks. Allowing a shift in the NAIRU of 0.1 percentage
point per quarter might be considered
as excessively rapid.
implausible;
reasonable
and of 0.4 percentage
The zig-zags in the series assuming a standard
why should the no-supply-shock
we propose
points per quarter
deviation
of O.4 appear
NAIRU jump up and down from quarter to
quarter?
In essence,
using a “smoothness
presented
by the various NAIRU series in Figure 3. We allow the NAIRU to move around
as much as it wants to, subject to the qualification
(negative serial correlation)
As shown
movements
the ambiguity
that sharp quarter-to-quarter
in the rest of the paper, we wlect a standard
deviation
in Figure 3, this results in a NAIRU series that exhibits
but just avoids sharp quarter-to-quarter
zig-zags.
in the mid-1950s
to a minimum
percent between
1967 and 1972, declines briefly between
of 5.3 percent around
hump of about 6.5 percent between
percent in the final quarter,
Figure 4 compares
zig-zags
are ruled out.
In the series developed
of 0.2,
prior” to reduce
(uc)
substantial
It declines from 6.0 percent
1962, rises to a plateau of about 6.2
1973 and 1978, then exhibits a
1978 and 1982, and then drifts down gradually to 5.7
1996:1.
the unemployment
gaps implied
by the textbook
NAIRU and
The Tim~Varying
NAIRU, Page 23
various TV-NAIRU series. We see that all the TV-NAIRU series indicate substantially
excess demand
than the textbook
the TV-NAIRU
somewhat
wries
corresponding
less excess demand
Previously
(Gordon,
expansion
and
assumption
of 6.0 percent.
textbook
1965-70,
to a standard
than the textbook
and 1979-80.
deviation
1990-91
recession
period
series.
was consistent
with
Indeed, we shall see that the textbook
rate in a dynamic simulation
that this evidence
presented
NA.IRU prior to 1987 or so.
For 1995-96
of 0.2 and 0.4 indicate
1994) we argued that the behavior of inflation
job of tracking the inflation
4 demonstrates
series in 1955-57,
previously
The textbook
the
in the 1988-89
textbook
NAIRU
NAIRU does a very good
applied to 1987-96.
is not sufficient
NAIRU performs
But Figure
to support
most of the period prior to 1987, the econometrically
Understanding
derived TV-NAIRU
the
well after 1987
simply because during that interval it happens to be quite close to the 7V-NAIRU.
higher than the textbook
more
During
is substantially
NAIRU.
the Ambiguity in Bounding the NAIRU
Staiger, Stock, and Watson (1996) have cast doubt on the enterprise
NAIRU, concluding
that “a typical 95V0 confidence
percent to 7.7 percent . . . . This imprecision
of estimating
the
interval for the NAIRU in 1990 is 5.1
suggests caution in using the NAIRU to guide
monetary
policy.” Interestingly,
our NAIRU estimate for the GDP deflator, using a standard
deviation
of 0.2, is 6.2 percent for 1990, close to the midway point of the Staiger et. al.
band.
Figure
4 displays
five different
unemployment
gap
series,
that
is, the
actual
The Time-Varying
unemployment
rate minus five alternative NAIRU series.
almost the same, are very highly correlated,
as well
as each
distinguished
smoothness
other.
from
Accordingly,
the other,
criterion
leading
proposed
ambiguity
regarding
differences
alternative
measures
acceleration,
constancy,
equations
criteria,
this ambiguity
to choose between alternative
see, the remaining
among
statistical
gap series look
that fit about
one
to the Staiger et. al. conclusion.
above cuts through
rather than a statistical criterion
The alternative
and resuit in inflation
by standard
NAiRU, Page 24
cannot
However,
which
NAIRU series.
exhibit
the
by using an economic
As we shall
the NAIRU for the very recent period
of inflation,
be
differing
concerns
degrees
of
or deceleration.
Estimated Equations for the GDP Defiator
The estimated equations
each are estimated
series (textbook
dependent
for 1955-87
in the four columns of Table 1. Two versions
and 1955-96,
corresponding
and TV with a, = 0.2).
(inertia) variable
of the correct
are presented
sign.
Estimated
and on the unemployment
No constant
is included,
sums of coefficients
alternative
version
gap zig-zags, indicating
of the equation
change in the unemployment
level, the coefficient
in column
gap are entered
NAIRU
on the lagged
gap are always highly significant and
an essential element
demand variabie is defined as a deviation from the NAIRU.
on the unemployment
to the two alternative
of the approach
if the
The pattern of lag coefficients
the presence of a rate of change effect.
(4), in which the current
In an
level and current
instead of the current and four lags on the
on the change is -0.99 with a t ratio of 4.0.
The significance
of the various supply variables
differs, depending
on the sample
The Tlm&Varying
period and on the length of the LDV distribution,
percentage-point
excess of productivity
NAIRU, Page 25
but they all have the correct sign. A one-
growth above trend reduces inflation
percent.
A one-percentage-point
inflation
by 0.06 to 0.09 percent, not far from the average share of imports in GDP during
the sample period.
through
Between 30 and 40 percent of the food-energy
to inflation
real exchange
increase in the relative price of imports
by about 0.1
in the GDP deflator.
first year.
The Nixon
explaining
the dynamics of inflation
during the 1971-75
that the TV-NAIRU
point appreciation
in the
by about 0.1 percent within the
“on” and “off’ dummy variables continue
the middle of Table 1 indicate
relative price effect feeds
And a ten percentage
rate of the dollar reduces domestic inflation
raises domestic
to be essential elements
period.
equation
about 17 percent lower than the textbook NMRU equation,
in
The summary statistics in
has residual variance that is
in both the 1955-87 and 1955-
96 sample periods.
The next-to-bottom
versions of the equations
to sum to unity.
1987:3-1994:3,
alternative
section of Table 1 lists the root-mean-squared
in which the sum of coefficients on the LDV have been constrained
These RMSE’S are shown
and 1994:4-1996:
for the TV-NAIRU versions.
in 1955-57
for four sub-periods
1) in order
NAIRU series. As would be expected,
period, indicating
by the textbook
series.
(1955-70,
the measures of fit are uniformly
of the
superior
in fit is during the pre-1970
NAIRU version mis=s an important
namely that excess demand was substantially
An important
1971-87:2,
to assess the relative performance
The largest relative improvement
that the textbook
and 1965-70,
errors (RMSE) of
result is that the equation
source of inflation
greater than implied
errors are substantially
The Time-Varying
smaller during
1987-94
and in 1994-95
than the average standard
sample period.
This indicates that the basic structure
NAIRU, Page 26
error for the entire
of the inflation
equation,
more than fifteen years ago, has proven to be very successful in tracking
quite different
sets of economic
as specified
inflation
during
conditions.
The final section at the bottom of Table 1 lists mean errors and RMSE’S for dynamic
simulations
in which the LDV is fed back endogenously
Separate errors are listed from the same simulations
the actual unemployment
over the period
1987:4-1996:1.
for the final six quarters during which
rate fell below 6.0 percent, 1994:4-1996:1.
The results in the left-
hand column, based on the textbook NAIRU, uses absolutely no information
1987:1
interval to estimate
NAIRU, uses post-1987
other post-1987
the coefficients.
information
The results in column
from the post-
(2), based on the TV-
to estimate the NAIRU using model (3)-(4) but uses no
information.
When actual inflation
turns out to be above the simulated
a positive mean error, and this occurs for 1987-96
rate of inflation,
in all four columns.
there is
This implies that
during this interval the assumed NAIRU series is too low. A negative mean error means that
the assumed
simulations
NAIRU
series is too high.
are quite encouraging.
The
results
for the 34-quarter
While the mean error is positive, both the textbook
TV-NAIRU versions are almost exactly on track in the final six quarters.
squared error of the simulations
estimated
equation.
inflation
and
And the root mean
in all four columns is lower than the standard
The textbook
series and overpredicts
post-sample
error of the
NAIRU series predicts almost as well as the TV-NAIRU
by only a modest amount
during
1995-96.
The Time-Varying
The simulation
full wmple
period
simulation.
Here it is important
sample period
through
is extended
have been during
(3) and (4) use the coefficients
results in columns
1987-96
1996 and of course yield smaller
to emphasize
estimated
from the perspective
over the
RMSE’S for the 1987-96
how little the coefficients
and how stable the structure
NAIRU, Page 27
change when the
of the inflation
of coefficients
process seems to
estimated
for the pre-1987
period.
How much do the supply-shock
5 displays two TV-NAIRU
variables change the estimated
series for the GDP Deflator
differing only that the solid line displays the TV-NAIRU
equation
and a standard
Figure
deviation
of 0.2,
for the full version of the 1955-96
displayed in column (4) of Table 1, while the dashed line shows an alternative
NAIRU series that omits all right-hand-side
and the set of unemployment
1973-81
W-NAIRU?
period influenced
the contribution
after 1982,
gap terms.
by adver=
variables other than the lagged inflation
The results are intuitively
supply shocks, the TV-NAIRU
of the supply shock variables to inflation
presumably
plausible
due to the declining
TVterms
— during the
is much higher when
is ignored.
The reverse is due
real prices of oil and imports.
Nonlinearity
Recently
both
Robert
Eisner (1996)
and George
Akerlof,
George Perry (1996) have suggested that the linear specification
is incorrect.
unemployment
Eisner argues that the Phillips
rate is below the conventional
rate is above the conventional
NAIRU.
William
Dickens,
of the inflation equation
curve is concave,
that is, flatter
and
(3)
when the
NAIRU and steeper when the unemployment
I have tested Eisner’s proposition
by adding
to
The TimeVarying
equation
(3), in the version displayed in Table 1, column
to zero when the unemployment
the latter is positive.
negative
unemployment
(entered
significance
conventional
a steeper
slope
for the short-run
The sum of coefficients
value and four lags) indeed
of the sum is very weak,
is negative,
with a significance
becomes
conventional
gap when
Phillips
curve
at
on the POSGAP variable
-0.12,
but the statistical
level of 0.61,
far from the
0.05 criterion.
Akerlof et. al. (1996) argue for the opposite
which
variable equal
this “POSGAP” variable would have a significant
negative
rates above the NAIRU.
as the current
(4), an additional
gap is negative and equal to the unemployment
If Eisner is correct,
sign, indicating
NAIRU, Page 28
much
NAIRU.
flatter
when
inflation
a convex Phillips curve
is low and unemployment
To test their proposition,
is above
was below 3,0 percent.
the
I defined another variable equal to zero in
gap was positive and the four-quarter
all quarters except when the unemployment
in the GDP deflator
nonlinearity,
The sum of coefficients
change
on this additional
variable, entered again as the current value and four lags, is precisely zero. Thus I conclude
that the short-run
unemployment
Phillips curve is resolutely linear, at least within the range of inflation and
values observed
over the 1955-96
period.
Estimated Equations for the PCE Deflator
Table 2 displays an identical
weighted
PCE deflator
set of results that differs only by using the chain-
in place of the chain-weighted
Table 2 are similar to the corresponding
except (as would be expected)
elements
the coefficients
GDP deflator.
of Table 1.
Most elements
Coefficients
of
are similar,
on changes in the relative price of imports
The Time-Varying
and of food and energy are higher and more significant
Table 2 than in the GDP deflator equations
are uniformly
small and insignificant
NAIRU, Page 29
in the PCE deflator
equations
in
in Table 1. The Nixon “off” dummy variables
in Table 2, in contrast
to Table 1. Goodness
of fit
statistics are similar in both tables. Perhaps the most notable difference occurs in the bottom
two lines of Table 2, where improvement
columns
in performance
(2) and (4), relative to the textbook
much greater for the PCE deflator.
of the inflation
rate during
of the TV-NAIRU
NAIRU versions
in columns
The textbook NAIRU causes a substantial
1994-96
equation
(1) and (3), is
overprediction
that does not occur with the TV NAIRU.
Further insight into the “big miss” of the textbook NAIRU series is presented
6, which plots the textbook NAIRU against the TV-NMRU
The TV-NAIRU
deflator
between
was fairly close to that for the GDP deflator
from 6.2 to 5.2 percent
there is a sharp
disagreement
over the 1990-96
between
the textbook
regarding demand pressure in the economy;
in Figure
series, using a standard deviation
of 0.2, for both the GDP deflator and the PCE deflator.
plummets
in
period.
series for the PCE
1980 and 1990 but then
In late 1995 and late 1996
NAIRU
and the PCE TV-NAIRU
the former implies excess demand and the latter
implies excess supply.
Two other consumption-based
for the fixed-weight
consumption
TV-NAIRU series are displayed in Figure 7. These are
deflator
and CPI-U-X1.
The two PCE deflators
roughly the same story up to the last few years, when PCE TV-NAIRU
weighted
PCE deflator drops well below that for the fixed-weight
that the chain-weighted
PCE deflator
places a substantially
series for the chain-
PCE deflator.
higher
tell
weight
It appears
on consumer
The Time-Varying
electronics,
especially personal
prices in the 1990s.
computers,
that have exhibited
During the mid 1980s the TV-NAIRU
for the two PCE deflators,
NAIRU, Page 30
a drastic decline in relative
for CPI-U-X1
but after 1990 it has been somewhat
was lower than
higher.
Splitting the Sample Period
of the preceding
One possible criticism
period.
the length
of the sample
Why should the Fed base its estimate of the current NAIRU on more than forty
Why is not the more recent past, say the last 20 years, a more
years of previous
data?
relevant
interval
for which
contrasts
the full-sample
deviation
(the same series as was plotted
to estimate
the inflation
jump in the estimated
estimate,
0.0 and 0.3 percentage
the purpows
for 1996:1
of conducting
is identical
8
The two sub-samples
that is between 0.1 and 0.5 percentage
and an estimate
of the NMRU
for 1975-96
points higher than the full-wmple
estimate.
result in
points lower
that ranges
However,
for
current monetary policy, it is reassuring that the NAIRU estimate
in the full-sample
and split-sample
alternatives.
statistics of the split-sample equations
the GDP deflator are displayed in Table 3. The sum of coefficients
The mean error and root-mean-squared
for
on the unemployment
higher in the second sub-sample, while the coefficients
variables are quite different.
estimates
Splitting the sample period results in a sharp
The estimated coefficients and performance
gap is somewhat
Figure
in Figures 3, 5, and 6) with alternative
NAIRU at the break point (1975:1).
an estimate of the NAIRU for 1955-74
than the full-sample
Accordingly,
equation?
NAIRU estimate for the GDP deflator with a 20 percent standard
based on the two halves of the sample period.
beween
results concerns
on the supply-shock
error in the 1987-96
The TimeVarying
dynamic simulation
full-sample
are considerably
NAIRU, Page 31
lower for the split sample results in Table 3 than the
results in Table 1. However,
a Chow test just misses accepting
of a structural break between the two sub-samples at the conventional
the hypothesis
5 percent significance
level.lg
Simulations
of Alternative Post-1996 Unemployment
How rapidly
economy,
would
inflation
accelerate
if the Fed “let her rip” (referring
not interest rates) and allowed unemployment
the NAIRU?
to fall one percentage
an acceleration
of inflation.
allows the unemployment
The particular
96 inflation equation
The
unemployment
point below
coefficients
predictions
gap scenario that generates
scenario plotted by the dashed line in Figure 9
gap (actual unemployment
to -1.0 in 1997:2 and thereafter.
NAIRU.
to the
We can simulate our inflation model, assuming all future values of the supply
shock variables are zero, and specify an artificial unemployment
1996:2
Scenarios
minus NAIRU) to decline from 0.0 in
The prediction
estimated
of inflation
is based on the 1955-
in column (4) of Table 1, that is, using the TV-
are compared
with
a baseline
prediction
that
leaves
the
gap at zero forever, starting in 1996:2.
The
simulations
of the
acceleration
of inflation
during 1997, reflecting the fact that the pattern
on the unemployment
negative
unemployment
gap variable embodies
gap
a “rate-of-change”
effect. After the economy settles down at an unemployment
scenario
display
a rapid
of lag coefficients
effect as well as a “level”
gap of -1.0 percent, the rate-of-
16. The F(28,108) ratio is 1.51, compared to a 5 percent significance value of 1.57 and a
1 percent significance value of 1.89.
The TimeVa~ing
change effect temporarily
the acceleration
and financial
although
interrupts
the acceleration
of inflation
in early 1998, after which
proceeds steadily, reaching 5.4 percent by the year 2005.
market
experts
would
be surprised
NAIRU, Page 32
Many journalists
at the slow pace of this acceleration,
it is clear that the bond market would be “spooked” by the rapid pace of inflation
acceleration
during 1997.
A constant unemployment
settled down to an inflation
gap set at zero causes the economy to
rate of 2.3 percent forever.
Conclusion
The Triangle Model and the Time-Varying NAIRU
The
inflation
macroeconomic
process
phenomena
in
the
United
in the world,
States
is one
of
by inertia.
actual unemployment
run.
The best example
one percentage
accelerated
of inflation
point
Inflation
important
is the 1988-90
over the three years 1987-90
small consequences
period, when unemployment
the 6.2 percent
estimated
NAIRU,
from 3.1 to 4.4 percent.
of a bit less than half a point per one percentage
In
the U. S. inflation process
changes little from year to year, and any deviation
rate from the NAIRU has extremely
below
most
but it is also one of the best understood.
contrast to the wild gyrations of inflation in many other countries,
is dominated
the
of the
in the short
was on average about
and the GDP deflator
This implies a response
point that unemployment
remains below the NAIRU for a single year. The estimated coefficient on the unemployment
gap in Table 1, line 2, ranges from -0.60 to -0.69, somewhat
Because the U. S. inflation
above one-half.
process has been so stable, and is so well characterized
by
The TlmeVarylng
the triangle model of inflation
performed
extremely
developed
well in dynamic
in the late 1970s and early 1980s, that model has
post-sample
decade after the end of the sample period.
capable of tracking the disinflation
of the late 1980s,
simulations
extending
In such simulations
of the early and mid 1980s,
and the subsequent
NAIRU, Page 33
deceleration
out for up to a
the model
has proven
the acceleration
of inflation
of inflation
in the 1990s.
Those
empirical successes were achieved despite the fact in previous research, the NAIRU inserted
into the model was assumed arbitrarily
after 1978 rather than estimated
The main contribution
of this paper has been to allow the NAIRU to vary each
1955 and 1996.
close to 6 percent
for the GDP deflator
The resulting
time-varying
over the entire four-decade
extreme values of 5.3 and 6.5 percent.
the NAIRU from around
at 6.0 percent for the entire period
econometrically.
quarter over the period between
stays remarkably
to be constant
interval,
(TV) NAIRU
ranging between
In recent years there has been a downward
6.2 percent in the late 1980s to current estimates
and 5.2 percent for the PCE deflator.
drift in
of 5.7 percent
The fact that the TV-NAIRU
was very close to 6 percent during the expansion
of the late 1980s and recession of 1990-91
helps to explain
that the NAIRU was fixed at 6.0 percent
performed
surrounding
criterion,
assumption
so well in tracking the acceleration
This
policy.
how my previous
paper
rejects
the recent
and deceleration
argument
the NAIRU is so broad as to render
We propose
an economic
criterion
to choose among alternative
that
of that period.
the band
the concept
of statistical
uncertainty
useless for the conduct
based on smoothness,
of
rather than a statistical
NAIRU estimates for any given measure of inflation.
The Time-Varying
NAIRU, Page 34
The recent suggestion of Staiger et. al. (1996)
that the NAIRU for the year 1990 could range
from 5.1 to 7.7 percent makes no economic
sense.
If the NAIRU had been 5.1 percent in
the period since 1987, inflation would not have accelerated
unemployment
rate never fell below 5.1 percent in any calendar quarter.
been 7.7 percent
1990-93,
quarter.
in the period
since 1987, inflation
since the actual unemployment
The fact that the inflation
the six quarters
constant
during 1987-90,
would
since the actual
If the NAIRU had
not have decelerated
during
rate never rose above 7.7 percent in any calendar
rate for the GDP deflator was roughly constant
(1994:4-1 996: 1), when the actual unemployment
during
rate was approximately
at 5.6 percent, suggests that the TV-NAIRU for the GDP deflator during those six
quarters was very close to 5.6 percent.
The new TV-NAIRU
measuring
the real GDP that can be produced
at the TV-NAIRU.
that written
series allows a new series for potential
I have produced
above in footnote
such a series by estimating
series on potential
1990:3 and 1996:1.17
is operating
an Okun’s law equation
output
like
increases at an
Since the TV-NAIRU
from 6.2 percent in 1990 to 5.7 percent in 1996, this potential
0.1 percentage
to be created,
each quarter when the economy
4; the resulting
annual rate of 2.07 percent beween
output
declines
output series grows at about
point faster than would be implied by a NAIRU fixed at 6.0 percent.
Thus
17. In estimating the Okun’s law equation written in equation (4), I invert it to regress the
unknown output gap on current and leading values of the unemployment gap implied by the new
TV-NA.IRU series based on the GDP deflator and a standard deviation of 0.2. I allow the sum of
coefficients on the unemployment gap to differ during 1990-96 from their values in 1972-90.
I
calculate the fitted output gap, and then compute a trial value of potential output as actual real GDP
minus the fitted output gap. The final potential output series is a 12-quarter centered moving
average of the trial series.
The Tim~Varying
caution
is advised regarding
the advice of “growth
hawks” that the U. S. economy
grow at 3 percent or more per annum if only the Fed’s monetary
Since the economy
is currently
NAIRU, Page 35
could
policy is less restrictive.
at the NAIRU, the ceiling on non-inflationary
growth
is
about 2.1 percent a year, unless the NAIRU falls further below its values of early 1996.
The Conduct of Monetary Policy
What evaluation
of past and current monetary
on the NAIRU?
According
excess demand
in 1955-57
to our new TV-NAIRU measures, there was considerably
and 1965-70
series, suggesting that monetary
than was previously
thought.
policy
unemployment
The new TV-NAIRU
in 1995-96
rate during
than implied
by the previous
NMRU
in the=
periods
series also boosts modestly
and 1988-90.
has been
the six quarters
almost
However,
precisely
on
1994:4-1996:1
more
textbook
policy was even more overly expansionary
of estimated excess demand in 1979-80
monetary
policy is implied by this new research
the extent
the new series implies that
target,
with
of 5.6 percent,
an average
only slightly
below the average estimated TV-NAIRU of 5.7 percent for the GDP deflator in that interval.
If the Fed considers
rather
than
its goal as the stabilization
the GDP deflator,
of the rate of change of the PCE deflator
then the estimated
interval was 5.3 percent, implying that monetary
average TV-NAIRU
during
the same
policy was slightly too restrictive in 1995-
96.
The TV-NAIRU
by any measure has declined
deliberations
about interest rate changes are intended
rate roughly
one year from now, should
in the 1990s.
If the Fed’s current
to influence the actual unemployment
the Fed extrapolate
the recent
decline
in the
The Time-Varying
NMRU
into the future,
equal to the current
or shouid
value?
the Fed set its estimate
The TV-NAIRU
walk and thus is just as likely to increase
decrease.
There is no information
specified
the lagged values of the explanatory
of the NAIRU one year hence
in equation
over the subsequent
about future inflation
NAIRU, Page 36
(4) above is a random
year as to continue
to
available beyond that contained
in
variables in the inflation equation
that are already used
to derive the NAIRU.
While the TV-NAIRU technique
does not provide a magic crystal ball that allows the
Fed to see into the future, it makes two valuabie contributions
policy.
First, it quantifies
to the conduct
in a systematic way the Fed’s intuitive
must have fallen in the 1990s, because as of early 1996 inflation
did in 1988-90.
alternative
Second,
inflation
the differences
concept
movements
had not accelerated
in the NMRU
series implied by
and forces the Fed to take a
over time naturally
This question
raise the question
series of Figure 7. There only
NO major changes occur, an increase in the NAIRU from about 5.8 percent
6.5 percent
percent
in 1990 to 5.3 percent
in 1965 to
in the two decades after 1970, and then a decline from about 6.4
in 1996.
The late 1960s were a time of iabor militancy,
relatively strong unions, a relatively high minimum
share in national
as to
is most easiiy posed for the three
price indexes used to generate the TV-NAIRU
roughly
as it
it is trying to stabilize.
which factors caused these movements.
consumption
feeling that the NAIRU
in the TV-NAIRU
measures, e.g., the GDP vs. PCE deflator,
stand on what inflation
Estimated
it highlights
of monetary
income.
wage, and a marked increase in labor’s
The 1990s have been a time of labor peace, relatively
weak
The TlmeVarying
unions,
a relatively low minimum
The role played
structure,
wage, and a very slight decline in labor’s income share.
in the recent decline
and other plausible
topic for future research.
NAIRU, Page 37
of the NAIRU by these aspects of labor market
causes relating to global competition,
remains a tantalizing
The Time-Varying
NAIRU, Page 38
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Eisner, Robert.
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“A Statistical
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Robert J.
‘The Impact of Aggregate
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Robert J.
“Can the Inflation
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Robert
J.
“Inflation,
Flexible
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Rates,
and
the
Natural
Rate
of
The TimeVarylng
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Springer Verlag, 1990(a), pp. 1-34.
Gordon, Robert J. “What Is New-Keynesian
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Joumf
of Economic Literature,
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James D. Time Series Analysis.
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Princeton
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The TimeVarying
Samuelson,
Paul A. and Solow, Robert M.
NAIRU, Page 40
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Staiger, Douglas, Stock, James H., and Watson, Mark W. “How Precise are Estimates of
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TABLE 1
Estimated Equations for Quarterly Change in
Chain-Weight GDP Deflator, Alternative Sample Periods and Unemployment Gaps
>
1955:2-1987:3
Textbk
Vartable
(1)
1955:2-1996:1
u
Tv (02)
Textbook
Tv (02)
(2)
(3)
(4)
1.01*”
1.05”*
1.01”*
4.69””
-0.62” ●
-0.64””
-0.60””
o-1
-0.10
-0.11”
-0.08
-0.09”
4. ARelative Import Price
1-4
0.06
0.08”
5. ARelative Pria Food-Energy
N
0.43
0.42”
7. AEff~e
o-3
4.01
-0.01
-0.01
-0.01
8. Nixon “on”
o
-156”
-1.62”*
-159**
-1.69**
9. Nixon “or
o
Ml..
2.19*”
209””
2.07”*
F
0.85
0.88
0.85
0,87
S.E.E.
1.01
0.92
0.95
0,87
1. AChain-We@t GDP deflator
1-24
2. Unemployment Gap
0-4
3. AProductivity deviation
Real Exchange Rate
104,8
S.S.R.
Restricted Versio~ RMSE in sub
internals of fitted sample
1955:2-70:4
1971:1-rn2
1987:3-94;3
1994:4-%1
Dynamic Simti
1987:Q4-lmQl
Mean Emor
Root Mean-Squared Error
1994:Q4-1996:Q1
Mean Error
Root Mean-Squared Error
Notes:
1.C%*”
(*) bd.i~tes that -fflaent
1 pereent leveL
%.7
-
0.07
0.09””
o.2a
0.30”
123.1
103.4
1.05
0.77
0.92
0.71
1.07
0.80
0.63
0.47
0.93
0.73
0.61
0.42
0.24
0.91
O.m
0.86
0.34
0.70
0.26
0.65
-0.10
o.4a
0.08
0,41
-0.01
0.39
0.12
0.40
or sum of coeMcients is si#lcant
at 5 percent level; (**) at
TABLE 2
Estimated Equations for Quarterly Change in
Chain-Weight PCE Deflator, Alternative Sample Periods and Unemployment Gaps
19552-1987:3
Texttik
(1)
Variable
1955:2-19961
I
Tv (02)
(2)
Textbook
(3)
1-24
1.09”’
1.01’”
2. Unemployment Gap
o-4
-0.77””
-0.66””
4.68*”
-0.67”’
3. AProduetivity detiation
o-1
-0.02
4.03
-0.02
4.03
4. ARelative Import Price
1-4
O.11**
0.14””
O.11”*
0.14””
5. ARelative Pn@ Food-Energy
o-4
0.74””
0.66””
0.66”*
0.64””
7. AEffetive Real Exeha.nge Rate
o-3
-0.01
-0.00
-0.00
-0.00
-1.82”*
-1.95”*
-1.74*”
-2.03””
0.01
-0.47
0.05
439
R
0.87
0,88
0.86
0.88
S.E.E.
1.03
0.99
0.98
O.w
1. AFud-weight
GDP deflator
8. Nixon “on”
o
9. Nkon ‘oR
o
108.8
S.S.R.
Restricted Versio~ RMSE .b subintemals of fitted sample
1955:2-704
1971:1-m2
1987:3-94:3
1994:4%:1
sim1987:W19%:Q1
Mean Error
Root Mean-Squared Error
1994:Q4-1S96:Q1
Mean Error
Rwt Mean-Squared Error
Notes:
that -ffiaent
(“) indicates
1 perunt level.
1.W**
w (02)
(4)
-
99.6
129.8
1.01*”
111.4
1.11
0.80
0.99
0.75
1.11
0.82
0.68
0.75
0.99
0.77
0.57
0,52
0.19
0.83
0.35
0.72
0.24
0.75
0.35
0.65
-0.72
0.78
-0.07
0.26
-0.61
0.68
-0.03
0.25
or sum of coefficients is si~lcant
-
at 5 percent level; (**) at
TABLE 3
Estimated Equations for Quarterly Change in
Chain-Weight GDP Deflator, Alternative Sub-Sample Periods and Unemployment Gaps
1955:2-1974:4
Textbook
(1)
Variable
Tv (02)
(2)
1975:1-1996:1
I
-
Textbook
(3)
m (02)
(4)
1.07**
I.M**
1. AChain-we@t GDP deflator
1-24
1.02”*
0.94””
2. Unemployment Gap
o-4
-0.63””
-0.68””
4.74””
-0.86””
3. AProductivity denation
o-1
-0.11
-0.u””
4.04
-0.04
4. ARelative Im~rt
1-4
-0.02
0.02
0.11””
o.13**
5. ARelative Prie Food-Energy
w
0.29
031
0.21‘•
0.03
7. AEffeuive Real Exchange Rate
0-3
4.05
-0.M
0.00
0.01
8. Nmon “on-
0
-1.80
-1.27
9. Nmn “or
o
Priu
4.74”
4.m”
3
0.78
0.83
0.92
0,93
S.E.E.
1.12
1.00
0.67
0.63
643
S.S.R.
Restricted VersioG RMSE in sub
internals of fitted sample
1955:2-704
1971:1-87:2
lm3-94:3
1994:4-%:1
0.93
Dynamic sire*
1987:Q4-19%al
Mean ErTor
Root Mean-Squared Error
1994:Q4-19%:Q1
Mean Error
Root Mean-Squared Error
Notes:
that -ficient
1 percent level.
(“) kdimtes
50.8
23.4
0.80
.
or sum of mficients
X.7
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0.42
0.4
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033
0.63
0.08
0.39
-oOal
0.31
0.23
0.01
at 5 percent level; (**) at
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