-
168 cHAprER 5 . Long-Run Economic Growth
Learmisus Sfu$ett$weExplain the bafancedgrowth path,convergence,
andlong-run equi l ibr ium.Balanced growth nsituation in which
thecapital-labor ratio anCreal CDP per hour workedgrow at the same
rate
The Financial System The role of the financial system is to help
the economy allocarresources by matching borrowen with lenders.
When the financial system works well, ind-viduals who want to
borrow to finance the accumulation of physical or human capital
car:find lenders. To theextent that firms and the government payfor
R&D with funds obtaino:through the financial system, a
well-functioning financial qrstem can also lead to moreinvestment
in R&D. The financial system can also affect total factor
productivity brimproving the efficiency of the economy. The
financial system allocates funds to the ind:-viduals and firms who
are willing to pay the most to obtain the funds. These
individud.and firms are also those whose investment projects have
the best likelihood of succesiTherefore, a good financial system
ensures that resources flow to their most productirtuses, and total
factor productivity for the economy increases. As a consequence,
labor pia-duaiviry and the standard of living are higher.
Research by Thorsten Beck of the World Bank, Ross Levine of the
University ofMirrnesota, and Norman Loayza of the Central Bank of
Chile has shown that the finan-cial system has a significant effect
on total factor productivity growth.ra Interestingly, it isnot just
bank that matter for econonic growth. Ross Levine and Sara Zervos
of the Worl,jBank have found that stock market liquidity also
affects productivity and capital accumu-lation.t5 The more liquid a
stock market, the easier it is for investors to sell
stock.Investors are more likely to purchase stocks that they know
are easy to sell. As a conse-quence, stock prices are higher, and
it is less costly for firms to issue new stock to pay
forinvestmerit projects. This research tells us that the
development of financial markets plarsan important role in
sustaining economic grorvth in both developed and
developinseconomies.
The Balanced Growth Path, Convergence, andLong-Run
EquifibriumThe steady state is the equilibrium for the economy;
however, it is an equilibrium in rvhichthe key economic quantities
such as the capital-labor ratio and real GDP per hour workeciare
growing. Balanced growth occurs when the capital-labor ratio and
real GDP per hourworked grow at the same rate. The bahnced growth
paflr shows how real GDP per hourworked groil's over time r+'hen
the economy is in the stefv-shte and experiencing
balanceCgro*'th.,lVe can thin-li of the balanced growth path a{the
equilibrium time path for realGDP per hour r+'orked. We can also
think of each steadN state as having its own unique bal-anced
grorrth path. Understanding the equilibrium time path is critical
for understandinethe long-run behavior of real GDP per hour worked
and real GDP.
i. i, i i",ai{i:nie tr i i ' i ; l i* ianced {tr*vytb FathFigure
5.i on page I45 shows that the gror4h rates for most countries have
been roughlvconstant since 1820, rvhich suggests that most of these
countries have typically been on ornear their balanced growth
paths. ]ust as the steady state is the equilibrium for the
economvat a point ia tir:re, the balanced growth path is the
equilibrium for the economy orcr time.Horvever, some countries,
such as |apan, appear to have been off their balanced growthpaths
for extended periods of time.
The experiences of Germany and fapan after World War II provide
a good example oihow an economy that is off its balanced growth
path eventually converges back to that path.By the end of 'v\torld
War II, both Germany and fapan had experienced large decreases
in
Ialhorsten tseck, Ros Levine, and Norman Loayza, "Ijinance and
the Sources of Growthl' Journal ofFinancial Econorrics, \iol. 58,
No. l-2, October-November 2000, pp. 261-300.r5Ross l*vine and Sara
T.ervos, "Stock Markets, Banks, and Economic Grcwthl' Americnn
FronomicReyiaw, Vol. 88, No. 3, )une 1998, pp. 537-558.
-
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The Balanced Growth Path, Convergence, and Long-Run Equilibrium
769
$20105
1
1820 1840 1860 1BB0 1900 1 920 1940 1 960 1 980 2000
,h.i1. .upitul-labor ratios as the United States and its allies
bombed the factories, bridges':nd transportation networks in both
countries. Figure 5.14 shows real GDP per capita 9ve1::rne tbr both
Germany and ]apan. Both countries experienced a large decrease in
real GDP
-r capita at the end oiWorldWar II, due to the destruction of
their capital stodi' However'
,i.., th. war, both countries grew much more rapidly than they
did before the war.3ermany grew rapidly from ttre end of the war
until about 1960' After 1960, Germany;npears io hut grown at the
same rate as it did prior to the war. In fact, Germanv
apPears:.-,iar,* been on th. ru*. growth path since 1960 that it
u'as on before World War II' japan
-d a similar experience. ih. .ountry grew rapidly from the end
o{thewar until the mid-
- i-Us when it appears to have moved to a higher balanced growth
path compared to the
rme :i rcas On 6ei6re ille War- illeru&r..,
rflr"t4ntv"-stgauf'*ert'ea4nital-lahn'^atin-anrlornl GDP per hour
worked must have increased'
Why do countries return to the balanced growth path? We :*::t
the Solorv growth
-nrlel and the experiences of Germany and Japan toi*pl"in rvhy.
Figure 5.15 shows for
ffi
krgas
The Solow GrowthModel and Post-WorldWar ll Convergence
inGerrnanyThe destruction of Germant/scapital stock at the end of
lYorldWar II caused the caPital-laborratio to decrease frotn [*
tokrgn:
'
and real GDP Per hourwprked to decrease frorn t' trt/tg+s. At
that point, GermanYrvas belorv its balanced grorvthpatir. Postrtar
GermanY exPgli-enced verv fast Srowth rates ofreal GDP as the
country raPidlYaccumrilated caPital goods whileaPProadring its
balanced growthpath. s
Post-World War IlConvergence inGermany and JaPanGermany and
|apan exPerienceda large decrease in real GDI' Percapita at the end
of World lvVar IIdue to destruction of their caPitaistoclc Germary
grerr raPidlYirom the end of the war untilabout 1960. After
1960,German,vaPPears to have grolfn at thesane rate as it did Prior
tothe rvat. Japan grew raPidlY fromthe end of the \'Var until
themid-1970s, but it aPPears to hi*tmoved to a higher
balancedgrowth path comPared to the oneit rvas on before the
wirr.
Sourcc': lbtal Frotroinv Datirba se,The Confercnce Board:
httP://wryw.conference-bo ard.orgldatalecono;nrdatabase/. s
sy
aL\
=ata-t * t
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E=:6r ' '=r i r -V
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hwS
Production, y
Break-even irwestmentline, (d + nrk
k. = ktsgs
Capital-labor ratio, k1 . The,capitalllaboi ratiodecreases af
the end
(d+ n)kre4s l. '-
-
17$ cHAPTER 5 r Long-Run Economic Crowth
Germany the effect of the destruction of tlre capital on real
GDP per hour rvorked- German'istarted off in the steady state prior
to world war II, with a capital labor ratio, ft* : ft rs:e,and real
GDP per hour worked, f = ygts. Because the country was in the
steady state, itwas also on the balanced growth path, so according
to Table 5.3 on page 163, thecapital-labor ratio and real GDP per
hour worked both grew at a rare of I.5ga. By the endof the war,
Iarge portions of Germanyl capital stock had been destoyed. As a
result, thecapital-labor ratio decreased from ts to ft1e45, and
real GDP per hour rvorked decreasedkam f to "/rg+s. The decrease in
labor productivity caused the decrease in real GDP percapita at the
end of \&brld War iI that we see in Figure 5.14. After the war
had ended, totalfactor productivity continued to grow, which caused
real GDP per hour worked and realGDP per capita to grow. Horvever,
because the capital-labor ratio had fallen to k1ea5, theGerman
economy grew for an additional reason: It accumulated capital more
quidily thaiit had along the balanced grorvth path.
At &19a5, the level of investment, slrgqs, was greater than
the break-even level oiinvestment, (d * n)k19a5, so the
capital-labor ratio increased toward the steady-statevalue of ,tl.
From 1945 to 1960, the capital-labor ratio in Germany increased for
tr+'o rea-sons. First, total factor productivity growth was
positive, so the growth rate of th:capital-labor ratio along the
balanced growth path was positive. Second, Germany u..a-,converging
from the capital-labor ratio of ft1ea5 toward the steady-state
capital-labor rariaof F. Because the gron'th rate of the
capital-labor ratio deterrnines the growth rate of reaiGDP per hour
worked, the growth rate of real GDP per hour worked rvas also the
resul:of balanced growth due to total factor productivity growth
and growth due to the conver-gence of /D+s to y'. In general, I\re
can think of the growth rate of real GDP per hou:worked as:
gy = (Balanced gronth rate) + (Growthfrom convergence).As long
as the capital-labor ratio is less than ts, growth from convergence
is positive.
so the German economy was growing more rapidly than it did along
the balanced growthpath- Therefore, real GDP per hour worked
converged toward y*, so real GDP per capitaconverged toward the
balanced growth path. In the very different situation rvhere an
econ-omy starts off with a capital-labor ratio that is greater than
ts, the capital-labor ratio willdecrease over time, so grorvth from
convergence will be negative. As a result, the econom:;will grow
more slowlv than along the balanced growth path, so real GDp per
worker \riiiconyerge to the balanced growth path.
Figure 5. t4 shows that |apan experienced a similar decrease in
real GDp per yp a:the end of the War and then rapid growth after
the War.
i i* i ie* Siates?In 2010, GDP per capita in the United States
was more than six times higher than GDP pe:capita in China.
However, the growth rate of real GDP per capita in the United
States hasaveraged onJy i.9olo per year since 1980 compared to
Chinat average rate of 8.9%o per yearover the same time period.
Because China's standard of living is growing more rapidly thanin
the United States, we could predict that China's standard of living
will exceed the U.S,standard of living in the 1'ear 2038. However,
for China to maintain ix high rates of grOwthin real GDP per
capita, it lvould harc to maintain high rates of growth for total
factor pro-ductiviry which is unlikely for several reasons. First,
the United States invests more in activ-itieg such as research and
developnrent, that result in new technologies and increases in
totalfactor productivity. Second, much of Chinat growth is likeh
due to the transition fron a
"#ilf f,hina's 5t*ru#ar{$ #{, L$rr$rs#' #v*r ilw****$ tt"x-*-t
*r"f tl-c*
-
The Balanced crowth path, Convergence, and Long-Run Equilibrium
171
centrally planned economy to 1 mlka e31:T,u' * China's gowth
rate is-likely to decrease
as the transitioo i. **piriliil ;;;b"bly U.tt to thinliof the
transition 1o a market
economy as moving Cd;'t t"l;."i gt"t-tli p"th higher. The htgl
tllt: of growth in real
GDP per capita are d".;;;;;;;;;; tT.trigt'er g"'o$th.lath'e'l
China approaches the
new higher balanced gro;; p"fi, we would eipeciCttinut growth
rate to decrease to a
rnore sustainable
rate.Anotherloomingproblemisdemographic.BecauseofChina!lowbirthrate,itwill
,oon experience a declina in its labor force. ouer the next two
decades' the population of
nren and lyomen u"*".nJi "ia
ir y*tr will-fall by about 100 milhon, or about 30olo'
China will also experien;;;i"A;.r!are ln oltler workers, a grouP
thlt will likely be less
e,lucated and less t "urtny;h;y";;g.r
*orkers. Given current trends, the U.s. census
Bureau projects f.*., ;;pi;;"iffiso i, china in 2030 than today,
with ferver in their
lOs and early 30s and many more intheir 69.:.*d older' More
ominous is that China has
:o national pubti. peorii-n'rffi. dti"a still has potential
sources for enhancing produc-
;viqv, including the rnigi;;;_;f ,yil rvorkers ro *or.
productive urban jobs and
'iiderar'lication of t".hoi.uf 'k"o'-how' These factors can fuel
future growth'
but at some point'
Jttir"t i""tographic problems could slow growth'The experienr"
,f i;;;;;; ,rrg rll two"decades offers a sobering lesson:
Throughout
:--re 1g70s, Iapan grew f;;; th"" the united states, and there
rvas much discussion about
n'hen fapan *oota ,,,,f-*-' 'tt"
U"i1ta States in real GDP per capita' But in the 1990s'
irpan s average annual ;r;;il;";. ;iler capita GDp rvas only
0.5016, well belorv the rate of
:m*rrh of theunitedd;;,;J;rytit"ntiit*ted a decrease in the rate
of growth of total
:rctor productirity. Alth;;;n grr"li, i" Iapan"increased during
the early 2000s, the coun-
:-r has never approached the growth rates of *. 1o1rt beforJ
1990. \4rtrether china will
,f i" t"ff.t "
,"pii a"cnt't in grorvth rates remains to be seen'
---o*rrces: Nicholas Eberstadt, "The Demographic.Future,"
Foreign Aflairs,Vg! 8?:lo 5' November/
le:ember 2010, pp. s+-+q; i[{u^,o ilayashi and.E-dward cl
Prescott, "The 1990s in Japan: A Lost
1...0.; " t*rrl.rninnuupolisfed'org/research / wp /wp617'pdf
: ' . :v i l t i i r " rn i i * lsta** l i r tgbyd*i*gr* latedp;
'chi ' l l ;d ' ic ' i : * :gelSSalth*e*dafthis: i . - - ] i f i '
.
::r:tr*stsr##@'/"'2i*Xa!!)&!t*:A{t$H-t!tl.$ryLit*-'svjPl4y?*:$81+Ko'$itd'F!9q
Figure 5.16 shows what the time paths ofreal GDP per capita
would look like for an
ionomy initially on tf'e ialanctJ g&lh p"th' an econ'omy
initiAty Ptt:l S" bd-T:t1
srowrh path, and "n
.ron-o*y iniriiny uu*. the balanced growth path.If an economy
rs
,-n the balanced growth prifr,'irr"*oins on the path until ari
event moves the econom off
*e path. When tfr. ..o"J"f it ""
*f* f'"f*ced growth path' the grou4h rate of real GDP
Time Path for a country initiallYabove the balancd growth
Path
6EE'ar iGOo2l-EOEo.io-EO8s6L.
6z
_ __ :- i_:r:::i::ii_
:s:J'::i*i:':''
Tirne Path for a country initiatlYbelow the balanced groMh
Path
Balanced growth Path
Potential Time Paths forReal CDP Per Capitali an econotny is on
the balanced
growth path, it rentains on the
path until an event m(|Yes theeconomy off the Path- If an
econ-
om,,v starts oii belorv the balanced
grorvth Path,the economy Srolvsiaster than it would along the
bal-
anced gon'th Path. lf an econonystarts otf above ttre
balancedgrowth Path, the economY gro\rs
more slowlY than invould along
the balanced grorvth P6[' sTime
-
172 CHAPTER 5 r Long-Run Economic Growth
#ffiffi Summary of Adjustunents to the Steady Statem growth
frarn
th* capital fa.bsF ratio .,. csnvergence is ...l f . . . and the
grcwth rale *f the e{onorfif, ...k:k* equals the steady-state
valuezero equals the balanced growth rate, and the econorny
remains on the balanced growth path.k>k" is greater than
the
steady-state valuenegative is less than
convergesthe balanced growth:rate, so the economy
to the balanced growth path,k
-
The Balanced crowth path, convergence, and Long-Run Equiribrium
1r3
fosease their saving rateg increase human capital, gr take other
mcasures to increase totalfuctor productivity' tl-r9 gap in real
GDp per capita betneen high-incorne and low-income'rauntries rvill
never disappear.
Answering the Key euestionAi the beginning of this chapter, we
asked the question:' ',Vhy isn't the whole world rich?"
Continued fram page i 43
cur discussion has shown that the growth 1at9 oj labor
productivity is the key determipant of theg'owth rate of the
standard of livint. 8ut what determines *relrowtn rate oi
raooifroauctivity;'{ccording to. the solow.growth.model, the growth
rate of total"faaor productivity is the determinantof the growth
rate of.labor productivity. As I resuh,,totar fagtor proau.tioity
growth causes improve-ri''enE in the standard of living- and
economic growth over the dn! ,un. we also saw that there is no
f *ngfe{actor that causes total}actor productivily.to grow. The
leveT of t"cr'notCihe qJdity of theI hq force, thequality of
government and sociaf initituuons,-geolr"pt'y, ana triJ'qrJiiT-Lr
tinanciatmsiitutions alf pfay an,important role. in explaining
differencesTn t6tui ruao,. t;jr;ti;;il across countries.if a
country fails to achieve sustained economic g-rowth then, it is due
to its failure in one or more oflhese areas' Therefore, whife some
countries 3t-" rirprv unlucky because of their geography,
otf,ercountries are poor because of institutions that their
go*rn*.ntt are unable, o. ,i*iirini to reform.
_
Befbre moving on to chapter 6, read An Inside Look on the nex.t
page for a comparisonm':rojected econorhic growth rates in India
and China.
-
AN INSIDE LOOK
Will lndia Catch Up With China?
The Fastest Lap:Indids Economy IsRacingwithCtrina'sNo other pair
of countries invitesstrch frequent comparison yet shareso little in
common. China is big-ger, stronger, richer and betterorganised than
India, the onlYother country with over a billionpeople. And yet
Indians, it is fair tosaf, et loy the comParisons withtheir
northern neighbour morethan the Chinese do. It was anlndian rvho
coined the wordChindia- lndia relishes being in thesalne league as
China, eYen if itloses most of the games.
In 201I, howel'er, India ma)'win a round- According to
someprojections, its econorn)' rna)' gro\t-as fast as China's. [t
mq'eYen growa little faster.
g By the conYentions oi Indiannational accountitg, nst
)'earbegins on April tst and ends onMarch 3lst }al[' over that
P'eriod'the World Bank exPects lndia'seconom,v to grow by 8.790'
slightl)'faster than the 8.506 growth it hasforecast for China oYer
the calendar
year. That is hardly the consensusview. But it is not an
isolated oneeither. . . .
Although only a handful ofeconomists think India's growthwill
outpace China's next Yeer, alarger number believe it will do sothis
decade. The reasons are largelydemographic. China's econonrYcannot
go on rapidly expandingonce its labour force starts shrink-ing.
Thanks to its one-child Poliry,introduced in L979,the number
ofyoung Chinese ( I 5-29-year-olds)rvill fall quite sharply after
201 l,depriving the countrl"s factories ofnomadic, nimble-fingered
r+'orkers.Within a couple of )ars, Chinese)'oungsters rr"ill be
outnumbered bytheir tndian peers, even thoughIndia's population
rvill not matchChina's until about 2025.
O India rnay also outpace Chinarhis decad,e for the simple
reasonthat it is poorer' giving it morescope to catch up. India's
incomeper head rvould have to grow at \a/oa year for I 7 years to
match theler"el China enjol's today. One yearof faster growth does
not, then,mean that India is somehor,v over-taking China. Rather,
it is like a5,000-metre runner doing a fasterlap than the
frontrunner, who isfive laps ahead.
O It would, nonetheless, be a rareachievement. India has not
grownfaster than China since 1990. ' . ' IfIndia is to pip China
again in 2011'several stars will also have to fallintoal ignrne,nt
. . . .
India s economY must maintainits momentum, despite its
centralbank's campaign against stubbornlyhigh intlation. And
China's mustslow appreciaL,ly. CLSA forecaststhat the Chinese
econom,Y willgrolv by 8016 in 2011, down frorn10Vo in 2010.
Such a (relatively) lorv exPecta-tion for growth reflects a
highopinion of China's leaders. Thatsounds paradoxical-surelv
slolvergrowth is a sign of Poliry failure,not success? But China's
leaders noIonger seek growth at anY cost. [fthq, believe rvhat they
saY; theYwould rvelcome a less breakneckpace of economic
expansiofi. .
-
.
India still has massive catchingup to do in infrastructure. It
is notyet clear, with due respect to Indiannationalists, whether
India willbecome the rvorld's fastest-growingbig economy in 2011' .
. .
Source; "The fastest laP: India'seconomy is racing with China's,
" TheEconomist; November 22,2010' @ TheEconomist Newspaper Limited,
London(Novernber 22, 2010).
-
Key Points in the Article*s a,tide discusses projected
economicplrr*rth in lndia and China. After rnoret".ar 20 yean of
traillng China in annualgqr*'ffi, some economic projections
showmfi,e's growth rate rnay actually equaf orrr-r=ss Srat of China
during this decade,Ie*eral factors have led economists tof'rs
:cndusion, including (1) the growing;;;:: it India's labor force
and (2) the factf.:: per capita incorne is less in India than
'r- ,lnn.na, leading to a more rapid rate of
rr-'r 3;gence between the two nations.
i"maiyri*g the f.les$s61 Aiihough China's overafl populationf| q
expected to outnurnber lndia's for1*r --ext 15 years, the size of
theI*rri.es labor force will soon decline duer :re country's
one-child policy, a popu-,,rtr'ir-control measure instituted in
1978t-c ,,innib most Chinese families to only:r-e :hild per
household. Wthin the nextr*$q '/ears, lndia's population of"
5-:,r29-year-olds is projected to;rn,ass that of China, giving
India air;6rgr', larger, healthier, and possiblyr{:re educated
workforce. These derno-{,fas'xic changes will give India a
bettertrirr,ltrrni$ to experience faster eco-'r'pl*', growth in the
coming decades.1q {ccording to the ClAs WorldEl ;actboak,lndia's
real CDP per capitalr,,n,,as 53,400 in 2010, less than one-half
of
;:i'ficandy lower Wr capita income, lessmfr*i economic growth is
needed in lndia',ira: in China for the annual percentagerT?ass in
grow$r in these two nationstr :p{,tverge. Even if lndia does
surpassl-rma in annual economic growth, Indiatffi a long way to go
to overtake China inur :apta income. At an annual growth;rr: cf
8"/o,lndia would still need justr**,s'- 10 years to equal the per
capitar-Lrl{:qe in China in 2010."q iven with a considerably lower
per$t :"pita incorne, surpassing China'snr,r;al gowth rate would be
a significantei:,:cmic rnilestone for India, as this feat-;s rct
been achieved in more than 20,';-5 The figure shows actual and
pro-ry::C gowth in CDP for lndia and Chinarrr* 2CO6 through 2015.
The actual:rs--s through 2W9 show a consistently
higher CDP growth rate in China than inIndia-with projections
that the gap willnarow considerably in 2An; the gap willdisappear
in 2A$; and lndia will overtakeChina in 2A16. Afew econornisb
predictthat this gap will close even faster, per-haps as soon as
2011, but for this out-come to occur tndia must maintain itsgrowth
momenturn while growth inChina will need to substantially
subside.
T}iIilIKINfi CRffiCALLY1. Labor productivity in emerging
nations
such as lndia and China has grownsignificantly in recent year.
Thegrowth rate of tolal factor proCuctivityis the key determinant
for labor pro-ductivity grawth and the growth rateof the standard
of living when laborinputs per person are constant. Usingthe
formulas for steady-state growthrates and the data in the table
for2008, calcufate the annual increases inlabor productivi$ and
real CDP forboth India and China. Based on Your
answers, explain which of these coun-tries has a higher rate of
growth in ibstandard of living.
lndia t?air'a
Capital's share of A37 0.58incomeTotal factor produc- 0,010
0.013tivity growth ratePotential labor 0.058 0.065hours growth
rate
2. Total factor productivity in emergingeconomies like those of
lndia andChina is growing significantly, lead-ing to increased
efficiency for bothworkei's and firrns. What effect doesan increase
in ioLal factor productivityhave on the sieady-state values ofthe
capital-labor i'atio and real CDPper hour vrorked? Wlty? Use agraph
showing a one-time increasein total factor producivily to
illus-trate your answei-.
Stowing dragon,crouchlng tlgerGDP grorth, %
2006 20a7 2008 2009 2010 2011 2012 z}fi 2A14 2015
2016Forecast
Actual and proiected growth in CDR 2AA5-2015Source: O lhe
Econonrist Nervspraper l.irnited,l,ondon (Novernber 22,2Ai0). s
An lnside Look 175