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Economic
MI C
R E V I E W
1988 Quarter 4
Vol. 2 4 , No. 4
Do the Earnings
ot Manufacturing
and Service Workers Grow
2
Economic Review
is published
q ua rterly b y the Research
at the Same Rate Over
D e p a rtm e n t of the Federal
Their Careers?
R e s e rve B a n k of C le ve la n d .
b y R andall Eberts
C opie s of the
and Erica Groshen
availa ble through our Public
Review
are
Inform ation D e p a rtm e n t,
With service-sector jobs comprising an increasingly greater share of total
2 1 6 / 5 7 9 -2 1 5 7 .
employment, one concern is that service jobs m ay not offer the same earn
ings growth potential over a worker’s career as manufacturing jobs. To
address this issue, the authors estimate separate age-earnings profiles for
service and manufacturing workers. They find that even though entry-level
C oordin ating Ec o n o m is t:
Randall W . Eb erts
service wages are lower than manufacturing wages, service wages grow at
roughly the same rate over a worker’s career as do manufacturing wages.
Editors: W illiam G . M u rm a n n
Robin Ratliff
D e s ig n : M ich ael G alk a
T y p e s e ttin g : L iz H a n n a
Procyclical Real Wages
11
Under Nominal-Wage
Op in ion s s ta te d in
Contracts With
Productivity Variations
Review
Economic
are those of the
a u th ors an d not n ecessarily
b y J a m e s G. Hoehn
those of the Federal Re s e rve
B a n k of C leve lan d or o f the
The notion of sticky wages has been used by macroeconomists to understand
B oard of G ove rn o rs o f the F e d
the effects of m oney and inflation on output and employment. The sticky-
eral R e s e rve S y s te m .
wage notion has been criticized as inconsistent with the mildly procyclical
movements of the real wage. This inconsistency is removed if autonomous
labor productivity variations occur, if wage contracts reflect expected produc
M aterial m a y be reprinted pro
tivity, and if demand shocks are not too great relative to productivity shocks.
vid e d th a t th e s ource is credited.
Ple ase send copies of reprinted
m aterial to the editor.
Real Business Cycle
Theory: a Guide,
an Evaluation, and
24
New Directions
by A la n C. S to ckm a n
Real business cycle analysis seeks to explain aggregate business cycle fluc
tuations as responses to changes in technology, tastes, and nonmonetary
government policies. It attempts to model in guantitatively accurate fashion
the persistence of disturbances and comovements of labor-market and
output-market variables across economic sectors. This study evaluates the
state of real business cycle (RBC) theory, presents a two-country version of
a simple RBC model, and examines the implications of this research for eco
nomic policy.
I S S N 0 0 13 -0 2 8 1
D o th e E a r n in g s o f
M a n u fa c tu r in g a n d
S e r v ic e W o r k e r s G ro w
a t th e S a m e R a te O ve r
T h e ir C a r e e r s ?
by Randall Eberts
and Erica Groshen
Randall Eberts is an assistant vice
president and economist and Erica
Groshen is an economist at the Fed
eral Reserve Bank of Cleveland.
The authors thank Ralph Day and
Paula Loboda for their expert assis
tance, and thank Robert LaLonde for
his comments.
Introduction
The U.S. labor market has undergone dramatic
structural changes over the last several decades.
Total employment has increased by 37 percent
since 1976, but most of this growth has been
concentrated disproportionately in the serviceproducing sectors. For instance, service
employment (SICs 70 through 89) has increased
80 percent since 1976, while manufacturing em
ployment (SICs 20 through 39) has increased
only 5 percent. 1
This uneven growth across sectors has resulted
in a significant change in the industrial compo
sition of the labor force. Twelve years ago, man
ufacturing claimed 24 percent of total employ
ment while the services comprised 18 percent.
Today, those roles have been completely reversed
with the service sectors claiming 24 percent of
total employment and manufacturing claiming
18 percent.
■
1
S ervice industries in S ta nda rd Industrial C lassifica tions (S IC s )
70 through 89 include h ote ls, personal s ervices , business services,
a u to m o tive and other repair, health s e rvic e s , edu cational services,
social se rvice s , and en gineerin g, ac cou ntin g and related services.
M a n u fa c tu rin g industries in S IC s 20 through 39 include all durable
and nondurable s ectors.
The transition from an economy dominated by
manufacturing jobs to one with predominantly
more service jobs raises the question of whether
or not service jobs in general offer the same earn
ings potential for workers as manufacturing jobs.
A popular notion is that the economic restructur
ing that has taken place over the last decade or
so has relegated skilled production workers to
jobs as hamburger flippers. Krueger and Summers
(1987), for example, support the view that service
jobs are lower paying by reporting that workers
in service sectors such as medical, welfare, edu
cation, and personal services earn significantly
less than workers in manufacturing sectors.
Wage differentials between service and manu
facturing industries are even evident for workers
in the same occupational categories, as shown in
table 1. Within occupation, manufacturing wage
premiums range from a high of 45 percent for
male equipment cleaners and handlers to a low
of 3 percent for female production, craft, and
repair workers. Also note that the distribution of
occupations employed in the two sectors is quite
different. For instance, the largest occupational
category for women in the service sector is pro
fessionals and specialists, while in manufactur
ing, machine operators and assembly occupa
tions employ the largest number of women.
Bluestone and Harrison (1986) report some
disturbing consequences of the restructuring of
D
T A B L E
1
Average Hourly Earnings by Selected
Occupation and Industry in 19 8 7
1. Males
Selected Occupation
Executives, Administrators,
& Managers
Professional & Specialists
Technical & Related Support
Sales Personnel
Administrative Support & Clerical
Production, Craft & Repair
Machine Operators & Assembly
Transportation & Material Movers
Handlers & Equipment Cleaners
Manufacturing
Mean Earnings
Number
2,156
1,964
858
701
1,068
4,977
5,863
1,111
1,311
$16.26
16.38
12.94
13.55
10.04
11.03
8.89
8.98
7.64
Number
2,428
5,162
971
370
943
1,788
486
403
393
Services
Mean Earnings
$13-98
13.20
11.15
9.85
7.75
8.80
6.79
7.47
5.72
2. Females
Selected Occupation
Executives, Administrators,
& Managers
Professional & Specialists
Technical & Related Support
Sales Personnel
Administrative Support & Clerical
Production, Craft & Repair
Machine Operators & Assembly
Transportation & Material Movers
Handlers & Equipment Cleaners
Manufacturing
Mean Earnings
Number
849
565
296
307
2,770
979
4,391
68
534
$11.76
12.30
10.49
9.89
8.09
7.66
6.20
9.40
6.26
Number
2,755
9,926
2,100
621
8,074
164
448
237
96
Services
Mean Earnings
$10.57
10.96
9.28
6.48
7.09
7.51
5.18
7.15
4.60
SOURCE: Female and male wage and salary workers aged 18 to 54 working in the indicated industries and occupations in the one-quarter
earnings sample drawn from all monthly C urrent P opulation Surveys in 1987.
employment. Their analysis shows that “...all of
the employment increases experienced since
1979 have been generated by the creation of jobs
which paid less than the median wage in 1973 ”
(p. 5) They go on to add that the disproportion
ate expansion of the low-wage sector is found to
be especially prevalent among younger entrylevel workers between the ages of 1 6 and 34.
Although these latter results have stirred some
controversy, they point to an essential question
in discussing the earning potential of the great
number of service jobs created in the economy.
As noted earlier, several studies, including this
one, have found that service workers consistently
earn less than their manufacturing counterparts.
The question that has not been addressed is
whether or not service workers can expect the
same growth rate in wages over their work life as
manufacturing workers enjoy, even though they
start out earning less.
To answer this question, we estimate ageeamings profiles, which approximate the growth
rate of earnings of individuals over their work
lives. Each profile depicts the pattern of earnings
of a cross section of individuals at each age level.
We then look for significant differences in ageeamings profiles between comparable workers
in manufacturing and service sectors. We inter
pret the results of this approach to represent the
earnings potential of typical service and manu
facturing workers over their work lives. This
interpretation rests on the assumption that the
behavior of individuals and labor market condi
tions affecting their earnings do not vary signifi
cantly among cohorts. Although this assumption
may be open to question, the approach provides
a starting point for analyzing this issue.
We estimate cross-sectional age-earnings pro
files using the 1987
(CPS) . 2 The year 1987 was chosen because it
provides the most recent evidence. In other work
not reported here, the same models were esti
mated for 1976 and 1986. Differences in ageearnings profiles between the two sectors were
qualitatively similar in all three years. The sim
ilarity in results across years also suggests that
cohort effects are probably not the driving force
behind the lack of sectoral differences in ageearnings profiles.
We test for sectoral differences in age-earnings
profiles at two levels of model complexity. First,
we test whether earnings increase at the same
rate over an individual’s career for each of the
two sectors by simply interacting the servicesector dummy variable with the age variables.
Next, we examine whether age-earnings profiles
differ between service and manufacturing sectors
within relatively broad occupational categories.
Our basic finding is that only slight differences
in age-earnings profiles exist between the two
sectors. However, when age-earnings profiles are
estimated separately for major occupational
groups, the differences between sectors all but
disappear. Consequently, the notion that service
jobs do not offer the same earnings growth as the
manufacturing jobs they are replacing is not sup
ported by this analysis. However, since the earn
ings growth rates are similar between sectors, the
gap between manufacturing and service wages
persists throughout the individual’s career. 3
Current Population Survey’
■ 2
Estimation of the relationship between earnings and age is performed
using both cross-sectional and longitudinal data. For example, Freeman (1980)
analyzes cross-sectional C P S data, Nakosteen and Zimmer (1987) use PSID
longitudinal data, and Hanoch and Honig (1985) use panel records of the
Social Security Administration. Ideally, one would follow an individual over that
person’s entire career in order to avoid cohort effects when estimating the
age-earnings profile. Tw o data sets are typically used in longitudinal studies:
I. Age-Earnings Profiles
Why might age-earnings profiles differ across sec
tors and over time? The stylized relationship
between earnings and age is that wages rise
steeply during the first part of a worker’s career,
level off in the middle years, and perhaps even
decline slightly in the final years. This pattern
was strikingly documented by Mincer (1974)
using I960 census data. Since then, a number of
studies have explored various aspects of the rela
tionship in more detail. 4 However, no one has
studied the age-earnings relationship for workers
in specific industries, in particular, service and
manufacturing.
Several reasons for this pattern have been
advanced. The most widely cited hypothesis is
the accumulation of human capital through onthe-job training (for example, Mincer [1974]).
Other explanations attribute the age-earnings
pattern to the knowledge an individual gains
about a specific firm (O i [1962]) or to workers’
showing their commitment to a firm by accept
ing low pay early in their career in exchange for
high pay later in their work life (Lazear [1981]).
In all three cases, prolonged participation in the
labor force or attachment to a firm increases the
value of the worker to the firm; consequently,
the worker’s wages increase with age.
Differences in demand and supply characteris
tics can account for differences in age-earnings
profiles across sectors and over time. On the
demand side, for example, differences in ageearnings profiles across industries may arise
because of differences in the amount of human
capital accumulated during a worker’s career.
Workers in low skill-accumulation jobs would
exhibit a shallower age-earnings profile that
would probably peak at a young age. Thus, if
service jobs are generally characterized as lowskill and manufacturing jobs as high-skill, then
the age-earnings profiles of service jobs should
be shallower than those of manufacturing jobs.
However, if workers in the two sectors are com
parable to begin with, total (discounted) earn
ings in the two sectors should equalize over the
course of the workers’ careers.
the Panel Survey of Income Dynamics (PS ID ) and the National Longitudinal
Survey (N L S ). Cross-sectional analysis almost exclusively uses the Current
Population Survey (C P S). The C PS offers a major advantage over N L S : it
includes significantly more individuals. Thus, estimates based on subgroups,
such as men and women in manufacturing and services, are more reliable.
■ 4
A recent stran d of literature explores the e xte n t to w hich p ro
files are prim a rily due to increases in s en iority (or tenure) rather than
■ 3
This paper addresses only the age -ea rn ings profile q ue stion .
general experien ce. S everal s tu d ie s , including A b ra h a m and Farber
A n o th e r e q u a lly interesting question is w h y service w orkers receive
( 1 9 8 7 ) and A lto n ji and S h a k o tk o ( 1 9 8 7 ) , h ave challenged the e m p ir
low er pa y at each age level than their m an ufac tu rin g co un terp arts.
ical v a lid ity of a positive relationship betw een w ag es and tenure.
W hile a n um ber of exp la n a tion s for the existe nc e of in terind ustry
A lth o u g h there is s upport for this relationship w hen em plo yer c h a ra c
w ag e differe ntials have been a d v a n c e d , none has been generally
teristics are included (H e rs ch and Reagan [ 1 9 8 7 ] ) , this co n tro ve rs y
ac c e p te d . See D ickens and K a tz ( 1 9 8 7 ) for a s u m m ary of the s ta te
does not directly pertain to our s tu d y since w e do not distinguish
of current research on the topic.
b etw een tenure and experien ce.
workers between the ages of 18 and 54. Earnings
are measured as hourly wages: weekly earnings
divided by usual weekly hours. Some studies use
weekly earnings and typically find little differ
ence (except for higher variation) in compensa
tion patterns from those derived from using
hourly wages. We choose hourly earnings to
minimize the problem of differences in hours
worked across the various groups.
Plots of the cross-sectional patterns of mean
hourly wages by age for male and female service
and manufacturing workers, aged 18 to 54, in
1987 are shown in figure 1. Although these plots
do not control for attributes of workers other
than age, sex, and industry, they provide a start
ing point for this discussion. This figure and the
analysis below can be viewed as a snapshot of
workers frozen at various stages in their careers. 5
Age-Earnings Profiles, Males and Females in
Manufacturing and Service Industries, 19 87
Dollars/hour
15
12
9
6
3
18
22
26
30
34
38
Age
42
46
50
54
SOURCE: Current Population Survey, one-quarter earnings sample, 1987.
The age-earnings profile may also be affected
by the relative abundance of workers of various
ages across industries. The effect of the supply of
workers in various age groups depends upon the
extent of, and variations in, the substitutability
between groups among sectors. For instance, if
younger service workers were imperfect substi
tutes for older workers in one sector, then an
influx of young workers into the sector would
bid down the wages of younger workers and, thus,
make the profile steeper in that sector. On the
other hand, if younger workers were perfect sub
stitutes for older workers in all industries, then
an influx ofyounger workers would leave the pro
file unchanged, but would reduce wages of work
ers of all ages. Estimates of elasticities of substi
tution between old and young workers generally
find them to be somewhat imperfect substitutes,
especially among men and the highly educated
(see Freeman [1980] and Hamermesh [1986]).
First, we see the familiar shape of the ageearnings profile in both sectors, but with marked
differences between the patterns of men and
women. Second, we see that wages for men are
lower in the service industries than in the manu
facturing industries for most but not all ages.
Third, although the youngest women earn more
in manufacturing than do their service-sector
counterparts, by the age of 28 female service
workers appear to be more highly compensated.
Finally, the service-sector profiles in these plots
are steeper than the manufacturing profiles. The
difference between manufacturing and service
earnings is greatest in the earlier years and nar
rows with the age of workers.
To investigate age-earnings relationships while
controlling for other employee characteristics,
the log of hourly earnings is regressed against
age and age-squared along with other worker
characteristics, such as education, race, union
affiliation, and full-time status. Age-earnings pro
files are estimated by entering age and agesquared into the wage regression and then inter
acting these two variables with a service-sector
dummy to distinguish between profiles for ser
vice and manufacturing jobs. 6
■ 5
II. Estimation of
A s discussed a b o v e , this ap proach does not control tor cohort
e ffe c ts . T h a t is, som e cohorts — such as the b a by boom ers — m ay
differ in their avera ge ch aracteristics from the m em bers of other
Age-Earnings
co h o rts . These average differences in unnoted ch aracteristics (s a y ,
Profiles
size of co h o rt, h e a lth , or a ttitu d e ) could a ffe c t the results reported
here.
Our sample of workers is drawn from the onequarter earnings sample of the 1987 CPS. We
limit the sample to manufacturing (SICs 20
through 39) and service (SICs 70 through 89)
■
6
T o be consistent w ith other em pirical studies of age -ea rn ings
profiles, we s p e c ify a qua dra tic relationship b etw een age and e a rn
ings. Furth er exploration of this topic should consider alte rn a tive
s p e c ificatio n s .
T A B L E
2
Regression Results
Characteristics ot Manufacturing
and Service Workers by Sex in 19 8 7
Characteristic
Mean Hourly Earnings
Services
Manufacturing
Females
$ 8.13
8.24
7.82
Males
$10.85
10.41
1 1 .2 1
Std. Dev. (Log Earnings)
Mean Log Earnings
Services
Manufacturing
Service Sector
0.517
1.967
1.972
1.952
74.7%
2.309
44.2%
Part Time
Services
Manufacturing
22.9%
27.7
8.9
13.1
3.2
Union
Services
Manufacturing
15.0%
15.1
14.5
21.3%
Nonwhite
Services
Manufacturing
15.5%
15.1
12.7%
14.2
11.4
Highest Grade Completed
Services
Manufacturing
13.4
13.8
12.2
13-4
14.3
12.7
Age in Years
Services
Manufacturing
35.0
34.9
35.0
34.9
34.1
35.6
42,950
36,669
Number of Observations
16.6
0.545
2.249
2.174
7.6%
16 .0
25.4
SOURCE: Female and male wage and salary workers aged 18 to 54 working in
manufacturing or service industries in the one-quarter earnings sample drawn
from all monthly Current Population Surveys in 1987.
The means of these variables are displayed in
table 2 by sex and industry. One interesting fact
is that women’s earnings are actually higher in
service jobs than they are in manufacturing jobs.
The apparent inconsistency of this finding with
the numbers in table 1 is due to sectoral differ
ences in occupational distribution. In general,
women in the service sector are more concen
trated in the highly paid occupations than are
women in the manufacturing sector.
Women are much more likely to work in
service-sector jobs than are men. And, it is
apparent that, compared to manufacturing
workers, a higher percentage of service workers
are part time, especially among women. Also,
male service workers are less heavily represented
by unions than are male manufacturing workers.
The results of the earnings regressions are dis
played in several tables. Table 3 presents the
coefficient estimates for variables that are not
part of the age-earnings profiles. These estimates
determine the intercepts of the estimated profiles
for each group. For example, the coefficient of
the service-sector dummy variable shows that,
controlling for the human capital and demo
graphic characteristics listed, service workers’
earnings are lower than manufacturing workers’
earnings for both males and females. It is inter
esting to note that, in contrast to figure 1 and
table 2 (which do not control for other charac
teristics), the “corrected” service-sector earnings
effect (that is, the coefficient on the service
dummy) for female workers is strongly negative.
The next two rows in table 3 present evidence
of the wage penalty experienced by part-time
workers. We see that for women the wage penalty
for working part time is smaller in the service
sector than it is in manufacturing. For males in
manufacturing, the penalty for part-time work is
larger than that for women in both sectors.
The relative attractiveness of unionism is sim
ilar between the two sectors for both sexes. For
both men and women, the union wage differen
tial is only slightly higher in services than in
manufacturing.
Far more striking is the smaller racial differen
tial in services compared to manufacturing, also
found by Montgomery and Wascher (1987). For
both sexes, this differential is reduced by almost
half in the service sector. The importance of dif
ferences in the returns to schooling vary by sex.
The results in table 3 suggest that returns to
education are significantly higher for women in
services, but the difference between sectors is
small and statistically insignificant for men.
Age-Earnings
Profiles
Age-earnings profile coefficient estimates are
presented in table 4. Hourly wages exhibit typi
cal profiles for men and women in each sector.
Males appear to have a steeper, more pro
nounced earnings path than women in both sec
tors. Presumably this is due in part to more
instances of nonparticipation in the labor force
or preferences for part-time work among
women. In addition, earnings taper off more
quickly for men than for women.
In general, female service workers exhibited a
steeper earnings path with greater curvature than
manufacturing workers. Male service workers
mmmmm
!
t
a
b
l
3
e
Coefficient Estimates of Age-Earnings
Equations by Sex in 19 8 7
Variable
Males
Females
Intercept
-0.276
(-4.52)
-0.508
Service Dummy
-0.361
(- 5 .2 1 )
-0.174
(-2.82)
Part Time Dummy
-0.204
(14.14)
-0.295
(-17.38)
Part Time x Service
0.029
(
)
-0.083
(-4.15)
Union Member
0.140
(11.85)
0.085
(12.33)
(
0.007
Union x Service
0.014
.
1 8 8
.
1 0 2
)
(-11.58)
(
.
0 6 0
)
Nonwhite Dummy
-0.129
(-11.69)
-0.153
(-16.67)
Nonwhite x Service
0.055
( 4.27)
0.075
( 5.67)
Years of School
0.082
(48.49)
0.079
(28.47)
School x Service
0.008
( 4.07)
had earnings paths that were not significantly dif
ferent from those of male manufacturing workers.
However, since the age at which wage growth
stops is a function of both initial slope and
degree of curvature, one way to compare the var
ious age-earnings profiles is to calculate the age
at which earnings peak. The results of such cal
culations are shown in the lower two rows of
table 4. Using the coefficient estimates in the first
four rows, hourly wages peak for male service
workers at age 47 while wages peak for compar
able manufacturing workers at age 49. The
results for women also suggest that earnings
peak at an earlier age in the service sector. How
ever, the difference between the sexes far dom i
nates the difference between sectors.
-0 . 0 0 2
(-1.48)
III. Effect of Age-
R-squared
.325
.411
NOTE: T-statistics appear in parentheses next to coefficient estimates. The
Earnings Profiles
on Sectoral Wage
symbol “ x” signifies multiplying the two variables shown, which results in an
Differentials
interaction term. The dependent variable is log (earnings). Other variables in
the m odel estimated are age and age-squared interacted with the service
dum my variable. Coefficients for those variables are reported in table 4.
SOURCE: Female and male wage and salary workers aged 18 to 54 working in
manufacturing or service industries in the one-quarter earnings sample drawn
from all monthly C urrent Population Surveys in 1987.
Age-Earnings Profile Coefficient
Estimates by Sex in 19 8 7
Variable
Age
Service x Age
Females
0.053
(15.79)
Males
(28.47)
0.070
-0 . 0 0 1
(-0.25)
Age2 / 1,000
-0.604
( -13-21)
-0.713
(-21.37)
Service xAge2/l,000
-0.136
(-2.27)
-0.024
(-0.49)
0 .0 10
( 2.71)
Implied Age of Peak Earnings
Manufacturing
44
Services
43
49
47
NOTE: T-statistics appear in parentheses next to coefficient estimates. The
symbol “ x” signifies multiplying the two variables, which results in an interac
tion term. The dependent variable is log (earnings). Coefficients on the other
variables included in the m odel estimated are reported in table 3SOURCE: Female and male wage and salary workers aged 18 to 54 working in
manufacturing or service industries in the one-quarter earnings sample drawn
from all monthly C urrent Population Surveys in 1987.
We have addressed the question of differences in
age-earnings profiles between manufacturing
and service workers by interacting service-sector
dummy variables with age and age-squared. The
next question is whether entry-level workers
should expect the wage differences they initially
encounter between sectors to persist, or to dissi
pate over their work life. Another way to ask the
same question is: do the service and manufactur
ing jobs have the same earnings growth potential?
The earnings equation estimates reported in
tables 3 and 4 allow us to calculate the earnings
difference between service and manufacturing
jobs (compared to manufacturing earnings) for
the average 18-year-old with 1 2 years of educa
tion. The top two rows of table 5 report the
results of that exercise for men and women in
four demographic groups. The upper row is
based on regressions on men’s earnings; the
lower row on women’s earnings. For instance,
the average nonwhite 18-year-old female work
ing in a full-time, nonunion service job earns 9 . 8
percent less than does a comparable worker in a
full-time, nonunion manufacturing job.
Note that in no case do the wages of entrylevel service workers exceed those of entry-level
manufacturing workers. And, the service differen
tials among women are sometimes larger and
sometimes smaller than those found for men.
Perhaps most interesting is the extent to which
the service differentials vary, from a low of 6.4
percent to a high of 2 0 . 0 percent for men and
from a low of 9 . 8 percent to a high of 14.6 per
cent for women. The relative disadvantage of
T
A
B
L
E
5
Comparison of Entry-Level Sectoral
Earnings Differentials to Lifetime
Sectoral Earnings Differentials
White
Nonunion
Full Time
Nonwhite
Nonunion
Full Time
White
Union
Full Time
White
Nonunion
Part Time
Proportional Earnings Differential of Entry-Level Service Workers Compared to Entry-Level Manufacturing
Workers (Age 18)
Males
-.131
-.064
-.125
-.200
Females
-.146
-.134
-.121
Discounted Present Value of Proportional Earnings Differential From Age 18 to Age 54
Males
-.166
-.101
-.160
-.232
Females
-.091
-.117
-.098
-.067
-.105
NOTE: The predicted wage differential between sectors for each demographic group is converted to a proportion o f manufacturing workers’
earnings. Estimates o f proportional discounted total earnings differentials are based on integration o f the estimated earnings functions for
each sector, as reported in tables 3 and 4, assuming a 3 percent real discount rate and 12 years o f education.
SOURCE: Derived from estimates shown in tables 3 and 4.
service-sector employment compared to a manu
facturing job varies strongly with race, sex, and
part-time status.
To determine whether these differentials will
persist over the workers’ careers, we calculate the
discounted present value of the earnings stream
over the work life. The discounted present value
simply adds up the annual earnings of an indi
vidual between the ages of 18 and 54. Earnings
are valued at the beginning of the career and so
earnings received after age 18 are discounted at
a 3 percent annual rate. The present value takes
into account the estimated differences between
age-earnings profiles between sectors.
The lower two rows of table 5 present esti
mates of the service differential in the present
value of earnings from a work life beginning at
age 18 and lasting until age 54, using the model
with varying age-earnings profiles between sec
tors estimated in tables 3 and 4. Results from this
exercise show that the earnings differential
between service and manufacturing workers is
primarily due to the straight differential paid to
all ages, although differences in profiles do affect
these sectoral wage differentials to some extent.
Again, all differentials suggest higher earnings
in manufacturing; white nonunion women work
ing full time experience an average difference of
11.7 percent over their work life. And the aver
age, white, nonunion, full-time, male worker
earns 16.6 percent less in a service job. For non
whites, the service differentials are much smaller.
These earnings differences over the entire
work life differ from the entry-level wage differ
entials because they depend on the relative
shape of the age-earnings profile in each sector.
In general, the lifetime sectoral differences in
age-earnings profiles shown in table 5 suggest
that starting wages underestimate the ultimate
earnings differences for men and overestimate
the lifetime pattern for women. The reason for
the difference is shown in figures 2 and 3. The
upper graph in figure 2 shows that for women,
the percent differential increases during their
middle years and then narrows during their later
years. For men (shown in figure 3), the earnings
gap continually increases, since service wages
peak earlier and taper off more quickly than
manufacturing wages.
It is interesting that the impact of service
employment on males’ earnings patterns appears
stronger than that for females, even though the
estimated service-age interaction coefficients
(reported in table 4) are far larger for females
than for males. This apparent anomaly stems
from the offsetting nature of the age and agesquared interaction coefficients for females. For
females, an increase in age increases the service
differential through the service effect on the age
coefficient, but reduces the service differential
through the service impact on the age-squared
coefficient. Among males, an increase in age is
associated with a lower wage for service workers
through the service impact on both the age and
—
m M
F
1
G
U
R
E
2
1
Estimated Sectoral Difference
in Female Age-Earnings Profile
the age-squared coefficients. However, since the
results for men are based on statistically insignif
icant sectoral differences in wage growth, any
conclusion must be drawn with care.
Dollars/hour
IV. Age-Earnings
Profiles Within
Occupations
Age
Percent difference
Age
SOURCE: Author’s calculations.
S —
F
1
G
U
R
Estimated Sectoral Difference
in Male Age-Earnings Profile
E
3
]
Implicit in the model presented above is the
assumption that education and other demo
graphic variables are good controls for human
capital. Occupation provides another way to con
trol for human capital. An alternative assumption
is that sectoral differences in profiles result from
occupational differences that are constant across
industries. Since manufacturing and services
employ a different mix of occupations, differ
ences between the sectors may be largely a prod
uct of differences in occupations employed.
To address this issue, we estimate separately
the simple wage equation with age and agesquared for various occupational categories. The
sectoral differences in age-earnings profiles
found earlier disappear within many of the
occupations. This finding suggests that employ
ment in the services has no independent effect
on age-earnings profiles. But, it does not suggest
that the changing industrial structure of
employment has no impact. Rather, the impact
stems from the effect of the industrial shift on
the occupational distribution.
Dollars/hour
V. Summary and
Conclusion
Over the last decade, service-sector employment
has grown at twice the rate of total employment,
while manufacturing employment has grown
very little. As a result, service-sector employment
now claims a larger proportion of total employ
ment than manufacturing. This restructuring has
drawn attention to concerns that service-sector
jobs don’t pay as much as manufacturing jobs.
To answer the question posed by the title of
this paper, our findings suggest that service
workers start out at a lower wage than that of
comparable manufacturing workers, but then
service-sector wages grow at roughly the same
rate as manufacturing-sector wages.
Percent difference
Age
SOURCE: Author’s calculations.
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Hanoch, Giora, and Marjorie Honig. “ True’ Age
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“Race and Gender Wage Inequality in Services
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Industrial Relations,
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u
P r o c y c lic a l R e a l W a g e s
U n d e r N o m in a l- W a g e
C o n t r a c t s W ith
P r o d u c tiv ity V a r ia tio n s
by James 6 . Hoehn
Jam es G. Hoehn is an economist at
the Federal Reserve Bank of
Cleveland. The author gratefully
acknowledges helpful discussions
with Charles T . Carlstrom, William T.
Gavin, and Alan C. Stockman, and
acknowledges useful comments on a
draft by Randall W . Eberts, Erica L.
Groshen, and John B. Taylor.
Introduction
A frequent criticism directed at many macroeco
nomic models, especially those with wage stick
iness, concerns their inability to account for the
procyclical pattern of real wages. This article
offers a resolution of this problem by introduc
ing productivity factors into the determination of
sticky wages. This resolution makes the resulting
model more consistent with standard microeco
nomic theory about the determination of wages.
The problem of accounting for real-wage cycli
city arises both for sticky-wage models such as
those of Keynes (1936) and Fischer (1977), and
for the incomplete-information models such as
those of Friedman (1968) and Lucas and Rapping
(1969). Economists favoring these models have
offered a wide variety of prospective solutions to
the puzzle of real-wage cyclicity, including com
plex reinterpretation of the evidence and a variety
of modifications to the models. However, none
of these solutions has been widely accepted and
the failure of proponents of these models to
resolve the real-wage puzzle has been consid
ered a serious shortcoming of the models.
The inability of existing sticky-wage and
incomplete-information models to account for
the cyclicity of the real wage has given impetus
to the development of two alternative ex
planations of macroeconomic fluctuations. These
alternatives are capable of resolving the realwage puzzle, but have problems of their own.
First, the real-business-cycle approach explains
economic fluctuations without invoking sticky
wages or prices or incomplete information:
employment, output, wages, and prices are deter
mined by people’s informed responses to vary
ing productive opportunities. Real wages will
generally be procyclical in such models, reflect
ing the variations in factor productivity that drive
the real business cycle. Indeed, real-businesscycle models can easily generate implausibly
high real-wage cyclicity. 1 The real-business-cycle
approach also cannot account for the observed
effects of money supply changes on real activity, 2
and provides no guidance for monetary policy.
Second, the real-wage puzzle has redirected
many Keynesians away from wage rigidities and
toward commodity price rigidities or monopolis
tic price-setting behavior. The sticky-price mod
els, like the sticky-wage models, can account for
■
1
■ 2
See Christiano and Eichenbaum (1988).
But see King and Plosser (1986), which attributes the observed relation
of money and income variables to the effects of technology shocks on both
variables.
the effect of policy on activity. For example, if
suppliers accommodate the demand at sticky
prices, and the real demand for goods depends
on real-money balances, then increases in
demand due to monetary expansion are met by
increases in output. If the nominal wage is flexi
ble, such an increase in output will raise the
demand for labor, raising both the nominal and
the real wage. Variations in demand within a
sticky-price, flexible-wage model are thus able to
generate procyclical variations in the real wage.
The argument here is that there is no necessity
to reject the notion of a sticky wage on account
of the real-wage puzzle; a more conservative
solution exists in the introduction of productivity
shocks into the determination of the sticky wage.
However, sticky-wage models are subject to
some criticism on more theoretical lines. They
have the problem of explaining why firms and
workers would agree to fix wages for a period in
nominal terms and then allow the quantity of
employment to be determined by the firm’s
labor demand at that wage. 3 The objection that
sticky-wage models result in nonoptimal
employment determination has prompted
Keynesians to endeavor to understand how con
straints on the feasibility of ideal contracts, such
as problems of information, contract enforce
ment, or transaction costs, prevent firms and
workers from determining employment and
output in an ideal manner. The sticky-wage
model would be more explicitly consistent with
microeconomic theory and might be more useful
for understanding and controlling the business
cycle if it made these constraints explicit.
But essentially the same issue can be raised
concerning sticky-price models: what constraints
would lead sellers to fix a commodity’s price in
nominal terms and allow quantity to be deter
mined by the demand at that price? 4 ' 5
Thus, the theoretical arguments against sticky-
■
3
Ideally, output and employment should be determined by the condition
that the marginal disutility of work equals the marginal product of labor. See
Hall (1980), Hall and Lilien (1979), and Barro (19 77).
■
4
Akerlof and Yellen (1985a, 1985b, 1988) provide a partial answer to
wage models do not compel their abandonment
in favor of alternatives, returning the focus to the
empirical arguments against sticky-wage models.
The crucial issue separating different views about
the source and policy implications of macroeco
nomic fluctuations is whether the real-wage puz
zle can be resolved without abandoning sticky
wages as part of the explanation of the business
cycle. Economists have increasingly come to
view the puzzle as fatally damaging to stickywage models. For example, Mankiw (1987, p.
105), concludes the case against them by saying
“...perhaps [the] most serious...problem with the
unadorned nominal wage story is that real wages
do not move over the business cycle as the the
ory predicts....” Likewise, McCallum (1986, p.
408) claims that “ [i] f wage stickiness alone was
responsible for the real effects of monetary
actions, with product prices adjusting flexibly,
then we should observe countercyclical move
ments in the real wage.”
This article offers a reconciliation of sticky
wages with observed cyclical behavior of real
wages by introducing productivity factors into
nominal-wage contracts. It shows that sticky
nominal wages can be consistent with the pro
cyclical real wages of the United States— even if
prices are perfectly flexible— under quite reason
able conditions: wage bargains reflect expected
labor productivity, productivity variations are
persistent and procyclical, and aggregate demand
fluctuations are not too large relative to produc
tivity fluctuations.
The introduction of productivity factors into
the determination of nominal wages is most
readily accomplished within a wage-contracting
setup like Fischer’s (1977), and so a modifica
tion of his approach will be used here. 6 All con
sidered, it is worthwhile to attempt to modify
sticky-wage theories to make them consistent
with procyclical real wages. A successful attempt
yields a model consistent with orthodox macroeconomic theory, with the important stylized
facts of U.S. business cycles, 7 and with the
microeconomics that links wages to productivity.
Furthermore, the model is able to provide guid
ance to monetary policymakers about the effects
of monetary policy.
this problem, by showing how small discrepancies of individual behavior from
full, explicit rationality— discrepancies associated with sticky prices and
wages— can be consistent with large departures of aggregate activity from
optimal levels. McCallum (1986) couples this idea that there are small private
costs associated with sticky wages and prices with the notion of menu costs,
or expenses incurred by changing price lists, to arrive at an economic theory of
■
stickiness. A final and more difficult requirement of a completely explicit theory
wage and price stickiness as part of a complete model. Price stickiness can,
5 A more symmetric treatment of these issues would allow for both
of stickiness, as playing an effective role in economic fluctuations, is a ratio
as explained in the text, help to resolve the real-wage puzzle. The argument
nale for quantity determination at the sticky wage or price. This requirement is
that sticky wages are consistent with procyclical real wages is stronger for not
important, because economists such as Barro (19 77) have conjectured that
relying on price stickiness. If procyclical real wages can be generated in a
sticky prices or wages m ay not have any effects on allocation, but may
model economy without sticky prices then, a fortiori, so much more easily can
instead be a facade for optimal quantity determination.
a procyclical real wage be generated when price stickiness is allowed.
y
I. Sticky Wages Play an
Important Role in
Keynesian Models
At least since the Keynesian revolution, sticky
wages have played a prominent role in macroeco
nomic theories of the interaction between prices
and quantities, providing an explanation of a
number of stylized facts of the business cycle,
particularly the tendency of employment to
increase with inflation caused by demand stimula
tion, such as increases in the money supply
Keynes (1936, chapter 2) formalized the stickywage mechanism linking money and prices to
output and employment. A decrease in the money
supply lowers the price level, raising the real
wage at the fixed nominal wage, forcing an
employment-contracting movement along a fixed
real demand for labor schedule. Keynes assumed
that the real-labor-demand schedule was identi
cal to the marginal-productivity-of-labor schedule.
More recent sticky-wage models account for
the eventual adjustment of money wages to price
level variations. Wages must eventually adjust
one-for-one with prices, ruling out money illu
sion. For example, price deflation will eventually
lead to lower nominal wages. Because of the
unemployment caused by price deflation and
the associated rise in the real wage, a firm can
find workers willing to work for less than the
initial money wage. But collective bargaining
and other conventions concerning compensation
make it difficult for money wages to decline as
rapidly as prices can fall. Typically, nominal
wages remain stuck until scheduled, periodic
renegotiations are undertaken.
■
6
Keynes’ analysis was a short-run or period
analysis, in which wages were taken as histori
cally given. Newer Keynesian sticky-wage models
make the wage decisions of workers and firms
respond to events and expectations of future
events. Current wages in newer models are
influenced by economic conditions; wages are
predetermined, not exogenous. 8
The emphasis on long-term contracts in new
sticky7
-wage models has been accompanied by
increased attention to expectation formation. As
Taylor (1983, p. 63) says, “...long-term relation
ships do not diminish the importance of expec
tations in macroeconomic analysis. O n the con
trary7 expectations of the future significantly
,
affect the terms of contractual arrangements.
They are of greater quantitative importance in
contractual situations than they are in more flex
ible auction-market situations.” Recognition of
the role of forward-looking expectations about
productivity thus seems well in the spirit of the
new genre of wage-contracting models.
II. The Puzzle of the
Procyclical Real Wage
Keynesians originally attempted to explain the
fluctuations in output and employment strictly
by variations in aggregate demand. This
approach ruled out or abstracted from techno
logical change, and is associated with a fixed
marginal product of labor schedule. It follows
that the real wage will be negatively related to
employment and, in this sense, is necessarily
countercyclical. In the words of Keynes (1936, p.
17), “...an increase in employment can occur
only through the accompaniment of a decline in
real wages. Thus, I am not disputing this vital fact
Productivity factors could be introduced into wage determination in
other models, such as the incomplete-information models mentioned. This mod
ification could make them consistent with procyclical real wages, although this
improvement would not satisfy other objections to them. Am ong the objec
■ 7
tions to incomplete-information models is that information lags in reality are
nomic model should be consistent include the following: (i) A short-run Phillips
Stylized facts of the U .S . economy with which a successful macroeco
too short to account for persistent macroeconomic fluctuations. The business
curve: Changes in aggregate demand generate a positive relation between
fluctuations to be accounted for by a business-cycle theory have a duration of
output (and employment) and inflation. For example, large increases in the
years, while delays of information available to people is at most a few
money supply, which increase aggregate demand, are associated with high
months, aside from statistical revisions; money supply data are available
inflation and high output increases, (ii) Supply shocks generate a negative rela
within a few weeks. The gap in the frequencies of cause and effect is sus
tion between output and inflation. For example, an increase in the price of
pect. Also, in incomplete-information models that involve intertemporal substi
imported oil is associated with high inflation and below-normal output growth,
tution like those of Lucas and Barro, positive output effects of money shocks
(iii) Long-run vertical Phillips curve (natural-rate hypothesis): regular increases
are hard to reconcile with reasonable microeconomic assumptions. Barro,
in aggregate demand and/or prices are anticipated and leave output and
Grossman and King (1984) confess that it is difficult to specify a plausible set
employment unaffected, (iv) Output and employment display persistent devia
of assumptions concerning the nature of utility functions, capital depreciation
tions from normal levels in the face of both demand and supply shocks, (v)
and correlations of shocks that is consistent with a positive relation in
Wages are institutionally sticky— more so than commodity prices, (vi) Real
incomplete-information models; it is easier to specify assumptions that lead to
wages display a modest positive correlation with both output and employment,
no relation or a negative one! Even if Keynesian sticky-wage theory lacks the
(vii) Output per worker-hour is mildly procyclical.
explicit individual rationality of the incomplete-information theories, it is at least
capable of generating the stylized facts that increases in money generate per
■
sistent and positively related changes in inflation and in output growth.
advance.
8
McCallum (1987) argues convincingly that this represents a substantial
which the classical economists have (rightly)
asserted as indefeasible. ” 9
Although a fixed marginal-product-of-labor
schedule necessarily implies that real wages are
negatively correlated with employment, it remains
possible, albeit unlikely, for real wages to be posi
tively correlated with output, if the productivity
of nonlabor factors of production varies. For exam
ple, an increase in the productivity of fixed factors
would increase output, lowering the price level
for a given money supply, raising the real wage,
and inducing a contraction of employment along
the fixed marginal-product-of-labor schedule.
Shocks of this kind would tend to make the real
wage procyclical as measured against output, but
countercyclical as measured against employment.
But while nonlabor productivity may vary, it is
unlikely to do so independently of labor produc
tivity. For example, a new wave of technology,
say, low-cost personal computers, might raise the
productivity of capital but ought to raise the pro
ductivity of labor simultaneously. In many empir
ical and theoretical studies, the production func
tion is specified in such a way that labor and
other factors are subject to equal proportional
productivity shocks.
In any case, the introduction of independent
variations in the productivity of nonlabor factors
cannot be much relied upon to enhance the
sticky-wage model’s conformity with the stylized
facts of the business cycle. Such variations do not
provide a mechanism for a positive realwage/employment correlation and tend to create
a counterfactual negative correlation between
output and employment. Hence, it seems
unlikely that independent variations in nonlabor
factor productivity are of great enough impor
tance to reverse the presumption that a sticky
wage and a fixed marginal-product-of-labor
schedule will generate a countercyclical real
wage, whether the measure of the business cycle
is employment or output.
■ 9
Like the classical economists he criticized, Keynes never seemed to
question the idea that labor was an input of fixed quality, whose productivity
was determined by iron laws of technology. The concept of labor as a homo
geneous physical input whose productivity is subject to rigid technological law
is not taken as seriously by today's economists as it was by British econo
Unfortunately for Keynes’ theory, real wages
have not been countercyclical as predicted. 10 The
literature on the behavior of real wages over the
business cycle is large, controversial, and defies
simple summary. The behavior of aggregate realwage measures over the business cycle has been
found to reflect changes in the composition of
employed labor as well as changes in the real
wage received by a representative worker. These
factors are difficult to disentangle. Lucas (1970)
attempted to resolve the real-wage puzzle by
showing that aggregation over straight and over
time pay rates masks an underlying real-wage
countercyclicity. On the other hand, aggregation
of young and experienced workers has been
found to bias downward the measured cyclicity
of the real wage. 1 1 By now it is probably the
consensus that, for the postwar U.S., real wages
for a representative worker are mildly procyclical
or at least acyclical. This unambiguously negates
the Keynesian prediction; the real-wage anomaly
arises even if the real wage merely fails to be
countercyclical. Some of the most important
recent studies leading to this conclusion are
Bodkin (1969), Mitchell, et al.( 1985), and Bils
(1985). Rayack (1987) offers a balanced and
fairly comprehensive bibliography of empirical
studies on the cyclical behavior of real wages.
As the mild procyclicity or acyclicity of the real
wage became regarded as a robust empirical
result, economists responded with a wide range
of proposed solutions to the real-wage puzzle—
a range that is a monument to the inventiveness
of the profession. Among the responses are
monopoly or oligopoly pricing models (Keynes
[1939], Modigliani [1977], and Okun [1981]);
allowance for prices being stickier than wages
(Blanchard [1986], and McCallum [1986]); the
general disequilibrium model (Barro and
Grossman [1976]); Lucasian capital dynamics or
Blinder inventory dynamics (both suggested by
Leiderman [1983]); retaining the sticky wage but
making prices equal to a markup over wages,
which makes the real wage essentially acyclical by
assumption (as in Taylor [1979a, 1979b, 1980]);
rejecting the notion of sticky wages as relevant to
the U.S. business cycle (as have partisans of the
real-business-cycle approach); or, most radically,
rejecting neoclassical economics in favor of
Ricardian or Marxian theory (Schor [1985]).
mists from Malthus and Ricardo to Keynes. A better understanding of laba is
a skilled attention to purposive activity, whose marginal value to an employer
is influenced by innumerable social and cultural conditions, such as the
weather, science, art, religion, politics, various international tensions, demo
■ 10
graphic and epidemic events, and other institutional and historical factors. The
changes in real wages and money wages would be negatively correlated. Dun
production function and the marginal product-of-labor schedule are useful ana
lop (1938) and Tarshis (1939) presented contrary evidence, evoking Keynes'
lytical devices subsuming the influence of all of these factors. But it is prepos
(1939) reply.
Keynes (1936) predicted, on the basis of the sticky-wage model, that
terous to insist that they remain frozen and do not contribute to macroeco
nomic fluctuations.
■
11
See, for example, Mitchell, et al. (1985).
Many of the solutions offered, particularly
those of economists favoring sticky-wage m od
els, will appear contrived or opportunistic, dis
turbing an idealized conception of scientific
method. Okun confesses that “ [w] ith a sufficient
display of ingenuity, a ‘quasi-Keynesian’ [stickywage] model can be concocted that is consistent
with the cyclical facts on productivity, real wages,
and factor shares....These analytical pyrotechnics
really illustrate that anything goes under condi
tions of monopoly . ” 12
However, ad hoc solutions are common and
useful elements of scientific practice. “ [W] ithin
what Kuhn calls ‘normal science’— puzzlesolving— [scientists] use the same banal and
obvious methods all of us use in every human
activity. They check off examples against criteria;
they fudge the counter-examples enough to
avoid the need for new models; they try out var
ious guesses, formulated within the current jar
gon, in the hope of coming up with something
which will cover the unfudgeable cases. ” 13 The
real-wage puzzle increasingly seems to be an
unfudgeable counterexample calling for some
modification of the sticky-wage model. My guess
of what can cover the unfudgeable case without
abandoning sticky wages is formulated in the
jargon of production functions and productivity
shocks, recently made current in macroeconom
ics by real-business-cycle theorists.
It is certainly remarkable that the productivity
solution to the real-wage puzzle has not, appar
ently, been explored before. However, a recent
contribution by Leiderman (1983, p. 77) came
close: “...the relationship between real wages
and economic activity to be found in a given
sample of data is likely to depend on the specific
real and monetary shocks that affected the econ
omy during the sample period. For example, it
seems quite plausible that the specific pattern of
wages/activity comovement emerging during
periods of important productivity (or technol
ogy) shocks would sharply differ from that aris
ing during monetary cycles.” Leiderman found
evidence that real wages declined in response to
unanticipated money growth, generating a coun
tercyclical pattern, if the oil shocks of the seven
ties, a kind of productivity shock, are controlled
for with dummy variables. Thus, Leiderman
approaches, but does not actually arrive at, an
explicit recognition that shifts in the productivity
■ 12
See Okun (1981), p. 19.
■ 13
See Rorty (1982), p. 572.
of labor (other than those associated with capital
or inventory responses to money surprises)
could generate procyclical real wages, consistent
with declining returns to labor.
Keynesians favoring sticky-wage models may
have overlooked or sometimes even dismissed
the productivity solution to the real-wage puzzle
because of doubt that autonomous variations in
labor productivity are important in the business
cycle. Literature in the real-business-cycle genre
has made the notion of productivity shocks
appear useful in accounting for procyclicity in
real wages. But this does not motivate a rejection
of sticky-wage models, which can incorporate
productivity shocks.
III. A Formal WageContracting Model
This section reconciles the Keynesian real-wage
mechanism with the stylized fact of mildly pro
cyclical real wages by extending Fischer’s (1977)
model, in which nominal wages are negotiated
in light of expectations of inflation. The exten
sion involves persistent or autocorrelated shifts
in the marginal-product-of-labor schedule, as
plotted against the level of employment, which
are taken into account in setting wages.
For example, a positive innovation in labor
productivity raises expectations of future produc
tivity because high productivity tends to persist.
Firms and workers bargaining over nominal
wages for the periods to come will take account
of the higher expected productivity. In particular,
money wages will be set at the expectation of
the marginal product of labor (at a targeted
employment level) times the price level. This
theory is well within the spirit of Keynes’ stickywage model, but also embodies the neoclassical
notion that wages reflect expectations of produc
tivity as well as expectations of inflation.
This amendment to the Keynesian sticky-wage
mechanism can easily account for a real wage
that is positively correlated with output. Consider
separately the effect of demand and productivity
shocks. An aggregate demand shock changes
output and the real wage in opposite directions.
A productivity shock changes output and real
wages in the same direction. In an economy sub
ject to both kinds of shocks, if supply shocks are
important, and if wage bargainers are adroit at
adjusting money wages to keep them in line
with the expected marginal revenue product of
labor, it is easy for an overall pattern of mildly
positive correlation between output and real
wages to arise.
It is somewhat more difficult to generate a
positive correlation between employment and
the real wage. In order to do so, productivity
shocks must have important positive effects on
employment. This is difficult because initially,
increased productivity, by raising output, reduces
the price level and raises the real wage at the
contract wage. The rise in the real wage reduces
the incentive of a firm to expand employment.
When a contract is subsequently renegotiated,
the real wage can be adjusted downward
(though it will remain above the level occurring
prior to the productivity improvement). This
downward adjustment in the real wage can pro
vide for expanded employment and is therefore
consistent with a preference among workers for
more employment at a temporarily high real
wage. A critical part of the mechanism for gener
ating a positive relation between the real wage
and employment under sticky wages is this
desire of workers to increase expected employ
ment under renegotiated contracts as the
expected real wage under the contract rises.
In the rest of this section, a formal model is
developed that is similar to Fischer’s (1977), but
which incorporates productivity shocks and
explicit profit-maximization by firms. The supply
behavior of firms implies a kind of Phillips curve
(equation 1 3 below) in which output supply
responds both to unbargained-for inflation and
to productivity. The model is completed with a
velocity equation ( 1 6 ) and a money-supply feed
back policy rule (17), and solutions for output,
employment, and real wages derived (18,19,20).
In the next section, the model here developed is
used to resolve the real-wage puzzle.
Following Fischer (1977), consider a hypo
thetical economy with two-period staggered, or
overlapping, contracts. The economy is com
posed of two groups of firms, identical in all
respects, except for the date at which currently
effective labor contracts were signed. Firms hav
ing signed wage contracts at the end of last
period
1 ) are referred to as group-one firms,
while those that signed wage contracts at the
end of the period before last
-2 ) are referred
to as group-two firms. The groups are competi
tive in that they take the commodity price as
given. Economy-wide aggregates are simulated
by taking the average of the two groups.
The firms’ production function is
(t -
(t
i
where Y is the output of a firm in group in
it
period
is the labor input of a firm in group
and Z is a global productivity shock. The mar
ginal product of labor is
t, Nit
i,
<2)
^
= zv (N‘ )(1" ”■» =
'
In logarithmic form, output is
(3)
y it = z, + y n it, i =
Ylt= ZtNjt ,
0
< 7
<1,
i=
1,2,
1, 2,
y, z,
n
where the lowercase letters
and
are natu
ral logarithms of their uppercase counterparts.
The ( log of the) marginal product of labor is
(4)
dYit
In (
i=
z t + ln ( 7 > ( 7 - l )n it,
=
1
,2 .
i
t, nd
it,
The demand for labor by firm in period
is given by the condition that the real wage
equals the marginal product of labor:
(5)
wit - p it) = z t + ln (y )+ (y -l)n d
it,
(
i=
1
,2,
where wit is the (log of the) wage received by
group firms’ workers in period and
is the
(log of the) price level. The notional (in the
sense of Clower [1965]) supply of labor to a
firm is conditioned on the real-wage rate:
i
t,
n% =
/30 +
/? !>
(6 )
,
0
i=
p
Px(u>it- p it\
1
,2.
If wages were not sticky, but varied to clear
the market, they would equal w ) the labor
*
market clearing wage, or the wage for which
labor demand equals the notional labor supply,
s
it:
nd = n
(7)
(1)
z
w*it =
where
J
p,
+
= [1 +
[In (
) -
7
(1 -
7
( 1
-7)/30]
J + Jz t>
)] _ 1 •
The contractual wage rate is the expectation of
the rate that would clear the labor market. The
contract wage for group is found by taking the
i
D
expectation of (7) conditioned on information
available in period t i , when the contract was
signed.
-
(13) y t = y [ f i 0 + P xln ( 7 )] J
1
________
1
(8 )
w*t = Et_ip t + [In (
+
7
) -
( 1
- y ) P 0]
J
+( 1 +
JEt-i z t >
z t = PjZM + e t ,
e t ~ N (0,
o2 ).
(
These elements are sufficient to specify the
supply sector of the economy, under the
assumption that labor input is demanddetermined:
(10)
ni t = n d
it.
Using (3), (5), ( 8 ), (9), and (10), it can be shown
that the (log of the) output of group one is
2 - 7/
(1 - 7 )
2
1- 7
_f
2
P1)jp]zt_2
+ y
where Et
is the operator that conditions random
variables on realizations at t - i and earlier.
Finally, let z t be a first-order autoregressive
process,
(9 )
‘
- 7
■
Equation (13) provides a characterization of the
supply sector of the economy. It can be thought
of as a kind of Phillips curve: the equation shows
that output depends on inflation not expected
when contracts were signed and on productivity
shocks, with coefficients that depend uniquely
on the elasticity of output with respect to labor
input, 7 , and on the elasticity of notional labor
supply,
It is useful to compare and contrast the modi
fied Fischer supply equation, (13), with the orig
inal Fischer supply equation, which was based
on the assumption that wage-setters seek to sta
bilize the real wage. In order to see the differ
ence clearly, rewrite ( 1 3 ) as
.
c+ (a + 2b)et + (a + b )pxt,_ x
(14) y t =
00
(11)
y lt = 7 [j30 + fixln ( 7 ) ] / +
+ a % P J, - t
f
J= 2
where
+ (1 +
+ p - ( p , - Et _ xp t),
a
=
I— SUL
1
where
b=
and the output of group two is
where c
-
+ — 1—
1- 7
t
(p, -Eh, p , ),
/'= 1
7
_ _____
_
2(1 - 7 )
=7
[0 O+ $ xln ( 7 )]/.
(12) y 2t = y[(3 0 + (3X n ( 7 )] J
1
+ —— e, +
1-7
'
e
1-7
+ (1 + /8 x)Jp\zt _ 2
1
-
7
(pt ~ Et-2 p t y
Total output for the economy (taken as the aver
age across firm groups) is
The parameter a shows the elasticity of the
response of output to productivity variations,
once wages adjust. The parameter shows the
extra output response of each group of firms that
occurs prior to recontracting, reflecting the advan
tage employers take of productivity advances not
yet reflected in wages. Both groups of firms are
in a position to take such advantage in the cur
rent period of a supply shock, but group-one
firms have already recontracted to reflect shocks
in period
These considerations explain
why the parameter is doubled in the e, - term,
why it appears singly in the
- term, and
why it does not enter in the e-terms of longer
lags. O f course, productivity shocks can also
influence output indirectly through their influ
ence on price surprises.
b
t- 1 .
b
et_ x
The modified equation (14) can be compared
with Fischer’s original:
O
O
(15)
y,= % + X ^ ' - j + 5i
2
S (/>,-
E,_ ,Pt )•
n5 and p6 do not influence output, but do
influence the behavior of the price level.
The final-form solutions for economy-wide
averages of output, employment, and the realwage are
(18)
There are two minor differences in output
supply behavior implied by (14) as opposed to
(15). First, the modified equation has terms for
productivity shocks, the
, that can be repres
ented as an ARMA( 1,2) process, while the original Fischer equation has productivity shock
terms that can be represented as an AR(1) process. Second, the coefficients of (14) are determined by the taste and technology parameters,
7
and , , and must obey special restrictions.
Yet (14) has much the same qualitative implica
tions for output and price behavior as (15). This
es
y t = k0 + y[p Q+ p xln ( )]/+ + y p x)et
y^^ + p ^2 - y j )
+
-y
+ 1 - 7J y pj €
1 - 7 JT
' J
y
r
\\
+
+
-y ^ +
7
2
( 1
1
2
1
2
5
1
(3
is so, even though they have potentially different
qualitative implications for the response of
employment to supply shocks.
In order to complete the model, specifications
of aggregate demand and monetary policy are
needed. Let aggregate demand be given by the
quantity theory equation, as
y, = mt - p t+vt , vt = p2vt _ j + A,,
(16 )
(19)
nt =
[/30 +
(3xln (
7
)]/+
p xet
+ ^
.
+ — — —--- -—
et_ j
2
- 7
+ (3 J ^ P \et
3
p1+ u ,
y= 2
1
,
+»
4 --- ^ . . . a n d
2-7
+
(20) ( wt - p t ) =
[In ( 7)- 0o 7)] J
(l-
+ [1 — 1 — ) Mi] e,
( 7
m
where
is the (log of the) quantity of money
and is the (log of the) velocity of money. As
indicated, velocity, t , is a stochastic first-order
autoregression, whose innovation, A t , is nor
.
mally distributed with variance
The money stock can be chosen by the poli
cymaker in light of his assumed information
about the state of the economy. The rule for
monetary policy is specified as
v
[1 + / ( 1
v
o£ .
- 7 )]Pj-(l - 7 V 2
2-7
00
+
- ( 1 - 7 X 1 + M)X/
4
j £ p \ et-j
7=2
_ (1 - 7 ) ( p 2 + m 5)
2-7
where / = [l + / ^ ( l -
(17)
mt = p0 + n { t + M
2 e/ - 1
+
+ M3 E
2
7
)]
- 1
.
z,_ x
+ M E /_ 2 *Vl >
6
IV. Determinants ot RealWage Cyclicity
where the
p x are choice parameters. The policy
Et _2 z t-\
rule’s arguments in
an^ E t - 2 v t - \ reP'
resent money responses to an infinite series of
past innovations realized in periods
and
earlier. This specification of monetary policy is
sufficient to satisfy output- or price-stabilization
objectives, for example, to minimize the variance
of either or
The policy rule parameters,
M4 » and ju5 help determine output behavior;
t-2
p 2,
y
p.
p x,
Whether or not real wages are procyclical (posi
tively correlated with output and employment)
depends upon the relative size of productivity
versus velocity innovations (a| versus
), upon
their autocorrelations
), upon the elastic
ity of notional labor supply with respect to the
real wage (/ ), upon the elasticity of produc
tion with respect to labor input ( 7 ), and upon
the policy rule (the
). In this section, some
(p x , p2
3X
p is
Id
examples displaying the dependence of realwage cyclicity on these elements provide a
robust basis for the view that procyclical or
acyclical real wages are consistent with sticky
nominal wages.
Consider a simple, benchmark example in
which the money supply is constant (/^( = 0 ,
i - 1 ,2 ...6 ) and notional labor supply is inelastic
(/3 j = 0). In this case, the final forms for
economy-wide averages of output
), employ
ment ( n ), and the real wage ( w - p ) are
(henceforth ignoring constant, or intercept
terms):
(y
(2i)
y, - Z=op Jt,.j+
,
-L p \
^ -7
j
(2 2 )
n = k t + — _\
'
(23)
'
2- 7
1’
(w,-p,)= X p ' t ' - j j=
- 1- 7
0
\
The correlation between output and the real
wage can be either positive or negative in this
example, depending on the relative importance
of contrary tendencies. Productivity innovations
have positive effects on output and real wages,
tending to create a positive correlation between
them. Contrariwise, demand shocks have posi
tive effects on output, but negative effects on real
wages, tending to create a negative correlation.
The benchmark example provides a plausible
illustration of how sticky wages are consistent
with either a positive or negative correlation
between real wages and output.
The example fails to provide an illustration of
how real wages and employment could be posi
tively correlated. This is because employment,
unlike output, is unaffected by the productivity
shocks, as may be seen in the absence of e-terms
in (22). The reason productivity increases do not
lead to employment increases is that productivity
increases also lead to identical increases in the
real wage, leaving firms’ labor demand un
changed. A one- unit rise in productivity raises out
put by one unit at the unchanging-employment
level, which— given the unitary elasticity of
demand inherent in the velocity equation— leads
to a one-unit fall in the price level. Thus, margi
nal labor productivity and the real wage both
rise by one unit, leaving the profit-maximizing
employment level unchanged. After old contracts
expire, there will be no adjustments to make to
the nominal wage, since the real wage is not
driven out of equality with labor productivity by
productivity shocks, and workers are satisfied
with supplying the unchanged employment level
(which would not be the case if notional labor
supply were elastic, or /?j> 0 ).
The correlation between the real wage and
employment is necessarily negative in the
benchmark case, reflecting the effects of demand
shocks. If the real-wage puzzle is to be fully
resolved, employment must respond positively
to productivity shocks.
At least four modifications of the simple
benchmark case can provide for positive employ
ment effects of productivity shocks. All seem to
be reasonable features of the world rather than
ad hoc contrivances. These modifications allow
for ( 1 ) notional labor-supply elasticity, /?j> 0 ; ( 2 )
monetary policy feedback,
0 ; ( 3 ) nonunitary elasticity of demand with respect to price;
and (4) less-than-complete, unilateral discretion
by the firm in choosing employment levels.
First, allow for a positive notional labor-supply
elasticity. This modification means that renego
tiating wage contractors will aim for less increase
in the real wage following a productivity innova
tion, in order to provide for a higher expected
level of employment— one matching the higher
notional labor supply induced by the higher
expected real wage. This means that, while the
nominal wage will be reduced under a new con
tract, it will not fall by as much as the price level
falls. After this modification, the final-form solu
tion for employment is
(24)
nt= \(3X
(1 -
7
) p 1 f /_ i
+ P i/ £ P i V y + M j T T ^ V i .
j= 2
r
which shows the positive delayed effect of a
productivity shock on employment if ,>0. The
e,_ ,-term reflects positive employment
responses of the first group of firms to renego
tiate (reduce) nominal wages; the e,_y-terms for
0 reflect responses by both groups. The
initial impact,
e remains at zero because
the effect of labor supply elasticity occurs only
through renegotiations of nominal wages, which
occur with a lag. In spite of this delay, allowing
/3
j>
dnt / d t ,
for labor-supply elasticity produces positive
employment effects of productivity shocks and
thus makes possible a positive correlation
between the real wage and employment.
Second, allow for monetary policy responses
to shocks. The effect of this modification will
depend on the kind of policy feedback intro
duced. The most plausible case would involve
negative responses to demand, ju4< 0 , /us 0 ,
<
0 ,
and positive responses to productivity,
^ > 0 , M2 > 0 , m3> 0 . Such responses could be
motivated by a price-stabilization objective, or by
a desire to alleviate the output- and employmentdistorting influence of sticky wages. The object
and effect of such a policy is to offset or elimi
nate demand shocks from the determination of
employment and output, and to encourage
employment and output to expand and contract
to more fully reflect positive and negative pro
ductivity shocks. Objective-seeking monetary
policy thus tends to reinforce the importance of
productivity relative to demand shocks and to
encourage positive employment responses to
productivity shocks, tipping the scales toward a
positive correlation between real wages and
both output and employment.
Interestingly, if policy sought to totally elimi
nate the effects of a sticky wage, it could do so
by setting the
appropriately. 14 Then, a
demand shock would have no impact, the real
wage would definitely be positively correlated
with both employment and output (assuming
y j> 0 ), and the economy would behave as if the
u
sticky wage was not a problem because the labor
market would always clear.
Third, allow for nonunitary elasticity of aggre
gate demand. This modification makes the
income velocity of money vary to cushion the
effect of either shock on the price level. By
reducing the deflationary consequence of a posi-
■ 14
Note that by assumption (10), the real labor demand condition is
always satisfied. So the monetary authority can get the labor market to clear
tive productivity shock, the modification moder
ates the real-wage increase accompanying such a
shock, encouraging a positive employment
response during the contract interval. One way
to implement the modification is to substitute
the IS-LM apparatus for the simple velocity equa
tion, but the resulting model’s complexity
requires a separate treatment.
Fourth, allow for the degree of discretion over
employment exercised by a firm to be less than
complete. Keynes and other Keynesians have
built sticky-wage models that assume that an
employer always chooses employment to equate
real wages with marginal labor productivity.
While analytically convenient, such an assump
tion is both extreme and unnecessary to give an
important role to a sticky wage. It is extreme
because it implies that employment bears no
neccesary relation to its market-clearing or
Pareto-optimal level. A more moderate approach
is to allow employment decisions to reflect both
the optimal employment level and the one-sided
discretionary profit-maximizing employment
level. One artifice for doing so is to let employ
ment decisions by firms be a weighted average
of the market-clearing employment level and the
demand at the fixed nominal wage. Formally,
with
replace ( 1 0 )
ni t - ndit
(25)
«„=0w * +( l- 0 ) w * ,
0<
0
<
1
,
n*t
where
is the market-clearing level of
employment. The lower the degree of firm dis
cretion, 4 > the less important are sticky wages in
,
determining economic outcomes. Just as in the
case of monetary policy feedback, this modifica
tion blunts the empirical impact of demand
shocks and increases the employment and out
put responses to productivity shocks, increasing
the correlation of the real wage with employ
ment and output.
V. A Numerical Example
of Procyclical Real Wages
each period by choosing a policy rule that keeps the employment-real-wage
relation on the notional labor supply schedule. This policy is given by
M -P]J , M =Pi/V ■ ="1 ^5=-02,fo J = f1^l(1
i
2
^4 r
+
with
/13
and
^
irrelevant. Then, assuming notional labor supply has a posi
tive response to the real wage, the real wage is necessarily procyclical, mea
sured against either employment or output. If policy sought to eliminate the
familiar Harberger welfare-loss triangles due to sticky wages, then sticky
wages would not imply countercyclical real wages. Ironically, such a policy
would conceal the potential importance of the sticky wage, and thus conceal
the usefulness of active policy feedback.
A numerical simulation provides an example of
procyclical real wages under nominal contracts.
The commodity supply equation is (13), pre
serving the traditional Keynesian assumption of
equality of the real wage and marginal labor pro
ductivity. The demand equation is (16), preserv
ing the unitary elasticity of demand with respect
to price. The parameter values assigned are
HI
(26)
7
= - , 0, = .5
5
° l = 2> al
= 5;
P\ = f>2 = 8-
In the money-supply function, (17), the particu
lar values for the feedback parameters were onehalf the values required to completely stabilize
the price level. (Choice of the values that com
pletely stabilize prices would have resulted in an
implausible simulation, and one whose numeri
cal results would have been uninteresting: the
effect of demand shocks on output, employ
ment, and the real wage would have been com
pletely removed, resulting in a positive correla
tion between output, employment, and the real
wage of nearly 1.) The policy parameters
assumed in the simulation are
(27)
n 2 = .56, n } = .48,
)U = .8,
j
= --5, M = --4,
s
^ 6
= -4
--
The example modifies the benchmark exam
ple in two ways: notional labor supply has posi
tive elasticity /^ = .5, and the money-supply rule
provides a positive response to a productivity
shock and a negative response to a demand
shock. The final-form equations for aggregate
output, employment, and the real wage are
(28)
y t = 1.50e,+ 1.07c,. j
oo
+ 1.20 2 (-8) j e t ,+ -25A.+ .13A, , •
'- J
7= 2
(29)
nt -
1.00e,+.53e,_ j
oo
+ .40
(30)
%
j=
(.8)
Jet
.+ ,50A,+ .27A,_, .
2
(wt - p t ) = .50et +.55et_1
oo
+ .80 2
j=
(.8 ) ' e , _ r .25A,- .13A, j .
2
The two modifications to the benchmark spec
ification are sufficient to generate positive cycli
city in the real wage: the correlation between
output and the real wage is +.67; between
employment and the real wage, +.15. Positive
correlations arise even though the variance of
the demand shock is five times as great as the
variance of the productivity shock, and even
though demand shocks actually account for a
slightly larger portion of the variance in
employment than do productivity shocks.
Incidentally, measured productivity or total
productivity of labor,
has the same cycli
cal behavior as the real wage, so that the procy
clicity of measured productivity of the postwar
U.S. economy can also be accounted for by the
sticky-wage model.
The numerical simulation provides an
implausibly high correlation between output and
the real wage, which is ironic in view of the puz
zle it was designed to resolve. The correlation
can easily be reduced by changing the relative
size of the disturbance variances or by other
adjustments in free parameters. However, it is
difficult to reduce the correlation between out
put and the real wage to realistic levels without
making the correlation between employment
and the real wage negative, unless more funda
mental changes in the model are made. Addition
to the model of some elements of price sticki
ness, partial indexation of wages to the price
level, and other features of a complete macroeconomic theory might help make a sticky-wage
model capable of accounting even more closely
for the stylized facts of the business cycle. Such
an effort, while indicated, goes beyond the
scope of the present article.
yt - nt ,
VI. Conclusion
The analysis has shown that introduction of pro
ductivity factors into the determination of wages
and employment permits sticky-wage models to
generate positive cyclicity in the real wage.
Hence, the notion of the sticky wage cannot be
rejected on grounds that it is inconsistent with a
procyclical real wage. By the same token, the
analysis suggests that allowance for autonomous
cyclical variations in labor productivity and
forward-looking expectations are very useful in
resolving the real-wage puzzle, and may point
out the incompleteness of simple sticky-wage
models lacking these features. This incomplete
ness can be remedied without reducing the use
fulness of the sticky-wage notion. While the sticky
wage cannot alone explain or account for an
observed procyclical real wage, the usefulness of
sticky-wage models has always been seen else
where, specifically in understanding the effect of
nominal variables, like money and prices, on
real variables, such as output and employment.
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ing.
foum al of Money, Credit, and Bank
Real Business
Cycle Th e o ry:
a Guide, an Eva lu a tio n ,
and N e w Directions
by Alan C. Stockman
Alan C. Stockman is a professor of
economics at the University of
Rochester and was formerly a visit
ing scholar at the Federal Reserve
Bank of Cleveland. The author would
like to thank the Federal Reserve
Bank of Cleveland for research
support.
Introduction
The purpose of real business cycle (RBC) mod
els is to explain aggregate fluctuations in busi
ness cycles without reference to monetary policy.
Much of the existing RBC analysis also seeks to
explain fluctuations without reference to market
failures, fiscal policies, or even disturbances to
preferences or demographics.
The concentration on technology shocks that
characterizes most, though not all, of the current
models is not in principle a defining feature of
RBC analysis. This concentration indicates both
the early state of research and the substantial
progress that has been made by considering
technology shocks.
This paper summarizes and evaluates in a
mostly nontechnical way the state of RBC theory,
outlines some useful directions for research in the
area, and discusses the implications of this
research on economic policy. For space reasons, I
■
1
Earlier nontechnical introductory essays on RBC models include Walsh
(1986) and Rush (1987). Manuelli (1986) summarizes Prescott's arguments,
Summers’ criticisms, and Prescott's reply. More recent summary papers
include McCallum (1989) and M ankiw (1988).
will regard sectoral-shift models (Lilien [1982],
Abraham and Katz [1986], Loungani [1986],
Davis [1987], Hamilton [1987a], and Murphy
and Topel [1987]) as a separate topic that
deserves its own treatment, though those models
clearly form one class of RBC theory.1
Real business cycle analysis is important and
interesting for several reasons. First, the evidence
that monetary policy affects real output is much
weaker than most economists had thought.
Second, even if monetary policy affects real out
put, the evidence that it is the dominant influ
ence on business cycles is also much weaker
than previously thought. A detailed discussion of
the evidence on these topics is beyond the
scope of this essay; see, for example, Barro
(1987), Eichenbaum and Singleton (1986),
Christiano and Ljungqvist (1988), and the refer
ences cited in those works.
Third, even if monetary disturbances play a
major role in many real-world business cycles,
most economists believe that supply shocks and
other nonmonetary disturbances, originating
from sources such as oil price changes and tech
nical progress, also play important roles in some
aggregate fluctuations.
RBC analysis is designed to determine how
such “real” shocks affect output, employment,
hours, consumption, investment, productivity,
and so on. RBC models are also designed to
n
A
B
L E
1
I. A Prototype Real
Business Cycle Model
U .S . Business Cycle Statistics,
19 5 4 :IQ -19 8 2 :IV Q
What Real Business Cycle
Models Try to Explain
Corr.
with
Standard
Deviation GNP ( -1)
Variable
Corr.
with
GNP
Corr.
with
GNP ( + 1)
GNP
1.8%
.82
1.00
.82
Consumption
On services
Nondurables
.6
1.2
.66
.71
.72
.76
.61
.59
Fixed
investment
Nonresidential
Structures
Equipment
5.3
5.2
4.6
6.0
.78
.54
.42
.56
.89
.79
.62
.82
.78
.86
.70
.87
Average nonfarm
hours worked
In mfg. only
1.7
1.0
.57
.76
.85
.85
.89
.61
GNP/hours
1.0
.51
•34
-.04
1.7
.15
.48
.68
.4
-.20
-.03
.16
1.0
.03
•23
.41
Capital stocks:
Nonfarm
inventory
Nonresidential
structures
Nonresidential
equipment
NOTE: Corr. = correlation. All data were first detrended with the HodrickPrescott filter.
SOURCE: Prescott (1986a).
determine how disturbances at a specific time or
in one sector of the economy affect the economy
later and in other sectors, and to study the
dynamics of the transitions.
Fourth, RBC models can be used to determine
how any disturbance, even if monetary in origin,
spreads through different sectors of the economy
over time. While monetary policy, or monetary
disturbances, may frequently set business cycles
in motion, it is possible that the subsequent
dynamics and characteristics of the cycles differ
little from those that would have resulted from
disturbances to tastes or technology. That could
explain the evidence on seasonal cycles without
precluding money as a major force in business
cycles. Whether or not the more extreme claim
that monetary policy is unimportant for business
cycles turns out to be correct, RBC analysis is
making important contributions for the third and
fourth reasons cited above.
The characteristics of business cycles that the
RBC models have been designed to explain
include the sizes of the variances and covari
ances in table 1. Among these characteristics are
the following:
1. Consumption varies less than output, which
varies less than investment; the standard devia
tion of investment is three to five times that of
output. Consumer purchases of durables vary
about as much as investment, while purchases of
nondurables and services vary less but remain
procyclical (defined to mean positively corre
lated with output).
2. Hours worked are procyclical and vary
about as much as output.
3. The average product of labor is procyclical
and varies about half as much (in standard devia
tions) as output; the correlation between pro
ductivity and output is smaller than the correla
tion between hours and output.
Some RBC models attempt to explain other
characteristics. For example, Long and Plosser
(1983) have a multisector model that attempts to
explain why output moves together across most
sectors of the economy (including various
manufacturing industries, retail and wholesale
trade, services, transport, and utilities, with agri
culture the main exception) as well as why tem
porary disturbances have longer-lived effects.
Christiano (1988) adds inventories to an RBC
model to try to account for the fact that quarterly
changes in inventories are about half the size of
changes in GNP, even though inventories are on
average only a small fraction, about 0.6 percent,
of GNP. Kydland and Prescott (1988) also
attempt to explain inventory behavior, particu
larly inventories of goods in process, through
their time-to-build technology.
Real business cycle models have not yet been
developed to address still other features of busi
ness cycles:
1. Nominal money and real output are highly
correlated; most of this correlation is with inside,
rather than outside, money (compare with Barro
[1987]).
2. Prices vary less than quantities.
3. Nominal prices are acyclical.
4. Real wages are acyclical or mildly
procyclical.
5. Real exports, imports, and net exports (the
balance of trade surplus) are all procyclical.
Backus and Kehoe (1988) and Phillips (1988)
have documented the last feature; they have
shown that many of the same qualitative features
found in U.S. business cycles also characterize
business cycles in other countries. I will argue
below that
differences across coun
tries in business-cycle phenomena and the cycli
cal behavior of international trade variables can
form important new sources of evidence on RBC
models. The fourth feature, the acyclical or
mildly procyclical behavior of real wages, has
been addressed recently by Christiano and
Eichenbaum (1988), who conclude that existing
models do not adequately explain this fact.
quantitative
A Description of a Prototype
RBC Model
Real business cycle models typically begin with
assumptions such as (1) there is a representative
household that maximizes the expected dis
counted value, over an infinite horizon, of a util
ity function defined over consumption and lei
sure, or (2) there is a constant-returns technology
that transforms labor and capital into output,
which may be consumed or invested to augment
the capital stock in the next period.
In most RBC models, the production function
is subject to random disturbances. Firms are per
fectly competitive, and there are no taxes, public
goods, externalities, or arbitrary restrictions on
the existence of markets. The maximization
problems for households and firms imply deci
sions for consumption, investment, the division
of time between labor and leisure, and, thus,
output (along with the capital stock, which is
predetermined from last period). These deci
sions are functions of the
the
capital stock and the exogenous disturbance(s)
to the production function.
Given some particular production and utility
functions, an initial capital stock, and a stochastic
process for the random disturbances, the model
can be solved for the decision rules and, there
fore, for the probability rules for all of the endog
enous variables.2 These probability rules then
yield variances, covariances, and other statistical
moments that can be matched against real-world
data. A more technical description of a simple
RBC model, in a multicountry context, is pre
sented in section VI.
state variables:
■ 2
The key technical papers on which the RBC models are based are
Brock (1982) and Donaldson and Mehra (1983).
In principle, with enough freedom to choose
arbitrary production and utility parameters and
parameters of the stochastic process on the exog
enous disturbances, one can always find variants
of the model that match any given set of variances
and covariances from real-world data. Lawrence
Summers has criticized RBC models on this
issue, claiming that it is easy to find incorrect
models that match any given set of observations.
Obviously, to avoid this kind of criticism, RBC
models must use some additional information to
limit the arbitrary choices of utility and produc
tion parameters and exogenous stochastic proc
esses. In the limit, it would be desirable to elim
inate
arbitrary choices of parameters by
relying solely on other information to parameter
ize the model, and then by showing that the
model necessarily reproduces the kinds and
characteristics of aggregate fluctuations that are
observed in real-world data. Then there would
be little controversy over Prescott’s (1986a)
assessment that
it would be puzzling if the
economy did not display these large fluctuations
in output and employment with little associated
fluctuations in the marginal product of labor.”
Early RBC models, such as Long and Plosser
(1983), made some of their assumptions in
order to obtain analytically tractable models, so
that the models would actually have closed-form
solutions. The assumptions required to obtain
analytic solutions to the models, however, are
very stringent and, obviously, totally ad hoc.
Consequently, RBC theorists have largely aban
doned attempts to make their models analyti
cally tractable and have instead turned to numer
ical solutions. Quantitatively accurate models are
ultimately more appealing than analytically trac
table models, anyway. The parameter restrictions
from outside information used in RBC models
are discussed in section II.
all
Some Variations on the
Prototype Model
Kydland and Prescott (1982, 1988) include a
number of additional features in their model, in
cluding time to build (so that investment cannot
be installed instantly but only after a lag), varia
ble utilization of capital, lagged effects (as well
as contemporaneous effects) of leisure on utility,
and imperfect information about productivity.
Hansen (1985) adds lotteries on employment
(Rogerson [1984, 1988]) to the Kydland-Prescott
model. People are assumed to be able to work
either full time or not at all, rather than part time.
If productivity conditions dictate that everyone
would work part time if labor were divisible, a
a
some
Pareto-optimal allocation may involve
peo
ple working full time and others not working,
The
choice of who works and who does not is
assumed to be determined totally randomly, by
an exogenous lottery.
Economies with this random allocation give
everyone higher expected utility than economies
without it. Hansen’s application of Rogerson’s
theory to the Kydland-Prescott model results in a
better match between the model and the data for
the variability of hours worked (relative to the
variance of GNP), but results in a poorer match
for the average product of labor. Hansen’s model
also requires smaller exogenous productivity dis
turbances to generate the same variability of GNP.
Greenwood, Hercowitz, and Huffman (1988)
investigate a model with shocks to the expected
return to current investment that do not affect
current output. These shocks raise investment in
their model (the substitution effect dominates the
wealth effect) and induce intertemporal substitu
tion in labor supply, so that more labor is cur
rently supplied in order to take advantage of the
good investment opportunities. In addition, the
utilization rate of existing capital rises to increase
output and take advantage of these opportunities.
The higher utilization rate of existing capital
raises the marginal (and average) product of
labor. This raises the opportunity cost of current
leisure to households and induces them to sub
stitute into greater current consumption. Con
sumption also increases because of the wealth
effect associated with the technology disturbance.
In the Greenwood, et al. model, these two
forces tending to raise consumption dominate
the intertemporal substitution effect, which tends
to reduce consumption so that households can
use the goods they otherwise would have con
sumed in order to augment investment, which
the technology shock made more productive. So
consumption rises along with labor supply, out
put, investment, the capacity utilization rate, and
the marginal and average products of labor.
It should be noted that in this model, fluctua
tions in current output do not result directly
from assumed changes in current technology7
,
since that technolog}7affects only
output
by augmenting the increase in future capital
obtained from one unit of current investment.
The entire increase in
output in the
model results from economic forces responding
to this productivity shock.
Kydland and Prescott (1988) also added varia
ble utilization of capital to their earlier 1982
model by introducing an endogenous workweek
of capital. In contrast to Greenwood, et al.,
where greater utilization raised depreciation,
even though people are identical ex ante.
future
current
Kydland and Prescott assume that the cost of
greater utilization (that is, a longer workweek) of
capital is greater utilization (a longer workweek)
of labor. They find that their model, with a varia
ble workweek and with technology shocks meas
ured as in Prescott (1986a), predicts essentially
all of the observed variance in U.S. aggregate
GNP, substantial variability for inventories (with
results somewhat sensitive to the definition of
inventories), and greater variation in hours
worked than in their original model (but still
below measured variation).
Benzivinga (1987) and Christiano (1988) exam
ine models in which shocks to preferences play
an important role. Parkin (1988), in contrast, finds
little role for preference shocks in his model.
Parkin uses data on labor’s share of GNP at
each moment in time to obtain a time series on
the corresponding parameter in the CobbDouglas production function. He assumes, fol
lowing Solow — and in contrast to Prescott —
that this function varies over time. He then uses
this time-varying parameter and the production
function to measure the multiplicative technol
ogy shock at each point in time (one can think
of the time-varying parameter representing
labor’s share as a second productivity shock).
Given measured wages, labor time, consump
tion, and the rental price of capital (taken as the
average payment to capital), Parkin then com
putes a time series for the utility parameters in his
model and the depreciation rate. He describes
this procedure as “solving the model backwards,”
by which he means that he calculates, given the
model, what the parameters must (approxi
mately) have been to generate observations on
the time series of output, consumption, and so
on. Unlike most other business-cycle models,
Parkin allows some parameters to vary over time
in order to fit the data (almost) exactly.
Parkin then displays these implied time series
and argues that they support RBC models in the
following senses: (1) none of the parameters
except the productivity term varies much over
time, and (2) the values of the parameters are
not wildly out of line with what would have
been expected, based on other information.
Parkin’s assumed utility function takes the
form of the expected discounted value of
(
- s)/ s ?w here
is consumption, is lei
c(1
y
c
s
I
sure, and with the parameter (the share of
leisure) and the discount rate time-varying. Parkin
estimates the mean of 5 at .828, and the percent
age change in has a mean of only .026 with a
variance of .007. This parameter is therefore stable
over time, implying that shocks to preferences, at
least of this form, are unimportant to RBC mod
els, and that people allocate about one-sixth of
s
their total time to working. This estimate is
smaller than the one-third value used in some
other studies, but is consistent with the value
cited by Eichenbaum, Hansen, and Singleton
(1986) and is the value preferred by Summers
(1986) in his critique of Prescott.
Parkin’s estimated discount parameter varies
somewhat more over time, and is somewhat
higher than expected: its mean is consistent with
an average real interest rate of 12 percent per
year, which is too high. Labor’s share is esti
mated to be 58 percent, as compared to the 64
percent figure used by Prescott based on histori
cal data with the services of consumer durables
included as part of output.
Finally, Parkin, after accounting for measure
ment error in labor and capital, examines the
connection between changes in the money
supply and variations over time in the parame
ters of the model, including productivity shocks.
He finds little connection, either contemporane
ously or at leads or lags, between money and the
parameters of the model.
Christiano and Eichenbaum (1988) add
government consumption shocks to an RBC
model to induce shifts in labor
These
shifts, along with shifts in the marginal product
of labor due to technology shocks, might induce
acyclical or mildly procyclical real wage changes,
as in the data. The authors argue that govern
ment consumption is insufficiently variable to
reduce (by very much) the highly procyclical
movements resulting from productivity shocks.
Further work with preference shocks or technol
ogy shocks, as in Greenwood, et al., may be
promising in this regard.
supply.
II. Restrictions on
Parameters and
Functional Forms
Several sources of restrictions have been used to
determine the appropriate functional forms and
parameter values, aside from the behavior of the
macroeconomic variables that the models seek
to describe:
1.
The fraction of total time spent working
(and, consequently, the time spent at leisure,
which enters the utility function) enters most of
the models as a parameter. Some studies, such as
Prescott (1986a), have used the figure of onethird, while others, such as King, Plosser, and
Rebelo (1988a), have used one-fifth based on
historical measurement of average weekly hours
worked in the U.S. in the postwar period.
Summers (1986) and Eichenbaum, et al. (1986)
suggest one-sixth, which is close to the value
found by Parkin (1988).
2. The psychological discount rate enters all
of the models as a parameter (or a variable, as in
Parkin’s model). King, et al. choose this parame
ter at .988 per quarter to obtain an average real
interest rate of 6.5 percent per year. Kydland and
Prescott, Hansen, Greenwood et al., and others
choose discount factors of .96 percent per year
rather arbitrarily.
3. The rate of capital depreciation enters the
models as a parameter. Kydland and Prescott
assume a depreciation rate of 10 percent per
year, on the grounds that the steady-state capital
stock would then be about 2.6 times annual out
put if the real interest rate is 4 percent per year,
and this 2.6 figure is close to the historical aver
age in the United States. Most other models also
assume 10 percent. Christiano (1988) assumes
that capital depreciates at 1.83 percent per quar
ter, in order to try to match average U.S. data for
the change in the public and private capital
stock, including consumer durables, as a fraction
of output. Greenwood, et al. have a variable
depreciation rate depending on the utilization
rate of capital. They assume that the elasticity of
the depreciation rate with respect to the utiliza
tion rate is 1.42, chosen to yield a deterministic
steady-state rate of depreciation in their model
equal to .10 per year.
4. The marginal rate of substitution over time
in consumption, which corresponds to the
degree of relative risk aversion (say, ) for intertemporally separable utility functions, enters the
models as a parameter. Log utility is frequently
assumed, as in Kydland and Prescott (1982),
implying that
1. Greenwood, et al. report
results for
1 and
2, based on estimates by
Hansen and Singleton (1983) and Friend and
Blume (1975); Kydland and Prescott (1988)
assume
1.5.
5. The marginal rate of substitution over time
in leisure is an important parameter of most of
the models. King, et al. (1988a) assume alter
nately that (a) utility is logarithmic and separable
between consumption and leisure, as well as
over time, giving a value of unity for the elasticity
of the marginal utility of leisure with respect to
leisure, or (b ) the elasticity of the marginal util
ity of leisure is -10, based on panel data studies
reviewed by Pencavel (1986), or (c) the elasticity
is zero, which yields a linear utility function in
leisure and so an infinite intertemporal substitut
ability of leisure, based on theoretical considera
tions of an economy with indivisible labor and
lotteries, examined by Rogerson (1984, 1988)
and Cho and Rogerson (1988).
The latter study examines an economy popu
lated by families in which males are primary
r
r=
r=
r=
r-
m
workers with an elasticity of intertemporal substi
tution close to zero, and females have the same
preferences as males but, because of the fixed
costs of having both parents in the labor force,
females have a larger (but finite) elasticity of
intertemporal substitution of labor. The authors
show that, as in Rogerson’s earlier work, the
economy behaves as if the elasticity of
substitution were infinite. This linear specifica
tion based on Rogerson’s work is also adopted
by Christiano. Greenwood, et al. choose the
absolute value of the elasticity of marginal utility
of labor supply with respect to labor supply to
be .6, based on studies by MaCurdy (1981) and
Heckman and MaCurdy (1980, 1982) that give
estimates of the inverse of this number that
range from .3 for males to 2.2 for females. The .6
figure chosen by Greenwood, et al. corresponds
to an intertemporal elasticity of substitution of
labor equal to 1.7.
6. Labor’s share of total GNP is another impor
tant parameter in existing RBC models. Prescott
estimates the share to be 64 percent, based on
historical data with the services of consumer
durables included as part of output, and this fig
ure has been adopted in other studies as well.
Without treating services of durables in this way,
the historical share is higher, around 71 percent
since 1950. This higher figure has been used in
some other studies, such as Greenwood, et al.
Christiano (1988) argues that accounting for
measurement error places labor’s share in the
range of 57 percent to 75 percent; he assumes 66
percent.
7. The variance and autocovariances of produc
tivity shocks play an important role in most RBC
models. Prescott ( 1986a) estimates productivity
shocks as the residuals from an aggregate CobbDouglas production function, with labor and
capital inputs, estimated in first-difference form.
He estimates that the standard deviation of these
productivity shocks is 1.2 percent per quarter
between 1955 and 1984, and that the technology
shock is close to a random walk with drift plus
serially uncorrelated measurement error. After a
downward revision (that he argues is required
because of measurement errors in the labor and
capital inputs), Prescott ends up with an estimate
of the standard deviation of .763 percent per
quarter, and a first-order autoregressive coeffi
cient of .95. Hansen also makes this assumption.
In Greenwood, et al., productivity shocks affect
only future output from current investment, and
not current output directly. Less serial correlation
of productivity shocks is required in this model,
in order to replicate the first-order autocorrela
tion of output in the U.S. data. The authors esti
mate that the first-order autocorrelation of pro
aggregate
ductivity shocks is about .50 per year, while the
figure of .95 per quarter would imply .81 per year.
Still other restrictions are specific to particular
variations on the prototype RBC model. These
include the relative wage of men and women,
which appears in Cho and Rogerson and is
chosen to be .6 on the basis of evidence from
the Current Population Survey from 1979-84. The
growth rate of the economy is another parameter
that appears in some models. Prescott (1986a)
sets the growth rate at zero, after using the
Hodrick-Prescott filter, on the grounds that the
character of fluctuations does not depend greatly
on the growth rate.
The Kydland-Prescott (1988) model requires as
parameters the elasticity of substitution between
inventories and other factors of production, and
a production-function parameter that determines
whether variation in total hours occurs through a
longer workweek or through more employees
per hour; there is currently little evidence on
which to base choices of such parameters.
As will be discussed in section VI, there are
some quantitative differences between the United
States, the United Kingdom, and Japan in fea
tures of business cycles. RBC models imply that
some of the parameters discussed above should
differ across these countries and that these dif
ferences should explain the observed differences
in business cycles. There has not yet been much
research devoted to determining these differences
in parameters and examining whether they suc
cessfully explain cross-country differences.
III. Business Cycles
and Long-Run Growth
A number of economists have recently argued
that the traditional distinction between issues
involving long-run secular growth on the one
hand, and short-term fluctuations in GNP asso
ciated with business cycles on the other, is mis
placed, and that business cycles and long-run
growth are intertwined.
Nelson and Plosser (1982) argue that there is
a secular or growth component to real GNP that
is nonstationary, and another component that is
stationary. They find that, empirically, the var
iance of the innovations to the nonstationary
component is larger— the standard deviations
are from one to six times as large— than the var
iance of the innovations to the stationary com
ponent. Given the assumption that monetary dis
turbances have only temporary effects on real
output, Nelson and Plosser argue that
real
(nonmonetary) disturbances are likely to be a
much more important source of output fluctua-
T A B L E
2
U .S . Business Cycle Statistics,
19 5 4 :IQ -19 8 2 :IV Q
Classified by Hamilton's "Normal
States” and “ Recession States"
First-Difference Filter
Normal States
(103 observations)
Standard
Deviation
Variable
GNP
. 7%
Consumption
Total
On services
Nondurables
Corr.
with
GNP
Recession States
(36 observations)
Standard
Deviation
Corr.
with
GNP
1.00
.9
1.00
.6
.4
.7
.50
.09
.26
.7
.5
.7
.45
.21
.27
2.3
2.6
2.7
3.5
.48
.28
.28
.23
2.7
2.4
2.7
3.2
.68
.74
.41
.76
Average nonfarm
hours worked
In mfg. only
.4
.8
.26
.32
.4
.8
.12
.21
Employment
.6
.29
.7
.45
Productivity =
GNP/total hours
.9
.56
1.0
.68
Fixed
investment
Nonresidential
Structures
Equipment
NOTE: Corr. = correlation. Hamilton’s recession states during this period
are (dates are inclusive) 1957:IQ-1958:IQ, 1960:IIQ-1960:IVQ, 1969:IIIQ1970:IVQ, 1974:IQ-1975:IQ, 1979:IIQ-1980:IIIQ, and 19 8 1:IIQ 1982:IVQ.
Other dates in this period are normal states.
SOURCES: Hamilton ( 1987b) and Citibase.
tions than monetary disturbances.” They also
note that their conclusion
is strengthened if
monetary disturbances are viewed as only one of
several sources of cyclical disturbances.”
Subsequent work by Campbell and Mankiw
(1987b), Clark (1987), Cochrane (1986), Evans
(1986), Stock and Watson (1986), and Watson
(1986) has generally corroborated the finding
that real GNP has either a unit root (a nonstationary component) or a root that is close to unity
(the power of the test for a unit root versus a
root of .96 is small). However, measures of the
relative sizes of the nonstationary (if it exists)
and stationary components vary depending on the
methods used. Cochrane, for example, finds that
there may be a random walk component to GNP,
but that its innovation variance is small relative
to the variance of the transitory component. The
difference between his finding and that of Nelson
and Plosser results largely from his use of informa
tion from autocorrelations at long lags. Cochrane
finds that the in-sample behavior of real GNP is
represented well by a second-order autoregres
sive process around a deterministic trend.
Hamilton ( 1987b) estimates a simple nonlinear
model of real GNP in which the economy shifts
periodically from its “normal growth states” into
“recession states” associated with negative aver
age growth rates. Hamilton’s model is an alterna
tive to the assumption made in most previous
work, that the first-difference of GNP is a linear
stationary process (either white noise or purely
deterministic). He uses a time-series model for
real GNP that involves a stochastic trend: a random
walk with drift in which the drift term takes one
of two values, depending on the state of the econ
omy. The state itself is a stationary Markov proc
ess. GNP is the sum of this stochastic trend com
ponent and a zero-mean ARIMA(4,1,0) process.
Hamilton’s nonlinear model implies that a
term is missing from an AR(4) model of the
growth rate of GNP (a standard linear representa
tion), and that addition of the extra term yields a
large and significant coefficient, indicating that
the nonlinear model is a better predictive model
than the linear model.
He finds that, first, the dynamics of GNP dur
ing recessions are considerably different from
the dynamics during normal, nonrecession peri
ods. In particular, the economy is expected to
grow at a rate of 1.2 percent per quarter during
normal times and at a negative rate, -0.4 percent,
during recessions. If the economy is in a normal
state, there is a 90 percent chance that it will
remain in the normal state next quarter; if the
economy is in a recession, there is a 75 percent
chance it will remain in that state next quarter.
This suggests that there may be differences in
the “facts” regarding business cycles across those
states, and that these facts should be included in
tables that RBC models seek to replicate. Table 2
shows that the main difference in correlations
with GNP between normal states and recessions
occurs in nonresidential investment, which is
much more highly correlated with GNP during
recession states.
Second, Hamilton finds that business cycles
are associated with large
effects on
the level of output. When the economy enters a
recession, current output falls on average by 1.5
percent, while the permanent level of output
falls by 3 percent. When the economy is in a
normal state, a 1 percent fall in output reduces
permanent output by two-thirds of 1 percent. In
fact, Hamilton’s results imply that most of the
dynamics of GNP result from switches in the
permanent
ill
state of the economy generating the stochastic
growth component rather than from the ARIMA
process added to this component.
Finally, he finds that the dating of recessions
estimated by the nonlinear model closely repli
cates the NBER dating. Hamilton’s results suggest
that while business cycles and long-term growth
are subtly related, they are also separable in that
one can study the switches between states of the
economy, and characteristics of the recession
states, separately from the characteristics of the
normal growth state.
King, Plosser, and Rebelo (1988b) argue that it
is inappropriate to study business cycles and
long-term growth separately for two reasons.
First, business cycles may
changes in the
long-run growth path. Using models based on
Romer (1986) and Lucas (1988), the authors
construct examples of economies in which
purely temporary shocks permanently affect the
level of output. Similarly, permanent shocks (or
policies) can change the economy’s long-term
rate of growth. While Hamilton’s nonlinear
model suggests that temporary shocks have
permanent effects, it also suggests that business
cycles differ substantially from “normal” changes
in the long-run growth path.
Second, the authors argue that the characteris
tics of long-term growth—such as constancy of
growth rates (although see Romer [1986]),
rapidly rising consumption per capita with con
stant or only slowly rising leisure per capita, and
the absence of a strong secular trend in the aver
age real interest rate— imply restrictions on forms
of production and utility functions and on their
parameter values, and that RBC models must be
made consistent with these restrictions. As
McCallum (1989) argues, "... if technical change
were exogenous, then there would be little neces
sary relation between the magnitude of growth
and the extent of cycles, as they depend on two
different aspects of the technical-progress proc
ess...” (that is, the mean and the short-term varia
tions from this mean). However, even with exog
enous growth, there are restrictions on the model
that are required to produce steady-state growth,
or large secular increases in real wages with a
small reduction in hours worked, and so on.
be
IV. Seasonal Fluctuations
and Business Cycles
Barsky and Miron (1988) have shown that
deterministic seasonal fluctuations in macroeco
nomic variables exhibit the same characteristics
(discussed above) as fluctuations at businesscycle frequencies. In addition, the seasonal fluc
tuations are large relative to the business-cycle
fluctuations.
Using quarterly data, the authors find that
deterministic seasonal fluctuations account for
more than 85 percent of fluctuations in the
growth rate of real GNP and over half of the fluc
tuations in real GNP relative to trend. Similar
measures of the quantitative importance of sea
sonal fluctuations relative to business-cycle fluc
tuations apply to other macroeconomic time se
ries, such as consumption, investment, the labor
force, hours worked, and so on.
More important, they find that the
and
of movements in var
ious macroeconomic variables are similar for
seasonal and business-cycle fluctuations. This
similarity also applies to the positive comove
ments of monetary aggregates and real output.
As Barsky and Miron conclude, this “...suggests
the possibility of a unified explanation of both
business cycles and seasonal cycles.” Miron
(1988) has shown that the same qualitative con
clusions also apply to seasonal and businesscycle fluctuations in many other countries.
If one accepts the view that business cycles
and seasonal cycles have the same explanation—
and are the results of the same types of distur
bances as well as the same propagation
mechanisms— then these results cast doubt on
some popular theories of business cycles. Such
theories include those based on unperceived
monetary disturbances and confusion of sellers
about changes in nominal and relative prices (as
in Lucas [1975, 1982] and Barro [1976, 1980])
and those based on unanticipated changes in
economic conditions in the face of predeter
mined nominal wages or prices. The seasonal
changes in average weather and seasonal occur
rence of holidays, such as Christmas, are clearly
both perceived and anticipated.
An alternative, weaker, interpretation of the
Barsky-Miron results is that business cycles and
seasonal fluctuations are the results of different
underlying disturbances (with the former unan
ticipated and the latter anticipated), but that
most of the key features of business cycles are
driven by the propagation of these disturbances
through the economy and are largely indepen
dent of the source of the disturbance. Under this
interpretation, monetary, rather than real, distur
bances might play an important role in instigating
business cycles. But RBC analysis would be
extremely important in trying to understand the
characteristics of business cycles, because the
propagation mechanism studied in these models
would be responsible for generating the particu
lar comovements and relative sizes of movements
of economic variables that are observed. In this
ments
relative sizes
comove
sense, the focus on RBC analysis as a means of
determining how disturbances affect the econ
omy and how they spread through different sec
tors of the economy over time (the third and
fourth reasons for RBC analysis mentioned in the
introduction) would be very important.
economy, negative productivity growth is com
monly observed. Are all of these individual
experiences of negative productivity growth to
be attributed to monetary policy or macroeco
nomic coordination failures? Would such a tradi
tional macroeconomic explanation of these neg
ative productivity shocks— providing such a
model could even be built— be a
better explanation than an RBC explanation?
quantitative
V. Criticisms of Real
Business Cycle Models
Several popular criticisms that have been levied
against RBC models are presented here, along
with some responses to those criticisms. For
further arguments, see Summers (1986) and
Prescott (1986b).
What Are These
Technology Shocks?
An additional question, posed by Robert Hall
(1988), is how to interpret periods in which real
output actually falls: what are the negative tech
nology shocks? Summers, having suggested that
oil price changes could constitute such a shock,
cites a study by Berndt (1981) which concludes
that energy shocks had little role in the fall in
manufacturing labor productivity from 1973 to
1977. Summers also asks, “What are the sources
of technical regress? Between 1973 and 1977, for
example, both mining and construction dis
played negative rates of productivity growth. For
smaller sectors of the economy, negative produc
tivity growth is commonly observed.”
Our inability to document the changes in
technology that produced business cycles may
not be important, however. We can
the
technical change— up to problems associated
with measuring inputs—by estimating produc
tion functions. Further, much of the technical
change may occur in forms not easy to under
stand without specialized knowledge of a partic
ular industry, and, as Prescott stresses, the sum of
many (nonindependent) technical changes is
the aggregate technical change.
As for reductions in output, there are many
possibilities for technical changes that
cause reductions in measured aggregate
output, and some that cause permanent reduc
tions in
output but increases in true
total output (which includes unmeasured or
poorly measured components, such as household
production). In addition, it may be unnecessary
to
the sources of technical regress in an
industry in order to use the
of
that regress to account for economic fluctuations.
As Summers notes, for smaller sectors of the
measure
tempo
rarily
measured
explain
measured facts
There Is Some Evidence
that Money Affects
Real Output
Christiano and Ljungqvist (1988) present simula
tion evidence about the failure of monetary aggre
gates to Granger-cause real output in systems
that have been first-differenced to achieve stationarity. They find that this phenomenon results
from a lack of power caused by first-differencing
the data and by inducing specification error. In
contrast, this Granger-causality does typically
show up in systems estimated in levels or with
deviations from deterministic linear trends.
These results are important because most rea
sonably specified models in which money affects
real output imply Granger causality7from money
to output (though it is possible to construct
examples— perhaps unrealistic ones— in which
such Granger causality is absent). The estimates
presented by Christiano and Ljungqvist are, as
they argue, economically as well as statistically
significant: about 18 percent of the conditional
variance in the log of industrial production 12
months into the future is accounted for by lagged
values in (the log of) Ml, and this figure rises to
nearly 30 percent at the 48-month horizon.
Other, less formal, evidence suggests that
money affects real output, real interest rates, and
other real variables in the short run. In addition,
McCallum (1985, 1986) has argued that mone
tary policy has been implemented through
interest-rate instruments and that, consequently,
innovations in monetary aggregates may have no
explanatory power for output once nominal
interest rates are controlled for, as in Sims (1980,
1982). McCallum also contends that the explana
tory power of nominal-interest-rate innovations
may reflect the real effects of money on output.
A statistical association between money and
output, however, does not imply that exogenous
changes in money affect output, rather than vice
versa (or both resulting from some other distur
bance). As was noted in the introduction, the
major component of the money supply that
changes with real output is not high-powered
money, but bank deposits.
These changes in deposits may be endoge
nous reponses to changes in output or may be a
joint result of another underlying change. Alter
natively, RBC models may not account for all
fluctuations in output, but only a major part of
them, with monetary disturbances accounting for
the remainder. Clearly, RBC models are better
equipped than monetary models to study the
seasonal fluctuations in aggregate variables that
mimic business-cycle behavior.
There Is Evidence
that Nominal Prices
Are Sluggish
The implication is that traditional, sluggish-price
macroeconomic models are good models of
aggregate fluctuations. But that implication does
not necessarily follow. Even if nominal prices are
sluggish (and there is some evidence to that
effect), RBC models might explain most aggre
gate fluctuations for two reasons.
First, in the presence of price sluggishness,
there are incentives to develop alternative alloca
tion mechanisms, associated with long-term con
tracts or other devices, that bypass or supple
ment the use of prices in the resource allocation
mechanism. The competitive equilibrium may
closely approximate the solution to an RBC
model if the alternative market mechanisms are
sufficiently well developed.
Second, even if sluggish nominal-price
adjustment affects resource allocation in impor
tant ways, it may play a subsidiary role to the
features emphasized in RBCs for explaining
aggregate fluctuations, either because the effects
of monetary disturbances are not large relative
to the effects of real disturbances or because, as
discussed in the introduction, the characteristics
of business cycles (once they have begun) are
largely independent of the source of disturbance.
While some evidence supports nominal price
sluggishness, it is largely concentrated on a few
commodities such as newspapers. Moreover,
much of the evidence from microeconomic data
is weak because all characteristics of goods
(including deliver}7lags, warranties, and quality
control) are not held fixed. In any case, long
term contracts can involve ex-post settling up
that occurs in ways that do not show up in the
current price.
The Success of RBC
Models Rests on Incorrect
Parameter Values
Summers argues that RBC models have not
explained the data as well as they seem to have,
because the parameters they have chosen are
incorrect. For example, he argues that the degree
of intertemporal substitution is smaller than that
assumed in most RBC studies. While Prescott
chooses parameters to make the average real
interest rate 4 percent per year, and King et al.
choose them so that the rate is 6.5 percent per
year, Summers argues that, based on historical
data, the average real interest rate is closer to 1
percent per year. Similarly, Summers argues that
Prescott’s calculation of the fraction of time spent
working, one-third, is much too large, and
should be closer to one-sixth.
Prescott ( 1986b) has defended his choice (and
the Kydland-Prescott choice) of parameters. He
cites Rogerson’s work (see above) to rationalize
a high degree of intertemporal substitution in
labor at the aggregate level, regardless of its mag
nitude at the individual level. The fraction of time
spent working in his model is the fraction of time
not devoted to sleep or personal care, so that the
figure one-third would be close to that found
from micro data. Finally, Prescott’s real interest
rate is intended to represent the real rate of return
on capital, which can be measured approximately
from GNP accounts and is about 4 percent per
year, rather than a riskless real interest rate.
Technical Change Is
Overstated by Prescott’s
Measurement
The residuals from the production functions that
Prescott has estimated are not, according to this
argument, correctly interpreted as mainly involv
ing technical change.3 There are both neglected
factors and mismeasured factors.
One argument, made by Summers (1986) and
McCallum (1989), involves labor-hoarding. When
output is lower than normal (for example, due
to a fall in aggregate demand), firms continue to
employ workers who do not actually work much.
The employees are measured as working, how
ever, so the labor input is overstated when output
■ 3
Actually, Prescott calculates the production functions using a fixed
value of the share parameter, rather than estimating by ordinary least squares.
is low. Similarly, it is understated when output is
high. Calculation of residuals from a production
function will then yield residuals that are too low
when output is low, and too high when output is
high. If the residuals are incorrectly interpreted
as productivity shocks, these “shocks” will seem
to explain the level of output, when they actually
result from measurement error.
Summers cites a study by Fay and Medoff
(1985) to argue that this labor-hoarding
(employment of people who do not really work
during recessions) is quantitatively important.
McCallum points out that the growth literature
following Solow (1957) typically found modifica
tions of his procedure that would reduce the
contribution of the disturbances (interpreted as
technical progress in total factor productivity) to
the overall growth in output. McCallum cites a
study by Jorgenson and Griliches that used cor
rections for “aggregation errors” and changes in
utilization rates of capital and labor to reduce the
contribution of the residuals from nearly half of
the variance of output to only 3 percent.
Prescott ( 1986b) notes that the Fay-Medoff
study asked plant managers how many extra
workers they employed in a recent downturn,
rather than how many
extra workers they
employed in the downturn than in the upturn.
The latter question would be required to deter
mine the quantitative significance of laborhoarding. In addition, Prescott points out that
labor-hoarding may
in recessions: firms
would be less reluctant to lay off workers in
recessions because it is less likely that those
workers would find alternative jobs. If so, the
measurement error in the labor input would
make measured technical change too small
rather than, as Summers argues, too large.
Horning (1988) examines a model in which
heterogeneous industries experience industryspecific as well as aggregate shocks, and shows
that the number of firms hoarding labor is pro
cyclical while the amount of labor hoarded per
firm is countercyclical. Labor-hoarding will result
in overstatement of the size of technology
shocks only if the first effect dominates the
second. Similarly, Kydland (1984) shows that
measured technical change will be too small if
workers are heterogeneous in skills and that
highly skilled workers have less variability in
weekly hours worked than do low-skilled
workers. More generally, it would be desirable to
have better estimates of technical change from
production function studies, and these could be
incorporated into RBC models.
more
fall
The RBC Models Fail
Formal Econometric Tests
The implication is that the RBC models should
be rejected. The question is, in favor of what?
Rogerson and Rupert (1988) have shown that
very small measurement errors can lead to rejec
tion of such models, even if the models are
good approximations to reality.
If models are to be used for policy purposes, a
formal policy decision problem should be ana
lyzed to determine whether policymakers are
better off in terms of expected utility when they
make use of RBC models. The models may, for
example, be wrong but give better advice than
the other incorrect theories. If models are to be
used for additional scientific research, then
clearly the models should not be dismissed
entirely when they fail, until they have been
examined for the source of failure and, perhaps,
changed accordingly.
The Models’ Implications
for Prices Fail
An example cited by Summers is the “equity
premium” studied by Mehra and Prescott (1985).
McCallum (1989) notes that the observed pro
cyclical movements in real wages (see, for
example, Bils [1985]) are smaller than the pro
cyclical wage movements implied by RBC mod
els such as that of Kydland and Prescott. Sim
ilarly, models such as the ones developed by
Greenwood, Hercowitz, and Huffman presuma
bly imply larger procyclical movements in ex
ante real interest rates than those calculated from
ex post data, as in Mishkin (1981) or based on
survey data for inflationary expectations.
Prescott ( 1986b) replies that his representativeagent RBC model may be poorly designed to
explain the equity premium but is well designed
for aggregate fluctuations. Nevertheless, a busi
ness cycle theory that is also consistent with
observations on prices would be better than
having different models for different purposes.
Kydland and Prescott (1988) report implica
tions of their model for the cyclical behavior of
the real interest rate. The behavior of real interest
rates is, of course, difficult to measure because
inflationary expectations are not well measured.
Similarly, there are notorious problems with
treating measured average pecuniary compensa
tion at a point in time as a measure of the mar
ginal product of labor. Thus, Bils’ (and the other)
evidence may understate the true procyclical
behavior of the marginal product of labor.
The Models Oo Not
Explain Involuntary
Unemployment
Involuntary unemployment is generally asserted
to be a “fact” of business cycles. Perhaps it is, but
one can check the truth of this claim only after
the term has been precisely defined. Rogerson’s
model with indivisible labor is promising in this
regard. Because everyone is alike ex ante, yet
some people find work and others do not, mod
els like this may eventually be able to explain
involuntary unemployment in the sense that a
person without a job is no different in tastes,
experiences, and other characteristics from
someone else with a job. Alternatively, RBC
models may have to be modified to include
some market failures in order to account ade
quately for such phenomena.
There Are Large
Nation-Specific
Components to
GN P Fluctuations
I have argued (Stockman, 1988a) that RBC mod
els based solely on technology shocks seem
unable to account for the empirical finding
(documented in that paper) that there are large
changes in output across all industries that occur
in one country but not in another. Technology
shocks would be more likely to affect a particu
lar group of industries, irrespective of nation (at
least in developed, OECD countries) than to
affect a particular country, irrespective of indus
try. Instead, the evidence in my paper suggests
that while technology shocks are important,
some nation-specific disturbances play at least as
large a role in output fluctuations.
Whether these nation-specific disturbances are
monetary or “real” (for example, resulting from
fiscal policy) remains unclear. It is possible, of
course, that technology is more specific to
nations than to industries, though that seems
unlikely. These conclusions may also result from
international transmission of aggregate distur
bances. I discuss these issues briefly in the con
text of the formal two-country model in section
VI, which illustrates one of the important reasons
for developing multicountry, multisector RBC
models, as outlined in that section.
mimic any given set of facts; that one theory can
does not mean that it is even close to right.” The
assertion is clearly correct in general, but it is
beside the point. While it is possible that many
theories could replicate the facts of business
cycles and meet the other criteria of being con
sistent with basic economic theory, the fact that a
theory is consistent with the facts
(and
certainly does not lower) the conditional proba
bility that it is a good and useful theory.
In any case, RBC models such as those devel
oped by Kydland and Prescott have set a stan
dard to which alternative models, including those
with sluggish price adjustments and coordination
failures, should aspire: to present a prima facie
case that the model is
accurate.
The alternative models favored by Summers and
by other critics of RBC analysis may prove to be
better models of aggregate fluctuations, but
those models as yet have not been developed
sufficiently to even enter the race against RBC
models in mimicking the quantitative as well as
qualitative aspects of business cycles.4
raises
quantitatively
VI. Outline of a StrippedDown Two-Country
RBC Model
This section outlines a two-country version of a
simple RBC model. It illustrates formally the
setup of a prototype model, describes one
method of solving the models (as in King,
Plosser, and Rebelo [1988a]), and discusses the
reasons for an international extension of the RBC
model. Frequently, international extensions of
closed-economy macroeconomic models have
little motivation (except, perhaps, to turn one
idea into two papers); there are better reasons
for an international extension in this case.
The first reason is that RBC models have been
calibrated with a single set of parameters to
explain a single set of standard errors and covar
iances of macroeconomic variables. One way to
improve on the models is to add additional vari
ables, but this requires adding more equations
and more parameters to obtain additional impli
cations from the models.
A second way to check an RBC model is to
apply the same model to a
set of
different
It is Easy to Produce
Models to Mimic Facts
Summers cites Ptolemaic astronomy as an exam
ple of how “...many theories can approximately
■ 4
The large econometric models do not qualify because they are not true
structural models in the sense of the Lucas critique of econometric policy
evaluation.
macroeconomic facts (standard errors, correla
tions, and so on), using the
criteria for
choosing parameter values. The different sets of
macroeconomic facts can be obtained by using
data from different countries. Application of the
models to data from other countries will there
fore provide a valuable check on the models, as
Rogoff (1986) also suggested. Differences in the
characteristics of business cycles across countries
are substantial enough to provide powerful
checks on the models, as I will discuss below.
The second reason for an international exten
sion is that the RBC models have implications, in
an international setting, for additional variables
such as exports, imports, and the balance of
trade. RBC models with multiple sectors can also
be shown to have implications for relative prices,
such as the terms of trade or the relative price of
nontradeables. These additional implications can
be checked against the data.
same
In addition, the models can be used to exam
ine issues associated with the international
transmission of real disturbances, and the effects
on aggregate fluctuations of various government
policies toward international trade. Finally,
equilibrium models of exchange rates imply
that changes in real and nominal exchange rates
result from “real” shocks; in this sense they are
closely linked to RBC models.5
Also, like RBC models, equilibrium models of
exchange rates are based on simple dynamic,
stochastic, general-equilibrium models. But the
RBC models have been quantitatively developed
(in closed economies) in ways that the equilib
rium models of exchange rates have not; appli
cation of the RBC models to open economies
therefore has the potential of advancing the
equilibrium exchange-rate models and further
ing our understanding of exchange rates.
There are two categories of differences
between countries: differences in parameters
and differences in exogenous disturbances. To
keep the issues associated with international
extensions clear, consider a simple model sim
ilar to that in King, Plosser, and Rebelo with
exogenous growth. There is a representative
individual in each country who maximizes the
expected discounted utility of consumption of
two goods— one produced in each country—
and leisure, 1
, where
is labor supply and
total time is normalized to one,
-N
N
(1)
U=2
,:0
p ‘u (C u ,C2ll- N t),
and the foreign representative individual
maximizes
( 1*) u - = £ ,? „ /3‘u(C *u ,C *2t
Each country produces only one good, and its
production is described by constant-returns-toscale production functions
(2)
Y, =
A , F ( K t , N tX t)
and
(2*)
K *=
A * t F * ( K * t>N * t X * , \
*t
t-
where K t and K
are chosen at date
1, and
investment in each country utilizes only that
country’s good, that is,
(3)
K t+ l =
(1 -5 )* ,+ /,
and
(3*)
K*l+1 = (1-6
*
* ) * * ,+ / * ,,
where K and K are the foreign and domestic
capital stocks,
and * are depreciation rates,
and / and / * are investments using domestic
and foreign goods.
This model includes some assumptions that
should be relaxed in further work but are made
here for simplicity: that utility functions are
identical across countries, that countries are
completely specialized in production, and that
all goods are internationally traded. Also, the
production functions do not allow one good to
be used as an input into the other, which pre
cludes certain types of sectoral interactions as in
the model of Long and Plosser (1983).
The resource constraints differ from those of
a closed economy due to international trade:
8
(4)
Cu
+
8
C mu + /,
=
Yt
and
■ 5
See Stockman (1980, 1987, 1988b), Lucas (1982), Stockman and
Svensson (1987), Salyer (1988), and Stockman and Dellas (1988).
*/)■
(4*)
C2t + C*2t + I*t - Y*t .
y
Given initial conditions on the capital stock in
each country and weights on domestic versus
foreign utilities (which correspond to relative
wealth positions in competitive equilibrium),
equations (1) through (4) and nonnegativity
constraints on consumption, leisure, labor
supply, and capital stocks can be solved for time
paths of consumption, labor, and capital for
given time paths of the exogenous productivity
disturbances
and
Suppose we adopt the restrictions on prefer
ences that King, Plosser, and Rebelo argue are
implied by the observation of steady-state
growth, and we assume that the degree of rela
tive risk-aversion is unity. Then, for the threeargument utility function postulated here,
A, A*, X,
(5)
u (C x,C2,l-N )
(8b)
c2, -
c \t
- lg x* k * t+i - ( l - 8 ) k * t ],
and the inequality constraints listed above.
Necessary conditions for this problem include
the resource constraints (8), the inequality con
straints listed above, and
X*.
(9a)
w /cu = $ t = ( l- w ) /c * lt
(9b)
w /c2t =
$*,
= (1 - w )/c * 2t
=
lo g ( C 1) + l o g ( £ 72 ) +
v ( 1-AO,
(9c)
v'
A*t k \ l-* 'N ** -
j U , 0 V , / * , ) « + ( 1-6)] =
v
<>
t tgx
where
> 0 and " < 0. The production
functions are assumed to be Cobb-Douglas,
(9d)
(6)
Yu = At Ktl-a(N t Xt) a
p * * t+1[A *,(N 0t /k * t )** + ( 1-6)]
= *% 8X-
and
Y2t = A*tK*t1~a\ N t X t) a\
A
all variations in
are assumed to be temporary,
and all variations in
are assumed to be per
manent (explained below).
Define the transformed variables c, =
=
=
*,
=
=
and * =
Then a social
planning problem for this economy can be
expressed as
X
(9e)
&tAt k t UaN t a/N t = v '( \-N t)
(90
$ ? A* t k* ? ~ aN *
(9h)
(6*)
limt^ ao p l $ * l k*t+ j
*/N * t
=
v '( l
- N * t)
Cx /X,
c \ C \ / X , c 2 = C2/ X \ c \ _ C \ / X
i I/X , i* = I*/X *, k K/X, k* = K*/X*,
g X '/X, g X *'/X *.
(7)
Maximize
X t T 0 P‘i w {log ( cu )
+ log ( c2l) + v (l-N ,)}
+ (1 -w ) {log (c *j,)
+ log (c *2/) + v ( l- N \) } ]
{cu , c 2t, c*lt,
c*2t,k t+ v k * t+ v Nt , N *t -, t = 0, ... } for
given utility-weight w , and subject to the
with respect to the sequence
sequence of constraints (with multipliers $ and
<*>*),
(8a)
At Kt UaN ta - cu - c*u
- igx kt+ i - (1 - 5 )^ ] ,
= 0.
One undesirable characteristic of the solution
is evident from these conditions: consumption
of each good is perfectly correlated across coun
tries. This prediction is not borne out by data.
One way to modify the model would be to
include nontraded goods, as in Stockman and
Dellas (1988). Because numerical methods are
required to solve the model anyway, it is feasible
to relax the special assumption imposed in that
paper that utility is separable between traded
and nontraded goods.
In fact, traded goods may have to be proc
essed in each country before they are bought
and consumed by a production technology that
includes nontraded goods (such as retailing,
transportation to markets, and storage). This fea
ture of traded goods has been emphasized in
work by Kravis and Lipsey (1983) and explains
their strong empirical finding that countries with
higher wealth have higher prices of nontraded
goods
higher prices of traded goods at the
retail level. With this modification, trade would
take place in intermediate goods rather than final
goods, and final goods production would occur
in each country with the use of a nontraded fac
tor, as in Jones and Purvis (1983).
Next, define the operator
so that
is the
log-deviation of
from its stationary steady-state
value, , that is
= log (
). Then take
linear approximations of (9) around these sta
tionary values,
(lOg)
+
D
c
Dc,
c,/c
[1
- sc l -
\-8x /(g x [! -
(lO h)
DA*,+
=
s c 2D
(10b)
D c u = Dc* j,
D clt
=
(10c)
=
-D Q t
Dc* 2, = -D Q *t
1+
S )]D k,+j
8X/(S X(1 c
2,
+
1+
8)]D k,
a *)Dk *,
s c 2* D
c
+
a*D N *t
*2,
+ [ 1 - 5t. j - 5 , * j ]
[ g j c * / ( & c *
-
1
8)}Dk\ +
+
i
+ [ 1 - 5c l - 5 , » j ]
[1 -
(10a)
5 t. M ]
+ [1 - 5 ,i - St..j]
and
c,
Dc,
DA, + (1 - a)D k, + aDN,
= sc,Dc Xt + sc |
*Dc .,,
8
x*/(gx * -
1 + <5)]Z)& *,
.
Next, solve (10a), (10b), (lOe), and (lOf) for
the optimal decisions
as functions of the state variables
,,
*,,
,,
*,} and {£>$,,
Then substitute these solutions into (10c),
(lOd), (10g), and (lO h) to obtain the difference
equations
DN, DN*},
{Dk Dk DA DA
{Dcv Dc2, Dc*x, Dc*2,
D$>*,}.
D $ , +1
d )/g x ][DAt+l
+ a ( DNt+ | - D k,+ j)]
+ [1 - 0(1 -
(lO d)
£><£*, =
£>4>*,+1
5 )/g x .][D A * t+1
+ a* ( D N *t+1 - D k* t+ j)]
+ [1 - j8( 1 -
+
(lOe)
(100
DA, + (1 -a )D k t - (1 - a )D N t + D<t>t
= ~ ( l- N ) ( v " /v ') [ N /( l - N ) ] D N t
DA*t + (1 -a*)D k*t
- (\-a * )D N * t + D$>*t
[N * /(l-N * )]D N * l
H*DA*t +j
+
J*DA*t ,
each of which is analogous to the system in
King, Plosser, and Rebelo (1988a), shown there
as having a solution of the form
and
=
G
a
j
=o
i -j
+
1
Assume that certainty equivalence holds
approximately and that the vector
,,
follows a Markov process,
(DA DA *,)'
DA
Po P
\
1
t+
DA * i +l
P\P\
u - (uA, uA )
where
is a random variable with
mean zero and covariance matrix
Then the
system can be written in the form of a first-order
difference equation
f
VA .
Dk,. i
V
DA, +1
DA* /+1
Dk* ' +1J
,
*A h *
rjA
h
0
0
0
Po
0
0
P* i P* 0 0
Pi
*7
h
( Dk' \
DA,
DA * ,
\o k -J
A
At + 1
lA
The parameters of this model are the two
depreciation rates of capital; the utility-of-labor
functions
and
the production param
eters
and *; the utility weight
; the dis
count rate ; the growth rates
and *; the
parameters of the Markov process on productiv
ity shocks,
o,
and the covariance
matrix of productivity shocks
These param
eters can be chosen in the ways described above
to match historical observations on growth rates,
labor’s share of gross domestic product (GDP),
and so on, and estimated parameters from
microeconomic studies (such as the elasticity of
the function
and to make the model repro
duce some of the variances and covariances of
key macroeconomic aggregates.
As noted above, the model has implications for
the terms of trade, which is the only “real
exchange rate” in the model and is, in real-world
data, very highly correlated with the exchange
rate. Consequently, the model has implications
for exchange rates as in the equilibrium models
referred to previously. Tables 3 through 8, de
scribed below, show roughly zero correlations
between GNP and the U.S. dollar exchange rates
of Japan and the United Kingdom. When U.S.
GNP is controlled for, however, the partial corre
lation between the exchange rate and GNP in
Japan and the United Kingdom rises to the range
of .2 to .3.
Tables 3 through 8 display correlations
between some macroeconomic aggregates and
GDP for Japan and Great Britain, and the corre
sponding standard errors of the variables.6 Baxter
and Stockman (1988) show that these and many
other similar variances and covariances are inde
pendent of the exchange-rate system, so the
correlations in the tables refer to the time peri
ods 196l:IQ-1986:IIQ for the United Kingdom
and 1964:IQ-1987:IQ for Japan.
On the other hand, that research also indi
cated that covariances such as these are some
times very sensitive to the method of detrending
the data. The tables therefore present correla
tions with output after each of two types of
detrending: the removal of a deterministic linear
time trend and first-differencing.7 In addition,
i
t+ 1
J
Let w and w* denote (real) wage rates, let
r and r * denote real interest rates in terms of
good one and good two, respectively, and let
denote the relative price of good two in terms
of good one. These and the other endogenous
variables
,,
*,,
,,
,,
*,,
- , *t - *,
, } can then be written as
linear functions of the state vector
v ()
a
(3
v*()\
p0 ,p v p p \,
gx
w
g
VA .
v(),
q
{Dcx,, Dc2t, Dc* u , Dc*2t, DN
DN Dy D y*,, Di,, D i*,, Dw Dw
r, r r r Dq
■
6
The series presented have been chosen to make the tables analogous
to table 1.
5, =
(D k,, DA,, DA*,, D k* ,)'
■ 7
Use of the Hodrick-Prescott filter always resulted, with the data used
for these tables, in a correlation bounded by those presented here.
m
T A B L E
Japanese Business Cycle Statistics,
19 6 4 :IQ -19 8 5 :IV Q
Linear Trend Filter
Japanese Business Cycle Statistics.
19 6 4 :IQ -19 8 5 :IV Q
First-Difference Filter
Corr.
with
GNP
(-1)
Corr.
with
GNP
Corr.
with
GNP
(+
1)
1.8%
.03
1.00
.03
GNP
Consumption
1.5
.11
.56
.01
Consumption
Investment
3.2
.08
.70
.17
Investment
Government
spending
7.8
-.11
.18
-.08
Government
spending
Real exports
4.9
-.01
.10
.02
Real exports
Standard
Deviation
Variable
GNP
Corr.
with
GNP
Corr.
with
GNP
(- 0
10.5%
Variable
Corr.
with
GNP
.98
1.00
.98
8.9
.93
.94
.93
15.6
.95
.97
.96
11.5
.75
.78
.78
13.9
.64
.66
.65
Standard
Deviation
(+
D
Real imports
5.6
.05
.08
.16
Real imports
21.6
.49
.53
.56
Net exports
4.6
-.07
.02
-.18
Net exports
12.3
-.12
-.19
-.26
.8
-.01
.30
-.06
Average hours
worked
2.8
-.50
-.50
-.53
3-3
-.35
-.38
-.42
Average hours
worked
1.0
.11
.29
.03
Total hours
worked
Employment
.5
.24
.09
.17
Employment
1.1
.24
.19
.11
Labor force
.5
.22
.08
.11
Labor force
1.0
.19
.13
.05
GNP/total hours
1.8
-.04
.85
.00
GNP/total hours
12.0
.94
.96
.95
GNP/worker
1.8
-.04
.97
-.02
GNP/worker
10.4
.98
.99
.98
Exchange rate
4.2
•03
-.02
-.03
Exchange rate
10.8
.10
.10
.05
Total hours
worked
NOTE: Corr. = correlation. Correlations above .2 are significant at .05;
correlations above .27 are significant at .01.
SOURCES: Japanese Central Bank and International Monetary Fund.
NOTE: Corr. = correlation. Correlations above .2 are significant at .05;
correlations above .27 are significant at .01.
SOURCES: Japanese Central Bank and International Monetary Fund.
the tables show results for the components of
the foreign variables that are orthogonal to U.S.
GNP, calculated by taking residuals from an OLS
regression of the variables on U.S. GNP before
applying the other filters.
The tables clearly indicate quantitative differ
ences across countries in the characteristics of
business cycles. The results using the HodrickPrescott filter are closest to those reported in the
tables for the deterministic linear trend filter, so I
focus on those results. The standard deviation of
consumption in the United Kingdom and Japan is
about equal to the standard deviation of GNP; in
the United States, the standard deviation of con
sumption is only about three-fourths that of GNP.
In Japan, the standard deviation of investment
relative to that of GNP is about half the size of
that ratio in the United States or in the United
Kingdom. The relative variability of the average
number of hours worked per week in Japan is
also much smaller than in the other two coun
tries. The standard deviation of the average pro
ductivity of labor is about twice as large, relative
to that for GNP, in Japan and the United King
dom as in the United States. Finally, the variabil
ity of imports exceeds that of exports in all coun
tries. Net exports, as discussed above, are
countercyclical in all three countries.
The correlations with output also differ. The
most striking difference is in the correlation
between GNP and the average number of hours
worked per week. In the U.S. data, this correla
tion is large and positive; for the United King
dom and Japan, it is negative. In Japan, average
hours variation dominates employment variation
so that total hours worked, calculated by the
product of employment and average hours, is
actually countercyclical. The correlation between
the average productivity of labor and GNP is
much higher in Japan and the United Kingdom
than in the United States.
These differences must be explained either by
differences in parameters or by differences in the
disturbances facing the three economies. Each
EH
T
A
B
L E
T A B L E
5
6
British Business Cycle Statistics,
1961 :IQ -19 8 6 :IIQ
First-Difference Filter
Japanese Business Cycle Statistics,
19 6 4 :IQ -19 8 5 :IV Q
Filter: Linear Trend and
Residuals from Projection
onto U .S . GN P
Standard
Deviation
Variable
Corr.
with
GNP
(-1)
Corr.
with
GNP
Standard
Deviation
Corr.
with
GNP
(-1)
Corr.
with
GNP
Corr.
with
GNP
(+
D
Corr.
with
GNP
GNP
1.7%
-.18
1.00
-.18
(+
1)
Consumption
1.9
-.03
.47
-.15
Variable
GNP
9.2%
.96
1.00
.96
Investment
4.4
-.22
.31
.04
Consumption
8.5
.83
.90
.88
Investment
13.6
.92
.92
.86
Government
spending
2.2
.16
-.04
-.08
Government
spending
Real exports
9.7
.19
.26
-.21
11.8
.70
.76
.77
Real imports
4.8
.07
.34
-.01
Real exports
15.7
.69
.70
.65
Net exports
9.1
.16
.10
-.22
Real imports
22.8
.61
.61
.56
Net exports
12.3
-.22
-.23
-.20
Average hours
worked
1.2
-.11
.33
.06
2.7
-.56
-.59
-.61
Total hours
worked
1.5
-.14
■4
3
.17
Employment
6.5
-.11
.16
.22
Average hours
worked
Total hours
worked
3-3
-.44
-.46
-.48
Labor force
4.6
.06
.03
.02
Employment
1.1
.07
.08
.05
GNP/total hours
1.8
-.10
-.10
-.04
Labor force
1.2
.01
.05
.02
GNP/worker
1.7
.00
.00
.00
GNP/total hours
9.0
.95
.99
.94
Exchange rate
3.9
.03
-.07
GNP/worker
9.2
.95
.99
.96
11.5
■6
3
•32
.26
Net capital
stock
0.3
.02
.07
.10
0.3
0.3
-.02
.04
.06
.08
.10
.10
Exchange rate
NOTE: Corr. = correlation. Correlations above .2 are significant at
.05; correlations above .27 are significant at .01.
SOURCES: Japanese Central Bank, International Monetary Fund,
and Citibase.
explanation has implications for the behavior of
exports, imports, and the trade balance. The
question of whether RBC models like those cur
rently being analyzed will survive such exten
sions must await future research.8
■
8
Other useful extensions of RBC analysis include further research inte
grating it with growth theory, as emphasized by King, Plosser, and Rebelo
(1988b); the inclusion of private information into the analysis so that fluctua
tions are not unconstrained-Pareto-optimal; the inclusion of distorting govern
ment policies such as taxes and regulations (also emphasized by King, et al.);
further examination of the behavior of prices, including interest rates, relative
prices in multisector models, and so on; work on heterogeneity and aggrega
tion problems; and extensions of the theory to include roles for financial inter
mediaries (and possibly government regulation of them), particularly since
there is evidence connecting intermediation to business cycles.
Equipment
Buildings
•13
NOTE: Corr. = correlation.
SOURCES: Bank of England, European Economic Community, and
International Monetary Fund.
VII. Policy Implications
Should any of the developments so far in RBC
analysis affect current policy? Obviously, the
answer involves the optimal formation of policy
under uncertainty. If the standard macro models,
say with sticky prices, are correct, then monetary
policy can be designed to help, while if the RBC
models are correct, then monetary policy will
have no effects. It is clearly not correct to argue,
however, that because we do not know which
model is correct, we should use monetary policy
as if the standard model were correct: even if it
is wrong, there is little or no cost in trying it.
That argument is wrong precisely because there
may be a large cost in using monetary policy if
the standard and the RBC models have
both
British Business Cycle Statistics,
British Business Cycle Statistics,
19 6 1:IQ -19 8 6 :IIQ
Linear Trend Filter
1961 :IQ -19 8 6 :IIQ
Filter: Linear Trend and
Residuals from Projection
onto U .S . GNP
Corr.
with
GNP
Corr.
with
GNP
(+1)
(-1)
Corr.
with
GNP
GNP
3.5%
.88
1.00
.88
Consumption
3-6
.71
.73
.64
Investment
9.0
.81
.88
.86
Standard
Deviation
Variable
with
GNP
(-1)
Corr.
with
GNP
with
GNP
(+1)
2.5%
.76
1.00
.76
Consumption
2.5
.40
.43
.23
7.3
.52
.60
.67
Variable
Standard
Deviation
GNP
Government
spending
4.8
.56
.55
.55
Investment
Real exports
10.2
•38
•43
.36
Real imports
12.2
.59
.66
.67
Government
spending
5.2
.46
.46
•38
-.47
Real exports
10.5
.37
.42
.27
Real imports
11.6
.60
.65
.60
Net exports
9.6
-.33
-.33
-.42
Average hours
worked
2.2
-.18
-.15
-.20
Total hours
worked
3.0
-.15
-.06
-.04
Employment
2.0
-.04
.01
.08
Labor force
1.4
-.22
-.19
-.15
GNP/total hours; 4.1
.59
.67
.51
GNP/worker
3.2
.62
.77
.54
Exchange rate
12.6
.27
.27
.25
Net capital
stock
Equipment
Buildings
3.6
3.2
3-8
•43
.45
.41
.46
.48
.45
.41
.42
.40
Net exports
9.6
-.36
-.39
Average hours
worked
2.2
-.29
-.27
-.33
Total hours
worked
2.7
.13
.22
.22
Employment
1.9
.58
.65
.71
Labor force
1.4
-.03
-.03
-.03
GNP/total hours
3.9
.68
.73
.63
GNP/worker
Exchange rate
Net capital
stock
Equipment
Buildings
2.6
•73
.83
.63
11.8
-.06
-.12
-.17
3.5
3-4
3.8
.78
.76
.79
.79
.77
.80
.79
.77
.80
NOTE: Corr. = correlation.
SOURCES: Bank of England, European Economic Community, and
International Monetary Fund.
NOTE: Corr. = correlation.
SOURCES: Bank of England, European Economic Community,
International Monetary Fund, and Citibase.
some explanatory power for business cycles. The
cost is the
introduced into the econ
omy if monetary policy does have real effects but
is used in response to a
shock for which the
economy is responding in an optimal way.
If policymakers want to use monetary policy
for short-run stabilization rather than solely for
longer-term inflation goals, they should base
monetary policy on some indicators of the
of disturbances. If a previous change in the
money supply has led to a change in output, and
distortion
real
source
if there is time to reverse the money supply
change to avoid the output change, then that
reversal will reduce the inefficiency.
Similarly, if the economy is responding in an
manner to some disturbance, and if
monetary policy can help reduce the ineffi
ciency, then it may be reasonable for policy to
do so. But if the change in output is an optimal
response to a real disturbance, then monetary
policy will only introduce inefficiencies.
If policymakers could be sure of the source of
disturbances, then they could use that informa
tion to formulate policy. O f course, they cannot
be sure of the source. Therefore, an optimal sta
tistical decision framework should be used for
policy. This involves using existing information
to try to determine, in the best way possible, the
inefficient
ia
source of the disturbance, and using some esti
mates of the effects of money on output and of
the losses from an inefficient level of output to
set monetary control variables in the face of
uncertainty.
The contribution of RBC theory has been to
show that many aggregate fluctuations can pos
sibly be viewed as optimal responses to external
disturbances. If monetary policy is to be con
ducted with a goal of short-run stabilization,
policymakers should use the information in RBC
models to try to avoid interfering with these
optimal responses.
One way to use the information would be to
use a set of estimates similar to those in Christi
ano and Ljungqvist (1988), along with estimates
of the difference between actual GNP and that
predicted by RBC models, to infer the probabil
ity that the economy is responding optimally to a
disturbance—as RBC models would predict— or
whether it is responding, presumably ineffi
ciently, to a monetary disturbance. The greater
the likelihood that the fluctuation in GNP can be
explained by the RBC model, the weaker the
case for activist monetary policy, and vice versa.
O f course, this presumes that the existing class
of RBC models, in which the economy responds
to disturbances in an optimal way, provides a
good description of the response.
An alternative possibility is that disturbances
are real rather than monetary in nature, but that
the responses of the economy are suboptimal
due to market failures of some kind.9 This
appears to place a caveat on the policy discus
sion here. But the caveat is not particularly
strong, given the current state of knowledge, for
several reasons. First, there is the question of
whether government — particularly monetary
policymakers — can do anything to improve
welfare in suboptimal real business cycles, or to
lessen the magnitude of business cycles (if that
would improve welfare). Can monetary policy
be of any use here, or must the government pol
icies, if any are useful at all in this regard, be
real? Second, attempts at such policies might do
more harm than good in our current state of
knowledge, even if they might be useful in the
future. Third, there is the question of how much
weight should be placed on the view that the
economy responds in suboptimal ways to real
disturbances. Inclusion of these features in RBC
models has not been necessary to yield the
degree of fit obtained so far.
Is there any reason to think that in the future
RBC models will advance particularly by introduc
ing these features, or is the tendency to include
them more the result of a particular political
propensity? No quantitative RBC model has yet
been developed along these lines.1
0
Multicountry models such as the one outlined
in section VI would be required to determine the
appropriate policy response to a foreign shock. A
disturbance that induces inefficient aggre
gate fluctuations in that country might also induce
inefficiencies in the U.S. economy and therefore
warrant a domestic policy response. Alternatively,
such a foreign disturbance might change oppor
tunities only in the U.S. economy and result in
efficient reactions to the inefficient foreign fluc
tuations, which would not warrant a domestic
policy response. Further research on interna
tional transmission is required to determine the
best policy response to foreign disturbances.
I
do not want to minimize the difficulties in
using RBC analysis, in its current state, to deter
mine whether a policy response might be
appropriate. But the existence of these difficul
ties neither precludes the use of the models in
their current state nor warrants ignoring the evi
dence that, given current models, business-cycle
phenomena can be quantitatively explained at
least as well as an optimal response than as a
suboptimal response to exogenous disturbances.
Prescott ( 1986a) states that the key policy
implications of his research are that costly efforts
at stabilization policy are likely to be counter
productive, because they may reduce the rate of
technological change, and that economic fluctua
tions are optimal responses to uncertainty in the
rate of technological change. He also contends
that optimal policies should be designed to
affect the long-run rate of technological change,
but that the precise designs of institutions and
policies requires further research on the deter
minants of technical progress. Given the current
evidence on inflation and long-term economic
growth, this conclusion supports a monetary pol
icy geared toward low inflation and with less
concern about fluctuations in real GNP.1 Fortu
1
nately, this conclusion is consistent with the one
based on stabilization considerations.
foreign
■
1 0 The most promising modifications in this regard may be the
introduction of imperfect competition as in Hall (1988). However, in this case,
it is not clear that
■ 9
These failures might involve externalities or inefficiencies resulting from
monetary
policy would have a role in an optimal policy
response to external disturbances.
government policies such as distorting taxation, unemployment insurance,
effects of Social Security on savings, or government regulations.
■
11
See Gavin and Stockman (1988).
Campbell, John Y., and N. Gregory Mankiw.
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