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W a g e G r o w t h a n d Sectoral Shifts:
Phillips C u r v e R e d u x
Ellen R. Rissman
LIBRARY
F E B 11. 199 3
FEDERAL r e s e r v e
BANK OF CHICAGO
Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
December 1992 (W P-92-23)
FEDERAL RESERVE BANK
OF CHICAGO
W a g e G r o w t h a n d Sectoral Shifts: Phillips C u r v e R e d u x
E llen R. R issm an 1
Federal Reserve Bank of Chicago
December 3, 1992
1All correspondence should be sent to the author at the Federal Reserve Bank of Chicago, 230
S. LaSalle St., Chicago, IL 60690. This paper is a revised version of a 1987 working paper titled
“Wage Growth and Sectoral Shifts: New Evidence on the Stability of the Phillips Curve”. The author
would like to thank Prakash Loungani and Steve Strongin for their helpful comments, suggestions,
and encouragement. I alone am responsible for any remaining errors. The views expressed here are
not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System.
Abstract
Standard Phillips curve analyses of nominal wage growth performed poorly over the Seventies.
Because wage pressures arising from sectoral shocks largely balance out, only that portion
of unemployment that is net of the effects of compositional shifts in the structure of labor
demand should influence nominal wage growth. Sectoral disturbances in the Seventies caused
the unemployment rate to rise independently of cyclical activity. Once unemployment has
been corrected to reflect the effects of sectoral shifts, the apparent instability of the Phillips
curve is resolved. This result holds for both an employment and a stock price dispersion
measure of sectoral shifts.
1
In trod u ction
Advocates of the Phillips curve approach to modeling the inflation process typically relate
wage or price inflation to some measure of current economic activity and an inflationary
expectations variable. Economic activity is usually proxied by the unemployment rate or
some function of the unemployment rate, and expected inflation is specified as a function of
lagged values of actual inflation.
This traditional approach to the inflation process appears to have dwindled in popularity
in recent years as many researchers have found that the parameters of the Phillips curve
changed over the Seventies. Cagan (1975), Sachs (1980), and O ’Brien (1985) argue that the
trade-off between inflation and unemployment has worsened in that a given decline in the
rate of wage inflation requires a larger increase in the rate of unemployment than previously
needed, i.e. the short run Phillips curve has become flatter. In contrast, Wachter (1976) and
Schultze (1981) suggest that the opposite is true with wage inflation becoming more cyclically
sensitive, implying a steeper short run Phillips curve.
Attempts to resurrect the Phillips curve have typically fallen along two lines of reasoning.
First, unstable parameters may be the result of an initial misspecification of the inflation
ary expectations process. Noting this, several researchers including Sachs (1980) and more
recently Neumark and Leonard (1991) have experimented with alternative expectations for
mulations and more sophisticated models of wage and price dynamics. However, as Sachs
(1980) observes, the evidence indicates that more complicated models of expected price in
flation do not account for what appears to be a significant change in the short run trade-off
between inflation and unemployment.
Omitted variables offer an alternative explanation for the parameter instability. Several
researchers, including Gordon (1977), Perry (1980), and Hamilton (1983), have suggested
that demographic changes combined with oil price shocks, the acceleration and termination
of the Vietnam War, and the implementation of wage and price controls account for the
instability of the Phillips curve. These theories have met with only modest success. Others,
including Sachs (1980), Barro (1977), and Taylor (1980), argue that there has been a change
1
in the underlying structure of the inflation process. For example, an increase in the use of
longer term labor contracts and a belief held by the public that monetary and fiscal policy
will be used so as to promote high employment and stable prices have worsened the trade-off.
Although there issome theoreticaljustification for this hypothesis, empirical evidence on this
point islacking.
Oddly, in light of research on sectoral shifts and their relation to the unemployment
rate, the search for alternative specifications of the Phillips curve has led to relatively little
consideration ofthe appropriate measure ofeconomic activity to be employed in the analysis.1
Typically, the unemployment rate or some function of the unemployment rate is used to
capture the disequilibrium aspect although some researchers, including Sachs (1980) and
Gordon (1977), have chosen instead to use alternative measures such as deviations of real
Gross National Product from potential. These variables are allmeant to measure the current
level ofeconomic activity.
While rigorous theoretical underpinnings of the Phillips curve phenomenon are conspic
uously absent in these works, discussion of wage inflation is typically expressed in terms
of labor market tightness. Controlling for inflationary expectations, the negative coefficient
on the unemployment rate in a reduced form regression of wage inflation is interpreted as
indicating that tight labor markets, as signaled by lower unemployment rates, put upward
pressure on wages and, therefore, on prices through some sort of markup equation.
According to the sectoral shiftshypothesis ofunemployment [Lilien (1982)], changes in the
distribution ofdemand, given itslevel, cause the unemployment rate to increase as itiscostly
both for the employer and employees to adjust instantaneously. Therefore, the sectoral shifts
hypothesis suggests that higher unemployment is not necessarily indicative of a weakening
economy, while similarly lower unemployment need not signify stronger aggregate demand. In
the case of structural realignment, the unemployment rate is no longer an accurate measure
1R ecent works on the topic of sectoral shifts and the unem ploym ent rate include Lilien (1982, 1990),
N eum ann and Topel (1991), Loungani (1985), Loungani, R ush, and Tave (1990), D avis (1985), Abraham and
K atz (1986), and Brainard and Cutler (1990). A braham and M edoff (1982) exam ine different m easures of
econom ic activity but do not relate this to the sectoral shifts hypothesis.
2
oflabor market activity.
Unemployment resultingfrom sectoral reallocations does not affect the wage inflation pro
cess in the same way as cyclical unemployment since any upward wage pressure that results
in one sector will be tempered by downward wage pressure in another. Ifthe sectoral shifts
hypothesis is correct and sectoral reallocation was responsible for the higher unemployment
rates in the Seventies, the Phillips curve would then appear to be unstable over this time pe
riod. Specifically, a higher unemployment rate would be required to induce a given reduction
in wage inflation than needed when sectoral shifts were relatively unimportant.
The purpose of this paper is to analyze the effect of permanent sectoral shifts on the
wage inflation process. The remainder consists of four sections. In Section 2 two different
measures ofsectoral shifts are examined, namely Neumann and Topel’s(1991) construction of
permanent changes in the distribution ofemployment across industries and the stock market
dispersion index of Loungani, Rush, and Tave (1990). These measures are then used in
Section 3 to construct estimates of the natural rate of unemployment.
In Section 4 the stability ofthe Phillips curve isexamined with particular emphasis given
to the role of sectoral shifts. A test of the sectoral shifts hypothesis in its strictest form is
proposed that tests whether the coefficients on the natural and actual rates ofunemployment
are of equal and opposite signs as would be expected if sectoral shifts are noninflationary.
Conclusions and suggestions for further research are found in Section 5.
2
M easuring S ectoral Shifts
Generally, two distinct ways have been proposed in the literature formeasuring sectoral shifts.
One is based upon dispersion in employment growth across industries and the other upon
stock price dispersion.2 Abraham and Katz (1986) argue that employment-based dispersion
measures poorly capture sectoral shifts since, ifa declining industry is also relatively more
cyclically sensitive, a positive correlation between an employment-based dispersion index
2Lilien (1982, 1990) and N eum ann and Topel (1991) have focused on the former while Loungani, Rush and
Tave (1990) and Brainard and Cutler (1990) have exam ined the latter.
3
and the unemployment rate can result purely from aggregate disturbances. They suggest
that these two factors have been present in post-War U.S. data so that a sectoral shifts
interpretation ofemployment growth dispersion isinappropriate. As a result oftheir criticism,
researchers have attempted to both refine their employment-based measures ofsectoral shifts
and create new measures that do not suffer from the Abraham and Katz critique.
Ifchanges in the distribution of employment across industries are fundamentally related
to the business cycle, then a given industry’s employment response should be consistent
over the various cycles after controlling for the intensity of the cyclical shock. Define gi as
the growth rate of employment in the
industry from business cycle peak to subsequent
trough. Similarly, define g as aggregate employment growth. Relative employment growth,
<7*/<7, for the 20 two-digit manufacturing industries over the eight post-War business cycles
is found in Table 1. The industry response varies greatly from cycle to cycle. For example,
Non-Electrical Equipment lost over twice as much as the industry average in the recession of
1949 but in 1974 the industry lost almost no workers, even though the ’74 recession was more
severe. Similarly, Electrical Equipment was particularly hard-hit in 1970 but fared relatively
well in the 1960 downturn.
Ifthe business cycle hypothesis is correct, then the cross-cycle variance ofg ijg should be
relatively small. In testing this hypothesis, a fundamental problem arises in determining how
small the variance should be under the null. A somewhat weaker variant ofthe business cycle
hypothesis isthat the underlying distributions ofthe observations are the same across cycles.
A likelihood ratio test of the equality of the variances of the observations across cycles can
be easily constructed from the sample within-cycle variances.3 The hypothesis of constant
3T he com puted test sta tistic ,—2 log A, equals 33.73 and is asym ptotically distributed as
degrees o f freedom . T h e likelihood ratio is given by:
A = n < * ; > ‘v
;=i
where
20 /
4
\ 2
w ith (8-1)
variance across cycles is rejected.
Although some industries may fare relatively better than others in terms of employment
over the course ofthe business cycle, there issufficient variation in the employment response
of a given industry across cycles to suggest that changes in the sectoral composition of
employment over time are driven by more than simply general cyclical fluctuations. While
a cyclical interpretation is not precluded, any cyclical explanation must necessarily explain
the differing character of these cycles.
2.1
D ispersion M easures
In the analysis that follows, two different measures ofsectoral shifts are examined: Neumann
and Topel’s (1991) employment-based measure, A p,and Loungani, Rush, and Tave’s (1990)
stock price dispersion measure
SQ .
Unlike Lilien’s (1982) original measure, each of these
is constructed in such as way as to capture perm anent shifts in the relevant distribution.
Neumann and Topel (N-T) focus on decomposing deviations inemployment shares from trend
into two components— one predictable from observations on future employment shares and
one which is orthogonal to it. Loungani, Rush, and Tave (LRT) suggest that a stock market
dispersion index is weighted towards capturing permanent shifts in an industry’s expected
profitability. Since stock prices reflect the present discounted value of expected industry
profits over an infinitely long horizon, the impact of a current innovation in profits on stock
price depends on whether that innovation is expected to be temporary or permanent.*
4
The Abraham and Katz critique suggests that an appropriate measure of sectoral shifts
should be independent of past unemployment, i.e. that the unemployment rate should not
Granger-cause sectoral shifts. The advantage to the stock price dispersion measure is that
movements in stock prices precede changes in unemployment.5 However, reallocation timing
arguments such as proposed by Hamilton (1983), Davis (1985), and Rogerson (1987) suggest
and j = 1 , . . . , 8 indexes the cycles. T he sm all sam ple properties of the test sta tistic are unknown.
4First differences in A p and S Q have a correlation coefficient of -0.11.
5T o sum m arize the results of Granger-causality tests, unem ploym ent appears to Granger-cause A p but
does not Granger-cause S Q .
5
that reallocation in response to a sectoral disturbance will occur when the economy is in a
low state and the opportunity cost issmallest. In light ofthe reallocation timing arguments,
one would expect to see unemployment Granger-causing dispersion to the extent that the
unemployment rate also reflects cyclical disturbances.
Both
Ap
and
SQ
have the benefit of being forward looking and capturing permanent
changes. However, the interpretation ofS Q isunclear ifmarkets are not efficient. In addition,
there may be factors that affect the return on capital that do not necessarily influence labor
demand. To that extent, stock market dispersion would be a poor measure of those sectoral
shifts that entail some reallocation oflabor. For this reason an employment-based measure of
sectoral shifts seems better able to capture those disturbances that do influence the pattern
of labor demand and presumably have some bearing on the unemployment rate.
3
T h e N atu ral R a te
3.1
S ectoral Shifts and U nem ploym ent
There are many factors which may affect the unemployment rate. According to the standard
sectoral shifts theory of unemployment as suggested in Lilien (1982), permanent changes in
the distribution of employment across industries should increase the unemployment rate in
the short run as a mismatch between workers and employers results. Over time the long term
effects of a sectoral shift disappear as agents adjust to the disturbance.
The demographic composition of the labor force has been cited as one cause for the rise
in the unemployment rate over the Seventies as a larger proportion of those groups having
traditionally higher levels ofunemployment, namely women, nonwhites, and youths, entered
the labor market. In the analysis that follows a Perry-weighted unemployment rate ( W U R )
that has been adjusted to reflect the age-race-sex composition of the labor force in 65Q1 is
used to capture this demographic effect.
Traditional macroeconomic models focus on cyclical factors as the driving force behind
movements in the unemployment rate. Following Lilien (1982), this cyclical effect isassumed
6
to be captured by ‘unanticipated money growth’,D M t,and deviations ofreal Gross National
Product from trend, D G N P t.e
Finally, unemployment insurance and other social welfare programs are thought to have
an effect on the unemployment rate. On the one hand, such programs subsidize job search
with the effect of encouraging a longer period of unemployment. On the other hand, the
extended length ofjob search that results should lead to better employee/employer matches
and a reduction in future unemployment. The net effect is ambiguous. The effect of social
welfare expenditures is assumed to be measured by social insurance expenditures expressed
as a percentage of Gross National Product,
S it - 6
7
Because social insurance expenditures
typically rise during economic downturns, the ratio ofsuch expenditures to G N P iscounter
cyclical. Thus, S I may simply proxy for additional cyclical information independent of any
hypothesized effect it may have upon job search or job matching.
Unemployment rate regressions were estimated of the form:
[1-
b0( L ) L ] W U R t = c + bx{ L ) D G N P t
+ b2( L ) D M t + b3( L ) S I t +
b4( L ) a t
+ et
(1)
where the bi(L) are polynomials in the lag operator, L, and a t is some dispersion measure of
sectoral shifts.8 For a = A p,the preferred regression includes bo(L) and b4(L) as first order
polynomials, with b\(L) and b2( L )as second order polynomials, and b3(L) as a constant. The
preferred regression for a
= SQ
is of the same form as for the employment-based dispersion
measure with the exception that b4(L) has a lag length of 16 quarters.
6 A s defined in Barro (1978), unanticipated m oney growth is constructed as the least squares residuals from
a regression o f M l growth on a vector of explanatory variables. T he construction varies slightly from that
described in Barro since the d ata employed here are quarterly while Barro’s estim ates were com puted from
annual data. A side from a constant, the vector of explanatory variables includes eight lags of m oney growth,
current and three lags o f the log of real federal government expenditures calculated as d eviations from a one
sided m oving average of past values, and four lags of the ratio of unem ploym ent to em ploym ent expressed in
logarithm s. Current and eight lags o f the log of real federal governm ent expenditures are used to calculate the
moving average w ith geom etrically declining weights that sum to unity and adaptive param eter o f 0.2. T he
variable D G N P t is the deviation in the log of real G N P from a linear trend.
7T he data are reported annually in the Social Security A dm inistration’s S o c i a l S e c u r i t y B u l l e t i n : A n n u a l
S t a t i s t i c a l S u p p l e m e n t . Linear interpolation was used to obtain quarterly figures.
8 D etailed results are available from the author.
7
3,2
C o n stru c tio n of th e N a tu ra l R a te
The “natural rate ofunemployment”,according to Lilien (1982), isthe rate ofunemployment
that would occur in the absence of cyclical fluctuations. In Lilien’s formulation it reflects
only the unemployment that occurs as a consequence of sectoral shifts and the resulting
temporary mismatch of workers and employers. The terminology is somewhat misleading
as the “natural rate” has typically referred to the rate of unemployment compatible with
nonaccelerating or nondecelerating wage growth and has usually been derived from a relation
between unemployment and nominal wage growth. The natural rate that Lilien refers to
does not necessarily have any bearing on the question of nominal wage growth. In fact,
one can view equation (1) above as derived from a production function or Okun’s Law with
sectoral shifts affecting the production possibility frontier. In this context the “natural rate
of unemployment” is unrelated to the Phillips curve phenomenon. Perhaps a more accurate
expression for the construct that Lilien proposed is ‘structural unemployment’as it refers to
that unemployment which isthe result ofthe changing structure oflabor demand. However,
in keeping with the literature on sectoral shifts, I will continue to use the ‘natural rate’
terminology.
The natural rate of unemployment, in this context, is simply calculated as the rate of
unemployment that occurs when the cyclical variables, namely
DGNP
and Z?M, are set
identically equal to zero over the entire time period analyzed. How one treats other variables
in constructing the natural rate isopen to some debate. Ifone isconcerned exclusively with a
measure ofunemployment associated with sectoral reallocation, then the natural rate should
be constructed holding these other variables equal to their mean values as in Lilien (1982)
for example. However, a broader measure that is consistent with an interpretation of the
natural rate as non-cyclical or structural unemployment would permit these other variables
to vary over time. The latter approach is taken here.9
Figure 1 presents the actual age-weighted unemployment rate and estimates of the nat
9T o im plem ent these com putations, it is necessary to specify initial values o f the natural rate, NUR. Initial
values of the natural rate are taken to be the actual values o f the dem ographically-w eighted unem ploym ent
rate. T h e effect o f these initial values on the calculations decreases over time.
8
ural rate of unemployment calculated from the estimated parameter values of the preferred
equations (1). The natural rate series calculated from A p and S Q are denoted as N U R jv t
and N U R l r t respectively. It should be noted that because the dependent variable in the re
gression analysis, W U iZ,isa demographically fixed-weight unemployment rate, the estimates
of the natural rate constructed are also independent of demographic effects.
Generally, it is presumed that low unemployment rates signal a healthy economy while
high unemployment rates indicate low aggregate demand. Such an interpretation is valid
only ifother non-cyclical factors influencing unemployment are stable. In this case, move
ments in the unemployment rate correspond to changes only in the cyclical component of
unemployment. The estimates of the natural rate constructed above indicate that the im
portance of such other factors has varied considerably over the time period examined. The
series N U R l r t ismore or less levelin the Sixties at about 5.5% and climbs over 2 percentage
points during the Seventies to a peak of 7.5% in the fourth quarter of 1982. This measure of
the natural rate falls to 6.4% by the end of the sample period.
The natural rate series constructed from
SQ
is much smoother than that constructed
from A p . However, the time series patterns are more or less consistent. The two natural rate
series have a correlation of 0.87 in the levels but only 0.17 in first differences. The natural
rate constructed from A p has varied considerably being as high as 8.0% in ’83 and as low as
4.7% in ’66.
The relation between the natural rate and the actual rate ofunemployment has changed
considerably over time. N U R n t remained fairly stable until the late Sixties while the actual
unemployment rate fluctuated around it. The natural rate exceeded the actual rate ofunem
ployment for a brief period from ’55 to ’57 and then for a much longer period of time from
65Q2 until 74Q3. However, between 69Q1 and 71Q3 the natural rate of unemployment rose
over 1.5 percentage points in response to underlying sectoral shifts. Between 74Q3 and 77Q3
actual unemployment exceeded the natural rate. This was followed by a briefperiod oftight
labor markets in the late Seventies. Both the natural rate and actual rate of unemployment
continued to rise during the early Eighties with labor markets appearing slack. From 85Q4
9
until the end of the sample period labor markets again appear to be tight with the natural
rate exceeding the actual rate by a small amount.
4
W age In flation and th e N atu ral R a te
4.1 S ta n d a rd A nalysis
Traditional approaches to modeling the inflation process describe the rate of change ofwages
or alternative price variable in terms ofitsequilibrium and disequilibrium components. Thus,
itishypothesized that the rate ofgrowth ofwages, w ,isa function ofexpected price inflation
and the difference between labor demand and labor supply. Assuming that wage inflation is
a linear function of these variables, then wage growth is expressed as:
wt —
+ 6\ ( L t — L\)+ 62Pt
(2)
where w is the logarithmic rate of change of wages at time £,and L * and L \ are respectively
labor demand and labor supply at time t,pt isthe inflation rate at time /,and the superscript
4e’indicates that the variable is in expectations form. The parameter <$1 is hypothesized to
be positive.
In estimating equation (2) the labor market conditions variable, L*}— L*,isusually proxied
by the actual unemployment rate. It has been suggested that the wage response is larger as
labor market conditions become tighter. Therefore, the unemployment rate isusually entered
in inverse form to capture this nonlinearity.
Implementation of equation (2) also requires that the expectations process be specified.
Various forms have been investigated in the literature. Typically itisassumed that expected
inflation depends upon lagged realizations of actual inflation so that p\ = b(L)pt, where
b(L) is a polynomial in the lag operator L. In the analysis that follows it is assumed that
expected inflation isdescribed by a second order polynomial distributed lag model so that the
coefficient on the
lag,
isexpressed as (a0+ aiz+ a2 *2)- The inclusion ofbeginning and
endpoint constraints changes this three parameter model to a one parameter model. Finally,
10
for purposes ofestimation itis assumed that an additive error term isincluded at the end of
equation (2).10
Table 2 provides OLS parameter estimates and associated t-statisticsforthe wage inflation
model described above using quarterly observations for two sample periods. The restricted
sample extends from 60Q2 to 81Q3 while the full sample includes data through 87Q1. There
are two reasons for separating the data in this way. First, it is widely accepted that the
parameters ofthe Phillips curve shifted over the Seventies.11 The restricted sample facilitates
comparison with previous results. Second, as noted by Neumark and Leonard (1991), the
rapid decline in nominal wage growth over the Eighties suggests that the parameters of the
Phillips curve may have changed yet again. For this reason, the full sample is analyzed.
The dependent variable in the analysis is the difference in logarithms of average hourly
earnings for production workers in manufacturing and nonsupervisory workers in nonmanu
facturing. The labor market activity variable isthe demographically-weighted unemployment
rate, W U R ,entered linearly. Price inflation is calculated as the difference in logarithms of
the Consumer Price Index for urban workers. The coefficient on p e reported is the estimate
of 820,2 in an eight quarter polynomial distributed lag on past inflation with beginning and
endpoint constraints. A negative sign on the coefficient estimate indicates that the 6t-are all
positive and concave in i assuming that 82 > 0.
In column (1) of Panel A the coefficient estimates ofthe standard specification are found.
The sign of the coefficient on the unemployment rate is negative and clearly significant at
traditional confidence levels. In addition, higher expected price inflation is associated with
higher wage growth as indicated by the parameter estimate on pe.12 The relatively low
10Any measure o f expected price inflation that may be used in the regression analysis is m easured with
error. It is well known that such a classical errors in variables problem biases the OLS param eter estim ates.
Specifically, the coefficient on the expected inflation variable will be biased towards zero w ith the m agnitude
depending upon the variance of the m easurem ent error relative to the true series. Furthermore, the other
param eters of the m odel are also biased with the direction depending upon the variance-covariance m atrix
of the observations. W ithout prior knowledge of the variance o f the errors, it is difficult to correct for the
problem . However, the estim ates o f the coefficient on expected inflation are surprisingly robust to alternative
specifications. Therefore, it is hoped that the biases introduced are small.
11See Cagan (1975), Sachs(1980), Gordon (1977), W achter (1976), and Schultze (1981).
12T he estim ation was carried out using a one-step procedure. Several other lag structures were tested that
11
Durbin-Watson statistic suggests that some underlying factors have not been properly in
cluded in the analysis and that the estimated standard errors are incorrect.
Various alternative specifications were estimated to investigate the idea that the wage
inflation process was somehow different over the Seventies. The results are presented in
columns (2) through (4) of Panel A. A dummy variable D is defined equaling 1 after the
second quarter of 1971, when wage and price controls were introduced, and 0 otherwise. The
regression reported in column (2) tests ifthe trade-offbetween wage inflation and unemploy
ment worsened in recent years, holding all other parameters constant over the entire time
period, by checking the significance ofthe interaction term D X W U R . The results appear to
support the contention of Cagan (1975) and Sachs (1980) that the trade-offbetween inflation
and unemployment worsened over the latter partof the sample. The Durbin-Watson statistic
improves with this specification.
The regressions in columns (3) and (4) test whether a change in the effect of expected
inflation on wage growth occurred post-’71. There isno significant change in the effect of the
expected price variable in the latter part ofthe sample when the coefficient on W U R is held
constant over the entire period. However, when both W U R and p e are permitted to change
in the latterpart ofthe sample, both interaction terms are significant and the Durbin-Watson
statistic increases to 1.9.
Various other specifications were tried testing whether the shift in the parameters could
be explained by the wage and price controls of the early Seventies, changes in the union
composition of the labor force, and changes in the competitive position of the economy as
are less restrictive. However, the regression results did not im prove significantly and are unreported here due
to space lim itation s. In addition, the estim ation was also performed with the unem ploym ent rate variable
entered in inverse form. T h ese regressions in general had lower Durbin-W atson sta tistics and lower values of
R 2.
A tw o-step procedure which is unreported in the tex t was also performed. First, the param eters of the
polynom ial b ( L ) were estim ated by an unrestricted regression o f current price inflation on eight lagged values.
T h e sum of the coefficients was 0.95. An F -test of whether the coefficients sum to unity produced an F-value
of 2.70 which is below the 5% critical value o f 3.91. T h e predicted values from this m odel were then used as
the expected inflation regressor in estim ating equation (2). T h e estim ate of 62 calculated in this way is 0.50
w ith a standard error o f 0.05. Because o f the errors in variables problem that occurs, this estim ate o f 62 is
more properly thought o f as a lower bound. By calculating the variance-covariance m atrix o f the observations,
the coefficient estim ate on the unem ploym ent rate is also found to be biased towards zero.
12
measured by the ratio of imports to Gross National Product. Although inclusion of these
variables helped explain some ofthe apparent instability ofthe Phillips curve, the coefficient
on D X W U R remained positive and significant in the restricted sample period.
The remaining columns in Table 2 reproduce the analysis for the full sample period. The
only difference in specification is that a dummy variable, D U M
M Y ,has been included that
takes on a value of 1 from 81Q4 to 87Q1. It appears that post-’81 nominal wage growth
dropped independently ofany changes in the coefficients on W U R and p e. The similarity of
the results between the two sample periods once a change in the intercept has been permitted
isquite striking. The estimated parameters are ofsimilar magnitudes and are estimated with
similar accuracy as those estimated on the restricted sample. Various other specifications
were tried that permitted the coefficients on W U R and p e to change post-’71 while keeping
the intercept constant. In general, these regressions did not perform well.
4.2
A d ju stm e n t for S ectoral Shifts
Unemployment due to sectoral reallocation does not affect the wage inflation process in the
same way as cyclical unemployment since any upward wage pressure that occurs in one sector
would be tempered by downward wage pressure in another. These tendencies for wages to
rise or fall in response to the the shifting composition of labor demand would net out on
average. Unemployment could be high as a result of sectoral shifts while aggregate demand
is also high and wage inflation would result.
This suggests that the Phillips curve as typically estimated may well be misspecified if
the unemployment rate is not a good indicator of the performance of the economy overall.
A more appropriate measure of labor market tightness would filter out the effects of factors
such as sectoral shifts. A natural way to measure only cyclical fluctuations is to calculate
the difference between the actual and natural rates of unemployment, a measure which by
construction reflects only cyclical variations provided that the measure of sectoral shifts is
independent of the cycle.
The regression results reported in Table 3 include the age-weighted unemployment rate
13
and the natural rate of unemployment,
N URn t,
as separate explanatory variables with
tests of the hypothesis that the estimated coefficients are of equal and opposite signs. Ifthe
hypothesis is accepted, then it suggests that the difference between the actual rate and the
constructed natural rate is a good indicator of general economic performance and supports
the sectoral shifts hypothesis.13
Panel A reports regression estimates from the restricted data set. From column (1) it
appears that the natural rate provides additional information independent of the level of
unemployment that is relevant to the modeling of the wage inflation process. Increases in
the natural rate relative to the actual signal a tightening oflabor market conditions. A one
percentage point increase in the natural rate relative to the actual causes quarterly wage
growth to rise by 0.3 percent. Similarly, given the natural rate, increases in the actual
unemployment rate are associated with a weakening economy and, therefore, wage inflation
islower. An F-test of equal and opposite signs on the actual and natural rates cannot reject
the hypothesis, suggesting that the difference between actual and natural unemployment is
a good measure of general economic conditions. Both the R 2 and Durbin-Watson statistic
improve with this specification.
Inclusion of N U R n t clearly adds to the performance of the estimating equation. The
parameter instabilityofthe modified Phillips curve isexamined in the regression results found
in columns (2) through (4). As in the preceding analysis, a dummy variable D is defined
taking on the value of 1 for the period from the third quarter of 1971 through the end of the
sample period, and 0 otherwise. From column (2),once compositional changes in employment
are accounted for via the natural rate series, there is no evidence that the trade-off between
inflation and unemployment worsened over the latter part of the sample given that the other
parameters, namely the coefficient on inflationary expectations and the intercept, have been
constrained to be constant throughout the sample period.
Stability of the coefficient estimate on expected inflation, assuming constant parameters
13T h e errors in variables problem is more com plicated for this m odel than for the previous one. Both
expected price inflation and the natural rate o f unem ploym ent are measured with error and OLS may either
underestim ate or overestim ate the true param eters o f the m odel.
14
on the other variables, istested in column (3). The results suggest that over the earlier part of
the sample, inflationary expectations was not an important determinant ofthe wage inflation
process. In fact,over this period the parameter estimate on p e isinsignificantly different from
zero. However, the latter part of the sample shows a significant positive effect of expected
inflation on wage growth. Because inflationary expectations exhibit relatively little variation
in the earlier part of the sample, the effect is picked up in large part by the constant term.
In column (4) the coefficients on both the labor market tightness variables and the expected
inflation variable are permitted to vary over the sample period. Due to multicollinearity,
most of the coefficient estimates are insignificant at traditional confidence levels with the
exception of the intercept, expected inflation, and the interaction term D x
N URn
t
•
The basic regression of column (1) was reestimated with the added constraint that the
coefficients on the unemployment rate and the natural rate be of equal and opposite signs.
The results are reported in column (5). In summary, once sectoral shifts have been included
in the analysis, there is very little support for the claim that wage growth has become less
cyclically sensitive. It would appear that much of the debate about the stagflation of the
Seventies is in large part attributable to a failure to distinguish among the sources of the
underlying disturbances to the economy.
Regression results for the full sample are found in Panel B. Even after the inclusion ofthe
natural rate of unemployment as an explanatory variable, the Phillips curve still appears to
have an unstable intercept, ceteris paribus, as wage growth declined by between 0.6 and 0.8
percent post-’81.14 It has been argued that inflationary expectations were somehow different
over the Eighties as monetary policy shifted its focus. However, even after inclusion of the
inflationary expectations variable in columns (3) and (4), the intercept still seems to have
changed significantly since ’81.15
14T he coefficient estim ates on W U R , N U R n t , and p e are similar to those found in the restricted sam ple.
To sum m arize the results, inclusion of the natural rate as an explanatory variable seem s to improve the fit
o f the equation. T h e coefficient on the unem ploym ent rate no longer rises significantly over the latter half of
the sam ple. T h e expected inflation variable appears to differ p o st-’71. T he sam e caveats apply here as in the
above discussion.
^ Inflationary ex p ectation s are calculated here from past inflation rates. If there were a fully anticipated
regime change th at affected expected future inflation, it would only be incorporated in the expected inflation
15
The decline in wage growth observed over the Eighties has many potential explanations
including the decline inunion strength, changes in “wage norms,”import penetration, deregu
lation, and a change in the inflationary expectations mechanism. Union strength, as measured
by the percentage of the labor force claiming union membership, has been declining continu
ously since the Sixties. As an empirical matter, itisunlikely that unionism can explain only
a relatively recent decline in wage growth. In addition, the decline in union membership is
predominantly a phenomenon encountered in manufacturing industries and other traditional
union strongholds. These industries have allbeen undergoing a long term decline in employ
ment share. Thus, itisquite possible that the shiftin employment captured by the measure of
sectoral redistribution and the decline in union membership are simply two different aspects
of the same phenomenon.
The relation between union wages and membership is difficult to disentangle. Rissman
(1987) suggests that an optimizing monopolistic union facing deregulation and reductions
in barriers to trade may initially increase wages and then permit wages to decline to their
new long run equilibrium level as unions weigh short term wage gains against long term
employment losses. In terms ofwage growth, import penetration results in higher short term
wage growth immediately after a change in trade barriers with lower wage growth thereafter.
This explanation ofdeclining wage growth focuses on the effect ofimports on predominantly
unionized industries. However, itisunlikely that the broader-based phenomenon that appears
to have occurred can be explained by industry-specific factors. This criticism isalso relevant
to the deregulation explanation.
The idea of a shifting wage norm is consistent with the data. However, the hypothesis
offers little insight into wage determination and is more a description of the data than an
explanation of it. Finally, the evidence supplied in Neumark and Leonard (1991) does not
support the hypothesis that a change in the inflationary expectations mechanism was respon
sible for the declining wage growth. In fact, they suggest that there was a true structural
shift in the Phillips curve in the Eighties. In accord with their findings, there isno significant
measure used here with some lag, thereby giving misleading results.
16
change in the coefficient on expected inflation over the Eighties and the intercept stillappears
to have shifted downwards.
The coefficient estimates of expected inflation and the actual and natural rates of unem
ployment are surprisingly robust to alternative specifications. In addition to modifying the
Phillips curve specification by concentrating on an alternative measure oflabor market tight
ness, the role ofdemographics, unionization, and wage and price controls were also examined.
Gordon (1977) and Perry (1980) suggest that the changing demographic composition of the
labor force has had an effect upon wage growth. However, the proportion of females, non
whites and youths in thelabor force were insignificant in the examined regressions, suggesting
that demographics has an impact on wage growth only via its affect on unemployment. Gor
don (1977) argues that wage and price controls were responsible for the parameter instability
of the Seventies. A test of this hypothesis was performed by creating a dummy variable for
when the controls were in effect. After controlling for sectoral unemployment, wage and price
controls did not significantly affect wage growth, suggesting that the impact ofwage and price
controls may be on the distribution of employment. Finally, union strength, measured as a
percentage of employment, did not significantly affect wage growth.
4,3
T h e P hillips C urve and A ltern ativ e N a tu ra l R a te Series
Regression results for an alternative natural rate series constructed from the stock price
dispersion index N U R l r t are found in Table 4. These results are surprisingly similar to those
based upon N U R n t • Coefficient estimates are generally of the same sign and magnitude
as those found in Table 3 and their standard errors are similar. The natural rate enters
positively in this set of regressions and is generally significant except when the interaction
term D
X N U R l r t is
included. This occurs because this particular estimate of the natural
rate varied little in the earlier part of the sample.
F-tests of the strict sectoral shifts hypothesis, i.e. that the coefficients on the actual rate
and the natural rate are equal and opposite in sign, are somewhat less strong than those
based upon employment dispersion, A p . However, with a 5% critical value of approximately
17
3.96 the hypothesis cannot be rejected.
5
C onclusions
Standard specifications of the Phillips curve employ the unemployment rate as a proxy for
the general level of economic activity. However, unemployment can be high either because
of sectoral realignment or because of low aggregate activity. Because wage pressures arising
from sectoral shocks largely balance out, only that portion of unemployment that is net of
the effects of compositional shifts in the structure oflabor demand should influence nominal
wage growth.
The worsening of the trade-off between inflation and unemployment over the Seventies
is illusory. Much of the nominal wage growth over this period can be explained by sectoral
shifts that caused the natural rate of unemployment to rise relative to the actual. Rather
than having slack labor markets, as indicated by the high levelofunemployment, the opposite
occurred with sectoral realignment attenuating the traditional linkage of unemployment to
the generallevelofeconomic activity. Once thenatural rateisexplicitly considered, itappears
that the cyclical sensitivity of wages has not changed over time.
The results reported here are consistent with the sectoral shifts hypothesis of unem
ployment. Sectoral shifts should not give rise to persistent inflationary pressures as wage
movements are averaged out across sectors. Only increases in the general level of economic
activity are inflationary. Ifsectoral shifts are truly independent of the cycle, then the differ
ence between the actual rate of unemployment and the constructed natural rate series is the
appropriate explanatory variable to use in a nominal wage growth regression. Tests of the
hypothesis that the actual and natural rates ofunemployment enter with equal and opposite
signs are generally supported by the data.
The experience ofthe Eighties poses a somewhat different problem. The Phillips curve ap
pears to be unstable over this period even aftersectoral shiftshave been explicitly considered.
Although the natural rate stillenters the wage growth regressions with the hypothesized sign
and is of the appropriate magnitude, there appears to be a downward shift in the intercept
18
term that is as yet unexplained. These results, specifically the stability of the trade-off, the
shifting of the intercept, and the coefficient restrictions, are generally robust to markedly
different measures of the natural rate.
Finally, the sectoral shifts hypothesis and its relation to the wage inflation process has
potentially important insights to yield for the role of government policy. First, and perhaps
most obviously, the sectoralshiftshypothesis suggests that a countercyclical policy may be not
be implementable because of the difficulty in interpreting movements in the unemployment
rate. An expansionary policy adopted at the wrong time in the cycle may serve only to
increase inflation rather than decrease the unemployment rate. Second, traditional monetary
and fiscalpolicy effectiveness may depend in large part on the composition ofunemployment.
Such policies seem better suited to dealing with unemployment that iscyclical in nature but
may prove to be largely ineffective in reducing unemployment that is attributable to long
term sectoral shifts. Therefore, a combination of monetary and fiscal stimuli combined with
an industrial and jobs policy may be a more effective means of dealing with the problem
of unemployment. Third, although the Phillips curve relations estimated here are reduced
form expressions, they suggest that there may be a trade-off that policymakers can exploit
between cyclical unemployment and the inflation rate. Before running monetary policy as if
the relation is stable, a better understanding of the downward shift in wage growth in the
Eighties is warranted. Finally, monetary policy may impact industries differentially, having
a larger effect upon those industries that are relatively more interest-sensitive. Changes in
policy may therefore affect the natural rate of unemployment and, hence, the nature of the
trade-offbetween unemployment and inflation.
19
R eferences
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Shifts or Aggregate Disturbances?” Journal of Political E c o n o m y , 94, June, 507-522.
Abraham , K atharine G. and James L. Medoff (1982), “Unemployment, Unsatisfied Demand
for Labor, and Compensation Growth, 1956-80” in M artin N. Baily, (ed.), Workers,
Jobs, a n d Inflation. Brookings Institution: W ashington, D.C., 49-88.
Barro, Robert J. (1978), “Unanticipated Money, O utput, and the Price Level in the United
States” Jou r n a l of Political E c o n o m y , 8 6 , August, 549-80.
Barro, Robert J. (1977), “Long Term Contracting, Sticky Prices, and M onetary Policy”
Journal of M o n e t a r y E c o n o m i c s , 3, July, 306-316.
Brainard, S. Lael and David M. Cutler (1990), “Sectoral Shifts and Cyclical Unemployment
Reconsidered” NBER Working Paper #3491, Cambridge: National Bureau of
Economic Research.
Cagan, Philip (1975), “Changes in the Recession Behavior of Wholesale Prices in the 1920’s
and Post-World War II” Explorations in E c o n o m i c Resources , 2 , 54-104.
Davis, Steven J. (1985), “Sectoral Shifts and the Dynamic Behavior of Unemployment: A
Theoretical Analysis” University of Chicago: Working Paper No. 86-35.
Gordon, Robert J. (1977), “Can the Inflation of the 1970’s Be Explained?”
P a p e r s o n E c o n o m i c Activity,
1 , 253-277.
Brookings
Hamilton, James D. (1983), “Oil and the Macroeconomy since World War II”
Political E c o n o m y , 91, April, 228-248.
Lilien, David (1982), “Sectoral Shifts and Sectoral Unemployment”
E c o n o m y , 90, August, 777-793.
Journal of
Journal of Political
Lilien, David (1990), “Labor M arket Dispersion and the N atural Rate of Unemployment”
University of California, Irvine.
Loungani, Prakash (1985), “Sectoral Shifts and Business Cycles: A Fresh Look at the
Evidence” University of Rochester.
Loungani, Prakash, Mark Rush, and William Tave (1990), “Stock M arket Dispersion and
Unemployment” Journal of M o n e t a r y E c o n o m i c s , 25, June, 367-388.
20
Neumann, George R. and Robert H. Topel (1991), “Employment Risk, Diversification, and
Unemployment” Quarterly Journal of E c o n o m i c s , 106, November, 1341-1366.
Neumark, David and Jonathan S. Leonard (1991), “Inflation Expectations and the
Structural Shift in Aggregate Labor-Cost Determination in the 1980s” Working
Paper.
O’Brien, Anthony (1985), “The Cyclical Sensitivity of Wages”
75, December, 1124-1132.
Perry, George L. (1980), “Inflation in Theory and Practice”
Activity, 1 , 207-41.
Rissman, Ellen R. (1987), Imp o r t Penetration a n d
University: Unpublished doctoral thesis.
American E c o n o m i c Review,
Brookings P a p e r s o n E c o n o m i c
Union W a g e D y n a m i c s .
Northwestern
Rogerson, Richard (1987), “An Equilibrium Model of Sectoral Reallocation”
Political E c o n o m y , 15, May, 309-321.
Journal of
Sachs, Jeffrey (1980), “The Changing Cyclical Behavior of Wages and Prices: 1890-1976”
A m e r i c a n E c o n o m i c R e v i e w , 70, March, 78-80.
Schultze, Charles L. (1981), “Some Macro Foundations for Micro Theory”
o n E c o n o m i c Activity, 2 , 521-592.
Taylor, John B. (1980), “Aggregate Dynamics and Staggered C ontracts”
Political E c o n o m y , 8 8 , February, 1-23.
Brookings P a p e r s
Journal of
Wachter, Michael J. (1976), “The Changing Cyclical Responsiveness of Wage Inflation”
Brookings Pap e r s o n E c o n o m i c Activity, 1 , 115-168.
21
22
Table 1: R elative E m ploym ent G row th R ates, Peak to Trough
M anufacturing Industries
Trough
Food and Kindred
Tobacco
Textiles
Apparel
Lumber and Wood
Furniture and Fixtures
Paper
Printing and Publishing
Chemicals
Petroleum
Rubber and Plastic
Leather
Stone, Clay, and Glass
Primary Metals
Fabricated Metals
Non-Electical Equipment
Electical Equipment
Transportation Equipment
Instruments
Miscellaneous
49Q4
54Q2
58Q2
61Q1
70Q4
75Q1
80Q3
82Q4
0.1870
0.7301
0.5858
-0.0084
0.7495
0.3643
0.3448
0.0854
0.8005
0.2425
0.9235
0.5777
0.9833
3.9298
1.5214
2.2828
1.3763
1.2793
1.1461
0.5261
0.1481
-0.0392
1.3147
0.7475
0.7356
1.1439
0.1369
-0.1044
0.4067
0.2026
1.3431
0.5432
0.7543
1.7375
1.3775
1.1431
1.7443
1.7906
1.1825
1.0771
0.2037
0.1913
0.8313
0.4685
0.9208
0.7816
0.1940
-0.0249
0.2831
0.3704
1.2619
0.6333
0.7304
2.2966
1.1944
1.8257
1.1522
2.1732
0.8194
0.5253
0.1395
0.7588
1.1760
0.6880
2.0548
1.6467
0.2241
-0.0837
0.2480
0.8369
1.3716
0.3554
1.2942
3.0539
1.4187
1.1531
0.4529
1.5374
0.7971
1.1513
0.1189
0.0512
0.5892
0.5779
0.4155
0.7176
0.5202
0.1656
0.3589
-0.0663
0.0000
1.1004
1.1528
1.2381
1.4564
1.0608
3.5602
3.6392
-3.8166
0.8592
0.4533
0.3845
2.0448
1.8173
2.5514
2.2149
0.8473
0.1732
0.2349
0.2537
1.4406
1.6489
1.2675
0.6968
1.1608
0.0864
1.5333
1.2951
0.6101
1.2008
0.1130
-0.2017
1.2078
0.5494
2.4544
1.9006
0.6003
0.1383
0.3076
-3.4369
2.0872
0.9319
1.8818
2.6628
1.6891
0.7189
0.9491
1.3834
0.2858
1.3883
0.1779
0.3661
1.1537
0.8533
0.9440
0.8869
0.5021
0.0110
0.4425
0.5965
0.8544
1.3616
1.2228
3.1209
1.5431
1.8902
0.6776
1.2114
0.5228
0.9879
23
Table 2
Param eter S tab ility o f th e Standard P hillips Curve Specification
Panel A: 60Q2 to 81Q3
WUR
ve
D
x
WUR
(1)
(2 )
(3)
(4)
(1)
(2 )
(3)
(4)
-0.0013
-0.0017
-0.0014
-0.0015
- 0.0010
-0.0014
- 0.0010
-0.0013
(3.519)
(4.216)
(3.281)
(3.810)
(3.225)
(4.062)
(2.949)
(3.981)
-0.0050
-0.0039
-0.0047
-0.0060
-0.0048
-0.0038
-0.0048
-0.0063
(10.065)
(5.516)
(4.612)
(5.890)
(10.795)
(6.467)
(5.150)
(6.773)
-
0.0005
-
0.0015
-
0.0005
-
0.0014
(2.247)
D
x
pe
c
DUMMY
Panel B: 60Q2 to 87Q1
-
-
(2.512)
(3.619)
-0.0003
0.0041
(0.331)
(2.785)
-
-
(4.282)
0.0000
0.0041
(0 .0 12 )
(3.375)
0.0145
0.0168
0.0150
0.0142
0.0134
0.0154
0.0133
0.0130
(8.235)
(8.427)
(6.617)
(6.655)
(8.915)
(9.235)
(7.158)
(7.540)
-
-
-
-
-0.0036
-0.0053
-0.0036
-0.0082
(3.010)
(3.939)
(2.996)
(5.311)
R?
0.569
0.594
0.570
0.630
0.636
0.657
0.636
0.692
D -W
1.505
1.693
1.516
1.883
1.443
1.614
1.443
1.812
NOTE: The dependent variable is the first difference in the logarithm of Average Hourly Earnings reported in various issues of E m p lo y m e n t
the BLS. T-statistics are in parentheses.
and E a rn in g s
by
24
Table 3: T he P h illip s Curve and Sectoral Shifts
Panel A: 60Q2 to 81Q3
WUR
N U Rnt
Pe
x
D
x
D
x
D
WUR
(5)
(1 )
(2 )
(3)
- 0.0020 - 0.0022 -0.0031
-0.0004
- 0.0020
-0.0016
-0.0023
-0.0019
- 0.0002 -0.0015
c
(4)
(4.403)
(3.482)
(4.944)
(0.331)
(4.366)
(4.128)
(4.029)
(4.105)
(0.204)
(4.046)
0.0027
0.0027
0.0046
- 0.0011
0.0020
0.0022
0.0026
0.0027
-0.0028
0.0015
(2.517)
(2.397)
(3.534)
(0.423)
(4.366)
(2.476)
(2.639)
(2.759)
(1.189)
(4.046)
-0.0041
-0.0031
-0.0009
-0.0080
-0.0044
-0.0041
-0.0028
-0.0029
-0.0098
-0.0044
(6.758)
(3.230)
(0.606)
(2.521)
(10.966)
(8.228)
(3.851)
(2.593)
(3.365)
(12.018)
—
-0.0009
-0.0017
—
(0.652)
NURnt
pe
(3)
(5)
(4)
(1 )
(2 )
Panel B: 60Q2 to 87Q1
0.0014
- 0.0002
(1.160)
(1.416)
(0.207)
0.0014
0.0031
-0.0008
0.0020
(1.157)
(1.946)
(0.914)
(1.463)
—
-0.0026
0.0055
0.0011
0.0076
2.429
(1.620)
(1.208)
(2.479)
0.0047
0.0055
0.0017
0.0132
0.0079
0.0049
0.0071
0.0043
0.0177
0.0080
( 1 . 10 2 )
(1.342)
(0.391)
(2 . 1 1 2 )
(10.801)
(1.316)
(1.891)
(1.149)
(3.145)
(11.922)
-0.0057
-0.0080
-0.0062
-0.0073
-0.0047
(3.952)
(4.699)
(4.140)
(4.292)
(5.294)
DUMMY
R?
0.600
0.644
0.627
0.655
0.597
0.657
0.680
0.662
0.698
0.654
D -W
1.654
1.991
1.902
2.004
1.631
1.554
1.768
1.616
1.814
1.532
0.563
0.381
2.781
1.047
-
0.715
0.117
1.235
3.687
-
F
—value
NOTE: The dependent variable is the log first difference in the BLS’s Average Hourly Earnings. T statistics are in parentheses. The F statistic reports tests
for equal and opposite signs on the coefficients of W U R and the natural rate,
NURn
t
•
25
T a b l e 4: T h e Phillips C u r v e a n d S e c t o r a l Shifts
Panel B: 60Q2 to 87Q1
Panel A: 60Q2 to 81Q3
(1)
lrt
(4)
(2)
(3)
(4)
(5)
(2.617)
(4.208)
(1.753)
(4.529)
(4.302)
(3.137)
(3.826)
(1.964)
(4.169)
0.0036
0.0018
0.0045
0.0011
0.0018
0.0031
0.0028
0.0040
0.0016
0.0014
(3.216)
(0.984)
(3.479)
(0.600)
(4.529)
(3.127)
(1.752)
(3.604)
(0.999)
(4.169)
x
W U R
(5.150)
(4.378)
(4.558)
(5.624)
(11.061)
(6.268)
(4.695)
(5.402)
(5.842)
(12.093)
-
-0.0008
-
-0.0004
-
-
0.0005
-
0.0005
-
xN
U R
lrt
-
0.0010
(0.435)
-
0.0017
(1.052)
D
(1)
(4.728)
(0.827)
D
(5)
-0.0035 -0.0038 -0.0044 -0.0066 -0.0044 -0.0036 -0.0033 -0.0047 -0.0065 -0.0044
pe
D
(3)
-0.0018 -0.0015 -0.0017 -0.0010 -0.0018 -0.0014 -0.0016 -0.0013 -0.0010 -0.0014
W U R
N U R
(2)
x pe
c
DUMMY
-
-
(0.643)
-
-
-0.0003
(1.831)
0.0013
0.0048
(1.337)
(3.328)
(0.651)
-
(0.377)
-
-
-
0.0007
-
(0.928)
0.0015
0.0046
(1.737)
(3.604)
-
-0.0023
0.0056
-0.0081
0.0052
0.0073
- 0.0011
0.0013
-0.0075
0.0028
0.0076
(0.420)
(0.646)
(1.159)
(0.637)
(9.458)
(0.230)
(0.175)
(1.243)
(0.392)
(10.761)
-
-
-
-
-
-0.0053 -0.0060 -0.0059 -0.0081 -0.0039
(4.204)
(3.728)
(4.542)
(4.958)
(3.906)
R?
0.617
0.625
0.626
0.671
0.603
0.668
0.741
0.677
0.709
0.657
D - W
1.702
1.752
1.703
2.017
1.629
1.596
1.645
1.610
1.860
1.532
3.096
0.052
4.907
0.0042
-
3.293
0.741
6.207
0.167
-
F
—value
NOTE: The dependent variable is the first difference in the logarithm of the BLS’s Average Hourly Earnings. T-statistics are in parentheses. The F statistic
reports tests for equal and opposite signs of the parameters on
W U R
and the natural rate,
N U R
l r t
•
@FedFRASER