Journal of Environmental Economics and Management 45 (2003) 523–545
Instrument choice for environmental protection when
technological innovation is endogenous
Carolyn Fischer, Ian W.H. Parry, and William A. Pizer
Resources for the Future, 1616 P St. NW, Washington, DC 20036, USA
Received 22 February 2000; revised 13 March 2001
Abstract
This paper compares, qualitatively and quantitatively, the welfare effects of emissions taxes, auctioned
emissions permits, and free (grandfathered) permits, when technological innovation is endogenous. We find
that there is no unambiguous case for preferring any of these policy instruments. The relative welfare
ranking of instruments depends on the costs of innovation, the extent to which innovations can be imitated,
the slope and level of the marginal environmental benefit function, and the number of polluting firms. We
illustrate the types of situations when there can be significant welfare discrepancies between the policies and
when there are not.
r 2003 Published by Elsevier Science (USA).
JEL classification: Q28; O38; H23
Keywords: Technological innovation; Externalities; Environmental policies; Welfare impacts
1. Introduction
Policy-makers must often choose amongst alternative policy instruments for protecting the
environment. A key consideration affecting this choice is the impact of different policies on firm
incentives to develop cleaner production technologies.1 Over the long run, the cumulative effect of
technological innovation may greatly ameliorate what in the short run can appear to be serious
conflicts between economic activity and environmental quality [11,16].
Corresponding author.
E-mail address: fi[email protected] (C. Fischer).
1
A number of other factors affect this choice. For example, the ease of monitoring and enforcement, political
feasibility, and the expected costs of policy instruments in the presence of uncertainty, firm heterogeneity and preexisting tax distortions. For literature reviews see for example [3,28].
0095-0696/03/$ - see front matter r 2003 Published by Elsevier Science (USA).
doi:10.1016/S0095-0696(03)00002-0
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There is a blossoming literature, mainly theoretical, on the effects of environmental policies on
technological innovation. Several early studies showed that emissions taxes and emissions permits
generally provide more incentives for firm-level innovation than technology mandates and
performance standards (e.g., [5,18,33]). However, many innovations are applicable to more than a
single firm. Indeed at the heart of most R&D models in the industrial organization literature are
the spillover benefits of innovation to other firms, and the inability of innovators to fully
appropriate the rents from innovation. In an ideal world, the government could target the R&D
externality and environmental externality separately. However, in practice, research stimulants
are often far from perfect, and consequently the effects of environmental policies on innovation
may have important implications for social welfare.
Milliman and Prince [19] and Jung et al. [12] evaluate separately the private gains from
improved abatement technologies to the innovating firm and to the other adopting firms. They
find that—when policies are fixed over time—innovation incentives are greater under an emissions
tax than under free (grandfathered) emissions permits, and higher still under auctioned emissions
permits.2 However, their particular assumptions about how innovators can appropriate the rents
accruing to the rest of the industry prove critical to their ranking of policy incentives for
innovation. When we add an explicit model of the adopting firms’ decision, the policy rankings
can change.
Prior literature identifies two main determinants of the private gains to innovation, which
we term the abatement cost effect and the emissions payment effect. The former is the cost
savings from the impact of innovation on reducing (marginal) abatement costs. The effect is
larger under an emissions tax since this policy induces additional abatement, while under permits
the industry-level amount of abatement remains constant. The second effect applies only to
auctioned permits and stems from the impact of reduced marginal abatement costs on lowering
the equilibrium permit price. When firms have to pay for permits to cover their emissions they
gain from the fall in permit price. This effect is absent in the aggregate under free permits as the
gains and losses to net buyers and sellers of permits cancel out. If the innovating firm can
appropriate these gains from the emissions payment effect that otherwise accrue to all firms in the
industry (as in [12]) or a fixed proportion thereof (as in [19]), the private return to innovation
under auctioned permits is much larger than under free permits, and typically larger than under
the emissions tax.
This paper differs from previous studies in several important respects. First, we relax the
assumption in [12,19] that innovators appropriate a fixed fraction of the abatement cost and
emissions payment effects. This assumption is plausible when firms collude over R&D but not for
a competitive setting, which is more appropriate for current applications to sulfur dioxide and
carbon dioxide emissions trading where there are a large number of market participants. In our
competitive equilibrium, where non-innovating firms choose whether to license technologies from
the innovator, the innovator cannot appropriate any of the emission payment effect accruing to
non-innovators because the marginal firm has no effect on the equilibrium permit price. As a
result, the extra incentives for innovation from auctioning permits rather than grandfathering
2
These results apply for both homogeneous and heterogeneous firms [12].
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
525
them—i.e., the emissions payment effect—are typically much lower in our analysis than in other
papers.
Second, we incorporate imperfect appropriation into our analysis by assuming that other firms
can potentially imitate around a patented technology. Combining this imitation effect with our
competitive model creates another avenue by which the fraction of industry rents that the
innovator can capture varies with the choice of policy instrument. We show that the level of R&D
can depend importantly on this imitation effect, in addition to the abatement cost and emissions
payment effects.
Third, previous studies mainly focus on the impact of environmental policies on the demand for
innovation. However, from a welfare perspective more innovation is desirable only if the benefits
outweigh the costs. Our model incorporates the supply side of the innovation market so we can
examine the welfare effects of environmental policies. Finally, we provide a quantitative—as well
as qualitative—comparison of policy instruments. This enables us to identify parameter scenarios
for which the welfare differences between policies are ‘‘significant’’ and when they are not. For the
most part we assume that policies remain fixed at their optimal, Pigouvian levels ignoring the
possibility of innovation, although we discuss the implications of policy adjustment in response to
innovation.3
Our results reject the idea of a general preference for auctioned permits over emissions
taxes, and emissions taxes over free permits, either on the criterion of welfare gains or the
amount of induced innovation, in contrast to the earlier studies noted above. Under different sets
of circumstances, we find that each of the three policies may generate a substantially higher
welfare gain than the other two policies. In particular, the relative welfare ranking of policy
instruments depends on four important factors: the ability of adopting firms to imitate the
innovation, the cost of innovation, the slope and level of the marginal environmental benefit
function, and the number of firms producing emissions. In certain situations, however, these
welfare differences are small enough to be of little practical relevance for the choice of policy
instruments. Thus, an evaluation of the circumstances specific to a particular pollutant would be
required in order to judge whether a case for one instrument over the other two instruments can
be made.4
The rest of the paper is organized as follows. In Section 2 we derive a number of theoretical
results concerning the welfare and innovation effects of environmental policies. Section 3 presents
quantitative results. Section 4 discusses some of our simplifying assumptions and we draw
conclusions in Section 5.
3
Although allowing for induced innovation raises the overall welfare gain from environmental policies (relative to
that in a fixed technology model), the optimal stringency of environmental regulation, which depends on the marginal
rather than the total welfare gain, is not necessarily greater than the Pigouvian level (e.g., [7,24]).
4
Other papers that compare free permits and with emissions taxes include [4,23]. Our paper differs from [4] by
allowing for imperfect appropriation, by providing quantitative results, and by considering auctioned permits. Parry
[23] focuses on some other issues, such as the welfare losses from distortions in the R&D market under environmental
policies, although he also shows that the case for using emissions taxes over free permits is strong only when innovation
achieves a substantial reduction in abatement costs. Econometric work has focused on the incentives for innovation
under market-based environmental policies versus command and control (e.g., [10,15]). For more discussion of the
literature see [11,13,30].
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2. Theoretical analysis
2.1. The basic model
To keep the analysis transparent we make a number of simplifying assumptions. However, as
discussed below, many of these simplifications do not appear to affect the main results.
We model a three-stage process of innovation, diffusion, and emissions abatement, involving a
fixed number of n competitive firms.5 One of these firms is an innovator. In the first stage, the
innovating firm decides how much to invest in R&D to develop a better emissions abatement
technology. In the second stage, the other n 1 firms decide whether to adopt this technology in
return for a royalty fee. Alternatively, they can use a costless imitation technology that is not fully
equivalent to the original innovation. In the third stage, all n firms choose emissions abatement to
minimize costs given an emission tax or a permit price. The environmental policy is set prior to
innovation, although implementation (including any auctioning of permits) takes place in the last
stage. The model is best solved backwards.
2.1.1. Abatement cost minimization
The abatement cost function for a firm in the third stage is Cða; kÞ; where a is firm-level
emissions abatement. The state of technology for reducing emissions, k; is determined prior to the
third stage.6 Abatement costs are assumed to be increasing and convex in a and decreasing in k
with diminishing returns to technology: Ca 40, Caa 40, Ck o0, Ckk 40; Cak o0, Ca ð0; kÞ ¼0. An
augmented state of technology (higher k) reduces the slope of the marginal abatement cost
function.7
Let t denote the ‘‘price’’ of emissions. Under an emissions tax this is simply the tax rate, while
under a permit policy it is the equilibrium permit price. Firms take the emissions price as given
when making abatement decisions. In the third stage each firm solves
mðk; tÞ ¼ minfCða; kÞ þ tðe aÞg;
a
ð2:1Þ
5
The industrial organization literature on innovation has tended to focus on strategic models involving a small
number of firms where monopoly rents, timing, and preemption are important (see e.g. the survey in [29, Chapter 10]).
While appropriate for major R&D industries such as pharmaceuticals, these studies may be less appropriate where
environmental issues are concerned. Major pollutants like sulfur dioxide, nitrogen oxides, particulates and carbon
dioxide are produced by large numbers of firms. See [22] for some empirical justification for the competitive assumption
in models of environmental policy.
6
Abatement reduces emissions per unit of output and represents the substitution of cleaner inputs for polluting
inputs in production, or the use of end-of-pipe clean-up technologies. In practice emissions also fall as industry output
contracts in response to higher pollution abatement costs. Our simple form can incorporate the opportunity cost of
forgone output, but implicitly assumes then that equilibrium product prices are fixed (such as with large national or
international markets). Still, this seems a reasonable approximation because abatement costs are typically only a minor
fraction of total production costs [27]. Indeed, Goulder et al. [8] find that around 98 percent of NOX emissions
reductions come from firms reducing emissions per unit of output and only 2 percent from reductions in industry
output.
7
The impact of successive increases in innovation on reducing abatement costs is declining sooner or later, since there
is a limit on the ability to reduce abatement costs (costs cannot become negative). Assuming innovation reduces
marginal abatement costs is standard in the literature, with the possible exception of [14] (see below).
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
527
where e is emissions with no abatement ðapeÞ; and mðk; tÞ is the minimized sum of (i) abatement
costs and (ii) tax payments on emissions, or the cost of purchasing (or forgoing sales of) permits.
The first order condition is
Ca ða; kÞ ¼ t:
ð2:2Þ
That is, marginal abatement costs equal the price of emissions.
2.1.2. The technology adoption choice
Typically innovators can only partially appropriate the spillover benefits to other firms from
new technologies. In particular, other firms may benefit from the public good nature of
information to develop alternatives to the original innovation. We represent imperfect
appropriation by assuming that the new innovation is patented but that other firms can
(imperfectly) imitate around the patent. Thus, in the second stage, non-innovators decide whether
to pay a fixed-fee royalty Y for licensing the technology ðkÞ developed in the first stage.
Alternatively, they can use an imitation that improves their technology level by sk rather than k;
where 0psp1: When s ¼1 the innovation is effectively a pure public good and can be perfectly
reproduced by imitation; when s ¼0 imitation is unable to improve the technology level of a noninnovator and innovation is a pure private good. A firm will adopt the patented technology if its
costs (including the royalty payment) are no higher than costs with the imitation.8
Each firm makes its technology adoption decision taking the adoption decisions of all other
firms and the equilibrium permit price as given. In the resulting Nash equilibrium, the maximum
royalty the innovator can charge, denoted as Y ; leaves the last adopting firm indifferent between
the patented technology and the imitation:9
Y þ mðk; tÞ ¼ mðsk; tÞ:
ð2:3Þ
We assume complete diffusion of the original innovation—this is socially and privately optimal
for the range of parameters used in the simulations below (Section 4 discusses incomplete
diffusion). Thus, while in equilibrium no firm chooses to imitate, the threat of imitation limits the
ability of the innovator to fully appropriate the social benefits from innovation.10 From (2.1)
8
We assume zero costs to developing imitations; however, relaxing this assumption would have the same effect as
reducing s: An alternative, though more complex, formulation might involve allowing for several competing and
patented technologies (e.g., [1]). However, the presence of alternative patented technologies reduces the return to an
individual innovator in the same way that increasing s does in our model.
When multiple firms innovate competition for a given amount of rent can be excessive due to the ‘‘common pool’’
problem (e.g., [32]). Allowing for this effect would be roughly equivalent to reducing the imitation effect (reducing s),
since it dampens the severity of the public good problem associated with innovation. Empirical evidence suggests that,
despite the common pool problem, innovation incentives are still suboptimal (e.g. [9]).
9
We assume the innovator cannot price-discriminate among adopters, charging initial adopters more while permit
prices are high. Otherwise, each adopter would want to adopt last and get the lowest price.
10
An alternative approach to incorporating imperfect appropriability would be to allow the willingness to pay for the
new technology to differ across firms—the innovator can only charge one royalty rate and therefore cannot extract the
full willingness to pay from all firms [1]. Imperfect appropriability also arises when one firm’s R&D in one period raises
the productivity of another firm’s R&D in future periods. Each of these cases essentially boils down to a higher value of
s in our analysis.
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and (2.3), the maximum royalty can be expressed:
Y ðkÞ ¼ fCðas ; skÞ Cða1 ; kÞg þ tða1 as Þ;
ð2:4Þ
where superscripts s and 1 denote the solution to condition (2.2) for a firm with technology level
sk and k; respectively.
Under emissions permits, as the industry-wide marginal abatement cost curve shifts down the
permit price falls and therefore t ¼ tðkÞ (t is fixed under the emissions tax). To the extent that
innovation brings about a fall in the permit price, adopting firms will benefit from lower payments
on their inframarginal emissions (they gain Dtðe a1 Þ). However, the innovator cannot
appropriate these gains since any one firm can free ride on the fall in permit price and enjoy
this benefit whether it adopts or not.
Differentiating (2.4) with respect to k gives the marginal change in royalty payments:
Y 0 ðkÞ ¼ sCk ðas ; skÞ Ck ða1 ; kÞ þ t0 ðkÞða1 as Þ:
ð2:5Þ
2.1.3. The innovation decision
We assume that innovation results from R&D activity by one firm (Section 4 discusses the
implications of multiple innovators). The cost of the R&D necessary for technological innovation
is F ðkÞ; where F 0 X0, F 00 40. In the first stage the innovator chooses R&D (or, equivalently, the
amount of technological innovation) to maximize profits:11
ðn 1ÞY ðkÞ Cða1 ; kÞ FðkÞ tðkÞðe a1 e%Þ:
ð2:6Þ
Innovator profits equal royalties from the other n 1 firms minus the sum of own abatement
costs, innovation costs and payments on own emissions (either tax payments or permit
purchases).12 e% is the (exogenous) permit allocation of the innovating firm under the free permits
policy (e% ¼ 0 for the emissions tax and auctioned permits policies).13
Maximizing (2.6) with respect to k gives
F 0 ðkÞ ¼ ðn 1ÞY 0 ðkÞ Ck ða1 ; kÞ t0 ðkÞðe a1 e%Þ:
ð2:7Þ
From (2.5) and (2.7) we obtain the following condition for the privately optimal amount of
innovation:
F 0 ðkÞ ¼ nCk ða1 ; k1 Þ
|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
abatement cost effect
0
þ ðn 1ÞsCk ðas ; skÞ
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
imitation effect
t ðkÞðe a e%Þ þ ðn 1Þt0 ðkÞða1 as Þ :
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
1
emissions payment effect
ð2:8Þ
adoption price effect
11
We simplify by assuming that innovation is continuous rather than discrete. ‘‘Innovation’’ in our analysis
effectively represents the aggregate amount of innovation over a given period, and in this sense it is more reasonable to
regard it as a continuous variable. An alternative formulation would be to assume that firms invest in R&D to increase
the probability of successfully inventing a discrete technology (e.g. [23,32]).
12
Abatement levels are implicitly a function of k and superscripts denote their equilibrium values. However, since
both the innovating and adopting firms maximize their profits with respect to abatement, by the Envelope Theorem we
recognize in deriving (2.6) and (2.7) below that small changes in a due to changes in k will not affect profits.
13
e% does not appear in Eqs. (2.1) or (2.3), since individual firm decisions about emissions and technology adoption do
not affect the price of emissions, and hence the rents obtained from permit allocations.
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
529
Table 1
Determinants of the incentives for innovation
Abatement cost effect
Imitation effect
Emissions payment effect
Adoption price effect
Emissions tax
Free permits
Auctioned permits
+
0
0
+
0
+
+
Eq. (2.8) equates the marginal cost and marginal private benefit of innovation, where the latter
is decomposed into four components. First, the (marginal) abatement cost effect is the willingness
of the n firms to pay for reduced abatement costs brought about by an incremental increase in
innovation. Second, the (marginal) imitation effect is the reduction in the willingness of the ðn 1Þ
non-innovators to pay for the new technology, due to the impact of innovation on increasing the
possibility of abatement cost-reducing imitation.
The third and fourth components apply only under emissions permits. The (marginal) emissions
payment effect is the reduction in the innovator’s permit costs, net of any permit endowment, due
to the effect of innovation on reducing the permit price. Under auctioned permits, the innovator
must pay for all emissions ðe a1 Þ: Under free permits, if the allocation e% is less (greater) than
emissions ðe a1 Þ; the innovator would be a net buyer (seller) of permits. We assume that all firms
receive the same allocation. Therefore, since in equilibrium all firms’ emissions are the same and
equal to their endowment, no permit trading occurs and there is no emissions payment effect.14
The final term in (2.8) is the adoption price effect. Under free or auctioned permits, if a noninnovator were to use the imitation instead of the patented technology, it would have higher
emissions and would pay tðkÞða1 as Þ for the additional permits. By reducing the permit price,
innovation reduces these payments and hence the willingness to pay for the new technology. In
most of our simulations however this final effect is of relatively minor importance. We summarize
the determinants of the incentives for innovation under alternative policies in Table 1.
2.1.4. The first-best outcome
To examine the welfare properties of the policies we first need to define the first-best or social
planning outcome. To do this we specify the environmental benefit function BðnaÞ where B0 40,
B00 p0. Social welfare ðW Þ equals environmental benefits less abatement and innovation costs:
W ¼ BðnaÞ nCða; kÞ F ðkÞ:
ð2:9Þ
Maximizing with respect to a and k gives
14
Ca ða ; k Þ ¼ B0 ðna Þ;
ð2:10Þ
F 0 ðk Þ ¼ nCk ða ; k Þ:
ð2:11Þ
More generally, if the innovator is a net buyer of permits, the amount of induced innovation will lie between the
amount under our free and auctioned permit cases. If the innovator is a net permit seller, innovation will be below that
in our free permit case.
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Eq. (2.10) shows that a social planner would equate the marginal abatement cost per firm with
marginal environmental benefits. In Eq. (2.11), the planner equates the marginal cost of
innovation with the marginal social benefit in terms of reducing abatement costs across all firms.
2.2. Comparing policy instruments
We now compare the effects of policies on innovation and welfare, assuming policies are fixed
at their Pigouvian levels (i.e., set to equate the marginal costs and benefits of abatement prior
to innovation). We discuss the implications of policy adjustment in response to innovation in
Section 4.
2.2.1. Innovation incentives
Fig. 1 shows the private gains from innovation at the innovating firm (panel (a)) and a noninnovating firm (panel (b)) under the emissions tax. In panel (a) the innovator gains the shaded
area 0hj from reducing its own marginal abatement costs. However, it can only extract area 0lj in
panel (b) from a non-innovating firm, since that firm’s marginal abatement cost is Ca ða; skÞ if it
does not adopt the patented technology. The areas 0hj in Fig. 1 correspond to the abatement cost
effect while area 0hl in panel (b) corresponds to the imitation effect (for non-incremental
innovation).
Fig. 1. Gains to innovation: emissions tax.
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
531
Fig. 2. Gains to innovation: auctioned permits.
Fig. 2 illustrates the gains under auctioned permits, where the equilibrium abatement for firms
is constant at a0 and the permit price falls to tðkÞ with innovation. The innovating firm gains from
its abatement cost effect (0hi) and emissions payment effect (hsri). Indeed the overall gains to the
innovator exceed those under the emissions tax by area ijsr. On the other hand, the innovator
extracts a lower royalty than under the emissions tax because the abatement cost effect is smaller
by area glji. In addition, the royalty is smaller by the adoption price effect (qgi).15
From Figs. 1 and 2 one can easily visualize how either the emissions tax or auctioned permits
might induce more innovation under different circumstances. Suppose imitation were perfect
(s ¼1) so that the innovator does not appropriate any of the gains to other firms in the lower
panels of Figs. 1 and 2. Innovation incentives are greater under auctioned permits by area ijsr in
Fig. 2(a). Suppose instead that no imitation is possible (s ¼0). In this case the innovator would
extract (n 1) times area hjiu more in royalties from non-innovators under the emissions tax than
under emissions permits. This extra gain is likely to dominate area ijsr when n is large.
We now rigorously establish two propositions with respect to ordering policies in terms of
induced innovation.
15
If a non-innovator were to use the imitation rather than the patented technology it would reduce abatement to asp
and purchase a0 asp extra emissions permits. This option to buy permits at the new lower price reduces costs with the
imitation by qig.
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C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
Proposition 1. For a large enough level of emissions abatement, a critical imitation parameter s
exists such that an emissions tax leads to a greater (lower) level of innovation than auctioned permits
whenever the imitation parameter is smaller (greater) than this critical level.
Proof. Subtracting the right-hand side of (2.8) for permits from that for the tax, and noting that
in equilibrium a1 ¼ a0 for permits, gives the difference in marginal profits for any k:
nfCk ða1t ; kÞ Ck ða0 ; kÞg þ sðn 1ÞfCk ðast ; skÞ Ck ða0 ; skÞg
þ t0 ðkÞðe a0 Þ ðn 1Þt0 ðkÞða0 ; asp Þ:
ð2:12Þ
For a given k; a positive expression in (2.12) means that marginal profits to innovation
are greater under the emissions tax. If this holds at the optimal k for auctioned permits,
then innovation will be greater at the optimum for the tax because under a tax policy it is
profitable to innovate further. Similarly, a negative expression at the optimal k for auctioned
permits implies it is profitable to innovate less under the tax policy. Two equalities help us
simplify (2.12):
Ck ða1t ; kÞ Ck ða0 ; kÞDCka ða0 ; kÞða1t a0 Þ;
t0 ðkÞ ¼ Cak ða0 ; kÞ ¼ Cka ða0 ; kÞ:
ð2:13Þ
When s ¼1, asp ¼ a0 and ast ¼ a1t : Therefore the last term in (2.12) cancels and the first two
terms sum to Ck ða0 ; kÞ Ck ða1t ; kÞ: Using (2.13), that costs are convex, the expression in (2.12)
amounts to ðe a1t ÞCka o0: Therefore, with full imitation, marginal returns to innovation are
always higher under auctioned permits than under the tax and auctioned permits lead to more
innovation.
When s ¼0, the second term cancels and asp oa0 : Using (2.13), the expression in (2.12) can be
shown to be positive if na1t ðn 1Þasp 4e: In other words, if the number of adopting firms is
sufficiently large, the extra royalties extracted from them under a tax outweighs the emissions
payment effect at the innovating firm under auctioned permits and the marginal returns to
innovation are always higher under an emission tax. That is, with no imitation, taxes lead to more
innovation. If this is the case, given that all the terms in the first-order conditions are well
behaved, then as s increases from 0 to 1 the policy that induces the most innovation flips from the
emissions tax to auctioned permits. &
Proposition 2. Innovation under free permits is less than that under both the emissions tax and
auctioned permits.
Proof. Under free permits there is no emissions payment effect, hence innovation is always lower
under free permits than auctioned permits. Setting e% ¼ e a0 in (2.12) gives
nfCk ða1t ; kÞ Ck ða0 ; kÞg þ sðn 1ÞfCk ðast ; skÞ Ck ða0 ; skÞg
ðn 1Þt0 ðkÞða0 asp Þ:
ð2:14Þ
Following the same steps as in the previous proof it is straightforward to show that (2.14) is
always positive, hence the emissions tax always induces more innovation than free permits. &
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
533
2.2.2. Welfare effects
The welfare effects of environmental policies are a bit tricky to compare because they depend
both on how innovation differs from the first-best level under alternative policies, and on whether
the level of abatement (after innovation) is suboptimal. Two situations offer clear orderings of
policies, demonstrated in the next two propositions. Propositions 5 and 6 explore the situations
that lead to reversals in the policy rankings.
Proposition 3. With constant marginal environmental benefits and no imitation, an emission tax
induces the first-best outcome while both permit policies produce lower welfare gains.
Proof. Let BðnaÞ ¼ bna and the Pigouvian tax t ¼ b: Then (2.2) is identical to (2.10) as the tax is
always first-best in terms of correcting the environmental externality; when s ¼0 (2.8) reduces to
(2.11) since the innovator can appropriate the full social benefits from innovation to other firms.
Thus, the first-order conditions in the private outcome are identical to the social planner’s and the
tax induces the socially optimal abatement and innovation. Under both free and auctioned
permits the permit price falls below marginal environmental benefits after innovation occurs,
tðkÞob; implying abatement is suboptimal. In addition, innovation differs from the first-best
level: (2.8) differs from (2.11) by t0 ðkÞðe a0 e% ðn 1Þða0 asp ÞÞ; which is non-zero for all
but a fortuitous choice of initial permit allocation. &
Proposition 4. With constant marginal environmental benefits, free permits induce a lower welfare
gain than an emissions tax for all values of the imitation parameter.
Proof. From Proposition 3 with constant marginal benefits an emissions tax is optimal with no
imitation. As s rises, innovation under the tax falls below the first-best amount. But from
Proposition 2, innovation is even further below the first-best level under free permits.
Furthermore, since the emissions tax reflects marginal environmental benefits, abatement is
closer to the first-best amount than under permits. Therefore, welfare is unambiguously lower
under free permits than under the emissions tax. &
Proposition 5. With constant marginal environmental benefits, auctioned permits can induce a higher
(lower) welfare gain than an emissions tax when the imitation parameter is greater (less) than some
critical level.
Proof. Consider an innovation cost function such that nCk ða0 ; kÞ4F 0 ð0Þ but Ck ða0 ; kÞo
F 0 ð0Þo Ck ða0 ; kÞ t0 ð0Þðe a0 Þ: When s ¼1, innovation is zero under the emissions tax, but
positive under auctioned permits due to the emissions payment effect. Abatement is the same
under both policies, but as long as ðn 1ÞCk ða0 ; kÞX t0 ð0Þðe a0 Þ (i.e., the emissions payment
effect does not induce too much innovation), welfare is necessarily higher with auctioned permits.
When s ¼0, taxes are superior (Proposition 3); therefore, at some critical s; the dominant policy
choice switches. &
534
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
Fig. 3. Welfare tradeoffs.
Discussion. This result holds generally even when F 0 ð0Þ ¼0. According to Proposition 1 at some
critical value for s; auctioned permits induce more innovation than the tax. Until this point (and
slightly beyond) it is easy to show (as in Proposition 4) that the tax induces higher welfare when
marginal benefits of abatement are constant. Fig. 3(a) illustrates the welfare tradeoff at the
industry level after this point: auctioned permits induce more innovation and generate gains 0hi,
while taxes induce more abatement but less innovation and gains of 0hl. Thus, whether emissions
taxes or auctioned permits induce higher welfare depends on whether area hgl is greater or less
than area 0gi, after netting out the costs of innovation. In the simulations below welfare tends to
be higher under auctioned permits beyond the critical value of s:
Proposition 6. The more steeply sloped is the marginal environmental benefit curve, the greater the
welfare gains under emissions permits and the smaller the gains under the emissions tax.
Proof. Since policy is set where marginal benefits equal marginal costs before innovation,
changing the slope of marginal benefits at that point does not change any behavior. However,
more rapidly declining marginal benefits imply more excess abatement and greater efficiency
losses from the emissions tax and less under-abatement and smaller efficiency losses from permits.
Therefore, as marginal benefits become steeper, the permit policies become relatively more
attractive compared with the tax. &
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
535
Discussion. Fig. 3(b) illustrates the welfare tradeoffs for a given level of innovation. The emissions
tax induces an excessive abatement per firm a1t following innovation, resulting in a welfare loss of
area ljr. The welfare loss from abatement per firm under permits remaining at a0 rather than
adjusting to the optimal level a is now area hil. Pivoting the marginal benefit curve through the
initial optimum point h; while a1t and a0 do not change, reduces hil and increases ljr.16
Of course, the relative size of these areas also depends on the relative innovation amounts (as
was depicted in Fig. 3(a)). Since at is largest in the absence of imitation, the welfare losses from
over-abatement with the tax are strongest for a low imitation parameter. The extra abatement can
also imply too much innovation; both these effects lessen as imitation increases. Meanwhile, as
imitation opportunities become complete the gains from extra innovation grow stronger, and
auctioned permits gain preference. Therefore, depending on the particular functions, one or the
other policy can dominate the whole time or part of the time. In particular, the policy rankings
can switch more than once, with permits (auctioned or free) preferred at low imitation
parameter,17 then taxes in the middle, and auctioned permits at high imitation parameter.
3. Numerical simulations
This section conducts numerical simulation exercises to illustrate under what conditions the
different innovation and welfare effects of alternative environmental policies are significant and
when they are not.
3.1. Model calibration
We adopt the following functional forms:
nCða; kÞ ¼ ek
ðanÞ2
;
2
F ðkÞ ¼ f
k2
;
2
a
BðanÞ ¼ ban ðb anÞ2 ;
2
ð3:1Þ
where f ; b and a are parameters and ape: Aggregate abatement costs nC decline exponentially with innovation, k; thus, additional cost reductions are increasingly difficult to
generate through innovation. Environmental benefits and abatement costs (for a given k)
are quadratic in aggregate emissions abatement an.18 The costs of innovation are also
16
This is reminiscent of Weitzman’s [31] result concerning instrument choice in the presence of uncertainty: Steep
marginal benefits favor permits and flat marginal benefits favor taxes. The reason here is the same: When marginal costs
are shifting after policy has been set, either due to random shocks or to innovation, the policy that most closely mimics
the slope of the marginal benefit curve tends to perform better.
17
If auctioned permits provide too much innovation at low imitation, free permits can then dominate.
18
These assumptions imply the first-best emissions abatement is b in the absence of innovation and the slope of
marginal benefit function, a; affects the optimal abatement only when innovation is positive. This allows us to isolate
the effect of declining marginal benefits from effects related to the initial abatement level in the absence of innovation.
In addition, the first-best abatement level (and the optimal innovation level) does not depend on the number of firms, n.
This allows us to consider the effects of market size in isolation from effects related to the magnitude of costs and
benefits.
536
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
Fig. 4. Benchmark simulations of alternative policies.
quadratic.19 Even these simple functional forms in (3.1) produce non-linear first-order conditions
for abatement and innovation, requiring numerical solution methods.20
We generate benchmark results providing a quantitative comparison of welfare and innovation
under different policy instruments and then provide a detailed sensitivity analysis. To start with
we assume marginal environmental benefits are constant (a ¼0),21 and that first-best emissions
abatement would be 20 percent prior to innovation. That is, the parameter f is chosen to imply
that innovation in the first-best outcome would reduce abatement costs by 20 percent. To
approximate a competitive market we assume the number of firms is 100. We begin by considering
all possible values for sð0psp1Þ; and subsequently a ‘‘low imitation’’ case (s ¼0.25) and a ‘‘high
imitation’’ case (s ¼0.75).22
3.2. Main results
3.2.1. Benchmark results
The left-hand panel of Fig. 4 shows the welfare gain under each policy as a fraction of the firstbest welfare gain and plotted against the degree of imitation. The right-hand panel indicates
19
This seems plausible due to the increasing scarcity of specialized inputs (e.g. scientists and engineers) at higher
levels of research activity. However our results are not very sensitive to assuming linear marginal costs.
20
Substituting (3.1) in our expression for social welfare (2.9), we can derive conditions (2.10) and (2.11) and hence
obtain the first-best outcome, a and k : To solve the model under alternative policies, we use condition (2.2) to obtain
aðk; tÞ ¼ t=nek : Using this, (2.4), (2.6), and (3.1), we obtain we expression for innovator profits that is maximized with
respect to k; where t ¼ B0 ðna0 Þ ¼ Ca ða0 ; 0Þ under the emissions tax, while under permits a ¼ a0 ; and t adjusts to satisfy
(2.2). The welfare gain from innovation under each policy, W ðna; kÞ W ðna0 ; 0Þ; is computed and expressed as a
fraction of the welfare gain in the first-best outcome W ðna ; k Þ W ðna0 ; 0Þ:
21
This seems a plausible approximation for air pollutants like sulfur dioxide and particulates, because the number of
fatalities (the major damage component) is roughly linear with respect to pollution concentrations [2]. It is also
reasonable approximation when one period’s emissions have only a small effect on the accumulated stock of pollution,
as in the case of greenhouse gases, even environmental damages are convex with respect to the stock [26].
Declining marginal environmental benefits apply when there are threshold effects in the assimilative capacity of the
environment [20].
22
Studies for commercial (or non-environmental) innovations suggest that appropriation rates vary considerably
over different types of innovations, with an average rate of perhaps around 50 percent (e.g., [9,21]).
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
537
innovation induced by each policy, again expressed relative to the first-best level and plotted
against the degree of imitation.
When the imitation effect is weak, emissions taxes induce a significantly higher amount of
innovation and welfare compared with permit policies. For example, when s is below 0.2, the tax
achieves 95–100 percent of the first-best welfare gain, while emissions permits induce 60–70
percent of the first-best welfare gain. The reason is that the larger abatement cost effect under the
emissions tax is only moderately offset by the imitation effect.
When the imitation effect is strong, innovation and welfare are a much smaller fraction of firstbest welfare levels because the private benefit from innovation is small relative to the social
benefit. Furthermore, the absolute differences between the policies become less important: for
example, when s ¼0.8, the welfare difference between the most efficient and least efficient policies
is 8 percent of the first-best welfare gains. Finally, when s40.75, innovation and welfare are
highest under auctioned permits, since the emissions payment effect at the innovating firm
becomes large relative to royalties obtained from other firms. However, the extra welfare gain
under auctioned permits in these cases is typically not that large.
3.2.2. Declining marginal environmental benefits
On the horizontal axes in Fig. 5 we vary the (magnitude of the) slope of the marginal
environmental benefit curve between one-tenth and ten times the slope of the marginal abatement
cost curve. We do this by pivoting the marginal environmental benefit curve about the initial
Pigouvian abatement level of 20 percent (a0 in Figs. 1–3). The level of policy instruments—and
hence the private incentives for innovation and abatement—are constant in this exercise: varying
marginal environmental benefits affects first-best outcome but not the policy-induced outcomes.
The left- and right-hand panels illustrate welfare effects under our low (s ¼0.25) and high
(s ¼0.75) imitation scenarios.
This figure shows that the relative slope of the marginal environmental benefit function can
crucially affect the relative welfare impacts of alternative policies. For example, in the left-hand
panel when the marginal environmental benefit curve is half as steep as the marginal abatement
cost curve, the welfare gain under the tax is around 25 percent larger than the welfare gain under
Fig. 5. Effect of marginal benefit slope on welfare gains.
538
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
Fig. 6. Effect of R&D costs on welfare gains.
(free or auctioned) emissions permits. But when the marginal environmental benefit curve is twice
as steep as the marginal abatement cost curve, the welfare gain under (free or auctioned) permits is
about double the welfare gain under the emissions tax. In this case, innovation and ex-post
abatement levels are excessive under the emissions tax (the abatement cost effect overcompensates
for the imitation effect) and emissions permits induce outcomes closer to the first-best. This
underscore the potential danger from ranking policies based on innovation rather than welfare—
here, the emissions tax induces more innovation than the permit policies but generates a smaller
welfare.
In the high imitation scenario (right-hand panel) the incentives for innovation are suboptimal
under all policies and the welfare gain curves are shifted down (compared with the left panel).
Again, the steeper the marginal benefit curve, the more likely that welfare is higher under permits
than under the tax.23 The additional welfare gain from auctioned over free permits is a more
substantial 25 percent in this case, reflecting the larger size of the emissions payment relative to the
royalties obtained from other firms.24
3.2.3. Innovation costs
Fig. 6 illustrates how the cost of innovation affects the relative welfare ranking, with constant
marginal environmental benefits. As the innovation cost parameter ðf Þ increases, innovation and
the downward shift in the marginal abatement cost curve decline under each policy.
With low imitation, taxes provide roughly the optimal incentive to innovate and abate for the
full range of R&D costs and come close to achieving the first-best outcome (left panel). In
23
However, note that welfare under the tax exceeds that under free permits over a wider range in the right compared
with the left panel. Even when the marginal benefits curve is relatively steep and abatement is excessive under the
emissions tax, up to a point the tax may still be more efficient overall than free emissions permits. The greater incentives
for innovation under the tax, due to the higher abatement cost effect, now serve to mitigate the inadequate incentives
due to high imitation (in contrast, in the low imitation scenario this higher abatement cost effect is more likely to induce
excessive innovation).
24
Auctioned permits perform slightly better than the emissions tax even when the marginal benefit curve is relatively
fat. In this case abatement under the tax is closer to the first-best level. However, innovation is closer to the first-best
level under auctioned permits because of the relatively large emissions payment effect.
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
539
Fig. 7. Effect of number of firms and benefit level on welfare gain.
contrast, the welfare gains forgone under emission permits are quite large when the cost of
innovation is low and the socially optimal level of innovation is high. When f=1 the welfare
effects of all three policies are similar, but when f=0.07, the emissions tax induces a welfare gain
about 80 percent larger than under permits (innovation reduces abatement costs by 3 percent and
35 percent in the first-best outcome when f equals 1 and 0.07, respectively). This reflects the larger
difference between the abatement cost effect under taxes than permits when the downward shift in
the marginal abatement cost curve is greater.
These results change somewhat when imitation is strong, however. In the right panel, a stronger
imitation effect reduces innovation and welfare under all three policies. The proportionate
reduction in welfare is greatest under the emission tax, since the abatement cost effect is greatest
for this policy. Again, high imitation raises the relative importance of the emissions payment
effect, and auctioned permits typically induce the highest welfare.25
3.2.4. Number of firms and benefit level
Fig. 7 illustrates some more cases in the high imitation scenario where the emissions payment
effect under auctioned permits can be large relative to the other determinants of innovation
incentives. As we reduce the number of firms (left panel) the emission payment effect becomes
larger because the innovator purchases a larger share of industry permits. With fewer than five
firms, innovation is so excessive under auctioned permits that the net welfare gain from
innovation is negative.26 In contrast, welfare rises for both taxes and free permits because the
detrimental effects of imitation are less important with fewer firms.
In the right panel we vary the level of marginal benefits, b; between 0 and 0.25, which implies
the initially optimal abatement level a0 varies between 0 and 25 percent. The smaller is a0 the
25
Innovation need not always be large in order for there to be significant welfare differences among policies. When
f ¼1 welfare is 20 percent higher under auctioned permits than other policies in the right panel even though innovation
only lowers abatement costs by 3 percent.
26
Of course with few firms our assumption of competitive firms becomes more dubious. Nonetheless, even with
strategic behaviour, it is still the case that the emission payment effect becomes more important, hence widening the
difference between auctioned and free permits.
540
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
larger the emissions payment effect relative to the abatement cost effect (see Fig. 2). This mitigates
the adverse impacts of the imitation effect under auctioned permits and this policy may induce the
highest welfare gain when abatement is modest.27
3.2.5. Further sensitivity analysis
Varying each parameter individually may obscure some important interactions among
parameter combinations. Table 2 illustrates innovation and welfare under each policy (relative
to first-best levels) as we consider ‘‘high’’ and ‘‘low’’ values for all parameters simultaneously.
There are several points in this table worth noting. So far we have only seen situations where
either the emissions tax or auctioned permits induce the highest welfare gain. But free permits
produce the greatest welfare gain in the case of high imitation, steeply sloped marginal
environmental benefits, low innovation costs, a small number of firms, and high benefits/
abatement (case x32). In this situation, auctioned permits lead to too much innovation while taxes
lead to too much abatement. We can also see cases (x3, 7, 11, 15, 19, 23, 27, and 31) where the
emissions payment effect under auctioned permits generates such an excessive amount of
innovation that welfare is actually negative, namely when there are a small number of firms and a
small level of initial abatement. Finally, we can see cases (x14 and 16) where taxes induce an
excessive amount of innovation and a welfare loss. This occurs when marginal benefits are steep,
and innovation incentives are large (innovation costs are low, the imitation effect is weak, and
initial abatement/benefit levels are high).
4. Further issues
4.1. Policy adjustment and optimization
In the above analysis environmental policies are not adjusted in response to innovation and
remain at their ex-ante Pigouvian levels ignoring innovation. Suppose instead that policies are
instantly adjusted to the ex-post Pigouvian levels after innovation occurs, and this adjustment is
anticipated by the innovator.28 When marginal environmental benefits are constant, all three
policies become functionally equivalent. Ex-post abatement levels, and hence the abatement cost
effect, are identical under all policies. In addition, the quantity of permits is reduced to prevent the
emissions price from falling, and hence there are no emissions payment or adoption price effects.
However, innovation will still be below first-best levels due to the imitation effect.
When marginal environmental benefits are declining, the emissions price falls with policy
adjustment. Both the tax and auctioned permits then have an equivalent emissions payment
effect, but free permits do not. Consequently, auctioned permits and the emissions tax
remain equivalent, but innovation is lower under free permits. Thus in general the
27
In the very extreme case (less than 1 percent abatement), however, innovation again becomes so excessive that
auctioned permits are welfare-reducing overall.
28
In practice policy instruments are not perfectly flexible; rather, they can be adjusted periodically when
environmental legislation comes up for re-authorization.
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
541
Table 2
The interaction of alternative parameter values
Case Imitation MB Innovation Number MB
level
slope costs
of firms level
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
High
Low
Low
Low
Low
Low
Low
Low
Low
High
High
High
High
High
High
High
High
Low
Low
Low
Low
Low
Low
Low
Low
High
High
High
High
High
High
High
High
High
High
High
High
Low
Low
Low
Low
High
High
High
High
Low
Low
Low
Low
High
High
High
High
Low
Low
Low
Low
High
High
High
High
Low
Low
Low
Low
High
High
Low
Low
High
High
Low
Low
High
High
Low
Low
High
High
Low
Low
High
High
Low
Low
High
High
Low
Low
High
High
Low
Low
High
High
Low
Low
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Optimal Welfare
shift
(relative to first best)
Innovation level
(relative to first best)
in MAC Tax
Auction
Free
Tax
Auction
Free
0.02
0.25
0.02
0.25
0.06
0.77
0.06
0.77
0.02
0.19
0.02
0.19
0.06
0.41
0.06
0.41
0.02
0.25
0.02
0.25
0.06
0.77
0.06
0.77
0.02
0.19
0.02
0.19
0.06
0.41
0.06
0.41
0.95
0.57
22.69
0.20
0.87
0.13
14.31
0.11
0.97
0.76
23.25
0.26
0.93
0.59
15.30
0.48
0.65
0.35
20.90
0.29
0.61
0.09
13.63
0.11
0.67
0.46
21.42
0.38
0.65
0.40
14.57
0.49
0.89
0.56
0.92
0.60
0.81
0.13
0.85
0.14
0.91
0.73
0.95
0.79
0.86
0.58
0.91
0.64
0.43
0.30
0.72
0.49
0.40
0.08
0.67
0.13
0.44
0.40
0.74
0.65
0.43
0.35
0.72
0.56
0.75
0.73
0.83
0.82
0.75
0.95
0.83
0.96
0.77
0.98
0.85
1.10
0.80
2.62
0.89
2.67
0.25
0.21
0.50
0.44
0.25
0.14
0.49
0.38
0.26
0.29
0.51
0.59
0.27
0.39
0.52
1.05
0.87
0.43
5.70
1.15
0.77
0.16
4.55
0.41
0.89
0.58
5.85
1.55
0.82
0.44
4.87
1.15
0.42
0.20
5.52
1.10
0.39
0.09
4.47
0.41
0.43
0.27
5.66
1.47
0.42
0.25
4.78
1.14
0.70
0.41
0.78
0.47
0.63
0.15
0.71
0.18
0.72
0.55
0.80
0.64
0.67
0.42
0.76
0.51
0.25
0.17
0.48
0.33
0.23
0.08
0.45
0.14
0.25
0.23
0.49
0.44
0.25
0.21
0.48
0.40
0.94
0.93
0.97
0.97
0.94
0.99
0.97
0.99
0.93
0.72
0.96
0.63
0.92
15.90
0.93
15.88
0.44
0.39
0.75
0.69
0.43
0.16
0.74
0.39
0.45
0.47
0.75
0.74
0.46
0.51
0.75
0.28
Parameters values: imitation level high (s ¼0.75), low (s ¼0.25); slope of marginal environmental benefit (MB) curve
high (b ¼1), low (b ¼0); innovation costs high (f ¼0.21), low (f ¼0.08); number of firms high (n ¼100), low (n ¼3); level
of marginal environmental benefit (MB) curve low (a0 ¼0.1), high (a0 ¼0.3).
welfare difference between the policies tends to shrink the more frequently they are reoptimized.29
29
Environmental policy adjustment has received some attention in prior literature. Milliman and Prince [19] analyze
whether firms are better off or not with policy adjustment. Kennedy and Laplante [14] find that a time inconsistency
problem can arise between ex-ante incentives for adoption and ex-post abatement efficiency for discrete technologies
requiring a fixed installation cost. The result is a non-convexity in the overall abatement cost function. The planner sets
a tax rate, but becomes stuck if marginal benefits of abatement are declining and partial adoption is optimal. With
542
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
In addition to the reactive and myopic policies described so far, we can also imagine a smart
policy-maker seeking an optimal but non-reactive tax or permit level that takes full account of
innovative behavior. Such a policy would try to correct both the pollution and R&D market
failures as effectively as possible, but fix the level of taxes or permits before innovation occurs. In
the absence of a second market failure30 the social optimum can be decentralized with (a time path
of) fixed taxes set equal to Pigouvian levels and given the optimal time path of technology. (This
proof would follow that of Proposition 3.) A permit policy, however, cannot decentralize the
optimum, even without imitation, since the price effects distort innovation incentives. With a
second market failure, neither policy instrument can fully correct both failures and will instead
need to trade off one against the other. In this case the ranking of alternative policy instruments is
again unclear. In sum, the planner’s ability to adjust policies (or not) and to set credible secondbest levels can indeed have an impact on the choice of instrument. Although we do not solve for
these additional scenarios here, they will interact with the other variables previously discussed
(slope of marginal benefits, imitation parameter, etc.) in determining welfare.31 The intuition
behind the trade-offs and incentives remains the same, as does the result that the ranking of policy
instruments depends on the particular situation.
4.2. Incomplete diffusion
Throughout the analysis we have assumed complete diffusion of the new technology. In theory,
under emissions permits an innovator may maximize revenues by limiting diffusion and hence the
fall in the permit price. However this is an extreme case, and in fact it is precluded in our
numerical simulations by functional form assumptions (see [6, appendix]).
More generally, firms are heterogeneous and differ in their willingness to pay for new
technologies. Under these conditions it may be optimal for an innovator to limit diffusion to keep
the royalty fee above that required for the firm with lowest willingness to pay to adopt the
technology. However, this complication may not be that significant in practice, at least when the
number of firms is large. Parry [23] finds that the (second-order) efficiency loss from suboptimal
diffusion is likely to be small relative to the (first-order) social benefits from firms that do adopt
abatement technologies (see his Fig. 2).32
(footnote continued)
identical firms, all adopt or not at fixed prices. Thus, where full adoption is overkill (and none is sufficient) the tax price
that is optimal with the old technology induces full adoption and is then too high ex-post. Meanwhile, the postadoption tax rate is too low to induce adoption. The tax policy is therefore time-inconsistent. Petrakis and Xepapadeas
[25] compare optimal pre-commitment and time-inconsistent policy strategies for emissions abatement when the
polluter is an innovating monopolist.
30
Imitation, or non-convexities as in [14], or product market monopoly as in [25].
31
Petrakis and Xepapadeas [25] perform this type of analysis for a polluting monopolists, finding that innovation is
higher with the time-consistent (reactive) policy due to a type of emissions payment effect), but welfare is lower
compared to a pre-commitment strategy. The former result is less likely here, due to the existence of the adoption price
effect, which can dominate the innovating firm’s emission price effect.
32
If technology adoption involves real resource costs, and these costs differ across firms, complete diffusion of new
abatement technologies may not be socially efficient (e.g., [14]). This does not apply to our model as there are no
resource costs to adoption.
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
543
4.3. Innovation by an ‘‘outside’’ supplier
Suppose that an upstream supplier conducts innovation rather than a firm that is engaged in
polluting activities. In this case the innovator gains only from licensing the technology, and not
from any reduction in its own costs. There is no emissions payment effect, and auctioned permits
become equivalent to free permits. Thus, innovation would always be greatest under the emissions
tax, and permits could only induce a higher welfare gain when the marginal environmental benefit
curve is more steeply sloped.33
4.4. Additional policies to stimulate research
Governments often buttress the patent system by directly subsidizing research and by offering
preferential tax treatment for corporate R&D expenditures. To the extent that these policies
promote more innovation they would widen the welfare gap between emission taxes and permits
in our benchmark case (see the discussion of Fig. 6). Nonetheless it would be useful in future work
to explore to what extent the second-best optimal subsidy for R&D might vary under different
environmental policy instruments.34
5. Conclusion
This paper presents a theoretical and quantitative comparison of the innovation and welfare
effects of emissions taxes and free and auctioned emissions permits when technological innovation
is endogenous. Contrary to some results from earlier (non-competitive) models, we do not find a
general preference for auctioned permits over emissions taxes and emissions taxes over free
permits. Under different circumstances either auctioned permits or taxes can induce larger
amounts of innovation but any of the three policies may induce a significantly greater welfare gain
than the other two. The relative ranking of policy instruments depends on the scope for imitating
new technologies, the costs of innovation, the relative level and slope of the marginal
environmental benefit function, and the number of polluting firms.
Some rough policy guidelines can be summarized: First, when imitation opportunities are
limited and diffusion is wide, what matters is inducing the optimal level of emissions abatement
over time. If marginal environmental benefits are relatively flat an emissions tax is the most
efficient instrument; if marginal benefits are relatively steep then free or auctioned permits are
more efficient. Second, when imitation rates are high, auctioned emissions permits may induce the
highest welfare gain. However, the danger exists that this policy may induce excessive innovation
when the number of polluters, or the initial abatement level, is relatively small. Third, the welfare
33
Markets might offer the innovator an opportunity to capture more of the industry gains from emissions price
changes by shorting permits. By contracting to sell permits in the second period at pre-innovation prices, the innovator
gains from the post-innovation price fall on those promised permits. However, it is not credible that an innovator could
short the entire permit market and capture all the industry gains.
34
Research subsidies have their own problems, however. For example, it is difficult for governments to allocate
research funding efficiently when it knows less about the expected return on different projects than the private sector.
See [17] for more discussions of this issue.
544
C. Fischer et al. / Journal of Environmental Economics and Management 45 (2003) 523–545
discrepancies between policies are typically smaller when less innovation occurs during the period
for which policy instruments are fixed. Frequent policy adjustment means the choice of
instrument will matter less.
Our analysis ignores a number of complications that might be worth exploring in future
research. We abstract from the possibility of strategic behavior in the technology adoption
decision. We also assume the innovation process is deterministic—in reality, the fruits of
innovation investments can be highly uncertain. This makes it difficult to adjust environmental
policies optimally over time and to credibly commit to future policies.
We also focus on welfare maximization measuring both costs and benefits. Sometimes
(particularly when environmental benefits are highly uncertain) the policy objective may be to
minimize the cost of stabilizing environmental quality at a target level—ignoring benefits—and
this alternative criterion may affect the appropriate choice of policy instrument. Finally, we
assume that technological innovation results exclusively from deliberate investments in innovation
activity. Firms may instead learn by doing and become more efficient at pollution abatement as
they gain more experience over time.35
Acknowledgments
We are grateful to Tim Brennan, Raymond Prince, Mike Toman, and three referees for helpful
comments and suggestions. We also thank the Environmental Protection Agency (Grant CX
82625301) for financial support.
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