Relative Efficiency and Productivity Dynamics of the Metalware Industry in Hanoi

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1 Relave Effcency and Producvy Dynamcs of he Mealware Indusry n Hano Nguyen Khac Mnh Dau Thuy Ma and Vu Quang Dong Absrac Ths paper focuses on relave effcency and producvy dynamcs of he mealware ndusry n Hano durng he perod by usng wo mehods: daa envelopmen analyss (DEA) wh he Malmqus ndex and me-varan sochasc froner producon funcon (SFPF). Boh mehods confrmed a sgnfcan dsperson n relave effcency and producvy and a decreasng rend of he producon froner durng he sudy perod. Moreover analyss of facoral effecs on echncal effcency showed ha capal-labor rao real wage ownershp and frm age were no mporan facors whle frm sze was a sgnfcan facor ha nfluenced he effcency and producvy performance of he ndusry durng he sudy perod. Key words: effcency daa envelopmen analyss (DEA) Malmqus ndex mealware ndusry producvy sochasc froner producon funcon (SFPF) Tob regresson Venam JEL Classfcaon: C D4 L6 O47. Inroducon Evaluang he producve effcency of a frm can only be possble f he frm s performance s comparave wh ha of oher smlar frms. Such a comparson leads o a relave effcency level. Relave producve effcency was frs nroduced by Farrell (957) and was hen developed by ohers. Producvy and effcency are wo dfferen conceps. Producvy can be undersood smply n erms a frm s observed performance such as per capa produc or oupu-per-npu rao. However effcency s measured eher by he rao of he acual oupu o he maxmum oupu (oupu-based approach) or by he rao of he mnmum npu o he acual observed npu (npu-based approach). Froner producon funcons have been used o explan furher he erm relave effcency. Despe dfferences n esmaon mehods (paramerc or non-paramerc) producon funcons (sochasc or deermnsc) depend on he followng assumpons: Assumpon : All npu-oupu combnaons are under he producon possbly froner. Assumpon : Producon se s concave. Toal ransformed oupu over oal ransformed npus n he case of varous oupu and npu ypes. If m oupus ( y y... y m ) and npus ( x x... x n ) are assocaed wh her weghs of { λ } = for oupus and ( yλ ) γ for npus he producvy should be: = m (Ray 004). ( x γ ) n { } = n 7 j= j j

2 Assumpon 3: Producon se s free dsposal. Ths means ha f producon possbly hen possbly. Y * * ( x ; y );( x ; y ) and The followng are defnons of dfferen effcences. G ( x ; y ) s whn * * x x ; y y are also whn producon Defnon (Pure Techncal Effcency Oupu-based Approach): Pure echncal effcency s measured by he rao of a frm s acual oupu o he maxmum level of oupu ha frm could acheve usng s exsng echnology. Defnon (Pure Techncal Effcency Inpu-based Approach): Pure echncal effcency s measured by he rao of a frm s mnmum npu o s acual npu o produce a un of oupu. Fgure : Defnon of Effcency H D F E J I A C B O P Q R S X Fgure presens producon possbles wh npu X and oupu Y. Suppose ha fve frms are A B C D and E. The producon possbly froner goes hrough he pons P B J A D F and E. Frm C could reach maxmum oupu a F gven npu a S. Frm C s pure echncal effcency based on oupu approach s SC/SF. Is mnmum npu on oupu CS s OQ. The frm s pure echncal effcency based on npu approach s OQ/OS. If he froner s he lne OG (n he case of consan reurns o scale) OQ/OS and OC/OF are equal mplyng ha he wo approaches gve he same level of pure echncal effcency. Defnon 3 (Scale Effcency): Scale effcency of a frm s s opmal scale. The opmal scale s he consan reurns o scale. Defnon 4 (Allocave Effcency): Allocave effcency of a frm s based on s resource allocaons n erms of he relaon beween margnal npu subsuons and prces o maxmze s prof. Allocave effcency s assocaed wh npu and oupu prces 3. Because prces are no avalable n some observaons such a ype of effcency wll no be consdered. I s commonly agreed ha opmal scale s a consan reurns o scale. If markes are compeve economc prof wll be zero. If a frm has ncreasng (decreasng) reurns o scale should ncrease (decrease) s scale. 3 We assume ha oupu prce s normalzed o one relavely o npu prces. Assume ha he producon funcon s Y = F(X) where npu X = (X X. X n ) wh prce P = (P P. P n ). The necessary equaon F / X P for maxmum prof s = for all and j. F / X P j j 8

3 Agan Fgure shows ha scale effcency s un f a frm has consan reurns o scale and s on he lne OG. Scale effcency of a frm a C s SF/SG because hs frm could reach oupu SG f had consan reurns o scale bu s acual oupu s SF. Some sudes also consder congeson effcency whch descrbes a suaon ha a producon funcon s no non-decreasng wh a specfc npu. In hs paper we wll no ake hs ype of effcency no accoun and we assume ha congeson effcency s always un. The res of hs paper s srucured as follows. Secon wll provde model specfcaons n whch boh daa envelopmen analyss (DEA) and sochasc froner producon funcon (SFPF) models wll be dscussed. The esmaed resuls by hese models for he Mealware Indusry n Hano wll be analyzed n Secon 3. The las Secon concludes hs paper.. Model Specfcaons There are wo popular mehods o measure effcency and producvy: DEA and SFPF. Each mehod has some advanages and dsadvanages whch wll be dscussed laer n hs paper. In addon each mehod also depends on some assumpons whch wll also be menoned when needed. Boh mehods frs esmae he producon froner and hen evaluae echncal effcency... Daa Envelopmen Analyss (DEA) and he Malmqus Index DEA s a non-paramerc esmaon for producon froner and effcency. Ths mehod was frsly nroduced by Charnes Cooper and Rhodes (978or CCR n shor); Banker Charnes and Cooper (984or BCC n shor) laer conrbued o wh a case of varan scale. DEA models are based on hese wo early developmens wh some mproved seps o esmae he desred crera. DEA models have several common feaures. Frsly DEA s a non-paramerc esmaon mehod. I does no use any specfc funcons for producon and prof. Therefore elasces and margnal raos canno be calculaed. Secondly he mehod uses lnear programmng n esmaon process raher han he leas square mehod whch s ofen used n paramerc esmaon. DEA can herefore deal wh cases of mulple npus and oupus. Thrdly DEA esmaes under lnear programmng are no subjec o any sascal esng because hey do no brng any sascal properes. Any downward dsperson from he producon froner s regarded as neffcency. Färe and Grosskop (996) nroduced a mehod of echncal effcency esmaon assocaed wh me as follows: [ ] d ( x y ) = sup φ φ λ subjec o y Y x X or equvalenly = φ φ φ φ + λ 0; λ 0; λ 0 m () d ( x y ) sup : ( x y ) S ( x ) where S (x) ={(x y ): y f(x )}. () To esmae pure echncal effcency a consran λ = should be added. Scale effcency s hen equal o he rao of echncal effcency o pure echncal effcency. Based on DEA esmaes he Malmqus ndex of producvy whch represens decomposon of change n producvy and echnology s calculaed as follows: 9

4 + d ( X ) Y Y M ( + ) = x + d ( X ) Y Y or equvalenly where / (3) / + d ( X ) Y Y Y d ( X ) Y Y + Y + M ( + ) = x = E ( + ) T ( + ) (4) ( ) E ( + ) = represens echncal effcency change and + + Y + d ( X ) Y d ( X ) Y Y + + T ( + ) = x + + d ( X ) Y + Y + from o + for he frm. Moreover we have / represens he geomerc average of echnology + + d ( x + y + ); d ( x + y + ); d ( x y ) are as follows. [ ] + d ( x y ) sup φ + + φ λ = subjec o φ y + + Y + λ 0; x + X + λ 0; λ 0 (5) where (5) s echncal effcency a + usng daa and echnology a me +. [ ] d ( x y ) sup φ + + = φ λ subjec o y + Y x + X φ + λ 0; λ 0; λ 0 (6) where (6) s echncal effcency a usng daa and echnology a me +. + d ( x y ) = supφ λ φ subjec o φ y + Y + λ 0; x X + λ 0; λ 0 (7) where (7) s echncal effcency a + usng daa and echnology a me. DEA allows us o analyze he changes of echncal effcency pure echncal effcency echnology and oal producvy facor (or he Malmqus ndex). Addonally can also be used o analyze facoral effecs from soco-economc varables on effcency. Due o a consran ha effcency s whn [0;] Tob regresson s ofen used o decompose such effecs. Such a decomposon process s called a wo-sage process whch s somemes crczed as a based esmaon process because some varables n he frs process of effcency esmaon can affec he decomposon process. In conras some argue ha because he frs sage s non-paramerc wll no creae such bas... Sochasc Froner Producon Funcon (SFPF) SFPF s based on a known producon specfcaon. Such a funconal form can be Cobb- Douglas consan elascy of subsuon (CES) or ranslog. A common lkelhood esng s used o choose he bes funconal form among hem. Some feaures of SFPF are as follows. Frsly producon funcon has a known specfcaon and economerc echnques are used o esmae he producon funcon. Hence sascal esng can be used o examne a sgnfcan level of esmaes. Afer mplemenng some log-lkelhood esng hs paper uses a ranslog producon funcon ha generalzes CES and Cobb-Douglas. Such a funcon has a form as: 0

5 ln F( X ) = A + α ln X + β ln X ln X j j j n 4. (8) Secondly esmaed resduals are assumed o follow a specfc sascal dsrbuon. Such a dsrbuon can be normal half-normal runcaed normal Gamma or exponenal. Recen sudes have followed an dea ha he esmaed resduals conss of wo pars: sochasc resduals caused by exernal shocks (u) and neffcen resduals from he producon process (v). ln y = ln F( x ) + u v (9) Thrdly SFPF does no consder scale effcency. Effcency from SFPF s equvalen o pure echncal effcency n DEA. Measurng changes n relave effcency of he whole ndusry over me can be calculaed when me s regarded as an npu varable. In hs paper he SFPF model has one oupu (real value-added) and hree npus (average number of workers L real ne capal K and me ). The esmaon equaon s: ln y = A + α ln L + α ln K + α3 + β(ln L) + β(ln K) + β3( ) +. (0) + β (ln L)(ln K) + β (ln K)( ) + β ( )(ln L) + u v Varable wll cause changes n combnaons of K and L shfng he producon froner over me. Moreover varable allows dynamc esmaes of effcen resduals n erms of me. v Techncal effcency of a frm s equal o e. Wh he assumpons ha u follows (0 u ) N σ v follows runcaed normal dsrbuon of N ( µ σ v ) a zero and u and v are ndependen wha maers s how o decompose hese wo resduals n he esmaon process. Baese and Coell (995) argued ha aggregae resdual σ v ( u v ) had varance σ = σ u + σ v and condonal varance of v on u was γ = σ u + σ v whch represened how much he sochasc resdual could explan dynamcs n he producon froner. If γ was closer o he acual dsperson from he froner was caused manly by neffcency resdual. There s also a smlar regresson o DEA n whch he neffcency erm wll be decomposed no facoral effecs from soco-economc varables as follows: v = z δ + () w where z represens conrollable varables or soco-economc varables ha can affec echncal effcency level and w represens unconrollable varables. Recen echnques use one-sage esmaon n whch he facoral decomposon sage wll be regressed a he same me as he effcency esmaon sage. The coeffcen of δ has an oppose drecon of effec on echncal effcency.e. a negave (posve) sgn of δ means a posve (negave) effec on effcency. j j. j n 4 Cobb-Douglas producon funcon s ln F( X ) = A + α ln X. CES producon funcon n secondorder Taylor s expanson s ln F( X ) = A + α ln X + β (ln X ln X )

6 3. Emprcal Applcaon for he Mealware Indusry n Hano 3.. Daa Descrpon Daa used n hs paper were colleced from he Economc Census for Enerprses by he General Sascs Offce of Venam (GSO) durng In he models oupu s real value-added and npus are average number of workers and ne capal (.e. capal afer deprecaon). All npus and oupus are real values adjused wh nflaon.e. consumer prce ndex (CPI) 5. Table conans some core sascs of he sample. L: Labor K: Capal Table : Sascs of he Varables Varables Year Average Sd. Dev. Mn Max VA: Real Value Added Source: Auhors complaon from he daase Table shows ha here was a change n frm sze over me and he dfferences beween mnmum and maxmum values of npus and oupus grew over me. Ths mples ha he producon scale became more dvergen over me. Soco-economc facors whch could affec echncal effcency and producvy nclude ownershp average real wage per worker frm age frm sze and capal-labor rao. Ownershp consss of sae ownershp (4 observaons) and prvae and foregn ownershp (4 observaons) 6. Frm age s equal o he me lengh from he me a frm was esablshed o he me was surveyed. Frm sze s measured by real revenue. Average real wage s equal o he oal real wage over he average number of workers. Assumng a compeve labor marke and perfec nformaon average real wage could be a reasonable ndex for labor producvy. Capal-labor rao s equal o a frm s oal ne capal over average number of workers and hs varable capures how much a worker was equpped wh capal durng he sudy perod. Table shows a bref summary of hese soco-economc facors. An ncreasng rend n average real wage s evden alhough he sandard devaon of wage was sable over me. Capal-labor rao and real revenue also ncreased over he perod. 5 We acknowledge ha s no sasfacory o use a common nflaon rae o adjus boh normal npus and oupus no real values. Daa would have been reaed more reasonably f such adjusmens had used dfferen crera. However snce prces were no repored wh frm-level daa would be beer o use a common Consumer Prce Index (CPI) as an adjusmen for all normal varables and he base year should be he year Prvae and foregn ownershp are grouped no one n hs paper.

7 Table : Some Sascs of Soco-economc Facors of he Sample Varables Year Average Sd. Dev. WW: Average Real Wage (VND mllon) CLR: Capal-Labor Rao (VND mllon) R: Real Revenue (VND mllon) AF: Frm Age (years) Source: Auhors complaon from he daase 3.. Esmaed Resuls and Analyss 3... Techncal Effcency DEA SFPF Table 3: Esmaed Resuls of Effcency under DEA and SFPF Effcency Average Sd. Dev. 0% 5% 5% 50% 50% 75% 75% 00% crs crs crs crs se se se se vrs vrs vrs vrs vrs vrs vrs vrs Noe: crs: overall echncal Effcency vrs: pure echncal effcency and se: scale effcency Source: Auhors esmaes 3

8 Table 3 summarzes some of he esmaed resuls for effcency under DEA and SFPF models. DEA allows us o esmae echncal effcency pure echncal effcency and scale effcency whle SFPF only esmaes pure echncal effcency. The resuls can provde some mplcaons. Frsly he esmaes from DEA and SFPF confrm a low level of average echncal effcency. Four 5-percen effcency nervals show ha almos all frms had effcency scores of less han 5 percen (n DEA) and less han 50 percen (n SFPF). Few frms fell no he hghes 5-percen nerval (.e. 75% 00%). Effcency dsrbuon mples a large dsperson of effcency among frms. Secondly he DEA resuls prove a que hgh level of scale effcency n whch mos frms scale effcency was more han 75 percen. Thrdly pure echncal effcency under DEA was lower han ha n SFPF hough boh mehods show he same dynamc rend n hs ype of effcency. Ths dfference could be explaned by a beer reamen of SFPF over sochasc resduals Changes n Effcency Technology and Producvy Boh DEA and SFPF can be employed for dynamc analyss of echnology effcency and producvy. The esmaed ranslog producon funcon under SFPF s as follows: lnva = ln L ln K (ln L ) (ln K ) + ** * * * ** * ** ** 0.3 ( ) 0.89 (ln L )(ln K ) (ln K )( ) 0.38 (ln L )( ) u v Noe: (***): Sgnfcan a level of % and 5% respecvely; = 0 3. Sgnfcan coeffcens of (lnk)() and (lnl)() clarfy he changes n capal-labor combnaon over me n whch he share of labor ncreased whle he share of capal decreased. Changes n producon echnology caused he producon froner shf. Over me neffcency erm v was affeced by a change of ( ( ) ) per year. 7 Average echncal effcency changed (ncreased or decreased) yearly by ( e ) = 03 based on he year 000. The dynamc change of neffcency erm from () o ( + ) was e [ 0.68( + ) + 0.3( + ) ] [ ( ) ] = e where = 0. Under DEA dynamc changes of effcency oal facor of producvy (or Malmqus ndex) and echnology are presened n Table 4. Year Table 4: Dynamc Changes n Effcency Technology and Toal Producvy Facor under DEA Techncal Effcency Pure Techncal Effcency Scale Effcency Technology Toal Facor of Producvy 00 vs vs vs Average Source: Auhors esmaes Table 4 shows dramac changes of effcency n 00. Scale effcency was sable over me. On average echncal effcency and pure echncal effcency ncreased by.4 percen 7 Even hough he coeffcen of s no sgnfcan we need o add he varable for beer dynamcs of effcency n effec analyss. 4

9 and 4.5 percen from 000 o 003 alhough he effcency level was sll low. However he producon froner ended o shf downward (specfcally he froner shfed upward n 003 bu downward dramacally n 00 and 00) causng he oal facor of producvy o decrease by.7 percen per year n Analyss of he Facoral Effecs Table 5 summarzes he esmaed resuls from Tob regresson under DEA. All hree ypes of effcency are regressed. As explaned soco-economc varables nclude real wage per worker capal-labor rao revenue frm age and ownershp. Table 5: Facoral Effecs of Soco-economc Facors on Effcency under DEA Real Wage Capal-Labor Rao Revenue Frm Age Sae- Ownershp Consan Terms crs ** * * crs ** * ** ** crs * ** * crs * ** * vrs * * vrs ** ** * ** vrs * * vrs * * se * * * ** * * se ** * * se * * se * * * Noe: crs: Techncal Effcency vrs: Pure Techncal Effcency se: Scale Effcency (***): Sgnfcan a level % and 5% respecvely Source: Auhors esmaes The resuls mply some nerpreaons. Ownershp dd no sgnfcanly affec effcency dfferences beween frms durng he sudy perod. However sae-owned frms had hgher scale effcency n 000 and 00. Frm age dd no affec pure echncal effcency bu dd affec echncal effcency hrough scale effcency n 00 and 003. Frm sze ncreased echncal effcency and pure echncal effcency bu decreased scale effcency. The bgger he sze of a frm he hgher s echncal effcency even f had lower reurns o scale. Capal-labor rao had a posve effec on echncal effcency n 000 and 00 bu had no effec n 00 and 003. Real wage per worker had a smlar effec o ha of capal-labor rao. µ Real wage per worker Table 6: Facoral Effecs on Techncal Effcency under SFPF Capal-Labor Rao Revenue Frm age Sae Ownershp Consan Coef ** * γ = σ u = σ v = Noe: (***) means coeffcen s sgnfcan a sgnfcance levels of % and 5% respecvely Source: Auhors esmaes Under SFPF wh one-sage esmaon process and runcaed-normal dsrbuon a zero of effcency resduals he facoral effecs are also decomposed and presened n Table 6. Because 5

10 γ s valued a ha 89.9 percen varaon n he acual oupu from maxmum oupu could be explaned by neffcency resduals. Table 6 also confrms ha only capal-labor rao and frm sze really affeced pure echncal effcency. The oher facoral varables were no sgnfcan. A negave sgn of he coeffcen for he varable Revenue shows ha he bgger he frm sze was he hgher s pure echncal effcency. As shown n he producon froner dynamcs npu combnaon ncreased labor and decreased capal over me. As a resul capal-labor rao ended o go down reducng echncal effcency. 4. Concludng Remarks Ths paper has produced he followng fndngs for he frms n he mealware ndusry n Hano durng Frsly relave effcency among all frms was low and revealed a sgnfcan dsperson n effcency beween hese frms. Boh daa envelopmen analyss (DEA) and sochasc froner producon funcon (SFPF) mehods confrmed hs fndng. Secondly pure echncal effcency and echncal effcency ended o ncrease n he perod and he producon froner shfed dynamcally downward hrougou he sudy perod hus reducng he oal facor of producvy. Thrdly some soco-economc varables such as ownershp wage frm age and capal-labor rao dd no srongly affec echncal effcency. The resuls of boh mehods suppored he concluson ha frm sze had a posve effec on effcency level. Based on he esmaes of boh DEA and SFPF mehods a clear pcure of effcency and dynamc changes n echnology and producvy was presened for he mealware ndusry n Hano. Boh mehods provded smlar conclusons abou effcency froner shf and facoral effecs. However hs paper would have been more complee f some exreme observaons had been repored and analyzed separaely. In addon hs paper gnored he producon and marke srucure of hs ndusry whch mgh have mpacs on he effcency and producvy performance of frms. References Afra S. N. 97. Effcency Esmaon of Producon Funcons. Inernaonal Economc Revew 3 no. 3: Agner D.; C.A.K Lovell and P. Schmd Formulaon and Esmaon of Sochasc Froner Producon Funcon Models. Journal of Economercs vol. 6: 37. Agner D. J. and S. F. Chu On Esmang he Indusry Producon Funcon. Amercan Economc Revew 4 no. 58: Bauer P. W Recen Developmens n he Economerc Esmaon of Froners. Journal of Economercs vol. 46 ssues -: Banker R. D.; A. Charnes; and W. W. Cooper Some Models for Esmang Techncal and Scale Ineffcences n Daa Envelopmen Analyss. Managemen Scence 30 no. 9: Banker R. D. and A. Mandraa Nonparamerc Analyss of Techncal and Allocave Effcency n Producon. Economerca 6 no. 56: Baese G. 99. Froner Producon Funcons and Techncal Effcency: A Survey of Emprcal Applcaons n Agrculural Economcs. Agrculural Economcs vol. 7 ssues 3-4:

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