POI TCY RESEQARCH YJURKJTNTG PAPPR 89 5 7
iviarKups, Lkecuriis to Scaic,
and Productivity
A Case Study of Singapore's Manufacturing Sector
Hiau Looi Kee
The World Bank wimm
Development Research Group
Trade
June- 200vl2.
POLICY RESEARCH WORKING P APER 28557
Abstract
The results of this paper challenge the conventional maintained the assumptions of perfect competition and
wisUom In thLe literature t'at productivity plays no role constLant returns to scale and used olnyly aggregate macr
in the economic development of Singapore. Properly level data.
accounting for market power and returns to scale Kee uses industry ievel data and focuses on Singapore's
technology, the estimated average productivity growth is manufacturing sector. She develops an empirical
twice as large as the conventional total factor methodology to estimate industry productivity growth in
productivity (TFP) measures. the presence of market power and nonconstant returns
Using a standard growth accounting (production to scale. The estimation of industry markups and returns
function) technique, Young (1992, 1995) found no sign to scale in this paper combines both the production
of TFP growth in the aggregate economy and the function (primal) and the cost function (dual) approaches
mmJ.-nfatu-ring sector of Sigpr.Based on Young's wvhilp ront-rnllina for input endopneiry andl selectionn
results, Krugman (1994) claimed that there was no East bias.
tisia miracie as aii mnc economic growrn in aingapore T fie resuilts o01 fixed effectA p----I -e--esio-in show that
could be attributed to its capital accumulation in the past all industries in the manufacturing sector violate at least
three decades. Citing evidence on nondiminishing market one of the two assumptions. Relaxing the assumptions
rates of return to capital investment in Singapore during leads to an estimated productivity growth that is on
the period of fast growth as an indication of high average twice as large as the conventional TFP
productivity growth, Hsieh (1999) challenged Young's calculation. Kee concludes that productivity growth plays
findings using the dual approach. But all of these papers a nontrivial role in the manufacturing sector.
This. pape -AUprct of Trade, Develop ment Research Grou(p-ic nart of n lnrger Pffort in the groin to unnrst-and the
links between trade, productivity, and growth. Copies of the paper are available free from the World Bank, 1818 H Street
XT%Vr V/ I _ TE1 n An n Tl _ __ _ .X s _' _ T _*I _ ___ 1k lrwo ^1 1__1 _ _ n1N A 7 IC-0 1 _'I N 1 1Ca
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email address mkasilag@worldbank.org. Policy Research Working Papers are also posted on the Web at http://
econ.worldbank.org. The author may be contacted at hikee@worldbank.org. June 2002. (37 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
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papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
Apape are entirely those3 of theauthlor. They dot ,If'C.otncessarily ,-p-sn th vie of th I..o ak t xcui ietr,o h
countries they represent. l
Produced by the Research Advisory Staff
Markups, Returns to Scale, and Productivity: A Case Study of
Hiau Looi Keel
International Trade Team
Development Research Group
Tine 'world Bank
1818 H Street NW (MSN MC3 303), wasnington DC, 20433. leA: (202) 47 4;S5u, F:x; ( 52& 1'
E-mail: hlkee@worldbank org This paper reDresents part of my Ph D. dissertation. I would like to give
special thanks to my supervisor Robert F-eenstra, for hiq helpful comments and insightful guidence. I am also
indebted to Lee Branstetter Kevin Hoover, Dorsati.Madani, Catherine Morrison, Marcelo Olarreaga, Kevin
Salyer, Maurice Schiff, Deborah Swenson, David Tarr, and seminar participants at the World Bank for their
useful suggestions. Please address any comments to hlkee0worldbank.org.
1. introduction
Hall (1988, 1990) shows that when the assumptions of perfect competition and constant
returns to scale are violated, the growth rate of primal total factor productivity (TFP) no
longer reflects the true productivity growth. The growth rate of primal TFP, which is also
referred to as the Solow residuals in the literature, is defined as the growth rate of output
minus the revenue share-weighted average of the growth rates of inputs. Employing industry
data of tne U.S. manufacturing sector, naul finds that the primal TFP is correlated with
to scal-e and imperfert rnmmpAtitinn in the manumfacturing sPtor.
Hall's findings have generated a series of related studies. It has become a standard
technique in the literature to apply the primal "Hall regression" to determine the nature
of returns to scale and the competitiveness of an industry. For example, using a similar
technique, Caballero and Lyons (1990, 1992); Bartelsman, Caballero, and Lyons (1994); and
Basu and Fernald (1997) show the empirical importance of non-constant returns to scale in
explaining the procyclical movement of Solow residuals in both U.S. and European industries.
Levinsohn (1993) and Harrison (1994) also apply the primal "Hall regression" to show the
effect of trade liberalization on the monopoly power of domestic firms.
Focusing on the price-cost side of the production theory and applying the cost function
as the dual equivalent of the production function, Roeger (1995) shows that the presence of
market power not only causes the duai TFP to underestimate real productivity growth, it
- - - - J U 1 3 2 "n"1MTT ~ 1ln .. -L .- J---I. IrOn '
aiso creaWs a wedge bet-w-e priiuLi iiiid uui TFP gro-wI. J. The gx-WLUL rate of UUa l T1F is
defined as the enue share-eighted average of the growth rate of input prices minus the
growth rate of output Drice. In other words. while maintaining the assumDtion of constant
returns to scale, he relaxes the assumption ot perfect competition and shows that markup
greater than one could explain the difference between the primal and dual productivity
3
measures using U.S. manufacturing data.
jJ. thl's pap-er WU ruid UULLh UUZ tLbbt.UPUU VI PVIe(.b ULLPULMIUL MLU bUWU UL ;iULlWLdtlL
returns to scale aT the samne tsme2 (½ml,+o.exen4ary to+he ,.,r.Eta of HaIl (1988 1000),
wp show that in the presence of market imnerfections or non-constant returns to scale- dual
TFP growth rates no longer reflect actual productivity growth. In particular, imperfect
competition or decreasing returns to scale technology will result in a downward bias of both
of the conventional TFP measures. In addition, this paper derives the theoretical difference
between the primal and dual TFP measures without both assumptions and shows that the
wedge between the two productivity measures depends on the growth rates of factor shares
in revenue. Thus, as long as factor shares in revenue remain constant, which is one of the
stylized facts in the empirical data, the difference between the growth rates of primal and
dual TFP vanishes, even in the presence of imperfect competition or non-constant returns
to scale. In other words, in contradiction to the results of Roeger (1995), we show that
the difference between primal and dual TFP should not be attributed to the presence of
imperfect competition while maintaining The assumption oi constant returns to scaie.
Empirical v f prim l anA dua ..T iD te 4-n-A -g_ a inust panel at4a of the
S,incrgnTnre mnniifac-turinr secrtnr The nrnoduct.ivixt grnwth nf Singannre has hben stuldipd
previously by Young (1992, 1995) and Hsieh (1999). In a famous and surprising study,
Young (1992) finds little evidence of primal TFP growth in the aggregate Singapore economy
- virtually all Singapore's growth from the 1970s to the 1990s is attributed to its factor
accumulation. Similar poor performance of primal TFP is also documented in Young (1995)
when the manufacturing sector data is studied. Citing evidence of non-diminishing market
rate of returns to capital investment in Singapore during the period of fast growth as an
indication of high productivity growth, Hsieh (1999) challenges Young's finding using the
2 Similar to Haills approach, we maintain the assumptions that factor markets are perfectly competitive and
production functions are non-joint.
4
dual approach. While acknowleging that the primal and dual TFP should be equal, Hsieh
advocates Ilthla Li nsLiot n aLIU tiacoUU-- dtIatia onL 'Lh ca piUal endOw-wUent' of SIngaporU Li Uawtud
then the dual approach would provide a better me°Q.ement of nAp+o,A 4,,
The empirical section of this naper is an atte~mnt to adjudicate between Young and
Hsieh at an industry level by estimating the industry productivity growth in the presence of
imperfect competition and non-constant returns to scale. We first run a panel regression that
embraces both primal and dual approaches to estimate industry-specific markups and returns
to scale. Given that the primal and dual approaches are theoretically equivalent, combining
them in the empirical specification allows us to double the sample size of the regressions. We
then apply an Olley and Pakes (1996) type correction for input endogeneity and selection
bias at an industry level to estimate the average industry markup and returns to scale. We
also address the concern raised by Basu and Fernald (1997) regarding the differences between
value added and output functions.
Results of a panel regression on the combined data set pass a specification test on the
equivalence of the primal and dual regressions with flying colors. The resuits also indicate
th-at -a'"' of the inulustrites lin t1le sectort- viohlst atit leatum one VI thet Casspvuior,s1 of pIJVLL%t, comL-
petiton-.-A constant retu #tn c,e-1a This ipnnlie that, in ordelr to determine thei artuia
produetivitvy growth, conventional growth accounting techniaues, which are based on the two
assumptions, are not appropriate for the Singapore manufacturing sector. Controlling for
input endogeneity and survival probability of firms in the industries, the estimated markup of
an average industry in the sector is around 1.4, while production technique is best character-
ized as decreasing returns to scale. After correcting for imperfect competition and decreasing
returns to scale, the estimated productivity growth in the sector doubles the conventional
TFP measures. Thus, the results of this paper favor Hsieh's finding at the aggregate level
that the productivity growth of Singapore could in fact be quite high.
How sensible are the estimates on markup and returns to scale? While various authors
5
have found markups greater than one in U.S. and European industries, decreasing returns
to scale tethnology has been regarded as less acceptable in the literature. Basu and Fernald
(i9Y^ argue bhaL uecreasming returnsto scaie makes no economic sense aT a urm ievei as iT
i-plies that firs consistently p-ic op beloW ma.-gin .Acost. They aso. sofW that the
degree of decreasing returns to scale diminishes at a higher level of aggregation- The.y emlain
the observed puzzles as aggregation bias due to firm heterogeneity in the industries. For our
current data set, even after controlling for firm heterogeneity using an Olley and Pakes type
correction, we still obtain an estimated scale coefficient that is significantly less than one.
Thus, we argue that for the case of Singapore's manufacturing sector, decreasing returns to
scale is a result of the limited supply of industrial land and buildings in the tiny city-state
rather than aggregation bias due to firm's heterogeneity. In fact, in recent years, Singapore's
government has been actively encouraging firms to relocate production plants to Malaysia,
Indonesia and China while keeping the headquarter's activities in the island, to slow rising
business costs due to limited supply of land and labor in the economy.
This paper is organized as follows. Section 2 presents a theoretical model detailing the
relationship between primal and dual TFPr and true productivity growth in the presence of
iniperEfct UompeltitLil o Ln U 1and i1.AJ1d= n-cs Ut Lurns tO s Sctiun 3 deVelUop the UpiILLckl
strategy to esfrntiat in iiqtry m&rlcup" &nd era]. rna rlcnf- tln both -the pi al-&n
dual Hall regressions. Section 4 describes the data set. and Section 5 presents the regres-
sion results. Section 6 discusses various econometric and specification issues, and Section 7
concludes the paper.
2. Theory: The Relationship between PrimAl and Dalnn TFP
2=1 Th-e Neotlissical Model
The standard assumptions of a neoclassical model of production are constant returns to scaie,
LnULn-JiLLnL proUUc.tionLL, O.UU peLrfecty Iomeiulive market LsfI inputsG.LU d outputsaJL. ULnLdL thes
6
assumptions, let i be the industry index and t be the time index; the relationship between
the growth rate of output, Yit, the growth rate of labor input, Lit, and capital input, Kit,
can be represented by Equation (i),
kit = Ait + eiLLit + 6iKKit, (1)
where Ait is the growth rate of Hicks neutral productivity, Oix is the share of input X in
total revenue, and 9iL + 9iK = 1. Thus,
A {Yit I Lit ^
Ait = ) viLV g*-it
Using the dual approach of production theory, a similar relationship also exists between
the growth rate of output price, Pit, the growth rate of wages, iit, and rental price, fit:
Pit = OiL?Wit + OiKrit -Ait (3)
Ait = OiL (it) (pit) (4)
Thus it is straightforward to define the growth rate of primal TFP, which is also known
- - els' ----- .." A.` . d e ..- .. re- 2- . " '
as the SlDLOW Lri:UULua, LiUU Uit VrUWwI thL UL UUof irrd
- = P D
Definition 1 Let l F'it be the growth rate of primal TF'P, and TFPit be the growth rate
of dual TFP, then
, .Pit = (KA =nLK)(5)
it - lLit
TF4 6p0i (^i(t rit (6)
\rit,1\rit )
Notice that under the assumption of constant returns to scale and perfect competition,
the growth rates of the two TFP measures are theoretically identical, and they measure the
true productivity growth, Ait, exactly
7
2.2 Departure from the Neoclassical Model
2.2.1 The Primal Analysis
Let the production function of industry i in period t be
Yit = AitFi (Lit, Kit). (7)
g - .E _ /__wL_ _Il _ % _ .., I . . .. a
aKmg tne logtrlm snu uineu uulerenuiaTing Equation /r) witn respecT to Time will give us
8Yrit Ut = OA/it jit+ OL t/et L t d 8R + dKjt/Ot Kit O i (8)
Yiit A Lit Fit OLi Kit Fit 9Ki
Let kt = , and let XaF = XY = ax, the elasticity of output with respect to input
X. Equation (8) can be simplified to
[it = -t- +iLiLt + aiKnit-
For each industry i, assume that the production function Fi is homogeneous of degree Si.
The size of Si relative to 1 tells us the degree of returns to scale of the industry. Returns
to scale are increasing, constant, or decreasing as Si is greater than, equal to, or less than
unity.
Using Euler's theorem for homogeneous functions:
CeiL + CkiK = Si, (10)
we can re-express Equation (9) with the convention that x =X
Yit -Kit = Ait + CeiL tLit -Kit) + (Si -1) Kit =S(11)
pit = Ait + kiLJit + (Si - 1) kit. (12)
Let the price markup of firm over marginal cost of firm i be
P Pit ()
8
and recall that 6iL is the share of labor in total revenue.3 According to Proposition (A2)
in the Appendix, ciL = IIAiL, Equation (12) can be simplified to
Yit = Ait + PNi0iLtit + (Si - 1) Kit. (14)
Thus, in the presenice of imperfect competition (Oi i 1) and non-constant returns to scale
(S # 1), the relationship between the growth rate of primal TFP and Ait, the growth rate
of actual productivity, is
- Fit -Lt =SL&it, Uby UVLLUiUion
- lit (i - ) viLLit +t 1t - 1 it, (0)
which leads us to the following proposition:
Proposition 2 Let 0 < Lit < kit. The growth rate of primal TFP will be less than the
growth rate of true productivity if markup is greater than one and technology is decreasing
returns to scale.
Proof. Given 0 <.Lit < Kit => iit < 0.
Then /ii > 1 and Si < 1 =* TFFit < Ait, by Equation (15). e
Thus, in a world in which capital deepening is rapid relative to employment growth,
market power and decreasing returns to scale imply that the growth rate of primal TFP
falls short of actual productivity growth. The above proposition restates the results of Hall
(1988, 1990), where he shows that imperfect competition may cause the Solow residual to be
procyclical and correlated with some aggregate demand variables.
2.2.2 The Dual Analysis
Let C (wit, rit, Fi (Lit, Kit)) be a general cost function,
G(git..e r..t P. (Liz, .W-)) -" ats- T.. *ie-,r W (16A)
3 By omitting the time subscript from pi, we are assuming that firms in each industry follow some fixed
markup rules that is constant over time. Alternatively, we could interpretate pi as the average markup of
industry i over time.
9
Obviously C is homogeneous of degree 1 in Lit and Kit. As shown in the Appendix, since
Fi (Lit, Kit) is homogeneous of degree Si, Ci is homogeneous of degree ; in Fi (Lit, Kit).
Homogeneity of Ci enables us to simplify the function further:
C (wit, rit, Fi (Lit, Kit)) = (Fi (Lit, Kit))i Gi (wit, rit)
= (AYit ) Gi (wit, rit) X (17)
Ailt
where G (w, r) = C (w, r, 1) is the unit cost function, which depends only on input prices.
Thus, given unchanged input prices, the more the firm produces, or the less efficient the firm
is, the higher the total cost of production.
To find the marginal cost function, mit, differentiate Equation (17) with respect to Yit
lnmit = -lnS,+ 5 -') lnY,t - lni+ni(isi) (18)
Diffeen'ite Emuarin (18)~ i;th respctj, to+n .e
= 1) Y 1 +t
7INW (Ji L7w Gtt Aiit
( -InSi41)Yit-IYit + t + rInA tIG it (19)
Ti Ti ~~Cit Cit
From Equations (17) and (19), we derive
/nL. / 1 \ 1 A ,,2.T,............ Tq,\4(}:)(0
Y~~) = ~1) Y't - -=Ait + ~- ~ ) (20)
where = (A = is obtained from the definition of G (w, r).
Let cix = wx, the payment share of input X in total cost of industry i. Assume that
the markup coefficient, pi, is constant over time, such that
Pit = milit.
10
With this simplification, multiply both sides of Equation (19) by -Si and rearrange the
terms:
Pit \ n~~t rt
P t it SiCL( rit ) + (Si )(rt)(1
Using the property that SiCiL = liOiL (by Proposition (A2) in the Appendix), we can
further simplify Equation (21) to
(whr ) Ait + t /iiL ( rit ) + (Si 1) (Pt),2)
where OiL = ' the payment share of input L in total revenue of industry i.
MIhus, inU --- prsence of i.p;,tc copttion _i 1) ar -A nr-cosa. -eun to -scale--4-- 1
X liUa 1l1 tU1IV IJLA.V I UL 1IMJJ~ L~U %..ULIlFV~uUltl L ki -r AU ~Lri fl.VJ-lWUQ flfl
(S 4 1), the relntionQhin hbt.w.en the crowth rate of dual TFP And A, the ornwth rate of
actual nroductivitv is
TFPit = 6iL(r - ) by definition
= Ait + (/Ai-1) OiL ( it + (Si-1) (uilt) (23)
Pronosition 3 Let 0 < < # < and fIt < p;Yit. The growth rate of dual TFP unill be less
than the growth rate of true productivity if markup is greater than one and technology is
decreasigng -stur.e to sca|e
Proof. Given 0 < fit < tuit, and fit °
Then pi > 1 and Si < 1 = TFPit < Ait, by Equation (23). m
The above proposition shows that, with the right conditions, both imperfect competition
and decreasing returns to scale may result in dual TFP underestimatinig true prod-uctivity
growth1. NoUticeA ULMt by 1maintU.CLIL11r ULM GLaLu...pt.on V;cnttze ose ht
6etting S = 1, Roeger (1995) shows that imperfert competition crauseR the dual TFP to
underestimate true Droductivitv growth. In other words, Roeger considers only one of the
scenarios of the above proposition.
2.2.3 The Difference
It is clear that if I ¢ 1 or S ¢ 1, then neither the growth rate of primal nor that of dual TFP
will reflect the true growth rate of productivity. The difference between the two measured
growth rates of TFP can be derived by subtracting Equation (23) from Equation (15):
TFF,- TFF.F, = )uj-u)tit) + (S._1) (rptKit)(
Thus, in theory, the presence of imperfect competition and non-constant returns to scale
creates a possible wedge between the two measures. However, given that the shares of input
in totai revenue are mnostiy consant ii th e real± worid, the rigInt-hand siue of Equation (24)
-s-4;-11-l -;I even encr.ptioisi.pe.fec + ad returs to scwle ae not const-t
la _ .t.J*. _ Ac V tl TV l J1V nUIn A U; tA&) 01104f0U LAflWU404U.
Propositio 4 Uf the shares _ l,.-4 4,,A..L,.1-" t
growth rate of primal TFP equals the growth rate of dual TFP.
Pronf. Constant innut shares =. ( .&L) = (wt ) = ° (t ) n.
Then TFP.f - TFPi, = 0, by Equation (24). m
3J. EJIZ...pirL,eLS. lLSrt
To estimate productivity growth in the presence of imperfect competition and non-constant
returns to scale, we would first have to estimate markup and scale coefficient according to
Equations (14)and (22), which we shall call the primal and dual Hall regressions:
Pit = A1l + OQiJit + 6i3kit. (25)
(ri:) = Ai,+)Yi2OiL ( ri) +-3 ( . ) (26)
mb _^t;ntorl, o la4fc ^f AR. A i ._ . uAll S%o fhno ni nn,A 4 ,n 1 r"hicz +bh
..e V -U a-U2 1- bW VeV; - in-, spei_ mwcus V_ VJM- [k .._.- th.V
estimated values of Ai. or 'y- will be the industrv-snecific returns to scale coefficients.4 In
4 In other words, we consider pi and S, as the structural parameters of the model that can be estimated.
12
other words, the following restrictions hold if the primal and dual regressions are equivalent:
,61 = 7y
I62 = 72 (27)
B~3 = 73.
With consistent estimates of markup and scale coefficient, we can then infer the industry
productivity growth from Equations (14) and (22).
L-Owevel, it ,b UUvIUULLtl tat uatiouns (25) duu (26) havue seio-uu endugeneiyL problems.
Growth rate of technologica progress,A, e.n. trst a m f o conditions for ro fi
maximization (as well as that of cost minimization)i which determine the input de.mand and
also output of the firm. Thus, without controlling for Ait, the least squares estimates for the
coefficients of the growth rate of labor per unit of capital and the growth rate of capital will
be biased upward.
Moreover, there is selection bias in the above specification due to firm's entry/exit be-
havior, as shown in Olley and Pakes (1996). Given that while only productive firms choose
to stay in business and unproductive firms choose to exit, larger firms, especially those that
have invested heavily, would be able to survive a short period of low productivity. Without
controlling for survival probability of firms in the industry, least squares estimates for capital
growth would be biased downwards.
To address the problems of endogeneity and selection bias, we first try a simple fixed
effect approacn Dy moaemlling productivity growth as the sum or indusTry fixed efrect andi
year ed ., effet. 4,l,kethe -ppl an Ole-n -aze (-1996 finn pe co.ection to est mate the
U,AZt; CI L TV V t"UJ~L Cbp ly .J"q LLJ ~L LL a V k rre' P .J ~ I. ~I WI
average indslmirv msar>.ln stndi r-tlirns; to .1
13
3.1 Fixed Effect Correction
Without lost of generality, assume that the Hicks neutral technological progress parameter
is a random variable of the following form:
Ait = Aioeoitt
Ait = qit = ai + At + uit, (28)
where Ajo is the technological level of industry i at tne beginning, period 0, and (pit is the
growth rate of technological progress. Thus, the growth rate of the technological progress of
inds.try i in period t consists on indtry-specific th ratea n a periodspeific
grow.th rate. A.. which captures the macroeconomic shock that is common across industries
in the same period, plus a white noise, uit, which is a classical random error term with zero
mean and a2 variance.
Substitute Equation (28) into Equations (12) and (22) and we will get
-.t - - a.fl (0 I N v' .,. ON
Ui + At + btiViLfit + k.'i -j) xlit -r it(2
{rit A t .tr trityit, __ -Y (30)
U-t a i -t At -t 11jiL t U)i ) -t 1;3i - IL, rt ) , Uit.$tU
Using the cross equation restrictions, Equations (29) and (30) may be stacked to give
z Yil A r V~~~~~~iiil kil
AT 8 O due to business cycie fluctuation.
HIeUc, WlLIUthu aaJiLWtnLL, LUL %..PUQXy UWL1i4ULL, WU ago.U iLLtLd-UUIUC au omitJtedU V-L liaU1l
problem in +he reg.oaion, A,ilh .may rtIf in biw in estimator oteg
One way to correct for the variability of the utilization of capital input is to une an
instrument to proxy its rate. Harrison (1994) uses a measure of total energy used as the
instrument. However, not all capital is electrical machinery and not all electricity consump-
tion is due to the use of capital. The inclusion of total energy used in the regression may in
turn introduce some extra noise into the estimation.
Fortunately, the inclusion of the period-specific effect, At, takes care of the business cycle
fluctuation that is common across industries. Shocks that are specific to an industry will be
24
captured by the industry-specific dummies. Thus, without introducing any extra variable,
we are able to control for the capacity utilization of capital input.
7. Conclusion
The dufI SlmAanc a of T-Tall' J (18) nnfO A--iu-A i .-A -t-teA. ..a- paper VY
that. theoretically; the nresence of either imperfect competition or drewresing retirnR to
scale technology will cause both primal and dual TFP growth rates to underestimate ac-
tual productivity growth. The size of bias depends on the degree of deviation from perfect
competition and constant returns to scale.
On the other hand, the difference between the growth rates of primal and dual TFP
depends on the change in factor shares in revenue. Given that, in general, factor shares are
relatively constant, the difference between the two TFP measures is close to zero, even if
imperfect competition or non-constant returns to scale exist. These are the main theoretical
findings of the paper, and it can be viewed as a complement to Hall (1988, 1990) and a
contradiction to the results of Roeger (1995).
The empirical section of this paper focuses on establishing a procedure that is capable of
estimating actual productivity growth, even in the presence of imperrection competition and
ron,-c o nastrantu remn s to0 ac -1 tech-o-o- A par.el re1-ntate.bae bt .h 4-prna
and dual approaches is pronosed to fully litilize informattion derived frnm both the niiantitv
and price sides of the data. We also present an empirical model that follows an Olley and
Pakes (1996) type correction for input endogeneity and selection bias at an industry level to
estimate the average industry markup and returns to scale.
Using Singapore's manufacturing sector as a case study, the empirical result of this paper
shows that both the primal and dual regressions are empirically equivalent. In addition, all
industries in the sector violated at least one of the assumptions of perfect competition and
constant returns to scale. Controlling for input endogeneity and selection bias, the estimated
25
average annual growth rate of productivity of the sector is more than 7%, which far exceeds
both conventional measures. Thus, the regression result casts doubt on Young's (1992, 1995)
findings, as it suggests that the productivity growth of Singapore may be much higher than
what can be measured using the conventional growth accounting technique. In other words,
without testing the two assumptions of perfect competition and constant returns to scale,
, , , . ~ ~~~ . . I - - -
one shoula exercise caution when using conventional Fr r measures.
26
A Homogeneity of the Cost Function
Proposition 5 (Al) Let C (w, r, F (L, K)) = wL + rK, and Y = AF (L, K). IJ F is ho-
mogeneous of deoree S in (L. K) ;then
1. C is homogeneous of degree S in F
2. C is homogeneous of degree s in Y
S. Letr,-= 'In 14en m=sY
Proof.
1. Increase both L and K by 6A times, 6 > 0:
C (w. r.F (J L. As'K)) = C (w, r,JF (L, K)), 1- homogeneity of FP(1, K)
Since C is homogeneous of degree 1 in (L, K), the left-hand side of the above equation
can be reduced to os C (w, p, F (L, K)). Thus, C (w, p, 6F (L, K)) = os C (w, p, F (L, K))
in-'wthat C(w, p, F (L, In)) is nomogeneous of degree s in F (L, K).
2. Notice that Y is- homogeneous of degree 1 in F. Thus, C is homogeneous of degree sin
F nuu15iu 5oge leous 0o aegree s in Y.
3. By Euier equation of homogeneous function, C is homogeneous of degree in Y *
. g .
B Input Elasticity, Revenue Share, andl Cost Share
Definition 6 Let
°ex = X F-, the elasticity of output with respect to input X;
ox = Wy the payment share of input X in total revenue;
pY
Cx = the payment share of input X in total cost.
Proposition 7 (A2) Let Y = AF (L, K) be the production function of a firm, and F be
homogeneous of degree S in L and K. Let p be the price over marginal cost markup. Let firm
minimize cost. Then
27
1. ax =pOx, X=L,K
A JUA-- -P T TP-
2. cx = 'SaX-sx, " X-L, XI
3. CL+CKl=
4. CeL+CKS
5- uL + vK =IL'
Proof.
1. Firm facing given w and r, minimaize the following program:
min C = wL + rK
s.t. Y = AF (L, K)
r + ~TZ I ~/A rIIT T,' r.N Z
WLI + r'A (AyL, Kj -1 )
r .'j.u.:
A = 8F
By Envelope Theorem, m = 7 = A, the marginal cost of production. Thus,
w aF wL
-= TL- * aL= = y POL-
Similarly, ajK = ILK-
2. By Proposition (Al), m = 1 C = SmY Thus,
wL wL 1 1 n
CL =-= M =-aL =-IUL-
Similarly, CK = aK = OK
3. CL+ CK = W + r = 1, by the definition of C.
4. aL + ctK = L + BF = S, by Euler equation for homogenous function.
5. OL + OK =CLS + CKS, by 2.
O DL + OK = (CL + CK) S = S, by 3.
.
28
C Real Value Added vs. Real Output
To understand this problem, we need to go back to the construction of the real value added
statistics. According to the Report on the Censw of Indust6al Production of Singapore,
the nominal value added statistic is generated by subtracting the cost of intermediate input,
including materials, utilities, and operating cost, from the value of output. Formally, let vt
denote the real value added in period t, ptYt be the value of output, and pmtMt be the cost
of intermediate input. Then the nominal value added is defined as
ptVt = PYt -pmtMt. (42)
To find the growth rate of real value added, differentiate Eqiation (42) with respnect to
time:
aPt Ovat vpt Y t P PM Mt Mt
-,,Vt + Pt = Yt + P t- - nu_ - , PMt (43)
VI, CJb UG ut. Ut. Ut.
Using +he nontatin nf wrorfu,h rn, ep r:sn, simplifyu Eiatiion (4A- to
PtVtPt + ptvtfit = phYtht + PtYtYt - PMtMtPMt - pMtMt.t (44)
Let SM = DMtml, the share of intermediate input in total output. Dividing both sides of
ptYt
Equation (44) by ptYt and rearranging the terms, we can get
(1A-S.)'T = R -II ('qA, +i- 4-A-'
or
1-sjj 1-SM A-SM (45)
Thus, the growth rate of real value added is a weighted average of the growth rate of
output and intermediate input (deflated by price of output).
To link this with our earlier regression, we need to define a production function that
29
includes intermediate input. Let
Yt = AtF (Lt, Kt, Mt)
Yt = At + aLLt + aKkt + CMMt, (46)
where O = F M M,h te__t,-4+,, of 4n+orv,.eio+n input ni+h respen t to ou,+_put
Siihstituting Eauation (46) into Equation (45); we will Yet
1 _____ _____ - ___ __M-S M ^ S_ /P_ vii
vt = At + Lt + k Kt+am J MtM (47)
1- f 1-SM 1-SM 1-SM 1-S ] )Pt)
Recall that AM = I1SM, and aGL+oaK = S, the degree of returns to scale, and 1-SM = .
Equation (47) can be simplified further to
v. - A +_ i-t + kt + (u-i SM m _ SM OMt)
I-SM PtYt 1-SM ' -SM 1 -SM \ PtJ
1 S Kt + (0-1) M t- ( )
1-SM 1-SM 1-SM -SM Pt
So when we regress the growth rate of real value added, bt, on the growth rate of labor
per capital weighted by the share of labor in value added, 0LIt, and the growth rate of capital,
kt, in order to estimate the markup coefficient, p, and the scale coefficient, S, we need to
worry about a few things.
First, the growth rate of intermediate input must be included together with the growth
rate of relative prices in order to avoid the problem of omitted variables. If Mt and
are omitted, then the estimated mark-up and scale coefficient will be biased, since It and kt
are correlated with Mt and _p
Second, even if both iviMt and (' are incuded in te regression, the estimated scale
coeffiLLcUi, S, Well as At, -iJl b e o i 1 = M i 8 O e ha oe -In t he data,
the size of SM rnogeps from 40% to 905 Thus, we need to take this into account when we
interpret the regression.
30
T 1D1M1;17Vn1VTt"C!
A%ALI LJ. .I.LtjL N %_JJ.L1%_
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32
Table 1: Data at a Glance. 1974-1992
Average Annual Growth Rates of Average
Output Real Labor Rental Revenue Firrns'
Capital Rental Capital Wage Capital Renal Prirnal Dual Real Tumover
SSIC IndustryName Ratio Price Ratio Ratio' input Ratio TFP2 TFP3 Investmenq Rate4
311/312 Food f -0.070 -1.239 -2.458 -3.190 8.235 8.965 2.388 1.951 9.4341 101.553
313 Beverage -i0J.564 -9.149 -4.345 -3.034 i5.3U4 i3.89 -0.219 -.iS )5.4zi1 Y9. 12
314 Tobacco -9.956 -9.824 -3.605 -3.483 12.049 11.918 -6.351 -6.341 8.1271 95.725
32! TexfenAo i.!90 -A.!6S -3.525 0.2!i -n.4S3 A.6A5 A47!5 -in.2!9 99,97.4
322 Apparel 1.615 1.680 -3.502 -3.435 6.770 6.704 5.117 5.115 -2.808 102.707
323 L.ealher I 4.187 -5.891 -5.960 -7.660 11.429 13.132 1.773 1.769 13.029 99.326
324 Footwear -6.344 -3.992 -8.314 -5.972 7.383 5.031 1.969 1.980 -2.413 99.220
331 Wood -1.512 -1.855 -4.618 -4.963 -0.169 0.174 3.105 3.108 -9.001 96.051
332 Furniture 0.088 0.750 -3.381 -2.720 10.699 10.037 3.469 3.470 8.7721 105.952
341 Paper -0.841 -1.037 -3.831 -4.028 12.218 12.414 2.991 2.991 10.523 102.096
-4 13- _ ACI -095 -1.146 -3.485 -3.681 . 1.9'" 12.168 2.5I355 Ii IA IA Q106 I, l1032.676
351 Industrial Chemicals 1.015 0.879 -1.695 -1.828 13.326 13.462 2.710 2.707 8.436 108.026
352 CheniicalProducts 0.311 0.696 -1.726 -1.339 12.127 11.742 2.036 2.035 9.9631 101.197
353/354 Petroleum 0.245 -0.202 -0.168 -0.634 2.871 3.319 0.413 0.432 11.5741 103.222
355 Natural Rubber 2.796 1.937 -2.527 -3.395 -1.797 -0.939 5.323 5.332 -3.4691 96.230
356 Rubber Products -0.325 -1.573 -2.362 -3.612 5.666 6.914 2.038 2.040 6.5561 99.798
357 Plastic Products 0.806 0.063 -2.269 -3.017 12.209 12.953 3.075 3.080 8.388 106.002
361/362 Glas -4.702 -.7 3 4.881 14.1 2.162 2.233 2.172 ;7.4c I 101.502
363 Clay -4.265 -3.363 -5.505 -4.637 7.467 6.565 1.240 1.274 -3.408 97.185
364 CaTent 2R07 2-678 -0930 -1.112 4.899 5.029 3.737 3.790 0.577 103.426
365 ConcreteProducts | -1.126 -1.152 -2.834 -2.878 14.505 14.531 1.708 1.726 17.7451 103.769
369 Mineral Products -4.200 -5.769 -2.778 -4.341 7.266 8.834 -1.422 -1.427 -4.684 101.898
371 BasicMetal -4.502 -5.692 -2.004 -3.228 7.117 8.307 -2.498 -2.464 2.2171 100.197
372 Non-Ferrous Metal 5.330 4.906 -0.496 -0.973 3.288 3.711 5.825 5.880 14.3061 107.849
381 Fabricated Meiti -0.873 -1.089 -2.968 -3.184 12.930 13.147 2.095 2.094 9.8 o ;05.384
382 Machinery 1.322 0.020 -2.554 -3.873 10.426 11.727 3.876 3.893 7.105 106.164
383 Electi c 7al I h 4 l6 4 -.0 AIR 9 95R 9 976 572 5 724 6827 I 03 545
384 Electrnics 1.805 1.982 -3.067 -2.886 16.888 16.710 4.872 4.868 14.543 108.995
385 Transport Equipment I 3.100 2.985 -2.801 -2.908 7.290 7.406 5.902 5.893 3.228 104.171
386 Scientific Instrtnents 4.750 4.809 -1.876 -1.038 3.453 3.273 6.626 5.847 1.4601 104.267
390 Other -4.832 -5.572 -4.982 -5.721 13.211 13.952 0.150 0.149 6.206 102.788
300 Industry Average 1 -1.002 -1.129 -3.296 -3.394 i 5.15 527 2.294 2.26S SA691 iu2.2
Notes: nlss othen.ise stated, all values represent the avege anmual growth rates fmm 1974 to 1992 in peage terns.
I. Variable is nultiviied bv the share of labor in total reverue according to the specification of the rodel.
2.1he lgowth rate of prinal TFP is obtained by subtacting the growth rate of output-Capital ratio fwrn the grwth rate of labor-capital ratio.
3. The gowth rate of dual 2FP is obtained by sacting the grwdi rate of real rental prioe fiom the growth rate of rental-wage ratio.
4. FiLU tumover *CI 1-b .SLsW =a6U A -P. t US * _ _ _ acrU-om. conWseci-A v 700.-
33
Table 2: Dependent Variables - Growth Rates of Real Output and Rental Price
Method: Fixed Effect Panel Regression
Included observations: 36
Included cross sections: 31
Total panel (unbalanced) observations: 1115
1Estimated Robust Estimated Scale Robust
Industry IMarkups S.E. ICoefficients S.E.
Food 11.70** (0.73) 10.62 (0.53)
Beverage 11.09* (0.63) 10.15 (0.22)
Tobacco 1-0.01 (0.79) 1-0.52* (0.31)
Textiles 1.50*** (0.18) 0.64*** (0.19)
Apparel 1.78*** (0.21) 1.25*** (0.23)
Leather 1.21*** (0.21) 0.51*** (0.16)
Footwear 1.23*** (0.28) 10.74*** (0.25)
Wood 0.90*** (0.26) 0.33 (0.27)
Furniture 1.15*** (0.15) 0.79*** (0.07)
Paper I 1.26* (0.60) I0.59** (0.34)
Printing 1.55*** (0.32) 1.00*** (0.22)
Industrial Chemicals 3.75w** (0.54) 1.31w (0.31)
Chemical Products 4.57*** (1.40) 1.10** (0.51)
Petroleum 5.92.. (1.30) 0.2 (0.49)
Natural Rubber 0.86*** (0.27) -0.05 (0.21)
Rubber Products i.37::: (0.20) 0.;5:: (0.i6)
Plastic Products 1.91*** (0.17) 0.81*** (0.17)
G;ass ;.608* (0..;) ;.;3 (
Clay 2.03*** (0.25) 0.98*** (0.14)
Cr, e r.t A2*** (0.6 I0.0 A(0. 28)
Concrete Products 2.98*** (0.23) 0.96*** (0.10)
Mineral . I I,)*** (0.!9) I nA** (0.16)
Basic Metal -0.79 (1.03) I1.47*** (0.56)
Non-Ferrnus Met>! !.85*** (0.2!) n077** (t 44
Fabricated Metal 1.58*** (0.27) 0.98*** (0.21)
Machinerv 2.9°7*** (023) 1 47*** (0.18)
Electrical 1.12*** (0.17) 0.40* (0.20)
Electronics 2.16*** (0.23) 0.73*** (0.19)
Transport Equipment 1.5*** (0.29) 0.63*** (0.19)
Scientific Instruments 11.11 (0.74) 10.23 (0.51)
Other |1.64*** (0.21) 10.74*** (0.19)
R-squared 0.782142 Mean dependent var -0.01
Adjusted R-squared 0.758514 S.D. dependent var 0.243
S.E. of regression 0.119426 Sum squared resid 14.334
Log likelihood 845.2303 F-statistic 46.258
Durbin-Watson stat 1.843607 Prob(F-statistic) 0
Notes: * , and * indicate signiFcance at 90Y., 95Y, and 99%/ confidence levels, respectively.
Industry and year fixed effects are inchded but not mported.
34
_ _ _ _ _ _ _ _ _ _ _ _ (2) - (3) 1(4) j( j 6 ) (7)
Dependent Variable Growth Rate of Output Firms- Growth Rate of Output per
- Irtns* I~~~~~~~A*t Rte-
Per Cp-'UFLL .u1roverL Capi.al - 1.' v Pte of
Rate Labor per Capital
Es-rirmted indusry UaICiPI.Ap .2*** I-AA*** I i A -*** I I4*** 1 AA***
(0.08) (0.08) (0.09) (0.09) (0.09) (0.09)
in £*** A IA fl*AV * A ** (1/7*
Estimated industry scale coeffiLcient 0.6* .6n*** V.58Q* 0.5
1(0.10) (0.10) (0.03) (0.08) (0.08)
investment growt 0.03***
(0.01)
Polynornial of investUment j( ) 3rd order 4 order
and capital stock growthI
Powers ofthe es'u -ed 3rd arde
lagged productivity growth l l
Powers u oUlue uUI[iLVU 3rd order
lagged survival probabilityn
Pon;-m-mial of esfllna-..eud la;edu 3rd order
productivity and survival rate
Year fixed effects IYes Yes Yes Yes Yes Yes Yes
iInUUsuy ItxeU LAcU W I ..uI u. ue- Yes Yees Yes Yes Yes
Samplesize 11115 1115 1115 11115 11083 1083 1083
No-tes: Robu2tsi naea inA- e rors in
*- **, and * tndicate sigiuticance at 90%, 95%/o, and 99V0 confidence levels, rspectively.
Estimated productivity growth is obtaned from the fitted vahie of'the polynomial of investment and capital growth from Column (3).
Estimated survval mte is the fitted value of Column (4).
35
I - :rage
Textiles
! -_] Apparel
1D. 4 Leiather
3 Q ~~Footwear
S X ~~Mfood t
Furniture I
Paper
Printing
q In lustrial] Chemicals r
Q hemical Products
0 Petroleum
:r Natural Rnbberbb
s ! Rubber Products r f
Plastic Products I
1jilass 0
3 Clay )(
o z Ceinent 1
o Q bncrele Prociucts "a"
0 Mineral ProduQ
o = 3lasic asciMetal
IN Dn-FeiToU s Metal K¢
Fabricated Metal -
Machinery
Electrical
0 SElectronics
rTrasport Equipment
Scientific
Other _ -
Table 5: Dependent Variables: Growth Rates of Real Output and Rental Price (controlling
for the growth rate of intermediate input cost)
Method: Fixed Effect Panel Regression
Included observations: 36
Included cross sections: 31
Total panel (unbalanced) observations: 1115
Estimated Robust lEstimated Scale Robvust
Industry IMarkups S.E. ICoefficients S.E.
Food 12.09*** (0.84) 10.84 (0.66)
Beverage 0.96 (0.64) 0.15 (0.25)
Tobacco 1-0.17 (0.82) 1-0.59 (0.31)
Textiles 0.23 (0.26) 0 (0.17)
Apparel 1.49*** (0.25) 1.17*** (0.27)
Leather 0.69** (0.29) 0.18 (0.20)
Footwear 1.10*** (0.27) 0.71** (0.24)
Wood 0.86 (0.65) 0.33 (0.54)
Furniture 0.45** (0.19) 0.36*** (0.11)
Paper U.4 (0.77) U.24. (U.4U)
Printing 1_.50*** (0.32) 1.01** (0.21)
industriai Chnemicais ;.142 (0.1) 1i.2- (0.33)
Chemical Products 5.15*** (1.10) 1.08*** (0.43)
Pou 'A**& 11 (.7 10. '7A*** in (J
Natural Rubber 0.86*** (0.25) 1-0.03 (0.20)
Rubber D A-P nAQ** Qt^2fa ncIC* in. 1 Q\
*E"UUUL.l A *U*.Ut.b V.01 vy.OJZ V.JJ ~ V.- J
Plastic Products I.01** (0.50) 0.37 (0.33)
Glass 1.91** (0.21) 1"24*** (0.12)
Clay 1.18*** (0.31) 0.57*** (0.16)
Cement 2.30* (0.74) 7 -0 04 (0 27)
Concrete Products 2.12*** (0.37) 0.72*** (0.11)
Mineral Prducts 1.00*** (0.17) 10.28*** (0.13)
Basic Metal 0.5 (1.05) -1.38** (0.57)
Non-Ferrous Metal 1.82*** (0.24) 1 0.71*** (0.31)
Fabricated Metal 1.10** (0.53) 10.73*** (0.33)
Machinery 12.04*** (0.36) 11.21*** (0.22)
Electrical 0.76*** (0.22) 0.28 (0.22)
Electronics 1.50*** (0.50) 10.48* (0.28)
Transport Equipment 1.21 *** (0.42) 0.48** (0.22)
Scientific Instruments 10.86 (0.92) 10.01 (0.69)
Other 11.03*** (0.30) 10.38* (0.22)
R-squared 0.812598 Mean dependentvar -0.010013
Adjusted R-squared 0.785661 S.D. dependent var 0.243026
S.E. of regression 0.112513 Sum squared resid 12.33006
Log likelihood 929.1809 F-statistic 38.74653
Durbin-Watson stat 1.901742 ProbiF-statistic) 0.000000
o.,=-. _ ._.A _ _ ....4 .,,.CC. .. oaC,. n.,d - -_ . .i..i.. a-, .
Inrdustry and year fixed effects nluded but t reported.
Growth late of intennodiate input is included but reported.
37
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WPS2848 Administrative Barriers to Foreign jacques Morisset May 2002 M. Feghaii
Investment in Developing Countries Olivier Lumenga Neso 36177
WPS2849 Pooling, Savings, and Prevention: Truman G. Packard May 2002 T. Packard
Mitigating the Risk of Old Age 75841
Poverty in Chile
WPS2850 Determinants of Commercial Bank David A. Grigorian June 2002 S. Torres
Performance in Transition: An Vlad Manole 39012
Application of Data Envelopment
Analysis
WPS2851 Economic Development and the Bernard Hoekman June 2002 P Flewitt
VAW orld Trade Organization After rDoha LI3I2 724IA
WPS2852 Reginnai Agreements anri Trarde in Aaditva Matton IIiunp 2002 P FlAwitt
Services: Policy Issues Carsten Fink 32724
WPS2853 Private Interhousehold Transfers in Donald Cox June 2002 E. Khine
Vietnam in the Early and Late 1990s 37471
WPS2854 Rich and Powerful? Subjective Michael Lokshin June 2002 C. Cunanan
Power and Welfare in Russia Martin Ravallion 32301
WPS2855 Financial Crises, Financial Luc Laeven june 2002 R. Vo
Dependence, and Industry Growth Daniela Klingebiel 33722
Randy Kroszner
WPS2856 Banking Po!icy and Macroeconomic Gerard Caprio, Jr. June 2002 A. VYatenco
Stability: An Exploration Patrick Honohan 31823