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Environmental Policy and Biased Technical Change:A CGE Analysis

by Vincent M. Otto12, Andreas Löschel3, Christoph Böhringer3 and Rob Dellink1

AbstractThis paper investigates how, and to what extent, environmental policy has an effect on technicalchange. We explicitly focus on the direction of technical change next to its rate. For this purpose, wedevelop a stylized computable general-equilibrium (CGE) model that explicitly captures connectionsbetween environmental policy, the rate and direction of technical change, and economic activity. Ineffect, we show how to endogenize both the rate and direction of TC in a CGE model drawingextensively on endogenous growth models. Feedback loops between the phases of technical changeplay an important role. Network externalities, increased market size, learning-by-doing, learning-by-using, learning-by-researching, and knowledge spillovers all constitute such feedback loops. We showthat these feedback loops are key determinants of the equilibrium bias of technical change in our CGEmodel as is the substitution elasticity between final goods. If these model parameters are large, ourmodel tends to a corner solution in which only technologies will be developed that are complementaryto goods with a relatively low carbon content.

JEL classification: O32, O33, O38, H23, D58

Key words: environmental policy, endogenous technical change, computable general-equilibriummodels

1. IntroductionThe last one-and-half decade saw the emergence of several theoretical growth models in whichtechnical change (TC) was no longer specified exogenously, but rather endogenously. Perhaps themost well-known examples of such models are the product-variety model of Romer (1990) and thequality-ladder model of Aghion and Howitt (1992). Yet, for long attention was mainly focussed onhow to sustain positive growth and hence on the rate of TC. Acemoglu (2002) goes one step furtherand specifies the direction of TC endogenously as well in his model of directed technical change.At the same time do many modeling studies show the importance of an endogenous specification ofTC for climate-change analysis. Studies by, among others, Nordhaus (1999), Goulder and Schneider(1999), Goulder and Mathai (2000), Buonanno et al. (2003), Popp (2003), Gerlagh and van der Zwaan(2003), and Sue Wing (2003) all analyze effects of endogenous TC on the design, timing, orattractiveness of climate-change policies4. Though these studies recognize the importance of directedTC for climate change analysis, they do not capture this issue explicitly, or not at all, in their models. 1 Address: Environmental Economics and Natural Resources group, Wageningen University, Hollandseweg 1, 6706 KN,Wageningen, The Netherlands2 Corresponding author; this paper was written while Otto was fellow at ZEW; email: vincent.otto@wur.nl3 Zentrum für Europaische Wirtschaftsforschung (ZEW), Mannheim, Germany

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Gerlagh and Lise (2003) touch upon this issue when they analyze the role of endogenous TC intransitions in the energy sector that are induced by climate-change policy.We proceed by explicitly studying how, and to what extent, environmental policy has an effect on therate, but especially the direction of TC. For this purpose, we develop the Dynamics Of TechnologyInteractions toward Sustainability (DOTIS) model that explicitly captures connections between policy,the rate and direction of technical change, and the economy5. In effect, we show how to endogenizeboth the rate and direction of TC in a computable general-equilibrium (CGE) model drawing onendogenous growth models developed by, among others, Rivera-Batiz and Romer (1991), andAcemoglu. More specifically, we endogenize the rate and direction of technical change in four ways.First, R&D firms decide whether or not to enter markets for knowledge capital (innovation). Firmscan choose between markets for knowledge capital that is appropriate for production of carbon-intensive goods and of goods that are not carbon intensive. Both markets are characterized bymonopolistic competition. Second, producers decide upon adoption of these two types of knowledgecapital (diffusion). Third, one-period-delayed feedback loops between these phases of TC allow for arealistic representation of the diffusion of the two types of knowledge capital. Learning-by-doing,learning-by-using, network externalities, and knowledge spillovers, among others, constitute suchdelayed feedback loops. Finally, knowledge stocks built up in the specific intermediate sectors spillover to the respective production sectors as well. Relative profits determine the rate and direction ofTC.The rest of the paper is organized as follows. Section two provides the reader with a conceptualframework based on a survey of the relevant literature before we outline our model in section three.Section four presents and discusses results that we obtain with policy simulations. Section fiveconcludes.

2. A conceptual frameworkThe economic treatment of technical change can be traced back to Schumpeter (1942) whose ideas ontechnical change as a linear process comprising three phases of invention, innovation and diffusion,led to the first economic theories on this topic. Recently it has been propagated, however, that

4 Nordhaus (1999) specifies R&D expenditures in his R&DICE model creating an aggregate knowledge-stock, which has anegative effect on the emission-output ratio. He rudimentarily accounts for spillovers by assuming that the social- and privatereturns on R&D diverge. Popp (2003) follows Nordhaus except that R&D occurs in an energy-R&D sector in his ENTICEmodel, where energy R&D is subject to decreasing returns to scale and is assumed to partly crowd out other expenditures.His aggregate stock of knowledge enters the energy-production function as a substitutable input. Buonanno et al. (2003)specify a world-wide stock of knowledge in their ETC-RICE model that enters countries’ production functions and has anegative effect on countries’ emission-output ratios. Sue Wing (2003) specifies an aggregate knowledge-stock enteringsector’s production functions as a substitutable input. Goulder and Schneider (1999) incorporate sector-specific expenditureson R&D that form sector-specific stocks of knowledge capital, where these stocks spill over to representative firms in thespecific sector and where the resources available for all R&D expenditures are in fixed supply. Goulder and Mathai (2000)specify an aggregate knowledge-stock having a negative effect on abatement costs. Moreover, they incorporate a learningcurve in the abatement sector. Gerlagh and Lise (2003) specify in their DEMETER-2 model an aggregate energy R&D sectorbuilding a stock of knowledge that (i) enters production functions of two types of energy as a substitutable input, (ii) spillsover to these energy production functions, and (iii) leads to learning-by-researching. In addition, experience gained in theproduction of these two types of energy builds a second stock of knowledge that enters energy production functions as asubstitutable input as well. Learning rates, however, are constant and the same for both energy technologies. Finally, theyspecify S-shaped diffusion curves for both energy technologies.5 Environmental quality, however, has no feedback effect on the economy and in this sense our model is not an integratedassessment model.

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technical change is more than just a sum of its parts, it is a system complete with feedback loopsbetween its phases (Arthur, 1989).

Invention is the development of a new product or process, and innovation is the commercialization ofan invention. The phases of invention and innovation usually are referred to jointly as research &development (R&D) and are viewed as intentional investment activities that firms undertake tomaximize their profits (Jaffe, et al., 2002). Outcomes are profitable new products or processes that canbe represented as ‘knowledge’ capital. Enlarging the stock of knowledge-capital allows producers toincrease their output level given fixed levels of other inputs. Specific characteristics of theseinvestment activities, however, secure that they are not regular investment activities in that they arerelatively more subject to market barriers and market failures. One example of the latter is that it isdifficult to exclude others from using knowledge that is being generated in the R&D phases. That is,generated knowledge tends to spill over. Another example is that set-up costs related to R&D typicallycause markets for knowledge capital to be imperfectly competitive.Decisions regarding the rate and direction of R&D activities are governed by their expected returns.This notion dates back to Hicks (1932) who stated in The Theory of Wages: “A change in the relativeprices of the factors of production is itself a spur to invention, and to invention of a particular kind –directed to economizing the use of a factor which has become relatively expensive” (pp. 124-125).Acemoglu (2002) formalizes this notion when he presents a demand-and-supply framework to studydirected TC that is based on explicit micro-economic foundations. Three effects are identified. First, aprice effect increases expected returns of improving productivity of relatively scarce factors and henceof allocating more resources to R&D activities that favor such scarce factors. Second, a market sizeeffect increases expected returns of improving productivity of relatively abundant factors and hence ofallocating more resources to R&D activities that favor abundant factors. Third, current R&D activitiesthat positively depend on the state of previous R&D activities (‘state dependency’) increases theexpected returns of these R&D activities. If the production factors are gross complements, it is shownthat the price effect outweighs the market size effect resulting in TC being biased toward the relativelyscarce factor. If the factors are gross substitutes the opposite holds.

Diffusion occurs when the innovation gains market share as a result of firms’ rational decisionsregarding adoption of the innovation. Presence of market barriers and -failures again ensure that this isnot a regular investment activity. Prime examples of the latter are consumption externalities; adoptionof innovations by some users conveys valuable information to potential users for free (Berndt, et al.,2003). A consumption externality often encountered is the network externality that exists if adoptionof a product or process by some users causes the value of adopting compatible products or processesto increase (Katz and Shapiro, 1986). Diffusion of an innovation typically follows a S-shaped curvepartly reflecting these market barriers and –failures. Alternatively, one can deduce from this curve thepresence of positive feedback loops at the early stages followed by negative ones for more maturetechnologies.

One can identify three feedback loops (see influence diagram). First, current diffusion of innovationstypically have a positive effect on future diffusion due to, among others, consumption externalities andlearning-by-using. Learning-by-using occurs if adoption of a product or process causes its value to

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users to increase since users gain experience in using it (Rosenberg, 1982). Second, current diffusiontypically has a positive effect on future R&D activities as well due to, among others, learning-by-doing, learning-by-using, and an increased market size for related innovations. Increased diffusion ofan innovation increases the size of the market for related products or processes that in turn increasesthe expected returns of further investments in related R&D activities6. Learning-by-using can alsoincrease these expected returns if it creates a demand for related products or processes. For example,when cars were also used for agricultural purposes in the beginning of the previous century, the valueof the car to users increased. This increased value in turn increased expected returns of R&Dinvestments in the tractor (Sunding and Zilberman, 2001). Learning-by-doing occurs when adoption ofa product or process causes its production costs to fall or its quality to rise or both because itsproducers gain experience in producing it. Such cost- and quality improvements represent innovation.Third, current R&D activities can influence future R&D activities due to, among others, a fishing-outeffect, learning-by-researching and knowledge spillovers. Learning-by-researching occurs when R&Dactivities cause the unit costs of additional R&D activity to fall or its quality to rise becauseresearchers gain experience (Buonanno, et al., 2003). It can be thought of as the counterpart oflearning-by-doing in R&D. Knowledge generated in R&D processes tends to be nonrival, whichensures that this knowledge spills over to other researchers and developers (Griliches, 1979). Thesetwo effects increase the expected returns on additional R&D activities. Hence, it is often said thatresearchers ‘stand on the shoulders’ of their predecessors. As more and more innovations aredeveloped, however, the more difficult and costly it seems to get to develop a new innovation thatimproves upon the existing one because the easiest discoveries usually are made first. For this reason,R&D is often pictured as a ‘depletable pool’ that is subject to a ‘fishing-out effect’7.Positive feedback loops cause the process of TC to be inflexible in that once a dominant technologyemerges it might be difficult to switch to competing technologies (Arthur, 1989). This inflexibilityimplies that further TC is dependent on prior TC; a property that Arthur (1994) names ‘pathdependency’ and that Acemoglu names ‘state dependency’. Feedback loops and such path dependencythus are critical factors affecting the rate and direction of further TC.

3. Description of the modelSeveral economic agents interact over time by demanding and supplying commodities on markets.These agents are producers of final goods in production sector i, firms in an intermediate sectormanufacturing knowledge capital i for their respective production sector, and a representativeconsumer. Final good X has a relatively high carbon content whereas good Y has a relatively lowcarbon content. Each agent is assumed to behave rationally and to have perfect foresight. The marketsfor both final goods and for all production factors are perfectly competitive whereas markets for bothtypes of knowledge capital are characterized by monopolistic competition based on the Chamberlinianlarge-group assumption –firms have a monopoly over their own variety of knowledge capital althoughthere are many close substitutes. Monopolistic competition and external effects support nonconvexities

6 Note similarities with Acemoglu’s market size effect. His effect operates on the input side of TC whereas this market-sizeeffect operates on the output side.7 Popp (2003) finds that such diminishing returns applies to sectoral R&D rather than aggregate R&D. As expected returns toR&D within any one sector decreases, profit maximizing researchers and developers are expected to shift resources to moreprofitable sectors in the economy.

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in the production possibility frontiers of both final goods that arise because some of the inputs arenonrival. Nonrival inputs also cause nonconvexities in the innovation possibility frontier that aresupported by external effects only.Each agent solves its own optimization problem and when all markets clear simultaneously as well,the allocation- and price vectors constitute a competitive equilibrium. Economic growth is determinedby the growth rates of the stocks of physical- and knowledge capital, and of the labor supply. Growthof the labor supply is exogenous and constant over time. Growth rates of both capital stocks areendogenous and reflect investment decisions of the representative consumer. The economy achievessteady-state growth over time with the stocks of physical- and knowledge capital growing at the samerate as the labor supply. We present a more detailed structure of the model in appendix A.

Representative consumerThe representative consumer maximizes her intertemporal utility function subject to her lifetimebudget constraint. The intertemporal utility function is a nested constant-elasticity-of-substitution(CES) aggregate of the discounted sum of consumption of goods X and Y versus leisure time over thetime horizon (see equations A.7 and A.8 in the appendix). Unlike in integrated assessment models,environmental quality does not enter the utility function in DOTIS.

Producers of final goodsProduction processes of the final goods X and Y are characterized by production possibility frontiers,

which are Cobb-Douglas functions of physical capital ( ,i tK ), labor ( ,i tL ), emission rights ( ,i tE ) and a

Dixit-Stiglitz aggregate of available varieties of knowledge capital ( ,i tKC ), i.e. the “Romer”

production function. We assume knowledge capital i to be ‘appropriate’ for particular combinations ofinputs, i.e. the production function of final good i (Basu and Weil, 1998). Hence, one type ofknowledge capital cannot be used in the production of another type of final good. Vintages of thesevarieties are differentiated but equally preferred. Value shares are determined by base-year demands.Yet, this is not the complete picture because knowledge generated by intermediate sector i’s aggregateR&D activities spill over to production sector i enhancing their production possibilities:

1, , , , , ,=

Q Q Q Qii i i i i i

i t i t i t i t i t i tQ NS K L E KC� � � � �� � � � �

� � � � ( 1,.., )t T� , ( , )i X Y� (1)

where � i reflects the extent of spillovers from the stock of blueprints ( ,i tNS ). Together with adoption

of knowledge capital, these spillovers drive productivity growth in the production sectors. Firms inproduction sector i operate so to maximize their profits over time subject to these production-possibility frontiers. Homogeneity-of-degree-one, in addition to perfect competition, guarantees zero

profits. Market clearing implies that the relative price of the goods, , ,X t Y tPQ PQ , has to satisfy:

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, ,

, ,1

WCX t X tX

CY t X Y t

PQ QPQ Q

�

�

�

�

� �� �� �� �� �

( 1,.., )t T� (2)

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where CX� is the share of good X in total consumption and 2

W� is the substitution elasticity between

both final goods in instantaneous utility. The law of demand is satisfied because an increase in therelative supply of a good lowers its relative price, all else equal. The change in relative price is smallerthe more substitutable the goods are.

Manufacturers of knowledge capital

Two intermediate sectors, XZ and YZ , manufacture knowledge capital being an intermediate input in

respectively production sectors X and Y. Knowledge capital is assumed to be excludable but nonrival:its owner can prevent others from using it by deciding not to sell or rent it but its use by one firm doesnot preclude its use by another. Software is a prime example. To be able to manufacture knowledgecapital in the first place, however, firms in the two intermediate sectors require a blueprint. Blueprintsare also assumed to be nonrival but, in contrast to knowledge capital, they are assumed to be partiallyexcludable. Owners can prevent others from using their blueprints by means of patent protection butcannot completely prevent the knowledge or experience, that is being gained in the R&D processes,from spilling over to other researchers and developers in their sector. Neither can they completelyprevent this knowledge or experience from spilling over to firms in the respective production sector.This partial excludability causes the private- and social returns to R&D to diverge.There exist multiple institutional structures that support a decentralized equilibrium. We like to thinkof firms manufacturing knowledge capital separate from firms manufacturing final goods.Alternatively, one can think of firms in each production sector manufacturing their type of knowledgecapital themselves, i.e. in-house R&D. As long as knowledge capital is created according to identicalinnovation possibility frontiers, the institutional structure doesn’t matter. Likewise, it doesn’t matterwhether the innovation and manufacturing of new varieties takes place within departments of one firmor in two separate firms as long as these new varieties are manufactured according to identicalpossibility frontiers and as long as the manufacturing decision is separate from the patent-pricingdecision. In either case, the firm that owns the patent extracts the same monopoly profit. We assumethat the firm that develops and patents the invention of new varieties of knowledge capital alsomanufactures these new varieties and that he is the sole manufacturer so that there is a one-to-onecorrespondence between firms and varieties of knowledge capital. We therefore characterizemanufacturing of knowledge capital in each intermediate sector by a single innovation possibilitiesfrontier that comprises a fixed- and a variable cost component. We think of the fixed costs as a ‘set-up’cost related to the research and development of a blueprint for a new variety of knowledge capital, i.e.innovation, that a firm must incur once in order to be able to produce this new variety of knowledgecapital ( )n . We simply relate the variable cost component to their manufacturing. Finally, we make

the usual assumptions that manufacturing of knowledge capital is a deterministic process and thataggregate innovation possibility frontiers are continuous, which allows us to avoid problems due tointeger variables and uncertainty8.Set-up costs related to R&D merely involve final goods, and only at the time of entry. Rivera-Batizand Romer (1991) refer to this specification as the lab-equipment specification for its emphasis onphysical inputs. As they also point out, this doesn’t mean that final goods are directly converted into

8 Even though indivisibility of blueprints and knowledge capital and uncertainty related to R&D processes are facts of life,averaging out makes these facts matter less at aggregate levels (Romer, 1990).

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blueprints but rather that the inputs necessary for production of final goods are used, in the sameproportions, for research and development instead. Formally for sector i:

, , ,I

i t i t i t i tN Q C I�� � � � ( 1,.., )t T� , ( , )i X Y� (3)

where Ii� is sector i’s share in total investment ( tI ). This specification implies that R&D indirectly

has a carbon content, even though firms engaging in R&D do not have to purchase emission rights,because emission rights are an input of final goods, as discussed above. Following the same reasoning,this specification implies that R&D does indirectly use knowledge capital as an input. This is not thecomplete picture, however, because there exist one-period-delayed feedback loops affecting theseR&D costs9. One is that all previous R&D activities in sector i have an effect on current i R&D due tofishing out, learning-by-researching and knowledge spillovers, as described above. We assume apositive gross effect so that new firms stand on the shoulders of old firms. We consequently capturethe essence of what Rivera-Batiz and Romer refer to as the knowledge-driven specification of R&D:new blueprints benefiting from the ones already developed. Another feedback loop is that adoption ofany variety of knowledge capital i in the previous period has an effect on current i R&D due tolearning-by-doing, learning-by-using, and an increased market size. We assume this effect to bepositive. These feedback loops operate within each intermediate sector only because we assume thetwo types of knowledge capital to be too different from each other to benefit form each other’stechnical changes:

� �, , 1 , 1 , ,i i I

i t i t i t i t i t i tN N KC Q C I� ��

� �

� � � � � � ( 1,.., )t T� , ( , )i X Y� (4)

where i� measures the one-period-delayed feedback effect from the stock of blueprints in intermediate

sector i ( , 1i tN�

), and where i� measures the one-period-delayed feedback effect from aggregate

manufacturing of knowledge capital i ( , 1i tKC�

). The condition that in equilibrium demand for

knowledge capital equals its supply in any given period allows us to express the latter feedback loop interms of aggregate manufacturing of knowledge capital rather than in terms of its adoption.A quick glance at equation four reveals several interesting, though not surprising, implications for therate of innovation of blueprints. First implication is that higher expenditures on R&D, in terms of thefinal good, lead to a higher rate of innovation. Second implication is that a higher rate of innovation ordiffusion or both increases the productivity of resources devoted to R&D. Yet, a third implication isthat this increase in productivity does not continue to grow in proportion to the rate of TC if, and onlyif, the feedback effects are smaller than one. It might eventually become more productive to devotethese R&D resources elsewhere in the economy, if this is indeed the case.Once a blueprint has been developed, it is added to its respective stock and is therefore available formore than one period (see equation A.26). Variable costs of manufacturing this new variety of

knowledge capital i subsequently comprise costs of labor ( ,i tL ) and physical capital ( ,i tK ) in any

9 For illustrative purposes, we limit ourselves to one-period-delayed feedback loops only. Presence of multiple-period-delayed loops would simply add to the increasing returns in the intermediate sectors.

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period. Moreover, adoption of any variety of knowledge capital i in the previous period has an effecton current adoption due to consumption externalities and learning-by-using. We assume this effect tobe positive:

1, , 1 , ,

Z Zi i i

i t i t i t i tZ KC K L� � ��

�

� � � ( 1,.., )t T� , ( , )i X Y� (5)

where i� measures the one-period-delayed feedback effect from adoption of knowledge capital i.

Assuming symmetric cost structures for firms in the two sectors ensures that all varieties of knowledgecapital are supplied at the same level initially and allows us to express aggregate output of eachintermediate sector in any period as:

� �1

1, , ,

Ni

Ni

i t i t i tKC NS Z � ��

��

�

� � � ( 1,.., )t T� , ( , )i X Y� (6)

where the elasticity of demand for an individual variety, � , equals the compensated elasticity of

substitution between varieties. This is the usual Chamberlinian large-group assumption inmonopolistic competition that determines the height of the constant mark-up over marginal costs. Themark-up, in turn, drives a wedge between the marginal- and average costs of manufacturingknowledge capital and therefore causes the innovation possibilities frontier to be characterized byincreasing returns to scale. Not surprisingly, the feedback loops add to these increasing returns.Firms in each intermediate sector operate so to maximize their profits over time subject to theseinnovation possibility frontiers. The increasing returns generate profits in the immediate short-run,which attract new firms. Given that manufacturing knowledge capital is assumed to be a deterministicprocess, firms can enter freely and have perfect foresight, a new firm will enter at time t if, and only if,the present-value of profits into the future is equal to or greater than the present-value of the set-upcosts related to the research and development of a new variety of knowledge capital. Using dynamicprogramming:

1, 1N

ii i i i tir V V Z FC

�

��

� � � � � �� ( , )i X Y� (7)

where ir is the interest rate and FC are the set-up costs which we assume to be constant and equal for

both sectors. Equation seven relates the flow of profits, i� , to the present value of future profits, iV .

iV� allows future profits to differ from current ones, which might occur, for example, when moving

from one balanced growth path to another. Nevertheless, free entry ensures zero profits in a present

value sense in a balanced growth path so that the V� terms are zero. Moreover, we assume that theelasticity of substitution between varieties of knowledge capital is equal for both types as is theinterest rate. This allows us to write the relative profitability of developing knowledge capital

appropriate for production of XQ as (suppressing the time subscripts to simplify notation from now

on):

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X X

Y Y

V ZV Z

� (8)

To gain further understanding, we substitute the dual form of (6) (see equation A.23) into the market

clearance condition for ,i tZ (see equation A.24) and rearrange terms to get an expression for the

relative demand of XZ , which we finally substitute in (8):

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Q QX X X X Y X X

Q QY Y Y Y X Y Y

V PZ PQ QV PZ PQ Q

� � �

� � �

� � �

� � � �

� � �

(9)

Acemoglu’s price- and market size effects can now be easily identified. iV is increasing in the goods

prices, iPQ , confirming that there is an incentive to develop technologies used in the production of

more expensive goods. iV is also increasing in iQ , confirming that there simultaneously is an

incentive to develop technologies for which there is a greater market. Remember from (2) that the lawof demand implies that a change in relative market sizes creates a price effect as well, leaving neteffects ambiguous for now. On the supply side, the one-period-delayed feedback loops reduce costs of

developing and manufacturing technologies and raise associated profits, as shown by the fact that iV

is decreasing in iPZ . If these feedback loops are sufficiently strong, they can even lead to a corner

solution in which only one type of knowledge capital is developed and manufactured.To investigate the relative strength of the price-and market size effects, we follow Acemoglu bysubstituting the relative price of both goods, (2), into (9). This gives:

2 121

1 1

W

WQ Q C

X X X X X Y XQ Q C

Y Y Y Y X X Y

V PZ QV PZ Q

�

�� � � �

� � � �

�

� �� � �� � � �� �

� � � � �

(9)

This expression shows that the elasticity of substitution between both goods is a key determinant ofthe direction of TC as it regulates the relative strength of the price-and market size effects. The lesssubstitutable goods are, the more scarcity commands higher prices and the more powerful the price

effect gets relative to the market-size effect. If both goods are gross complements, 2 1W� � , and a

decrease in the relative supply of a good increases its relative price and profitability so that the price

effect dominates. If both goods are gross substitutes, 2 1W� � , and a decrease in the relative supply of a

good decreases its profitability so that the market-size effect dominates. Naturally, TC is not directedto any of the goods if both goods have a unit substitution elasticity.Finally, it should be noted that even when factors/goods are gross complements, a decrease in therelative supply of a factor/good biases some amount of TC away from that factor/good (Acemoglu,2002). The reason behind this ‘weak induced-bias hypothesis’ is an increased physical productivity ofthe relatively scarce factor/good and therefore an excess demand for the complementary factor/goodraising the marginal product of the complement, all else equal. If the substitution elasticity is

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sufficiently large, the induced bias in TC can overcome the usual substitution effect and even increasethe relative price of the factor/good that has become more abundant. A result Acemoglu refers to asthe ‘strong induced-bias hypothesis’.In short, the substitution elasticity between both goods as well as the one-period-delayed feedbackloops are key determinants of the equilibrium bias in TC. What the overall equilibrium bias amountsto is what we turn to below.

4. Model resultsWe consider a 27-year time horizon, defined over the years 2004 till 2030. We calibrate the model to abalanced growth path of two percent that serves as a benchmark. In this benchmark, markets forblueprints are monopolistically competitive. There are, however, neither feedback loops between thephases of TC nor are there knowledge spillovers from R&D activities to the production of final goods(I will refer to them jointly as ‘technology dynamics’ from now on). Neither is there policyintervention in the benchmark. We use baseline data and -parameters as reported in table B.1. and B.2.We use this stylized version of the DOTIS model to examine three scenarios. First, environmentalpolicy is introduced while both goods are complements, i.e. energy and energy-using machines.Second, environmental policy is introduced while both goods are close substitutes, i.e. energygenerated from conventional- and alternative sources. Finally, environmental policy is introducedwhile technology dynamics are present and while both goods are close substitutes. Environmentalpolicy takes the form of 25 percent fewer emission rights being granted relative to the benchmark.Table B.2. lists the parameter values used in each scenario.For each scenario, we compare outcomes to the benchmark where variables are reported as percentagechanges from their benchmark values. The benchmark is identical in each scenario by construction.We compare outcomes with respect to (i) the rate and direction of TC as indicated by the number ofblueprints in each intermediate sector, (ii) the structure of the economy as measured by consumptionlevels of both goods, and (iii) welfare of the representative consumer as measured by Hicksianequivalent variation (EV)10.

Scenario 1: fewer emission rights while both goods are complementsWe now consider the effects of granting 25 percent fewer emission rights annually, relative to thebenchmark, while both goods are complementary to each other. That is, the representative consumervalues both goods only in fixed proportions. One can think of these goods as energy and energy-usingmachines.Figure one shows the effects of this reduction in emission rights on innovation in each sector. Themoment we introduce the policy, fewer firms enter either R&D sector as production possibilities arenow limited and demand for knowledge capital is lower. Immediately following, producers substituteknowledge capital for emission rights and therefore the demand for blueprints bounces backsomewhat. This demand remains lower relative to the benchmark because the policy lowers theincome of the representative consumer. The usual deadweight loss and income effect associated to thepolicy outweigh its substitution effect. Further, allocating fewer emission rights changes relativescarcity of production factors and, indirectly both goods, leading to the price- and market-size effects 10 The EV is based on the intertemporal utility function optimized over the time horizon.

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discussed above. Given that both goods have no value without each other, it now becomes relativelymore profitable to develop and manufacture knowledge capital that can substitute for the scarceemission rights. As a result, the former effect outweighs the latter and innovation is biased toward thecarbon-intensive sector X. Finally, we find evidence for the weak induced-bias hypothesis: theenvironmental policy also causes some innovation to be biased away from the carbon-intensive sectorX. As can be seen in figure one, the demand for type-Y blueprints bounces back as well immediatelyafter the policy is introduced.

Insert figure one here

Both the deadweight loss and income effect associated to the policy outweigh the usual substitutioneffect and lower the welfare of the representative consumer (see figure two), relative to thebenchmark. This makes her consume less of each good in each period.

Insert figure two here

That she values both goods only in fixed proportions can be easily seen in figure three for herconsumption levels of both goods are identical.

Insert figure three here

Scenario 2: fewer emission rights while both goods are substitutesWe now consider the effects of the same policy but assume both goods to be substitutes of each otherrather than complements. The representative consumer derives value from either good and is thereforeindifferent between these. One can think of energy derived from conventional- versus alternativesources. For the time being, we assume that there are no technology dynamics present.Similar to the previous scenario, the rate of total innovation decreases from the moment the policy isintroduced as shown in figure four. The deadweight loss and the income effect still outweigh thepositive effect of firms substituting knowledge capital for emission rights as an input in theirproduction processes.

Insert figure four here

Unlike the previous scenario, however, the rate of innovation in the non-carbon intensive sector Ynow actually increases, relative to the benchmark. This increase comes at the expense of innovation inthe carbon-intensive sector X, whose rate of innovation is now considerably lower than in the previousscenario. As we discussed in the previous section, the reason behind this equilibrium bias toward thenon-carbon intensive sector Y is that the market-size effect outweighs the price effect when the goodsare gross substitutes. The representative consumer responds to the change in relative prices of bothgoods and consumes relatively more of good Y (see figure five), leaving firms in the intermediatesector Y with a greater market, all else equal. At the same time, scarcity does not command that muchhigher prices because there is a substitute available.

12

Insert figure five here

The deadweight loss and income effect associated to the policy still outweigh the usual substitutioneffect causing welfare losses for the representative consumer (see figure two), relative to thebenchmark. Relative to the previous scenario, however, welfare levels are higher because she now hasmore possibilities to adjust to the policy by substituting goods. Nevertheless, her total consumptionlevel remains lower in each period relative to the benchmark. Note that the higher consumption levelof good Y comes at the expense of consumption of good X implying a structural change in theproduction structure as well.

Scenario three: fewer emission rights while technology dynamics are presentWe now build on the previous scenario and allow for technology dynamics. We restrict thesedynamics to take on positive values only to exclude negative spillovers, ‘organizational forgetting’ etc.We still assume both goods to be substitutes of each other. Presence of technology dynamics makesthe economy more elastic in that a given policy leads to greater distortion and adjustments in theeconomy, as already pointed out by Goulder and Schneider (1999). Hence, it should come as nosurprise that the results of the previous scenarios are accentuated by the technology dynamics (seefigures four and five) but that their effects are nonetheless ascribable to the main effect of allocatingfewer emission rights. The equilibrium bias in innovation is a good example. Presence of positivefeedback loops reinforce this equilibrium bias because the more firms enter intermediate sector NY,relative to NX, the less costly it becomes for potential entrants to also enter NY, relative to NX.Welfare levels are higher, relative to the previous scenario without technology dynamics, because ofthe positive externalities associated to the dynamics (see figure two). Yet, welfare levels remain lowerrelative to the benchmark. A main reason is that too few resources are allocated to the intermediatesectors from a social point of view.

Sensitivity AnalysisTo gain further understanding of the model, we perform ‘piecemeal’ sensitivity analyses. We usecentral parameter values in all scenarios (see table B.2.) except for the parameter subject to analysis.We furthermore examine the sensitivity of the model to the policy in place. We report effects on therelative profitability of R&D in each sector, as defined in (8) or (9), and on intertemporal utility. Bothvariables are in present values. Table B.3. present these results.Allocating 50 percent fewer emission rights, instead of the regular 25 percent, causes greater welfarelosses. It biases innovation even more in the direction of the relatively scarce good, as in scenario one,or in the direction of the relatively abundant good, as in scenarios two and three. The opposite holds ifwe halve the reduction in emission rights. Halving the substitution elasticity between varieties ofknowledge capital translates into higher mark ups over marginal costs of manufacturing knowledgecapital, which attracts more firms to the intermediate sectors. The additional blueprints that arehenceforth developed generate additional positive externalities and can substitute for more emissionrights in production. The upshot is that welfare losses associated to the policy are smaller. Theopposite holds if we double the substitution elasticity between varieties. Effects on the equilibriumbias in innovation depend on which sector benefits from the policy in the first place. If goods arecomplements, for example, innovation is biased toward the carbon-intensive sector, mark ups are

13

higher in absolute terms, and innovation gets biased even more toward this sector. Doubling thedepreciation rate on knowledge capital raises the opportunity costs of resources devoted to R&D andleads to greater welfare losses, all else equal. At the same time, however, the additional R&D that isnow being undertaken generate positive externalities in the form of the one-period-delayed feedbackloop from innovation to innovation. A higher depreciation rate also leads to a smaller stock ofknowledge capital and therefore a higher price and lower profits (see (9)). This effect is slightlystronger for the sector that benefits from the policy in the first place, relative to the other sector, asinnovation is already biased toward this sector. Finally, we examine the sensitivity of the model to thetechnology dynamics. Doubling any of these parameters leads to smaller welfare losses associated tothe environmental policy as more external benefits are generated. Profits in the intermediate sectorsalso increases and innovation gets even more biased toward the sector that benefits from the policy,relative to the other sector. Again, the opposite holds if we halve any of these parameters.Given that we identified both the substitution elasticity between both goods and the one-period-delayed feedback loops as key determinants of the equilibrium bias in TC, we are particularlyinterested in the sensitivity of the relative profitability of innovation to a combination of these modelparameters. This reveals what the overall equilibrium bias amounts to in our model.

Insert figure six here

Figure six confirms that the equilibrium bias in innovation shifts away from the carbon-intensivesector as both goods become more substitutable. It also confirms that the delayed feedback loopsintensify the shifts in the equilibrium bias. This intensifying effect is not big when both goods aregross complements, but increases the more substitutable both goods are. If we increase both modelparameters simultaneously, the model can become unstable. It subsequently tends to a corner solutionin which only knowledge capital will be developed and manufactured that is appropriate for the non-carbon-intensive sector Y.

5. ConclusionsIn this paper, we developed a stylized version of the DOTIS model as a step in moving fromtheoretical- to empirical models, which can be used in applied work. We showed how to endogenizeboth the rate and direction of technical change in a CGE model drawing on endogenous growthmodels developed by Rivera-Batiz and Romer (1991), and Acemoglu (2002). More specifically, wespecified (i) monopolistically-competitive firms in intermediate sectors producing appropriate types ofknowledge capital (innovation), (ii) diffusion of these types of knowledge capital, (iii) delayedfeedback loops between these two phases of TC, and (iv) knowledge spillovers to production sectors,where profit incentives are the basic premise. Moreover, we explicitly captured connections betweenenvironmental policy, the process of technical change, and economic activity. We used our CGEmodel to analyze effects of environmental policy on especially the rate and direction of TC.Our model results show that the direction of TC depends most importantly on the substitutionelasticity between the final goods and dynamic effects of TC such as knowledge spillovers andfeedback loops between phases of TC. If the final goods are complementary to each other, say energyand machines, TC is biased toward the relatively scarce good, which is in our case the carbon-

14

intensive good energy. The opposite holds if the final goods are substitutes of each other, sayconventional- and renewable energy. These results are more pronounced if technology dynamics areallowed for. If both goods are very close substitutes, or technology dynamics are very strong, or both,the model can yield a corner solution in which only knowledge capital is developed and manufacturedthat is appropriate for the good that is not carbon intensive in its use. These results are in line withAcemoglu’s findings.Of great interest are thus the technology dynamics. Whenever, for example, feedback effectsassociated to renewable-energy technologies are greater than those of fossil-fuel technologies,marginal products will differ accordingly, resulting in TC directed at the more dynamic renewable-energy technologies11. This might entail some hope for such technologies if they are characterized byrelatively large feedback effects. Empirical studies will have to tell us.One should note that our model is specified for a closed economy, which is actually inappropriate foranalyzing technical changes. The same technologies are typically in use in many countries andtechnical knowledge crosses borders, as e.g. Coe and Helpman (1995) and Eaton and Kortum (1995)show. Such international knowledge spillovers have a bearing on domestic TC and should beaccounted for, especially if these spillovers affect sectors differently. One also should bear in mindthat we present a stylized model only. As the sensitivity of the relative profitability of innovation tothe model parameters demonstrates, empirical validation of our model is important if we want toderive more precise conclusions. We therefore see a specification of DOTIS as a small open-economyand calibrated on an OECD country as the foremost tasks for future research. A frontier approach canbe used to estimate feedback effects between the phases of TC (Otto et al., 2003).

AcknowledgementsTNO-MEP and the EC MarieCurie program are gratefully acknowledged for their financial supportand we would like to thank Ekko van Ierland, Timo Kuosmanen, Tinus Pulles, Toon van Harmelen,Reyer Gerlagh and colleagues at the ZEW for helpful comments. The usual disclaimer applies.

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809Aghion, Philippe and Howitt, Peter (1992), "A Model of Growth through Creative Destruction",

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of Economics, 113(4), pp. 1025-1054 11 As stated above, feedback loops can cause technologies to be ‘locked in’ production sectors. Yet, even though feedbackloops are necessary for technologies to be locked in, they are not sufficient. Costs of switching or of having paralleltechnologies also are important (Jaffe, et al., 2002). Note that a lock in is not a market failure in itself even though it mightresult from them. It remains unclear what policy can and should do.

15

Berndt, Ernst R., Pindyck, Robert S. and Azoulay, Pierre (2003), "Consumption Externalities andDiffusion in Pharmaceutical Markets: Antiulcer Drugs", The Journal of Industrial Economics,51(2), pp. 243-270

Buonanno, P., Carraro, C. and Galeotti, M. (2003), "Endogenous Induced Technical Change and theCosts of Kyoto", Resource and Energy Economics, 25(1), pp. 11-34

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Environment", in Mäler, K.-G. and Vincent, J. (ed.) Handbook of Environmental Economics,Elsevier Science, Amsterdam

Katz, Michael L. and Shapiro, Carl (1986), "Technology Adoption in the Presence of NetworkExternalities", Journal of Political Economy, 94(4), pp. 822-841

Nordhaus, W.D. (1999), Modeling Induced Innovation in Climate Change Policy, paper for workshop"Induced Technological Change and the Environment" June 21-22, IIASA, Laxenburg,Austria

Otto, V.M., Kuosmanen, T. and Ierland, E.C. van (2003), "Measuring Feedbacks in TechnologicalChange: A Frontier Approach", paper presented at the 30th Annual Meeting of the EuropeanAssociation for Research in Industrial Economics (EARIE), August 24-26, 2003, Helsinki,Finland

Popp, David (2003), Entice: Endogenous Technological Change in the Dice Model of GlobalWarming, NBER, Washington

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Rivera-Batiz, Louis A. and Romer, Paul M. (1991), "Economic Integration and Endogenous Growth",Quarterly Journal of Economics, 106(2), pp. 531-555

Romer, Paul M. (1990), "Endogenous Technological Change", Journal of Political Economy, 98(5),pp. S71-S102

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Sue Wing, I. (2003), Global Warming and the Macro-Economic Impacts of Environmentally-InducedTechnical Change, Cambridge, MA.

Sunding, David L. and Zilberman, David (2001), "The Agricultural Innovation Process: Research andTechnology Adoption in a Changing Agricultural Industry", in Gardner, B.L. and Rausser,G.C. (ed.) The Handbook of Agricultural Economics. Volume 1a. Agricultural Production.,Elsevier Science, North-Holland

17

Appendix A. Structure of the numerical modelThe appendix provides an algebraic summary of the DOTIS model. It is formulated as a mixed-complementarity problem (MCP) using the Mathematical Programming System for GeneralEquilibrium Analysis (MPSGE) [Rutherford, 1999 #97], which is a subsystem of the GeneralAlgebraic Modeling System (GAMS) [Ferris, 2000 #226]. In this approach, three classes ofequilibrium conditions characterize an economic equilibrium: zero-profit conditions for constant-returns-to-scale production activities, market clearance conditions for each primary factor and producedgood, and an income definition for the representative consumer. The fundamental unknowns of thesystem are activity levels, market prices, and the income level. The zero profit conditions exhibitcomplementary slackness with respect to associated activity levels, the market clearance conditions withrespect to market prices, and the income definition equation with respect to the income of therepresentative consumer. The orthogonality symbol, � , associates the variables for the complementaryslackness conditions. Differentiating profit and expenditure functions with respect to input and outputprices provides compensated demand and supply coefficients (Hotelling’s lemma), which appearsubsequently in the market clearance conditions. An equilibrium allocation determines productionlevels, relative prices, and incomes. The price of intertemporal utility is chosen as the numeraire and allprices are reported in present values.The model is solved for a finite number of time periods. To avoid that the complete stocks of physicalcapital and blueprints will be consumed in the last period, transversality conditions are necessary. Wefollow Lau, Pahlke and Rutherford [Lau, 2002 #67] by constraining the growth rates of investments inthe last period to the growth rate of a quantity-variable –in this case instantaneous utility. Theadvantage of these transversality conditions is that they impose balanced growth but neither specificstocks nor specific growth rates in the last period. This condition therefore suits models in whichgrowth rates are endogenously specified.Table A1 explains the notations for variables and parameters. Table A2 presents the social accountingmatrix that underlies the model. Table A3 gives key parameter values.

Zero profit conditions

(A.1)1,

,,

Q Q Q Qii i i i i

i

t t t i ti t

i t

RK PL PE PKCPQ

NS

� � � � ��

�

� � �

� � �� ,i tQ� ,i X Y� ; 1,..,t T�

(A.2) � �1

,, 1

1 1� �

��

�

�

�� � �

Z Zi i

i

Nt ti t i

i t

RK PL PZKC ,i tZ� ,i X Y� ; 1,..,t T�

(A.3) � �, , , 11 Ni t i t i i tPN PFC PN�

�� � � � ,i tNS� ,i X Y� ; 1,.., 1t T� �

, ,i T i T iPN PFC PNT� � ,i TNS� ,i X Y�

(A.4) , 1 , 1 , , 1i i

i t i t i t i tN KC PQ PN� �

� � �� � � ,i tN� ,i X Y� ; 1,.., 1t T� �

, 1 , 1 ,i i

i T i T i T iN KC PQ PNT� �

� �� � � ,i TN� ,i X Y�

(A.5) � � 11 Kt t tPK RK PK�

�� � � � tK� 1,.., 1t T� �

T TPK RK PKT� � TK�

18

(A.6) , 1,

Ii i t t

i X Y

PQ PK��

�

� �� tI� 1,.., 1t T� �

,,

Ii i T

i X Y

PQ PKT�

�

� �� TI�

(A.7)� �

� �

11 1 11

12 2 21

1 1

1 1, ,

1

1

W W W

W W W

W WC t C t t

C Ct X X t X Y t

PC PL PW

with PC PQ PQ

�

�

� �

� �

� �

� �

�

�

� �

� �

� �� � � � �� �

� � � � � �� �

tW� 1,..,t T�

(A.8)1

�

��

�

��WWT

T

tt

PW PU U�

Unit demand functions

(A.9) ,,

i tRKQ Qi t i

t

PQD

RK�� � ,i X Y� ; 1,..,t T�

(A.10) ,,

i tLQ Qi t i

t

PQD

PL�� � ,i X Y� ; 1,..,t T�

(A.11) ,,

i tEQi t i

t

PQD

PE�� � ,i X Y� ; 1,..,t T�

(A.12) � � ,,

,

1 i tPKCQ Q Qi t i i i

i t

PQD

PKC� � �� � � � � ,i X Y� ; 1,..,t T�

(A.13) ,,

i tRKZ Zi t i

t

PZD

RK�� � ,i X Y� ; 1,..,t T�

(A.14) � � ,, 1 i tLZ Z

i t it

PZD

PL�� � � ,i X Y� ; 1,..,t T�

(A.15)

21

,,

WW

W W Ct tX t C X

t X t

PW PCDPC PQ

��

� �� �� �

� � � �� �� � � �� � � �

1,..,t T�

(A.16) � �

21

,,

1WW

W W Ct tY t C X

t Y t

PW PCDPC PQ

��

� �� �� �

� � � � �� �� � � �� �

1,..,t T�

(A.17) � �1

1W

LW W tt C

t

PWDPL

�

�� �

� � �� ��

1,..,t T�

(A.18)1

WWU tt T W

ttt

PUDPW

�

��

� �

�1,..,t T�

Coefficients

(A.19) 1

Ni

Ni

PKCir

�

� �

� ,i X Y�

(A.20) � �� �

2 1

2 11 1 11

WQ Q W W tii i WT tW W t

U PKCi ir r

� � �

� � �

� � �� � �

�

� �� � � �� � � � � �� �� � � � � �

� � � � � ��,i X Y�

(A.21) � �1

01 �

� � �t

tL g L 1,..,t T�

19

(A.22) � �1

01 �

� � �t

tE g E 1,..,t T�

Market clearance conditions

(A.23), , ,

, ,

Ii t i t i t i t

Wi t i t t

Q C I N

with C D W

�� � � �

� �

,i tPQ� ,i X Y� ; 1,..,t T�

(A.24) � �1

1 1, , ,

N Ni i

i t i t i tNS PZ PKC� ���

� � ,i tPKC� ,i X Y� ; 1,..,t T�

(A.25)1

1, , , ,

Ni

PKCQi t i t i t i tZ D NS Q��� � � ,i tPZ� ,i X Y� ; 1,..,t T�

(A.26) ,0, 1 ii tNS NS�� , 1�� i tPN ,i X Y�

� �, , 1 , 11 Ni t i i t i tNS NS N�

� �

� � � � ,i tPN� ,i X Y� ; 2,..,t T�

� �, ,1 �� � � �N

i T i i T iNS N TN iPNT� ,i X Y�

(A.27) 1, 1N

ii t iZ FC

� �

� � ,i tPFC� ,i X Y� ; 1,..,t T�

(A.28) 01tK K�� 1�� tPK

� � 1 11 Kt t tK K I�

� �

� � � � tPK� 2,..,t T�

� �1 KT TK I TK�� � � � PKT�

(A.29) � �, , , , ,,�

�

�� � � � �

��

RKQ RKZt ti t i t i t i t i tK

i X Y

K RK D Q D NS Zir tRK� 1,..,t T�

(A.30)� �, , , , ,

,

�

� � � � �

� �

�LQ LZ

t i t i t i t i t i ti X Y

LWt t

L D Q D NS Z

D WtPL� 1,..,t T�

(A.31) , ,,�

� � ��EQ

t t i t i ti X Y

er E D QtPE� 1,..,t T�

(A.32) WUt tW D U� � tPW� 1,..,t T�

(A.33),

Ui

i X Y

MU rPU

�

� �� PU�

Income balance

(A.34) � �0 0 011

�

�

� � � � � � � � � � ��T

REF REFt t t t t t

tM PL L g PE E g er PK K TK PKT

Terminal constraints

(A.35)1 1� �

�T T

T T

I WI W TK�

(A.36),

, 1 1� �

�

i T T

i T T

N WN W iTN�

20

Table A.1. Nomenclature

Sets and indicesi ,X Y sectors and goodst 1,..,T time periods

Activity variables,i tQ Aggregate production of goods

,i tZ Production of an individual variety of knowledge capital

,i tNS Stock of blueprints / varieties of knowledge capital

iTN Terminal stock of blueprints / varieties of knowledge capital

,i tN Investments in blueprints (R&D)

tK Stock of physical capital

TK Terminal stock of physical capital

tI Investments in physical capital

,i tC Aggregate consumption

tW Instantaneous utility

U Intertemporal utility

Price variables (in present values),i tPQ Price of goods

tPC Composite price of goods

,i tPKC Unit cost of knowledge capital

,i tPZ Price of an individual variety of knowledge capital

,i tPN Price of a blueprint

iPNT Price of terminal stock of blueprints

,i tPFC Unit price of inputs to the R&D related set-up costs

tPK Price of physical capital

PKT Price of terminal stock of physical capital

tRK Rental rate for physical capital

tPL Wage rate

tPE Price of emission permits

tPW Price of instantaneous utility

PU Price of intertemporal utility

Income- and endowment variablesM Total income of the representative agent

,0iNS Initial stock of blueprints / varieties of knowledge capital

0K Initial stock of physical capital

tL endowment of labor

tE endowment of emission rights

21

Table A.1. Nomenclature (continued)

Unit demand variables

,PKCQi tD Unit demand for knowledge capital in the production of goods

,RKQi tD Unit demand for physical capital in the production of goods

,LQi tD Unit demand for labor in the production of goods

,EQi tD Unit demand for emission rights in the production of goods

,RKZi tD Unit demand for physical capital in the production of knowledge capital

,LZi tD Unit demand for labor in the production of knowledge capital

,Wi tD Unit demand for goods in instantaneous utilityLWtD Unit demand for leisure in instantaneous utilityWUtD Unit demand for instantaneous utility in the intertemporal utility function

Coefficientster Emission rights index

ir Interest rate

iFC Set-up costs related to R&Dg Growth rate

,K Ni� � Depreciation rates

PKCir Degree of homogeneity in the aggregate production of knowledge capitalUir Degree of homogeneity in intertemporal utility

, , ,I C W Wi X C t� � � � Share coefficients

, , , ,Q Z Q Zi i i i i� � � � � Cost price coefficients

i� Knowledge spillover coefficient

i� Coefficient on the one-period-delayed feedback loop from diffusion to diffusion

i� Coefficient on the one-period-delayed feedback loop from diffusion to R&D

i� Coefficient on the one-period-delayed feedback loop from R&D to R&D1 2, ,N

i W W� � � Substitution elasticities

22

Appendix B. Tables and figures

Table B.1. Social accounting matrixZero profits Income

balanceXQ XZ XN YQ YZ YN I W M

XPQ 300 -8 -105 -187

YPQ 220 -8 -28 -184

XPKC -100 100 -12 12

YPKC -100 100 -12 12

XPFC -20 20

YPFC -20 20

PW 133 431 -564

PL -30 -20 -90 -60 -60 260

RK -90 -60 -20 -20 190

Mar

ket c

lear

ance

PE -80 -10 90Note: numbers are in value terms.

Table B.2. Key parameter valuesValue per ScenarioDescription Symbol BM 1 2 3

Growth rate g 0.02

Depreciation rates

Physical capital K� 0.05

Blueprints Ni� 0.2

Degree of homogeneity in knowledge capital PKCir 1.25

Substitution elasticitiesBetween the composite good and leisure ininstantaneous utility

1W� 0.5

Between goods X and Y in instantaneous utility 2W� 1 0 2.5 2.5

Between varieties in aggregate production ofknowledge capital

Ni� 5

One-period-delayed feedback effects

From diffusion to diffusion i� 0 0.15

From diffusion to R&D i� 0 0.15

From R&D to R&D i� 0 0.15

Knowledge spillovers to production i� 0 0.15

Policies

Reduction in emission rights er 0 0.25 0.25 0.25

General R&D subsidy s 0Note: Scenario BM refers to the benchmark; scenario 1 to fewer emission rights while both goods are complements; scenario2 to fewer emission rights while both goods are close substitutes; scenario 3 to fewer emission rights while technologydynamics are present and while both goods are close substitutes.

23

Table B.3. Piecemeal sensitivity analysisSimulation Relative profitability of R&D:

VY /VX

PV of utility: U

Scenario Scenario1 2 3 1 2 3

Regular simulation 0.894 1.077 1.092 0.948 0.955 0.963Policies

ter halved 0.949 1.035 1.042 0.976 0.978 0.982

ter doubled 0.764 1.199 1.238 0.877 0.897 0.916Model parameters

Ni� halved 0.892 1.088 1.168 0.951 0.959 0.992Ni� doubled 0.895 1.074 1.083 0.947 0.953 0.959N

i� halved 0.894 1.079 1.097 0.948 0.955 0.964N

i� doubled 0.894 1.076 1.089 0.948 0.954 0.962

i� halved 1.085 0.959

i� doubled 1.146 0.988

i� halved 1.089 0.961

i� doubled 1.114 0.974

i� halved 1.090 0.962

i� doubled 1.100 0.967

i� halved 1.089 0.961

i� doubled 1.111 0.971Notes: All figures are indices relative to the common benchmark. Scenario 1 refers to allocation of fewer emission rightswhile both goods are complements; scenario 2 to fewer emission rights while both goods are close substitutes; scenario 3 tofewer emission rights while technology dynamics are present and while both goods are close substitutes.

24

Figure 1: Effects of fewer emission rights on innovation while both goods are complements

Figure 2: Equivalent variation in each scenario

25

Figure 3: Effects of fewer emission rights on consumption while both goods are complements

Figure 4: Effects of fewer emission rights on innovation while both goods are substitutes, withand without technology dynamics

26

Figure 5: Effects of fewer emission rights on consumption while both goods are substitutes, withand without technology dynamics

Figure 6: Overall equilibrium bias in innovation

0.5 11.5 2

2.5 3substitution elasticity0.05

0.100.15

0.200.25

0.30

feedback effects

0.8

0.9

1

1.1

1.2

1.3

VY

VX