An Inernaional Comparison of Foreign Paens Regisered in he USA Michael McAleer a, Felix Chan a and Dora Marinova b a Deparmen of Economics, Universiy of Wesern Ausralia b Insiue for Susainabiliy and Technology Policy, Murdoch Universiy Absrac: This paper analyses rends and volailiies in regisered paens for he op foreign paening counries in he USA. In erms of oal US paens by foreign counries, Japan is ranked firs, followed disanly by Germany and hen France. Paen regisraions from each of he counries have increased seadily over ime, bu a differen raes. Using monhly ime series daa for 975-998, he ime-varying volailiy of he paens raio, namely US paens regisered by each of he op foreign counries relaive o oal US paens, is examined in deail. Inernaional rankings based on boh he number of paens and paen inensiy (or paens per capia) are provided. The asymmeric AR()-EGARCH(,) model is found o be suiable for mos counries, while he AR()-GARCH(,) and AR()- GJR(,) models also provide useful insighs. Non-nesed esing procedures are used o discriminae beween GARCH(,) and EGARCH(,), and beween GJR(,) and EGARCH(,). Keywords: Paens, rends, volailiy, GARCH, GJR, EGARCH, asymmery, regulariy condiions, asympoic heory, inernaional rankings, non-nesed ess.. INTRODUCTION Trends in paen regisraions have frequenly been used o describe a counry s echnological capabiliies and inellecual propery, and have aced as a proxy for innovaion (see, for example, Pavi, 988; Pael and Pavi, 995; Griliches, 986; and Marinova, ). Having he world s larges economic marke, he USA has consisenly been a desinaion for regisering paens by innovaive US and foreign companies, as well as by individuals wih inenions o commercialise new echnologies. Consequenly, paens regisered a he US Paen and Trademark Office (PTO) represen an excellen source of informaion regarding echnological srenghs, inellecual propery and marke ambiions. Mos of he research on paens graned in he USA has examined snapsho images represening paen aciviies for a paricular ime period, based on a single year or on an aggregaed annual informaion base. For example, paens daa have been used in economeric models o analyse he facors affecing decisions by companies o paen innovaions (Dugue and Kabla, ). Aucion models have also been used o analyse he processes of paen acquisiion and/or paen renewal (Waerson and Ireland, ; and Crampes and Langinier, ). Paen numbers have been used as a measure of R&D oupu in several producion funcion sudies (Goel, 999). Cross-counry correlaions using paens daa are also very common (see, for example, Piana, 998). When ime series daa have been analysed, saionariy ess have ypically no been repored (see, for example, Archibugi and Piana, 998). Volailiy in paen regisraions has ypically no been 6 analysed in he lieraure. The aim of his paper is o examine he rends in paens regisraions and volailiy in he paens raio, namely paens regisered a he US PTO by each of he op foreign counries relaive o oal US paens, using monhly ime series daa from 975 o 998. The plan of he paper is as follows. Secion describes he rends and volailiy in he daa used, and provides inernaional rankings based on boh he number of paens and paen inensiy (or paens per capia). Secion 3 discusses he srucural and asympoic properies of he ime-varying AR()-GARCH(,), AR()-GJR(,) and AR()-EGARCH(,) models, and uses non-nesed esing procedures o discriminae beween GARCH and EGARCH, and beween EGARCH and GJR. Empirical resuls for he volailiies in he paens raio for he op foreign counries, and discriminaion based on non-nesed ess, are discussed in Secion 4. Some concluding remarks are given in Secion 5.. TRENDS AND VOLATILITIES IN PATENTS DATA. Daa The US economy has long been he larges marke in he world. For over wo cenuries, he USA has firmly adoped he paens sysem as a mechanism for proecion of inellecual propery and simulaion of innovaive aciviies. According o Goel (999), he paens sysem is suppored by governmen as a ool o correc marke imperfecions, hereby allowing imiaing firms o benefi from cosly echnologies developed
elsewhere. The sysem assures appropriabiliy of reurns o invenors, and benefis sociey by making he revealed informaion public knowledge afer he expiry of he paen. Paen laws were inroduced in he USA in he 78s. The US paens sysem has seadily araced inernaional companies and individuals ineresed in developing echnologies and esablishing rade links. In absolue numbers, he US PTO receives by far he larges number of foreign applicaions (Archibugi, 99). No surprisingly, close o 5% of all paens in he USA are graned o foreigners (Griliches, 99; Goel, 999), as will be seen in he discussion regarding Table below. There are, however, large variaions beween firms and counries in erms of wha coss hey can afford (such as paening fees) o proec heir invenions or o buy paens righs originaing elsewhere. This paper examines rends and volailiy in he paens raio, or US paens of he op foreign counries relaive o oal US paens. The foreign counries are lised in Table. The foreign counry wih he larges number of US paens is Japan, followed disanly by Germany and hen France. Of he op counries, he highes paen inensiy (or paens per capia) is held by Swizerland, followed by Japan, Sweden and Germany. 3 France and Ialy have numerous paens bu relaively low paen inensiies, whereas Swizerland and Sweden have relaively few paens bu high paen inensiies. The sample period seleced for he empirical analysis covers all graned paens wih daes of lodged applicaions beween January 975 and December 998 (inclusive), wih he daa exraced in April. Paens daa have been obained from he official Inerne webpage of he US PTO using he search engine available on he sie (hp://64.95../neahml/search-adv.hm), and populaion figures from (hp://www.census.gov/ ipc/www/idbprin.hml). The dae of lodgemen of graned applicaions for he ime series is used insead of he dae of issue of paens o avoid organisaional delays associaed wih he complicaed process of issuing a paen (which includes procedures such as A paen in he USA confers o he invenor a 7-year monopoly over he echnical idea(s) covered. However, a large number of paened invenions can remain dorman wihou ever reaching he innovaion sage (Oi, 995). Being an invenion of he neoclassical economic model, he paens sysem also incorporaes a number of deficiencies. For example, i has been used o esablish monopoly posiions in indusries, such as aluminum or shoe manufacuring (Mansfield, 993, 995). Paen fees can also be highly prohibiive, which can discriminae agains poenial applicans. The paens sysem canno accommodae a number of ehical and economic issues newly emerging from he scienific and echnological advances in he fields of bioechnology, pharmaceuical or informaion echnologies. Scochmer (99, p.4) describes he paens sysem as "a very blun insrumen rying o solve a very delicae problem." 3 The small economies of Liechensein and Monaco have higher paen inensiies han ha of Swizerland (Marinova, ), bu are no included in he analysis as heir paen numbers are very small. 6 examinaion, exper review, and appeals). Consequenly, he daa on paens by dae of applicaion represen more accuraely he process of commercial proecion for inellecual propery and innovaive oucomes from R&D. Alhough daa prior o 975 are also available, he US PTO search algorihm does no provide consisency wih he daa afer 975. In addiion, previous sudies have indicaed ha, during he 98s and 99s, he number of paens by foreign counries in he USA surged a an unprecedened rae (see, for example, Pael and Pavi, 995; Korum and Lerner, 999; Arundel and Kabla, 998). The US PTO updaes he informaion on paens graned on a fornighly basis. However, he ime from applicaion o he graning of a paen can be very long, and is esimaed o be wo years on average (Marinova, ). Thus, any daa on graned paens wih applicaion daes in 999 and will be incomplee for purposes of esimaing volailiies and conducing saisical ess. For his reason, daa from 975 o 998 are used in his paper.. Trends in Paens Daa Figures, and 3 show he annual rends in oal US paens and US paens held by foreign counries. All he counries exhibi increasing rends. However, he op performers can be divided ino wo groups. Group A includes Japan, France, Canada, Taiwan, (Souh) Korea and UK, all of which have much higher raes of increase in paening han hose in Group B (given below). Taiwan, Korea and he UK (and o a lesser exen, Canada) had high raes of increase in he 99s. Of paricular ineres are he wo Eas Asian counries which have sared o close he echnology gap wih he Wes. According o Pael and Pavi (998, p.59), echnology in Taiwan and Souh Korea is now aaining world bes pracice levels in an increasing number of fields a sriking example of echnological cach up compared wih he advanced counries. Group B consiss of Germany, Swizerland, Ialy, The Neherlands, Sweden and Ausralia. These counries have demonsraed a sable upward rend over he 3- year period, which is reasonably consisen wih he increase in he overall number of oal US paens. No surprisingly, he correlaions of US paens for he op counries and oal US paens are very high, in general, and are given in Tables and 3. As shown in Table 3, Canada is ranked firs wih a correlaion coefficien of.979, follow closely by France and Japan wih.9 and.96, respecively. Furhermore, correlaions wihin he op counries are also high, in general, as shown in Table. US paen regisraions from Taiwan and UK have he highes correlaion of.957, followed by Taiwan and Korea wih.96. Canada and France are ranked hird wih a correlaion coefficien of.93. Ineresingly, five of he six counries from Group A, namely Canada, France, UK, Korea and Taiwan, are highly correlaed among hemselves.
.3 Volailiies in Paens Raios The volailiies in he paens raios can be found in Figures 4, 5 and 6. Counries such as The Neherlands and Sweden are exremely volaile, especially in he lae 7s and early 8s. Asian counries such as Taiwan and Korea have low volailiies during he early periods, bu boh become volaile in he 9s, which can be viewed as anoher reflecion of echnological cach up (as suggesed in Pael and Pavi (998, p.59)). Volailiy clusering, as commonly found in financial daa, also appears o be a common feaure in he paens daa, paricularly for Ialy, The Neherlands, and Swizerland. Some counries, such as Ausralia, Korea, Taiwan and Japan also appear o have ouliers in he volailiies, which is anoher common feaure of financial ime series daa. Undoubedly, hese graphs provide srong suppor for he ime-varying naure of volailiies in paens raios, which jusifies he need for modelling condiional variances. 3. GARCH, GJR AND EGARCH The primary purpose of his secion is o obain an opimal model of he volailiy of he paens raio, namely he number of regisered US paens from a given foreign counry o he oal US paens. This new approach is based on Engle s (98) pah-breaking idea of capuring ime-varying volailiy (or risk) using he auoregressive condiional heeroskedasiciy (ARCH) model, and subsequen developmens forming he ARCH family of models (see, for example, he surveys of Bollerslev, Chou and Kroner, 99; Bollerslev, Engle and Nelson, 994; and Li, Ling and McAleer, ). Of hese models, he mos popular has been he generalised ARCH (GARCH) model of Bollerslev (986), especially for he analysis of financial daa. In order o accommodae asymmeric behaviour beween negaive and posiive shocks (or movemens in he ime series), Glosen, Jagannahan and Runkle (99) proposed he GJR model. Some furher developmens have been suggesed by Wong and Li (997), He and Teräsvira (999), and Ling and McAleer (a, b, c). Consider he AR()-GARCH(,) model for he paens raio, y : y = φ + φ + ε φ () y, < where he shocks (or movemens in he paens raio) are given by: ε = η h, () = + h ω αε βh, + and ω >, α, β are sufficien condiions o ensure ha he condiional variance h >, and η ~ iid(,). The ARCH (or α ) effec indicaes he shor run persisence of shocks, while he GARCH (or β ) effec indicaes he conribuion of shocks o long run persisence (namely, α + β ). 63 In equaions () and (), he parameers are ypically esimaed by he maximum likelihood mehod o obain Quasi-Maximum Likelihood Esimaors (QMLE) in he absence of normaliy of η. The condiional loglikelihood funcion is given as follows: l = log h + ε h Ling and Li (997) showed ha he GARCH(p,q) model is saionary and ergodic if E( ε ) <. Ling and McAleer (c) showed ha he QMLE for GARCH(p,q) is consisen if he second momen is finie, ha is, E( ε ) <. For GARCH(p,q), Ling and Li (997) demonsraed ha he local QMLE is asympoically normal if he fourh momen is finie, ha is, E( ε 4 ) <, while Ling and McAleer (c) proved ha he global QMLE is asympoically normal if he sixh momen is finie, ha is, E( ε ) <. Using resuls from Ling and Li (997) and Ling and McAleer (a, b) (see also Bollerslev (986), Nelson (99) and He and Teräsvira (999)), he necessary and sufficien condiion for he exisence of he second momen of ε for GARCH(,) is α + β < and, under normaliy, he necessary and sufficien condiion for he exisence of he fourh momen is ( α + β ) + α <. For he univariae GARCH(p,q) model, Elie and Jeanheau (995) and Jeanhau (998) esablished a weak sufficien condiion for consisency of he QMLE, and Boussama () derived asympoic normaliy under he same condiion. The sufficien condiion for he QMLE of GARCH(,) o be consisen and asympoically normal is given by he log-momen condiion, namely E (log( αη + β)) <. However, his condiion is no easy o check in pracice as i involves an unknown random variable and unknown parameers. The exension of his weak condiion o mulivariae models is paricularly complicaed (for furher deails, see Jeanheau (998)). Alhough he sufficien condiions for consisency and asympoic normaliy of he QMLE for univariae GARCH(p,q) given in Ling and Li (997) and Ling and McAleer (a, b), and for mulivariae GARCH(p,q) in Ling and McAleer (c), are sronger han he log-momen condiion, hey are also more sraighforward o check in pracice. The effecs of posiive shocks (or upward movemens in he paens raio) on he condiional variance, h, are assumed o be he same as he negaive shocks (or downward movemens in he paens raio) in he symmeric GARCH model. In order o accommodae asymmeric behaviour, Glosen, Jagannahan and Runkle (99) proposed he GJR model, which is defined as follows: h ω + α + γd ) ε βh, (3) = ( + 6
where ω >, α + γ, β are sufficien condiions for h >, and D is an indicaor variable defined by: D, =, ε < ε. The indicaor variable differeniaes beween posiive and negaive shocks, so ha asymmeric effecs in he daa are capured by he coefficien γ, wih γ >. The asymmeric effec, γ, measures he conribuion of shocks o boh shor run persisence, γ α +, and long run persisence, γ α + β +. Alhough he regulariy condiions for he exisence of momens for he GJR model are now known (Ling and McAleer, a), here are as ye no heoreical resuls regarding he saisical properies of he model. For GJR(,), Ling and McAleer (a) showed ha he regulariy condiion for he exisence of he second momen under symmery of η is α + β + γ <, and he condiion for he exisence of he fourh momen under normaliy of 3 is β + αβ + 3α + βγ + 3αγ + γ <. η An alernaive model o capure asymmeric behaviour in he condiional variance is he Exponenial GARCH (EGARCH(,)) model of Nelson (99), namely: log h ω log h, β <. (4) = + α η + γη + β There are some disinc differences beween EGARCH and he previous wo GARCH models, as follows: (i) EGARCH is a model of he logarihm of he condiional variance, which implies ha no resricions on he parameers are required o ensure h > ; (ii) Nelson (99) showed ha β < ensures saionariy and ergodiciy for EGARCH(,); (iii) Shephard (996) observed ha β < is likely o be a sufficien condiion for consisency of QMLE for EGARCH(,); (iv) as he condiional (or sandardized) shocks appear in equaion (4), i is likely ha β < is a sufficien condiion for he exisence of all momens, and hence also sufficien for asympoic normaliy of he QMLE of EGARCH(,). Furhermore, EGARCH capures asymmeries differenly from GJR. The parameers α and γ in EGARCH(,) represen he magniude (or size) and sign effecs of he condiional (or sandardized) shocks, respecively, on he condiional variance. However, α and α + γ represen he effecs of posiive and negaive shocks, respecively, on he condiional variance in GJR(,). As GARCH is nesed wihin GJR, a sandard asympoic es of H : γ can be used o discriminae beween = 64 he wo models. However, as EGARCH is non-nesed wih regard o boh GARCH and GJR, he non-nesed models are no direcly comparable. Ling and McAleer () proposed a simple non-nesed es o discriminae beween GARCH and EGARCH. Denoing GARCH as he null hypohesis and EGARCH as he alernaive, he opimal es saisic for H GARCH : δ = is given by: h = w + αε h gˆ + β + δ (5) where ĝ is he generaed one-period ahead condiional variance of EGARCH. For he reverse case, ha is, denoing EGARCH as he null hypohesis and GARCH as he alernaive, he opimal es saisic for H EGARCH : δ = is given by: log g = w + α η log g log hˆ + γη + β + δ (6) where ĥ is he generaed one-period ahead condiional variance of GARCH. Ling and McAleer () showed ha he QMLE of δ in boh (), () and (5) and (), () and (6) are asympoically normal under he respecive null hypoheses, and consisen under he respecive alernaive hypoheses. They also derived he power funcions of boh es saisics under he respecive hypoheses. I is also possible o develop non-nesed ess o discriminae beween EGARCH and GJR using a similar approach o he above. If EGARCH is he null hypohesis and GJR he alernaive, he es saisic for H EGARCH : δ = is given by: log g = w + α η log g log fˆ + γη + β + δ (7) where fˆ is he generaed one-period ahead condiional variance of GJR. Similarly, when GJR is he null hypohesis and EGARCH he alernaive, he es saisic for H : δ = is given by: GJR = w + αε + γd ε + βf + δ f log gˆ. (8) I can be shown ha he QMLE of δ in boh (), () and (7) and (), () and (8) are asympoically normal under he respecive null hypoheses, and consisen under he respecive alernaive hypoheses. 4. EMPIRICAL RESULTS 4. Esimaion This secion models he volailiy of he paens raio, or US paens by he op foreign counries relaive o oal US paens. The AR()-GARCH(,), AR()- GJR(,) and AR()-EGARCH(,) models, as defined in ()-(), ()-(3) and ()-(4), respecively, are esimaed using daa for he op foreign counries in he USA. The esimaes for he hree models are given in Tables 4, 5 and 6, respecively. 4.. AR()-GARCH(,) The esimaed parameers, and hence condiional volailiies, in Table 4 vary wildly across counries. When he esimaes of α and/or β are negaive, his
will no guaranee ha he esimaed volailiy is posiive. However, unless oherwise saed, all models which fail o saisfy he sufficien condiions for h > in his paper neverheless yield posiive esimaes of condiional volailiy, as required. Three counries fail o saisfy he second momen condiion for GARCH, namely, France, Korea and Taiwan, alhough he failure is only marginal for he firs wo counries. Five counries fail o saisfy he fourh momen condiion, namely France, UK, Korea, Sweden and Taiwan, wih he resul for Taiwan arising from an exremely high esimaed α (or shor run persisence). Ineresingly, all Asian counries have high esimaed α values, and relaively low esimaed β values, which reflec high levels of shor run persisence. The dramaic growh in regisered paens in hese counries is consisen wih he rapid economic growh in Asian counries in he 98s and 99s. Two counries have negaive esimaes of β, indicaing ha GARCH may no be an appropriae model. I is ineresing o noe ha he LM es proposed in Engle (98) and Bollerslev (986) did no rejec he null hypohesis of no GARCH effecs, bu subsequen resuls showed ha Ausralia had a significan asymmeric GARCH effec. Ialy also has a negaive esimae of β. Thus, even hough hese wo counries saisfy he second and fourh momen condiions, he GARCH model does no seem o be appropriae as i is possible o obain negaive condiional variances. Anoher ineresing feaure is ha he α and β esimaes for oher European counries, such as France, Germany, UK, The Neherlands and Sweden, are reasonably similar in magniude o hose in convenional financial ime series. 4.. AR()-GJR(,) The number of counries failing o saisfy he second momen condiion in Table 5 has decreased o hree, namely UK, The Neherlands and Taiwan, wih only Taiwan being exreme, arising from an excessively high shor run persisence in shocks. As menioned previously, he LM es failed o rejec he null hypohesis of no GARCH effecs for Ausralia. However, under he assumpion of normaliy, he - saisic for he esimae of γ in he GJR model for Ausralia is highly significan. Furhermore, he β esimae is now posiive, hough insignifican, and he α esimae is also saisically insignifican. These resuls sugges ha only negaive shocks will have a significan impac on volailiy, whereas he impac of posiive shocks is minimal. A similar inerpreaion holds for The Neherlands. Alhough he esimaes of he GARCH model for The Neherlands saisfy he second and fourh momen condiions, he esimaes from he more general GJR model fail o saisfy eiher 65 of he momen condiions. Moreover, he magniude of he γ esimae is much higher han ha of he α esimae. I would seem ha negaive shocks have far more significan impacs on he condiional variances han do posiive shocks. Furhermore, four counries have negaive esimaes of γ, namely, France, Ialy, Japan and Korea, bu only France and Ialy fail o saisfy he condiion ha α + γ >, which implies ha he posiiviy of he condiional variances is no guaraneed. If normaliy of he esimaes is assumed, hen he γ esimaes are no significan for France and Japan, bu are highly significan for Ialy and Korea. The β esimae for Ialy is now posiive, which implies ha he sign of he esimaes arising from hese models can provide imporan informaion regarding model misspecificaion. This is an ineresing area for fuure research. 4..3 AR()-EGARCH(,) As shown in Table 6, all he β esimaes from EGARCH for all counries are less han one in absolue value, which suggess ha all momens exis, wih he esimaes likely o be consisen and asympoically normal. There is no resricion on he parameer esimaes for condiional volailiy o be posiive, as EGARCH is a model of he logarihm of he condiional variances. Overall, he size effecs have posiive impacs on he condiional variances excep in wo cases, namely France and Ialy. Furhermore, he γ esimaes of hese wo counries, along wih Korea, are higher han for he corresponding α esimaes. This indicaes ha he sign effecs have larger impacs han size effecs on he condiional variances. I is also imporan o noe ha none of he hree models is adequae for he UK. Apar from failing he fourh momen condiion for GARCH(,), as well as he second and fourh momen condiions for GJR(,), EGARCH(,) does no seem o be idenifiable for he UK as he α and γ esimaes are no saisically significan. As Engle s (98) LM es does no rejec he null hypohesis of no ARCH effec for he UK, a possible explanaion is ha here is no ARCH or GARCH effec in he series.. 4. Model Discriminaion Model discriminaion beween GARCH and EGARCH and beween GJR and EGARCH can be underaken by using he non-nesed esing procedures proposed in Ling and McAleer (), and discussed in Secion 3 above. Table 7 shows he resuls of wo ses of nonnesed ess, namely GARCH versus EGARCH and GJR versus EGARCH.
As shown in Table 7, he es fails o discriminae beween GARCH and EGARCH for six counries, namely, France, The Neherlands, Sweden, Swizerland, Taiwan and he UK. Excep for Germany, which favours GARCH, EGARCH is favoured for he remaining six counries. Moreover, in discriminaing beween EGARCH and GJR, EGARCH is favoured for five counries, namely Canada, France, Germany, Japan, and The Neherlands. The non-nesed ess, however, fail o discriminae beween EGARCH and GJR for he remaining seven counries, which may indicae low power of he es. I is ineresing o noe ha he nonnesed ess do no provide srong suppor for GJR for any of he counries. I would seem ha he bes model for boh Canada and Japan is EGARCH. However, he non-nesed ess did no provide a definiive conclusion regarding he remaining en counries, which may arise from he presence of ouliers in he series. I is imporan o noe ha none of he hree models was designed o accommodae exreme observaions and/or ouliers. I is well known ha hese observaions have significan impacs on he QMLE (see for example, Verhoeven and McAleer (999)), which can subsequenly affec he performance of he non-nesed ess. Therefore, appropriae mehods of accommodaing hese observaions are imporan in order o apply hese ess more efficaciously. 5. CONCLUDING REMARKS The paper analysed he rends and volailiies in regisered US paens for he op foreign paening counries from 975 o 998. The ime-varying volailiy of he paens raio, namely US paens lodged by each of he op foreign counries relaive o oal US paens, was examined using monhly daa from he US PTO. Based on he momen condiions, significance of he esimaes and discriminaion using non-nesed ess, he asymmeric AR()-GJR(,) model was found o be suiable for Ausralia, while he bes model for Swizerland and The Neherlands was he symmeric AR()-GARCH(,). An alernaive asymmeric model, AR()-EGARCH(,), was found o be suiable for Canada, France, Germany, Ialy, Japan, Korea, Sweden and Taiwan. Fuure research migh focus on he effecs of exreme observaions and ouliers on he esimaes and diagnosic ess of hese models. Appropriae mehods o accommodae such observaions would be helpful in modelling hese series more accuraely and efficienly. 6. ACKNOWLEDGEMENTS The firs auhor wishes o acknowledge he financial suppor of he Ausralian Research Council. The second auhor acknowledges he financial suppor of an Ausralian Posgraduae Award and an Individual Research Gran a he Universiy of Wesern Ausralia. The hird auhor is mos graeful for he financial suppor of he Ausralian Research Council and he Deparmen of Economics a he Universiy of Wesern Ausralia. 7. REFERENCES Archibugi, D., Paening as an indicaor of echnological innovaion: a review, Science and Public Policy, 9(6), 357-368, 99. Archibugi, D. and M. Piana, Aggregae convergence and secoral specialisaion in innovaion: evidence for indusrialised counries, in D. Archibugi and J. Michie (eds.), Trade, Growh and Technical Change, Cambridge Universiy Press, Cambridge, -4, 998. Arundel, A. and I. Kabla, Wha percenage of innovaions are paened? Empirical esimaes from European firms, Research Policy, 7(), 7-4, 998. Bollerslev, T., Generalised auoregressive condiional heeroskedasiciy, Journal of Economerics, 3, 37-37, 986. Bollerslev, T., R. Y. Chou and K. F. Kroner, ARCH modelling in finance: a review of he heory and empirical evidence, Journal of Economerics, 5, 5-59, 99. Bollerslev, T., R. F. Engle and D. B. Nelson, ARCH models, in R. F. Engle and D. L. McFadden (eds.), Handbook of Economerics, 4 (Norh-Holland, Amserdam) 96-338, 994. Boussama, F., Asympoic normaliy for he quasimaximum likelihood esimaor of a GARCH model, Compes Rendus de l Academie des Sciences, Serie I, 33, 8-84, 995 (in French). Crampes, C. and C. Langinier, Informaion disclosure in he renewal of paens, in D. Encaoua e al. (eds.), The Economics and Economerics of Innovaion, Kluwer Academic Publishers, Boson, 43-66,. Dugue, E. and I. Kabla, Appropriaion sraegy and he moivaions o use he paen sysem: an economeric analysis a he firm level in French manufacuring, in D. Encaoua e al. (eds.), The Economics and Economerics of Innovaion, Kluwer Academic Publishers, Boson, 67-35,. Elie, L. and T. Jeanheau, Consisency in heeroskedasic models, Compes Rendus de l Academie des Sciences, Serie I, 3, 55-58, 995 (in French). 66
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Counry US Paens Paen Inensiy* Ranking by Paen Inensiy Japan 49,8 3,45 Germany 7,875,76 4 3 France 7,595,33 8 4 Canada 5,354,79 5 5 Swizerland 34,684 4,8 6 Ialy 3,3 57 7 Taiwan (China) 8,647,33 7 8 Neherlands 4,46,558 6 9 Sweden,96,589 3 Unied Kingdom,5 373 Korea,59 433 Ausralia,734 678 9 US Paens by Top 9,5,589 Toal US paens,397,49 - US Paens by Top Relaive o Toal US Paens 38.4% - Table. US Paens and Paen Inensiy for Seleced Counries, January 975 December 998 (as a 4 April ) * Paen inensiy denoes US paens per million of 998 populaion Source of daa: hp://64.95../neahml/search-adv.hm and hp://www.census.gov/ipc/www/idbprin.hml Counry Ausralia Canada France Germany Ialy Japan Korea Neherlands Sweden Swizerland Taiwan UK Ausralia..86.775.75.769.8.739.738.66.55.783.784 Canada.86..93.74.844.89.84.877.758.65.887.893 France.775.93..77.897.85.76.859.78.69.774.788 Germany.75.74.77..747.877.65.7.835.45.685.69 Ialy.769.844.897.747..857.694.88.67.57.744.744 Japan.8.89.85.877.857..775.848.75.45.83.86 Korea.739.84.76.65.694.775..785.739.43.96.899 Neherlands.738.877.859.7.88.848.785..73.56.789.83 Sweden.66.758.78.835.67.75.739.73..466.74.787 Swizerland.55.65.69.45.57.45.43.56.466..49.49 Taiwan.783.887.774.685.744.83.96.789.74.49..957 UK.784.893.788.69.744.86.899.83.787.49.957. Table. Correlaion Coefficiens Beween he Top Foreign Counries 68
Counry Toal Ausralia.839 Canada.979 France.9 Germany.76 Ialy.863 Japan.96 Korea.864 Neherlands.887 Sweden.77 Swizerland.634 Taiwan.899 UK.898 Table 3. Correlaion Coefficiens of he Top Foreign Counries wih Toal US Paens Counry ω α β nd Momen 4 h Momen Ausralia.3E-6.65 -.384 -.39. (.857) (.83) (-.587) Canada 7.6E-7.5.79.84.74 (.8) (.8) (3.64) France -.63E-7.8.98.8.8 (-4.43) (6.) (4.776) Germany.5E-6.5.93.975.956 (.49) (.5) (6.5) Ialy.E-5.8 -.96 -.778.638 (.6) (4.76) (-.949) Japan..33.445.776.8 (.88) (.36) (.) Korea.37E-7.33.69.4.5 (.873) (.63) (4.798) Neherlands.E-8.5.944.995.996 (.55) (.96) (9.63) Sweden.E-7.9.868.986. (.43) (.783) (5.45) Swizerland.95E-8.5.937.99.985 (.737) (3.6) (44.33) Taiwan.73E-9.758.56.84.795 (.39) (5.79) (9.67) UK.59E-8.46.849.995.34 (.748) (.96) (7.73) Table 4. GARCH(,) Esimaes for he Top Foreign Counries (-raios are in parenheses) Counry ω α γ β Ausralia Canada nd Momen 4 h Momen.3E-6..48.35.4.4 (3.359) (.) (.33) (.7).76E-6 -.84.69.594.644.4 (.88) (-5.7) (.636) (3.88) France.3E-6.86 -.4.869.884.783 Germany (.555) (.38) (-.739) (.57) 3.45E-5.46.34.63.785.669 (.496) (.44) (.69) (.98) Ialy 6.36E-7.97 -.83.86.868.754 (.5) (.6) (-3.3) (3.985) Japan.5E-5.65 -.64.698.93.976 (.677) (3.385) (-.668) (8.56) Korea.4E-7.394 -.574.843.95.97 (3.37) (5.7) (-6.63) (7.67) Neherlands -3.98E-8..3.999.5.3 (-3.743) (.6) (4.74) (4.774) Sweden 5.4E-8.9.8.96.993.3 Swizerland (.349) (.64) (.46) (7.38).49E-8.3.37.947.996.996 (.349) (.7) (.7) (39.758) Taiwan.76E-9.735.4.57.8.785 (.47) (3.766) (.55) (9.) UK.399E-8.73.99.8.44.87 (.587) (.8) (.78) (6.49) Table 5. GJR(,) Esimaes for he Top Foreign Counries (-raios are in parenheses) 69
Counry ω α γ β Ausralia -4.36.8 -.48.684 Canada (-.647) (.85) (-.859) (.38) -.9.94 -.5 -.86 (-4.59) (.4) (-.857) (-6.7) France -6.65 -.5.73.46 Germany (-.85) (-.8) (3.387) (.946) -5.644.56 -. -.546 (-.553) (3.59) (-.9) (-3.57) Ialy -3.55 -.3.373.73 (-4.49) (-.77) (4.89) (.735) Japan -.67.584.8.754 (-3.4) (6.4) (.7) (7.99) Korea -8.79.5.976.87 (-.383) (.5) (9.947) (7.96) Neherlands -.353.7..979 (-.796) (.849) (.59) (9.8) Sweden -5.7.478.37.63 Swizerland (-.487) (.94) (.49) (4.4) -6.454.4 -.3.54 (-.538) (3.36) (-.65) (.554) Taiwan -3.87.4 -.78.768 (-.4) (8.354) (-.77) (7.83) UK -8.3.3.6.363 (-.9) (.864) (.86) (59.4) Table 6. EGARCH(,) Esimaes for he Top Foreign Counries (-raios are in parenheses) Counry H : GARCH H : EGARCH A H : EGARCH H : GARCH A H : EGARCH H : GJR A H : GJR H : EGARCH Ausralia.4658.368.5797 -.8668 Canada 8.3346.686.4668 5.5633 France.8839 3.9.7849 8.6868 Germany.633 3.89.7944 3.378 Ialy 6.63.63.59 5.675 Japan 5.8698.864.86 3.6386 Korea.9693.587.34 3.5734 Neherlands.6.463.974.969 Sweden 4.96.37.546 5.537 Swizerland.73 5.337 5.69.4745 Taiwan 5.937 3.3539 3.698 7.745 UK 4.7 3.39.9485 9.34 Table 7. Non-nesed Tess of GARCH versus EGARCH and GJR versus EGARCH (he enries in columns -5 are he calculaed -raios from equaions (5)-(8), respecively). 7 A
3 5 5 5 5 4 3 9 75 9 8 985 99 99 5 TOTAL Japan G e rmany Figure. Toal US Paens and US Paens held by Japan and Germany, by Dae of Applicaion, 975-998 9 8 7 6 5 4 3 France 8 7 6 5 4 3 Canada 35 3 5 5 5 Swizerland 35 3 5 5 5 6 5 4 3 Ialy Taiwan Figure. US Paens held by France, Canada, Swizerland, Ialy and Taiwan, by Dae of Applicaion, 975-998 4 6 8 4 5 5 5 5 4 3 The Neherlands Sweden UK 7 6 5 4 3 6 8 4 Korea Ausralia Figure 3. US Paens held by The Neherlands, Sweden, UK, Korea and Ausralia, by Dae of Applicaion, 975-998 7
.6.5.4.3... Japan.7.6.5.4.3... Germany Figure 4. Volailiy of US Paens Raios of Japan and Germany, by Dae of Applicaion, 975-998.6..8.4. France.8.7.6.5.4.3... Canada.5.4.3... Swizerland.8.7.6.5.4.3..6..8... Ialy.4. Taiwan Figure 5. Volailiy of US Paens Raios of France, Canada, Swizerland, Ialy and Taiwan, by Dae of Applicaion, 975-998.4..6..8.4. The Neherlands.36.3.8.4..6..8.4. Sweden.7.6.5.4.3... UK.5.4.3...6.5.4.3... Korea. Ausralia Figure 6. Volailiy of US Paens Raios of The Neherlands, Sweden, UK, Korea and Ausralia, by Dae of Applicaion, 975-998 7