Discussion Papers in Economics

Transcription

1 Dscusson Papers n Economcs No. No. 2003/ /62 Toal Dnamcs Facor Producv of upu Growh Growh Consumpon Techncal Effcenc and Phscal Change Capal and Energ n Two-Secor Inpu. An Models Inernaonal of Endogenous Froner Analss Growh b b Lus R Murllo-Zamorano Farhad Nl Deparmen of Economcs and Relaed Sudes Unvers of York Heslngon York Y0 5DD

2 TTAL FACTR PRDUCTIVITY GRWTH TECHNICAL EFFICIENCY CHANGE AND ENERGY INPUT. AN INTERNATINAL FRNTIER ANALYSIS Lus R. Murllo-Zamorano ab a Deparmen of Economcs and Relaed Sudes Unvers of York Heslngon Y05DD York UK E-mal address: lrmz0@ork.ac.uk b Deparmen of Economcs Unvers of Exremadura Avda. de Elvas s/n 0607 Badajoz Span E-mal address: lmurllo@unex.es Aprl 2003 Absrac The man objecve of hs paper s o clarf he conroversal role of energ n producv growh. Ths s done b reconclng convenonal approaches o he measuremen of aggregaed producv growh wh he mcroeconomc foundaons provded b he energ economcs and froner producv measuremen leraure. The use of Malmqus producv ndces allows us o broaden prevous research b decomposng producv growh no echnologcal progress and echncal effcenc change as well as analsng he relaonshp beween energ and boh sources of producv change. B dong so our fndngs are ha energ ndeed maers and ha he consderaon of echncal effcenc conrbues o a beer undersandng of boh he emporal evoluon and cross-counr varabl of aggregaed producv growh. Kewords: Energ npu Toal facor producv growh Techncal effcenc change Malmqus producv growh ndces. JEL classfcaon: Q43; 30; 47 The auhor s mos graeful o B. Beaudreau H. Dxon K. Mumford S. Perelman and J. Vega for her valuable commens and o he Juna de Exremadura for fnancal suppor.

3 . Inroducon The conrbuon of energ o he producv of ndusralzed counres s a conroversal opc n economc heor. The nal works of Schurr (983) Rosenberg (983) and Jorgenson ( ) lef no room for doub abou he mporance of he energ facor n producv. The analsed he ndusral secors of he Uned Saes and concluded ha energ plas a fundamenal role n he emporal evoluon of producv. Laer work however such as ha of Denson (985) and Gullckson and Harper (987) called hose clams no queson. These auhors based her work on demonsrang ha energ has lle wegh n oupu growh so ha s oscllaons have hardl an nfluence on oal facor producv (TFP) growh. The showed ha he energ crses of 973 and 979 had onl slgh mporance n he producv declnes of he ECD counres durng he 980s. her auhors such as Feld and Grebensen (980) Bernd Morrson and Wakns (98) Bernd and Wakns (98) Pndck and Roemberg (983) Kns and Panas (989) and more recenl Wakns and Bernd (99) Hsnanck and Kmm (992) Gowd (992) Hsnanck and Ker (995) and Beaudreau (995) have also addressed he relaonshp of energ wh he srucure of producon and he subsequen role of energ n producv growh. The approaches used nclude dnamc models dual-kle echnolog specfcaons energ npu dsaggregaon and alernave producve facor compuaons. Despe all hs research effor here seems o be no unanm of crera e o explan he relaonshp beween producv growh and energ npu. In an aemp o acheve a beer undersandng of hs conroversal ssue unlke prevous leraure whch has manl focused on jus he measuremen of economc performance a he manufacurng level hs paper exends he research o an nernaonal pooled cross-secon framework where mos ndusralzed ECD counres are observed a an aggregaed level. In hs macroeconomc conex energ npu has regularl been negleced as a relevan facor whn he srucure of producon. Moreover producv growh has also ended o be denfed wh Aposolaks ( ) and Vega-Cervera and García-Herro (2000) consue excepons o hs general rule. 2

4 echnologcal progress gnorng he mporance of economc effcenc varaons as a furher source of producv change. In our vew none of hese approaches are n accord wh he mcroeconomc foundaons provded b he energ economcs and froner producv measuremen leraure. Thus he man purpose of hs paper s o reconcle convenonal approaches o he analss of aggregaed producv growh wh he underlng economc heor and so be able o shed some lgh on he conroversal role plaed b energ npu. Ths s done frs b decomposng producv growh no echnologcal progress and economc effcenc change and second b modelng energ consumpon as a relevan npu n he echnologcal seng of he ndusralzed counres. To he bes of our knowledge hs s he frs me ha he above mcroeconomc underpnnngs have been sasfacorl combned whn a macroeconomc framework. In dong so he decomposon of producv growh helps one o undersand he radonall ambguous and as e nsuffcenl well-nerpreed effec of energ on producv growh. Thus our resuls sugges a clear relaonshp beween energ consumpon and producv growh. Techncal effcenc seems o explan a sgnfcan par of he varabl of producv over me and across counres. And hgher energ prces due o ol shocks appear also o be mporan n he explanaon of he producv growh slowdown durng he 973 and 979 energ crses. The res of he paper proceeds as follows. The heor underlng our approach s presened n Secon 2 where he echnques used o calculae he producv growh ndces are also nroduced. Secon 3 conans a dscusson of he daa se and man emprcal resuls. Fnall Secon 4 presens he conclusons. 2. The measuremen of producv growh The earles approaches o he measuremen of producv 2 were based on paral ndcaors 3 where an ndex of aggregae oupu s dvded b he observed quan of a sngle npu generall labour. These paral measures provde a msleadng 2 See Nadr (970) for a surve of producv heor. 3 Ths approach was used n Denson ( ) and Kendrck (96 973). 3

5 ndcaor of overall producv. A more accurae approach o he measuremen of producv s based on oal facor producv measures 4 whch nvolve all oupus and facors of producon. These are he measures we shall use n hs nvesgaon. The economc leraure provdes us wh an ample se of mehods o deermne he TFP growh of a sample of boh mcro- and macro-economc uns. These mehods can be grouped no wo man pes: froner and non-froner echnques. The convenonal approach o producv measuremen b means of non-froner models (and whn hs group he growh accounng 5 and he ndex number 6 approaches) assumes ha all ndvduals are effcen. Hence hese mehods end o denf TFP growh wh echnologcal progress. Moreover snce Solow s (957) semnal conrbuon hs denfcaon has also been expored o he analss of economc growh sources b means of boh he above neoclasscal growh models and more recen endogenous growh heores 7. However as s poned ou b Nshmzu and Page (982) such a pe of analss neglecs anoher mporan source of TFP growh: economc effcenc change. Whle echnologcal progress hrough he adopon of echncal nnovaons pushes he froner of poenal producon upward effcenc change reflecs he capac of producve uns o mprove producon wh a se of gven npus and he avalable echnolog. The sarng pon o measure boh echncal effcenc and producv wll be o esmae a producon froner ha allows for he measuremen of echnologcal progress. Mos of he papers relaed o hs opc have based her analses on eher paramerc or non-paramerc mehods. The choce of esmaon mehod s a major ssue of debae wh some researchers preferrng he paramerc approach 8 and ohers he non-paramerc. 9 The man dsadvanage of non-paramerc approaches s her deermnsc naure ha precludes he dsncon beween echncal neffcenc and sascal nose effecs. n he oher hand paramerc froner funcons requre he 4 See Cowng and Sevenson (98) and Coell Rao and Baese (998) Hulen (2000) and ECD (200) for excellen surves of hese measures. 5 Solow (957) Denson (972). 6 Baumol (986) Dollar and Wolff (994) Bernard and Jones (996a). 7 Romer ( ) Lucas (988). 8 Berger (993). 9 Seford and Thrall (990). 4

6 defnon of a specfc funconal form for he echnolog and for he neffcenc error erm whch usuall causes boh specfcaon and esmaon problems 0. In hs sud he nheren characerscs of he sample of observaons and he greaer flexbl ha characerzes non-paramerc echnques whch requre neher a funconal form for he froner nor an assumpon abou he dsrbuon of he error erm led us o adop he laer approach. Namel we use he producv ndces proposed b Färe Grosskopf Lndgren and Roos (994). These ndces calculae producv change as he geomerc mean of wo Malmqus producv ndces and allow changes n producv o be decomposed no changes n effcenc and echncal progress. To defne a Malmqus ndex of producv change we mus explore he concep of an oupu dsance funcon 2. Followng Shepard (970) and Caves Chrsensen and Dewer (982) hs s defned a as D { : ( x / S } x 0 ( ) = nf θ ) θ (2.) where S represens he producon echnolog for each me perod =..T. Ths echnologcal se models he ransformaon of a vecor of npus x = (x...x M)0 R M no a vecor of oupus = (... N)0 R N boh correspondng o perod : S {( x ) : x can produce } = (2.2) The funcon D o (.) s defned as he recprocal of he maxmum expanson o whch s necessar o subjec he vecor of oupus of perod ( ) gven he level of npus (x ) so ha he observaon sands a he froner of perod. Ths funcon full characerzes he echnolog n such a wa ha D 0 (x )# f and onl f (x ) S. Moreover D 0 (x ) = f and onl f he observaon s echncall effcen accordng o he ermnolog used n Farrell (957). 0 See Murllo-Zamorano and Vega-Cervera (200) for a comparave analss of boh paramerc and non-paramerc groups of echnques. Malmqus ndces were frs so-named b Caves Chrsensen and Dewer (982) n her work based on Malmqus (953) who had prevousl presened npu quan ndces as raos of dsance funcons. 2 The npu dsance funcon s defned smlarl. See Deaon (979) for some applcaons. 5

7 6 In order o mplemen he Malmqus producv ndex s also necessar o defne he above dsance funcon wh respec o wo me perods such as D 0 (x ) and D 0 (x ). In boh hese mxed-perod cases he value of he dsance funcon ma exceed un. Ths happens when he un beng analsed n one perod s no feasble n he oher. In parcular f D 0 (x )> here has been echncal progress whle f D 0 (x )> here has been echncal regresson. n he bass of he above oupu dsance funcons defned for a varable reurns o scale reference echnolog 3 Caves Chrsensen and Dewer (982) defned her oupu orened Malmqus producv ndces for perod and respecvel as ) ( ) ( ) ( x D x D x x M = (2.3) ) ( ) ( ) ( x D x D x x M = (2.4) Each of he above oupu based producv ndces wll generall produce a dfferen producv ndcaor unless he reference echnolog s Hcks oupu neural 4. To avod he need o eher mpose hs consran or subjecvel decde for one of he echnologes some auhors defne an addonal producv ndex as he geomerc mean of hese wo ndces 5 : 2 ) ( ) ( ) ( ) ( ) ( = x D x D x D x D x x M (2.5) where M (.) s he composed geomerc mean of wo Malmqus producv ndces: he frs evaluaed wh respec o echnolog a me and he second wh respec o echnolog a me 6. 3 Hereafer all funcons refer o varable reurns o scale unless subscrped wh a c o ndcae consan reurns o scale. 4 Ths ssue s noed and analsed n Färe Grosskopf and Roos (998). 5 A frs example of hs sraeg can be found n Fsher (922). 6 Caves Chrsensen and Dewer (982) showed ha he geomerc mean of wo npu/oupu Malmqus quan ndces was equal o a Tornqvs (936) npu/oupu quan ndex. Moreover assumng a

8 The dea of usng he geomerc mean of wo Malmqus producv ndces s also exploed n he ke work of Färe Grosskopf Lndgren and Roos (994). Unlke he Caves Chrsensen and Dewer (982) ndex where producve uns are assumed o be full allocavel and echncall effcen he FGLR Malmqus producv ndex allows for he presence of neffcenc. Ths enables a furher decomposon of he producv growh no echnologcal progress and effcenc change 7. For he oupuorened case 8 hs decomposon s recovered from he expresson ( ( ) ( ) ( ) ) = D C x DC x DC x M ( ) ( ) ( ) C x x (2.6) DC x DC x DC x 2 where he frs rao represens he change n relave effcenc 9 beween perods and and he geomerc mean of he wo raos n he brackes measures he change or movemen of echnolog beween perods and. A M C (.) greaer han one mples ha producv has rsen beween perod and. Ths rse can be explaned on he bass of a echncal effcenc mprovemen and/or echncal progress. 20 ranslog echnolog wh dencal second-order erms and prof maxmzaon Equaon 2.5 can be expressed as a Tornqvs producv ndex plus a scale facor o accoun for he presence of varable reurns o scale. A ssemac analss of he relaonshps beween Tornqvs and Malmqus quan prce and producv ndces can be found n Coell Rao and Baese (998). 7 Alhough Caves Chrsensen and Dewer (982) dd no decompose her producv ndces s sraghforward o do so. Thus for he perod Malmqus producv ndex M (x x )= D (x )/D (x )= [D (x )/D (x )][D (x )/D (x )] where he frs facor n brackes measures echncal change usng perod daa and he second s he echncal change componen calculaed under a varable reurn o scale reference echnolog. 8 Under some producve frameworks where oupu s gven he dea of measurng effcenc and producv change on he grounds of maxmum proporonal reducons n all npus gven an avalable echnolog b means of npu dsance funcons raher han oupu ones ma provde mporan nsghs. Ths reasonng led o he leraure on he compuaon of Malmqus npu-based measures of producv change such as hose ulzed n Färe Grosskopf Yasawarng L and Wang (990) Berg Forsund and Jansen (992) Färe Grosskopf Lndgren and Roos (992) and more recenl n Yasawarng and Klen (994) and Fukuama and Weber (999). 9 Ths rao correspondng o he rao of he Farrell (957) echncal effcenc n perod o he Farrell s echncal effcenc n perod wll be greaer han one f here s an ncrease n effcenc. 20 If here s no change n effcenc beween and he changes n he FGLR Malmqus producv ndex wll be explaned onl b he movemen of he froner. If he second erm of M C s (no echncal change) he changes n producv wll be explaned onl b he changes n effcenc of uns over me perods. In oher cases he producv changes wll be a mxure of changes n effcenc and echncal progress/regresson. 7

9 The above decomposon can be nerpreed n erms of Fgure for a sngle oupu/sngle npu consan reurns o scale echnolog where a echnologcal advance (S d S ) occurs from o. <<Fgure >> In Fgure he producve un s operang a (x ) and (x ) npu/oupu bundles a and respecvel. These observaons le below he echnologcall effcen froners (S S ) a boh he and me-perods and consequenl correspond o non-echncall effcen combnaons. In erms of dsances along he -axs he decomposon of (2.6) s equvalen o he followng expressons for echncal effcenc change and echncal change Techncal effcenc change = (2.7) Techncal change = (2.8) where represen he maxmum aanable level of oupu for x and x levels of npu for each of he echnologcal ses (S and S ) consdered. Färe Grosskopf Lndgren and Roos (994) were also he frs o noe ha as he oupu dsance funcon s he recprocal of Farrell s oupu-orened echncal effcenc measure and gven suable panel daa he dsance funcons nvolved n (2.6) can be calculaed b usng lnear programmng echnques of he Daa Envelopmen Analss (DEA) pe 2. Hence for an cross-secon un D C (x ) s solved as 2 Daa Envelopmen Analss s frs nroduced n Charnes Cooper and Rhodes (978). A more dealed analss of alernave formulaons can be found n Al and Seford (993) and Coell Rao and Baese (998). 8

10 [ D ( x )] = max λ Φ s.. K k = K k = k λ k λ x k λ 0 sk mk Φ x m s s =... S m =... M k =... K (2.9) where K represens he number of cross secon uns for each me perod whn he panel daa S and M ndcae oupus and npus respecvel and λ k measures he wegh of each cross secon un whn he peer group o whch an parcular observaon s compared n order o deermne he dsance o he effcen froner. The calculaon of D ( x ) s dencal o D ( x ) bu subsung for. Wh respec o he dsance funcons nvolvng mxed perods of me D ( x ) for un s compued as [ D ( x )] = max λ Φ s.. K k= K k= k λ k λ x k λ 0 sk mk Φ x m s s =... S m =... M k =... K (2.0) and D ( x ) s calculaed as above bu ransposng he and superscrps. In addon o s wde use 22 he Malmqus producv ndex so far descrbed presen a number of major advanages over he convenonal approaches o he measuremen of producv whn a non-froner framework namel he Tornqvs 22 Malmqus-pe producv ndces have been appled o a wde range of boh mcroeconomc and macroeconomc sudes. A recen surve of hs emprcal leraure coverng sudes of he bankng elecrc ules ransporaon nsurance agrculure and publc secors as well as naonal and nernaonal comparson sudes can be found n Färe Grosskopf and Roos (998). 9

11 (936) and Fsher (922) ndex numbers. Thus as was noed above he Malmqus producv ndex perm TFP growh o be decomposed no echnologcal change and echncal effcenc change. I does no requre prce nformaon o be mplemened nor an behavoural assumpon such as cos mnmzaon revenue maxmzaon or prof maxmzaon o be made. Ths makes preferable n suaons where prces are dsored or mssng and n hose oher cases n whch producers objecves are dfferen unknown or smpl unfeasble. Moreover under ceran condons can be lnked o he convenonal ndces as s dealed n Caves Chrsensen and Dewer (982) Färe and Grosskopf (992) and Balk (993). 3. Daa and resuls The counres consdered n our sud are he European Unon naons excep German 23 plus Ausrala Canada Japan and USA. The aggregae oupu of each counr s measured b s Gross Domesc Produc (GDP). The oal capal sock s calculaed from he non-resdenal capal per worker. Boh capal sock and GDP varables are expressed n 985 nernaonal prces as rereved from he Penn World Tables (Mark 5.6) 24. The labour varable also rereved from he Penn World Table and compued from real GDP per worker represens oal emplomen. Fnall he energ npu aken from he Energ Balances of he ECD counres s obaned b reducng he oal consumpon of prmar energ b he gross consumpon of prvae households 25. The emprcal esmaon process n hs secon wll be developed n wo sages. The frs nvolves he decomposon of producv growh on he bass of consderng GDP as oupu and capal and labour as unque relevan producve npus. In he second we shall frs check for he sascal relevance of energ npu and hen recalculae he producv growh ndces akng he energ npu no accoun ogeher wh he classcal producve facors of capal and labour. Fnall a graphcal and comparave analss of he producv scores reached wh and whou energ wll also be dscussed. 23 The reunfcaon process precludes he avalabl of daa on he energ varable. 24 Ths s an updaed verson of Summers and Heson (99). 25 In dong so we avod he endogene of energ npu wh GDP gven ha as s known household energ consumpon s alread accouned for n he GDP. 0

12 3.. Classcal facors and producv growh We nall calculae 26 a se of Malmqus producv ndces akng GDP as oupu and capal and labour as he onl relevan npus. As Färe Grosskopf Lndgren and Roos (994) noe snce hs s an ndex based on dscree me each counr wll have an ndex for ever par of ears. Ths enals calculang he componen dsance funcons usng lnear programmng mehods such as hose descrbed above. Insead of presenng he dsaggregaed resuls for each counr and ear we nex collec n Table he average annual raes 27 for TFP growh (Tfpch) echnologcal progress (Techch) and effcenc change (Effch). << Table >> The resuls show here o be a major varabl of TFP growh raes across counres. Thus Fnland aans he hghes producv growh rae (.8%) followed b Luxembourg and Belgum. A greaer number of counres experenced on average producv declnes wh Span (-.7%) and Japan (-.2%) havng lowes average TFP growh raes. As an ad o he furher analss of he producv levels Fgures 2-4 presen he cumulave evoluon of he Malmqus producv ndex and s breakdown no echncal progress and effcenc change accumulaed componens for he EU Japan USA Ausrala and Canada 28. << Fgure 2 >> << Fgure 3 >> << Fgure 4 >> Accordng o Fgure 2 Ausrala and Canada presen a clear rse n her producv levels over he me perod consdered. Also he USA's accumulaed 26 Lnear programmng problems requred o mplemen he Malmqus producv ndces can be solved usng an of a vare of compuer programs. We use DEAP Verson 2.. A dealed descrpon of he compuer program s provded n Coell (996a). 27 These raes are calculaed as geomerc means due o he mulplcave naure of he Malmqus ndex. Dsaggregaed resuls are avalable on reques. 28 These accumulaed scores are calculaed as he sequenal mulplcave sums of he annual ndces.

13 producv levels are clearl above he European and especall he Japanese levels. Also whle Europe and he USA presen a more or less sable rend around he sead sae Japan shows a major loss of producv. Wh respec o he accumulaed levels of echncal progress one sees from Fgure 3 ha he dfferences beween counres are less pronounced and he behavoural rend s far more homogeneous. I would seem herefore ha he man deermnan of he dfferenaed behavour of he producv s o be sough n he emporal evoluon of he accumulaed effcenc as can be seen n Fgure 4. Ths graphcal analss hence shows he mporance of decomposng TFP growh no echnologcal progress and echncal effcenc change n order o beer undersand producv growh. Fnall lookng more closel a he aforemenoned fgures one sees how hgher energ prces durng he 973 and 979 ol prce shocks are assocaed wh a declne n boh he echnologcal progress and producv growh accumulaed levels. Some auhors such as Denson (985) and Gullckson and Harper (987) have concluded ha energ prces have no mpac on he growh of oupu a aggregae level snce energ self s onl a small proporon of aggregae oupu. ur resuls pon o he conrar. In lne wh Jorgenson ( b) energ crses seem o be relaed wh he declne n echnologcal progress and producv growh of ndusralzed counres and hence wh her economc growh slowdown. As n Jorgenson (988a) our resuls seem o suppor he dea ha energ crses could rever producon mehods o perods of echnologcal developmen ha exsed before he ol prce shocks. In hs pos-crss echnologcal se he energ prce rends could resul n he subsuon of capal labor and maeral npus for energ hus reducng he energ nens of producon. Dfferen cross-counr success n handlng hese npus mgh be responsble for he heerogeneous pah followed for he echncal effcenc accumulaed levels ploed n Fgure Energ facor and producv growh As Norsworh and Malmqus (983) noe he aforemenoned energ crses have hghlghed he mporance of ncludng energ npu n he analss of economc and producv growh. In he leraure he pcal form of nvesgang he ssue of 2

14 wheher or no a producon facor such as energ s a relevan npu s based on wo economerc producon models n whch he more general model ncludes hs facor whle he second does no. The more general model s hen esed agans he resrced model whch s nesed whn he more general model. An mmense vare of model specfcaons and esmaon echnques are avalable n he specalzed leraure for he economerc analss of froner funcons 29 such as hose needed o address hs ssue. In hs sud followng Baese and Coell s (992) approach 30 wo alernave specfcaons Model and Model 2 are mplemened o check for he sascal sgnfcance of he energ npu. Model represens a Cobb-Douglas producon froner funcon where he echncal neffcenc effecs are assumed o be me-varan and o have a runcaed-normal dsrbuon. Model 2 defnes a ranslog producon funcon wh echncal neffcenc effecs varng over me and also wh a runcaed-normal dsrbuon. The values of he log-lkelhood funcons for he general and resrced verson of each of hese models are lsed n Table 2. The generalzed lkelhood-rao sasc for esng he null hpohess ha he energ facor s no sascall sgnfcan s also gven. Ths value compared wh he upper one percen for he ch-squared dsrbuon crcal value ndcaes he rejecon of he null hpohess for an of he alernave specfcaon esed. << Table 2 >> Moreover applng a non-paramerc es based on he neffcenc scores repored b DEA-lke lnear programmng problems namel he Banker es we also fnd energ consumpon o be a sascall sgnfcan producve npu o be consdered n he defnon of he froner echnologcal se. The Banker es developed n Banker (996) checks for he sgnfcance of a se of addonal varables nroduced no a DEA model on he bass of her asmpoc properes. If he neffcenc s dsrbued as half-normal he Banker es s dsrbued as F nn wh n ndcang he 29 The reader s referred o Murllo-Zamorano (2003) for a comprehensve and updaed analss of boh paramerc and non-paramerc echnques for he measuremen of economc effcenc. 30 See he Appendx for deals on hs secon. 3

15 number of observaons. In our case under he null hpohess ha energ does no nfluence he producon correspondence beween he oupu and he npus we ge an F* crcal value of whch mples he rejecon of he null hpohess a a 99% confdence level. Gven hs se of paramerc and non-paramerc sascal ess seems o be boh advsable and convenen o consder energ consumpon as a relevan producve npu. If we dd no ever change n energ consumpon levels would be absorbed b he oher npus and herefore capal and labour would seem o be arfcall more producve 3. Moreover no ncludng he energ npu would lead o a bas n he levels and emporal evoluon of he producv aaned b he counres of he sud. The decomposon of TFP growh ncludng energ npu as an addonal producve npu s also gven n Table. The new scores show a generalzed ncrease n he raes of producv growh as can be seen b comparng he average producv growh raes wh (0.6%) and whou (-0.00%) energ. B counres Belgum Canada Ireland France and USA have greaer posve producv growh raes whle Porugal Span and he UK have smaller negave growh raes when he energ npu s nroduced. Ausra Denmark Ial Japan Neherlands and Sweden presen changes ha are mporan qualavel as well as quanavel movng from negave o posve producv growh raes. Ausrala Fnland and Luxembourg manan he same raes. nl Greece shows a recesson n s producv. In sum mos of he counres (foureen ou of egheen) have ncreased producv growh raes. An nernaonal comparson of he ncdence of energ n producv growh sources s shown n Fgures 5-7. In hese fgures he vercal axs s he performance 3 n he bass of a sasfacor sascal sgnfcance oher producve facors such as publc capal human capal or maerals could also be consdered as furher npus whn he srucure of he producon. The ncdence of human and publc capal n producv growh has been explored n Grosskopf and Self (200) and Peragla (2003) respecvel. As for maerals her consderaon whn he specfcaon of he producve echnolog has been an ssue of debae wh some researchers usng KLEM models (e.g. Bernd and Wood 975 and Morrson and Bernd 98) and ohers KLE models (e.g. Iqbal 986 and Aposolaks 987). In our case he lack of conssen nformaon for nernaonal panel daa a an aggregaed level such as ha emploed n hs paper smpl precludes her mplemenaon. 4

16 ncludng energ and he horzonal axs he performance whou energ. bservaons above he 45º bsecrx represen performance mprovemens n erms of producv growh (Fgure 5) echnologcal change (Fgure 6) and effcenc change (Fgure 7). As can be seen hs expanson s clearl homogeneous n erms of boh producv and echnologcal progress whle here s a greaer varabl n erms of raes of echncal effcenc change. << Fgure 5 >> << Fgure 6 >> << Fgure 7 >> Lasl movng from an analss n erms of growh raes o one n erms of cumulave levels he mprovemen n he producv growh rae as a consequence of he nroducon of he energ npu ma also be deduced from he graphcal comparson of Fgures 8-0 wh Fgures 2-4. In parcular f one agan focuses on he 973 and 979 energ crses new commens sugges hemselves. As before he 973 ol prce shock seems o generae a declne n echnologcal progress of he ndusralzed counres whch could sugges he exsence of an energ-usng producve echnolog. As Jorgenson (988b) pons ou f echnologcal progress s energ usng hen he rae of echncal change declnes when he prce of energ ncreases. However Fgure 9 shows ha hs declne n echnologcal progress raes s no so homogeneous afer he 979 energ crss. In lne wh Jorgenson (998b) would seem ha some counres such as Japan and Ausrala have adoped energ-savng producve echnologes whch would have precluded he correspondng reducon n echnologcal progress assocaed wh an energ-usng echncal change. n he oher hand ohers such as Canada and USA seem o connue o emplo energ-usng echnologes. These cross-counr dfferences are also observed n he producv accumulaed scores of Fgure 8 and he echncal effcenc accumulaed levels of Fgure 0. << Fgure 8 >> << Fgure 9 >> << Fgure 0 >> 5

17 In sum boh effcenc varaon and echnologcal change help o explan he evoluon of producv over me. Some of he more relevan resuls of a closer sud of he sascal sgnfcance of he relaonshps beween he above sources of producv growh and energ consumpon are presened n Table 3. In erms of smple sascal correlaon here seems o be a clear relaonshp beween energ and producv as well as beween energ and boh echnologcal progress and producve effcenc. Therefore he falure o consder he echncal effcenc componen and he denfcaon of he oal producv growh of he facors wh echnologcal progress ma lead o he appearance of based and even smpl ncorrec resuls. The ncluson of hs componen however seems o clarf he varabl of producv growh across counres as well as he dfferen role plaed b energ n he evoluon of ha growh. << Table 3 >> 4. Conclusons The role plaed b energ n producv growh s a conroversal opc. Whle par of he emprcal evdence suggess ha he energ npu plas a fundamenal role n producv change oher sudes pon o he conrar. Neverheless boh hese sreams of research have focused mosl on he analss of he manufacurng secor onl. ur resuls are clearl n suppor of he former group exendng her fndngs o a full aggregaed framework and provdng srong evdence for an acve role of energ n he producv growh of ndusralzed counres. In hs respec he man mehodologcal conrbuon of he presen work has been o reconcle convenonal approaches o he measuremen of aggregaed producv growh wh he underlng mcroeconomc heor developed n he energ economcs and froner producv measuremen leraure. In dong so we fnd ha echncal effcenc seems o explan a sgnfcan par of he varabl of producv over me and across counres. Therefore he radonal denfcaon of producv growh wh echnologcal progress made n much of he prevous leraure seems no o be approprae. Indeed neglecng echncal effcenc could lead o based and smpl ncorrec resuls. 6

18 The decomposon of producv growh no echnologcal progress and echncal effcenc change also seems o shed lgh on he crcal role of he ncrease n energ prces afer he 973 and 979 ol crses. ur resuls show ha he hgher energ prces durng hose crses are also mporan n explanng he emporal evoluon and cross-counr varabl of producv growh raes. Ths mgh also mprove he assessmen of he economc growh slowdown durng hose perods and move froner producv measuremen and he modelng of energ as a relevan npu n he echnologcal seng of he ndusralzed counres no he economc growh leraure where he ceranl belong. In lne wh he above consderable heorecal and emprcal work sll remans o be done. Thus he drasc changes n relave prces of capal labour and energ especall afer energ crses make advsable o mplemen dual paramerc froner approaches o he measuremen of producv growh n whch npu prces could be aken no accoun. Ths would also provde new nsghs no he radonal energcapal complemenar/subsuabl dchoom and hus perm a more slzed and suable framework for he dscusson of alernave economc polces. Greaer raonal would also be nroduced b usng dnamc models where some npus ma be modeled as fxed or quas-fxed npus. Fnall a breakdown of labour no producon (blue-collar) and non-producon (whe-collar) workers as well as dsngushng beween phscal and worker capal or energ dsaggregaed no elecrcal and non-elecrcal componens s also a ask for fuure research. In an case alhough much work remans o be done we beleve ha he prelmnar sep aken here provdes mporan nsghs no onl no how o revalze he role plaed b energ n he ndusralzed counres sources of producv growh bu also no he wa of approachng s measuremen and analss. 7

19 References Agner D.J. C.A.K. Lovell and P.J. Schmd 977 Formulaon and esmaon of sochasc froner producon funcon models Journal of Economercs Al A.I. and L.M. Seford 993 The mahemacal programmng approach o effcenc analss n: Harold. Fred C.A.K. Lovell and S.S. Schmd (Eds.) The Measuremen of Producve Effcenc: Technques and Applcaons (xford :xford Unvers Press) Aposolaks B.E. 984 Energ demand n an aggregae cos specfcaon Economa d Energa Aposolaks B.E. 987 The role of energ n producon funcons for souhern European economes Energ 2(7) Balk B.M. 993 Malmqus producv ndexes and Fsher deal ndexes: commen Economc Journal 03 (45) Balk B.M. 998 Inpu prce quan and producv ndexes for a revenueconsraned frm n: R. Färe S. Grosskopf and R.R. Russell (Eds.) Index Numbers: Essas n Honour of Sen Malmqus (Kluwer Academc Publshers: Boson) Banker R.D. 996 Hpohess ess usng daa envelopmen analss The Journal of Producv Analss Baese G.E. and T.J. Coell 988 Predcon of frm-level echncal effcences wh a generalzed froner producon funcon and panel daa. Journal of Economercs Baese G.E. and T.J. Coell 992 Froner producon funcons echncal effcenc and panel daa: wh applcaon o Padd farmers n Inda Journal of Producv Analss 3(-2) Baese G.E. T.J. Coell and T. Colb 989 Esmaon of froner producon funcons and he effcences of Indan farms usng panel daa from ICRISTAT s vllage level sudes. Journal of Quanave Economcs 5 (2) Baese G. and G. Corra 977 Esmaon of a producon froner model wh applcaon o he pasoral zone of Easer Ausrala Ausralan Journal of Agrculural Economcs 2(3) Baumol W. 986 Producv growh convergence and welfare: wha he long run daa show Amercan Economc Revew Beaudreau B.C. 995 The mpac of elecrc power on producv Energ Economcs Berg S. F.R. Forsund and E.S. Jansen 992 Malmqus ndces of producv growh durng he deregulaon of Norwegan bankng Scandnavan Journal of Economcs 94 (Supplemen) Berger A.N. 993 Dsrbuon-free esmaes of effcenc n he U.S. bankng ndusr and ess of he sandard dsrbuonal assumpons Journal of Producv Analss Bernard A.B. and C.I. Jones 996a Technolog and convergence The Economc Journal Bernard A.B. and C.I. Jones 996b Comparng apples o oranges: producv convergence and measuremen across ndusres and counres Amercan Economc Revew Bernd E.R. C.J. Morrson and G.C. Wakns 98 Dnamc models of energ demand: an assessmen and comparson n: Bernd E.R. and B.C. Feld (Eds.) 8

20 Modelng and Measurng Naural Resource Subsuon (Cambrdge MIT Press) Bernd E.R. and G.C. Wakns 98 Energ prces and producv rends n he Canadan manufacurng secor : some explanaor resuls awa Economc Councl of Canada. Bernd E.R. and D.. Wood 975 Techonolg prces and he derved demand for energ Revew of Economcs and Sascs Caves D.W. L.R. Chrsensen and W.E. Dewer 982 The economc heor of ndex numbers and he measuremen of npu oupu and producv Economerca 50(6) Charnes A. W.W. Cooper and E. Rhodes 978 Measurng he effcenc of decsonmakng uns European Journal of peraonal Research Coell T. 996a A gude o FRNTIER verson 4.: a compuer program for sochasc froner producon and cos funcon esmaon CEPA Workng Paper 96/07. Coell T. 996b A gude o DEAP verson 2.: a daa envelopmen analss (compuer) program CEPA Workng Paper 96/08. Coell T. D.S.P. Rao and G.E. Baese 998 An nroducon o effcenc and producv analss (Kluwer Academc Publshers Boson). Cornwell C. P. Schmd and R.C. Sckles 990 Producon froners wh crossseconal and me-seres varaons n effcenc levels. Journal of Economercs 46(/2) Cosello D.M. 993 A cross-counr cross-ndusr comparson of producv growh Journal of Polcal Econom Cowng T.G. and R.E. Sevenson 98 Producv measuremen n regulaed ndusres (Academc Press Inc. New York). Deaon A. 979 The dsance funcon and consumer behavour wh applcaons o ndex numbers and opmal axaon Revew of Economc Sudes Denson E.F. 962 The sources of economc growh n he U.S. and he alernaves before us (Commee for Economc Developmen Supple. Paper No.3 New York). Denson E.F. 967 Wh growh raes dffer: pos-war experence n nne Wesern counres (The Brookngs Insuon Washngon D.C.). Denson E.F. 972 Classfcaon of sources of growh Revew of Income and Wealh Denson E.F. 974 Accounng for Uned Saes economc growh 929 o 969 (The Brookngs Insuon Washngon D.C.). Denson E.F. 985 Trends n Amercan economc growh (The Brookngs Insuon Washngon D.C.). Deprns D. L. Smar and H. Tulkens 984 Measurng labour-effcenc n pos offces n: J. Marchand G. Peseau and H. Tulkens eds. The Performance of Publc Enerprses. Concep and Measuremen (Nor Holland Amserdam). Dollar D. and E.N. Wolff 994 Capal nens and TFP convergence b ndusr n manufacurng n: W.J. Baumol R.R. Nelson and E.N. Wolf eds. Convergence of Producv Cross-Naonal Sudes and Hsorcal Evdence (xford Unvers Press xford). Färe R. Grfell-Tajé S. Grosskopf and C.A.K. Lovell 997 Based echncal change and he Malmqus producv ndex Scandnavan Journal of Economcs Färe R. and S. Grosskpof 992 Malmqus ndexes and Fsher deal ndexes Economc Journal 02 (40)

21 Färe R. and S. Grosskopf 994 Cos and Revenue Consraned Producon Bllan Unvers Lecure Seres Volume 4 Sprnger-Verlag New York. Färe R. and S. Grosskopf 996 Ineremporal producon froners: wh dnamc DEA (Kluwer Academc Publshers Boson). Färe R. S. Grosskopf B. Lndgren and P. Roos 992 Producv changes n Swedsh pharmaces : A nonparamerc Malmqus approach Journal of Producv Analss Färe R. S. Grosskpof B. Lndgren and P. Roos 994 Producv developmens n Swedsh hospals: A Malmqus oupu ndex approach n: A. Charnes W.W. Cooper A.Y. Lewn and L.M. Seford eds. Daa Envelopmen Analss: Theor Mehodolog and Applcaons (Kluwer Academc Publshers Boson). Färe R. S. Grosskopf and C.A.K. Lovell 994 Producon Froners (Cambrdge Unvers Press Cambrdge). Färe R. S. Grosskpof M. Norrs and Z. Zhang 994 Producv growh echncal progress and effcenc changes n ndusralsed counres Amercan Economc Revew Färe R. S. Grosskopf and P. Roos 998 Malmqus producv ndexes: A surve of heor and pracce n: R. Färe S. Grosskopf and R.R. Russell eds. Index Numbers: Essas n Honour of Sen Malmqus (Kluwer Academc Publshers Boson): Färe R. S. Grosskopf S. Yasawarng S.-K. L and Z. Wang 990 Producv growh n Illnos elecrc ules Resources and Energ Färe R. and D. Prmon 990. A dsance funcon approach o muloupu echnologes Souhern Economc Journal 56(4) Fecher F. and S. Perelman 992 Producv growh and echncal effcenc n ECD ndusral acves n: R. Caves eds. Indusral Effcenc n Sx Naons (MIT Press Cambrdge Mass.). Feld B.C. and Ch. Grebensen 980 Capal-Energ Subsuon n U.S. manufacurng Revew of Economcs and Sascs 62(2): Fsher I. 922 The makng of ndex numbers (Houghon Mffln Boson). Fukuama H. and W.L. Weber 999 The effcenc and producv of Japanese secures frms Japan and he World Econom () Gabrelsen A. 975 n esmang effcen producon funcons Workng Paper no A-35 Chr. Mchelsen Insue Deparmen of Humanes and Socal Scences Bergen Norwa. Greene W.M. 980 Maxmum lkelhood esmaon of economerc froner funons Journal of Economercs 3(): Grosskopf D. and S. Self 200 Growh human capal and TFP Paper presened a he WEA meengs San Francsco. Gowd J.M. 992 Labour producv and energ nens n Ausrala Energ Economcs 4() Gullckson W. and M.J. Harper M.J. 987 Mulfacor producv n US manufacurng Monhl Labor Revew Hsnanck J.J. and B.L. Ker 995 Assessng a dsaggregaed energ npu usng confdence nervals around ranslog elasc esmaes Energ Economcs 7(2): Hsnanck J.J. and K.. Kmm 992 The mpac of dsaggregaed energ on producv Energ Economcs 4(4) Hulen CH.R Toal facor producv: a shor bograph NBER Workng Papers No. 747 Deparmen of economcs New York Unvers. 20

22 Iqbal M. 986 Subsuon of labor capal and energ n he manufacurng secor of Paksan Emprcal Economcs Jorgenson D.W. 983 Energ prces and producv growh n: S. Schurr S. Sonenblum and D.. Wood eds. Energ Producv and Economc Growh (Cambrdge Unvers Press Cambrdge Mass.). Jorgenson D.W. 984 The role of energ n producv growh The Energ Journal Jorgenson D.W. 988a Producv and poswar U.S. economc growh The Journal of Economc Perspecves 2(4) Jorgenson D.W. 988b Producv and economc growh n Japan and he Uned Saes Amercan Economc Revew 78(2) Kendrck J.W. 96 Producv rends n he Uned Saes (Prnceon Unvers Press Prnceon New Jerse). Kendrck J.W. 973 Poswar producv rends n he Uned Saes (Naonal Bureau of Economc Research New York). Kns A.A. and E.E. Panas 989 The capal-energ conrovers: furher resuls Energ Economcs (3): Lucas R. 988 n he mechancs of economc developmen Journal of Monear Economcs 22() Kumbhakar S.C The specfcaon of echncal and allocave neffcenc of mul-produc frms n sochasc producon and prof froners. Journal of Quanave Economcs Kumbhakar S.C. 990 Producon froners panel daa and me-varng echncal neffcenc. Journal of Economercs 46(/2) Lee Y.H. and P. Schmd 993 A producon froner model wh flexble emporal varaon n echncal neffcenc n: Harold. Fred C.A.K. Lovell S.S. Schmd eds. The Measuremen of Producve Effcenc: Technques and Applcaons (xford :xford Unvers Press) Malmqus S. 953 Index numbers and ndfference curves Trabajos de Esadísca Maudos J. J.M. Pasor and L. Serrano 999 Toal facor producv measuremen and human capal n ECD counres Economcs Leers Meeusen W. and J. van den Broeck 977 Effcenc esmaon from Cobb-Douglas producon funcons wh composed error Inernaonal Economc Revew Morrson C.J. and E.R. Bernd 98 Shor-run labor producv n a dnamc model Journal of Economercs Murllo-Zamorano L.R Economc effcenc and froner echnques Journal of Economc Surves forhcomng. Murllo-Zamorano L.R. and J.A. Vega-Cervera 200 The use of paramerc and nonparamerc froner mehods o measure he producve effcenc n he ndusral secor. A comparave analss Inernaonal Journal of Producon Economcs Nadr M.I. 970 Some approaches o he heor and measuremen of oal facor producv: a surve Journal of Economc Leraure Nshmzu M. and J.M. Page J.M. 982 Toal facor producv growh echnologcal progress and echncal effcenc change: dmensons of producv change n Yugoslava Economc Journal Norsworh J.R. and D.H. Malmqus 983 Inpu measuremen and producv growh n Japanese and U.S. manufacurng Amercan Economc Revew 73(5)

23 ECD 200 Measurng producv. ECD Manual. Measuremen of aggregae and ndusr-level producv growh. Pars. Peragla C Toal facor producv growh and publc capal: he case of Ial Esud Economc forhcomng. Pndck R.S. and J.J. Roemberg 983 Dnamc facor demands and he effecs of energ prce shocks Amercan Economc Revew 73(5): P M.M. and L.F. Lee 98 The measuremen and sources of echncal neffcenc n he Indonesan weavng ndusr Journal of Developmen Economcs Rchmond J. 974 Esmang he effcenc of producon. Inernaonal Economc Revew Romer P.M. 986 Increasng reurns and long run growh Journal of Polcal Econom 94(5) Romer P.M. 989 Capal accumulaon n he heor of long run growh n: R.J. Barro eds. Modern Busness Ccle Theor (Cambrdge: Hardvard Unvers Press). Rosenberg N The effecs of energ suppl characerscs on echnolog and economc growh n: S. Schurr S. Sonenblum and D.. Wood eds. Energ Producv and Economc Growh (Cambrdge Unvers Press Cambrdge Mass.). Schmd P. and R.C. Sckles 984. Producon froners and panel daa. Journal of Busness and Economc Sascs Schurr S. 983 Energ effcenc and economc effcenc: an hsorcal perspecve n: S. Schurr S. Sonenblum and D.. Wood eds. Energ Producv and Economc Growh (Cambrdge Unvers Press Cambrdge Mass.). Seford L.M. and R.M. Thrall 990 Recen developmen n DEA: he mahemacal programmng approach o froner analss Journal of Economercs Shepard R.W. 970 Theor of cos and producon funcon (Prnceon Unvers Press Prnceon New Jerse). Solow R.W. 957 Techncal change and he aggregae producon funcon Revew of Economc and Sascs Summers R. and A. Heson A. 99 The Penn World Table (Mark 5): an expanded se of nernaonal comparsons Quarerl Journal of Economcs Tornqvs L. 936 The Bank of Fnland s consumpon prce ndex Bank of Fnland Monhl Bullen 0-8. Vega-Cervera J.A. and J.M. García-Herro 2000 Energ as a producve npu: he underlng echnolog for Porugal and Span Energ 25(8): Wakns G.C. and E.R. Bernd 99 Dnamc models of npu demands: a comparson under dfferen formulaons of adjusmen coss n: J.R. Morone (Eds.) Advances n he Economcs of Energ and Resources vol. 7 (Greenwch CT: JAI Press): Yasawarng S. and J.D. Klen 994 The effecs of sulfur doxde conrols on producv change n he US elecrc power ndusr Revew of Economcs and Sascs 76(3)

24 Tables Table. TFP growh decomposon wh and whou energ facor. Average annual changes Whou energ Wh energ Counr Effch Techch Tfpch Effch Techch Tfpch Ausrala Ausra Belgum Canada Denmark Fnland France Greece Ireland Ial Japan Luxembourg Neherlands Porugal Span Sweden UK USA Mean Effch: Average annual changes for effcenc change. Techch: Average annual changes for echnologcal progress. Tfpch: Average annual changes for TFP growh. Models Table 2. Log-lkelhood funcons and generalzed lkelhood-rao sascs Whou energ (Resrced model) Wh energ (Generalzed model) Generalzed lkelhood rao Model Log L: Log L: LR=-2( )= χ 2 =6.63(99%) Model 2 Log L: Log L: LR=-2( )=89.8 χ 2 4=3.23(99%) Model : Cobb-Douglas Truncaed-Normal Tme Varan Model. Model 2: Translog Truncaed-Normal Tme Varan Model. Log L: Log lkelhood funcon value. LR: Generalzed lkelhood-rao sasc for esng he null hpohess. 23

25 Table 3. Producv echnolog effcenc and energ Models Producv/Energ Technolog/Energ Fxed effecs model N = 44 LM Tes df Hausman Tes df Random effecs model N = 44 Censored ob model N = (.962) (5.8) Prob. value = Prob. value = Prob. value = Prob. value = (.090) (28.995) Effcenc/Energ (7.963) Large values of he Hausman sasc argue n favour of he fxed effecs model over he random effecs model. Large values of he Lagrange mulpler (LM) sasc argue n favour of one of one of he one facor models (fxed or random effecs) agans he classcal regresson wh no group specfc effecs. Bold fgures denf he sascall relevan models. T-raos are gven n parenheses. Fgures Fgure. Malmqus Producv Indexes Y S S (x ) (x ) x x X 24

26 Fgure 2. Producv n ECD counres: 970= Europe Japan Usa Ausrala Canada Fgure 3. Technologcal progress n ECD counres: 970= Europe Japan Usa Ausrala Canada Fgure 4. Techncal effcenc n ECD counres: 970= Europe Japan Usa Ausrala Canada

27 Fgure 5. TFP growh average raes wh () and whou (-) energ fpch SPA JAP AUT ITA FRA DEN SWE NET IRE USA UK PR GRE AUS CAN BEL LUX FIN fpch- Fgure 6. Technologcal progress average raes wh () and whou (-) energ DEN ITA JAP AUS NET GRE UK PR IRE SPA FRA FIN BEL AUL SWE LUX USA CAN Fgure 7. Techncal effcenc change average raes wh () and whou energ (-) effcheffch LUX JAP CAN FRA PR BEL AUT SWE NET USA ITA SPA UK AUS DEN GRE IRE FIN echchechch 26

28 Fgure 8. Producv n ECD counres: 970= Europe Japan Usa Ausrala Canada Fgure 9. Technologcal progress n ECD counres: 970= Europe Japan Usa Ausrala Canada Fgure 0. Techncal effcenc n ECD counres: 970= Europe Japan Usa Ausrala Canada

29 APPENDIX The model The measuremen of producve effcenc b means of paramerc echnques requres he specfcaon of a parcular froner funcon. Such specfcaon can be eher deermnsc or sochasc. Deermnsc models envelope all he observaons denfng he dsance beween he observed producon and he maxmum producon defned b he froner and he avalable echnolog as economc neffcenc. n he oher hand sochasc approaches perm one o dsngush beween echncal neffcenc and sascal nose. Several echnques have been developed n he economerc leraure o esmae boh deermnsc 32 and sochasc froner models. Agner Lovell and Schmd (977) Meeusen and van den Broeck (977) and Baese and Corra (977) smulaneousl developed a sochasc froner model ha besdes ncorporang he effcenc erm no he analss (as do he deermnsc approaches) also capures he effecs of exogenous shocks beond he conrol of he analsed uns. Moreover hs pe of model also covers errors n he observaons and n he measuremen of oupus. These nal approaches were developed whn a cross-secon framework and based on srong dsrbuon assumpons for modelng he neffcenc effec. However f panel daa are avalable here s no need for an dsrbuon assumpon for he neffcenc effec and all he relevan parameers of he froner echnolog can be obaned b smpl usng he radonal esmaon procedures for panel daa.e. he fxed-effecs and he random-effecs model approaches. Ths was frs noed b Schmd and Sckles (984). In an case when he dsrbuon assumpons nvolved n boh he specfcaon and he esmaon of sochasc froner funcons are known smlar maxmum lkelhood echnques o he ones appled o he cross-seconal daa can be appled o a sochasc producon froner panel daa model n order o ge more effcen esmaes 32 Modfed rdnar Leas Squares (e.g. Rchmond 974) Correced rdnar Leas Squares (e.g. Gabrelsen 975) and Maxmum Lkelhood Esmaon (e.g. Greene 980) are some of he mos mporan. 28

30 of he parameer vecor and of he echncal neffcenc scores. In hs respec P and Lee (98) derved he normal-half-normal counerpar of Agner Lovell and Schmd s (977) model for panel daa whle Kumbhakar (987) and Baese and Coell (988) exend P and Lee s (98) analss o he normal-runcaed sochasc froner panel daa model. Maxmum lkelhood echnques are also appled o unbalanced panel daa n Baese Coell and Colb (989). Boh he fxed/random-effecs approaches and maxmum lkelhood echnques consdered echncal neffcenc effecs o be me-nvaran. However as he me dmenson becomes larger seems more reasonable o allow neffcenc o var over me. As wh he me-nvaran echncal neffcenc model me-varng echncal neffcenc can be esmaed b usng eher fxed or random effecs or maxmum lkelhood echnques. Cornwell Schmd and Sckles (990) and Lee and Schmd (993) are examples of he former; Kumbhakar (990) and Baese and Coell (992) of he laer. Followng Baese and Coell s (992) approach we nex specf wo alernave funconal forms for he producve echnolog of he ndusralzed counres under analss namel a Cobb-Douglas (Model ) and a ranslog (Model 2) sochasc producon funcon. Model : Cobb-Douglas Truncaed-Normal Tme-Varan Model ln M = β 0 β m ln x m= m v u 2 v N(0 σ ) u = δ ( ) u = [ exp( η ( T )] u =... K; m =... M ; =... T Model 2: Translog Truncaed-Normal Tme-Varan Model ln M M M β m ln xm m= m n= = β 0 β ln x ln x mn m n v u 2 N(0 σ ) v u ( ) u = [ exp( ( T )] u = δ η =... K; m n =... M ; =... T 29