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 1N W, Washington, u u 2043. rlease contact lvara Nasniag, room MC3 -32Vl-1, te lepholne 202-4 73-9 0 , fa 202----19 J7, 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 development issues. An objective of the series is to get the findings out quickly, even i/the presentations are less than fu;ly polished. The 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%_ Aw-, Bee Van, Yiarn^in Chen, anAd Mrk J. Pwberts (2001). "F _T -1 E-eAae on Productivity Differentials and Turnover in Taiwanese Manufacturing," Journal of De- vel&Up,FI&e&& .OLWIWII&..M, vvl. UV, no. 1, p. 51-86. Bartelsman, Eric J., Ricardo J. Caballero, and Richard k. Lyons (1994). "Customer- and Supplier-Driven Externalities." 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Productivity and U.S. Economic Growth. Amsterdam: North-Holland. Jorgenson, Dale W., and Martin A. Sullivan (1981). "Inflation and Corporate Capital Recovery." Depreciation, Inflation and the Taxation of Income from Capital, ed. Charles R. Hulten, p. 171-237. Krugman, Paul (1994). "The Myth of Asia's Miracle." Foreign Affairs, vol. 73, no. 6, e n s70 p. u.l-Io. Levinsohn, James (1993). "Testing the Imports-as-Market-Discipline Hypothesis." Jour- nal of International Economics, vol. 35, p. 1-22. 31 Levinsohn, James, and Amil Petrin (1999). "When Industries Become More Productive, Do Firms? Investigating Productivity Dynamics." NBER Working Paper, no. 6893. Levinsohn, James, and Amil Petrin (2000). "Estimating Production Functions Using T- d. F~ O., f TT, h,ap-m1-laa" NTfl-'f W^A V-n 7210 .Ly"pulto Gont:ol fo Unobser.b.s' V9E V**rbig Paper, n.Jt.789 Olley, G. Steven, and Ariel Pakes (1996). "The Dynamics of Productivity in the Telecommunications Equipment Industry." Econometrica, vol. 64, no. 6, p. 1263-1297. Roberts. Mark J.. and James R. Tvbout (1996). Industrial Evolution in Develovino Countries: Micro Patterns of Turnover, Productivity, and Market Structure, Oxford: Oxfnord TTnivprqitv Prpesq Roberts, Mark J., and James R. Tybout (1997). "The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs." American Economic Review, voi. 87, p. 545-564. Roeger, Werner (1995). "Can Imperfect Competition Explain the Difference between Primal and Dual Productivity Measures? Estimates for U.S. Manufacturing." Journal of Political Economy, vol. 103, no. 2, p. 316-330. Wong, Fot-Cnyi, and Wee-Beng Gan (1994). "Total Factor Productivity Growth in the Singapore Manufacturing Industries During the 1980's." Journal of Asian Economics, vol. 5, no. 2, p. 177-196. Young. Alywn (1992). "A Tale of Two Cities: Factor Accumulation and Technical Change in Hong Kong and Singapore." NBER Macroeconomics Annual 1992. p. 13-53. Aong Al - /1 f%nr% uter.i 'T- -: 'c 1 .2 - ''OUng, -JiIWyU (199ij). "lth ITyra-ny UL 1-bers CUU1i Ui%oULULLLtiLLg LtU S bL.tatMil Real,ties of the East Asian Growth Experience." Quarterly Journal of Economics, vol. 110, no. 3, p. 641-668. 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-, . 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