APPLES TO ORANGES:
PRODUCTIVITY CONVERGENCE AND
ACROSS INDUSTRIES AND COUNTRIES
COMPARING APPLES TO ORANGES:
PRODUCTIVITY CONVERGENCE AND
ACROSS INDUSTRIES AND COUNTRIES
*Wethank Roland Benabou, Antonio Ciccone, Steven Durlauf, Michael Kremer, Paul
Solow, John Taylor,and Alwyn Youngforhelpfulcomments as well as seminarparticipants at Boston
Uni-versity, U.C. Berkeley,Harvard, Stanford, and the
WeaJso thank Kevin Hetherington and Huijdng Li for excellent research<issistance. All errors are ours.
paper examinesthe role of sectors in the convergenceof aggregate productivity levels in 14
majorfinding is that
little evidence of either labor productivity or multi-factor productivity convergence while other sectors, especially services, are driving the aggregate convergence result.
measureof multi-factor productivity
problemsinherent to traditional
andspillovers is developed
whichcan explain convergence in
divergence in others.
performanceacross countries are central to
manyofthe ques-tions concerning long-run
economicgrowth: are less productive nations catching
andbusiness leaders express
profoundinterest in the
to the question of
whetherthe U.S. can
maintainits role as the world productivity leader.^
Thequestion itself is potentially misleading; should
webe interested in the productivity of
the entire private sector or that of individual industries;
and whateverthe level of analysis, are
weconcerned with labor productivityora
Using datafor a
groupof 14 industrialized countries
in aggregate productivity are also reflected at the individual industry level taking care to distinguish
betweenproductivity of labor
andthat of all factors taken together. In the process,
weconsider the complicated question of
measureoftotal technological productivity.
Theresults for individual industries are quite striking.
wasconverging over the period, the sectors
showdisparate behavior. For all
measuresof productivity, the
shows noor little convergence, while other sectors,
showstrong evidence in favor of convergence. This finding for services
together with the declining share of
manufacturingin all 14 countries contributes to the
foundat the aggregate level.
Thelack of convergence within
overthis seventeen year periodindicates that convergenceis not
economic growthpredict that
wouldcontribute to convergence across countries
andthus are not easily reconciled with
weinterpret this result in the context of
andargue that the lack of convergence within
not be all that surprising.
Theseresults are especiallypertinent to thestudy ofconvergence
in countries at
moreheterogeneous levels of development. In a recent
andSingapore apparentlyfollowed similar
performances werequite dramatically different.
Ourresults suggest further that convergenceofaggregate productivity
masksubstantial differences at the sectoral
onconvergence across countries has concentrated almost exclusively
labor productivity using
GDPper capitaas the measure. Thisis
duelargely toa lack ofdata
andcapital inputs necessary to construct broader
andSala-i-Martin (1991, 1992)
and Weil(1992) argue that countries
andregions are converging, or catching-up,
thantheir richer counterparts.
cross-section evidence is not uniform.
showthat the particular
onlonger series for
no tendencyfor convergence
in levels (for
Theuse of labor productivity necessarily entails restrictions
Byits very definition, a
changein labor productivity
confoundspotential changes in
Convergencein a neo-classical
heavy emphasis onthe accumulation of capital as the driving force behind convergence, but analysis oflabor productivity does not allow theidentification ofseparate influences of
andlabor productivity measures.
conductour analysis of convergence
both growthrates of productivity
andthe productivity levels themselves.
Mostanalyses of productivity concentrate
changes, thus avoiding complicated issues concerning the
productivity levels across industries
whichis particularly difficult for multi-factor productivity. In section 2.
wedescribe in detail our
measureof Total Technological Productivity
measureis constructed to ensure that
comparisonswith as few
OECDcountries is that
and outputper capita differences
Loglevels oflabor productivity,
shownfor total industry, excluding
from1970-1987 in Figure 1.^
onaverage at a rate of
2.4%per year, but the
mostproductive country, the U.S. over the entire period,
andthe least productive country declined consistently
from1970 to 1987.
qualitative results hold for the
TFP;there is substantial
betweenthe leader, again the U.S.,
andthe less productive countries.
of catch-up is less for the
TFPmeasure, suggesting that capital
accumulationis playing a
role in the convergence oflabor productivity.
Thereduction in cross-section dispersion can be seen again in the lower halfofFigure 1
whichplots the cross-section standard deviations of
TFP.Cross-section dispersion declines steadily
12%for multi-factor productivity. Tests for catch-up, regressions of average
oninitial levels ofthe productivity
measuresfor the 14 countries, confirm the visual evidence.'^ (i.i; 0.71
Rs.e. (0.0501) (0.0052)
'^Y/L isconstructed asoutput per worker.
TFPisconstructed asaweighted averageofcapital andlabor
productivities vnth theweights being the averagefactor shares over timeand across countries. All analysis
with productivity is done using the logs of the levels. Throughout the paper we maintain the assumptions
ofconstant returns toscale and perfectcompetition. This means wecalculateour laborshares usingoutput
rather than cost shares, notan innocent assumption. Here wehold the laborshareconstant across countries
and time. In Section 2 we discuss this assumption in greater detail. The countries in the sample are the U.S.,Canada, Japan, Germany, France, Italy, U.K., Australia,theNetherlands, Belgium, Denmark, Norway,
Sweden and Finland. The U.S. is denoted by a "o" and Japan by a "-(-" in most figures.
"'Average growth rates here and throughout the paper are constructed as the trend coefficient from a
regression of the log level on a constant and a linear trend. This minimizes problems with measurement
s.e. (0.0322) (0.0056)
onthe initial levels are negative
andstrongly significant for
andtotal factor productivity
less productive countries are catching-up to the
modelpresented in the third section, these estimates
implythat labor productivity is converging at a rate of
3.85%per year, faster than the
and1.2 suggest that convergence is continuing for these
whatis drivingthis strongevidenceofconvergencefortotal industry pro-ductivity,
nowturn to the evidence
fromthe sectoral data. First,
andconstruct an alternative
measurecalled total technological productivity, or
Wethen construct six broadly defined sectors for each
convergencein labor productivity
TTPwithin each sector across countries. Finally
modelof trade, learning-by-doing
manyof the empirical facts
Therest of the
paperis divided into 5 parts: Section 2 discusses
multi-factor productivity levels
newmeasure; Section 3 presents asimple
changewithin sectors; Section 4 analyzes the
andtechnological productivity within industries across countries
convergence; Section 5 develops a
modelof trade, leaning-by-doing
anddiscusses further research.
and comparisonsof factor
andthe theoretical foundations
growthrates are well-established. Following
by which output would
growthrate can be calculated as
""Time series testsalso provideevidenceofconvergence for measuresofTotal Industry TFP. SeeBernard
and Jones (1993).
^In contrast, Barroand Sala-i-Martin (1992) havefound
2%convergenceforaggregateoutput per capita
i.e. as the
where qis labor's share of final output.
Themotivation for this calculation is extremely general;
onthe specific functional
production function are required.^ In recognition of the fact that the labor share variesover
time, it is
employa Divisia index of multi-factor productivity growth,
in this case corresponds to the
+Q(_i) is used in place of
(e.g. see Caves, Christiansen,
andDiewert (1982)). This is the
employ throughoutthe paper. In contrast, the question of
convergence is intrinsically a question of
comparingproductivity levels, not
Moreover,the theoreticalfoundations for
comparingmulti-factorproductivity levels areless
Combiningthese observations, the
comparingproductivitylevels at all points
in time reduces to a
comparingproductivity levels at asingle point in time: the
remaininglevels can be calculated using the Divisia productivity
growthrates. In the
context of convergence, then, it is natural to think of the
initial levels of multi-factor productivity.
In this section,
weargue that the
TFPlevel measures, results in
can be arbitrarily altered
undervery simple assumptions.
documentthe use of such
workrelevant to this paper. Finally,
measureof multi-factor productivity.
L^, the Hicks-neutral
whichis equal to a weighted average of capital
measureis that ifthe
adiffers across countries,
TFPcan be misleading, for at least
sameinputs (i.e. the
as well as the
samelevel ofA, but they
havedifferent q's. Clearly, these
producedifferent quantities of output.
measureof technology here is that it is incomplete: the technology of production varies with the
parametersa^ well as with the A's,
andthe simple Hicks-neutral
TFPdoes not take this into
However,there is another
problemwith the Hicks-neutral measure;
ar-bitrarily small differences in the
implythat changes in the
measurementfor an input can
changethe ranking of productivity levels. This is
easily seen in equation 2.1 above.
that are equal to one, so that the
TFPis simply equal to
some powerthat differs across countries.
changingthe units of
measuringlabor in millions ofworkers),
^The key assumptions, ofcourse, are constant returns and competitive factor markets.
'Authors suchas Kendrick and Sato(1963), Christiansen, Jorgenson, and Lau (1971), and Caves, Chris-tensen, and Diewert (1982) haveproposed methods for comparing multi-factor productivity levels, and we
this will rescale
bya factor that varies across countries. It is easy to
onecan always reverse ranks in pairwise
TFPlevels given arbitrarily
small differences in the
temptingto infer that the
twopoints in time, implying that
growthrates are arbitrary. In
fact, this is the motivation for using Divisia
time. In the Divisia calculation, the
samefactor share (an average) is used to
twodifferent years to
growthrate,eliminating the problem.
twoperiods gets small, the changes in factor shares also get
small so that usingtheaveragefactorshare
comparisonsis that there is
the factor shares will necessarily be getting closer together:
wecan reduce differences in
byincreasing the frequency ofobservation
differences across countries.
Total Technological Productivity
Accordingto the results in the previous section, if factor shares vary substantially across countries,
comparisonsof productivity levels using the Hicks-neutral
TFPcan be misleading.
we mustask, therefore, is
whetheror not thisvariation in
factor shares is a
problemempirically. Figure 2 illustrates that it is: for total industry in
our data, the labor share varies substantially
Thejoint productivity of capital
andlabor varies with
termin front ofthe
andwith the factor exponents.
measurethat will be referred to as total technological
anypoint in time for country (or country-sector) i,
TTPhas a very intuitive interpretation: it
outputif all countries
andlabor. Since A'^
are constant across time
andcountry or sector,
measureincorporate only variation in the production function itself, not in the quantities of the inputs. In
'Weshow the following: Ifthe factor exponents in the production function differ, then a pairwise
TFPusing the simple measuredefined above can generatedifferences that are arbitrarily large
and either positive or negative bychoosing the appropriate unit ofmeasure for asingle input.
TFPin region 1 wdth
TFPin region 2. Without lossof generality, alter the units used to measurethe labor input by amultiple, 9. Thedifferencebetween the two
By choosing non-negative valuesof9, Dtfp(9) can takeon any value.
^Laborsharevariesover timeandacrosscountriesforothersectorsas well,especially manufacturingand
this sense, this definition of multi-factorproductivity is closely related to the definition of
by Solow(1957). In practice,
assumethat the function F(-) is
whereIn Ait is defined as:
Here, the labor share is allowed to vary across countries, sectors,
andtime to allow for the
possibility that different industries in different countries
haveaccess to different
technolo-gies. Similarly, recognizing that
weare usually dealing with aggregate data,
exponentsin the aggregate production function to vary over time. This variation could
fromtrue technological variation or
from changingsectoral composition within a
It is easy to
showthat this definition of multi-factor productivity is robust to the
crit-icisms of Hicks-neutral
TFPgiven above. First,
byits very definition, countries with the
sameoutput. Second, the
measureis alsorobust tochanges inthe units used to
measurethe inputs. Intuitively,
bychanges in the units of
aninput affect the calculation of
Ain exactly the opposite way, leaving
Thevariation in factor shares across countries
andover time suggests that the standard
Wechoose to generalize in the
wayof allowing the factor
Cobb-Douglas formto vary
across countries, sectors,
However, twoalternative generalizations are the
andthe translog production function,
have beenused elsewhere
in the literature
Whileextending our analysis to these
Onealternative is the
by Kendrick andSato (1963),
whichallows factor shares to vary monotonically with the capital-labor ratio. In our data,
however, it appears that factor shares
donot vary monotonically with the capital-labor
dothe factor shares
behavesimilarly across countries.
Withina country, for
example,the relationship is typically not monotonic,
andacross countries, factor shares
examineproductivity differences using the
would haveto allow theelasticity of substitution
betweenfactors tovary across countries
andeven, perhaps, overtime.
Diewert (1982). Theirdefinitionisbased
onthe translogproductionfunctionfirst considered
wouldbe useful to extend
the empirical results in this
paperusing the translog definition of productivity, tentative
explorations in this direction suggest that the extension
depend onthelevelof capital
andthelevel of labor. Specifically, Caves, Christensen,
wheresa represents factor
paymentsto labor as
ashareofoutput. Noticethat the intercept
in this equation is allowedto vary
bycountry, but the other coefficients are constant across countries
andover time. Empirical estimates of this equation using our
datareveal that the null hypothesis that the coefficients
Lare constant across countries is
strongly rejected. For
Ftest ofthis hypothesis for thetotalindustry aggregate
producesa statistic of 9.35
1%critical value of 1.70; for manufacturing,
the statistic is 7.54,
CESor translog production setup does not address the
parametersof the production function
mayvary across countries. For
andallow the factor shares to vary across time, country,
moredetail later, Dollar
and Wolff(1993) also focus
and employthe following
ais the labor share oftotal
assumedconstant across units of obser-vation.
It iseasy to
measureofproductivity is not robust to
example, bychoosing the units in
measurearbitrarily small sothat
winlook exactly like
comparisonsof capital productivity
bychoosing the units in
measure K, onecan
makethe contribution of
Karbitrarily small so that
comparisons wiUlook exactly like
comparisonsof labor productivity. If the rankings of capital productivity
andlabor productivity differ for
twocountries, theneither country can
shownto be the
bychoosingthe appropriate units at
datasuggests that such
problemsare not simply theoretical oddities: for
all three key aggregates (total industry, manufacturing,
andservices) in 1970,
Japanhas a highercapital productivity level
thanthe U.S. while the U.S. has higher labor productivity.
comparisonsof the U.S.
onthe units in
In addition, it is
worthnoting that the
abovebecausethis criticism holds
(the q's) are constant across countries. This
explanation for the differences
Several issues concerning Total Technological Productivity
remainto be discussed. First,
maybe sensitive to the capital-labor ratio
KolLo, as is obvious
havedifferent capital-labor ratios the
depending on whichcapital-labor ratiois chosen. This is
This aspect ofthe
measureis unfortunate. Ideally,
to the question, "In the aggregate,
moreproductive, the U.S. or
weuse the U.S. capital-labor ratio or the
Japanesecapital-labor ratio. This is analogous to the classic index
comparethe totaloutput of
Depending onthe relative price used to weight apples
Several other candidate
measuresof multi-factor productivity also share this problem. For
measure byconverting labor units into dollars to
However,the choice of the real
wageused in the conversion can alter the productivity rankings. It
shownthat this choice is analogous to choosing a capital-labor ratio since the
termin the production
measurecan alsoprovide misleadingresults.
havediffering outputs as a result of different factor
terms wouldnot capturethis productivity differential.
onecould return to the "naive"
seemsless naive because it is the only
However,the choice of the factor
andthe rankings of the productivity levels
sensitive to this decision. Moreover, this
movementin the factor exponents.
Thatis, it looks at only
whichfactorproductivity varies. Despite these
wewill report results based
aroundthe choice of the appropriate
capital-labor ratio. In the
remainderof the paper,
capital-labor ratiofor the initial year in the
TTPlevels in practice for 1970-87,
Equation2.4 to calculate the level in 1970
andgenerate levels for the subsequent years
by cumulatingthe Divisia multi-factor
The1970 level is used as an initial value.^^
oncon-stant factor shares across time
'°Wethank John Taylorfor pointing this out to us.
''The results are robust to this choice. Choosing the lowest capital-labor ratio causes convergence for
total industry andagriculture to weaken.
'^As an alternative, wealsoused
TTPlevelscalculated ateachpointintime using the
factor shares vary across time
shownearlier. Therefore, this simple
maydistort productivity comparisons. Figure 4 plots a
measureas well as
measureconstructed using q's that vary across country, i.e. a
subject to the
measuresare readily apparent.
Thecross country standard deviation for the varying
anddivergenceleaving the overall dispersion essentially
unchanged.In addition, the relative ranks ofcountries are dramatically different, with the
U.S. in the
middleof the 14 country
and Japannear the
andconsistent with the
data onlabor productivity.
TTPfor total industry
convergenceover the period 1970-1987, as is obvious
of the figure.
modelwithout technology predicts convergence in
workerfor similar, closed
in the neoclassical
exogenoustechnology processes follow different long-run paths across countries, then therewill be
outputlevels to converge.
weconstruct a simple
fromissues of multi-factor productivity
and assumethat multi-factor productivity, Pa, evolves according to
with 7,j being the
growthof sector j in
countryi, \ parameterizing
the speed of catch-up
bea functionof theproductivity
differentialwithin sector jin country i
fromthat incountry 1, the
wherea hat indicates
aratio of a variable in country i to the
Thisformulationofproductivity catch-up impliesthat productivity gaps
afunction of the lagged
sameproductivity measure. For
measureof productivity, then lagged
determinethe degree of
Thissimple diffusion process is subject to criticism.
Nguyen(1989) allow the catch-upin
be determined bylabor productivitydifferentials; however, it
supposethat technological catch-up
independentof capital deepening.
impetusfor "catch-up": productivity
between twocountries increase the relative
growthrate of the country with lower
=71 (i.e. if the asymptotic
productivity are the
same)will countries exhibit a tendency to converge. Alternatively, if A
=0, productivity levels will
growat diiferent rates
to converge asymptotically.^'^ Considering the relationship
growthrates across countries,
wecan rewrite the difference equation in 3.4 to yield
+Ini,j ) (3.5)
wherep, denotes the average
growthrate relative to country 1
T.^'* This is the familiar regression of long-run average
onthe initial level,
bya negative coefficient
This simple set-up for analyzing productivity
movementsacross countriesis convenient because the regression specificationis not
In this section
wepresent cross-section convergenceresults forlabor productivity, a "naive"
TTPfor six sectors for 14 countries.
dataset before looking at the
Results for /^-convergence
andcr-convergence foUow. Finally,
wereview previous empirical
employsdata for six sectors
andtotal industry for (a
OECDcountriesovertheperiod 1970to 1987.
Thefourteen countries are Australia. Belgium,
Denmark,Finland, France, Italy, Japan, Netherlands,
Norway, Sweden,U.K., U.S.,
Thesix sectors are agriculture, mining, manufacturing, electricity/gas/water
an updatedversion of the
'^Ofcourse, if the country with the lower initial level has a higher 7,, the countries
mayappear to be
convergingin small samples- thiscaseis extremely difficult to rule outin practice.
'*An alternative testing approach, employed in Bernard and Jones (1993), is to estimate Equation 3.4
>0, then the difference betweenthe technology levels in the twocountries will be stationary. Ifthereisnocatch-up (A
=0), then the difference of
TFPin countryifrom thatin country 1 willcontain a
unit root. Thedriftterm 7i-7i willtypicallybe small but nonzeroifthe countries'technologiesaredrivenby
differentprocesses(i.e. underthehypothesisofnoconvergence). Underthehypothesisofconvergence,7,
'^Forpotential problems with this typeofregression,see Bernard and Durlauf(1993).
'^With the exception ofthe services aggregate, all the other sectors are taken directly from the ISDB.
The services aggregate is constructed by summing Retail Trade, Transportation/Communication, F.I.R.E.,
and Other Services. GovernmentServices areexcluded. Ourmeasureofaggregate outputalso excludes the
The ISDBdatabase contains
AUof the currency
denominatedvariables are in 1980
our labor productivity
measuresusing these variables. In particular, since
measurelabor productivity as the log of value-added per worker. Since
obtain levelsof multi-factor productivity to
conductour convergence analysis,
measureof the log of total factor productivity
(TFP),designated A,t. This
measureis constructedinastandard way,as a
the weights are the factor shares calculated
returns to scale. In order to be able to
werestrict our labor share to
besector-specific, i.e. it is calculated as
formulain equation 2.4,
evaluated at the
mediancapital-labor ratioforeachsectorin 1970.
wecontinue to use the Divisia
andsubsequent productivity levels are calculated
growthrates using the initial level to
pin the series
Table6.1 reports average
andsector for the period 1970 to 1987.^* Similarly, Figures 5
6 plot the log of labor productivity
bysector for each country.^^
showssubstantial heterogeneity in
growthrates of labor productivity vary
from 4.0%per year in
showsimilar variation with agriculture
ex-periencing the fastest multi-factorproductivity growth, 3.0%,
and mining andconstruction
growthover the period.
Withinsectors, thereis alsosubstantially
Manufacturing growthinlabor productivity varies
manufacturing washighest in
andlowest again in
Norway, 0.7%per year.
services, the largest sector in these economies,
For every sector, average labor productivity
sug-gesting a continuingrole for capital
accumulationin changes in labor productivity
economiesover the 1970's
hadthe fastest labor productivity
growthbut the lowest,
evennegative, multi-factor productivity growth.
wassmallest in services.
onthe validity of these
productivity in the U.S. to productivity
Statistics (1991), as
shownin the following table:^°
''We relax this assumption later.
'*For a fewsectors, 1986is taken as the endpoint because ofdata avaUability.
TFPfigures look verysimilar.
BLSusedataon labor hours as opposed to the total employment measureused by the ISDB.
manufacturingsectoragreenicely, while thosefor totalindustry
Becausethe keyfindings in this
sector, the slightly
anomalousresults for the total industry
measureis less disconcerting.
Lookingat the labor productivity
bysector in Figures 5
can see several
movements shownearlier. Sectors
samepatterns in either trend or dispersion over time. Neither labor
changein dispersion formanufacturing, while in services,
both measuresdisplay a
betweenthe highest productivity country
Thefigures also bear out the substantial heterogeneity of productivity
perhapspuzzling feature of the figures concerns
Japaneseproductivity in the
Accordingto the labor productivity measure,
Japaneseproductivity in the
service sector in 1970
bottomofthe sample, while the
TFPmeasure, although this is not reported) place
Japanright at the top.
compari-son, Baily (1993) cites
McKinseyGlobal Institute that suggest that total
factor productivity in
55%of that of the
U.S. as of 1987,
mayplague theservice sector data.
Onceagain, however,as longas the
manufacturing dataareaccurate, the key resultsofthis
onthe sources ofconvergencein totalindustry productivity
the share of sectors in
Evenif there is convergence within sectors, aggregate conver-gence
maynot occur. Forexample, ifoutput shares of industriesvary across countries, then once all sectors
haveconverged to theirsector-specific long-run productivitylevelsthere will
still be differences in aggregate productivity levels across countries.
shares together with sector-specific convergence is sufficient for aggregate convergence. In
onthe share ofoutput
showsthe share oftotal industry output (excluding the
government)for each country in the six
and changein shares differs dramatically over time.
Withinmanufacturing, services, construction,
showsimilartrends overtime. Generally, the share of
(Japanis a notable exception to this trend), as are the shares ofconstruction
is the only sector to
mostcountries, accounting for at
64%oftotal industry output in 1987.
Thesefigures suggest that
manufacturing andservices mcike
twothirds of total
outputin every country
^To test whether these countries are becoming more similar inoutput composition, broadlydefined, we
In testing for convergence at the industry level,
onthe results for
Distinct definitions of convergence
have emergedin recent empirical work. Cross-section
tendencyof countries with relatively high initial levels of
growrelatively slowly (/3-convergence) or
onthe reduction in cross-sectional
worker(^-convergence), as in
andSala-i-Martin (1991, 1992).
This idea of
convergenceas catching-up is linked to the predicted
modelwith different initial levels of capital.
Oncecountries attain their steady-state levels of capital, there is
nofurther expected reduction in cross-section
Timeseries studies define convergenceas identical long-run trends, either deterministic or stochastic. This definition
assumesthat initial conditions
sample andtests for convergence using the
modelofcatch-up in Section 3 implies that
bothtypes ofconvergence should hold
given a long
enoughsample. If the 14
ontheir long-run steady state
growthpaths as of 1970 then the appropriate
frameworkfor testing industry level
conver-genceis that of cointegration.
However,if technology catch-up is still taking place as of
1970 then the cross-section tests are
moreinformative. In this paper,
cross-section analysis of convergence
havetested for convergence using the sectoral
Tables6.2 presents the results
on/^-convergencefor labor productivity. For
growthrate of productivity is regressed
onits initial level
(and aconstant) generating
anestimate of f3.
Theimplied speed of converge. A, is then calculated using the
from Equation3.5. In this
framework,the speed of convergence A can be interpreted as
the rate at
whichthe productivity levelis converging to
be growingover time.
For labor productivity, the basic convergenceresult for totalindustry
appearsto hold for
somesectors but not forothers. Forservices, construction,
a significant negative estimate of /3 is obtained, implying that there has
labor productivity during this period.
Theconvergencerates for these industries vary
sectors,thesimpleregressionformulationdifferswidelyinits ability toexplain cross-country
testedfor convergencein thesectoraloutput shares. Only agricultureand constructionshowed anarrowing
of the differences of output shares across countries during the sample. Mining shares diverge, due most
Likelyto dramatic changesin theoUindustry, whUeshares ofmanufacturing,servicesand
muchchajigein thecross-countrydispersion. Thecross-sectiongrowthrateregressionsconfirmtheseresults.
Agricultureandconstruction showconvergencein shares with negative andsignificant coefficientson initial
levels, Services is negative and significant at the
10%level, and the others have negative coefficients but
are insignificcint. These resultson sectoral output shares suggest that whileservices is growing as a share
ofoutput and majiufacturingis decliningin most countries, there remain substantial differences in sectoral
shares across countries. In particular,thereislittletendencyforshares tobecome more simUar, asmeasured
by standard convergencecriteria.
^^For a discussion ofthe theoretical and empirical inconsistenciesassociated with these two measures of
convergencesee Bernard and Durlauf (1993).
growthrates. In services, the regression accountsfor
growthrate variation while
R^is only 0.19 in the construction sector.
Surprisingly, the evidence for convergenceis
noconvergenceis not rejected
The R^is correspondingly low. Similar results hold for
andagriculture as well.
shows comparableresults for the
measureof multi-factor productivity.
TFP, wefind less evidence for convergence within
co-efficient, although still negative, is smaller
andthe f-statistic is lower.
TheR'^ for the
manufacturingregression is also smaller at 0.02. Services, once again,
at a rate of
andthe simple regression explains
56%of the cross-country
showsstrong evidence of convergence, suggesting that capital
evenbe offsetting technological convergence. Mining, construction,
showbroadly similar patterns for
Table6.4 reports our preferred estimates of /3-convergence in multi-factor productivity using
onconvergence roughly similar to those
andsignificanceofthe coefficient arereduced
negative. Total industry
TTPis catching-up at a rate of
2.68%per year. This
to apoint estimate for the
showstrong evidence of convergence in
EGWwith negative significant estimates of /3
andconvergence of productivity,
turn to a
measureof cr-convergence, the cross-section standard deviation of productivity over time.'^"^ In the graphs, cr-convergenceis indicated
by adeclining standard deviation,
reflecting the fact that countries' productivity levels are getting closer together over time.
Thedifferent sectoralcontributions toaggregate laborproductivity can be seen
in Figure 8
whichplots the cross-country sectoral standard deviations of labor productivity over time. Services
EGWdisplay substantial evidence ofcatch-up, as at is declining
manufacturingare particularly interesting: during
the 1970s there is gradual convergence as the standard deviation ofproductivity falls
18%;however, after 1982 the standard deviation rises sharply for the
the 1980s reaching
Evidence ontheother sectors is less clear-cut,
andagriculture fall initially
and miningrises dramatically
changeifthe U.S. is
sample. In fact, the increase in
Figure 9 plots the cross-country standard deviation in the log of
TTPfor the six
Theresults are similar to those for labor productivity
regressions. Services, agriculture,
EGWall exhibit substantial convergence,confirming the regression results. In contrast, productivity in the
convergencein the 1970s
anddiverges during the 1980s.
^^Combining the 13- and <T-convergence results allows us to avoid potential problems associated with
Quah(1993) shows that negative coefficients on /? are consistent with a constant
^*The resultsfor the
To compareour results with previous
wealso estimate /?-convergence regressions for
9 2-digit sub-sectors of
and4 2-digit sub-sectors of services.^^ Table 6.5
presents the results for manufacturing.
Only4 of the 9
evidence of convergence, textiles, chemicals,
growthin recent work,
showslittle evidence of convergence in TTP.'^^ This suggests that the lack of convergence
wholeextends to individual industries as well.
convergenceregressions for services are
shownin Table 6.6.
andsignificant estimates of/3 in
3 of the 4 sub-sectors.
Onlythe coefficient for Finance, Insurance
andReal Estate is not
significant at the
powerofthe regressions is higher here as well.
TTPresults of the previous section highlight
keyresults ofthis paper: the
convergencein technological productivity within the
twodecades is driven
non-manufacturingsectors; within manufacturing,there is
weakevidence for divergence.
TTPevaluated at the
mediancapital-labor ratio for each sector in 1970. This
result does not
appearto be sensitive to the choice of the capital-labor ratio, however, a
Instead of presenting additional tables of regression results,
demonstratethe point graphically. Figures 10
and11 plot the log of
TTPfor total industry
manu-facturing sector for a
TTPis plotted for each
and1986, together with U.S.
the figure indicates the U.S. capital-labor ratioforeach year (togetherwith the
maxfor each sector), while the
symbol'x" does the
samething for another
Figure 10illustrates that the convergenceof
TTPintotalindustryisrobust tothechoice ofthe capital-labor ratio, at least in these pairwise comparisons.
Withinthe relevant range (i.e.
andma.x capital-labor ratio for the sector), there are few crossings of the
andthe convergence result appears to apply at virtually every capital-labor
an example,consider the picture for Japan. U.S.
during this period, indicated
bythe relatively smaller shift
comparedto the shift for Japan. This is true at all (relevant) capital-labor
ratios, indicating that regardless of the capital-labor ratio chosen,
upto U.S. productivity in total industry.
Figure 11 illustrates that thelack ofconvergence within
manufacturingis alsorobust to
the choice of the capital-labor ratio. For
example,consider the picture for
growthis clearly faster
growthat all capital-labor ratios
that are relevant, including the U.S.
Germancapital-labor ratios. Since the U.S. ^^There are often fewer countriesfor the regressions within sub-industriesthus the results must be taken
^®The labor productivity results forthese sectorsshoweven less convergence withsome industries
regis-tering positive coefficients.
is the technological leader here, there is divergence in technological productivity for these
Ofthe six pairwise
comparisonsin the figure, only
Italy) potentially are converging to the U.S.
TTPlevel over this period, ajid
convergenceappears to be sensitive to the choice of capital-labor ratio (e.g. evaluated at
thelargest capital-labor ratio of11.5,
Overall, the results
fromthis section confirm that the empirical results for
docu-mentedearlier are robust to the choice ofthe capital-labor ratio.
onconvergence has concentrated
onaggregate data, looking in
outputper capita or labor productivity, output per worker.
to this is
andWolff (1988),Wolfr (1991),
whoconsider convergence using industry data.
andWolff (1993) consider
sameissues addressed in this paper, such as convergence within sectors
TFP.Largely in opposition to our findings,
they conclude that therehas
manufacturingduring the period 1963-1985.
mostofthe convergence occurred prior to 1973,
andsince that time
andthis analysis. First, they use
maycontribute to the different findings.
is that Dollar
andWolff (1993) find
mostproductive countryafter 1982, a
result not confirmed
by anyoutside source.
empirical analyses in that
andthose in this
stem fromdifferences the
of multi-factor productivity.
Asdiscussed in Section 2, their
measureof multi-factor productivity is not robust to a simple choice of units
(andthis is true
evenif the factor
donot differ across countries or sectors).
althoughnot in the context ofconvergence.
growthrate of industrial production for eight
component(by using the appropriate
combinationof indicator variables).
re-ports the fraction ofthe varianceof
output growththat is explained
betweenthe two. His
re-sults indicate that the
twotypes ofshocks explain roughly the
and examinesfive industries in six
countries. Costello's results areconsistent with thoseof
andsuggest the presence
ofnationaleffectsthatare atleast as
importantas sectoraleffectsinexplaining thevariation of
someevidence usingpairwise correlations suggesting