Irreversible Abatement Investment Under Cost Uncertainties

40 Pages·2000·0.37 MB·English

Irreversible Abatement Investment Under Cost Uncertainties:
Tradable Emission Permits and Emissions Charges
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Jinhua Zhao
May 22, 2000
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The author is an assistant professor in the Department of Economics, Iowa State University. I thank
David Hennessy, LarryKarp,CathyKling, HarveyLapan,and Quinn Weningerfor their helpful comments.
Theusualdisclaimerapplies. Address: DepartmentofEconomics,HeadyHall,IowaStateUniversity,Ames,
IA 50011. Phone: [phone]. Fax: [phone]. Email: [email protected].
Abstract
A major concern with TEPs is that stochastic permit prices may reduce (cid:12)rm incentive to
invest in abatement capital or technologies relative to other policies such as a (cid:12)xed emissions
charge. However, under eÆcient permit trading, the price uncertainty is caused by abatement cost
uncertainties whicha(cid:11)ect investment underboth permitandcharge policies. We develop a rational
expectations general equilibrium model of permit trading to show how cost uncertainty a(cid:11)ects
investment. Di(cid:11)erences between the two policies can be decomposed into a general equilibrium
e(cid:11)ect and a price-vs-quantity e(cid:11)ect. Except for the curvature of the payo(cid:11) functions, uncertainties
reduce both e(cid:11)ects so that tradable permitsinfact helpmaintain(cid:12)rms’investment incentiveunder
uncertainty. (JEL: Q20)
1 Introduction
Tradableemissionpermits(TEPs)aregainingpopularityinenvironmentalregulationasmanifested
by the successful sulfur trading in the U.S. and the global carbon trading proposed in the Kyoto
Protocol. Amongtheoften-citedadvantagesofTEPsistheargumentthatitprovidesmoreincentive
for (cid:12)rms to invest in abatement technologies or capital than the command and control policies(i.e.
standards). In the short run it provides as much incentive as an emissions tax. In the long run,
a constant emissions tax would provide more incentive than grandfathered permits because the
marginal abatement costs go down as (cid:12)rms invest, reducing permit price as well as the bene(cid:12)ts
of investment. These (cid:12)ndings have been discussed in Magat (1978), Milliman and Prince (1989),
and Jung, Krutilla and Boyd (1996). However, even in the long run, Parry (1997) showed that the
incentive o(cid:11)ered by permits would be close to that by a tax for many pollutants.
Despite these (cid:12)ndings, there is a serious concern that TEPs may reduce a (cid:12)rm’s incentive to
investbecausepermitpricesaretypicallyrandomandtheinvestmentistoagreatextentirreversible
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(Xepapadeas (1999) andChaoandWilson(1993)). Incontrast, otherpoliciessuchas standardsor
taxes do not introduce this additionaluncertainty. Consequently, in a stochastic world, investment
incentive under permits may be smaller. These studies typically assume exogenous and random
permitpriceprocesses (Xepapadeas (1999)) or exogenous andrandomdemandfunctionfor permits
(Chao and Wilson (1993)). In Baldurssonand von der Fher (1999), uncertainty is due to the entry
and exit of polluting (cid:12)rms.
These studies point out an important possibility. However, since permit price is directly de-
termined by (cid:12)rms’ abatement costs through (eÆcient) permit trading, a major force behind price
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randomness is the cost uncertainties. Such cost uncertainties will a(cid:11)ect the investment decisions
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That irreversibility and uncertainty (and future learning) reduces investment is a standard conclusion of real
option theory(Arrow andFisher (1974) and Dixitand Pindyck (1994)).
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Throughoutthispaper,wewill maintaintheeÆcientpermittradinghypothesis. Thishypothesisiscon(cid:12)rmedin
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underotherpoliciesaswell. TEPsdonotcreateuncertaintiesinitsownright,butrather\transmit"
cost uncertainties into permit prices. Thus the relevant question is, compared with other policies,
whether cost uncertainties reduce the investment incentive by a larger amount under TEPs when
the permit price is endogenously determined by abatement costs through permit trading.
In this paper, we introduce a general equilibriummodel of permit trading by price taking (cid:12)rms
with stochastic abatement costs and rational expectations about permitprices. In each period, the
government grandfathers a (cid:12)xed number of emission permits. The only exogenous factors in the
modelareabatementcost shocks. Giventhe(marginal)costs, eÆcientpermittradingendogenously
determines the equilibrium permit price. A (cid:12)rm can invest in capital or technology to reduce its
abatement cost. The investment is irreversible. The aggregate investment behavior of the (cid:12)rms
(together with the cost shocks) determine the time path of the permit price.
Thus,ourmodeldi(cid:11)ersfromtheliteratureinthatpriceuncertainty isendogenouslydetermined
by abatement cost uncertainties in the general equilibrium. In particular, cost shocks change
the price instantaneously through permit trading and overtime through capital or technological
investment. Our model captures several salient features of a TEP system. First, (arguably) the
mostimportantdeterminantofpermitpriceisthe(cid:12)rms’abatementcosts. Firms’input,outputand
entry/exit decisions do a(cid:11)ect permit price, but mainly indirectly through altering the abatement
costs. For example, railway deregulation in the U.S. raised the use of low sulfur coal by the utility
companies, contributing to the lower-than-expected SO2 permit price (Burtraw (1996)). Here the
regulatory change reduced permit price through lowering the (marginal) abatement costs. We
model the cost shocks without restricting them to be from a particular source. Second, a TEP
system is in essence similar to a pure exchange economy with (cid:12)xed endowment of permits. There
are no exogenous permit demand or supply functions. Rather, (cid:12)rms choose to be permit suppliers
one of the best knownTEP systems,the SO2 trading in theU.S. (Joskow, Schmalensee andBailey (1998)).
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or buyers through investment. Finally, capital or technological investments are diÆcult to reverse.
For example, a utility company will (cid:12)nd it costly to get rid of a scrubber it has installed.
Weuseourmodeltostudyhow(cid:12)rms’investmentincentiverespondstoindustryand(cid:12)rmspeci(cid:12)c
abatement cost uncertainties. There is a sizeable literature on investment decisions under uncer-
tainty and irreversibility, such as Arrow and Fisher (1974), Henry (1974) and Kolstad (1996). In
partial equilibrium models with exogenously given price processes, they (cid:12)nd that increased uncer-
tainty reducesinvestment incentive for riskneutral(cid:12)rms. Sincethe investment isirreversible,(cid:12)rms
may (cid:12)nditoptimaltoholdbacktheirinvestment(i.e.wait)untilthecostshocksare highenoughto
justify immediate action. Introducing general equilibriumgreatly complicates the analysis, mainly
because it is diÆcult to directly search for the equilibrium permit price process. Further, it is not
clear whether uncertainty, especially industry-wide uncertainty, will reduce investment. The rea-
son is that if one (cid:12)rm waits, other (cid:12)rms may invest and consequently drive down the permit price,
making further investment suboptimal. That is, facing industry shocks, the (cid:12)rms may \compete"
for the investment opportunity, reducing the value of waiting and consequently raising the invest-
ment incentive. Leahy (1993), Caballero and Pindyck (1996) and Baldursson and Karatzas (1997)
showed that this concern does not matter inmodelsof (cid:12)rmsmaking entry and exit decisionsfacing
exogenous demand shocks in competitive equilibrium. The (cid:12)rms may \pretend" that the price will
not be a(cid:11)ected by other (cid:12)rms’ investment, and uncertainty still reduces investment. Our model is
di(cid:11)erent in both the form of uncertainty and the (cid:12)rm decisions. We show that their results, with
some modi(cid:12)cation, still apply to our case.
We then consider (cid:12)rms’ investment strategies facing an emissions charge/subsidy that is con-
stant overtime. Following the tradition of Milliman and Prince (1989) and Jung et al. (1996), we
choose the charge policy to be \comparable" to the permit policy in that they lead to the same
abatement levels in the current period. In a deterministic model, future abatement levels will di-
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verge under the tax and permit policies since the policies lead to di(cid:11)erent investment paths. This
policy di(cid:11)erence is the general equilibrium e(cid:11)ect of permits where equilibrium permit price goes
down as (cid:12)rms invest. When abatement costs are stochastic, abatement levels can diverge even
withoutthe general equilibriume(cid:11)ect since tax isa price tool and permitisa quantity tool (Weitz-
man (1974)). We call this policy di(cid:11)erence the price-vs-quantity e(cid:11)ect. We will separate the two
e(cid:11)ects in comparing (cid:12)rm investment incentive under the two policies. We (cid:12)nd that uncertainty
reduces, but does not eliminate, the general equilibriume(cid:11)ect: the investment paths underthe two
policies converge as uncertainty level increases. Except for the curvature of the payo(cid:11) functions,
uncertainty also reduces the price-vs-quantity e(cid:11)ect. Thus TEPs help maintain (cid:12)rms’ investment
incentive under uncertainty relative to charges.
Like many papers on abatement capital or technological investment, such as Magat (1978),
Milliman and Prince (1989), Jung et al. (1996), Farzin, Huisman and Kort (1998) and Farzin and
Kort (2000), we onlyaddress the positivequestionof \what happens"underdi(cid:11)erentpolicieswhen
there is cost uncertainty and investment irreversibility. We do not tackle the normative issue of
what constitutes an optimal policy. In fact, we take a rather static view of the policies themselves:
thepermitandtax levelsare(cid:12)xedthroughouttime, regardlessof(cid:12)rms’investmentandcostshocks.
These policies are likely to be ineÆcient, but may resemble the real world better than policiesthat
adjust frequently to investment and cost shocks.
There seems to be a long-standing consensus among (at least) environmental economists that
an eÆcient environmental policy should encourage (cid:12)rms, in the long run, to invest in abatement
capital or technology (see, for example, Kneese and Schultze (1975) and Kemp and Soete (1990)).
From a purely theoretical standpoint, investment decisions and policy eÆciency do not have to be
related. After all, it is the environmental externality that the policy is trying to correct. If the
policy successfully does so and if there is no distortion in other sectors of the economy, investment
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decisions should be left to the (cid:12)rms themselves and should be determined by market forces. That
is, environmental policy should not even attempt to in(cid:13)uence (cid:12)rms’ investment incentive.
To the best of our knowledge, there does not exist a formal investigation into why environ-
mental policies should encourage such investment. There are, however, some peripheral evidence
that points to possibleexplanations. If traditionallyenvironmental externalities have been \under-
regulated" in the sense that the policies have corrected only part of the externalities, more invest-
ment helps reduce the \ineÆciency" of these policies by ameliorating the environmental problem
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and the need for strict regulation. That is, in the long run, (lax) environmental regulation that
encourages more investment should be more eÆcient. Another possibility is that regulators may
be subject to \hold-up" by (cid:12)rms who anticipate less strict regulation if they do not invest and thus
keep their abatement expensive(Gersbach andGlazer (1999)). Inthiscase, policiesthat encourage
investment help reduce this hold-up problem, and tend to be more eÆcient. Further, there may be
information spillover from adopters of new technologies to potential adopters, so there is less than
socially optimal adoption. Empirically, (cid:12)rms have been perceived not to be willing to invest up to
the socially optimal level, leading in part to the introduction of \technology-forcing" regulation in
certain cases (such as mobile source air pollution). The relevance of our paper for policy analysis
should be viewed in this broad context of regulation that targets the environmental externality
itself and (indirectly) the long-run investment incentive.
Thepaperisorganizedasfollows. Weconstructthegeneralequilibriummodelofpermittrading
in Section 2. We solve for the (cid:12)rms’ optimal investment strategies under permits in Section 3, and
underan equivalent charge policyin Section4. We discussthe generality of ourmodelin Section5,
and conclude the paper in Section 6.
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Whilepeoplemaydisagreeaboutwhetherwehavetoomuchortoolittleregulation, thefactthatmanyenviron-
mental problemsare getting worse over time and new regulations are constantly being introduced does point to the
possibility of insuÆcient regulation.
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2 Model Setup: Investment Under Permits
Irreversible investment models underuncertainty can quicklybecome intractable, even without the
added diÆculty of handling a rational expectations general equilibrium. We will assume special
functional forms in order to obtain analytical results. We will discuss the implications of these
assumptions in Section 5, showing that they are not likely to change our major conclusions. But
at the beginning, we work with more general functions to de(cid:12)ne and characterize the competitive
equilibrium.
Consider a tradable emissions permit market consisting of N price taking (cid:12)rms with rational
expectations about permit prices. We focus on emissions trading and ignore (cid:12)rms’ output de-
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cisions. Let the total abatement cost (TAC) of (cid:12)rm n be C(an;Kn;n;(cid:15)n;(cid:15)0), where an is the
abatement level, Kn the stock of abatement capital or technology, (cid:15)n the (cid:12)rm speci(cid:12)c shock, and
(cid:15)0 the industry shock a(cid:11)ecting every (cid:12)rm in the TEP market. By allowing TAC to depend on n,
we account for the heterogeneity of the (cid:12)rms, a major advantage of tradable permits. We assume
that the cost is increasing and convex in the abatement level: Ca > 0 and Caa > 0. Capital or
technological stock reduces the cost, but at a decreasing rate: CK < 0 and CKK > 0. Positive
(cid:12)rm and industry shocks increase the cost, but also make capital or technological investment more
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worthwhile: C(cid:15)n >0, CKn(cid:15)n <0, C(cid:15)0 >0, and CKn(cid:15)0 <0.
We consider (cid:12)rm decisions in continuous time over [0;1). We assume that (cid:12)rm speci(cid:12)c and
industry shocks follow independent generalized Brownian motions:
d(cid:15)n =(cid:11)n((cid:15)n;t)dt+(cid:27)n((cid:15)n;t)dzn(t); n=0;1;:::;N; (1)
where dzn(t) is the incremental Wiener process, with E(dzn(t)) = 0, var(dzn(t)) = dt, and
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Firms may be in di(cid:11)erent industries and produce di(cid:11)erent kinds of outputs. Requate (1998) studies speci(cid:12)cally
therelationship between outputchoice andpermittrading decisions.
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Thislastassumptionis notcritical for ourgeneral results. Sincearandomshockcanbe equallyhighorlow, the
e(cid:11)ectsofcostuncertaintyoninvestmentwillnotchangeevenifwereverseoneormoreconditionsinthisassumption.
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cov(dzn;dzm) = 0 whenever n 6= m. Random change in (cid:15)0 represents the industry shock and
that in (cid:15)n represents (cid:12)rm n’s speci(cid:12)c shock, for n=1;:::;N. The term (cid:11)n is the trend of (cid:15)n, and
can be either positive, zero or negative. The term (cid:27)n measures the degree of uncertainty of future
(cid:15)n values. Firm speci(cid:12)c shocks may be caused by the randomness in a (cid:12)rm’s internal production
process, andindustryshocksmay bedueto the pricesof some commoninputsusedbyallthe(cid:12)rms.
We assume that these shocks are independent of each other.
At any moment t, (cid:12)rm n observes Kn(t), (cid:15)n(t), and (cid:15)0(t) andthus knows itsown TAC function.
Based onthe TAC functions,orthe marginalabatement cost (MAC) functions,(cid:12)rmstrade permits
until the MACs are equalized across all (cid:12)rms. (We assume that the trading is eÆcient.) The
equilibriumpermitpricedependsonlyon the total number of permitsandnot on theirdistribution
across (cid:12)rms. Let e(cid:22) be the total number of permits distributed by the government, e(cid:22)n be (cid:12)rm n’s
0
free permits, and en (cid:12)rm n’s emission without abatement, all constant overtime. Then
0 0
an(t) = en(cid:0)e(cid:22)n = en(cid:0)e(cid:22)(cid:17)a(cid:22) 8t(cid:21) 0; (2)
n n n
X X(cid:0) (cid:1) X
where a(cid:22) is the total industry abatement. Note that there is a one-to-one correspondence between
e(cid:22) and a(cid:22), so that we can use a(cid:22) to represent the government’s permit policy. Firm n’s total cost
(including TAC and permit cost) is given by
0
D(p;Kn;n;(cid:15)n;(cid:15)0) =C(an(p;Kn;n;(cid:15)n;(cid:15)0);Kn;n;(cid:15)n;(cid:15)0)+p(en(cid:0)an(p;Kn;n;(cid:15)n;(cid:15)0)(cid:0)e(cid:22)n): (3)
The equilibrium permit price equals (cid:12)rms’ MACs, and can be written as
(cid:3) N
p =p (fKn;(cid:15)ngn=1;(cid:15)0;a(cid:22)): (4)
FirmncaninvestincapitalortechnologytoincreaseitsstockKn. Theinvestmentcostfunction
is linear in the investment level, with the unit cost given by (cid:20). Linearity implies that the stock
can be non-di(cid:11)erentiable (although continuous) in time: if the current stock is too low, (cid:12)rm n can
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instantaneously adjust the stock to its desired level.
In addition to the instantaneous permit market equilibrium, we need to specify the inter-
temporal competitive equilibriumof capital or technological investment. Suppose there is a permit
price process fp(t);t (cid:21) 0g, and further fp(t);Kn(t);(cid:15)n(t);(cid:15)0(t)g contains all of the information
about the future that a(cid:11)ects (cid:12)rm n’s payo(cid:11). A suÆcient condition for the latter condition to hold
is that fp(t);Kn(t);t (cid:21) 0g is Markovian, which we will con(cid:12)rm later. Assuming the (cid:12)rm is risk
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neutral, its optimal decision on investment is given by
V(p(t);Kn(t);(cid:15)n(t);(cid:15)0(t)) (cid:17)
1
(cid:0)r((cid:28)(cid:0)t) + (cid:0) (cid:0)r(w(cid:0)t)
max(cid:0)E D(p((cid:28));Kn((cid:28));n;(cid:15)n((cid:28));(cid:15)0((cid:28)))e d(cid:28) (cid:0) (cid:20)(Kn(w )(cid:0)Kn(w ))e ; (5)
Zt w
X
0 0 + (cid:0)
subject to (1), the price process p(t);t (cid:21) t, and Kn(w ) > Kn(w ). The discount rate is r, and
(cid:0) +
w’s are the instants when investment occurs, with w and w representing the instants just before
and after the investment.
Given K0, the optimization problem generates the optimal investment strategies
(cid:3) (cid:3)
Kn(t)=Kn(p(t);Kn(t);(cid:15)n(t);(cid:15)0(t)); n =1;:::;N: (6)
It measures the optimal level of stock in period t given the information available. From (4), the
rational expectations competitive equilibriumprice is given by
(cid:3) (cid:3) N
p(t) = p (fKn(t);(cid:15)n(t)gn=1;(cid:15)0;a(cid:22)): (7)
Equations (6) and (7) completely characterize the competitive equilibrium. Since (cid:15)n(t) and (cid:15)0(t)
are Markovian, we know the resulting fp(t);Kn(t)g is also Markovian.
Directly solving the competitive equilibrium proves to be too hard a problem. Instead, we
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Our result does not depend on the assumption of risk neutrality. When the (cid:12)rms are risk averse, we can either
use the risk adjusted discount rate or use risk neutral probabilities and the riskless discount rate if there are traded
assets that can span therisks.
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