Daniel Aaronson

Daniel Sullivan

English

Research Papers in Economics

Chicago Fed Letter
ESSAYS ON ISSUES THE FEDERAL RESERVE BANK MAY 2001
OF CHICAGO NUMBER 165
Cross-state evidence
on the relationship
between unemployment
and wage growth
The current economic expansion has
delivered the lowest unemployment
rates in 30 years. Yet wage growth has
remained relatively contained. This
failure of wages to accelerate more
rapidly suggests to some a shift, or
even a complete breakdown, in the
historical relationship between un-
employment and wage growth. How-
ever, looking across the years, the link
between unemployment and wage
growth has always been relatively loose.
Previous periods have seen wage
growth depart just as far from expec-
tations, only to return to the histori-
cal pattern. This historical looseness
in the relationship between unem-
ployment and wage growth implies
that it might take many years of time-
series data to conclusively identify  a
significant change.
In this Chicago Fed Letter, we provide
more timely evidence on whether the
relationship between unemployment
and wage growth might have changed.
We do this by looking, not only across
the years, but also across the 50 states.
The wide variation in state unemploy-
ment rates makes it possible to iden-
tify any significant changes in the
response of wages to unemployment
with many fewer years of data. We
find, however, that the relationship
between unemployment and wage
growth has changed relatively little.
Even in recent data, unemployment
and wage growth continue to be neg-
atively correlated. We do find evidence
that the elasticity of wage growth with
respect to unemployment has fallen
in recent years. However, as we ex-
plain below, we regard the evidence
of a weakened relationship between
unemployment and wage growth as
itself somewhat weak. In addition, we
show that the rates of real wage growth
associated with high, medium, and
low unemployment rates have been
reasonably stable in recent years.1
Background
Some shift in the relationship between
unemployment and real wage growth
in the 1990s would not be surprising.
Among the many changes in the labor
market in recent years, the general
drop in the level of job security, the
aging of the work force, its higher
levels of education, the growth of tem-
porary services employment, the use
of fax machines and the Internet in
job search, and even the increase in
the prison population could each be
changing the relationship between
unemployment and wage growth.
A rough indication of the time-series
evidence on this question can be
gleaned from figure 1, a scatter plot
of annual data on the excess of hour-
ly compensation growth over the
previous year’s Con-
sumer Price Index
(CPI) inflation versus
the natural logarithm
of the annual unem-
ployment rate. The re-
lationship depicted in
figure 1 is analogous to
the wage equations in
some macroeconomet-
ric models. The figure
shows that there is a
loose, but reasonably
clear, negative correla-
tion between unem-
ployment and wage
growth in excess of
lagged inflation. The
least-squares regression
line shown in the fig-
ure slopes downward
with an elasticity of –0.055 and an es-
timated standard error of 0.009. This
implies that a 10% decrease in the un-
employment rate leads to a 0.55% in-
crease in wage growth.
A line connecting the values from
1992 to 1999 highlights the data for
the current expansion, when the un-
employment rate was falling from 7.5%
to 4.2%. As can be seen, the growth
of hourly compensation was a percent-
age point or more below expectations
each year from 1993 to 1997. Though
the data for the last two years have re-
turned to the predicted line, the cumu-
lative loss of wage growth over the
expansion has been significant.
However, such departures of wage
growth from expectations are far from
unprecedented. In earlier years, the
data have strayed further from expec-
tations only to return to the basic
pattern of low unemployment being
associated with higher wage growth.
Of course, neither do the time-series
data in figure 1 rule out a significant
shift in the relationship between
percent wage growth
Note: Dashed lines indicate 90 percent confidence bands. Data were
compiled by subtracting lagged CPI inflation from hourly compensation and
comparing that to the natural logarithm of the annual unemployment rate.
1. Growth in compensation vs. unemployment
log unemployment rateunemployment and inflation. Unfor-
tunately, given the looseness of the
historical relationship, it would take
many years to confidently identify
even a relatively large change in the
relationship.
Our results
To get additional evidence on the re-
lationship between unemployment
and wage growth, we turn to the
kind of cross-sectional data shown in
figure 2, which displays the deviation
of 1999 state unemployment rates
from their state-specific averages over
the 1980–99 period. We focus on devi-
ations from long-term averages rather
than the simple unemployment rate
because differences in demographic
and industrial mix, generosity of so-
cial insurance, and other factors may
affect the natural rate of unemploy-
ment in a given state. In this case,
cross-state variation in the average
level of unemployment may be unre-
lated to average wage growth, and the
relative unemployment indicators de-
picted in figure 2 will give a clearer
picture of labor market conditions.
In recent years these unemployment
deviations suggest a markedly differ-
ent picture of where labor market con-
ditions are tightest than the standard
level of unemployment. For instance,
the states with the lowest (South
Dakota, 2.5%) and highest (District
of Columbia, 6.5%) unemployment
rates in 1999 are both 1.5 percentage
points below their long-run average
2. Unemployment deviation
rates. Therefore, we expect both states
to have similar real wage growth in
1999. In terms of unemployment de-
viations, in 1999, the tightest labor
market is Michigan’s, where the un-
employment rate of 3.7% is 4.7 points
lower than its 1980–99 average of
8.4%. In contrast, the least tight labor
market is Hawaii, where the 1999 un-
employment rate of 5.5% is 0.4 points
above its average over the last 20 years.
We estimate the response of wage
growth to unemployment with a stan-
dard statistical model that relates un-
employment deviations to a measure
of state-level wage growth. The latter
is derived from the outgoing rotation
files of the Current Population Survey
(CPS), the monthly survey that is also
the source for the national unemploy-
ment rate. The wage measure adjusts
for differences in worker characteris-
tics, such as age, education, and union
status, that might cause wage growth
to vary across states.
Our statistical approach also controls
for factors, such as expected inflation,
that are approximately constant across
states in a given year. Unlike the time-
series approach, which assumes ex-
pected inflation is equal to the previous
year’s actual inflation, the cross-state
approach does not require that infla-
tion expectations match any observ-
able series. Finally, our estimates are
based on a robust regression statisti-
cal technique that minimizes the ef-
fect of large outliers, such as frequently
occur in cross-sectional data.
The first row in figure 3
shows our estimates of
the response of wage
growth to unemploy-
ment based on cross-
state data from 1980–99.
The coefficient of –0.042
implies that a 10% low-
er unemployment rate
is estimated to reduce
wage growth by 0.42
percentage points.
This is comparable to,
though somewhat lower
than, the estimate de-
rived from figure 1 and
is highly significant,
both economically and
statistically. The first row of the fig-
ure also shows the rate of real wage
growth associated with 4%, 6%, and
8% unemployment. These figures
are for expected wage growth rela-
tive to the standard measure of price
inflation for the business sector and
control for the value of non-wage
benefits.
One of the virtues of the cross-state
approach is that we can obtain esti-
mates of the response of wages to
unemployment from relatively short
sub-periods of the data, an exercise
that would be close to meaningless
using only time-series data. In partic-
ular, the remainder of figure 3 shows
estimates for four five-year periods and
suggests that wage growth has become
somewhat less sensitive to unemploy-
ment in the 1990s. Specifically, our
methodology yields estimates of around
–0.045 for the early and late 1980s, but
only –0.032 in the late 1990s. (We
can reject—at the 10% significance
level—that this relationship has not
changed over time.) Of course, even
in the late 1990s, the estimates are
highly statistically significant, sug-
gesting that there is still an impor-
tant negative correlation between
unemployment and wage growth.
There are, moreover, some reasons
to believe that the finding of a weak-
ening relationship is not terribly
robust. First, when we go to the ex-
treme of estimating a separate elas-
ticity for every year of data, we find
that the magnitude of the elasticity
has decreased in recent years, with
1998 having the single smallest coef-
ficient. But as recently as 1994 and
1995, the coefficient was about as large
as it ever has been. And there have
been previous years—for instance
1985 and 1993—in which the coeffi-
cient has declined, only to increase
again subsequently. Therefore, we
would need to see more data before
concluding that there has been a per-
manent shift in the sensitivity of wages
to labor market conditions.
Second, the drop in coefficients is de-
pendent on somewhat arbitrary mod-
eling decisions. The statistical model
described thus far was estimated using
the logarithm of the unemployment
–2.0
–1.8
–2.2
–2.4
–2.1
–1.6
–2.2
–1.8
–1.5
–2.5
–3.8
–2.8
–2.1
–2.1
–2.1
–1.9
–2.3
–4.7
–2.6
–2.8 –3.6
–3.1
–2.9
–3.5 –3.3
–3.5
–1.9
–2.9
–2.5
–2.4
–2.1
–1.7
–1.5
–1.1
–1.2
–2.1
–1.9
–1.4
–1.1
–2.5
–1.4 –1.9
–1.8
–1.8
–2.7
–1.7
–2.2
–1.9
0.4
–2.6
–1.5
Note: The deviation is the difference between the 1999 average
unemployment rate and the 1980–99 average unemployment rate.rate, implying equal percentage
changes in the unemployment rate
have equal effects on wage growth.
For instance, a change in the unem-
ployment rate from 8% to 6% has
the same effect on wages as a change
in the unemployment rate from 4% to
3%. In general, we find this assump-
tion to fit the data well. However, an
alternative that works almost as well is
to assume that equal absolute chang-
es in the unemployment rate have
the same effect on wage growth. For
instance, a change from 8% to 6%
would have the same effect as a
change from 5% to 3%. When we re-
estimate based on this alternative
model, we find no evidence of a de-
cline in the sensitivity of wage growth
to unemployment. Rather, the late
1980s appear to be the period that
was different, having a higher esti-
mated coefficient than the other
three periods.
Third, because we chose to construct
wage data from the outgoing rotation
files of the CPS, our data start only in
1980 (as in figure 3). However, data
from the March CPS are available back
to 1964. Since wage estimates based
on these data are constructed from a
single month of data, they are highly
variable. Nevertheless, when we used
the March CPS data to estimate the
effect of unemployment on wages back
to 1964, the results suggest a stable re-
lationship between unemployment
and wage growth, with elasticity esti-
mates generally near –0.035 except
for the 1984–88 period when the
elasticity was estimated to be –0.045.
Thus perhaps it was the 1980s, not
the 1990s, that were unusual.
Figure 3 also shows estimates by time
period of the predicted average real
wage growth for unemployment rates
of 4%, 6%, and 8% based on our
model assuming equal proportion-
ate effects of unemployment and the
outgoing rotation files. For an un-
employment rate of 4%, predicted
real wage growth dropped between
the early and late 1980s, but has been
reasonably constant since then. Our
estimates currently predict real wage
growth of 2.8% when the unemploy-
ment rate is 4%, slightly below its cur-
rent value. The predicted real wage
growth rates associated with 6% and
8% unemployment also fell between
the early and late 1980s, and since
then have been fairly constant. The
0.6% level of wage growth predicted
for 8% unemployment in the last
period has, however, returned to
about its level for the early 1980s.
If there was a decline in the wage–
unemployment relationship, what
caused it?
As we mentioned earlier, if some shift
in the relationship between labor
market conditions and real wage
growth in the 1990s occurred, it would
not be terribly surprising given the many
changes in the labor market in recent
years. In previous work, we explored
two possible culprits: the changing na-
ture of the work force and the relative
decline of job security.
Many researchers have shown that wage
growth among college-educated work-
ers is less sensitive to unemployment
than that among other workers. Thus,
the increasing share of college-educat-
ed workers in the U.S. economy dur-
ing the 1990s could cause a decline in
the wage–unemployment relationship.
However, we believe that this is not the
case. A decline in the sensitivity of wag-
es to unemployment is seen both for
noncollege and college workers during
the 1990s. This is also true when we split
the sample by occupation or industry.
Therefore, something other than a
compositional shift toward skilled work-
ers explains the diminished late-1990s
wage–unemployment relationship.
We also do not believe that changes in
job security can explain a shift in the
sensitivity of wages to labor market
conditions. In previous work, we de-
scribe why real wage growth could be
related to job insecurity and empiri-
cally show that, in fact, such a rela-
tionship exists over the last 20 years.
However, the sensitivity of wages to
Michael H. Moskow, President; William C. Hunter,
Senior Vice President and Director of Research;  Douglas
Evanoff, Vice President, financial studies; Charles
Evans, Vice President, macroeconomic policy research;
Daniel Sullivan, Vice President, microeconomic policy
research;  William Testa, Vice President, regional
programs and Economics Editor; Helen O’D. Koshy,
Editor; Kathryn Moran, Associate Editor.
Chicago Fed Letter is published monthly by the
Research Department of the Federal Reserve
Bank of Chicago.  The views expressed are the
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Reserve System. Articles may be reprinted if the
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3. Relationship between real wage growth and unemployment
Elasticity of wage growth
with respect to unemployment 4% 6% 8%
1980–99 –0.042 3.2 1.6 0.4
(0.004) (0.2) (0.2) (0.2)
   1980–84 –0.047 4.1 2.2 0.8
(0.005) (0.4) (0.2) (0.1)
   1985–89 –0.046 3.1 1.2 –0.1
(0.005) (0.2) (0.1) (0.2)
   1990–94 –0.038 2.8 1.3 0.2
(0.006) (0.3) (0.1) (0.1)
   1995–99 –0.032 2.8 1.5 0.6
(0.006) (0.5) (0.2) (0.2)
Note: Numbers in parentheses are standard errors.
Source: Authors’ calculations based upon data from the U.S. Department of Commerce
and U.S. Department of Labor, various years, Current Population Survey.
Real wage growth associated
with unemployment rate ofinvoluntary job loss, our measure of
job security, is statistically and eco-
nomically important only for less ed-
ucated workers, much like in the
unemployment–wage growth litera-
ture. There is no robust effect on
higher educated workers. But the
rise in involuntary job loss during
the 1990s occurred primarily among
more educated workers. Therefore,
while we find evidence that job secu-
rity is related to real wage growth, it
cannot explain any trend in real
wage growth during the 1990s.
Conclusion
We have shown that the negative cross-
state correlation between unemploy-
ment and wage growth persists even
in recent data. We find some evidence
of a decline in the sensitivity of wage
growth to unemployment and other
labor market measures in the late
1990s. But, we regard that evidence
as being somewhat weak. Quantita-
tively, the changes in predicted wage
growth based on estimates for recent
years are not enormously different
than in previous years.
Our results have implications for work
on inflation forecasting. Traditional
short-run, or expectations-augment-
ed, Phillips curve methodologies have
tended to overpredict the change in
inflation in recent years. That method-
ology depends upon both the rela-
tionship between unemployment and
expected wage growth and the rela-
tionship between wage growth and
price inflation. Given the many fun-
damental changes that may be affect-
ing the labor market, it is natural to
look for a change in the relationship
between unemployment and wage
growth. But, our finding that the cross-
state relationship between unemploy-
ment and wage growth has been
relatively stable suggests that more
attention be given to the link between
wage growth and price inflation as
the source of instability in the short-
run Phillips curve. This seems consis-
tent with findings such as in Brayton
et al. (1999) that adding variables to
1More detailed information is available
in Daniel Aaronson and Daniel Sullivan,
2000, “Recent evidence on the relation-
ship between unemployment and wage
growth,” Federal Reserve Bank of Chicago,
working paper, No. 00-27, and Daniel
Aaronson and Daniel Sullivan, 1999,
“Worker insecurity and aggregate wage
growth,” Federal Reserve Bank of Chicago,
working paper, No. 99-30. A revised ver-
sion of the latter paper is available by
email from daaronson@frbchi.org.
2Flint Brayton, John Roberts, and John
Williams, 1999, “What’s happened to the
Phillips curve?,” Board of Governors of the
Federal Reserve System, working paper.
account for variation in the markup
of prices over wages may be the most
attractive way to stabilize the relation-
ship between unemployment and
changes in price inflation.2
—Daniel Aaronson
Senior economist
—Daniel Sullivan
Vice president and economic advisor
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Cross-state evidence on the relationship between unemployment and wage growth

http://www.chicagofed.org/digital_assets/publications/chicago_fed_letter/2001/cflmay2001_165.pdf

Cross-state evidence on the relationship between unemployment and wage growth

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Research Papers in Economics