A Stochastic Frontier Analysis on Firm-level Total Factor Productivity and Technical Efficiency in Korea

Transcription

1 A Stochastc Fronter Analyss on Frm-leel Total Factor Producty and Techncal Effcency n Korea Sunyoung Jung *, Hak K. Pyo ** Abstract The conentonal ndex number approach to the analyss of total factor producty cannot dstngush between a shft of producton functon (techncal progress and a moement along a producton functon (techncal effcency. Ths paper attempts to separate techncal effcency from the producty measurement usng the econometrc approach based on the stochastc fronter producton models. Ths study wll be lmed to the models that take frms heterogeney nto account because most of the aalable panel data consst of a large cross-secton and relately short tme seres. To the extent that frms producton s characterzed by heterogeneous producton condons, estmaton technques that do not account for unobsered heterogeney lead to based effcency estmates. The sources of total factor producty growth are decomposed nto techncal progress, the changes n techncal effcency, the changes n allocate effcency, and the scale effects by usng the estmated parameters n the stochastc-fronter producton models. Keywords: Producty decomposon, Techncal effcency, Stochastc fronter producton model * Fellow at World Class Unersy Program, School of Economcs, Seoul Natonal Unersy, Seoul , Korea. Tel: E-mal: trust14@hanmal.net. Correspondng author. ** Professor, School of Economcs, Seoul Natonal Unersy, Seoul , Korea. Tel: Fax: E-mal: pyohk@plaza.snu.ac.kr. 1

2 I. Introducton Producty s an mportant ndcator that represents the growth of each economc agent. By utlzng data on producty by country or ndustry as the OECD database or EU KLEMS, the productes of seeral countres are compared and large-scale researches are actely conducted n order to consstently dscuss producty measures and computng methodologes. Japan s RIETI has deeloped the Japan Industral Producty Database (JIP Database and s carryng out researches on producty and other actes that could mproe statstcal data by natng proects that promote the producty of seeral ndustres or frms. Korea also, wh the Korea Producty Center as the central fgure, has been buldng up a Korea Industral Producty Database (KIP Database. Untl today, producty analyss by ndustry has been predomnant. Howeer, many researchers analyzng producty pont out that the exstng approaches are que lmed because they do not reflect the characterstcs of a frm, whch s the standard un that makes actual decsons and mplements economc actes. Exstng approaches are lmed to eher establshment-leel analyss or comparate analyss on the ndustry un. It s necessary, therefore, to analyze producty usng the frm-leel mcro data. In researches on frms, what has been actely researched recently, together wh researches on producty, s the analyss on techncal effcency of a frm. Ineffcency occurs from a frm s external and nternal factors. A frm should begn by strng to dentfy such nternal factors of neffcency n order to elmnate these factors and thereby enhance s competeness and achee long-run growth. Ths s why s necessary to analyze the effcency of Korean frms and researches on the determnants that promote effcency. The obectes of ths paper are to dscuss emprcal and theoretcal ssues related to dentfyng and estmatng the sources of frms producty growth and techncal effcency n terms of

3 econometrc approaches. By s constructon, the ndex number analyss approach, whch s the manstay methodology of producty analyss, cannot dstngush between a producton functon shft, whch means techncal progress, and a moement along a producton functon, whch means changes n techncal effcency. The econometrc approach s a flexble technque not only for dentfyng the sources of producty growth but also for consderng the techncal effcency of frms by explcly specfyng the underlyng producton (or cost or prof structure. Therefore, ths paper attempts to separate techncal effcency from the producty measurement usng the econometrc approach, especally the stochastc fronter producton models. By usng stochastc fronter models, techncal effcency can be drectly estmated, and the estmated parameters of the underlyng structure are used to dere an ndex of total factor producty growth. In the followng Secton II, we descrbe the Kumbhakar (000 method and adopted stochastc fronter models for the decomposon of TFP. Then Secton III presents the results of an emprcal analyss ncludng econometrc results wh the summary descrpton of database. Fnally, we summarze conclusons n Secton IV. II. The Stochastc Fronter Producton Models and Decomposon of TFP Kumbhakar (000 addresses the estmaton and decomposon of TFP change usng mcro panel data n a parametrc framework. The Solow (1957 measure of producty change, and thus the ndex number analyss approach, s wdely used for measurng TFP, but ths approach s nothng but the ndex of techncal change when the constant returns to scale (CRS producton technology and perfect effcency are assumed. If effcency change s omted from the analyss, s omsson wll lead to an 3

4 oerstatement of the unexplaned resdual. Kumbhakar (000 focuses on the parametrc econometrc modelng of producton systems and the estmaton of TFP changes from the emprcal producton, cost, and prof functons. Furthermore, TFP change s decomposed nto the techncal-change, scale economes, and techncal- and allocate-neffcency components. The contrbutons of the techncaland allocate-neffcency effects are separately dentfed and estmated. Startng wh the determnstc producton fronter, y = f( x, t; β exp( u, = 1,,..., N, t = 1,,..., T (1 where y s the output for frm at tme t, f ( x, t; β the determnstc stochastc producton fronter wh the technology parameter ector to be estmated, x an nput ector, t a tme trend serng as a proxy for techncal change, and u 0 the techncal neffcency. Totally dfferentatng the logarhm y n equaton (1 wh respect to tme 1, dln f( x, t du y = dt dt du = TP + ε x dt ( where ln f ( xt, ε =. A conentonal Dsa ndex of producty (TFP change s defned ln x as the dfference between the rate of change n the output and the rate of change n the nput quanty ndex, and so TFP y S x (3 = 1 For smplcy, the subscrpts wll be omted from ths pont onward. 4

5 where S denotes the obsered expendure share of nput. By nsertng equaton (3 n equaton (, the growth of TFP can be represented as d ln f ( x, t du du y = = TP + ε x = TFP + S x dt dt dt du TFP = TP + ( ε S x dt du = TP + ( RTS 1 λ x + ( λ S x dt (4 where RTS = ε denotes the returns to scale and λ = ε / ε = ε / RTS k k. Thus, n equaton (4, TFP growth can be decomposed nto techncal change (TC, techncal-effcency change (TE, scale effects (SE, and allocate-effcency change (AE. Many leratures show that recent domestc researches attempt to analyze producty by applyng Kumbhakar (000. Howeer, despe the fact that care should be taken n measurng techncal effcency, snce the characterstcs of Kumbhakar (000 s methodology are such that the results of producty analyses are affected dependng on how the method of measurng the estmated alue of changes n techncal effcency s desgned, ths fact has not been suffcently taken nto account. The lmatons of such leratures are summarzed as follows. Frst, as mentoned preously, the stochastc fronter models that are used n the exstng leratures are ery lmed. Table 1 shows that all, except Lee and Pyo(007, estmated effcency by employng Battese and Coell(199. Ths s only a part of stochastc fronter models that are already known. The model self has exstng lmatons. Exstng models hae contnued to be mproed and more ratonal models hae contnued to be deeloped, but these hae seldom been reflected n domestc researches. Second, s necessary to establsh and accurately use stochastc fronter models that are suable to the gen research 5

6 obectes and to the characterstcs of data beng used. The frequently used Battese and Coell (199 model, for nstance, has the adantages of estmatng the changes of tme-aryng effcency beng taken nto account. Howeer, s lmed n that effcency of all sample frms demonstrates the same tme-aryng pattern. By usng the cross-secton data models n the analyss usng panel data, sometmes comms error because cannot utlze the adantages that panel data hae. 6

7 Study Industry Perod Cross-secton Table 1 Emprcal Studes on Korea s TFP Decomposon Usng Kumbhakar (000 Obserat ons Producton Technology Stochastc Fronter Model Dependent Varable Tme-aryng Component Results Km and Han (001 Manufacturng Lsted Companes 6,03 Translog Functon Battese and Coell (199 Value-added Producty growth was dren manly by techncal progress Changes n techncal effcency had a sgnfcant pose effect Allocate effcency had a negate effect. Kang and Park(004 Total Industry Frms 17,784 Translog Functon Battese and Coell (199 Sales Snce fnancal crss, restructurng manly depended on an ncrease n the total factor producty by reducng employment and sellng assets whout sgnfcant ncrease n TFP. Han(005 Manufacturng Lsted Companes 5,370 Translog Functon Battese and Coell (199 Sales The Contrbuton of techncal progress was hgher than that of techncal effcency mproement n the TFP growth. The ndustres wh hgher(lower rate of techncal change experenced the lower(hgher rate of techncal effcency change. 7

8 Lee and Pyo(007 Total Industry Industres 448 Translog Functon Lee (006 Gross Output Producty growth was dren manly by changes n techncal effcency n 1980s. Producty growth was dren manly by techncal progress n 1990s. Pa(007 IT Manufacturng Establshments 1,681 Translog Functon Battese and Coell (199 Value-added The producty growth of IT manufacturng was dren manly by techncal progress. Poor techncal and allocate effcency hndered the producty growth. Kang and Lee(008 Port-Logstcs Industry Industres 140 Translog Functon Battese and Coell (199 Value-added The man component of TFP growth s not effcency change but techncal progress. 8

9 As preously stated, many stochastc fronter models hae been deeloped for the estmaton of techncal effcency, and s mportant to choose the most approprate model or the one that s most suable for the purpose of analyzng the aalable data. Ths study was lmed to the consderaton of the models that take nto account frms heterogeney because the used data consst of a large crosssecton and relately short tme seres. Also due to the short tme seres, the models that consder the tme-aryng pattern of techncal effcency were excluded n ths analyss een though such models are currently the state-of-the-art models. All the models are based on the specfcaton gen n equaton (5. y = α0 + x' β u +, = 1,,..., N, t = 1,,..., T (5 Ths model postulates that the error term u, s made up of both the statstcal-nose term, a two-sded error term representng the usual statstcal nose found n any relatonshp, and of the one-sded error term u 0 representng techncal neffcency. The fronter s α 0 + x'β +, whch s stochastc because ncludes. The dfferences among the alternate models are related to the assumptons mposed on the stochastc components. Table summarzes the fe models that are used n ths paper. The frst model s a fxed-effects model followng Schmdt and Sckles (1984. Ths model can be defned as below. y = α + x' β +, α = α u (6 0 y = max( α + x' β + + [ α max( α ] = a+ x' β + u, u = max( α α 0 (7 The most effcent frm s u n the sample s 0, and the estmated effcency n ths model s not an absolute but a relate alue. The fxed-effects specfcatons are estmated as whn estmators 9

10 whout any addonal dstrbutonal assumpton regardng α snce they are treated as frm constants. Model s the Pt and Lee (1981 model specfed n lne wh the Mundlak (1978 formulaton. Pt and Lee (1981 ntroduced the maxmum-lkelhood estmator n equaton (5 by makng some assumptons. They take dstrbutonal assumptons on two error terms, d N σ and ~.. (0, u d N σ + ~.. (0, u, and u, and x are ndependent of each other. Bascally, the approach of Mundlak (1978 noles modelng the correlaton of unobsered heterogeney wh the regressors n an addonal equaton, under the assumpton that the unobsered enronmental-producton factors are correlated wh the group means of the explanatory arables. To explcly account for ths correlaton, the followng auxlary regresson can be ntroduced (Mundlak, 1978: T 1 α = γ + δ = δ σ δ (8 X, X X, ~ N(0, T = 1 where X s the ector of the explanatory arables and γ a ector of the parameters to be estmated. The model specfcaton can aod the heterogeney bas and at the same tme ges reasonable estmates of neffcency. Moreoer, other tme-narant explanatory arables can also be ncluded n the model. Model 3 s a pooled-fronter model n whch the frm-specfc effect s assumed to be zero. Thus, the sample s consdered a seres of cross-sectonal subsamples pooled together. Ths model s based on the orgnal producton fronter model proposed by Agner et al. (1977. Unlke models 1 and, model 3 can estmate tme-aryng effcency. Model 4 s the true fxed-effects model, whch contans α, representng the addonal frmspecfc effects and thus, the unobserable heterogeney of frms. Strctly speakng, the applcaton of fxed effects to the stochastc-fronter model, prmarly that of Schmdt and Sckles (1984, s a 10

11 renterpretaton of the lnear-regresson model wh fxed effects, not of the fronter models. Followng Greene (005, the true fxed-effects model s specfed as y = α + x ' β + u (9 Ths model s estmated by maxmum lkelhood. Unlke the usual fxed-effects specfcaton, n whch the fxed effects are nterpreted as neffcency, the fxed effects n Greene s model represent the unobsered heterogeney. Fnally, model 5 s the true random effects model followng Greene (005 and modfed by the Mundlak (1978 specfcaton. As wh the fxed-effects model, the random-effects model, especally that of Pt and Lee (1981, can be mproed nto y = α + x ' β + u α ~ N(0, σα (10 Ths model not only ncludes a frm-leel source of heterogeney ( α, whch s potentally correlated wh the explanatory arables but also allows for a tme-aryng neffcency term. The Mundlak (1978 adustment s also appled to model, as gen n equaton (8. The mproed random-effects model can estmate tme-aryng effcency. 11

12 Table Econometrc Specfcaton: Stochastc-Fronter Models Model 1 [FE] Model [RE (MLE wh Mundlak s Formulaton] Model 3 [Pooled (ALS] Model 4 [ True FE] Model 5 [ True RE wh Mundlak s Formulaton] Frm-specfc Component α Fxed α = γx + δ X δ T 1 = X T None Fxed = 1 σ ~ N(0, δ α = γx + δ X δ T 1 = X T = 1 σ ~ N(0, δ Random ε Error d σ.. (0, ε ε = u + u N + ~ (0, σ u N ~ (0, σ ε = u + u N + ~ (0, σ u N ~ (0, σ ε = u + u N + ~ (0, σ u N ~ (0, σ ε = u + u N + ~ (0, σ u N ~ (0, σ Ineffcency max{ ˆ α } ˆ α Eu [ u+ ] Eu [ u + ] Eu [ u + ] Eu [ δ + ε ] 1

13 III. Emprcal Results 3.1 Data and Descrpte Statstcs Ths study uses data from Surey of Busness Structure and Actes, whch conssts of unfed frm-leel mcro panel data ncludng een nformaton on management actes for polcymakng by the goernment and for frms busness strategy establshment, as well as basc nformaton. The purpose of conductng Surey of Busness Structure and Actes s to prode basc data for the frm of arous economc polces for busnesses by examnng the actual condons of frms management strateges and the changes n ther ndustral structure, through a comprehense surey of derse economc actes, such as the dersfcaton, globalzaton, and afflaton of the country s busness frms. The frst surey was conducted n 006, and the same surey wll be conducted eery year. The database for three consecute years ( has been bult. For analyss purposes, the ndustral sectors to be used are summarzed n Table 3. Snce each ndustral sector has a dfferent set of characterstcs, estmatng the same producton structure n all the sectors seems unreasonable. Therefore, s assumed that all frms can be classfed nto four sectors. In ths case, the frms whn the same sector hae common producton parameters to be estmated, and the producton structure between the sectors s dfferent. Table 3 Sectoral Classfcaton Code Sector ICT(Computer, Manufacture of Communcaton 1 Equpment Manufacturng Other Manufacturng/Mnng/ Electrcy, Gas and Water Supply 3 Producer Serce Serce 4 Non-producer Serce Table 4 shows the descrpte statstcs of the arables that were used for the estmaton of the stochastc-fronter producton functons. Report on Busness Structure and Actes (

14 Table 4 Varable Defnon and Descrpte Statstcs Varabl es Obser atons Mean Standard Deaton Mn mu m Maxmum Fracton of Varance due to the Betwee n Varato n 3 Gross Output Y 9, , ,395, ,000, Capal K 9,808 44, , ,000, Labor L 9, , , Materals M 9, , , ,000, (Note: Un: Gross Output, Capal, Materals: Mllon won, Labor: Person The standard deaton ndcates a hgh degree of heterogeney among the frms n the sample. The last column of the table presents the fracton of the arance of each arable due to the araton between the dfferent frms. The fgures ndcate that all the arables under consderaton show a sgnfcant araton between the frms rather than whn the frms. Therefore, can be concluded that ths dataset s more smlar to cross-sectonal data rather than tme seres. Ths fndng ustfes the use of models nolng heterogeney. 3. Testng for the Separably of the Producton Functon Pror to analyss for the estmaton of techncal effcency, s necessary to defne the functonal form for the producton functon. In the real producton process, output s produced usng the nputs of capal, labor, and ntermedate materals. The alue-added functon, howeer, conssts of the aggregate ndces of heterogeneous nputs: capal and labor. Ths means that the alue-added functon should not be affected by the change n the ntermedate nputs. To use the alue-added functon for analyss purposes, has to be assumed that the alue-added functon, whch s the functon of only 3 Whn araton and between araton are defned as ( x x = n ( x x, respectely. Here, x represents each arable. ( x x and 14

15 capal and labor, s ndependent of the nput of ntermedate materals. Ths assumpton s referred to as the separably of the real alue-added functon from the gross output. If the result of the separably test does not accept ths assumpton, then the studes on the alue-added functon are ncorrect, and gross output as a measure of output s the proper concept. The translog gross output producton functon wh three nputs can be specfed as follows: 1 ln y = α + α ln x + β ln x ln x + 0 t l l l l, = LKM,, (11 where the subscrpts and t are the nddual frms ( = 1,,..., N and the tme ( t = 1,,..., T, respectely; y the output; and x t the nput factors; and where the subscrpts and l are the labor ( L, capal ( K, and ntermedate materals ( M. s the typcal statstcal error term wh N σ. (0, Followng Pyo and Ha (007, f β = β = 0 n equaton (11, then the translog gross output km lm producton functon can be expressed as equaton (1. Thus, the separably assumpton can be accepted by the data. log Q= Y(log K, log L + G(log M (1 The test statstcs for the fxed- and random-effects models are summarzed n Table 5. Snce all the test statstcs are suffcently beyond the crcal alues at the 1% sgnfcant leel, the hypothess of separably s reected. Therefore, based on these results, may be nferred that the alue-added functon-based producty analyss may be ncorrect and that s more approprate to use gross output as an output measure. 15

16 Table 5 Test Statstcs of the Separably Test LR Test Wald Test Fxed-Effects Model Random-Effects Model Estmaton of the Techncal Effcency and Comparson of the Alternate Models 4 The translog stochastc-fronter functon that was used n the estmaton can be specfed as equaton (13. The functon conssts of one output, three nputs, and two error terms. Snce the perod that the data pertan to s ery short (three years, the tme arable s not consdered n the analyss. 1 ln y = α + α ln x + β ln x ln x + u 0 t l l l l, = LKM,, (13 where the subscrpts and t are the nddual frms ( = 1,,..., N and the tme ( t = 1,,..., T, respectely; y the output; and x t the nput factors; and where the subscrpts and l are the labor ( L, capal ( K, and ntermedate materals ( M. The statstcal-nose term s a two-sded error term that follows N σ and that represents the usual statstcal nose found (0, n any relatonshp, and u 0 s a one-sded error term representng techncal neffcency. In ths paper, s assumed that s ndependent of u, and f necessary, s also assumed that u follows N σ +. In the frst two models (1 and, the frm s neffcency s assumed to be (0, u constant oer tme, thus captured by the frm-specfc effects. In models 3, 4, and 5, on the other hand, the frm s neffcency can ary oer tme. In these models, the skewed stochastc-error term s nterpreted as neffcency. In all the models, except for the fxed-effects model, s assumed that the 4 The estmaton results of the producton functon s parameters can be obtaned by emal on request from the author. 16

17 frm s techncal effcency s not correlated wh the explanatory arables. At frst, a Hausman test of the null hypothess that the frm-specfc effects are uncorrelated wh the explanatory arables was conducted n the fxed-effects model. The test statstc yelded χ (9 = and the null hypothess was reected. Therefore, the specfcatons that do not allow for these correlatons may produce based and nconsstent results. Thus, the random-effects models, whch assume no correlaton between the frm-specfc effects and the explanatory arables, can be sad to be too restrcte and to prode nferor estmates. On the other hand, the fxed-effects model can be expected to produce unbased and consstent estmates of the stochastc-producton-functon parameters. If the neffcency s beleed to be persstent, the models wh tme-narant neffcency, such as models 1 and, may be more releant. In the case, howeer, of the panel data wh large crosssectons and short tme seres, the ncdental-parameter problem may occur, and therefore, model can be sad to be more suable than model 1. The heterogeney bas s expected to be relately low n models and 5, whch drectly control the correlaton between the nddual effects and the explanatory arables although they are random-effects models. A test of the null hypothess that the Mundlak terms are ontly equal to zero s reected for both models wh the Mundlak (1978 adustment. The alues of the lkelhood rato statstc for each ndustral sector are 19.0, 919.0, 550.4, and 64.1 for the random effects wh the Mundlak (1978 adustment. Thus, for models and 5, the Mundlak (1978 adustment s useful n obtanng consstent results. In fact, the estmators of model are almost dentcal to the fxed-effects estmators of model 1 (the whn estmators, and are thus unbased. If the tme-aryng pattern of neffcency s assumed, models 3, 4, and 5 are more reasonable. Snce model 3 does not consder the characterstcs of the panel data, s nferor to the other models. As shown aboe, the results of the Hausman test are reected, and the fxed-effects model s more releant than the random-effects model. It can be concluded ntuonally, howeer, that model 5 s the best model for the examnaton of effcency usng the panel data employed n ths analyss because the possbly of the ncdental-parameter problem s ntrnsc to model 4, and model 17

18 5 combned wh the Mundlak (1978 adustment takes care of the fact that techncal neffcency s correlated wh the explanatory arables. In sum, model 5 can be sad to be the best model for the examnaton of effcency usng the panel data employed n ths analyss, for the followng three reasons: (1 ths model can consder the tme-aryng pattern of effcency; ( heterogeney can be taken nto account; and (3 the estmated parameters are unbased and consstent. Table 6 prodes a summary of the weghted aerages of the estmated effcency measures usng dfferent models for each ndustral sector. The effcency scores are taken to be equal to the neffcency scores (1 exp( u obtaned from the regresson model. The share of each frm s sales to a sector s used as the weght. An examnaton of the result wll reeal that each model has a dfferent estmated-effcency score. The estmated-effcency score usng the Schmdt and Sckles (1984 method shows ery unrealstc alues compared wh the other models results. Ths seems to be due to the features of the Schmdt and Sckles (1984 model. Snce n ths model, relate techncal effcency s estmated rather than absolute techncal effcency, the wder the gap s, the smaller the effcency that s estmated. Especally, a problem arses when the maxmum effcency s an outler. Based on the results obtaned from all the models, except for model 1, the Schmdt and Sckles (1984 method, the estmated techncal effcency ranges from 77% to 86%. Moreoer, the results ndcate that the ntroducton of the Mundlak (1978 adustment, n whch the correlaton between the explanatory arables and frm-specfc heterogeney s accounted for n the models, can decrease the heterogeney bas. In fact, compared to the other models, model 5, whch consders the heterogeney bas and frm-specfc heterogeney, shows the hghest estmates of techncal effcency, and among the sectors, the estmate of the producer serce sector s the hghest. 18

19 Table 6 Aerage Effcency Scores by Technque: Obseraton Model Model 5 [RE (MLE Model 3 [ True RE Model 1 Model 4 wh [Pooled wh [FE] [ True FE] Mundlak s (ALS] Mundlak s Formulaton] Formulaton] ICT nonict ProdSer Ser Total ICT nonict ProdSer Ser Total ICT nonict ProdSer Ser Total ICT nonict ProdSer Ser Total Table 7 contans the Spearman rank correlaton coeffcents, computed at the frm leel, from the fe dfferent estmaton technques. These coeffcents show how close the rankngs of the frms are to one another, usng the full sample of frms. For the models wh tme-aryng effcency, the effcency score s computed as the frm s aerage effcency score oer the sample perod. The result shows that the use of dfferent models leads to dfferent rankngs of estmated effcency. Therefore, can be concluded that s mportant to choose the most approprate model or that whch s most suable for analyss purposes and consderng the aalable data. 19

20 Model 1 Table 7 Spearman Rank Coeffcents Model Model 3 Model 4 Model 5 [FE] [RE (MLE wh [Pooled (ALS] [ True FE] [ True RE wh Mundlak s Mundlak s Formulaton] Formulaton] Model 1 1 Model Model Model Model Decomposon of the Producty Change Usng the Stochastc-Fronter Producton Model In the preous secton, seeral stochastc-producton-fronter models were compared consderng the frms heterogeney. Among these models, model 5, the true random-effects model wh the Mundlak (1978 adustment, wll be used n the analyss n ths secton, whch wll attempt to decompose producty as model 5 s consdered the most suable model as far as the aalable data and the purpose of analyss are concerned. The functonal form of producton to be used s the same as that n the preous secton. The translog stochastc-fronter functon used n the estmaton can be specfed as equaton (13. Snce the perod that the data pertan to s ery short (three years, the tme arable was not consdered n the analyss. Therefore, among the effects, techncal change (TC s assumed to be zero. 1 ln y = α + α ln x + β ln x ln x + u 0 t l l l l, = LKM,, Table 8 shows the aerage output elastcy of each ndustral sector for the perod The estmate of returns to scale ( RTS, whch combnes the output elastcy of the capal ( ε K, of labor ( ε L, and of the ntermedate outputs ( ε M, shows an ncreasng return to scale (IRS when s greater than 1, a constant return to scale (CRS when s equal to 1, and a decreasng return to scale 0

21 (DRS when s less than 1. The estmate of RTS for the ICT sector exhbs IRS, wh a magnude of Ths result s smlar to that obtaned by Pa (007. On the other hand, the other sectors exhb DRS, wh 0.9, 0.866, and 0.98 magnudes, respectely. The man fndngs of the present study are summarzed n Table 9. Table 9 presents the changes n techncal effcency (TE, scale effects (SC, allocate effcency (AE, and total factor producty growth(tfp of each sector for It s shown that the contrbutons of each factor to producty growth dffer accordng to the ndustral sector. Frst, the estmate of TFP growth n the producer serce sector s negate, and the other sectors TFP growth s pose. Second, n the case of the changes n techncal effcency, all the sectors, except for the ICT sector, show pose growth. A poor contrbuton of techncal effcency to producty growth n the ICT sector was also shown n the study conducted by Pa (007. Thrd, the changes n allocate effcency contrbute posely to the producty growth n all the sectors. Lastly, n the ICT sector, the scale effect helps mproe the frm s producty, but n the other sectors, does not. Table 8 Output Elastces of the Input Factors Obseraton Capal Labor Materals RTS ICT 3, nonict 16, ProdSer 4, Ser 5, total 9, Table 9 The Rate of Changes n Techncal Effcency (TE, Scale Component (SC, Allocate Effcency (AE, and Total Factor Producty Growth (TFP TFP TE AE SC ICT nonict ProdSer Ser total

22 IV. Concludng Remarks In ths paper, we attempt to dscuss emprcal and theoretcal ssues related to dentfyng and estmatng the sources of frms producty growth and techncal effcency usng mcro leel panel datasets n Korea for the perod of In econometrc approach, pror to analyss for the estmaton of techncal effcency, s necessary to defne the functonal form for the producton functon. Based on the test statstcs for the fxed- and random-effects models, the hypothess of separably s reected. Therefore, may be nferred that the alue-added functon-based producty analyss may be ncorrect and that s more approprate to use gross output as an output measure. Many stochastc fronter models hae been compared for the estmaton of techncal effcency, and s mportant to choose the most approprate model or the one that s most suable for the purpose of analyzng the aalable data. In ths analyss, the true random effects model wh Mundlak s adustment can be sad to be the best model for the examnaton of effcency usng the panel data employed n ths study, for the followng three reasons: (1 ths model can consder the tme-aryng pattern of effcency; ( heterogeney can be taken nto account; and (3 the estmated parameters are unbased and consstent. The estmated techncal effcency ranges from 77% to 86%. Moreoer, the results ndcate that the ntroducton of the Mundlak (1978 adustment, n whch the correlaton between the explanatory arables and frm-specfc heterogeney s accounted for n the models, can decrease the heterogeney bas. In fact, compared to the other models, the true random effects model wh Mundlak s adustment, whch consders the heterogeney bas and frm-specfc heterogeney, shows the hghest estmates of techncal effcency, and among the sectors, the estmate of the producer serce sector s the hghest. Next, s shown that the contrbutons of each factor to producty growth dffer accordng to the ndustral sector. Frst, the estmate of TFP growth n the producer serce sector s negate, and the other sectors TFP growth s pose. Second, n the case of the changes n techncal effcency, all the sectors, except for the ICT sector, show pose growth. A poor contrbuton of techncal

23 effcency to producty growth n the ICT sector was also shown n the study conducted by Pa (007. Thrd, the changes n allocate effcency contrbute posely to the producty growth n all the sectors. Lastly, n the ICT sector, the scale effect helps mproe the frm s producty, but n the other sectors, does not. There are many methodologes and approaches that analyze the producty and effcency of frms, but to dere sgnfcant results, s ery mportant to choose a methodology that fs the purpose of the analyss and the data to be used n. Snce the results can be greatly affected by the choce of classfcaton crera and models when analyzng the factors that determne producty and effcency, needless to say, care should be taken n choosng such classfcaton crera and models. V. References Agner, D., C. A. K. Loell, and P. Schmdt, "Formulaton and Estmaton of Stochastc Fronter Producton Functon Models," Journal of Econometrcs, 6 (1977, Battese, G. E., and T. J. Coell, "Fronter Producton Functons, Techncal Effcency and Panel Data: Wh Applcaton to Paddy Farmers n Inda," Journal of Producty Analyss, 3 (199, Greene, W., "Reconsderng Heterogeney n Panel Data Estmators of the Stochastc Fronter Model," Journal of Econometrcs, 16 (005, Han, G., "Total Factor Producty, Effcency Change and Techncal Progress n Korean Manufacturng Industry: Stochastc Fronter and Data Enelopment Analyss", Kyong Jae Hak Yon Gu, 53 (005, (n Korean Kang, J. M., S-R Park, An Analyss on the Economc Performance of Restructurng by Publc Frms, Jaebol and Non-Jaebol Frms n Korea, Kuke Kyunge Yongu, 10 (004, (n Korean Kang, S. M., J. B. Lee, Total Factor Producty Growth and the Decomposon Components of Korean Port-Logstcs Industry, Journal of Korea Port Economc Assocaton, 4 (008,

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