Tom-Reiel Heggedal and Karl Jacobsen

Transcription

1 Dicuion Paper No. 536, April 2008 Statitic Norway, Reearch Department Tom-Reiel eggedal and Karl Jacoben Timing of innovation policie when carbon emiion are retricted: an applied general equilibrium analyi Abtract: Thi paper tudie the timing of ubidie for environmental reearch and development (R&D) and how innovation policy i influenced by the cot of emiion. e ue a dynamic computable general equilibrium (CGE) model with both general R&D and pecific environmental R&D. e find two reult that are important when ubidizing environmental R&D in order to target inefficiencie in the reearch market. Firtly, the welfare gain from ubidie i larger when the cot of emiion are higher. Thi i becaue a high carbon tax increae the ocial (efficient) invetment in environmental R&D, in exce of the private invetment in R&D. Secondly, the welfare gain i greater when there i a falling time profile of the rate of ubidie for environmental R&D, rather than a contant or increaing profile. The reaon i that the innovation externalitie are larger in early period. Keyword: Applied general equilibrium, endogenou growth, reearch and development, carbon emiion. JEL claification: E62, 3, O38, Q55 Acknowledgement: The author would like to thank Birger Strøm for excellent computer aitance in coding and calibrating the model. e would alo like to thank Geir. Bjertnæ, Brita Bye, Taran Fæhn, Snorre Kverndokk, and Knut-Einar Roendahl for ueful comment. Finally, we gratefully acknowledge financial upport from the Norwegian Reearch Council program SAMSTEMT and RENERGI. Addre: Tom-Reiel eggedal, Statitic Norway, Reearch Department. tom@b.no

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3 . Introduction In the coming decade, indutrialized countrie will have to face large reduction in emiion of greenhoue gae (GG) to curb anthropogenic interference with the global climate ytem. Thi may be through retriction tipulated in international agreement under the United Nation Framework Convention on Climate Change or through apirational goal and voluntary reduction of individual countrie. Norway i at the forefront of planning unilateral GG reduction, with a goal of being carbon neutral by The EU ha implemented legilative meaure to cut emiion by 20 percent from 990 level by 2020; thi reduction will increae to 30 percent if other indutrialized countrie follow. In the US and Canada, everal tate are involved in regional cap-and-trade program, uch a the etern Climate Initiative and the Regional Greenhoue Ga Initiative. California ha taken a leaderhip role, with a goal of reducing GG emiion by 80 percent by 2050, compared with 990 level. One expect that a variety of policy meaure will be needed to achieve the cut in GG. Mot likely thee will include a cap-and-trade ytem that give a price to carbon emiion, like the European Trading Scheme, and a policy to improve clean energy technology like power production with carbon capture and torage (CCS). The mot cot-efficient ingle policy to reduce emiion i an environmental policy that directly target emiion, uch a a tax or cap-and-trade ytem. owever, in the preence of induced technological change and market failure in R&D, a combination of environmental and innovation policie may be more cot effective. 2 Jaffe et al. (2005) argue that market failure aociated with environmental pollution interact with market failure aociated with the innovation and diffuion of new technologie. Thee combined market failure provide a trong rationale for a portfolio of public policie to foter emiion reduction a well a the development and adoption of environmentally beneficial technology. Key argument for ubidizing innovation activitie are external pillover from previou R&D and love of capital variety in demand, combined with inefficiencie ariing from imperfect competition in the capital variety market. 3 The market inefficiencie imply that the private return from environmental R&D are lower than the ocial return, which lead to underinvetment in environmental R&D. Thi underinvetment i the rationale for ubidizing R&D activity. Several environmental economic R&D model include pecific policie to target inefficiencie in innovation market. A typical policy i providing a contant ubidy for R&D. 4 owever, the optimal ubidy rate would not necearily be contant over time. art (2008) find that the gap between ocial and private return from R&D invetment may vary acro time along a tranition path. e implement optimal econd-bet carbon taxe, which may be higher than the Pigouvian level outide the balanced growth path in order to encourage invetment in emiion-aving technology at the expene of ordinary production technology. art (2008) doe not tudy the implication thi ha for firt-bet environmental R&D ubidie. Thi paper add to the literature by tudying the timing and impact of environmental R&D ubidie when future emiion are limited, e.g., by a binding international agreement See Schneider and Goulder (997), Popp (2006), Parry et al. (2003). 2 See Schneider and Goulder (997), Goulder and Schneider (999), Roendahl (2004), Ficher and Newell (2008), Otto et al. (2006). 3 See Jone and illiam (2000). 4 See Gillingham et al. (2007) for a urvey of induced technological change in climate policy modeling. 3

4 implemented via a carbon tax. In our model, emiion are reduced through a carbon tax that repreent the full cot of emiion. Thi mean that the R&D policy only target innovation externalitie, and not environmental externalitie. e ak two quetion. Firtly, we ak whether the welfare gain from environmental R&D ubidie are larger when the future cot of emiion are higher. Raiing the cot of emiion caue an increae in the ocial value of R&D in environmental technologie. Thi may only partly be captured by private firm and thu change the welfare gain from ubidizing R&D. Secondly, we ak if welfare gain would be greater with heavy ubidization of environmental R&D in early period, rather than ubidization at a contant level. Thi timing problem of R&D ubidie ha not received much attention in the literature, to our knowledge. Rather than tudying optimal policy directly, we focu on market repone to a et of policie. e tudy the welfare gain from ubidizing environmental R&D when emiion are reduced through a given et of carbon taxe. e find two reult that are important when ubidizing environmental R&D in order to target inefficiencie in the reearch market. Firtly, the welfare gain from R&D ubidie are larger when the emiion reduction are larger. Thi i becaue tricter emiion reduction require a high carbon tax, which implie that the underinvetment in environmental R&D increae. hen the underinvetment increae a ubidy to R&D give more welfare. Thi reult indicate that there i an interaction between the cot of emiion and the gain from ubidizing environmental R&D. Thi i not oppoed to the conventional widom of de-linking climate policy from R&D policy, i.e., that in a firt-bet world, there hould be a carbon tax to target the environmental externality and an R&D ubidy to correct for innovation externalitie. 5 Rather, the reult mean that optimal innovation policy i influenced by the carbon tax, ince the tax influence the innovation externalitie. Greaker and Roendahl (2006) find a imilar reult in a three-tage game between the government, polluting indutrie, and upplier of abatement technology. They find that an R&D ubidy i a trategic complement to a tringent environmental policy. The reaon i that when environmental policy i more tringent, there i an increae in inefficiencie ariing from imperfect competition in the upply of abatement technology. owever, they do not take into account intertemporal inefficiencie, e.g., knowledge pillover. Secondly, we find that the welfare gain are greater when there i a falling time profile for the ubidy rate for environmental R&D, rather than a contant or increaing rate, when the economy i ubject to emiion retriction. Thi mean that, when facing increaed carbon price, it i better policy to ubidize environmental R&D more heavily initially than to ditribute policy incentive evenly acro time. The reaon for thi i that underinvetment i greatet in early period. Gerlagh et al. (2008) alo tudy the optimal timing of R&D ubidie; however, they tudy inefficiencie in the R&D market related to limited patent lifetime. In our model, patent lifetime i infinite and not the ource of underinvetment in R&D. Externalitie from knowledge pillover which are included in thi paper are not included in their tudy. They find that the externality related to finite patent lifetime make the optimal R&D ubidy fall over time. The reaon i that the value of abatement increae rapidly in the beginning a the carbon tax increae. The early innovator get a maller hare of the benefit from thi increae than late innovator, ince patent lifetime i finite. In another tudy, Kverndokk and Roendahl (2007) find that optimal technology ubidie alo decreae over time, ince newly adopted technologie have higher pillover than older technologie. 5 In a econd-bet ituation where, e.g., only environmental policy, and not innovation policy, i et optimally, the de-linking break down. In thi cae, the innovation externalitie call for an environmental tax that exceed the Pigouvian level. See Parry (995), Nordhau (2002), and art (2007). 4

5 Their technology externalitie, however, come from learning effect, a oppoed to R&D externalitie in our paper. hen learning effect are preent, the technology ha to be implemented in order to reduce the future cot of the technology. Thi i not the cae in R&Ddriven model, a the development of the technology can be eparated from implementation. In uch model, it i efficient to conduct R&D in early period and implement the technology later, when cot are driven down. Goulder and Mathai (2000) how that the preence of R&D i an argument for delaying the implementation of abatement technology; the preence of learning by doing, on the other hand, may be an argument for immediate abatement action. In order to tudy quantitatively how future emiion reduction will influence the gain from ubidizing environmental R&D, we develop a dynamic CGE model with both general and pecific environmental R&D. The model i theoretically founded in the product-variety model by Romer (990), in which technological change happen a a reult of patent by profitmaximizing R&D firm. In addition, we take into conideration the high reliance of mall, open economie on externally et international price, competition, and growth. The cae of a mall, internationally expoed economy i exemplified by the Norwegian economy. Section 2 decribe the CGE model and the imulation and calibration procedure. The policy effect and enitivity tet are preented and dicued in Section 3. Section 4 conclude. 2. The model 2. General feature The CGE model i a dynamic growth model with intertemporally optimizing firm and houehold. The model replicate a detailed indutry tructure with two R&D indutrie, two variety-capital indutrie (Romer intermediate indutrie) and 9 final good indutrie 6 (one public, 8 private; ee Appendix A for a lit). The final good indutrie deliver good to each other according to the empirical input output tructure. Growth i perpetuated through dynamic pillover from the accumulated knowledge temming from R&D production, though with decreaing return, a in Jone (995). R&D production create new patent. The patent production take place in two indutrie, one directed toward general technology, and the other toward environmental technology. The patent are bought by firm in the two variety-capital indutrie. Each patent repreent a fixed entry cot for a capital variety firm, and give that firm a monopoly on the production of a eparate capital variety. Due to love of capital variety, the productivity of variety capital within final good indutrie increae with the number of capital variety firm. The model preented in thi paper i an extenion of that of Bye et al. (2007) in three dimenion. Firtly, GG emiion are included. Emiion from both conumer and producer are ubjected to a carbon tax that i et in accordance with an emiion-reduction target. Secondly, we develop a detailed electricity market with everal power-producing indutrie. Finally, we include environmental R&D directed at improving the technology for clean power production. Thi environmental technology develop eparately from general technology ued by the other indutrie in the economy. 7 6 The following indutrie are treated exogenouly: the government ector, offhore production of oil and ga, pipeline tranport, and ocean tranport. 7 Otto and Reilly (2006) develop a imilar model but tudy different policy quetion to our. 5

6 The model fit a mall, open economy and i applied to Norway. It give a detailed decription of the empirical tax, production, and final conumption tructure. Labor i perfectly mobile within the country, but immobile internationally. Other input, including invetment good, are internationally traded at given world-market price. Import are modeled a imperfect ubtitute for dometically produced good (Armington function), and export deliverie a imperfect ubtitute for home-market deliverie (contant elaticity of tranformation CET technology). Both aumption imply that the trade volume are determined by the ratio of dometic to world-market price. The world-market price are exogenou, while dometic price are determined by the repective market equilibrium. The interet rate i alo externally given. Financial aving are endogenouly determined, ubject to a non-ponzi game retriction that prevent foreign net wealth from exploding in the very long run. In the following, we broadly preent key element of the model tructure, with function and equation lited in Appendix B. See Bye et al. (2008) for a detailed decription of the model. 2.2 Indutrie Final good indutrie e aume that all firm within the final good indutrie are identical and take price a given by the factor and good market, dometically and abroad. The technology of production i given by contant elaticity of ubtitution (CES) function. The entire neted input factor tree of CES aggregate i preented in Appendix C. Each firm ha perfect foreight and maximize the preent value of after-tax cah flow. Thi give firt-order condition that equate price with marginal cot for deliverie to the repective market. Productivity change in the final good indutrie come from two ource, one foreign and one dometic. There i an exogenouly driven factor-productivity change from abroad, which repreent the adoption of international technological change. Thi i aumed to be neutral acro factor and indutrie and to increae the efficient input of each factor. The dometic ource of productivity change i the capital varietie ued in production. The input of capital varietie i repreented by o-called Spence-Dixit-Stiglitz (love-of-variety) preference for variety. Thi mean that the variety-capital productivity within final good indutrie increae with the number of inputted varietie. Production of R&D ervice There are two R&D indutrie, one general and one environmental. The environmental technology in thi tudy i exemplified by ga power production with CCS. Thi technology enable power production with low GG emiion. More low-emiion technologie could have been included, but thi i unneceary for analyzing how the cot of emiion influence the impact and optimal timing of environmental R&D ubidie. Moreover, ga power production with CCS i a hot technology in Norway, and plant with full-cale carbon extraction are cloe to realization. The general R&D indutry deliver new patent to dometic firm that wih to enter the general variety-capital indutry, while the environmental R&D indutry deliver new patent to dometic firm that wih to enter the CCS variety-capital indutry. The firm in the R&D indutrie have the ame neted CES production technology a the final good indutrie, 6

7 except that the R&D indutrie do not ue the differentiated capital varietie. 8 A for final good production, the exogenou change in factor productivity capture the adoption of international technological change. In addition, productivity i enhanced by endogenou dometic pillover that are freely acceible by all incumbent and potential patent producer. Thee originate from the accumulated tock of knowledge. Thi tock of knowledge grow with the production of new patent. owever, the elaticity of cale related to previou knowledge mean that the pillover effect of the knowledge bae decreae with time. Thi mean that the productivity gain for future R&D from a new patent i declining a the knowledge tock grow. There are no pillover in knowledge between general and environmental R&D. All firm in the two R&D indutrie are identical and take price a given in factor and output market. Each firm ha perfect foreight and maximize the preent value of the after-tax cah flow. Thi give firt-order condition that equate dometic price with marginal cot. Production of capital varietie A for the R&D indutrie, there are two capital-variety indutrie, general and environmental. Each firm producing capital variety buy one patent from one of the R&D indutrie a a fixed etablihment cot, and produce one capital variety that i baed on the patent. The general indutry deliver capital varietie to all final good indutrie except the ga power indutry with CCS. The directed environmental indutry deliver only to the ga power indutry with CCS. e aume that the cot tructure i identical for all the firm within the indutrie. A for the R&D indutrie, we exclude variety capital a a production factor. Technological change from abroad i accounted for through the exogenou productivity change, therefore we do not allow for additional productivity growth through the import of capital varietie. The capital-variety firm have market power in the dometic market. Thi give a monopolypricing rule that i a markup factor above marginal cot. The firm exhibit no market power in the export market, where price are externally given. Thi i a reaonable aumption for a mall, open economy. Each firm ha perfect foreight and maximize the preent value of after-tax cah flow. The patent price in each period (etablihment cot) i determined from the free-entry condition in the capital-variety market. Firm enter their repective capital-variety indutry until the repreentative firm total dicounted net profit equal the entry cot. In each period, new patent are produced and new firm will enter the variety-capital indutrie. Production of electricity There are three power-producing indutrie: hydropower, ga power without CCS, and ga power with CCS. Thee three indutrie are modeled like the other final good indutrie, with three exception. Firtly, they produce the ame good, namely electricity, with a homogenou price. Sale of electricity to demander i organized by the ditribution indutry. Thi indutry charge ditribution and tranmiion cot that may vary between demander. Secondly, the net export of electricity i exogenou. Thi mean that the price of electricity i et in the dometic market. Thirdly, the production of hydropower i exogenou. Since the unit cot of production in hydropower i relatively low, thi indutry earn high profit, which are to be undertood a a natural reource rent that i committed to taxation. 8 Thi choice i made to avoid cumulative multiplier of the love-of-variety effect. 7

8 The ga power indutrie adjut their production according to normal optimization. To avoid zero production in one of thee indutrie ariing from their having unequal production cot we aume that ga power with and without CCS are cloe but imperfect ubtitute. 9 The total upply of electricity from ga power production i a CES aggregate of ga power with and without CCS. 2.3 Emiion Emiion of GG 0 are baed on factor input to conumer activitie and production in all indutrie. The ue of factor input i converted into emiion according to activity- and indutry-pecific technical parameter, ee Bye et al. (2008). Emiion are converted into CO 2 equivalent, and a uniform tax i impoed on them. Thi carbon tax can be een a either a direct tax or a quota price in a well functioning market. Either way, the tax can be thought of a repreenting the marginal cot of emiion for the economy, where the cot may reult from international agreement or dometic target. The environmental impact of emiion are not included in the model. 2.4 Conumer behavior Conumption and aving reult from the deciion of a repreentative conumer with an infinite lifetime who maximize intertemporal utility with perfect foreight. The conumer chooe a conumption path ubject to an intertemporal budget contraint that require the preent value of conumption not to exceed total wealth (preent non-human wealth plu the preent value of labor income and net tranfer). The labor upply i exogenou. e aume that the conumer rate of time preference equal the exogenouly given nominal interet rate for the entire time path. Total conumption i allocated acro 0 different good and ervice according to a neted CES tructure. The tructure i given in Figure D., Appendix D. 2.5 Equilibrium condition The model i characterized by equilibrium in each period in all product market and the labor market. It alo incorporate a detailed account of the revenue and expenditure of the government. The government produce ervice and purchae intermediate from the indutrie and abroad. Change in government budget are neutralized by lump-um tranfer. Intertemporal equilibrium require fulfillment of two tranverality condition: the limit of the total dicounted value of net foreign debt and real capital mut both be zero. The model i characterized by a path-dependent balanced growth path olution (or teady-tate olution). Thi implie that both the path and the long-run tationary olution differ between imulated cenario. 9 Thi i technically motivated: it i to avoid problem connected with zero production when olving the model. 0 The GG included in the model are: carbon dioxide, methane, nitrou oxide, ulfur hexafluoride, hydrofluorocarbon, and perfluorocarbon. 8

9 2.6 Data and parameter The model i calibrated to the 2002 Norwegian National Account. The elaticity of ubtitution between the different capital varietie i aumed to be 5.0, giving a markup factor of.25 for the dometic price of capital varietie. The elaticity of cale related to previou knowledge i equal to 0.4, in order to enure decreaing pillover effect of the knowledge bae, upported by both theoretical and empirical finding (ee Jone, 995 and 999; Leahy and Neary, 999). See Appendix B.6 for an overview of elaticitie of ubtitution and other parameter value. The technical parameter that calculate emiion from factor input and conumer activitie are taken from Strøm (2007). Emiion are pread over indutrie and conumer in line with Strøm (2007), which give total emiion from the Norwegian economy in 2002 correponding to 56. million tonne of CO 2 equivalent. In 2008, there i one ga power plant in operation and one under contruction in the Norwegian economy. 2 Several other plant are planned. Not one of thee plant will initially incorporate CCS technology. owever, the political majority in Norway have apirational goal of ga power production with low GG emiion. Therefore, the plant have timetable for the eventual full-cale extraction of CO 3 2. Thee plan to implement CCS technology are joint project with the government, energy producer, and potential upplier of CCS technology. It i unclear how the cot of implementing and developing the technology will be hared between the partie. To roughly reflect the Norwegian ituation, the model i calibrated to include two 860 megawatt ga power plant, one with CCS and one without CCS. The production cot of ga power in our calibration are baed on Statoil (2005). 4 Baically, capital and operating cot are doubled for a CCS plant compared with a non-ccs plant, and the required ga input i about 20 percent larger for a CCS plant. See Appendix E for more information on cot and price in the ga power indutry. The Norwegian National Account lack a good expoition of R&D cot and production, o we ue pecific R&D tatitic. See Bye et al. (2008) for more detail. The hare of R&D targeting CCS technology i et to match the hare of variant capital ued by the ga power indutry with CCS relative to the total production of capital variant in the economy. 5 Thi i in line with the Jone and illiam (2000) computation, which exclude creative detruction, imilar to our model. Numerical pecification of Romer Cobb Dougla production function, a in Diao et al. (999) and Lin and Ruo (2002), reult in far larger markup. Markup factor of.25 are neverthele in the upper bound of econometric etimate (Norrbin, 993; Bau, 996). Our motivation for taying in the upper bound area i the fact that the capital varietie repreent a mall hare of machinery capital and, thu, of total input. Thi, in iolation, drive up the markup required to calibrate the model. 2 The plant in operation i at the Kårtø indutrial facility; the one under contruction i at Mongtad. In addition, ga power i ued in pecific indutrie offhore and in proceing. Thi power i geared toward procee in the indutrie, not the electricity market. In the model, thi power production i not eparated from the uer indutrie. 3 CCS technology i planned to be operational by 20 at Kårtø and 204 at Mongtad. 4 Statoil (2005) bae cot on combined-cycle power plant with amine-baed pot-combution eparation of CO2. Reduced energy efficiency, pipeline tranport, and torage in geographic formation are included in the cot. 5 Thi R&D production, from the environmental R&D indutry, i quite low in the bae year, about US$35 million, and i in line with information obtained from the Norwegian Reearch Council. 9

10 2.7 Buine-a-uual path and balanced growth Along the buine-a-uual path (BAU), the exogenou growth factor are aumed to grow at a contant rate. In mot cae, rate are et in accordance with the average annual growth etimate in the baeline cenario of Norwegian Minitry of Finance (2004), which report the government economic prediction until In the government evaluation, total factor productivity growth i entirely exogenou and valued at, on average,.0 percent annually. Our model ditinguihe between exogenou and endogenou factor productivity component. In line with empirical finding (ee, e.g., Coe and elpman, 995; Keller, 2004), we acribe 90 percent of dometic total factor productivity growth to the exogenou diffuion of international technological change; the remaining 0 percent i the reult of dometic R&D. 6 The latter form a bai for calibrating the 2002 level of knowledge, 7 which, together with the remaining parameter of the model, determine the productivity growth from dometic knowledge accumulation. The international nominal interet rate i 4 percent. All policy variable are contant in real term at their 2002 level. In the long run, i.e., year from now, the economy reache tationary growth rate. The GDP grow by.5 percent annually; conumption grow 0.5 percentage point lower, a net export are increaing more in thi period. The 0 percent contribution from the endogenou productivity impact of dometic innovation require a relatively trong growth in general R&D production and the generation of new general varietie: both grow about 3 percent annually. 8 In the period up to 2070, the demand for electricity increae ubtantially. Mot of thi i covered by ga power without CCS. Ga power with CCS doe not grow, a the production cot are relatively high when the carbon tax faced by the ga power indutry without CCS i low. Thi lead to low demand for the environmental capital varietie, which again lead to low production in the environmental R&D indutry. The low level of invetment in environmental R&D yield poor productivity growth in the ga power indutry with CCS, and increae the cot difference between power production with and without CCS. Note that ga power without CCS experience the general productivity growth from general R&D, and that there i no pillover between general and environmental R&D in the model. The uniform carbon tax replace a variety of taxe on GG in the Norwegian economy. It i et at about US$6 per tonne of CO 2 equivalent (US$6/tCO 2 ) to replicate baeline emiion in 2002 of 56. million tonne of CO 2 equivalent. Emiion rie ubtantially through the period to 92.0 million tonne in 2050 and 20.5 million tonne in About 6 percent of the increae in emiion come from the ga power indutry. 6 Ten percent from dometic R&D i in the lower bound of etimate for mall, open countrie like Norway. e have choen thi lower-bound etimate becaue everal mechanim believed to drive dometic innovation are excluded from the model, like baic government reearch, endogenou education, learning-by-doing, and an extenion of the direct aborptive capacity related to R&D. 7 The environmental knowledge tock i et o that it grow at the ame rate a the general knowledge tock when the two ga power indutrie demand equal amount of capital varietie. Since both knowledge tock are indexed to unity in the bae year, thi mean that an equal growth in the knowledge tock give the ame productivity increae in the ue of general and environmental capital variant. See Bye et al. (2008) for more detail. 8 Eventually, in the ditant future (after about 90 year), all exogenou and endogenou growth mechanim are cut off. Thi i technically motivated, in order to enure that the economy i on a balanced growth path (teady tate) and that thi growth path atifie the tranverality condition decribed in Section 2.5. The relative effect of the different policy analye are independent of thi aumption. 0

11 3. Policy analye and numerical reult e explore how innovation incentive hould be deigned when future emiion are limited. The reaon for ubidizing R&D come from two ditortion in the innovation market. Firtly, there are knowledge pillover in the production of patent. The production of patent contribute to the knowledge tock, which lower the cot of future R&D. Thee knowledge pillover are freely acceible to all R&D firm. Secondly, the capital variety producer engage in monopolitic competition, giving rie to the urplu appropriability problem. The capital variety firm are unable to appropriate the entire conumer urplu from the good they ell. Thu, the price of patent facing the R&D firm i lower than the ocially optimal price, ince the former price i equal to the preent dicounted value of a capital variety firm holding a patent. 9 Rather than tudying optimal policy directly, we focu on market repone to a et of policie. In particular, we tudy the timing and welfare impact of environmental R&D ubidie when the future price of carbon i high. To do that, we etablih two carbon reduction regime, one high and one low. The two regime repreent different carbon cot facing the economy through the carbon tax. e imulate everal ditinct innovation policy alternative on the two reduction regime. The focu i on the welfare gain from ubidie to the environmental R&D indutry. The policy alternative are contant innovation policy, falling innovation policy, and increaing innovation policy. In the imulation, all the policy alternative are implemented through ad valorem ubidy rate to the R&D indutry. To make the ditinct policy alternative comparable, the ubidy rate are dimenioned o that the preent dicounted value of the ubidie are equal. The public revenue annuity i approximately US$9 million, which i about one-fourth of the total environmental R&D effort by the R&D indutry in The carbon reduction regime The carbon reduction regime give two different path for the cot of emiion. In the high carbon reduction regime, we impoe a carbon tax that correpond to a 25 percent reduction in national GG emiion by 2050, compared with BAU. In the low carbon reduction regime, the carbon tax i lower and correpond to a 5 percent reduction. e implement thi by a linear increae of the carbon tax until it reache a table level in The carbon tax tart at the BAU level in 2002, i.e., US$6/tCO 2, and increae to about US$40/tCO 2 in 2050 in the high carbon reduction regime, and about US$68/tCO 2 in the low carbon reduction regime. For the ret of the imulated period, the tax i kept contant. The carbon tax i a firt-bet policy intrument to achieve the emiion reduction, i.e., it doe not target any other market failure. The carbon tax i not under the influence of policy maker when innovation policy i decided; underinvetment in R&D i addreed olely through the R&D ubidie. All other exogenou input are the ame a in BAU. Dometic emiion reduction can be achieved through factor ubtitution, emiion abatement in ga power production (by CCS), or by general factor productivity growth. CCS i the only abatement technology available in the power market in thi tudy, and we do not include other pecific energy-aving technological change, uch a low-emiion vehicle or increaed energy efficiency in building. 9 See Jone and illiam (2000).

12 The long-run effect of the carbon reduction regime, meaured a percentage deviation from BAU, are given in Table. Table : Long-run effect of the carbon reduction regime, given a percentage deviation from the BAU path in 2070 Carbon reduction regime igh carbon reduction Low carbon reduction regime regime Emiion reduction in GG emiion in 2050 in actual 69.0* 78.2* million of tonne of CO 2 equivalent Production of general patent Production of environmental patent General knowledge tock Environmental knowledge tock Production of general capital varietie Production of environmental capital varietie Production of ga power without CCS Production of ga power with CCS Production of main final good Production of power-intenive good Nominal wage rate Gro dometic product (GDP) elfare CO 2 tax, actual value in US$/tCO *Million of tonne of CO 2 equivalent; Value in US$/tCO Thi include return from the factor labor, capital, and knowledge, and exclude exogenou, offhore petroleum production. 2 elfare i meaured a the preent value of utility in the period

13 A the carbon tax increae, ga power production ue more CCS technology. The demand for environmental R&D invetment increae, improving the productivity growth in the CCS power indutry. owever, the total cot of electricity production increae ince the carbon tax increae cot for ga power production without CCS. Thi lead to a reduction in the production of electricity. The carbon tax paid on emiion combined with the increaed price of electricity induce a fall in the power-intenive ector. Thi free reource in the economy like labor and capital good, and o labor cot decreae. The total effect of the higher carbon tax and changed input cot differ between indutrie, depending on their carbon and energy intenitie. Both R&D indutrie and capital variety indutrie experience reduced cot, and the production of patent and capital varietie increae. Thi yield productivity gain through an increaed level of technology and contribute to offet ome of the overall cot of the carbon tax. Production in the main final good indutry i almot unchanged from BAU. Both the welfare and GDP reduction from the emiion reduction are modet. 3.2 The innovation policy alternative e implement three different innovation policy alternative for each of the carbon reduction regime. The alternative are all ubidie for environmental R&D, but with contant, falling, or increaing time profile on the ubidy rate. The carbon tax doe not change between the ubidy alternative. e do thi in order to analyze the effect of different ubidy policie given a et carbon price, e.g., determined in an international carbon market. 22 The long-run effect, meaured a percentage change caued by the innovation policie in the high and low carbon reduction regime, are given in Table 2. Table 2: Long-run effect of different time profile for environmental R&D ubidy rate, given a percentage change for each carbon reduction regime in 2070 Innovation policy Contant Falling Increaing Carbon reduction regime igh Low igh Low igh Low Production of general patent Production of environmental patent General knowledge tock Environmental knowledge tock Production of general capital varietie Production of environmental capital varietie Production of ga power without CCS In the reult reported, the carbon tax i not changed when environmental R&D i ubidized. Thi lead to a change in the carbon emiion when the policy alternative are implemented. e have done imilar imulation where we keep emiion contant o that the carbon tax change when the innovation policy alternative are implemented. Thi doe not change any of our reult. See Appendix F, Table F.2. 3

14 Production of ga power with CCS Production of main final good Production of power-intenive good Nominal wage rate Electricity price GDP elfare The contant innovation policy e firt conider the cae with a contant ubidy rate. 23 The reported reult are for the long run and relative to the two carbon reduction regime without ubidie for environmental R&D. Effect on production The ubidy given to producer of new patent in the environmental R&D indutry puhe down the marginal cot of environmental R&D production. For a given patent price, upply increae, and for the environmental capital-variety indutry to be able to aborb more patent, the price of patent mut fall. The marginal willingne to pay for patent i determined by the dicounted profit for the lat new firm entering the capital indutry. More patent in the indutry mean more firm. A a reult, production by each firm fall a a proportion of the given total indutry production, and thu individual firm profit fall. The marginal cot of the environmental R&D firm will be further hifted downward becaue of dynamic, poitive pillover effect from the accumulated environmental knowledge tock, and thi reinforce the partial market dynamic. In the long-run equilibrium, the environmental R&D production more or le triple. The number of patent, and thu the environmental knowledge tock, alo increae coniderably. In the market for CCS variety-capital, the demand faced by each variety firm hift downward a the number of varietie increae. Thi reduce both the markup price and the dometic production of each variety. The increaed number of patent for CCS technology will increae the efficiency of uing the capital compoite. Thi love of capital variety in the ga power indutry with CCS, combined with the price effect, increae the overall demand for environmental capital varietie. Improvement in CCS technology decreae the cot of ga power production with CCS, and the production increae. Ga power production without CCS decreae from the already-low level becaue of the carbon tax. The total effect i that overall ga power production increae, and the electricity price fall. 23 All ubidie are phaed out in 2090, at the ame time the endogenou growth mechanim i turned off. 4

15 Reallocation and welfare The reult reported above are influenced by indirect change in all factor market. The R&D ubidy increae demand in both the environmental R&D indutry and the environmental variety-capital indutry for other input, like labor, intermediate, and other invetment good. Combined with higher final conumption, thi contribute to a rie in all factor price except variety capital and electricity. The power-intenive indutry benefit trongly from a decreae in the cot of power production and increae it production. For mot of the remaining indutrie, the unit cot of production increae, and production fall in both the hort and long run. Thi include the general R&D indutry, ince production here ue the ame factor input a the ubidized environmental R&D indutry. Thu, general R&D i affected wore than other indutrie by the expanion of environmental R&D. In both carbon reduction regime, general R&D fall by 0.8 percent, while the large main final good indutry fall only marginally. General capital variety production i alo reduced and the general knowledge tock i lowered. The total effect on the economy i a GDP increae of percent. elfare increae by and percent in the high and low carbon reduction regime, repectively. elfare increae becaue the ubidy for environmental R&D target externalitie connected to knowledge pillover and the urplu appropriability problem. The main contribution to welfare gain in our model come from increaed environmental R&D and environmental variety-capital production through two channel: the poitive pillover effect in patent production of a larger environmental knowledge tock, and the poitive loveof-variety effect in the demand for variety capital a the number of capital varietie increae. Thee are counteracted by two negative effect: the welfare lo through lower production within each monopoly firm producing capital varietie, and the negative contribution from higher overall fixed entry cot in term of patent expenditure. The welfare increae i larger in the high carbon reduction regime than in the low one. Thi indicate that higher cot of emiion, through a higher carbon tax, lead to larger innovation externalitie. Larger externalitie imply that the underinvetment in environmental R&D increae, and o the ubidy for environmental R&D give a greater welfare gain (ee the dicuion in Section 3.3) The falling innovation policy To analyze the effect of the time profile of ubidie, we next conider a falling ubidy for environmental R&D production in the two carbon reduction regime. The ubidy rate i high in the firt year and decreae linearly until it ceae in The preent value of government pending on innovation policy i the ame in all the three innovation policy alternative. The ubidy increae long-run environmental R&D production coniderably, but not a much a in the contant innovation policy alternative. The reaon i that in the latter, the long-run ubidy rate for environmental R&D i coniderably higher. alfway through the tudy period, however, the increae in environmental R&D production i larger under the falling innovation policy than the contant innovation policy, o the environmental knowledge tock i developed earlier. Under the falling innovation policy, the long-run environmental knowledge tock increae by about 70 percent in both carbon reduction regime. The production of environmental capital varietie increae by about 65 percent. Both thee increae are larger than thoe under the contant innovation policy. By having larger ubidie early on, the technology i more rapidly developed and the cot of producing patent in later period are more greatly reduced through the pillover effect. 5

16 The total effect on the economy i a GDP increae of about 0.06 percent. elfare increae by and percent in the high and low carbon reduction regime, repectively. Both GDP and welfare increae lightly more with falling ubidie than with contant ubidie for a given carbon reduction regime. The reaon for thi i that the innovation externalitie are large in early period. Thi mean that underinvetment in environmental R&D i larger in early period (ee the dicuion in Section 3.3) The increaing innovation policy Finally, we conider an increaing time profile for environmental R&D ubidie in the two carbon reduction regime. The ubidy rate i low in the early year and then increae linearly throughout time. A with the other innovation policie, the ubidy ceae in The long-run increae in environmental R&D production lie between the increae for the contant innovation and falling innovation policie. The environmental knowledge tock, however, i lowet for the increaing innovation policy, with an increae of le than 50 percent. Becaue of a lower tart, the environmental knowledge tock i not a rapidly developed, and the cot of environmental R&D production tay higher throughout the tudy period. Smaller pillover lead to lower accumulation of patent and higher cot for power production with CCS technology. The total effect on the economy i a GDP increae of about 0.04 percent. elfare increae by and percent in the high and low carbon reduction regime, repectively. Both GDP and welfare increae le with increaing ubidie than with falling or contant ubidie. The reaon for thi i that an increaing ubidy rate fail to correct for the underinvetment in environmental R&D in early period. 3.3 Comparion of the policy alternative in the different emiion reduction regime An R&D ubidy to increae innovation i intended to correct for underinvetment in R&D originating from innovation externalitie. 24 A carbon tax above the marginal cot of emiion could alo target underinvetment in R&D. Thi i not the cae in our tudy, a the carbon tax only repreent the cot of emiion for the economy and doe not target innovation externalitie. The carbon tax may, however, influence the underinvetment in environmental R&D through it effect on the demand for clean ga power technology. The level of welfare gain from R&D ubidie i not the ame for the two emiion reduction regime. Thi indicate that underinvetment in R&D doe not tay the ame for different carbon tax level. R&D induced by a ubidy give a higher welfare gain for the economy when the initial underinvetment in R&D i large. In tating thi, we have implicitly aumed that the economy get more welfare out of correcting for the firt dollar of a large underinvetment than from the firt dollar of a mall underinvetment. In other word, the marginal ocial return from R&D invetment increae with the level of underinvetment. The welfare gain from the innovation policy alternative in the two carbon reduction regime are given in Figure. 24 hen the ocial (welfare) optimal level of invetment i greater than the actual private invetment, the difference i called underinvetment. In thi context, we mean by invetment the actual dollar inveted (or not) in a particular year of the model. The ocial and private level of invetment in a year depend on the rate of return on the invetment. In thi tudy, we do not meaure relative rate of return, only the abolute level of underinvetment. 6

17 Figure : elfare effect of innovation policy alternative, meaured a percentage change for each carbon reduction regime 0,035 0,03 0,025 0,02 0,05 0,0 0,005 Falling innovation policy Contant innovation policy Increaing innovation policy 0 igh reduction regime Low reduction regime e ee that the welfare change are larger in the high carbon reduction regime than in the low carbon reduction regime for a given innovation policy. The difference in welfare gain from introducing the ubidie tem from difference in underinvetment in environmental R&D. Thi mean that it i more important to ubidize the environmental R&D indutry when the cot of emiion, through the carbon tax, are higher. Thi lead to the firt reult: Reult : The welfare gain from ubidizing environmental R&D increae with the cot of emiion, ince the level of underinvetment increae with the carbon tax. The underinvetment increae becaue a higher carbon tax mean larger return from carbonaving technology that are not internalized fully by the private R&D firm. One of the reaon for the underinvetment i knowledge pillover from environmental R&D. hen the carbon tax i higher, the value of ga power production with CCS goe up relative to production in other ector. Thi increae demand for CCS technology, which again increae demand for environmental R&D. The individual R&D firm do not take into account that their activity reduce the cot of future R&D. Thu, the increaed invetment in R&D under a high carbon tax becaue of tronger demand i lower than the increae in the ocial optimal invetment level. Another reaon for the underinvetment i that the environmental capital varietie producing firm do not take into account the full value of the carbon-aving technology for the ga power indutry. Since the environmental capital varietie producer cannot reap the full benefit from the increaing number of varietie through the love-of-variety effect in the CCS ga power indutry, the price of patent doe not reflect the full value of idea. Thi urplu appropriability problem i larger when the carbon tax i higher, ince a higher tax increae the value of abatement technology. The effect from both the urplu appropriability and the knowledge pillover mean that the higher carbon tax reult in increaed ocial return from environmental R&D. Thee are not fully covered by an increae in the private return from R&D. Thu, the underinvetment in environmental R&D increae. 7

18 In both carbon reduction regime, the level of welfare i higher for the falling innovation policy than for the other policie. Thi indicate that the underinvetment in environmental R&D decreae over time, ince a ubidy give a larger welfare gain when the underinvetment i larger. Thi lead to the econd reult: Reult 2: There i a greater welfare gain from a falling time profile of ubidy rate for environmental R&D than from contant or increaing time profile when the economy face increaed emiion cot. Thi i becaue the level of underinvetment i larger in the beginning of the period than the end. The reaon for thi time difference in underinvetment i that the knowledge externalitie from R&D are larget in early period. There are two explanation for thi. Firtly, early R&D invetment contribute over a longer time period. In other word, knowledge generated early pill over to a larger number of later period, compared with knowledge generated later. Thee pillover are ignored by the private firm, and therefore the underinvetment i larger in early time period. Secondly, there i a declining increae in the benefit from new idea (i.e., concave curve) in both the R&D production function and the love-of-variety component. Thi mean that R&D activity ha a larger impact on the economy when the knowledge tock i mall. A the knowledge tock grow over time, there are fewer pillover and productivity gain from new idea. Thu, the innovation externalitie are maller in the later period and the underinvetment i falling over time. owever, the welfare gain from a falling time profile of ubidie compared with contant ubidie i larger in the high carbon reduction regime than in the low carbon reduction regime. Combining reult and 2 explain thi. Reult implie that the value of pillover from invetment in all period increae with the carbon tax level. Reult 2 implie that early invetment yield pillover over more period than later invetment do, and therefore the total value of pillover from early invetment increae more compared with that from later invetment when the carbon tax increae. Thi i why the time difference in underinvetment i larger when the carbon tax i higher. 3.5 Senitivity analye 3.5. Contant carbon tax regime In the carbon reduction regime, the emiion are retricted through a carbon tax that increae over time. To analyze whether thi i a driving mechanim for our reult regarding the timing of ubidie for environmental R&D, we contruct a carbon tax regime with a contant carbon tax. The carbon tax i impoed on the BAU path in the firt year of imulation and kept contant throughout the imulation period. The contant carbon tax i the ame a the average tax in the high carbon reduction regime and give approximately the ame accumulated emiion reduction. The welfare gain from environmental R&D ubidie are percent for the contant innovation policy, percent for the falling innovation policy, and percent for the increaing innovation policy. The ranking of the innovation policy alternative doe not change when the carbon tax i contant. ence, we conclude that it i the overall carbon tax level and not the time profile of the tax that i the driving mechanim for our reult See Appendix F, Table F.. 8