NBER WORKING PAPER SERIES NEOCLASSICAL GROWTH AND THE ADOPTION OF TECHNOLOGIES. Diego Comin Bart Hobijn

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1 NBER WORKING PAPER SERIES NEOCLASSICAL GROWTH AND THE ADOPTION OF TECHNOLOGIES Dego Comn Bar Hobn Workng Paper 0733 hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massachuses Avenue Cambrdge MA 0238 Augus 2004 The vews expressed n hs paper solely reflec hose of he auhors and no necessarly hose of he Federal Reserve Bank of New ork nor hose of he Federal Reserve Sysem as a whole. We would lke o hank Bess Rabn and Rebecca Sela for her grea research asssance. We have benefed a lo from commens and suggesons by Jess Benhabb Smon Glchrs Boyan Jovanovc John Leahy and Peer Rousseau as well as semnar parcpans a NU he SED and UC Sana Cruz.The vews expressed heren are hose of he auhor(s) and no necessarly hose of he Naonal Bureau of Economc Research by Dego Comn and Bar Hobn. All rghs reserved. Shor secons of ex no o exceed wo paragraphs may be quoed whou explc permsson provded ha full cred ncludng noce s gven o he source.

2 Neoclasscal Growh and he Adopon of Technologes Dego Comn and Bar Hobn NBER Workng Paper No Augus 2004 JEL No. E3 O4 O33 O4 ABSTRACT We nroduce a growh model of echnology dffuson and endogenous Toal Facor Producvy (TFP) levels boh a he secor and aggregae level. A he aggregae he model behaves as he Neoclasscal growh model. Our goal s for hs model o brdge he gap beween he heorecal and emprcal sudes of echnology adopon and economc growh. We brdge hs gap n hree mporan drecons. Frs of all we use our model o show how one unfed heorecal framework s broadly conssen wh he observed dynamcs of boh economc growh as well as of many dfferen measures of echnology adopon lke adopon raes capal o oupu raos and oupu raos. Secondly we esmae our model usng a broad range of echnologcal adopon measures coverng 7 echnologes and 2 ndusralzed counres over he pas 80 years. Ths allows us o show how s predced adopon paerns f hose observed n he daa. Fnally we esmae he dspares n secoral producvy levels as well as aggregae TFP ha can be arbued o he dfferences n he range of echnologes n use across counres. These dspares are almos compleely deermned by he qualy of he wors echnology n use raher han by he qualy of he newes echnology ha has us been adoped or by he number of echnologes n use. Furher we fnd ha he TFP componen arbuable o he range of echnologes used s hghly correlaed wh overall secoral TFP dfferences across counres hough he varance s smaller. Dego Comn Deparmen of Economcs New ork Unversy 269 Mercer Sree 725 New ork N 0003 and NBER dego.comn@nyu.edu Bar Hobn Domesc Research Funcon Federal Reserve Bank of New ork 33 Lbery Sree 3 rd Floor New ork N 0045 bar.hobn@ny.frb.org

3 . Inroducon Recen evdence lke Jerzmanowsk (2002) Hall and Jones (999) and Klenow and Rodríquez-Clare (997) suggess ha he bulk of cross-counry dfferences n levels of oupu per capa s due o dfferences n he level of oal facor producvy (TFP) raher han dfferences n he levels of facor npus. These cross-counry TFP dspares can essenally be dvded no wo pars. The frs par consss of he producvy dfferences due o counres usng dfferen ranges of echnologes. The second par s due o he dfferen levels of effcency wh whch all echnologes are operaed. There are several heores ha propose mechansms ha mgh lead counres o adop dfferen ses of avalable echnologes. Among hese are Basu and Wel (998) and Parene and Presco (994) for example. The problem wh heores ha clam ha echnology adopon lags.e. he frs componen of TFP dspares descrbed above are an mporan facor par of TFP dfferences s ha here s lle or no emprcal evdence o hs exend. There are wo mporan reasons why he emprcal growh leraure rals he heorecal one n hs respec. Frs and foremos here used o be no daa ses ha would allow for an exensve analyss of cross-counry dfferences n he adopon paerns of several echnologes. Because of hs lack of daa mos of he sudes on echnology adopon dfferences focused on one parcular echnology a small number of counres and only a few pons n me. Recen examples of hs approach are Saxonhouse and Wrgh (2000) and Casell and Coleman (200). However Comn and Hobn (2004) nroduced a hsorcal cross-counry daa se on echnology adopon ha covers no only a relavely broad sample of counres bu also a broad range of echnologes as well as a very long me perod. The second reason for he gap beween he emprcal and heorecal leraure on echnology adopon s ha here are no many macroeconomc models ha provde a mappng beween her heorecal concep of echnologcal progress and varables ha are acually measurable n he daa. On he heorecal sde mos models provde predcons on he pah of capal labor and capal oupu raos. On he emprcal sde convenonal measures of echnology adopon lke he adopon shares analyzed n Grlches (957) Mansfeld (96) and Gor and Klepper (982) are no drecly nerpreable n he conex of hese varables. They are also harder o compue snce hey requre a measure of he number of poenal adopers. In hs paper we nroduce a growh model where dfferen frms smulaneously produce nermedae goods wh varous producvy levels. New nermedae goods are poenally more producve bu are nally operaed below her full-effcency. The array of nermedae goods adoped for producon s endogenous. A he mcro level our model s a model of slow dffuson of echnologes (embobed n new nermedae goods) qualavely conssen wh he sylzed facs: S-shaped dffuson curves and nvesmen n old vnages. The endogenous adopon of new echnologes provdes a heory of TFP boh a he secor and aggregae level. Furher he aggregae behavor of our model s dencal o he Neoclasscal growh model. The heorecal leraure on growh and dffuson s que hn. Char and Hopenhayn (99) presen he model ha we beleve comes closes o ours. There are several mporan dfferences beween Char and Hopenhayn (99) and our model: Frs our model has capal. Ths s mporan because mos of he echnologes ha we measure are emboded. Char and Hopenhayn nsead model dsemboded echnologes. 2

4 Second our model aggregaes o he Neoclasscal growh model. Ths grealy smplfes he nvesgaon of he aggregae and secoral behavor of our model along he ranson pah. Bu beyond he ndependen neres of our model wha s mporan for our purposes s ha s very well sued o brdge he exsng gap beween he heory on growh and adopon and he daa. In he radon of he growh leraure our model provdes predcons for he pah of aggregae capaloupu raos. I also has mplcaons for he pahs of echnology specfc capal-oupu and oupu raos. I shows how he laer can be used as measures of echnology adopon and wha growh heory predcs abou her dynamc behavor. I also shows how hese measures map no he more convenonal adopon shares whch were used by Grlches (957) and Mansfeld (96). The advanage of developng a heory n erms of capal-oupu and oupu raos s ha hese correspond drecly o he cross-counry measures of echnology adopon for whch we have mos daa. We use he Hsorcal Cross-Counry Adopon Daa se (HCCTAD) nroduced n Comn and Hobn (2004) o esmae our model. Specfcally we use daa for 7 echnologes n 2 ndusralzed counres spannng 80 years. We show ha he dynamcs of echnology adopon predced by he model are qualavely and quanavely conssen wh he general paerns of echnology adopon observed n he daa for hs broad range of echnologes and counres. Our resuls sugges ha here are subsanal dfferences n he rae a whch counres absorb new echnologes and ncrease he effcency level a whch hey use hem. Fnally we use he srucural esmaes ha we oban from our model o measure he producvy dfferenals beween counres ha can be arbued o he dspares n he echnology adopon paerns ha we observe. Ths componen of producvy s deermned manly by he level of he leas advanced echnology n use. We call hs margn capal draggng. We observe also ha dfferen counres end o lead n he producvy componen assocaed wh echnology adopon for dfferen echnologes. These dfferences are n general sgnfcanly correlaed wh overall secoral producvy dspares. However her varance s subsanally smaller. Hence our analyss sll leaves a large par of secoral producvy dfferences o be explaned by convenonal TFP facors ha affec all echnologes ha are used n he same way. The srucure of hs paper s as follows. In he nex secon we nroduce our model. In Secon 3 we derve s equlbrum dynamcs. Secon 4 conans he man heorecal conrbuon of he paper. I explans wha we assume for he pah of vnage specfc echnologcal progress n hs model and wha mples for he adopon of echnologes. Secon 5 s devoed o mappng our heorecal concep of echnologcal change no varables ha are measured n he daa. Secon 6 conans a descrpon of our esmaon sraegy whle Secon 7 conans he resuls obaned by applyng o he daa from Comn and Hobn (2004). Secon 8 concludes. 2. Model Our am s o model he neracon beween economc growh and he adopon of several maor echnologes. Ths s why we consder a mul-secor growh model n whch each secor uses a maor echnology. 3

5 Households Households derve uly from a counably fne number of dfferen fnal goods and servces. These goods and servces are ndexed by N. Consumpon of each of hese goods n perod s denoed by C. Overall uly s derved from a CES compose of hese ndvdual goods. Ths compose equals N / ρ ρ C C where 0<ρ< () The household maxmzes he presen dscouned value of uly derved from s pah of consumpon C. Ths presen dscouned value s gven by { } s s + 0 σ σ 0 and s maxmzed subec o he flow budge consran & e βs C σ σ + s ds B + s r + sb + s + W + sl + s + Π + s + Ξ+ s C+ s (2) (3) Here B +s reflecs he household s bondholdngs r +s s he real neres rae a me +s W +s s he real wage rae Π +s are he aggregae real flow profs ha are dsrbued o he households and Ξ +s represens addonal paymens ha households receve from busnesses. We absrac from employmen flucuaons and assume ha he represenave household nelascally supples a un measure of labor such ha L +s for all s[0 ). Noe ha we have wren he budge consran such ha he consumpon compose C s he numerare good whch by defnon has a prce equal o one n every perod. Le P be he prce of good a me and le P be he prce of he consumpon compose C. The CES srucure ha we have assumed mples ha n ha case ρ ρ ρ N ρ P (4) P In erms of he consumpon aggregae hs opmzaon problem yelds an Euler equaon of he form C & σ [ r β ] C (5) Demand for he ndvdual goods s mpled by he CES srucure and deermned by C P ` ρ C (6) Ths s he consumpon demand funcon ha he fnal goods producers face. 4

6 Fnal goods secors Ths economy has N fnal goods secors each of whch produces a dfferen fnal good or servce ndexed by. The secor ha produces he fnal good of ype consss of a connuum of perfecly compeve frms ha each use a consan reurns o scale CES producon echnology. Ths allows us o represen he aggregae acons of hese frms as f aken by a represenave frm. The fnal good of ype s produced usng a connuum of nermedae goods. The connuum of nermedae goods ha v. These nermedae goods are s used for he producon of fnal good s denoed by he nerval [ ] combned o produce fnal good usng he producon funcon / v v vdv where 0<< (7) v The fnal good producers sell her oupu a prce P and buy he nermedae good of ype v a prce P v. Ths resuls n he demand funcons for he nermedae npus ha read v P v P (8) Where P s deermned by he zero prof condon for hs perfecly compeve secor and equals v P dv (9) P v v For smplcy and o allow for aggregaon of he varous secors we wll assume ha he elascy of subsuon beween dfferen nermedae goods.e. /(-) s consan across he fnal goods secors. Inermedae goods secors Each nermedae good used n he producon of he fnal good s produced usng capal goods of a parcular echnology vnage. In parcular he oupu of nermedae good v for fnal good a me s assumed o be produced usng a Cobb-Douglas producon echnology of he form K L (0) v v α α v v Levhar (968) provdes a mcrofoundaon of a CES producon funcon n an envronmen where each producer faces a heerogeneous level of producvy. Closer o our conex Anderson de Palma and Thsse (993) nroduced he mcrofoundaons of CES preferences. They show how hey can be nerpreed as he aggregae uly represenaon of a marke conssng of a connuum of heerogeneous agens each makng a dscree choce among he goods avalable and hen choosng how much o consume of ha good. Ths analyss can easly be exended o a producon conex where frms selec whch nermedae goods o use. 5

7 Here v s he vnage specfc producvy level whch poenally vares over me and K v s he capal sock ha embodes echnology vnage v for he producon of. Fnally L v s he amoun of labor npus used n he producon of v. The vnage specfc producvy level s smlar o ha n classc vnage capal models lke Johansen (959) and Solow (960). Wha s dfferen here from hese models s ha v changes over me. The nermedae goods producers are monopolsc compeors. The monopoly power ha hey possess s due o her propreary knowledge of how o conver a un of he sandardzed nvesmen good no a un of he capal good ha embodes echnology v for he producon of good. Ths converson s reversble so ha also yelds a un of he sandard nvesmen good for every un of K v dsnvesed. Frms are assumed o ake he npu prces.e. he nvesmen prce and he real wage rae as gven. In each perod he suppler of vnage v for good makes flow profs equal o s revenue mnus s capal and labor expenses as well as mnus a fxed cos of dong busness n secor n perod. Mahemacally hese flow profs can be wren as where Ξ represens he per perod cos of operang n secor n perod. Π P I W L Ξ () v v v Each nermedae goods suppler s assumed o maxmze he presen dscouned value of s flow profs over he perod ha s n busness. Le v denoe he me n whch he suppler eners he marke. Smlarly le v denoe he me he suppler exs he marke. The suppler s obecve s o maxmze v v v rs ds 0 e Π vd (2) v subec o he echnologcal consran (0) he demand funcon (8) as well as he capal accumulaon equaon K & I δk (3) v v Solvng he above dynamc prof maxmzaon of he producer of vnage v for good yelds he followng opmaly condon for labor demand W ( α ) P v v v (4) Lv where (-α) s he labor elascy of revenue. Smlar o Jorgenson (963) he dynamc opmaly condon for nvesmen of hs suppler s a form of he user cos equaon of capal. I reads Where (r +δ) s he user cos of capal. ( r ) P v v + δ α (5) Kv 6

8 So far we have solved he problem for he suppler under he assumpon ha he was operang n he marke. Here we deermne he condons under whch hs s acually he case. Tha s we derve wha deermnes v and v. The suppler of vnage v for good wll produce as long as s flow profs excludng capal expendures exceed he user cos s ncurs on s capal sock. Tha s wll produce as long as [ Pvv W Lv Ξ ] ( r + δ ) Kv (6) Subsung n he opmaly condons ha we derved above we oban ha hs mples ha vnage supplers are n busness as long as her revenue sasfes Ξ P v v (7) Hence supplers ha do no generae enough revenue o recoup he operang cos n her secor wll ex he marke. Invesmen goods secor Wha remans o be defned s how he sandardzed nvesmen good s produced. Throughou hs paper our am s o consder echnologcal adopon n a model ha s as smlar as possble o he benchmark one good neoclasscal growh model. Because of hs we have chosen o specfy he nvesmen good producng secor n such a way ha he prces of he consumpon and nvesmen goods are equal a any pon n me. We do so by assumng ha he nvesmen good producng secor s perfecly compeve. Each compeor n hs marke uses nvesmen demand of each fnal good whch we wll denoe by I n a producon funcon ha hs smlar o he preferences of he household. Tha s N / ρ ρ I where I s he oal oupu of he sandardzed nvesmen good. I (8) Ths choce of producon funcon and he zero prof condon for hs perfecly compeve marke yeld ha he prce of he nvesmen good has o equal N P ρ ρ ρ ρ (9) whch equals he consumpon prce level derved n (4) whch n urn equals one by assumpon. 3. Equlbrum and aggregaon Before we solve for he dynamc equlbrum pah of hs economy s worhwhle o frs derve some aggregaon resuls ha reduce he se of aggregaes relevan for he equlbrum dynamcs. 7

9 Dervaon of aggregaes The aggregae represenaon of he model economy ha we develop s dencal o ha of he sandard onesecor neoclasscal growh model. Hence he aggregaes ha we derve wll concde wh he equlbrum varables of he neoclasscal growh model. The mporan dfference wh he sandard neoclasscal growh model s ha he endogenous adopon of echnologes provdes a heory for endogenous TFP boh a he secor and aggregae level. Under he opmaly condons derved above oupu n each fnal goods secor can be represened as beng produced usng a Cobb-Douglas producon funcon of he form 2 K L α α where he labor npu L s us he oal amoun of labor demanded by he producers n he secor. Tha s v v v (20) L L dv. (2) Wrng he capal npu n erms of uns of he sandardzed nvesmen good allows us o aggregae capal across he varous vnages as follows: The oal facor producvy level s gven by v K K dv. (22) v v v v dv. (23) v The heory of endogenous TFP ha we presen n hs paper can be undersood by lookng a hs expresson. Recall ha each nermedae good has a specfc oal facor producvy level ( v ). The TFP level n he secor resuls from wo mechansms. Frs an endogenous measure of nermedae goods (deermned by he v ) are used n producon. Hence he TFP level depends on he oal facor producvy emboded nerval [ ] v n he nermedae goods ha ener n producon. Second he CES aggregaon of he nermedae goods creaes an exernaly from he varey of nermedae goods used n producon. Ths exernaly shows up n he TFP measure. Wha s mporan for our analyss s no only ha he producon funcons aggregae o a smple represenaon bu also ha he opmaly condons for each secor can be aggregaed. Tha s as shown n Appendx A he opmaly condons derved n he prevous secon aggregae o W P L ( α ) and ( r ) P + δ α (26) K 2 We leave he deals of he dervaon of hese secoral producon funcons for Appendx A. 8

10 whch mples ogeher wh he derved secoral producon funcon ha he decenralzed allocaon of resources n each secor s as f decded upon by a sngle represenave frm whch equaes margnal revenue o margnal cos. Smlar o he Cobb-Douglas vnage producon funcons aggregang o a Cobb-Douglas secoral producon funcon he Cobb-Douglas secoral producon funcons aggregae o an aggregae Cobb-Douglas producon funcon. Ths producon funcon reads K L α α C + I and he correspondng oal facor producvy level s defned as whle he capal and labor aggregaes equal ρ ρ N ρ ρ (27) (28) N K K N and L L (29) As s shown n Appendx A he opmaly condons also aggregae o he economy wde level. Jus lke he secoral npu aggregaes he aggregaes K and L sasfy W L ( α ) and ( r ) δ α + (30) K The decsons of he connuum of dfferen producers ha are dsrbued over N secors n hs economy can be represened as f made a by a represenave frm usng a Cobb-Douglas echnology. Moreover he aggregae capal sock also sasfes he accumulaon equaon where aggregae gross nvesmen s defned as K & I δk (3) N I I and v I I dv (32) v v Thus a he aggregae level hs economy s equvalen o ha of he sandard one-secor neoclasscal growh model. The only dfference s ha because of he monopoly power of he nermedae goods supplers n each secor facor paymens o capal and labor only make up a fracon of nomnal oupu. We wll assume ha he flow profs of he nermedae goods supplers as well as he coss of dong busness hese supplers ncur flow back o he households n he form of Π and Ξ respecvely 3. Here 3 The resuls n Casell and Venura (2000) mply ha aggregae household behavor gven he CRRA preferences n our model does no depend on how he (lump-sum) paymens of Π and Ψ are dsrbued across households. Therefore we do no make any specfc assumpons abou o whch households hese paymens are made. 9

11 Π N v v Π v dv Ξ N and [ ] v v Ξ (33) These wo paymens make up he remanng fracon (-) of nomnal oupu. Aggregae equlbrum dynamcs The precedng resuls mply ha he dynamcs of he aggregaes n hs model are deermned by he followng wo dfferenal equaons. The frs s he equlbrum consumpon Euler equaon whch equals C & α σ α δ β C K (34) The second s he capal accumulaon equaon K& K K α C δ K (35) Apar from one excepon hs sysem s dencal o he one ha deermnes he equlbrum dynamcs of consumpon and capal n he sandard one secor neoclasscal growh model. The excepon s he neffcency due o he wedge ha he monopolsc compeon beween he nermedae goods supplers drves beween he socal and prvae margnal reurn o capal. Ths s refleced by he facor mulplyng he socal reurns o capal n (34). Secoral equlbrum dynamcs Underneah he aggregae dynamcs of our economy are he secoral dynamcs. These deermne he pah of echnology adopon n each of he N fnal goods secors. We explan he deals of he dervaon of hese equlbrum dynamcs n Appendx A. The followng rao s make up he gs of hem and are wha s relevan for he res of hs paper. Frs of all he secoral o oal oupu rao and he vnage o secoral oupu rao are gven by ρ and v v (36) respecvely. Moreover he resulng prces are gven by P P P ρ and P P v v v (37) Thus hs dervaon allows us o wre he secoral and vnage specfc equlbrum quanes n erms of he underlyng levels of oal facor producvy. Conrary o he sandard neoclasscal growh model n whch oal facor producvy evolves exogenously he secoral oal facor producvy level n hs economy s deermned endogenously. Equaon (23) mples 0

12 ha he secoral oal facor producvy level s a funcon of he range of echnology vnages ha are operaed n perod. Thus depends on v and v. These vnages are deermned by he enry and ex condon (7) whch usng he equlbrum resuls above can be wren as Ξ v P (38) Solvng hs equaon requres makng a se of addonal assumpons abou he pahs of v and Ξ. These assumpons deermne he shape and paern of echnologcal progress n our model. Snce hese assumpons are one of he maor conrbuons of hs paper and above all are crucal o he adopon dynamcs n our model we nroduce hem n deal n he nex separae secon. 4. Technologcal progress and adopon In he prevous secon we derved he aggregae equlbrum dynamcs of our model economy and showed ha a he aggregae level hs economy s observaonally equvalen o he sandard neoclasscal growh model. The man focus of hs paper s he negraon of hese aggregae dynamcs wh a heory of echnology adopon of varous maor echnologes n he economy. In hs secon we nroduce our specfcaon of echnologcal progress and show wha mples for he dynamcs of echnology adopon n our model economy. We do so n hree seps. In he frs sep we nroduce our assumpon abou he shape of echnologcal progress n hs economy. In he second sep we solve for he mpled values of v and v under hese assumpons. In he hrd sep we solve for he heorecal measures of echnology adopon ha resul from hs soluon and ha are of neres for our emprcal analyss. The shape of echnologcal progress The man dfference beween our model and he mos commonly used vnage capal models s ha we allow for he vnage specfc producvy level v o vary over me. In fac hs varaon wll be crucal n wha s o follow. For v we wll assume ha sasfes v ( v v ) f (39) v Ths specfcaon of he vnage specfc producvy profle n self does no provde us wh a soluon o our model. However provdes us wh a framework o capure he shape of echnologcal progress ha we are afer. In order o capure hs shape we make he followng addonal assumpons. The frs s ha v g a v e (40) Whou loss of generaly we wll also assume ha v v 0 +. Ths assumpon allows us n equlbrum o nerpre g as he rae of echnologcal change n secor. For he funcon F we assume ha

13 gx 2 2 F ( x) e for x 0 ln F ( x) x < g and ln F ( x) x < 0 for x>0 and lm ( x) 0 F x (4) The economc mplcaons of hs assumpon are eases dscussed n he conex of an example. For hs purpose consder Fgure. Ths fgure plos a represenave shape of he logarhm of he vnage echnology froner a a parcular pon n me. The dashed lne depcs he feasbly froner for each vnage. Ths s he maxmum producvy level ha each vnage wll converge o as goes o nfny. All vnages below v are operaed a hs maxmum producvy level and can be nerpreed as fully maured echnologes. Vnages ha are beyond v are operaed below her long run poenal. In fac our assumpons on F are such ha vnages ha are furher beyond v are operaed a a smaller fracon of her long-run maxmum. We v goes o nfny. assume ha n he lm hs fracon goes o zero when ( ) In prncple our specfcaon of echnologcal progress s raher mechancal and we prefer o nerpre as a reduced form specfcaon raher han a mcrofounded one. There are several papers however ha provde some nsgh n whch economc processes mgh generae such a shape of he echnologcal froner. Frs of all he ncreasng fracon of maxmum effcency a whch he echnology s operaed can be drecly nerpreed as a learnng curve. Tha s evdence on learnng by dong as n Bahk and Gor (993) Irwn and Klenow (994) and Jovanovc and Nyarko (995) would generae a vnage producvy profle ha s smlar o ha n Fgure. Learnng by dong s no he only mechansm ha could be behnd hs paern hough. If ncumben frms lobby he polcal sysem o essenally ax newer enrepeneurs hen one mgh also observe a paern lke hs. An example of a model where ncumbens apply resources o lobbyng o he dermen of her poenal compeors s Holmes and Schmz (200). Fernandes (2003) argues ha new echnologes mgh no be adoped because complemenary fnancal nnovaons mgh be needed o accommodae he rsk assocaed wh her use. Alhough her argumen s no drecly applcable here does pon ou he fac ha he producvy of newer echnology vnages mgh mprove over me because markes as well as complmenary nvenons adus o hem. v Enry and ex revsed Our assumpons abou he funconal form for he shape of he echnologcal froner n each secor allow us o wre he secoral oal facor producvy level as v d ( x) dx F where d ( v v ) < ( v v ) d d (42) Because he enry and ex condon (38) holds wh equaly for boh v and v we know ha F Ξ P d d ( d ) F ( d ) F ( x) dx (43) 2

14 In order for us o be able o solve hs condon we need o make an assumpon abou he pah of Ξ over me. We wll assume ha he operang cos n a secor s proporonal o he oal revenue n ha secor. Mahemacally Ξ ζ P (44) When hs assumpon s appled o he enry and ex condon above we oban ha n every perod v and v are deermned by he followng wo condons ζ d F ( ) ( ) ( ) d F d F x dx where d ( v v ) < ( v v ) d d (45) Noe ha hs sysem does no depend on me. Thus n equlbrum d and d are consan over me. Because of hs we wll denoe hem by d and d n he res of hs paper. The above resul also means ha he wdh of he range of vnages used n each secor s consan over me 4 and moves because of he progress n v. In fac we can use he soluon for d and d o calculae he secoral level of oal facor producvy whch equals d F v d ( ) g d x dx a e F ( x) d dx (46) Snce he negral erm of hs expresson s consan over me he growh rae of equals g. Hence our se of assumpons here mples ha secoral oal facor producvy levels grow a a consan rae over me. Graphcally he underlyng process of echnologcal change n each secor bols down o Fgure 2. In each perod he echnologcal froner moves parallel o he feasbly froner. Ths shf makes he producvy level of he se of mplemened vnages grow a he rae a whch he producvy of v grows. Ths causes he secoral TFP level o grow a he same rae as well. Measures of echnologcal adopon Our man am s o derve he pah of echnologcal adopon n each of he secors n he economy. In order o derve hs pah we frs have o defne how we measure echnologcal adopon. The measures ha we are neresed n are ones ha we subsequenly are able o measure n he daa. In hs subsecon we nroduce he heorecal counerpars of our emprcal measures. The avalable emprcal measures are dscussed n Secon 6. There are wo man measures of neres ha we use n our emprcal analyss. The frs s he vnage oupu o GDP rao. Mahemacally hs s defned as v /. The second s he vnage capal o GDP rao whch equals K v /. These wo raos are dfferen from he measures ha are mos commonly consdered n sudes of echnologcal progress. Generally sudes of echnologcal progress lke Grllches (957) Mansfeld (96) and 4 The consancy of hs range s a resul of equaon (44). Oher assumpons abou he pah of secor specfc coss poenally lead o me varaon n hs range manly because hey could mply an neracon beween secor s echnology choce and macroeconomc aggregaes. 3

15 Gor and Klepper (982) for example consder adopon shares and noe ha adopon share curves are commonly S-shaped. As urns ou our model also generaes such curves. They can be derved from he wo raos consdered above. In order o show how our model s conssen wh prevous emprcal work on adopon we wll presen our heorecal resuls n erms of he wo raos ha we use n our emprcal analyss as well as n erms of he adopon shares. These adopon shares n our model 5 wll be he share of oupu of vnage v n oal oupu of secor and he share of capal of vnage v n he capal sock of secor. These equal respecvely v v u v v du and K K du (47) The above raos v / and K v /K are perfecly well defned from a heorecal pon of vew. However hey are no emprcally vable ye because hey requre measurng daa on a connuum of vnages of echnologes. Such daa are smply no avalable. Therefore n order o make our heory emprcally applcable we need o map he connuum of vnages no a counable number of echnology vnages ha s observed n he daa. 5. From adopon n he model o adopon n he daa Where our model has a connuum of vnages for each secor we only observe a dscree number of echnology vnages n he daa. Ths secon explans he way we map hs connuum of vnages no he dscree number of vnages ha we observe n he daa. We wll sar off hs explanaon wh an example and hen proceed o generalze from here. Afer explanng hs mappng we derve wha our heory predcs for he varous observed measures of echnologcal adopon. v v Example: Merchan vessels Merchan shps have hsorcally been classfed no hree dfferen caegores: () salshps () seamshps and () moorshps. Consder merchan shppng servces as one of he secors n he model economy. Then our heorecal seup consders a connuum of dfferen echnology vnages ha are have been or poenally could be used o provde shppng servces. Wha we wll assume s ha he connuum of merchan shppng echnology vnages can be spl no hree nervals as depced n Fgure 3. The frs nerval (- v seam ] s assumed o be he se of vnages ha are all salshps. The second (v seam v moor ] s assumed o be he se of seamshp vnages. Fnally we wll assume ha (v moor ) consss of moorshps. For our emprcal applcaon he cu off vnages v seam and v moor are boh unknown parameers. We do have some hsorcal nformaon hough ha allows us wh approxmae values for hese parameers. The frs seamboa was bul n 788 n Phladelpha by Fch. Hence v seam probably corresponds o dae shorly afer 788. The desel engne whch propels mos moorshps was nroduced n 892. Therefore we ls hs as he approxmae dae for v moor n he fgure. u 5 In he emprcal adopon leraure hese share are generally defned n erms of he fracon of frms raher han he fracon of he capal sock or oupu. 4

16 Mappng no a dscree number of vnages Our daa cover several maor echnologes whch we group no echnology groups lke merchan shppng n he example above. For our emprcal applcaon we use hese echnology groups as he equvalen of our secors. Whn each group we order he echnologes sequenally; lke salshps seamshps and moorshps are ordered n he example above. We denoe hese echnologes whn each group by he ndex τ. For each of hese observed echnologes we hen assume ha hey correspond o a se of vnages whch we denoe by V (τ) such ha V ( τ ) ( vτ + ] ( vτ vτ ] ( v ) + τ for for for echnologes whou a predecessor echnologes wh boh a predecessor and successor echnologes whou a successor (ye) The adopon measures for he connuum of vnages ha we consdered before can be convered no measures for he counably fne number of vnages ha we have daa for by negrang hem over he above echnology ses V (τ). Predced echnology adopon paerns Now ha we have defned he heorecal equvalen of he observed echnologes n our daa se we can derve wha our model predcs abou he paerns of adopon of hese echnologes. Frs of all consder he oupu and capal o GDP raos. For echnology τ of group we wll denoe hese raos by m (τ) and m K (τ) respecvely. These raos equal ( τ ) ( v ) dv and m K ( τ ) ( Kv ) m V ( τ ) (48) (49) ( τ ) V dv They map no he adopon shares ha have been used n a broad number of sudes n he followng way s V ( τ ) ( τ ) s V v ( s) dv u du s m m ( τ ) V ( τ ) and s K ( τ ) () s s V K ( s) v K dv u du s m K m ( τ ) () s K (50) The calculaon of hese shares n (50) requres havng observaons on all echnology vnages used whle he calculaon of he raos n (49) only requres daa on one echnology vnage and a measure of real GDP. In appendx A we derve he pah of he adopon measures as a funcon of me. Ths yelds where m ρ v ( τ ) v ξ ( τ ) and m ( τ ) ξ ( τ ) K α α ρ ρ K (5) α 5

17 { { } max v~ mn v~ d mn{ ~ v + { v~ τ max τ d } τ τ + τ τ + ξ ( τ ) F ( x) dx and ( τ ) F ( x) { { } max v~ mn v~ d ξ K dx (52) mn{ v~ { } + max v~ τ τ d and v ~ τ s defned as he me gap beween he me of he nroducon of he τ echnology and he effcen vnage a me 0.e. ( v τ v 0 ) and he negraon lms n he ξ erms denoe he vnages used ha are assocaed o he echnology τ n secor a me. 6 Adopon dspares and cross counry per capa ncome dfferences Our emprcal goals n hs paper are hreefold. Frs of all we am o compare he heorecal adopon paerns generaed by our model wh hose observed n he daa for a broad range of maor echnologes. Secondly we wan o measure he TFP componen ha s assocaed wh he adopon of new echnologes and undersand wha deermnes he observed cross-counry varaon n hs componen. Fnally we ry o undersand wha par of he producvy dspares across counres s he resul of dspares n he rae a whch hey adop new echnologes. To pursue hese las wo quesons proves useful o decompose he secor level TFP ( ) as follows: ln d ln a g gv0 ln F d ( x) dx Throughou we assume ha long run growh n each secor s he same across counres such ha here s no cross-counry varaon n g. Furhermore we assume ha echnologes across counres are dencal excep for a v 0 and he funcon F (x). Hence for our emprcal analyss we mpose ha s also consan across counres. 7 These wo assumpons mply ha he percenage dfference n secoral producvy levels beween wo counres can be approxmaed by (53) ( ) d ( ) d ln + + ln ln a ln a g v v ln ( ) F x dx ln d F x 0 0 d ( ) p p ln a + ln a ln ln dx (54) The second par of hs erm s he par ha s arbuable o he dfferences n cross-counry echnology adopon paerns.e. o he dfferences n he ranges of vnages of echnologes ha counres employ n producon. 6 See he appendx for he deals on he negraon lms. Here v τ - f he echnology does no have a predecessor and v τ+ f does no have a successor (ye). 7 Equaon (54) shows ha our model mples ha here are perssen cross-counry dspares n secoral producvy levels. Ths mplcaon s conssen wh some of he evdence presened n Bernard and Jones (996a 996b). They sugges ha here s lle evdence of convergence n ndusry producvy levels especally for manufacurng. 6

18 For he nerpreaon of he resuls o follow s acually worhwhle o consder he nerpreaon of he above decomposon. Fgure 4 llusraes hs decomposon graphcally. The model mples a dsrbuon of v. Ths capal for echnology K v over a me varyng suppor of echnology vnages gven by [ ] dsrbuon s depced n he fgure. There are hree aspecs of hs dsrbuon ha are drecly refleced n he TFP measure ln( ). These aspecs are ndcaed by (I) (II) and (III) n he fgure. They correspond o he followng decomposon v ln d ( ) F x ln a ln { + dx + g v d exp g ( I ) d ( III ) ( II ) ( ) { where v v 0 + d (55) Par (I) of hs decomposon reflecs specfc TFP dfferences ha are unrelaed o he echnology adopon decson ha s cenral o hs paper. I essenally deermnes he hegh of he dsrbuon and can hus be nerpreed as he deermnan of capal deepenng n hs model. Pars (II) and (III) are relaed o he range of echnology vnages n use a each me. Par (II) reflecs he wdh of he range of echnologes n use because of hs we refer o as he capal wdenng par. Because of he CES srucure of he producon funcon n our model he margnal produc of each capal vnage s nfne a zero. Therefore TFP s ncreasng n he degree of dversfcaon of producon among dfferen echnology vnages. Fnally par (III) s deermned by he locaon of he range of vnages whch we denfy by s lowerbound. Because hs par s denfed by he leas producve vnage used we refer o as capal draggng. Tha s he less advanced he vnages ha are dragged along he lower oal facor producvy. The capal deepenng par.e. (I) on he one hand corresponds closely o he radonal concep of TFP n he neoclasscal growh model. I conans all facors ha whch affec he producvy of all capal n place n he same way. The capal wdenng and draggng pars.e. (II) and (III) on he oher hand are specfcally denfed by he echnology adopon srucure wh whch we exended he model n hs paper. I s exacly he magnude of he dspares n capal wdenng and draggng across counres ha s our focus. All he parameers ha are necessary o calculae pars (II) and (III) of (55) can be esmaed by fng he observed adopon paerns. Hence our esmaon resuls serve hree purposes. Frs of all hey enable us o consder how well our model fs he observed echnology adopon paerns. Secondly hey allow us o nfer he secoral producvy dspares due o echnology adopon dfferences and o undersand he role of capal wdenng and capal draggng n hs TFP componen. Fnally hey perm us o compare he mpled measure of TFP dspares due o echnology adopon dfferences wh he secor level cross-counry producvy dfferences. 6. Esmaon We esmae he parameers of our model separaely for each of maor echnology caegores / counry combnaon usng he Generalzed Mehod of Momens (GMM). Our esmaon procedure s an applcaon of GMM wh nonlnear deermnscally rendng varables consdered n Andrews and McDermo (995). In hs 7

19 secon we explan how we apply hs procedure o our model. The resulng mehod s a hybrd of reduced form and srucural esmaon. Afer calbrang a unque se of values for g and ζ across me counres and echnology groups we only srucurally esmae he parameers ha are relevan for accounng for he producvy dfferences due o adopon dspares. The oher parameers are esmaed n reduced form. Funconal form of F(.) Snce our esmaon procedure s paramerc requres us o make a specfc assumpon abou he funconal form of he funcon F(.) whch deermnes he vnage producvy profle. In prncple any funconal form ha sasfes he properes descrbed n (4) can be used. In pracce however s mporan o choose a funconal form ha sasfes hree man crera. These are () all relevan parameers needed for he accounng exercse of equaon (54) are separaely denfed () he funconal form s flexble enough o f he wde varey of adopon paerns n he daa () he funconal form s parsmonous n s parameerzaon and all parameers have an economc nerpreaon. There are many funconal forms for F(.) ha mgh f hs bll. The one ha we wll use for our analyss s closely relaed o he logsc funcon and equals F ( x) exp( gx) (( +ψ ) g max{ 0 x} ) 2 + exp where 0 < ψ < (56) Here g s he growh rae of whle ψ deermnes he rae a whch he producvy profle falls below he feasbly froner for x>0. Ths can be seen by consderng he percenage change of F(.) wh respec o x for x>0. Ths growh rae equals ln F x ( x) g ( + ψ ) exp + exp Model specfcaon (( + ψ ) ) (( ) ) gx + ψ gx For each echnology/counry combnaon we observe a me seres ha reflecs he echnology adopon paern for he echnology vnages n he parcular counry. The model ha we esmae for each echnology caegory / counry combnaon ndexed by hus has a panel daa srucure. Each cross-seconal observaon s made up of a echnology vnage ndexed by τ. Dependng on wheher we have daa on he vnage oupu o GDP rao or he vnage capal o oupu rao he observed me seres reflec m (τ) or m K (τ). Equaon (5) mples ha n reduced form we can wre ( τ ) β + β ξ ( τ ) ln m 0 τ τ + ln (58) (57) and ( τ ) β + β + β ln ξ ( τ ) ln m K 0 K τ K τ 2 K τ + ln K (59) These are he equaons ha we wll esmae for each echnology caegory. 8

20 In prncple he reduced form coeffcens.e. he β s depend on he srucural parameers 8. We wll however gnore hs dependence and wll focus our esmaon effors on obanng esmaes of he parameers ha deermne he nonlnear deermnsc rends lnξ (τ) and lnξ K (τ). These are he same parameers ha are needed o accoun for secoral producvy dspares followng equaon (54). In parcular for each echnology caegory / counry combnaon we wll esmae he he me gap beween he me of he nroducon of he frs echnology (n he caegory) and he effcen vnage a me 0 v ~ v ) and he curvaure of he funcon ha deermnes he effcency of each vnage (ψ ). We do ( τ v 0 so condonal on he calbraed values of he parameers g and ζ as well as he ransformed echnology cuoff vnages v τ v for he varous echnology vnages τ>. The esmaes of he parameers condon holds. Ths resrcon reads d and d are mpled by he resrcon ha equlbrum enry F ζ ( ) ( ) d d F d F ( x) d dx (60) I defnes ψ as an mplc funcon of g d and d. We denoe hs funcon as d D( ψ ; g ) and D( ψ ; g ) d (6) All of hs ogeher mples ha he equaons we esmae are of he form (58) and (59) where he nonlnear deermnsc pars equal 9 lnξ ( τ ) mn{ v~ τ + D ( ψ ; g )} ln max { ~ ( ψ )} τ ; exp v D g exp ( g x) ( + ψ ) g max{ 0 x} ) dx (62) and lnξ K ( τ ) mn{ v~ τ + D ( ψ ; g )} ln max { ~ ( ψ )} τ ; exp v D g exp ( g x) ( + ψ ) g max{ 0 x} ) dx. (63) 8 The reduced form parameers β 0 also depend on among ohers uns of measuremen. If besdes qualy growh one would also nclude (consan) prce declnes of uns of oupu and capal n he model (lke models of nvesmen specfc echnologcal change) hen β would also depend on he relave prce declnes/ncreases. In ha case g s he combned growh rae of emboded and nvesmen specfc echnologcal change. Even hough our model only ncludes emboded echnologcal change n our applcaon we wll be agnosc abou he relave mporance of emboded versus nvesmen specfc echnologcal change. Hence we wll no resrc β based on our model. 9 The lms of he negrals n hese wo equaons smplfy because we only consder he case n whch ξ (τ) and ξ M (τ) are srcly posve. Ths s by defnon he case for he observaons n our daa se. 9

21 The esmaon of hs model requres he on esmaon of all he non-lnear equaons n he panel under v are consan for all several cross equaon resrcons. Ths s he case because boh ψ and ( ) echnology vnages n a echnologcal group. 0 Momen condons and esmaon v 0 For he esmaon of our model we use GMM. Our model s one wh a nonlnear deermnsc rend n he form of ξ (τ) and ξ K (τ). The properes of GMM n case of nonlnear deermnscally rendng varables are derved n Andrews and McDermo (995). They prove ha n hs case GMM parameer esmaes are boh conssen as well as asympocally normally dsrbued. The applcaon of GMM requres he choce of a se of momen condons ha are used o denfy he parameers. Snce our model s fully deermnsc does no conan any srucural sochasc componens ha can be used o defne he condons. Insead we defne he momen condons n erms of he devaons of he observed varables from her fed values.e. he resduals of he equaons. In hs sense our emprcal mehodology amouns o advanced rend-fng. I s very smlar n naure o he emprcal analyss n Laner and Solyarov (2004). Defne he resduals u and u K respecvely as ( τ ) ln m ( τ ) β β ξ ( τ ) u 0 τ τ ln (64) and u ( τ ) ln m ( τ ) β β β ln ξ ( τ ) K K 0 K τ K τ 2 K τ ln K (65) hen for each counry we assume he exsence of a se of nsrumens z z r for whch [ u z ] E[ u z ] 0 E for s r (66) s M s One underlyng assumpon s mporan o noe here. Tha s ha our applcaon of GMM s based on assumpon ha u and u K are zero mean saonary processes. Snce he logarhm of GDP per capa.e. ln s par of he equaon for ln m K (τ) hs means ha we mplcly assume ha he logarhm of GDP per capa s rend saonary. Our GMM esmaes of he parameers are he values for ( ) v s and he curvaure parameers ψ v 0 ha mnmze a quadrac obecve of he sample approxmaons of he momen condons of equaon (66). The form of he GMM obecve he srucure of he mnmzaon problem as well as he way n whch he resuls of Andrews and McDermo (995) are applcable o hs model are explaned n deal n Appendx B. v s he acual componen esmaed because τ 0 Noe ha ( v 0 ) v~ τ ( v τ v ) + ( v v ) where ( v v ) 0 ~ can be decomposed n he followng way v τ denoes he number of years afer he dscrezaon pon of he frs vnage he dscrezaon pon of he τ vnage falls and remember ha we use nformaon abou he nvenon of he dfferen echnologes o calbrae hese erms. 20

22 Idenfcaon Before we presen he esmaes of he srucural parameers ψ and ( ) v s mporan o consder v 0 whch feaures of he daa allow us o denfy hem. The ncluson of an nercep and rend n (58) and (59) v o explan s he common non-lnear deermnsc rend par n means ha wha s lef for ψ and ( ) v 0 he adopon curves of he echnology vnages n each echnology group. Wha he model and he daa have n common s ha he non-lneary of he adopon curves has wo very dsnc feaures. These wo feaures are bes llusraed usng an emprcal example. For hs reason consder he acual as well as he fed adopon curves for elephones and elegrams n he U.S. whch are depced n Panel B of Fgure 5. The frs obvous propery of hese adopon curves s her curvaure boh n he early adopon phase of a echnology vnage lke ha for elephones as well as n he phase n whch a echnology vnage declnes lke ha for elegrams. Ths curvaure s wha deermnes our esmae of ψ. The second feaure s where he v. curvaure sars n me. Ths s wha deermnes he esmae of ( v 0 ) I s mporan o emphasze ha boh of hese srucural parameers (ψ and ( ) v ) are he same for v 0 all adopon curves fed whn he same echnology group. Hence he fed curvaures for he curves for boh elegrams elephones as well as cellphones are all based on he same value of ψ. 7. Emprcal resuls Ths secon s he culmnaon of hs paper n he sense ha we presen esmaes of he model nroduced obaned usng an exensve hsorcal daase on he adopon of several maor echnologes across counres spannng almos wo cenures. Our focus s on wo parcular aspecs of he resuls. Frs of all how well does he model f he adopon paerns for he broad range of echnologes for whch we have daa? Does he model capure he common pars of he adopon paerns observed n he daa? Secondly wha does he model mply for he producvy dspares across counres ha are caused by hem usng dfferen ranges of echnology vnages? We presen our resuls n four pars. In he frs par we descrbe he daa used for he esmaon. In he second par we focus on he frs aspec of our resuls namely he parameer esmaes and he qualy of he f of he model. In he hrd par we dscuss wha our resuls reveal abou TFP dspares due o dfferences n he ypes of echnologes used across counres. Fnally n he fourh par we summarze wha we consder he boom lne of our resuls and some of her lmaons. Daa For our emprcal analyss we use daa from a unque daa se he Hsorcal Cross-Counry Technology Adopon Daa se ha we assembled and explaned n deal n Comn and Hobn (2003). The daa ha we use here conan boh aggregae measures of economc growh as well as measures of echnology adopon for 7 maor echnologes. The daa cover he perod and a sample of weny-one of he World s leadng ndusralzed counres. Table lss he counres and echnologes covered n he daa. 2

23 As can be seen from Table we denfy seven man echnology caegores denfed by. These echnology caegores range from exles for whch we have daa on he adopon of spndles o elecommuncaons. Each caegory conans wo or more echnology vnages ndexed by τ. The measures for hese vnages range from seel oupu measured n ons produced n ceran ypes of seel furnaces o he capal sock of passenger cars n each counry. Besdes he ndex τ and he descrpon of he vnage Table conans wo more peces of nformaon for each vnage. I lss he ype of he measure for he vnage. In he ype column K denfes a capal sock measure and ndcaes an oupu measure. The (v τ -v ) column denoes how many years afer he dscrezaon pon of he frs vnage he dscrezaon pon of vnage τ falls. As descrbed above we keep hese nerval lenghs fxed across counres durng our esmaon. The way we have calbraed hem s by seng hem equal o he dfference beween he nvenon daes of he relevan vnage and he frs vnage. We used he nvenon daes lsed n Fgure 4 of Comn and Hobn (2004). For salshps we assume ha hey make up he whole merchan flee a he begnnng of our sample and we do no have a vnage sarng dae. Parameer esmaes and f We sar off he presenaon of our parameer esmaes wh a dscusson of he parameers ha we acually do no esmae. Tha s he resuls ha we presen n he followng are condonal on a se of calbraed parameers namely g and ζ. We hold hese hree parameers consan for all our esmaes across me counres and echnology groups. We calbrae g o equal.4% annually whch s he growh rae of TFP conssen wh a long-run average growh rae of real GDP per capa of 2% and s also approxmaely equal o he average pos-war growh rae of aggregae TFP for he U.S. economy. Calbraon of he parameers and ζ s no as sraghforward. Our resuls here are based on he choce of 0.9 and ζ0.5. The combnaon of hese wo parameer choces mples an aggregae prof margn ne of fxed operang coss equal o 5%. Ths s roughly conssen wh he average operang margn repored for publcly raded frms n he U.S. over he las hree decades. A sensvy analyss of our resuls suggess ha hey do no change dramacally for beween 0.8 and For operang coss hgher han 5% of nomnal oupu.e. ζ>0.5 we found ha he model would predc much shorer echnology lfecycles han we observe n he daa. The gs of wha he acual daa looks lke and how closely he model f he daa s conaned n Fgure 5. I dsplays he f and acual adopon curves for seel n he U.S. (panel A.) elephones and elegrams n he U.S. (panel B) and passenger ransporaon for he U.S. and he U.K. (panels C. and D.). The f depced for he four examples n Fgure 5 s acually very represenave for ha of he oher counry / echnology group combnaons. As can be seen from hs fgure he model seems o f que well he adopon paerns of a broad range of echnologes well. Gven he one sze fs all naure of our esmaon n whch we apply our one model o a wde varey of echnology groups hs conssen qualy of f mples ha our srucural model manages o successfully replcae he common general hsorcal adopon paerns of maor echnologes. Furher he fac 22

24 ha we oban a good f despe all he resrcons mposed (boh n he funconal forms and n he calbraed parameer values) means ha hese resrcons canno be reeced n a sascal sense. So wha are he parameer esmaes ha yeld such a f and do hey make economc sense? To answer hs v as well as he assocaed sandard queson consder Table 2. Ths able lss he esmaes of ψ and ( ) v 0 errors for all counry / echnology group combnaons. The parameer esmaes confrm he general mplcaons of he model. Tha s for echnology groups where he adopon of new vnages ook relavely long lke he shppng and he oher wo ransporaon echnologes we oban low esmaes of ψ generally beween 0.3 and 0.6. Technologes wh more rapd adopon of vnages lke mass communcaon and seel yeld much hgher esmaes of ψ generally beween v presumably n large par and.5. For early echnologes lke exles we oban low esmaes of ( ) v 0 because v n ha case s much smaller han for laer echnologes lke elecommuncaons and ransporaon. A noable excepon s shppng where he seamboa was nvened n he early par of our sample bu our v are relavely large. Combned wh he assocaed low esmaes of ψ hs suggess ha esmaes of ( ) v 0 akes a very long me of shppng echnologes o fully maure. I urns ou ha our parameer esmaes are no parcularly sensve wh respec o he echnologes ncluded n he echnology groups. Tha s where he groupng of he echnologes for exles seel and shppng s farly unconroversal he groupng of he echnologes n he oher caegores s less so. However elmnang cell phones from he elecommuncaons group or droppng ar ransporaon from he wo ransporaon caegores does no really nfluence he resul. Ths s because he parameers are manly denfed by he curvaure n he adopon paerns of he oher echnology vnages. The sandard errors of he esmaes are revealng. Andrews and McDermo s (995) GMM mehod s very unforgvng n erms of he mpled sandard errors. In cases where he model does no yeld a good f o he daa he sandard errors are a facor en hgher han n case of a sasfacory f. As he sandard errors show he one sze fs all characer of our emprcal analyss yelds resuls ha are bes characerzed as one sze fs many. For mos counry / echnology combnaons we oban farly relable parameer esmaes. However n v. Furher analyss of some cases he daa do no allow us o allow for accurae nference on ψ and ( ) v 0 our daa reveals ha here are bascally four reasons why hs mgh be he case. The frs s smply a lack of daa. Ths s he case for seel n Greece Ireland and Porugal where we do no have daa on open-hearh seel. There mgh be wo reasons for hs lack of daa. On he one hand hey mgh smply no have been colleced. On he oher because of he relavely small sze of he seel manufacurng ndusres n hese counres open hearh seel mgh acually no have been produced. The second reason relaes o he laer pon above. Somemes daa s avalable bu based on a very small sample. Ths s he case for Dansh seel producon whch shows several knks n he adopon curve of seel. These knks presumably correspond o new furnaces comng onlne. The ndvsbly of nvesmen n such furnaces combned wh he small sze of he Dansh seel producng secor hus leads o a falure of our model o f he observed seel adopon paern. 23