Producvy, Reurns o Scale and Produc Dfferenaon n he Real Trade Indusry --- An Emprcal Analyss usng Japanese Frm-Level Daa --- Asuyuk KATO Research Insue of Economy, Trade and Indusry Absrac Ths paper examnes producvy and reurns o scale under he assumpon of monopolsc compeon usng Japanese frm-level daa. Alhough dfferenang producs (servces) s consdered mporan n frms sraeges and producvy growh, has no been suffcenly nvesgaed n prevous sudes. In hs paper, we sudy hs ssue n wo real rade ndusres, deparmen sores and supermarkes, applyng he model of Melz (2000). Our resuls ndcae ha he real rade ndusres possbly follow ncreasng reurns o scale f we consder he effecs of produc dfferenaon. In addon, produc dfferenaon has a posve effec on frms revenue. Thus, polcy measures ha promoe economes of scale and produc dfferenaon should conrbue o furher growh n hese ndusres. In addon, he resuls ndcae ha he regulaory reform of he real rade ndusry n 2000made a posve conrbuon. Ths research s a par of he projec Servce dfferenaon and Producvy underaken a he Research Insue of Economy, Trade and Indusry (RIETI). The auhor would lke o hank Sadao Nagaoka, Masahsa Fuja and oher semnar parcpans a RIETI. The auhor also wshes o hank Hajme Takasuka for hs helpful commens on he model. The opnons expressed and aurgmens employed n hs paper are he sole responsbly of he auhor and do no necessarly reflec hose of RIETI. E-mal: kao-asuyuk@re.go.jp
2 Producvy sn everyhng, bu n he long run s almos everyhng --- Paul Krugman ---. Inroducon Producvy has been suded by economss and polcy makers for a long me. Ths s because only producvy growh s consdered as an engne o yeld economc growh n he long run. The surge of producvy growh n he U.S. n he laer half of he 990s renforces her neress. I shows ha he servce secors whch were hough as sagnan secors before can also rase her producvy growh and become a drvng force of macro economc growh. To beer undersand hese facs and oban useful mplcaons, many heorecal and emprcal sudes have been conduced. In parcular, he ncreased avalably of mcro (frm or esablshmen level) daa has produced many emprcal papers o esmae producvy and examne he relaonshps beween producvy and ndusral polcy (ncludng he regulaory reform). In hose sudes usng frm level daa, dfferenaon of producs (servces) has no been well examned alhough s hough o play some mporan roles n frm sraeges and producvy growh. Ths s parly because he daa avalably for produc dfferenaon s sll poor, parcularly for servce producng frms. Neglecng hs problem n esmaon, however, may bas he esmaed reurns o scale and producvy. For hs ssue, Melz (2000) proposes an neresng model whch ncorporaes monopolsc compeon no he esmaon of producon funcon. Hs model also explcly ackles he problem ha oal sales are dfferen from acual oupu of frms producon f produc (servce)-specfc prces are heerogeneous alhough hey Krugman (990)
3 are nerpreed o be dencal n esmang producvy. In hs model, producvy esmaon does no rely on he produc-specfc prce daa alhough mposes some lmaon on producvy esmaon. Loecker (2007) modfes Melz s model addng produc-specfc prce daa. Ths model mproves esmaon of producvy by decomposng demand shocks and producvy growh. Bu, s no much applcable for servce ndusres because servce-specfc prce daa are no usually avalable. In hs paper, we examne producvy, reurns o scale, and produc (servce) dfferenaon, applyng a slgh modfcaon of Melz s approach o Japanese frm-level daa. To he bes of our knowledge, hs s he frs paper whch ncorporaes produc dfferenaon no producvy esmaon followng Melz. In addon, n order o compare he resuls and dscuss he effecs of produc dfferenaon on producvy, we esmae hree dfferen models usng daa for he real rade ndusry, n parcular deparmenal sores and supermarkes. Furhermore, we examne he relaonshps beween producvy and he regulaory reform. The layou of hs paper s as follows. In secon 2, we deal he model whch we examne. Secon 3 descrbes he daa whch we use. In secon 4, we dscuss he emprcal resuls and her mplcaons. And he las secon draws concludng remarks from he above dscusson. 2. The Model Ths secon brefly descrbes he model whch we examne. Followng Melz, we sar wh he case where any frm produces a sngle produc or servce 2. Suppose ha frms n an ndusry produce symmercally dfferenaed producs wh a common elascy 2 To avod redundancy, he erm, produc, ncludes boh meanngs of produc and servce, henceforh.
4 of subsuon (CES) beween any wo of hem. Accordng o Blanchard and Kyoak (987), we assume he uly funcon of a represenave consumer for producs n ndusry c s descrbed as follows 3 : N U ( Λ ) c = Q, () = N where N s he number of frms n hs ndusry 4. Λ and Q denoe he consumer s valuaon of he produc qualy of frm, and he quany of, respecvely. The parameer s resrced o be greaer han uny oherwse here mgh be no equlbrum. The uly funcon s assumed o be dfferenable and quas-concave. In addon, an ncrease n he number of producs does no change margnal uly afer opmsaon because he uly funcon s normalsed by N. In hs smple model of monopolsc compeon, changes n Λ over me sem from changes n he acual qualy of he produc or changes n he consumer s preference. To smplfy he model, he shfs of preference whch affec all producs are excluded. For hs uly funcon, he budge consran of he consumer o purchase producs of ndusry c s N B, (2) = = PQ, N 3 Melz assumes he uly funcon as ( Λ ) = Q Z, where Z s an overall demand shfer. Bu we don follow because equaon () s mahemacally compable wh he followng equaons. 4 Holz-Eakn and Lovely (996) uses a smlar framework of dfferenaon for producon funcon wh a large npu varey (n parcular, nermedae npus).
5 where P s he prce of frm s produc. From he frs order condon of uly maxmsaon, we oban he followng: P = N ~ N = P Λ D, (3) where P ~ s he average prce of producs adjused on he qualy n hs ndusry 5. From he above equaons, he demand for frm s produc s wren as follows: Q ( ) P = Λ U c ~ N P, (4) Now, we denoe he sales of frm s produc as P Q = R, and oal sales n he ndusry whch s equvalen o oal revenue as N = R R. Usng hem, equaon (4) = s rewren as follows. Q P R = Λ ~ ~ P N P (5) Ths equaon ndcaes ha he number of frms whch equals he number of producs deermnes oupu of frm, ogeher wh oher facors. On he oher hand, he producon funcon n hs paper s defned as follows. Frs, 5 D s a Lagrange mulpler.
6 we assume ha frms use he producon echnology whch s homogeneous of degree γ > 0. We do no assume ha γ = bu raher examne hs ssue emprcally. s he vecor of npus whch are consumed n producon of Q. X s an aggregae npu ndex whch s consruced as a lnearly homogeneous funcon of npus, f Χ. Χ ( ) Smlarly, he vecor of he facor prces s Ω, and an aggregae facor prce ndex s W = Ω ). Followng hem, our producon funcon for frm s descrbed as h( follows: Q = Φ X, (6) γ where Φ represens producvy of frm. Now, we ake logs of equaon (5) and (6), and solve he demand funcon for frm-specfc prce p no he revenue funcon, producon funcon:. Pluggng n he producon and he nverse demand funcons r ~ p = q + p ~ p, we oban he followng revenue r ~ p = γx + [( r ~ p ) n ] + ( φ + λ ), (7) where lower case varables are logs of upper case varables n equaon (5) and (6). The subscrp represens me. From he defnon of Φ and Λ, adjused producvy ndex, and s denoed as ϕ ( φ + λ ) nformaon, neher φ nor λ s separaely denfed. φ + λ s a qualy =. Whou addonal As Melz deals, equaon (7) does no nclude he produc-specfc prce whch s
7 no usually avalable n emprcal sudy. Equaon (7) also reveals ha esmaon of revenue producon funcon whou produc dfferenaon may undersae he degree of reurns o scale by. Ths s conssen wh a fndng of Klee and Grlches (996). Producvy dfferences Δ ϕ are also undersaed by addon, an ndusry aggregae sales regressor ( ) p as well. In r ~ does no always oban a sgnfcan and posve coeffcen, and only he esmaed coeffcen greaer han possbly means ha here are exernal economes unlke Cooper and Johr (997) 6. Nex, we expand he above model o he case where frms produce dfferen numbers of producs. Now, frm produces M producs. Snce we do no add any change on he srucure of he model, he producon and demand are respecvely presened as follows; Q j = Φ X, (8) j γ j Q j = Λ j Pj ~ P M R P, (9) where M N = = M. We also assume N M N R j j = = = = R = R, P Q = R and j j j M X = j = X j. We add he assumpon ha nroducng an addonal produc has a sunk cos for frms as well. An average qualy adjused producvy for each frm s denoed as ~ ϕ, and formulaed as follows: 6 Melz also dscuss ssues relaed o frm markups, and concludes ha producvy dfferences can be separaely esmaed whou frm specfc prce nformaon because he frm markups s nseparably relaed o he npus.
8 e ~ ϕ γ = = M R j ϕ j M j M R e γ, (0) where ϕ s a qualy adjused producvy of each produc. Under hese assumpons, a revenue producon funcon of frm dvded by he number of producs a perod s descrbed as follows. r m ~ p = γ ~ ( x m ) x + [( r ~ p ) m ] + ϕ The erm m n he lef hand sde s ransposed o he rgh hand sde. Then, he followng revenue funcon of frm s obaned. [( r ~ p ) m ] + ~ ϕ + ( ) m r ~ p = γx + γ () In hs equaon, as Melz dscusses, he erm ( γ ) should be larger han zero f frms produce more han one produc whle he posve effecs of ncreasng produc varees for each frm have a rade-off agans ncreasng he sunk cos. Followng Levnsohn and Pern (2003) (henceforh, LP), we esmae equaon (). LP dscusses he ssue of poenal correlaon beween npus and producvy and proposes o use he nermedae npu s demand funcon whch s assumed as a monoonc funcon of producvy 7. Inverng he monoonc funcon can uncover he 7 Olley and Pakes (995) also propose an approach where he esmaon of producon
9 unobserved producvy erm as a monoonc funcon of he nermedae npu and capal 8. To dscuss a bas n reurns o scale and effecs of produc dfferenaon, we examne he models wh hree dfferen assumpons, () producs are homogeneous across frms, (2) he average number of producs per frm s consan over me, and (3) he numbers of producs vary across frms. For assumpon, he esmaed model s equvalen o he LP model. An equaon based on assumpon 2 s equvalen o he model proposed by Melz and s descrbed as follows. [( r ~ p ) n ] + ˆ( k e ) u r ~ p = β, + (2) 0 + β k k + β ll + β ee + β ϕ where ˆ ϕ ( k, e ) ϕ + ( γ ) m =. On he oher hand, he model wh assumpon 3 s a modfed one of equaon (2) and s wren as follows. r ~ ( p = β + [( r ~ p ) m ] + β mm + ( k, e ) u 0 + β k k + β ll + β ee + β ϕ (3) ( where ϕ( k, e ) = ϕ. An ssue whch we should dscuss s wha varable s examned as a proxy of he number of producs sold by a frm. In hs paper, we use he floor space per shop for each frm under an assumpon ha frms wh smlar busness models n he real rade ndusry follow smlar use of space for her commercal esablshmen 9. Esmang hese hree equaons, he LP equaon, equaon (2) and funcon suffers problems due o endogeney. Unlke LP, hey propose o use nvesmen as a proxy of unobserved producvy. I, however, has a sgnfcan shorcomng ha nvesmen daa conan many zeros n convenonal frm level daa. Droppng many zeros remans he smulaney problem unsolved. 8 Souza (2006) deals he LP mehodology under monopolsc compeon. 9 Ths assumpon seems o be reasonable beween frms n he same counry.
0 (3), we examne producvy, reurns o scale and produc dfferenaon. 3. Daa In hs sudy, we use frm-level daa of he real rade ndusry n Japan over he 995-2004 perod. In parcular, we focus on frms caegorsed as he deparmen sores and supermarkes. The daa are exraced from he annually compled offcal sascs of frms acves by he Mnsry of Economy, Trade and Indusry of Japan 0. Ths sascs cover many acves of frms and are consdered relable. In addon, we oban fgures on floor space of shops for each frm from he sascal yearbook named as Nkke Almanac of he Dsrbuon Indusry. To consruc a proxy of frms produc varey, hey are dvded by he number of commercal esablshmens for each frm. From hese daa source, we consruc our own daase composng of oal revenue, labour, capal and nermedae npus, and floor space per shop for each frm. In our daase, oal revenue of each frm s represened as oal sales. The proxy of accumulaed capal s he angble fxed asses. Labour npu s calculaed as man-hours 2. Followng Toku, Inu and Km (2007) and Km, Kwon and Fukao (2007), henceforh KKF, he nermedae npu s obaned as follows 3 : ( TW + Dep + T D Purchase) Inermeda e Inpu = COGS + SGA & +, (4) where COGS, SGA, TW, Dep and T&D are he cos of goods sold, he sellng and 0 Ths sascs s named as he Basc Survey of Busness Srucure and Acvy. Kyoa and Masuura (2004) 2 The daa of workng hours are avalable from Monhly Labour Survey. 3 In calculaon of nermedae npu, we slghly modfy boh Toku e al. and KKF. The former does neher nclude ax and dues nor purchase n calculaon of he nermedae npus whle he laer does no nclude ax and dues.
general admnsrave expenses, he oal wages, he deprecaon and he ax and dues, respecvely. In consrucng our daase, we rule ou he frms whch repor zero or negave values as oal sales, he number of regular workers, he angble fxed asses, oal wage, or nermedae npus. Snce fgures on oal revenue, capal and nermedae npus n he orgnal daa source are repored as nomnal values, we need o consruc real seres of hose varables usng relable deflaors. For oal sales and nermedae npus, JIP ndusry-specfc deflaors of oupu and nermedae npu are used 4. Capal s repored as book values ncludng he land possessed by frms n he daa source. We consruc real seres of capal followng KKF. However, we don subrac he esmaed values of he land from he values of he angble fxed asses because we consder he land s an mporan facor for producon, parcularly n real rade ndusres. 4. Emprcal Resuls Ths secon dscusses he resuls of esmaon and her mplcaons. Bu, before ha, we should dscuss an ssue relaed o he deflaors. In our model framework, he ndusry-specfc prce ndex s defned as an average prce of producs adjused on her qualy. The acually avalable prce ndex s, however, no exacly dencal o ha one. I means ha our esmaon mgh oban based coeffcens. In fac, hs s a shorcomng no only n our esmaon, bu also n all emprcs usng me seres daa 5. Bu we do no hnk ha sgnfcanly harms our emprcal analyss. Snce equaon (3) s essenally he mehodology used o consruc he ndusry-specfc prce ndces, our 4 JIP daabase s consruced as a jon projec of REITI and he Hosubash Unversy global COE program (H-Sa), and s avalable from he followng webse. hp://www.re.go.jp/jp/daabase/jip2008/ndex.hml 5 The ssues of deflaors are also dscussed n Kao (2007).
2 model framework s consdered reasonable. Tables and 2 presen he resuls from esmang he LP, equaon (2) (Melz ) and (3) (Melz 2) for boh deparmen sores and supermarkes, respecvely. The resuls of he ess f γ = unless consderng a bas,, are n he boom rows. The erm Varey denoes he number of producs. In our esmaon, he floor space per shop for each frm s used as a proxy of. In boh ables, he esmaed coeffcens on he nermedae npu are unrelable excep for wo esmaons, Melz and 2 n Table because hey are sascally nsgnfcan 6. Therefore, we do no dscuss hem. On he oher hand, he coeffcens on capal are sgnfcanly posve, save for he LP n Table. I reveals ha land should be ncluded n he capal socks n hs esmaon 7. These ables show ha he Wald ess do no rejec he assumpon of consan reurns o scale (CRS) n boh deparmen sores and supermarkes. Those resuls are, however, possbly based because hey do no nclude effecs of he elascy of subsuon beween producs. Therefore, we oban he degree of bas from he esmaed coeffcens, and carry ou a es of he followng null hypohess. H 0 : k l e = ( β + β + β ) Snce he coeffcens on he erm, [( r p ) n ] [ m on ( r p ) ~ are sgnfcanly posve whle hose ~ ] are negave, we calculae he degree of bas usng he former ones. 6 We examned some slghly dfferen forms of nermedae npus as well. Bu none of hem s sgnfcanly esmaed. 7 We also esmaed he producon funcon where capal sock does no nclude he land, bu he esmaes were nsgnfcan.
3 Accordng o he resuls of, he p-value of he Wald ess on he CRS assumpon are 0.005 (deparmen sores) and 0.084 (supermarkes), respecvely. Tha s, he null hypohess ha reurns o scale are consan s rejeced a he one and en percen levels. I ndcaes ha he valdy of he CRS assumpon s sgnfcanly conroversal n he sudy of producvy a leas n he real rade ndusry f producs are dfferenaed. The esmaed coeffcen on he varable, Varey, s sgnfcanly posve for supermarkes. I reveals ha produc dfferenaon has a posve effec on frms revenue. Wh qualy adjused producvy, s posvely assocaed wh he esmaed oal facor producvy (TFP) n convenonal approaches. On he oher hand, he erm, Varey, s nsgnfcanly esmaed for deparmen sores. I ndcaes ha deparmen sores and supermarkes follow dfferen busness models as s well known 8. These resuls ndcae ha he ndusral polcy whch s helpful for pursung economes of scale and produc dfferenaon conrbues o producvy growh of supermarkes. Relang o he above ssue, we dscuss he effecs of regulaory reforms on producvy. Among varous ndusral polces, regulaory reform, n parcular deregulaon, s usually consdered as mporan nsrumens o promoe a favourable economc envronmen. In 2000, he Japanese governmen enaced he Large-Scale Real Sore Locaon Law n order o lberalse locaon for large scale real sores. From he above emprcal resuls, hs regulaory reform s expeced o have a posve effec on producvy as a whole 9. To es for he effec, we add a dummy varable whch equals zero unl 999 and one afer 2000 and re-examne he revenue funcons 20. 8 Deparmen Sores are hough o provde her dfferenaed servces hrough varous enans such as hgh-class bouques as well as her own servce. In hs meanng, he number of enans per commercal esablshmen s possbly a beer proxy alhough s no examned because of daa absence. 9 Our daa do no nclude small busnesses. 20 Snce our daa are relavely small, s dffcul o reasonably deec any paern n a
4 The resuls are presened n Tables 3. In he ables he esmaed coeffcens on he deregulaon dummes are sgnfcanly posve a he one percen level. Alhough hs dummy varable conans no only effecs of he deregulaon bu also all he economc envronmens varyng before and afer he mllennum, he posve esmaes sll mply ha he regulaory reform possbly conrbued o mprovemen of producvy. The above resuls ndcae ha he producon funcon wh he monopolsc compeve srucure can be a useful nsrumen for esmang producvy and dscussng desrable ndusral polces. 5. Concludng Remarks Ths paper examnes reurns o scale, producvy, and produc dfferenaon usng he frm-level daa of deparmen sores and supermarkes n Japan beween 995 and 2004. Followng Melz, we ncorporae a monopolsc compeve srucure no he producon funcon, and compare he resuls from hose of a convenonal approach. In hs sudy, our fndngs are as follows. Frs, he CRS assumpon s conroversal n emprcs of producon funcon of he real rade ndusres. In boh ndusres, he alernave assumpon ha he degree of reurns o scale s no equal o uny s no sascally rejeced n he bas correced esmaes. I mples ha he CRS assumpon should be carefully examned n he esmaon of producvy snce oherwse he esmaed producvy mgh be based. Secondly, produc dfferenaon seems o gve a posve conrbuon o producvy of supermarkes alhough s no deeced for deparmen sores. Ths resul suggess ha fuure research should apply hs approach o oher ndusres usng relable proxes of produc varey because produc dynamcs of her average producvy levels.
5 dfferenaon s an mporan n many oher ndusres as well. Thrdly, he regulaory reform n 2000 seems o promoe producvy growh n boh forms of large-scale real raders. These resuls gve a polcy mplcaon ha he ndusral polces whch promoe economes of scale and produc dfferenaon are favourable for he real rade ndusry. Appendx: Descrpve Sascs of Produc Dfferenaon Deparmen Supermarke Max 253490.00 4323.00 Mn 245.25 43.5 Ave 2266.55 2406.0 Med 6869.00 235.39 Sd 20768.57 5703.38 Skw 3.95 4.20 Sample 900 606 The gaps of he floor space per shop beween frms are sgnfcanly huge for boh deparmen sores and supermarkes. For boh busness models, daa are consderably skewed oward he lowes range.
6 References Blanchard O. J., and N. Kyoak (987), Monopolsc Compeon and he Effecs of Aggregae Demand, Amercan Economc Revew, 77, 647-666 Cooper R. and A. Johr (997), Dynamc Complemenares: A Quanave Analyss, Journal of Moneary Economcs, 40, 97-9 Holz-Eakn D. and M. E. Lovely (996), Scale Economes, Reurns o Varey and he Producvy of Publc Capal, Regonal Scence and Urban Economcs, 26, 05-23 Kao A. (2007), Survey on Producvy n he Servce Secor (n Japanese), RIETI Polcy Dscusson Paper, 07-P-005 Km Y. G., H. U. Kwon and K. Fukao (2007), Enry and Ex of Companes and Esablshmens, and Producvy a he Indusry Level (n Japanese), RIETI Dscusson Paper, 07-J-022 Kyoa K. and T. Masuura (2004), Consrucon and Usage of A Panel Daa of he Basc Survey of he Busness Srucure and Acvy : Problems n Applcaon o Economc Analyss and Arrangemen of Daa (n Japanese), RIETI Polcy Dscusson Paper, 04-P-004
7 Klee T. J. and Z. Grlches (996), The Inconssency of Common Scale Esmaors When Oupu Prces Are Unobserved and Endogenous, Journal of Appled Economercs,, 343-36. Krugman P. R. (990), The Age of Dmnshed Expecaons, MIT Press, MA Levnsohn J. and A. Pern (2003), Esmang Producon Funcons Usng Inpus o Conrol for Unobservables, Revew of Economc Sudes, 70 (2), 37-342 Loecker J. D. (2007), Produc Dfferenaon, Mul-Produc Frms and Esmang he Impac of Trade Lberalzaon on Producvy, NBER Workng Paper, No. 355 Melz M. J. (2000), Esmang Frm-Level Producvy n Dfferenaed Produc Indusres, Harvard, mmeo Olley S., and A. Pakes (996), The Dynamcs of Producvy n he Telecommuncaon Equpmen Indusry, Economerca, 64, 263-297 Souza S. De (2006), Levnsohn and Pern s (2003) Mehodology Works under Monopolsc Compeon, Economcs Bullen, 2 (6), - Toku J., T. Inu and Y. G. Km (2007), The Emboded Techncal Progress and he Average Vnage of Capal (n Japanese), RIETI Dscusson Paper, 07-J-035
8 Table : Deparmen Sores Coeffcens LP Melz Melz2 Capal 0.065 0.422*** 0.298*** (0.088) (0.37) (0.09) Labour 0.260*** 0.268*** 0.258*** (0.035) (0.033) (0.033) Inermeda e 4.38e-24 0.543** 0.374** [( r p ) n ] (0.05) (0.228) (0.89) ~ 0.60*** [( r p ) m ] (0.070) ~ -0.246*** (0.024) Varey 0.04 ( P value) (0.02) Wald 0.000 0.434 0.77 Noe: ***, **, ** are %, 5%, and 0% sgnfcance Sandard Errors are n Parenheses Table 2: Supermarkes Coeffcens LP Melz Melz2 Capal 0.50*** 0.733*** 0.809*** (0.8) (0.20) (0.234) Labour 0.289*** 0.269*** 0.283*** (0.022) (0.024) (0.027) Inermeda e 0.020 0.0 0.6 [( r p ) n ] (0.22) (0.52) (0.232) ~ 0.282*** [( r p ) m ] (0.057) ~ -0.28*** (0.080) Varey 0.07** ( P value) (0.008) Wald 0.306 0.624 0.244 Noe: ***, **, ** are %, 5%, and 0% sgnfcance Sandard Errors are n Parenheses
9 Table 3: Revenue Funcon wh he Deregulaon Dummy Coeffcens Depar Super Capal 0.429*** 0.69*** (0.04) (0.74) Labour 0.265*** 0.274*** (0.032) (0.025) Inermeda e 0.557*** 7.65e-09 [( r p ) m ] (0.96) (0.0) ~ -0.78*** 0.097* (0.027) (0.054) Varey 0.05 0.07** (0.00) (0.007) Dummy 0.090*** 0.060*** ( P value) (0.02) (0.03) Wald 0.298 0.42 Noe: ***, **, ** are %, 5%, and 0% sgnfcance Sandard Errors are n Parenheses