ROBERT J. GORDON
Northwestern University
Unemploymentand Potential Output
in the 1980s
most outstandingfeatures to date of the 1983-84 economic
expansion are the unusually rapid decline in unemploymentand the
continuingdecelerationof inflation.The 3.1 percentagepoint decline in
the civilianunemploymentratein the firstseven quartersof the recovery
(from10.6percentin 1982:4to 7.5 percentin 1984:3)was greaterthanin
any postwar recovery since the Korean War. The inflation rate as
measured by the fixed-weight deflator declined from a peak of 11.3
percentin 1980:4to just 3.8 percentin 1984:3.
The sharp decline in unemploymentand the associated creation of
millions of new jobs, while creating good news for jobseekers and
incumbentpoliticians,raisetwo seriousquestionsfor economicanalysts
andpolicymakers.First, is the extent of the declinein the unemployment
rate consistent with the historicalrelationshipbetween unemployment
and output, or is there some additional,unexplainedcomponentof the
recent unemploymentperformance?Second, does the rapid drop in
unemploymenthave as its counterpartan unusuallypoor performance
of productivitygrowth?If so, this would have importantimplications
for competinghypotheses that have attemptedto explainthe post-1973
slowdown of productivitygrowth and in additionmightimply that the
underlyinggrowth rate of potentialoutputis slower than has generally
been assumed.
The term "potential real GNP" designates the level of real gross
nationalproduct that the economy could produce at a given time if it
were operatingat its hypothetical "natural"unemploymentrate that
would,in the absence of supply shocks, be compatiblewith a nonaccelTHE TWO
537
538
Brookings Papers on Economic Activity, 2:1984
eratingrate of inflation.1 If we definethe "GNP gap" as the percentage
differencebetween actual and potentialreal GNP, and if we define the
"unemploymentgap" as the difference in percentagepoints between
the actual and naturalunemploymentrates, then one indirectmethod
for estimating the level of potential GNP is to use historical data to
estimate an Okun's law coefficient, which links the two gaps. A rapid
decline in the unemploymentrate implies a rapiddecline in the unemploymentgap and, usingthe historicalcoefficient,in the GNP gap. Since
the growthof actualrealGNP is known, use of the historicalOkun'slaw
relationshipthus provides evidence on how fast potentialreal GNP has
been growing.
This paper analyzes why the unemploymentrate fell as fast as it did
in the recovery and provides new estimates of the level and growthof
potential real GNP. The growth rate of potential real GNP, in turn, is
decomposed into the growth rates of population,laborforce participation, hoursperperson, andproductivityperhour,thusallowinga verdict
on whether, after adjustmentfor cyclical effects, the much-discussed
slowdownof productivitygrowthafter 1973was intensifiedor alleviated
after 1979. To anticipate, it appearsthat the slow rate of productivity
growth experienced in 1974-79 has not changed appreciably since
then.
The point of departurefor the analysis is an identity that links real
GNP with the unemploymentrateandothervariables,includingproductivity, hours, and the laborforce participationrate. After a brief initial
inspectionof the data, a statisticalrelationshipis estimatedbetween the
detrended level of each component of this identity and, as a single
explanatory variable, detrended real GNP. The estimated equation
relating the detrended employment rate to detrended real GNP is a
historical Okun's law relation that can be used to determinethe most
plausible growth rate since 1979 for the unobservablepotential real
GNP.
The estimatedequationsfor the othercomponentsof the identityare
1. Althoughin otherwritingI havepreferredthe term"naturalrealGNP," hereI defer
to the "potential real GNP" usage that is customary in BPEA and in government
publications.There does not seem to be any consistent official terminologyfor the
correspondingunemploymentrate.
RobertJ. Gordon
539
thenused to decompose the post-1979growthof potentialrealGNP into
cyclicallyadjustedtrendgrowthratesin productivity,hours,laborforce
participation,and so on. The end result of the paper is a consistent
decompositionof the observedgrowthof realGNP andeach component
of the GNP identity between a cyclically sensitive component and a
cyclically adjusted"potential"trendcomponent.
The Cyclical Behavior of Output and Unemployment
OKUN S LAW AND THE OUTPUT
IDENTITY
Okun's law postulates a regularrelationshipbetween the GNP gap
and the unemploymentgap. This relationshiphas remainedpopularin
macroeconomicanalysisbothbecause it has been sufficientlystableand
reliablein the past two decades to deserve being labeled a law and also
because it short-circuitsthe rathercomplex identity that links output
and unemployment.2A simple version of this identity can be written
as in one of my earlierpapers,3in which real GNP, Q, is decomposed
into the employmentrate, EIL; hours per employee, H; laborproductivity, QIEH; the labor force participationrate, LIN; and the population,N.4
(1)(1)
Q L H N..
Q _ ~~~E
Q=ffEHN
The typical estimate of 2.5 to 3.0 for the Okun'slaw coefficientrelating
cyclical fluctuationsin outputto those in the employmentor unemployment rate implies, accordingto identity 1, that more than half of the
2. Forthe originalstatementof Okun'slaw, see ArthurM. Okun,"PotentialGNP:Its
Measurementand Significance,"in AmericanStatisticalAssociation,Proceedingsof the
Business and Economic Statistics Section 1962, pp. 98-104, reprinted in Okun, The
Political Economy of Prosperity (Brookings, 1970), pp. 132-45.
3. RobertJ. Gordon,"The WelfareCost of HigherUnemployment,"BPEA, 1:1973,
pp. 133-95.
4. The employmentrate, EIL, is simplyunity minusthe unemploymentrate, thatis,
(1 - UIL).
540
Brookings Papers on Economic Activity, 2:1984
cyclical fluctuationsin output have their counterpartin cyclical movements of productivity,participation,and hoursper employee.'
Whileidentity 1 is an adequateformulationfor theoreticalanalysis, it
is incomplete for a real-worlddata investigationbecause the conventionalmeasuresof employment,participation,andpopulationcover the
entirecivilianpopulation(aged 16and over), while the productivityand
hours componentscover the nonfarmprivatebusiness sector, which is
smaller.Further,the data source for civilianemployment(households,
in the currentpopulationsurvey)differsfromthe datasourcefornonfarm
business employment(the establishmentsurvey). These complications
requirethat identity 1 be expandedas follows:
(2)(2)
EQB
-L
Q-LEBHBN
HBN2QE
QB E'
where the variableswith the B superscriptsare those for the nonfarm
business sector and the variableswithout superscriptsare those for the
total economy or civilian laborforce.6Identity2 differsfrom identity 1
in the finaltwo terms, which can be describedas mix-effectterms and
which changewheneverthere is a changein the ratioof total outputper
civilianemployee, QIE, to the same ratioin the nonfarmprivatesector,
QBIEB.
Among the factors contributingto the mix-effect terms are
changesin the governmentandfarmsharesof output,differentialgrowth
in government, farm, and nonfarm productivity, and discrepancies
between the householdand establishmentemploymentsurveys.
Identity2 can be simplifiedby labelingthe ratioswith a single letter;
with R for the employmentrate, V for productivity,F for the participation rate, MQfor the output-mixeffect, andMEfor the employment-mix
effect, it becomes
(3)
Q=R
VFHNMQ
ME,
5. Since population,N, includesonly those aged 16 and over, it is clearlyunaffected
by the business cycle except to the (presumablyminor)extent that recessions raise the
deathrateby increasingthe incidenceof stress, mentalillness, malnutrition,andsuicides.
6. The expandedidentityis the same (otherthan differentnotation)as equation3 in
PeterK. Clark,"Okun'sLaw and PotentialGNP," WorkingPaper(Boardof Governors
of the FederalReserveSystem, June 1983).Clark'sequationis also used in modifiedform
inDouglasM. Woodham,"PotentialOutputGrowthandtheLong-termInflationOutlook,"
Federal Reserve Bank of New YorkQuarterly Review, vol. 9 (Summer 1984), pp. 16-23.
RobertJ. Gordon
541
wherefor convenience the B superscripton the hours termis dropped.
The equivalent identity for components of the growth rate of real
GNP is
(4)
q-r + v + f + h + n + mQ +
mE,
where each lowercase letter representsthe annualpercentagegrowth
rate of the levels expressed as correspondinguppercaseterms in identity 3.
Another form of the identity that is useful for statistical analysis
expresses the relationshipin terms of the naturallogs of the ratios of
each component to its own trend. With asterisks to designate trend
variablesand a circumflexto denote the naturallog of each ratio of an
actualvalueto its trend[forexample, = Iln (QI Q*)],identity3 becomes
(5)
Q = R + V + F + H + N + MQ +
ME
This states that deviations from trend in the employment rate, R,
productivity, V, and the other components must sum to the deviation
fromtrendof real GNP, Q, which in turnis the GNP gap or, in language
I sometimesuse, the outputratio.
Okun'slaw states that the unemploymentgap is a constantfraction,
k, of the GNP gap. Using the terms definedin equation5, Okun's law
can be written as the statement that the employment ratio, R, is a
constantfraction,k, of the outputratio, Q:
A
(6)
k
R
Q
This,in turn,impliesthat 1 - k mustbe equalto the sumof the remaining
detrendedratiosto the outputratio:
(7)(7)
+ + + +
1l --k=V
k =-+V F H N+ MQ
+ + ME
Q
A byproductof the statistical research reportedbelow is a decompositionshowingthe ratioto Q of each termin the numeratorof equation7
in the typicalpostwarbusiness cycle.
Brookings Papers on Economic Activity, 2:1984
542
COMPONENTS
POSTWAR
OF THE IDENTITY
IN SEVEN
RECOVERIES
The first step in our analysis of the data takes the form of table 1, a
simple display of the growth-rateversion of identity 4. This version
decomposes the observed growth rate of real GNP for the first seven
quartersof each postwarrecoveryamongthe seven termsin the identity;
the abortedrecovery of 1980-81 is excluded, because it did not last for
seven quarters.Each figurelisted is an annualgrowthrate, so that the
actual change over the seven quartersin each case is seven-fourthsof
the rate shown. In the 1983-84 recovery, for instance, the employment
rate grew in the first seven quartersby a total of seven-fourthsof 1.97,
or 3.45 percentage points.7 Table 1 confirms that this was by far the
fastest growthin the employmentrate of any post-Korean Warrecovery and almostmatchedthe recordof the ebullient1950-51 KoreanWar
expansion, in which outputgrew much faster. The 1983-84 increase in
the employmentratewas morethansix times fasterthanin 1975-76, the
most recent comparablerecovery.
On a purelyarithmeticalbasis, most of the fasteremploymentgrowth
in 1983-84 comparedwith 1975-76 can be attributedto fastergrowthof
output:
Output
Othercomponents
Difference:
employmentrate
1975-76
1983-84
4.94
- 4.64
6.24
- 4.27
0.30
1.97
But this arrangementof the numbersis misleading,because it ignores
Okun's law. Of the 1.30 extra points of output growth in 1983-84
comparedwith 1975-76, Okun'slaw states that only roughlyone-third
should have taken the form of growthin the employmentrate. By this
reckoning, employmentrate growth in 1983-84 should have been the
1975-76rate (0.30)plus one-thirdof the extraoutputgrowth(0.33 times
1.30), or 0.73 points instead of the 1.97 points actuallyobserved. From
7. The employmentrate rose by 3.5 points while the unemploymentrate, as stated
above, fell by 3.1 points. This discrepancyoccursbecausethe 1982:4base for calculating
the growthrateof the employmentrateis 0.894, not unity.
Robert J. Gordon
543
Table1. First SevenQuartersof PostwarRecoveries:GrowthRatesof Real GNP
and Componentsof Identitya
Percentat annualrates
Period
Real
GNP,
q
Employ- Output ParticiEmployment
per
pation Average Popula- Output ment
rate,b
hour,c rate,d hours,e tion,'
mix,h
Mix,g
mQ
r
v
f
h
n
mE
1949:4-1951:3 10.27
2.27
4.83
-0.15
0.39
0.06
0.53
2.34
1954:2-1956:1
1958:2-1960:1
1961:1-1962:4
1970:4-1972:3
1975:1-1976:4
1982:4-1984:3
1.05
1.34
0.77
0.12
0.30
1.97
2.50
3.04
4.15
4.11
3.29
3.34
1.07
-0.71
- 1.04
0.05
0.52
0.31
0.43
0.51
0.14
-0.01
-0.03
0.86
1.21
1.57
1.33
2.53
1.93
1.16
-1.04
- 1.30
-0.40
- 0.95
-0.86
- 2.00
0.07
1.33
0.24
-0.40
-0.21
0.60
5.29
5.78
5.19
5.45
4.94
6.24
Source:Computationof text's identity4. Real GNP, U.S. Bureauof EconomicAnalysis.All other data, U.S.
Bureauof LaborStatistics.
a. Growthrates computedas differencein logs. The 1980-81recoveryis excluded,becauseit did not last for
seven quarters.The secondthrougheighthcolumnsadd to the firstcolumn,net of roundingerror.
b. Civilian.
c. Nonfarmbusinesssector.
d. Civilianlaborforce.
e. Nonfarmbusinesssector, hoursof all personsdividedby employment.
f. Civilianpopulationaged 16 andover.
g. RealGNP dividedby nonfarmbusinessreal GNP.
h. Nonfarmbusiness employment,from establishmentdata, divided by civilian employment,from household
survey.
thisperspectiveit seems understandablethatmostforecastershavebeen
surprised,if not startled,at the pace of the increase in the employment
rateand the correspondingdecline in the unemploymentrateduringthe
1983-84recovery.
However, we shouldnot maketoo muchof the rawnumbersdisplayed
in table 1. The 1983-84 recovery has differedfromthose in the past, but
we expect recoveries to differ in the relative growth rates of the
componentsof the identity. First, the growthrates in the table are not
detrended,but underlyingtrends in the growthof productivity,hours,
andthe other terms changefrom time to time. Second, the components
of the identityadjustto changes in outputwith varyinglag patternsand
would tend to behave differentlyin a recovery that begins slowly and
thenaccelerates(like 1971-72)thanthey wouldin a recoverythatbegins
rapidlyand then decelerates (like 1983-84). Thus in orderto determine
whetherthe behavior of unemploymentin the 1983-84 expansion has
been unusual,there is no alternativeto the econometricestimationof
historicalrelationshipsthattakesaccountof laggedadjustmentandshifts
in underlyingtrends.
544
BrookingsPapers on EconomicActivity, 2:1984
Regression Equations for Components-of-OutputIdentity
REINTERPRETING
"SURPRISES
AS REGRESSION
RESIDUALS
Was the 1983-84 decline in the unemploymentrate unusual?And if
so, why did it occur? To answer these questions, we need to identify
moresystematicallythe normalcyclicalpatternslinkingoutput,employment, and the other componentsof the outputidentity. In this section I
askwhetherthe 1983-84experiencewas unusual,in the sense of yielding
large regression residualsfor the employmentrate and any other components of the output identity, by using equationsthat take account of
the relationsunderlyingOkun's law andthe changesin the trendsof the
key variablesin the identity.
Equation 5 decomposes the detrended output ratio, Q. into the
detrendedvalues of the other componentsof the outputidentity. If we
are interested in allocatingthe observed GNP gap among the components of the right-handside of equation 5, then we can express each
componentas a linearfunctionof currentand laggedvalues of the GNP
gap:
(8)
ai + , bis
where Yitstandsfor each of the seven componentsof the outputidentity,
which are R, Vt, Ft, Ht, Nt, M,, and A.
Peter Clarkhas used equationsof this form togetherwith an addingup constraintimposedby equation5 to study Okun'slaw relations,and
my exposition in this section follows his very closely.8 Equation5 imposes adding-upconditionson the set of equationsinthe formof equation
8, in particularthat X ai = 0, X bio = 1, Xi bis = 0 for all s $ 0, and
Ei uit = 0 for all t. Clark shows it is possible to relate cyclical fluctuations
in the employmentrate to the GNP gap in two equivalentways, one of
8. I have estimatedequationslike equation8 for employment,productivity,participation, and hours in numerous papers dating back to "Inflationin Recession and
Recovery,"BPEA, 1:1971,appendixB. However,the idea of presentinga symmetricset
of equationssubjectto the adding-uppropertyof equation-set8 is attributableto Clark,
"Okun'sLaw andPotentialGNP."
RobertJ. Gordon
545
which is Okun's law in the form of equation8 for R~,and the other of
whichis an indirectroutethatuses the othercomponentsof the equation:
7
(9)
R,=-Rai
7
+
i=2
I - I bio
i=2
sO_
THE CHOICE OF BENCHMARKS
7
t
-
7
b iu.
i=2
i=2
AND THE MEASUREMENT
OF TRENDS
Estimationof equation-set8 requiresthat each variablebe expressed
relativeto its trend. However, a single trendfor the postwarperiodfor
each variableis not adequate.The growthrates of productivity,participation, hours, population, and the mix variables have all displayed
markeddifferences duringdifferentparts of the postwar era. To allow
for changes in the trend for each variable, trends are assumed to run
throughactual values of the variablesin particular"benchmark"quarters, which are those when the economy was operatingat its natural
unemploymentrate. These quarterswere chosen using a series for the
"no shock" naturalunemploymentrate that I estimated several years
ago using datafor 1954-80.9
The actual unemployment rate falls and rises smoothly, without
pronouncedjumpsor erraticmovements;thereforeduringeach business
cycle it crosses my estimatednaturalunemploymentrateon two separate
occasions, once when it is decliningin the recovery and expansion, and
once when it is rising at the end of the expansion and beginningof the
subsequentrecession. To establishjust one benchmarkfor each business cycle, the second crossing point is used, primarilybecause this
allowsus to base trendsfor the 1980son the mostrecentavailablequarter
(in 1979)when the actual unemploymentrate was equal to the natural
rate. To allow for lags in the adjustmentof unemploymentto the rapid
increasesin the GNP gap that are typicalat the beginningof recessions,
my exact procedureis to choose as the benchmarkthe quarterbefore
thequarterwhen the actualunemploymentratewas closest to the natural
9. The source is Robert J. Gordon, "Inflation,Flexible Exchange Rates, and the
NaturalRate of Unemployment,"MartinNeil Baily, ed., Workers,Jobs, and Inflation
(Brookings,1982), pp. 89-158. The same naturalrate of unemploymentseries is also
publishedin RobertJ. Gordon,Macroeconomics,3d ed. (Little,Brown, 1984),appendix
B, whereit is extendedbackto 1900.
546
Brookings Papers on Economic Activity, 2:1984
rate. These quartersare 1948:4,1953:4,1957:3,1960:1,1970:3,1974:2,
and 1979:3. These quartersoccur at varying intervals after the peak
designatedby the NationalBureauof EconomicResearchforeach cycle,
because the unemploymentrate was operatingin those peak quartersat
vaLyingamounts below the naturalrate of unemployment.'0(Data for
the output and unemploymentgaps from 1954 to 1984 are shown in
appendixtable A-1.)
Table 2 displays the growthrates between these benchmarkquarters
for real GNP and each of the componentsof identity4. Since we define
"potentialreal GNP" as the economy's real output when operatingat
the naturalrate of unemployment,the first column of table 2 provides
estimatesof the growthrateof potential(or natural)real GNP over each
majorcycle between 1948 and 1979. Familiarphenomenainclude the
rapidpotentialgrowthachievedduringthe KoreanWarcycle, a potential
growthrate close to 3.0 percent in the remainderof the 1950sand close
to 3.75 percent between 1960 and 1974, followed by a decelerationto
3.25 percent after 1974. A key question addressedbelow is, what has
happened to the growth rate of potential real GNP after 1979? To
facilitatecomparison,the cyclically correctedvalues, derivedfrom the
subsequentanalysis, are displayedin the bottomline of table2, but their
discussion is postponedfor now.
Because the naturalrate of unemploymentseries, used to establish
the benchmarkquarters,graduallyincreasesduringthe postwarperiod,
the correspondingnaturalrate of employmentdeclines. Most of this
decline shows up in the second columnof table2 in the 1957-60interval.
Between the other benchmarkquarters,the change in the employment
rate was negligible. The third column displays the growth rate of
productivitybetween benchmarkyears, with a rateof 2 percentper year
or fasterbefore 1970,1.5percentbetween 1970and 1974,and 1.1percent
between 1974and 1979. Ourchoice of benchmarkquartersassigns the
sharpdecline in productivityin the firsthalf of 1974to 1970-74 instead
of 1974-79, and this partly accounts for the two-step phasingin of the
productivitygrowthslowdownof the 1970s.
Otherfeaturesof the postwargrowthprocess can be identifiedin the
10. For instance at the NBER peak in 1969:3the actualunemploymentrate was 2.0
points below the estimatednaturalrate, but in 1973:4it was only 1.0 point below. This
accountsfor the fact that our benchmarksin 1960:1and 1979:3occur before the NBER
peakquarter.
547
Robert J. Gordon
Table 2. Periods between Benchmarks: Growth Rates of Real GNP and Components
of Identity, 1948-79a
Percent at annual rates
Population,
n
Output
mix,
Employment
mix,
mQ
mE
-0.29
-0.16
-0.11
-0.44
-0.30
- 0.43
0.77
1.20
1.49
1.56
2.28
1.87
0.74
-0.29
- 0.22
-0.03
-0.06
-0.16
0.80
-0.23
-0.11
0.04
-0.11
0.23
0.22
-0.25
1.35
-0.26
-0.18
0.47
-0.38
1.35
-0.23
Period
Real
GNP,
q
Employment
rate,
r
Output
per
hour,
v
Between
benchmarks
1948:4-1953:4
1953:4-1957:3
1957:3-1960:1
1960:1-1970:3
1970:3-1974:2
1974:2-1979:3
4.34
2.84
2.96
3.70
3.67
3.23
0.02
-0.14
- 0.40
0.00
0.00
-0.14
2.42
1.95
2.78
2.35
1.49
1.09
-0.12
0.51
- 0.47
0.22
0.37
0.77
2.09
-0.35
1.56
1.01
Addendum:
Post-benchmark,
1979:3-1984:3
Actual
Cyclically
corrected
2.80
0.00
Pasrticipation Average
rate,
hoiurs,
h
f
0.58
Source:Post-benchmark
cyclicalcorrection,table 5. Otherdata, same as table 1.
a. Benchmarkquartersimmediatelyprecede quarterswhen the actual unemploymentrate was closest to the
naturalrate;they are as follows: 1948:4,1953:4,1957:3,1960:1,1970:3,1974:2,and 1979:3.See text description.
remaining columns of table 2. The growth rate of the labor force
participationrate, primarilyas a resultof an influxof adultfemales, was
substantiallyfasterin the 1974-79periodthanin the otherintervals.The
proceduredeveloped below for allocatingthe post-1979growth rate of
potentialreal GNP to the variouscomponentsshows thattherehas been
a slowdown in the growthrate of the potentiallaborforce participation
rate since 1979.The decline in hoursper employeewas morerapidafter
1960than before, but this decline appearsto have become a bit slower
since 1979. The growth rate of population after 1979 is treated as
exogenous and unresponsive to cyclical factors. But we will need to
interpretthe behaviorof the two mix termsin this period,whichtogether
contributedno more than - 0.18 point to the growth rate of potential
real GNP in the 1960-79 interval,but which have moved more sharply
since then.
REGRESSION
RESULTS
THROUGH
1979
Preliminaryversions of equation8 were estimatedwith the current
value and eight lags on the log output ratio, Q. Since the fifth through
C) cn lr
"t
C
w.l
eq lr 0 --
1.
C)
CD
cn cn C)
o a\
n cnD C)
ct 0CD
I
CI
-cq110 ell0
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0U:' ro0oN
0
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-
W
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0
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0
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0
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c
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r'
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-0~a cq 110-00
ei1. 00
m
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t~~~~~~~~~~~~~~~~~~~~~~~~~~~~t
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r~~~
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M~~~~~~~~~~~~~
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549
Robert J. Gordon
eighth lags were jointly insignificant,the equations were reestimated
without these terms. Each of the equations displayed evidence of
significantpositive serialcorrelation,however, and so we do not report
the individualcoefficientshere.
The serial correlation problem can be eliminated by adding four
laggedvalues of the dependentvariableto each equation.Thus, in place
of seven equationsin the formof equation8, I estimateseven equations
in the formof
4
(10)
Yit= ai +
>
4
ciS
Yi ts+
bis
+ u,it
where, as in equation 8, Yistands for one of the seven componentsof
theoutputidentity.Thisapproachhasa disadvantage:becausea different
set of lagged dependent variablesenters each equation, the adding-up
propertyof equation8 is not preserved.The long-runresponses of Yto
Qin equations specifiedas in equation 10 are displayedon the last line
of table 3. These responses sum to 0.6, so that the loss of the adding-up
property is a moderately serious problem. The small long-runeffect
shown for output per hour indicates there is virtually no permanent
productivitybonus to be enjoyedfroma periodof highutilizationof the
economy's resources; there is only a transitory productivity bulge
associatedwith an increasein the outputratio.1I
The remainderof table 3 shows the individualcoefficients in the
formatof equation 10 for each of the seven components of the output
identity. In each case the first lagged dependent variable is highly
significant,indicatingthat the dynamicrelationshipbetween the seven
componentsand the output ratio involves a response of the change in
each component to the change in the outputratio. The first-difference
relationshipis particularlyevident in the columns for outputper hour
and for hours per employee. In these columns note that the coefficient
on the output ratio lagged once is significantlynegative and about the
sameorderof magnitudeas the positive coefficienton the currentvalue.
A test for thejoint exclusion of currentandlaggedoutputvalues showed
outputwas significantin all equationsexcept thatfor population.
11. Thisresultconflictswithmypreviousfindingthatthereis a permanentproductivity
bonus. See Robert J. Gordon, "The 'End-of-Expansion'Phenomenonin Short-Run
ProductivityBehavior,"BPEA, 2:1979,pp. 447-61. The long-runeffect appearsto turn
on whetherthe dependentvariableis total hours, as in that paper,or productivityitself,
as in thispaper.
550
Brookings Papers on Economic Activity, 2:1984
In table 3 two features of the employment-ratecolumn, the Okun's
law equation, are evident. First, the long-runOkun's law coefficient,
which is the entryin the last row, is close to 0.5, not the 0.33 popularized
by Okun's original work."2Second, leaving aside the equation for
population,which is includedonly for symmetry,the standarderrorin
the Okun's law equation is lower than for any of the other equations.
This occurs because of negative correlationsamong the residuals in
some of the other equations. For instance, a decline in productivityis
accompaniednot only by an increasein hoursbut also by an increasein
the two mix-effect terms. Such negative correlationsmay explain why
Okun'slaw has remainedrelativelyreliableover the years. (The correlation matrix of the residuals of the table 3 equations is presented in
appendixtable A-2.)
The Post-1979 Growth Rate of Potential Real GNP
MINIMIZING
THE POST-1979
IN THE EMPLOYMENT
ERROR
RATE
The estimated Okun's law relationshipin table 3 can be used to
estimate the growth rate of potential output since 1979. Because the
Okun's law equation has a relatively low standarderror before 1979,
there is a presumptionthat it may also track the relationshipbetween
the employmentrate and the outputratio, Q, since 1979.An additional
advantageof choosing the employmentrateequationfor this exercise is
that its trend value, the natural rate of employment, was virtually
constant in the five years before 1979 and can be presumed to have
changedlittle since 1979. In contrast, several of the other components
of the identity have significanttrends between benchmarksand, as we
shall see, some of these trendshave changedsince 1979.
The basic idea of using an Okun'slaw equationto trackpotentialreal
GNP growth is straightforward,but several choices must be made
regardingthe details of implementation.We must search for a growth
12. ThisresultconflictswithClark'sfindingthatOkun'soriginalestimateof one-third
is correct.The discrepancymayresultfromrestrictionsClarkimposeson the shapeof the
lag distributionand on the formof the serialcorrelationcoefficients,in contrastwith the
unrestrictedformatin table3. Also, Clark'sequationsincludeleadingvaluesof the output
ratiovariable.
Robert J. Gordon
551
rateof potentialreal GNP, q*, that minimizesthe post-1979errorin an
equationfor the employmentrate. The firstchoice that mustbe madeis
the time interval for the error. The obvious choice is the root mean
squarederror over the entire post-1979period. This places relatively
more weight on observations in 1983-84 than in 1980-82, since an
incorrectvalue of q* would cause potentialreal GNP to driftaway from
its "true" value as time goes on. For instance, a value of q* that is 1
percentagepoint per year too high would cause the outputratio, Q, to
be five percentagepoints too low by mid-1984,and the impliedemployment rate for mid-1984would be much lower than the actual observed
employmentrate.
The criterionbased on the root mean squarederrorover the 1979-84
period differs from the related exercise carriedout by Clark. While I
choose a single value for q* by minimizingthe errorover the full fiveyear period, Clark chooses a differentgrowth rate of q* each quarter
that minimizes the error in an Okun's law equation in that particular
quarter.13The resultof Clark'sprocedureis a highlyvariabletime series
for q* instead of the fixed growthrate between benchmarksthat results
frommy procedure.An undesirableside effect of Clark'smethodis that
it translatestemporaryerrorsin the Okun's law equationdirectly into
variationsin q*. In 1981-82 the unemploymentrate rose more rapidly
thanOkun'slaw can explainwith a fixed value of q* and in 1983-84 fell
morerapidly,so Clark'smethodreaches the conclusionthat q* grew in
1982andfell in 1983-84.
The Okun's law equation presented in table 3 provides a set of
coefficientsthat can be used to calculate the employmentrate implied
by alternativeGNP gaps correspondingto different assumed growth
rates of potentialreal GNP, q*, since 1979.Table 4 displays six sets of
long-runcoefficient estimates and standarderrors of estimate, correspondingto six differentassumptionsaboutthe post-1979growthrateof
q*, varyingfrom2.0 to 3.5 percentper year. In each of the six columns,
the post-1979trendvalue of the employmentrateis assumedto be fixed
at 94.0 percent.
Note firstthat the long-runsum of coefficientson Q varies inversely
withthe assumedvalue of q*. This is intuitivelysensible, because a low
assumedvalue of q* means a small GNP gap during1979-84, so that a
largeOkun'slaw coefficientis then requiredto "explain" the observed
13. Clark,"Okun'sLaw andPotentialGNP."
552
Brookings Papers on Economic Activity, 2:1984
Table4. AlternatePotentialGrowthRatesand Errorsin Okun'sLaw Equations,
1954:1to 1984:3
Assumed value of potential real GNP growth, 1979:3-1984:3
Statistic
2.00
2.50
2.75
3.00
3.25
3.50
Long-runsum
of coefficients
on Q
0.538
0.497
0.461
0.425
0.385
0.338
Standarderror
of estimate
0.2228
0.2171
0.2169
0.2185
0.2211
0.2238
Errors,
dynamic
simulationa
1981:4
1982:1
2
3
4
-0.938
- 0.783
-0.791
- 0.905
- 1.303
-0.527
-0.348
-0.327
-0.412
-0.780
- 0.377
-0.190
-0.161
- 0.238
-0.596
-0.252
-0.060
-0.025
-0.096
-0.449
1983:1
2
3
4
-0.961
- 1.073
-0.815
-0.405
-0.408
-0.490
- 0.249
0.253
-0.216
-0.287
- 0.030
0.493
1984:1
2
3
-0.466
-0.731
- 1.123
0.242
0.034
-0.291
0.511
0.337
0.051
Mean error
- 0.596
- 0.163
0.722
0.340
Root mean
squared
error
-0.142
0.056
0.096
0.027
-0.326
-0.036
0.067
0.210
0.141
-0.213
-0.065
-0.127
0.143
0.684
0.059
0.002
0.280
0.823
0.169
0.113
0.394
0.950
0.728
0.584
0.333
0.894
0.772
0.547
1.020
0.910
0.699
0.124
0.230
0.322
0.339
0.407
0.476
-0.004
0.298
Source:Equation10 appliedto the employmentrate. Data, as in table 1.
a. Simulationperiod1979:4-1984:3.
employment-rategap. A highvalue of q* means a largeGNP gap during
1979-84, and a small Okun'slaw coefficientis required.The best-fitting
value of q* is 2.75 percent per year. Because each of the estimated
equations includes four lagged values of the dependent variable, the
estimatedresidualsarenot very informative.Moreinterestingareerrors
calculatedfrom a dynamic simulationthat begins in 1979:4.In light of
the fact that the lowest standard error of estimate occurs for the
assumption that q* equals 2.75, it is not surprisingto find that this
assumptionalso implies the lowest mean error and lowest root mean
squarederrorfor the 1979-84 dynamicsimulation.
For each assumedq* value, the simulationerrorsin table 4 displaya
553
Robert J. Gordon
consistentpattern.The errorsfor 1982:4,the troughquarterof the 198182 recession, always have the largestnegativevalues, andthe errorsfor
1983:4and 1984:1have the largestpositive (or smallestnegative)values.
This pattern of errors reinforces the impressionthat the employment
rate has risen "too rapidly"since the recession trough,partlybecause
it was "too low" at the trough. The difference between the errors in
1982:4and 1984:3is 0.65 percentage points, comparedwith an actual
increase of 3.46 percentage points in the employmentrate duringthe
same interval. Thus about one-fifthof the increase in the employment
rateis left unexplainedin this approach.
OTHER
OF
COMPONENTS
THE
OUTPUT
IDENTITY
SINCE
1979
HavingconcludedthatpotentialrealGNP has grownat a rateof about
2.75 percent since 1979, the next step is to account for this growth by
the separate components of the output identity-productivity, hours,
participation,and the rest. In doing so, pre-1979trendsfor the separate
components cannot be used, because these may have changed; and
observedpost-1979trendsare contaminatedby cyclical effects, because
the economy has not yet reached a natural-employmentbenchmark.
ThereforeI developed a modifiedsearchprocedureto identifythe post1979 trends of six components of the identity, with no trend change
assumedfor the seventh component, the employmentrate, R, because
I treat the naturalunemploymentrate as constant at 6.0 percent during
1979-84. Given the 2.75 percent annual growth rate of potential real
GNP determinedin table 4, the equationsfor the six componentsof the
identityfrom the second throughseventh dependentvariablesof table
3, all estimated over the 1954:1-1979:3period, are simulatedfor the
interval 1979:4-1984:3.The fitted value of this dynamic simulationis
the detrendedlevel of each componentof the identity, expressed as a
functionof its own lagged simulatedvalues and the currentand lagged
values of the outputratio:
4
4
(11)
Yi, ai +
>
ci Y
+
E
b Qt
+
it
Hereequation 11is identicalto equation10except for the primeson the
detrended Y terms, which indicate simulated values for the 1979-84
period.The outputratiotermsare constructedusingthe pre-1979trends
s: woIS
0
00
'r
t
II 0
S
'
0e
C)
+
o-rie
a,\
I
tE~~i~
OO
c en
I
I
~
o~
-e^
,
0-'
000000"t
I
oo
r
I
I
oo5
^
^
,
n
0 W -0
I
I
too
I
I
I
000
oo
_
.
LU2
Z-
*
*I
eoo en
~
~
~~
e
~
~
0r~~~-~-
-
en 0
m
.
i~~~
'I
0
0-W)'C
I
Cm
';
ONbOO
o-
X
I
F~~~~~~~~~~~~~~~e
en
en "t*_t
S
o
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o
AR
A
I
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> I II
~~~I
W
l
i
0
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rie0r
I
I I
en 0
?
O.N It
I I
00
00
'IC^^
N
00
U2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C
C,~~
x
00
0000
000
0>
m
ONO^N
ON
ON
O
ON
ONOOO
E
0d
0
--
k4~~~~II4
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00
00
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00
00
0
RobertJ. Gordon
555
for potentialoutput growth, q*, shown in table 2 and 2.75 percent per
year as the potentialoutputgrowthratefor 1979-84.
Alternativevalues for the trend value for each component in each
quarter, Yi*,were computedby searchinga grid of possible values for
the 1979-84growthrateof Yi*,for example,0.00, 0.05, and so on. These
alternativevalues, Yi*,were then comparedwith the values of the trend,
Yi*',implied by the observed actual values, Yit,and the simulated
detrendedvalues fromequation 11, that is, Yi',:
(12)
Y.=
i
i
exp Yi't
The exponent enters because of our originaldefinitionof all detrended
variablesin log form, that is, Y = ln (Y/Y*).The grid is searched for
small increments above and below the previous 1974-79 trend to
determinethe value of the 1979-84 trendthat minimizesthe sum of the
squareddifferences between the alternativeconstructed trend values
alongthe grid, Yi*tand Y:' of equation12. Thus we minimizethe sum of
t for each of the six
the squarederrors, that is, the sum Of(Yt
Y:')2,
componentsof the identity.
Table 5 is arrangedwith a columnfor each componentof the identity
andis dividedinto three sections. The top section shows the value of the
optimalconstructed 1979-84 trend for each component, Yi*,and compares it with the previous trend between the 1974:2and 1979:3benchmarks, taken from table 2. The middle section of table 5 shows the
calculatedlog deviationsbetween the actualobserved values and these
Thebottomsectionshowsthe dynamic
optimaltrends,thatis, ln (Yit/Yi*t).
simulationerrorsfrom equation 11that are the key ingredientin finding
the optimalpost-1979trends.
The most interestingresultsarefor productivitygrowthin the second
column of table 5. The top section shows that cyclically adjusted
productivitygrowthin the nonfarmprivatebusiness sector in 1979-84,
1.01percent, was almostthe same as the 1.09percenttrendexperienced
duringthe 1974-79interval.Thisis the sameconclusionrecentlyreached
by Clark.14There is no evidence at all that the productivitygrowth
slowdown of the 1970s was transitory, at least in the data available
through1984:3.
14. Peter K. Clark,"Productivityand Profitsin the 1980s:Are They Really Improving?" BPEA, 1:1984, pp. 133-67.
556
BrookingsPapers on EconomicActivity, 2:1984
Productivitygrowthin 1984:2and 1984:3soaredjust about3 percentage points above the estimated1.01percenttrendline, as shownin table
5, middle section, second column. But the relatively small simulation
errors,bottomsection, second column,indicatethatthe excess of actual
productivityover the estimatedtrendline was a normalcyclicalphenomenon andcan be explainedby the fact, evidentin the regressionequation
displayedin table 3, thatproductivitygrowthrespondspositively to the
growthof the outputratio, not its level, and thus was unusuallyhigh in
response to the rapid pace of the 1983-84 recovery. As actual output
growthrecedes towardits estimatedpotentialrate of 2.75 per year, this
analysispredictsthatthe deviationof productivityfromtrend(shownin
the middlesection of table5) willrecedetowardzero. Duringthisprocess
we could observe several quartersof zero or even negativeproductivity
growth, a possibility confirmedby the government'spreliminaryestimate of zero productivitygrowthin 1984:3.
Fortunatelythe assumedannualrate of q*, 2.75, yields a set of trend
estimates for the components of the identity that sum to 2.80 percent,
very near the assumed value. The top section of table 5 also shows that
two factors, slower trend growth in participationand in population,
have contributedto slower growth in potential real GNP since 1979.
Togetherthese two factors have reducedq* by 0.79 percentagepoints,
andtheireffect has been only partiallyoffset by a slightlyslowerdecline
in hours (0.05 points) and a more positive trend in the sum of the two
mix effects (a shift from0.06 to 0.36 points). Overall,the growthrate of
potentialreal GNP slowed by 0.43 points from 1974-79 to 1979-84, and
withunemploymentalreadyat7.5 percentthiswill soonplacea constraint
on the feasible path of actualreal GNP.
The middle section of table 5 shows that the deviationfrom trendof
average hours, like that of productivity,has been positive in 1984. As
table 3 showed, hours respond strongly to the rate of change of real
GNP, and thus hours, like productivity,have been boosted by the rapid
pace of the economicrecoveryto date. In contrast,the participationrate
has made large and continuingnegative contributionsto the log output
ratio (GNP gap) duringthe past two years. The errors in the bottom
sectionof table5 arenot large,indicatingthatthispatternof participation
is trackedfairly accuratelyby the dynamic simulationsof the 1954-79
equations.
Takentogether,the mix-effectvariablesare not entirelysatisfactory.
RobertJ. Gordon
557
Outputmix shows a cyclical patternthatbroughtit froma largepositive
at the end of the recession back to near zero in recent quarters.The
modest errors in the bottom of the table indicate this pattern was
predictable.Althoughthe largepersistentnegativedeviationsfromtrend
in the employment-mixterm are typical and occur in every business
cycle, the largenegative simulationerrorsin the latest quartersindicate
that the behavior of the two employmentmeasures has been unusual
recently.15
We can now use the simulationerrorsin the bottomsection of table 5
to ask, Why was the unemploymentrate so highin late 1982?And why
did it decline so rapidlyin 1983-84? Althoughthe sum of the errorsof
the first throughseventh columns is not zero, because these equations
do not observe an exact adding-upproperty, the sum varies within a
relatively narrowrange between -0.34 and -0.46. This allows us to
matchlargeerrorsin the employment-ratecolumnwithcorrespondingly
large errors of the opposite sign in one or more of the other columns.
Because the behaviorof the employmentmix does not appearto have
been capturedwell by the presentmodel, andbecause the employmentmix errorsmay involve data problemsinstead of behavioralissues, we
will confineour attention,for now, to the otherelementsof the identity.
Between the trough of the recession, in 1982:4, and 1984:3, the
unemploymentrate fell from 10.6percentto 7.5 percent, corresponding
to a rise in the employmentrateof 3.5 percentagepoints. The simulation
errorsof table 5 indicate 0.8 point of this rise was not predictedby the
Okun's law equation (first column), so that 2.7 points, or 80 percent
of it, was predictedfromthe behaviorof real GNP.
Of the 0.8 point error, it appearsthe employmentrate was 0.5 point
too low in 1982:4.In thatquarter,a 0.6 pointpositive errorin the outputmixtermindicatestotalrealGNP was unusuallyhighrelativeto nonfarm
business real GNP. In other words, the outputratio, Q, based on total
realGNP, madethe economylook moreprosperousandpredictedhigher
employmentthancan be explainedby normalcyclical relations.
Therapiddeclinein unemploymentandcorrespondingincreasein the
employmentrate in 1983:4and 1984:1show up as positive simulation
15. Untilrecentmonths,commentatorsnotedthe morerapidrise in E thanin EBas an
interestingphenomenon.See "An EconomicIndicatorTakeson New Luster,"Business
Week(July23, 1984),p. 20. However,by 1984:3,employmentgrowthduringthe recovery
hadcome togetherin the two measures.
558
Brookings Papers on Economic Activity, 2:1984
errors in the first column.16 These positive errors have as their
counterpartnegative errors in productivity,participation,and output
mix, again ignoring the employment-mixerrors for now. The rapid
decline in unemploymentappearsto be connected with relatively slow
growth in productivityand participationand slow growth in total real
GNP relative to nonfarm business real GNP. By 1984:3, errors are
relativelysmallexcept for productivity,which is highrelativeto prediction in that quarter.Over the entire intervalfrom 1982:4to 1984:3,the
productivityerrorsmove in the same directionas the employmentrate
errors, so they add to, ratherthan explain, the mystery of why unemployment declines so much. By contrast, the output-mixerrors, taken
alone, do offset the employment errors for this interval and thus
contributeto an explanationof them.
Turningnow to the employmentmix, largenegativeerrorsin the two
latest quartersindicate that total employmentin the household survey
grew rapidly relative to nonfarmemployment reported by establishments. This could reflect an underreportingof new establishments,
which could also understateoutput.Orit could be a transitoryphenomenon, with no such meaning.
The simulationerrorsin table5 arelinkedtogetherby an identity,and
so the connectionsdiscussed above do not implycausation.Some of the
offsetting errors in particularcomponents of the identity are to be
expected and are consistentwith the negativecorrelationsamongerrors
for the 1954-79 period displayedin the correlationmatrixof appendix
table A-2. In particular,some correlationsinvolve the employment-mix
term, whose behaviorhas been puzzlingin the presentrecoveryaccording to this analysis. The offsetting productivityand employment-mix
errorsin 1984:3,forinstance,areconsistentwiththe negativecorrelation
between those two componentsobservedin 1954-79.
Combiningthe two mixeffects revealsa strongtrendin theircombined
errorsin the past two years. We can offer some conjecturesas to the
observed shifts in the combinedmix effect. Recall that the output-mix
effect is definedas MQ = Q/QB, where the B superscriptrefers to the
16. The simulationerrorsin the firstcolumnof table 5 differfrom those in the third
columnof table 4, because the table 5 errorsare based on coefficientsfroman equation
estimatedfor the 1954-79 period,whereasthose in table4 use coefficientsestimatedfor
1954-84.
559
Robert J. Gordon
nonfarm private sector. The employment-mix effect is ME = EBIE.Thus
the two effects togetherare
(13)
MQME =
QIE
QB/EB
'
thatis, the ratioof averageoutputper employee in the total economy to
average output per employee in the nonfarmprivate business sector.
Negative shifts in equation 13 mighthave occurredif there had been a
shiftin the economy's outputmix fromthe higher-productivitynonfarm
private sector to the lower-productivitygovernmentand farm sectors,
but this does not seem to providea plausibleexplanation.17 Thuswe fall
backon the possibilityof datameasurementerrorsto explainthe decline
in the productivity ratio expressed in equation 13. This could have
occurredif household employment,E, were measuredcorrectly, while
the remainingthree componentsthat rely to some extent on establishmentsurveys (Q, QB, andEB)were understateddue to the undersampling
of new firms.If this were true, it would accountfor underpredictingthe
decline in the unemploymentrate by the fact that the real GNP rise has
been understatedin official data. It is likely that the validity of this
hypothesis cannot be assessed for several more years until there is a
majorbenchmarkrevision of the real GNP data.18
In light of the evidence that the productivitytrend for total private
nonfarmbusinesshas notquickened,it is worthcomparingthataggregate
sector's productivitywith the productivityperformanceof the manufacturingsector alone. By convertingpublishedindex numbersinto actual
levels, the aggregateprivatenonfarmdata are dividedinto productivity
indexes for manufacturingand nonfarmnonmanufacturingseparately.
17. Publishedtables of the Bureauof Labor Statistics indicateno majordifference
betweenproductivitygrowthin the privatebusinessandnonfarmprivatebusinesssectors,
indicatingthat the farmsector does not contributeto the puzzle. As for the government
sector,the nationalincomeandproductaccounts(comparingtables6.1 with6.8B)indicate
that real GNP per full-time-equivalentemployee in the nonfarmprivatesector is more
than50 percenthigherthanin the governmentsector. Thusthe unusuallyslow growthof
government-sectorreal GNP in 1983-84 should have created a positive ratherthan a
negativeproductivitymix effect.
18. Such a datarevisioncould take as long as seven years,judgingfromthe example
of the recent $58 billionupwardrevision of 1977GNP reportedin GeraldF. Donahoe,
"The NationalIncome and ProductAccounts: PreliminaryRevised Estimates, 1977,"
Survey of Current Business, vol. 64 (May 1984), pp. 38-41.
Brookings Papers on Economic Activity, 2:1984
560
The annualgrowth rates for all three between the benchmarkquarters
and since 1979:3are as follows:
1948:4-1953:4
1953:4-1957:3
1957:3-1960:1
1960:1-1970:3
1970:3-1974:2
1974:2-1979:3
1979:3-1984:3
Total private
nonfarm
Manufacturing
Nonfarm
nonmanufacturing
2.4
2.0
2.8
2.4
1.5
1.1
1.6
2.7
2.4
2.2
2.6
3.6
2.1
3.0
2.4
1.6
3.1
2.3
0.5
0.7
1.0
Productivityoutside manufacturingslowed sharplyafter 1970, well
before the first oil shock. All the slowdown in aggregate nonfarm
productivityin this intervalcomes fromthis sector;productivityspeeded
up in manufacturing.Even in the post-OPECintervalof 1974:2-1979:3,
manufacturingproductivitygrowthis only moderatelybelow its performance in the 1950sand 1960s,while outside manufacturingthe productivity trendis still very slow. Since 1979:3all three sectors show faster
productivitygrowth, althoughthe statisticalanalysis for the aggregate
nonfarmsector attributesall of this speedupto the cyclical recoveryand
none to a quickeningtrend. Determiningwhether the speedup to 3.0
percent growth in manufacturingproductivity in this latest period
represents some improvementin trend requires a further statistical
analysis and, probably,more quartersof observation.
Conclusion
The point of departurefor this paperwas the surprisinglyrapid, 3.1
point decline in the aggregateunemploymentrate duringthe first seven
quartersof the 1983-84 recovery. Analysis of potentialoutput growth
over this period and the Okun's law relationshipbetween unemployment and output indicates that a 2.4 point decline in unemployment
could have been expected given the rapidrise in GNP and the modest
growthof potentialGNP in this period. The remaining0.7 point decline
occurredbecause, relative to prediction, the unemploymentrate was
RobertJ. Gordon
561
about0.5 point "too high" in 1982:4at the troughof the recession and
about 0.2 point "too low" in 1984:3.It was a bit more than 0.5 point
"too low" during1983:4-1984:2.Analysis of the outputidentityreveals
severalfactors that have been the counterpartsof these surprisesin the
unemploymentrate:a disappointingproductivityperformancein 1983:41984:1, an unusual rise in nonfarmbusiness output relative to GNP
during1983,and an unexplainedsurgein 1984:2and 1984:3in the ratio
of householdto establishmentemployment.
The analysis of historical Okun's law relationships between unemploymentand output yields as a byproductseveral findingson the
growthof potential real GNP and productivity.It appearsthat natural
or potentialreal GNP, Q*, which measureshow muchthe economy can
producewhen operatingat its naturalunemploymentrate, roughly6.0
percent since 1975, grew by 3.75 percent per year between 1960 and
1974,3.35 percentper year between 1974and 1979,and2.80 percentper
yearsince 1979.Themajorfactorscontributingto a slowdowninpotential
outputgrowthafter 1979are slower growthin the working-agepopulation, owingto the decline in the birthratethatoccurredin the 1960s,and
slower growth in the labor force participationrate, indicatingthat the
rapidinflux of adult women into the labor force that characterizedthe
late 1970smay have passed its peak.
The analysisindicatesthatthe relativelyrapidproductivitygrowthin
the period 1983:1to 1984:2was a normal cyclical phenomenon, the
counterpartof the rapid output growth that occurred in the same six
quarters.The cessationof productivitygrowthin 1984:3,the counterpart
of relativelyslow ouputgrowthin that quarter,supportsthe pessimistic
assessment offeredhere.
The findingthat aggregateproductivitygrowthhas not revived since
1979,after adjustmentfor normalcyclical effects, has importantimplications for alternativehypotheses that have been developed to explain
the post-1973 slowdown in productivitygrowth. Several of these hypotheses, by focusingon factorsthatwere adversein the 1970sbut have
improvedin the 1980s, suggest that we now should be witnessing an
ameliorationof the productivityslowdown. These hypotheses include
the impact in the 1970sof higheroil prices, higherprices of other raw
materials,slower capitalaccumulation,and more stringentgovernment
regulation. Another approach, Nordhaus's "depletion hypothesis,"
based on a decline in innovationand a general "runningout of ideas,"
562
Brookings Papers on Economic Activity, 2:1984
does not call for any turnaroundin the 1980sand seems to be supported
by the evidence in this paperthatthe nonfarmprivateproductivitytrend
has not revived when 1979-84 is comparedwith 1974-79.19
The analysis in this paper contains some further implicationsfor
policymakersandpolicy debates. First, the regressionresults show that
a permanentincrease in the economy's use of its resources causes only
a temporaryincrease in productivityabove its long-runtrend, not a
permanent increase. Thus any argumentfor raising the economy's
utilizationrate must rest on the benefits of job creationratherthan on
the benefits of a permanentproductivitybonus. Second, the relatively
slow 2.8 percentgrowthrateestimatedfor potentialrealGNP since 1979
defines the outputgrowthrate that is consistent with a constant unemploymentrate; it will constrainthe growthof outputonce the economy
arrives at its naturalunemploymentrate of roughly 6 percent. As of
1984:3, however, there is still slack in the economy, with the actual
unemployment rate 1.5 percentage points higher than the assumed
naturalrate, and the actual level of real GNP 3.1 percent below the
estimatedlevel of potentialreal GNP.
Finally,this analysisraises seriousdoubtsaboutsupply-sideanalyses
that predicteda floweringof productivityand work effort as a result of
the tax rate reductions that have been put in place. After cyclical
correction,there appearsto have been no improvementin productivity
growthin the nonfarmprivatesector as a whole. Any improvementthat
may have occurredin the manufacturingsector, whereactualproductivity gains have been relatively large, has been offset by a deterioration
elsewhere in the economy. As for the predictedresponsein work effort,
there is no importantchange in the downwardtrendin average hours,
and there has been a slowdown of 0.3 percentagepoints in the trend
growthrate of laborforce participationbetween 1974-79 and 1979-84.
19. WilliamD. Nordhaus, "Economic Policy in the Face of DecliningProductivity
Growth," European Economic Review, vol. 18 (May-June 1982), pp. 131-57.
563
Robert J. Gordon
APPENDIX
TableA-i. Outputand UnemploymentGaps, 1954-84
Percentexcept where otherwisenoted
Unemployment
rate
Natural
unemployment
rate
Unemployment
gap
(percentage
points)
-2.1
1.6
5.6
4.4
5.1
5.1
0.5
-0.7
665.6
684.8
705.1
726.2
750.1
0.9
-0.2
-3.5
-0.6
-1.8
4.1
4.3
6.8
5.5
5.5
5.1
5.1
5.0
5.1
5.2
- 1.0
-0.8
1.8
0.4
0.3
1961
1962
1963
1964
1965
778.2
807.5
837.8
869.3
901.9
-2.8
-0.9
-0.7
0.8
3.0
6.7
5.6
5.6
5.2
4.5
5.2
5.3
5.4
5.5
5.6
1.5
0.3
0.2
-0.3
- 1.1
1966
1967
1968
1969
1970
935.8
970.9
1,007.4
1,045.2
1,084.5
5.1
4.1
4.9
4.0
0.1
3.8
3.8
3.6
3.5
5.0
5.6
5.6
5.6
5.6
5.6
-1.8
- 1.8
-2.0
-2.1
-0.6
1971
1972
1973
1974
1975
1,124.9
1,166.7
1,210.2
1,254.1
1,295.5
-0.2
1.6
3.6
-0.6
-5.1
6.0
5.6
4.9
5.6
8.5
5.8
5.8
5.8
5.9
6.0
0.2
-0.2
-0.9
-0.3
2.5
1976
1977
1978
1979
1980
1,337.9
1,381.6
1,426.8
1,473.0
1,515.9
- 3.0
-0.9
0.8
0.4
-2.7
7.7
7.0
6.0
5.8
7.1
5.9
6.0
5.9
5.9
5.9
1.8
1.0
0.1
-0.1
1.2
1981
1982
1983
1,558.8
1,602.9
1,648.3
- 3.0
-8.0
-7.1
7.6
9.7
9.6
6.0
6.0
6.0
1.6
3.7
3.6
1982:4
1,619.7
-9.1
10.6
6.0
4.6
1983:1
2
3
4
1,631.1
1,642.5
1,654.0
1,665.5
-9.0
-7.4
-6.5
-5.7
10.4
10.1
9.4
8.5
6.0
6.0
6.0
6.0
4.4
4.1
3.4
2.5
1984:1
2
3
1,677.2
1,688.9
1,700.8
-4.0
- 3.0
-3.1
7.9
7.5
7.5
6.0
6.0
6.0
1.9
1.5
1.5
Potential GNP
(billions of 1972
dollars)
Output gap
1954
1955
628.9
647.0
1956
1957
1958
1959
1960
Period
Source:Unemployment
rate, BLS. Otherdata, author'scalculations.
564
Brookings Papers on Economic Activity, 2:1984
Table A-2. Correlation Matrix of Residuals for Equations in Table 3
Employment
rate,
R
Output
per
hour,
V
Participation
rate,
F
Average
hours,
H
Population,
N'
Output
mix,
MQ
Employment
mix,
E
...
Employment
rate,R
1.00
...
...
...
...
...
...
...
...
.
1.00
...
...
...
Output
per hour, v
-0.11
1.00
.
Participation
rate, F
- 0.33
-0.18
-0.08
- 0.57
0.14
1.00
. .. ...
0.10
-0.43
-0.18
0.07
-0.06
0.03
1.00
-0.28
-0.35
-0.52
-0.01
0.10
...
Average
hours, H
Population,N ~ 0.10
Outputmix, MfQ -0.18
Employment
0.21
mix, M~IE
...
1.00
-0.23
...
1.00
Comments
and Discussion
Peter K. Clark: In this paper,RobertGordonhas attackedanimportant
fiscal policy issue: what is the trendrate of growthin U.S. real output?
If the underlyinggrowthrateis high,thenprojectinghigherfutureoutput
and lower future federal deficits may be justified. Conversely, if the
underlyingtrendis weak, then projectionsof slower growthand higher
futuredeficits are more appropriate.
Gordonfinds that the trendgrowth rate of real GNP has been about
2/4 percentper year, well below the postwaraverageof 3?/2percent, and
on the pessimistic end of the rangeof estimates one usually hears. This
figureis generatedby a complicatedprocedurethatcombinesanarbitrary
estimate of Okun's law for 1954-79 with a nonlinearsearch routineto
findthe best-fittinggrowthratefor 1979-84.
A simplerroute to the same result is to estimate Okun'slaw in firstdifferenced form, as shown below (standarderrors in parentheses,
sampleperiod 1954:1-1984:2).The ratioof the constanttermto the sum
of the outputcoefficientsin such an equationprovidesan estimateof the
growth rate of trend GNP; the dummy variableD80 (which equals 0
before 1980:1andequals 1thereafter)generatesanestimateof the decline
in the trendoutputgrowthat the turnof the decade.
AU,
-
=
0.416 -
0.099 D80 - 24.9 Alog Y, - 16.0 AlogY,1
(0.03)
(0.06)
=
(2.2)
(2.3)
6.2 A10gY,-2
(2.2)
0.74
Standard error of estimate = 0.23
Durbin-Watson = 1.69
According to this regression, trend output growth has declined
significantlyin the 1980s-from 3.6 percent per year before 1980to 2.7
565
566
Brookings Papers on Economic Activity, 2:1984
percentperyearthereafter.However, four-and-a-halfyearsis not a very
longtimefor estimationof a new outputtrend,anda rateanywherefrom
2.2 to 3.2 percent is consistent with the unemploymentand real output
statistics since 1979. A substantialfraction of the reduction in trend
outputgrowthcan be tracedto the steep declinein unemploymentin the
last year and a half; if the sampleperiodis truncatedat the end of 1982,
the estimatedtrendrealGNP growthratefor the 1980sis 3.3 percentper
year, with a rangeof 2.7 to 3.9 percentfittingthe datafairlywell.
Given its impact on the trend outputgrowthrate, the recent decline
in unemploymentdeserves furtherscrutiny.Gordonattemptsto do this
by using the linear regression decomposition that I introducedin an
earlierpaper on Okun's law. However, one of the main conclusions in
thatpaperwas that unemploymentis moreclosely linkedto the cyclical
movementsin real outputthanothercomponents(such as productivity,
labor force participation,and work weeks) of the identity that relates
employmentto real GNP. This impliesthat an investigationof the large
errorsin these componentsis unlikelyto revealthe cause of the smaller
errorsin Okun's law, except in the vacuous sense that they will meet
one linearconstraintto makean identityhold. Thus, it is no surprisethat
Gordonends up attributingthe 1983-84unemploymentdecline to shifts
in his employment-and output-mixterms, which have erraticcyclical
behavior.
Probablythe best explanationfor the recentdeclinein the unemployment rate is that reductions in real GNP duringrecession and sharp
increases in real GNP duringthe early stages of recovery each generate
largermovementsin the unemploymentratethanwouldbe predictedby
Okun'slaw. For example, in the 1957-58, 1969-70, and 1974-75recessions, the unemploymentrate rose an average of 0.7 percentagepoint
morethanpredictedby Okun'slaw. In the ensuingrecoveries,it declined
0.3 percentage point more than the Okun's law prediction(this figure
rises to 0.6 percentagepoints if the slow recovery in 1971is excluded).
In 1981-82,the unemploymentraterose 0.3 percentagepoint too much,
while in 1983-84 it fell an excess 0.7 percentagepoint, roughlyin line
with historicalexperience. The big decline in unemploymentduringthe
last year and a half is not surprisingat all, given the strengthof the
recoveryand the systematicdeviationsfromOkun'slaw in the past.
And what about future growth in real GNP? As the table below
indicates,prospectsfor the second half of the 1980sare little betterthan
567
Robert J. Gordon
the performancein the firsthalf. Even if it is assumed that the trendin
laborproductivitygrowthwill average I1/2percenta year between 1984
and 1989(which is very optimistic, given the 1 percent trendfor 197984)andthatthe unemploymentrateis 6 percentin 1989,realGNPgrowth
will average only 3?/2percent per year for the next five years. Under
pessimistic assumptions(1 percent laborproductivitygrowth, 7/2 percent unemploymentin 1989, and no labor force participationgrowth),
the 1984-89 growth rate of real GNP turns out to be substantiallyless
than 2 percent per year. Overall, both Gordon's estimates and the
projections in the table below are very bad news for anyone who is
seriousabout reducingfuturefederaldeficitsin the United States.
GrowthRates of Real GNP and Componentsin the UnitedStates, 1955-84,
and Projections to 1989a
Percent at annual rates
Measure
Real GNP per employee
Ratio of employment to
working-agepopulation
Working-agepopulation
Real GNP
1965-72
1972-79
1979-84
1984-89
2.1
1.4
0.5
0.8
0.6 to 1.7
-0.1
1.4
3.5
0.2
1.9
3.5
0.7
1.9
3.2
0
1.3
2.2
0 to 0.6
1.0
1.6 to 3.3
1955-65
Source:Data through1983are fromEconomic Report of the President, February 1984.
a. Assumptionsfor 1984are that real GNP equals $1,648billionand civilianemploymentequals 105.3million.
growthis 0 to 0.3 percentper year.
Projectionassumptionsdiscussedin text; rangefor laborforce participation
General Discussion
Martin Baily questioned Gordon's conclusion that the economy's
productivitytrendhas not improved.In his work, Baily had found that
the measurementof trend productivitywas extremely sensitive to the
choice of benchmarksand concludedthat pessimismon productivityis
unjustifieduntil cyclical patternscan be isolated with more certainty.
Gordonreplied that his benchmarksfor measuringwhen productivity
was on trend were based on the correspondencebetween the actual
unemploymentrate and the calculated natural unemployment rate.
Because the latter was estimated without any assumptionsabout productivity, there was no reason to believe the estimated trends were
biasedby the actual cyclical behaviorof productivity.However, Baily
568
Brookings Papers on Economic Activity, 2:1984
noted that for the post-1980period, no new benchmarkwas available;
thus estimates of the current trend will depend on whether growth
continues or collapses, as it did in 1973-74 and 1978-79. William
Nordhausnoted that manypast attemptsto explainthe slowingproductivity trend had concluded the slowdown was a mystery. Because
mysteriesare martingales,therecould be no basis for expectingthatthe
mystery that caused the slowdown would reverse itself. Thus he was
not surprisedby Gordon's finding(or Clark's,BPEA, 1:1984)that the
slow productivitytrendof the 1970shad not quickened.
Charles Holt offered an alternativeto Gordon's "output mix" hypothesis to explainwhy the recent recovery was characterizedby large
increases in employment. Because of the length and depth of this
recession, by the end of it firmswere not hoardinglabor to the extent
they had in milderdownturns.As a result, the outputexpansionduring
recoveryrequireda relativelylargeincreasein employmentratherthan
a moreproductiveuse of formerlyunderutilizedlabor. BarryBosworth
pointed out that Gordon's explanationfor the drop in unemployment
was different dependingon the methodology used. In the accounting
frameworksummarizedin table 1, the exceptionally rapid decline in
unemploymentwas attributedto the changein outputmix: comparedto
the averageof previous cycles, outputfromthe privatebusiness sector
was growingfaster thanthe aggregateeconomy. By contrastthe regression analysis in the simulationerrors section of table 5 attributedthe
exceptional drop in unemploymentto employmentmix. That suggests
muchof the rapidemploymentgrowthis largelya statisticalartifactthat
comes from differencesbetween the establishmentsurvey data and the
householdsurvey data.