WPS4215
Does Uncertainty Matter?
A Stochastic Dynamic Analysis of Bankable Emission Permit Trading
for Global Climate Change Policy*
Fan Zhang1
Abstract
Emission permit trading is a centerpiece of the Kyoto Protocol which allows participating
nations to trade and bank greenhouse gas permits under the Framework Convention on Climate
Change. When market conditions evolve stochastically, emission trading produces a dynamic
problem, in which anticipation about the future economic environment affects current banking
decisions. In this paper, I explore the effect of increased uncertainty over future output prices and
input costs on the temporal distribution of emissions. In a dynamic programming setting, a
permit price is a convex function of stochastic prices of electricity and fuel. Increased
uncertainty about future market conditions increases the expected permit price and causes a risk
neutral firm to reduce ex ante emissions so as to smooth out marginal abatement costs over time.
The convexity results from the asymmetric impact of changes in counterfactual emissions on the
change of marginal abatement costs. Empirical analysis corroborates the theoretical prediction. I
find that 1% increase in electricity price volatility measured by annualized standard deviation of
percentage price change is associated with an average decrease in annual emission rate by 0.88%.
Numerical simulation suggests that high uncertainty could induce substantially early abatements,
as well as large compliance costs, therefore imposing a tradeoff between environmental benefits
and economic efficiency. Policy implications for designing an effective and efficient global
carbon market are discussed.
World Bank Policy Research Working Paper 4215, April 2007
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange
of ideas about development issues. An objective of the series is to get the findings out quickly, even if the
presentations are less than fully polished. The papers carry the names of the authors and should be cited
accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors.
They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they
represent. Policy Research Working Papers are available online at http://econ.worldbank.org.
* I thank the World Bank Research Committee for funding, and Dr. Zmarak Shalizi and Philippe
Ambrosi for helpful comments and suggestions.
1Author's affiliation: Harvard University, Cambridge, MA 02138, USA.
email: Fan_Zhang@ksgphd.harvard.edu
1
I. Introduction
Capandtrade emission permit systems that allow permits to be traded over time (hereafter
bankable emission permits trading or intertemporal emission trading) are witnessing growing
regulatory interest as a costeffective way to reduce total emissions. The grandest use for
marketable permit trading is contained in Kyoto Protocol which allows participating nations to
trade and bank greenhouse gas permits under the Framework Convention on Climate Change
(Intergovernmental Panel on Climate Change, 1996). The U.S. sulfur dioxide (SO2) emissions
2
trading program established under Title IV of the 1990 Clean Air Act Amendments is one of the
first, and by far the most extensive application of bankable emission permit trading. Under Title
IV, firms are not only allowed to transfer allowances for emission of SO2 among facilities, but
also allowed to bank them for use in future years.
Despite the large interest in intertemporal emission trading, important theoretical and policy
issues under this trading mechanism remain unexplored. In particular, although the theoretical
literature on tradable emission permits has established an indepth discussion regarding the
efficiency and properties of their use since the early 1970s (Montgomery, 1972; Hahn, 1984; and
see Titenberg [1985] and Cropper and Oates [1992] for thorough reviews), most of the literature
considers trading between units, implicitly within a single time period. Theoretical analyses of
intertemporal emission trading have only recently received attention (Rubin, 1996; Cronnshow
and Kruse, 1996; Kling and Rubin, 1997; Schennach, 2000; Yates and Cronshaw, 2001; Leiby
and Rubin, 2001; Stevens and Rose, 2002; Sedio and Marland, 2003; Maeda, 2004; Stranlund, et
al., 2005; van Steenbergh, 2005; Feng and Zhao, 2006; Wirl, F. 2006). With few exceptions,3
these studies assume firms have perfect foresight. There has been no formal analysis of the
impact of output market uncertainty in the intertemporal permit literature.
No environmental policy is implemented in the ideal world of certainty. In fact, uncertainty
is a prevailing feature of many environmental policies, especially the global climate change
program. For example, countries subject to Kyoto Protocol have to deal with various
uncertainties over time, including the demand for energy, the speed and arrival of technology
development, the engagement of other countries in the market, the total emission cap, and the
interest rate etc. Revenue uncertainty, acting together with technological and policy uncertainty,
will have important implications for countries' intertemporal carbon management, including
those decisions on investment in lowcarbon and renewable technologies.
The purpose of this paper is to explore the effects of uncertainty on the temporal pattern of
emission trading. In particular, we ask how a meanpreserving increase in output price volatility
would affect firms' banking and abatement decisions. I develop a stochastic dynamic
optimization model of a riskneutral pricetaking firm, which uses high and/or lowcarbon fuel
2In particular, Kyoto Protocol sets legally binding emissions targets and timetables for Annex B countries. Together,
Annex B countries must reduce their emissions of six greenhouse gases by at least 5% below 1990 levels over the
commitment period 2008 2012. One Annex B country is allowed to purchase the rights to emit greenhouse gases
from other Annex B countries. The protocol also allows for banking of permits, or mitigation in excess of
commitments in some periods, with the prospect of mitigation at levels lower than commitments at some future date.
Borrowing, however, is not explicitly mentioned.
3Studies that mention uncertainties include Schennach (2000), Feng and Zhao (2006).
2
to produce electricity. Current prices are known, but the future prices evolve stochastically. I
show that in equilibrium, the marginal abatement costs of all firms are equalized with the permit
price in each period; for each firm, the expected present marginal abatement costs are also
equalized across time periods. When future compliance costs are expected to increase, firms will
demand positive permits, bidding up the permit price (and therefore marginal abatement cost)
until current and expected future prices are equal.
The permit price is subject to output price shocks, which alter firms' abatement costs by
changing the industrywide counterfactual emission level.4 I prove analytically that the permit
price, as well as firms' marginal abatement cost, is a convex function of the electricity price. By
Jensen's inequality, this leads to a positive relationship between the marginal abatement cost and
the increase in volatility of the stochastic variable. This convexity relationship results from the
asymmetric impact of electricity price change on the change in marginal abatement cost. Because
marginal abatement cost is convex (as long as the marginal productivity is decreasing), when the
electricity price increases (and therefore the abatement level increases), the marginal abatement
cost increases faster than it decreases when the electricity price falls. When uncertainty is
pronounced, very high and very low electricity prices become more likely, and this asymmetric
impact becomes more salient. In the presence of extreme electricity prices, firms would have a
much higher incentive to reduce ex ante emission and accumulate permits so as to smooth out the
marginal abatement costs over time. This conclusion holds whether the output market is perfectly
competitive or not. In addition, the model is extended to allow uncertainties to enter through
input costs and industry wide productivity. The conclusion follows the same line.
In the second part of the paper, I empirically test the theoretical prediction using data
observed from the U.S. SO2 allowance trading market from 1996 to 2004. Empirical analysis
shows that one percent increase in electricity price volatility measured by annualized standard
deviation of percentage price change is on average associated with a 0.88% decrease in annual
emission rate. Overall, increased price volatility induced by electricity market restructuring over
the last decade may explain 811% of the total amount of the banked allowances during Phase I
of the U.S. SO2 trading program.
To estimate the impact of market uncertainty on social welfare, I simulate the banking
pattern, emission stream and the time path of permit price resulting from various degrees of
output price uncertainties. Numerical results are quite suggestive and consistent with the
empirical evidence. The results indicate that high uncertainty may generate substantially large
compliance costs in the early years, deterring new entrants and cause efficiency loss; from the
environment perspective, uncertainty encourages overcopmliance in early years; when a
pollutant such as a greenhouse gas, creates stock damage, benefits from early abatement could be
substantial.5
The remainder of the paper is organized as follows: Section II provides a literature review.
Section III develops a firm model of intertemporal emission trading and derives the relationship
4Counterfactual emission is the level of emission that would prevail when there is no environmental regulation.
5Currently, the transfer of unused allowances from the period 2005  2007 to the first commitment period under the
Kyoto Protocol, i.e. 20082012, is not allowed under an EUwide ban on banking (except for Poland and France),
which from an environmental point of view, seems to be a troubling decision.
3
between ex ante emissions and uncertainty; Section IV presents the empirical model and the
estimation results. Section V discusses numerical simulation, welfare analysis and policy
implications and Section VI concludes the paper.
II. Background and Literature Review
This paper is related to two strands of literature, that on intertemporal emission permit
trading and that on capital investment under uncertainty. Previous theoretical investigations of
intertemporal permit trading generally do not consider the presence of uncertainty. Rubin (1996)
shows that when firms are allowed to freely bank and borrow permits across time, permit prices
and pollutant emissions must evolve following the deterministic path described by Hotelling's
rule. Within a similar framework, Kling and Rubin (1997) compare the emission path firms
would choose with the social optimal solution and show that when borrowing and banking are
allowed private solutions diverge from social optimum. Cronnshow and Kruse (1996) show that
in a competitive tradable and bankable permit market, a competitive equilibrium exists and
achieves aggregate emission targets for the least system cost.
Schennach's (2000) research is a first effort to study the implications of output market
uncertainty on individual firms' emission trading strategy. Among other conclusions, Schennach
(2000) suggests that the higher the expected electricity price, the lower the emissions in earlier
periods. Schennach (2000) also emphasized the role of the nonnegativity constraint, a special
feature associated with the U.S. Acid Rain Program, arguing that the expectation on a potential
stockout of the banked permits may induce reduction of emissions in earlier periods. Feng and
Zhao (2005) explore efficiency of the permit system when there is information asymmetry
between regulatory agency and the regulated firm regarding uncertainty and find that the higher
the degree of asymmetry, the more potential benefits form a bankable permit regime. While these
papers constitute important steps toward an understanding of the potential consequences of
uncertainty, they do not answer the question of how increased output market price volatility
would modify the path of emissions. After all, it is the significant variation, not the level of
prices that defines a volatile market.
In spirit, this paper is closer to Hartman (1972) and Abel (1983, 1985). In these models, the
presence of adjustment costs, together with a constantreturnstoscale technology, make the
marginal revenue product of capital a convex function of output price. Therefore, increased
uncertainty about the future price of output increases the expected marginal revenue product for
a competitive firm and hence increases the intensity of investment. Similarly, in this paper, I
demonstrate the positive relationship between electricity price uncertainty and the expected
marginal value of an permit by applying Jensen's inequality for a convex function. However, the
analysis of the marginal value of a permit has no direct analogue to the problems in the capital
investment literature. In addition, I present the analysis in a more general framework, without
assumptions of constantreturnstoscale and perfect competition in the output market.
Neither the theory nor the empirical assessment of the implications of the increased output
market uncertainty for emission trading has been fully examined in the intertemporal trading
literature. Therefore, this paper makes two specific contributions. First, I introduce uncertainty
into the intertemporal trading model, which is theoretically more interesting and empirically
4
more relevant. In this model, firms' decisions regarding permit trading is an ex ante choice in the
sense that optimal emissions and permit banking decisions depend not only on current but also
on expectation of future output and input prices. Second, I empirically test the theoretical
prediction in a real trading program. To the best of my knowledge, this is the first attempt to
quantitatively estimate the effects of uncertainty on emission trading based on actual market data.
Although empirical analysis is conducted in the context of the U.S. SO2 allowance trading
program, the conclusion is general enough to be extended to the analysis of global carbon trading
program.
III. Modeling Framework
This section contains the basic theory of intertemporal permit trading under uncertainty. I
begin by setting up a firm's dynamic optimization problem, and then state and prove Proposition
1 and Lemma 1 on the relationship between uncertainty, and banking/emissions. I then go on to
show how conclusions can be affected by imperfect competition in the permit and output markets
and returns to scale of production technology.
III.(i) A Firm Model of Intertemporal Permit Trading Under Uncertainty
Consider a risk neutral firm that uses adjustable levels of low and highcarbon fuel to
produce electricity. In each time period, the firm decides the electricity output (gt) chooses the
mix of low and highcarbon fuel (lt and ht), and the amount of permits to buy (xt> 0) or sell (xt<
0) to maximize its discounted present profits for a constrained level of emissions. Uncertainty
exists in the supply and demand for electricity. Suppose this uncertainty is characterized by
electricity prices Pe, which is a random variable that follows a Markov process. The probability
law of Pe is known to all firms. At the start of each period t, the firm observes electricity price
(Pet), permit price (Pat), the price for low and highcarbon fuel (Plt and Pht), and the initial
endowment of permits which is the sum of permits issued by the government at current period
(At) and the amount of banked permits carried from the previous period (Bt). Refer to Table I for
a thorough description of all model parameters used in the section.
Firms are facing a dynamic optimization problem because choosing how many permits to
save for the future has to be made before uncertainties over future prices are resolved. Assuming
that firms are price takers in all markets, I model individual firm behavior as an intrafirm game.
Taking the strategies of other firms as given, each firm picks a strategy in each time period that
is optimal from the firm's perspective in that period. The firm's strategy is thus a map from the
Markov state t = {Pt, At,Bt} to choose variables {lt, ht, xt}, where Pt is a price vector, i.e. Pt =
{Pet, Pat, Plt, Pht}.
I assume firms employ three compliance strategies: abating emissions through blending or
switching to lowcarbon fuel, purchasing allowances in addition to initial allocation, and
adjusting output levels. Other capital intensive strategies such as scrubbing, repowering or
permanently retiring a facility are not considered because regulatory, financial and other
uncertainties in today's volatile energy markets provide firms incentive to avoid capital intensive
investment as long as possible.
5
Let Vi(Pt, Bt, At) denote firm i's value at time t. The firm's maximization problem can be
written as:
Vi(Pt,Bt, At) max{ Petgit(lit,hit)  cit(lit,hit)  Patxit + Et[Vi(t+1)(Pt ,Bi
+1 (t+1), Ai(t+1))]}(1)
lit ,hit ,xit
s.t. Bi (t+1)= Ait + Bit eit(lit,hit)+ xit (2)
Bi (t+1) 0 (3)
where is the discount ratio. In a discretetime setting, = 1/(1 + r) and r is the riskfree
interest rate.6 E[·] is the expectations operator. Eq.(2) is the state equation and defines the stock
of banked permits in period t. Eq.(3) corresponds to the nonnegativity constraint,i.e. borrowing
against future emission reductions is not allowed. For simplicity, hereafter I suppress unit index i.
The production function with low and highcarbon fuels as two distinct inputs is
represented by g(l, h), which is assumed to be concave, increasing in both arguments,
homogenous of degree 1, and twice differentiable everywhere. 7 Most of the previous studies
assumed output as given (Rubin [1996], Arimura [2002]). In competitive electricity markets, an
assumption of fixed output seems untenable. In this model, I assume that producers may alter the
output level as a way to meet the required emission standard.
c(l, h) is the cost function. When a firm undertakes production, it incurs costs that can be
described in terms of three components: (1) fuel costs, (2) adjustment costs associated with fuel
blending or fuelswitching, and (3) other fixed costs including capital costs for mixing fuel. Once
the binary choice determining whether or not to switch/blend fuel has been made, this sunk cost
will have no impact on the factor input ratio. Thus I do not explicitly take account of the initial
capital cost in this analysis. 8
For the model to be tractable, I assume that the adjustment costs are continuous and linear in
l.9 Specifically, I combine the variable adjustment cost and purchasing cost of lowcarbon fuel as
an augment cost and represent the cost function as a standard linear one.
c(l,h) = Pll + Phh
where Pl is the sum of both purchasing cost and the variable adjustment cost of lowcarbon fuel.
Implicitly, there is Pl > Ph.
Finally, I denote the emission function as e(l,h) = (ll +hh) , where l and h are the
carbon contents of low and highcarbon fuel (l < h ), and is the converting rate from
carbon to carbon dioxide.
6 In fact, interest rate itself imposes another uncertainty on the optimization problem. To focus the attention on the
effect of output market uncertainty, here I assume r remains constant.
7 To include labor (a) and capital (k) inputs in the production function is straightforward and yields an almost
identical analysis.
8Philippe Ambrosi made another point that fuel switching may also be linked to the decision to operate one power
plant rather than another, and there are no sunk costs involved.
9 As will be shown later, the abatement cost is strictly convex.
6
To analyze the above constrained stochastic dynamic optimization problem, consider a firm
that is in place for two periods t = 1, 2. The KuhnTucker sufficient conditions for a maximum at
(h*,l*, x*, *) yield the following firstorder conditions:
Pa1 = E1[VB2 ]+ * (4)
*
Pe1gi 'f1 = c'f1 + ( E1[VB2 ]+ *)e'f1 f = l, h (5)
* * * *
A1 + B1 + x1  e1 0, * 0, *(A1 + B1 + x1  e1 ) = 0
* * * * (6)
where *is the multiplier associated with inequality (3). * > 0 if and only if the nonnegativity
constraint is binding, i.e. A1 + B1 + x1 e*1 > 0 implies * = 0 .
Eq.(4) is the Eulerintertemporal condition.10 Eq. (5) discloses that producers choose the
optimal levels of fuel so that the fuel's marginal value product equals its marginal cost. The
marginal cost includes both the direct production cost and the opportunity cost of surrendering
the option to use permits in a future period. Therefore, expectations on the marginal value of a
unit of allowance in next period (E1[VB ]) affect current emission decisions.
2
The secondperiod optimization problem is
V2 = max Pe g(h2,l2)  c(h2,l2)  Pa x (7)
l2,h2,x2 2 2 2
s.t. A2 + B2  e(h2, l2) + x2 = 0 (8)
Eq.(8) shows that firms deplete the pmiert bank in the terminal period. The Lagrangian is
L = Pe gi(h2,l2)  c(h2,l2)  Pa x + 2(A2 + B2  e(h2,l2) + x2) (9)
2 2 2
The solution (l2,h2, x2,2 ) is described by the following firstorder equations:
* * * *
Pa = 2 * (10)
2
Pe2gi 'f2 = c'f2 + 2e'f2
* f = l, h (11)
* * *
2 can be interpreted as the shadow value of a unit of banked permit in period2. Eq.(10) says
that firms will buy or sell permits such that the shadow value of the marginal permit equals to its
market price. The optimal input mix (l2,h2) is given by Eq.(11).
* *
An important feature of the above optimal solution is that it is independent of the level of
banked permits (B2). The value function in period 2 is only linearly linked to B2 through the
profit function. Specifically, the value function in Eq.(7) can be written as
10g'f, c'f , e'f (f = l, h) represent the marginal productivity, marginal production cost, and marginal emission rate of
the two types of fuel. Hereafter, ' represents the calculation of a derivative.
7
V2 = Pe2g(h2(P2),l2(P2))  c(h2(P2),l2(P2))  Pa2[A2 + B2  e(h2(P2),l2(P2))]
* * * * * * (12)
where P2 = {Pe2, Pl2, Ph2, Pa2}. Differentiating Eq.(12) with respect to B2 we get the marginal
revenue product of permits:
VB = Pa (13)
2* 2
Substituting this expression for VB2 into Eq.(4) leads to a nonarbitrage pricing formula:
Pa1 = E(P2) + * (14)
The right hand side of Eq.(14) is the expected return of holding one unit of permit. It
consists of two components: expected present permit price in period 2 and a convenience yield
*. The left hand side of the equation represents the opportunity cost of carrying an additional
unit of permit, which is an instantaneous gain from selling it in the spot market. To simplify
notations while not affect the generally conclusions on the relationship between uncertainty and
permit trading, I assume the convenience yield related to the scarcity of the permits bank is not a
factor affecting banking decisions of individual units. i.e. *= 0.
Combining equations (11) and (14) yields the following policy function for intertemporal
emission trading:
E(Pa2) = 1Pl1  Ph1
*
(h 1l) (15)
*
where 1 = g 'h*1/ g 'l*1 is the ratio of the marginal productivities of high and lowcarbon fuel.11
*
The right hand side of Eq.(15) is the additional cost an operator has to pay in order to reduce one
ton of carbon dioxide emission. It reflects both price and productivity differences between low
and highcarbon fuel. Following Montgomery (1972), emission abatement costs are defined as
the difference between the unconstrained profits and the profits in which the firm adopts an
emission level which is less than the unconstrained emission level. Therefore, the right hand side
of Eq.(15) presents a notation for marginal abatement cost.
Eq.(15) together with Eq. (14) exhibit the spatial and temporal efficiency properties of a
tradable emission permit regime: in each period, the marginal abatement costs are equalized
across firms through the current allowance price (therefore the total pollution reduction cost is
minimized)12; the present value of the marginal abatement costs are equalized across time
periods in an expectation sense. Thus, expectations on higher future permit prices raise the
current abatement level.
11The expected permit prices are positive implies h /l > g 'h/ g 'l .
12This conclusion is based on the assumption that firms have interior solutions, i.e. both low and highcarbon fuels
are used. If firms only use one type of fuel, marginal abatement costs are not equalized between firms having
interior solutions and firms having corner solutions; however, an emission trading program still yields a cost
effective result.
8
Plugging = 1/ (1+r) into Eq.(14), we obtain Hotelling's rule under uncertainty.
E(Pa )  Pa
2 1 = r (16)
Pa 1
Eqs. (14) and (15) show that firms have incentives to save permits for future use (forward
banking) every time they expect the discounted future permit price to be greater than the current
market price; at the industry level, such forward banking will drive up the current permit prices,
as well as the current marginal abatement costs, to reflect the expectation of future permit prices.
Eq.(16) shows that a direct result of forward banking is to prevent the expected permit price from
increasing at a rate higher than the interest rate.
III (ii) Uncertainty, Banking and Emission
Although price is given for each individual unit in the permit market, allowance price is
endogenously determined by the aggregate behavior of the generating units. Previous theoretical
analysis of emission permit trading reveals that when allowed to trade with one another in a
competitive allowance market, units will collectively behave like a central planner who
efficiently allocates emission permits to each unit in a manner that minimizes total costs (Rubin,
1996; Schennach, 2000; Feng and Zhao, 2006). This insight allows me to model the aggregate
industrial behavior as a single representative unit and solve the equivalent and simpler problem
without considering internal spatial trading. Assuming the representative agent uses low and
highcarbon fuel to produce electricity according to the CobbDouglas production function13
g(l,h) = Glh1 , where G is a productivity parameter, and 0 < <1 is the share of lowcarbon

fuel. To avoid confusing the issues of increasing price volatility with increasing price trends, I
consider electricity price Pe evolves following a meanpreserving stochastic process with the
mean equal to Pe . Formally, I define the probability distribution function of Pe as f (Pe,) such
that
P e2df (,) = Pe
where is an index of the meanpreserving spread and if ' > , f (,) secondorder
stochastically dominates f (, ') (or f (, ') is more risky than f (,) ) . Therefore, the value of
characterizes the level of marketwide risk. The representative firm's optimization problem in
period2 shown below is simplified by leaving out the term x.
maxV = Pe g(l2,h2)  c(l2,h2) (17)
2
s. t. B2 = e(l2,h2) = (ll2 +hh2) (18)
There is no closedform solution for the above optimization problem. Nonetheless, I prove
analytically in Appendix A that the marginal profitability of permitsV /B , or the permit price
Pa, is convex in the stochastic variable Pe. This leads to a negative relationship between ex ante
emissions and the level of uncertainties about electricity prices.
13In Appendix A I extend the model to a more general CES production function and prove that the conclusions do
not change.
9
Proposition 1. Increasing uncertainty over electricity price generates lower ex ante emissions
and higher banking in the following sense: For ' > , B(Pe ') > B() and ei( ') < ei(), where
is the meanpreserving spread of electricity price, B is the aggregate stock of banked
emission permits of the industry, and ei is the individual ex ante emissions.
Proof. I prove in Appendix A that the marginal profitability of permits is convex with respect to
Pe. It follows directly from Jensen's inequality that an increase in the mean preserving spread of
Pe increases the expected marginal value of permits. According to Eq.(15), in anticipation of
higher expected future marginal value of permits, firms will reduce ex ante emissions by
increasing the current marginal abatement costs, which leads to an increased aggregate stock of
allowances at the industry level,
It is essential that the marginal value of allowances be convex in electricity prices to derive
the above conclusion. This convexity reveals an asymmetric distribution of future marginal
values of allowances due to output prices change. To understand the intuition, note that because
the total number of allowances is fixed, and is less than the emissions expected to produce by all
of the affected units, the rise of electricity prices increases the counterfactual emissions, as well
as the total required pollution reduction. Since abatement costs are convex (more discussion of
this property in the next section), marginal abatement cost rises with the quantity of abatement.
Therefore, when electricity price increases, the marginal abatement cost increases faster then it
decreases when electricity price falls. This means that the potential gain from saving an
additional unit of permit is higher when electricity price increases than the potential loss when
electricity price decreases. When uncertainty is more pronounced, very high and very low
electricity prices become more likely, and this asymmetric relationship becomes more salient. In
the presence of extreme prices, firms would have a higher incentive to save permits as the
potential gain is much higher than the potential loss.
In addition, when there are multiple time periods, the convexity effect also works through
firms' ability to vary the input of permits in response to the resolution of uncertainty. When there
is a "bad" shock such that the stock of permits is larger than the desired stock of permits, firms
can choose not to use extra permits. Thus, the marginal gain from saving a unit of permit today
equals max [0, Pa  Pa ]. A "good" shock is unchecked, while a "bad" shock is bounded below.
2 1
Therefore, a unit of permit is like a set of American call options on future production, which is
worth more when good and bad outcomes are more extreme with the same expected mean value.
Based on a similar analysis, I show in Appendix B that the marginal value of permits is also
a convex function of input costs: the prices of low and highcarbon fuel. The intuition follows
the same line: the fluctuation of input costs changes the counterfactual emission level, leading to
an asymmetric probability distribution for the marginal profit of permits: negative shocks which
increase the input costs will reduce the marginal value of permits less than positive shocks will
increase them, Hence, in equilibrium more permits will be saved in presence of a mean
preserving spread in the distribution of Pl or Ph which raises the expected marginal profitability
of permits.
Lemma 1. The greater the uncertainty in input costs Pl and Ph, the lower are the ex ante
emissions.
10
Proof. See Appendix B.
To be noticed, that assuming perfectly competitive allowance market, the above conclusions
are derived regardless of firms' market position (net seller or buyer) and the initial allocation of
allowances.
III.(iii) Imperfect Competition and Return to Scale
Proposition 1 and Lemma 1 are proved under the assumptions that individual firms are
pricetakers and production technology is linearly homogeneous. In this section, I discuss the
role of perfect competition and returns to scale. I show that imperfect competition in an
electricity market and decreasing returns to scale do not affect the negative relationship between
uncertainty and emission. However, this negative relationship may not be robust to increasing
returns to scale or imperfect competition in the permit market.
A. Imperfect Electricity Market
To isolate the impact of imperfect competition in electricity market, assume the technology
is still described by a homogenous of degree one CobbDouglas production function: g = Glh1 . 
Suppose an individual firm faces an isoelastic demand curve Pe = g(1 )/ W , where ( 1) is a
markup coefficient with =1 corresponding to perfect competition. W is an exogenous
stochastic demand shifter that captures industrywide shocks. Under these conditions, the value
function is equal to:
V =W(Glh1 )  Pll  Phh
 (20)
where =1/ , 1, can be considered as the returntoscale parameter. Appendix C shows
that with a value function described by Eq.(20), the convexity of the marginal value of permits in
output price and input costs persists. Therefore, the fact that an electricity market may not be
perfectly competitive does not affect the conclusion regarding the negative relationship between
uncertainty and ex ante emissions given constant returns to scale and perfect competition in
permit market (as well as risk neutrality).
This result confirms the intuition of the above analysis. Recall that a crucial insight from
Eq.(12) is that abatement decisions do not depend on either past or future permit stocks. This
lack of "intertemporal links" holds true as long as firms are price takers in the permit market and
does not depend on the elasticity of the demand curve facing individual firms in the electricity
market. Therefore, an industrywide shock will have a similar impact on abatement decisions for
a competitive firm and a monopolist with constant returns to scale in the electricity market: how
many permits is saved now affects profits in the future, but not the level of emissions in the
future. As such, any increase in the expected marginal profitability of permits, including the one
caused by an increase in market uncertainty raises the emission banking today.
One concern about above analysis is that the industry itself may face a downwardsloping
demand curve even when individual firms are perfectly competitive and have constant returns to
scale. When price is endogenously determined by the industry output, the amount a price can rise
under good industrywide outcomes is limited by the entry of new firms and the expansion of
existing ones. If investment is irreversible, as shown by Pindyck (1993), there is no similar
11
mechanism to prevent price from falling under bad demand outcomes. As a result, a mean
preserving distribution of future output prices might not be sustained. However, because fossil
fuel fired peak power plants which are usually the marginal producers, can be fairly easily turned
on or shut down in response to the realized market price, the possibility of an asymmetric
distribution of future output price is reduced. That is the operational flexibility of peak load
power plants weakened the notion of irreversibility which is instrumental in Pindyck(1993)'s
analysis.
B. Return to Scale
Analysis so far assumes constant returns to scale. Relaxing this assumption, however, does
not convey any additional difficulty. Eq.(20) reveals that a decrease in returns to scale operates
exactly like an increase in the markup coefficient and vice versa. Therefore, conclusions of
Proposition 1 and Lemma 1 fully carry over to the case of decreasing returns to scale.
The above result has an intuitive interpretation. Note that Proposition 1 and Lemma 1 hinge
on the convexity of abatement costs. In principle, this convexity arises from decreasing marginal
productivity of factor inputs.14 To see this, observe from Eq.(15) that marginal abatement costs is
positively related to the ratio of marginal products of high and lowcarbon fuel ( ). Because of
declining marginal productivity, when producers use a greater share of lowcarbon fuel to reduce
emissions, increases as the marginal product of lowcarbon fuel declines relative to that of
highcarbon fuel. Therefore, abatement costs are convex in the sense that a lower level of
emissions is associated with higher abatement costs at the margin. In obtaining this result,
diminishing marginal productivity is the paramount factor. Because decreasing returns to scale
(so as constant returns to scale) guarantees diminishing marginal productivity (given the
production function is quasiconcave) 15 , the negative relationship between emissions and
uncertainty holds in the presence of decreasing returns to scale resulting from imperfect
competition or diseconomies of scale technology, or both. Note that some cases of increasing
returns may also satisfy diminishing marginal productivity. For example, suppose >1, but
0 < < 1; the marginal productivity of l decreases with the increase of l. However, as the
returns to scale ( ) becomes larger and larger, from the insights gleaned above, the inverse
relationship between emissions and uncertainty would eventually lose its strength.
C. Imperfect Permit Market
So far we have assumed a competitive permit market, where the distribution of future
allowance price is independent of an individual firm's abatement decisions. The effects of
uncertainty are mediated through the equilibrium behavior of all firms and the resulting impact
on prices of an allowance market. A logical question to explore is what if at least one of the units
exercises market power in the allowance market. In this case, the current emission of the
dominant firm would affect the expected path of the marginal value of permits. For a dominant
firm, Eq.(14) becomes
Pa1 x1 + Pa1 = E[x2 x2 + Pa2]+ *
Pa2 (21)
x1
14Increasing marginal abatement costs or decreasing marginal productivity both imply that the firm attains a regular
minimum in solving the problem.
15A formal mathematical proof is available upon request.
12
The price function Pa and its relationship with Pe is intractable without further assumption of
the price or quantitysetting behavior of the dominant firm. However, as the dominant firm has
the flexibility to make ex post decisions on x2 after the demand for output market is known, the
permit price Pa becomes less convex with respect to Pe. When the ability of the dominant firm to
affect the permit price increases, the firm would respond less and less to changes in the level of
uncertainty. Qualitatively, I show that imperfect competition in an permit market threatens the
negative relationship between price uncertainty and ex ante emissions. Further rigorous analysis
is needed based upon more detailed assumptions of the market structure of the permit market and
the strategic behavior of a dominant firm.
IV. Empirical Analysis
Building on previous discussions on the dynamics of intertemporal emissions trading under
uncertainty, this section empirically explores the electricity utilities' responses regarding
emissions reduction to price fluctuations in the U.S. electricity markets.16 The empirical analysis
is based on a panel dataset consisting of 207 Phase I coalfired generating units from 1996 to
2004. In many ways, the U.S. SO2 allowance trading program can be compared to the emerging
global carbon dioxide trading market. With 10 years of observation data and many lessons
learned from the SO2 allowance market, to study SO2 trading occurred in the U.S. provides a
unique opportunity to estimate the implications of different features of the global carbon dioxide
trading program, including the impact of uncertainty on future development of the global carbon
market.
The SO2 allowance trading program, also known as the Acid Rain Program, was established
under Title IV of the Clean Air Act Amendments of 1990. By creating a national clean air
market, it was a grand application of a marketbased regulatory approach to achieve emission
reduction goals. The basic idea behind permit trading is simple. The regulatory agency first sets a
cap that limits the total SO2 emissions by more than 40% from their 1980 level (from 18.9
million tons in 1980 to 8.9 million tons by 2001). It then divides the quantity up to a number of
tradable allowances and allocates them to individual firms based on their historical heat input.
Each allowance grants the holder the right to emit one ton of SO2. Firms that can reduce
emissions relatively cheaply may increase their profits by selling extra allowances; while those
that find it expensive to reduce emissions can buy extra allowances from the market. The SO2
allowance trading program institutionalized a couple of innovations in that it not only allows
unlimited trading of permits among firms, but also allows permits to be traded over time.
Therefore, power producers who can reduce emissions below the number of allowances they
hold may sell allowances to other firms, or bank them for future use. The only limitation the U.S.
Environmental Protection Agency (EPA) imposes on the trading program is that firms cannot
borrow allowances from their future allocation. At the "trueup" date (usually at the end of
March of each year), each unit must submit enough allowances to cover its emissions for that
year.
16I do not test the effect of coal prices uncertainties. As coal is the most abundant and affordable energy source in
the United States, its price in fact remains quite stable during the sample period.
13
Another important feature of this program is that it is a phasedin program. Phase I began in
1995 and affected 263 units at 110 mostly coalburning (and a few oilfired units) electric utility
plants located in 21 eastern and Midwestern states. Phase I units had emissions greater than 2.5
pounds of SO2 /mmBtu and a generating capacity greater than 100 megawatts (MW). Phase II
began in the year 2000. It establishes a permanent cap of 8.95 million per year and affects all
existing utility units with an output capacity greater than 25 MW, and all new utility units.
Figure 1 shows the annual emission cap, aggregated emissions and banked allowances from
1995 to 2004. It is apparent that the temporal dimension is a key component of this trading
program. Indeed from 1995 to 1999, 11.65 million allowances had been banked, which was
about 30% of the total allowances allocated during Phase I.17 These extra allowances were
produced through reducing emissions in early periods below the allowable standard.
The main reason for units to bank permits is due to the phasedin aspect of the program: an
allowance is perceived to be worth more in later years under the stricter cap of the Phase II. As
expected, the bank accumulated during Phase I started being drawn down in year 2000, easing
the transition to Phase II. However, the size of the bank generated in Phase I was unexpectedly
large. Some argue that banking in this program has been excessive and was economically
inefficient (Ellerman, et al., 2000; Smith, et al., 1998). In addition, the drawdown rate at the
beginning of Phase I was also lower than previously expected (Ellerman and Montero, 2005). In
the following, I show that part of the bank can be explained by the increased electricity price
volatility during electricity market restructuring in recent years.
The implementation of the acid rain program happens to have coincided with electricity
restructuring which dramatically changed the way the power industry was structured and
regulated over the past decade. Before restructuring, under rateofreturn regulation, electricity
price is set administratively by the regulatory agency on the basis of average production cost.
After Federal Energy Regulatory Commission (FERC) issued Orders 888 and 889 in 1996, a
number of auction based wholesale markets were established. In these markets firms bid to
supply power and the dispatch order was set by the bids. Since electricity has been traded in
these wholesale markets, uncertainty becomes a salient feature in the electricity market. In fact,
electricity price volatility has exceeded that of any other commodity market in recent years.
In what follows, the model specification, data sources and empirical estimation results are
discussed.
IV (i) Econometric Specification
In this section, I lay out the underlying econometric specifications for empirical tests and
describe the dependent and independent variables.
17The number of banked allowances does not include allowances sold at public auction each year, nor does it
include the contribution from substitution units that entered or exited the market in different years.
14
I assume a generating unit i has a production function of the following form: gi = Gilaihbi
(ai > 0, bi > 0); electricity price is given by Pe =Wgi i1 . Recall that W is an exogenous process
that influences the value of Pe and is the elasticity of demand. When the unit is a pricetaker
in the electricity market, there are =1 and W = Pe .
Multiplying factor inputs l and h on both sides of Eqs.(5) and (26) (intertemporal firstorder
conditions for competitive and regulated units, respectively) gives the input demand functions
for l and h:
lit = iWtgit i
i (27)
Plt + Mlit( E[Pa(t+1)  Ni(t+1)]+it)
hit = i(1i)Wtgit i
(28)
Pht + Mhit(E[Pa(t+1)  Ni(t+1)]+it)
where Mif = f
1 Ritit (f = l, h), Ni = Ri (t+1) i(t+1), Ri is a dummy variable which takes value 1 if
unit i is subject to ROR regulation, and 0 otherwise.
Substituting l and h from Eqs. (27) and (28) to the expression for e, we get a emission
function:
eit(lit,hit) = llit + hhit = iWtgit i
i i(1i)Wtgit it
Plt + Mlit( E[Pa(t+1)  Nit]+it) + Pht + Mhit( E[Pa(t+1)  Nit]+it)
(29)
Dividing both sides of Eq.(29) by git and taking logs yield
ln( g )it = lni + ln Peit + ln(Plt
e ai Pht + Mhit( E[Pa(t+1)  Ni]+i))
bi
+ Mlit(E[Pa(t+1)  Ni]+i) +
(30)
Eq. (30) shows that the total emissions of unit i is determined by exogenous demand shifter
W, the output level git, current and expected factor input prices (Pl and Ph), and the current and
expected profit regulations (M and N), a series of unit specific characteristics (ai, bi, i ), and
expected future allowance prices E[Pa(t+1)], which as postulated by the theoretical analysis, is
positively correlated with the variance of Peit. The probability of a potential stockout measured
by i may also affect emission decisions.
Therefore, emission rates can be estimated by the following reduced form
ln( g)it = 0 + 1Pet + 2 ln Pt + 3Rit + 4Zi + Sj +
e 20 2004
Tt +it +uit (31)
j=1 t=1996
where the dependent variable is the observed annual average SO2 emission rate (in log forms) of
unit i in calendar year t. Emission rate is calculated by dividing the total annual emissions (tons)
by the annual electricity output in megawatt hours (MWh).
15
Peit is the volatility of electricity prices. It is the key variable of interest in gauging the
effect of output price uncertainty on decision makers' perception of future allowance prices and
multiperiod emissions distribution decisions. Observations of monthly fuel purchasing database
reveal that plants frequently purchase coal from spot markets during the year. Therefore,
decisions as to how much of each type of coal to buy and how many allowances to hold till later
periods can be adjusted in response to the monthly electricity price fluctuations. I measurePeit
as the standard deviation of the percentage change (between two adjacent months) of monthly
average electricity price in the state where unit i is located. As we tend to see higher overall
underlying prices in highly volatile periods, this definition facilitates normalizations and
reasonable comparison across high and low price levels. The calculation is described by Eq.(32).
12
Peit = [P Peitm  E(Peit(m1))]2 ×100
Peitm (32)
m=1 eit(m1)
where t indexes year and m indexes month. Peitn is the monthly average retail electricity price to
industrial customers in state i during month m year t.
The coefficient of Pet provides a measure of the elasticity of annual average emission rate
to electricity price volatility. A negative coefficient will provide supporting evidence for the
theoretical prediction in previous sections.
The above analysis implicitly assumes current price fluctuation as a proxy for expected price
uncertainty in the future. One concern with this specification is whether current price uncertainty
reflects plant operators' expectation of future price uncertainty at the time of making operation
decisions. To evaluate the possibility that historical price uncertainty does not provide insights
into expectation of future price changes, I also assume mangers perfectly predict price volatility
in the future ( Pe (t+1)), and test for the response of current emission rate to future price
fluctuation. This alternative specification does not change the result qualitatively.
Given input costs, an increase in electricity prices will increase the marginal value of
allowances. According to Eq.(A6), the higher the marginal value of allowances, the higher the
input ratio for lowsulfur coal, which implies a lower emission rate. Therefore, the coefficient
associated with Pe is expected to be negative.
Pt is a price vector including the price of allowances Pat; lowsulfur coal price Plt,; high
sulfur coal price Pht , and retail electricity price to industrial customers Pet.
Current price Pat is an indicator of the market's perception of allowances future prices. A
higher Pat would reduce current emissions and the coefficient of Pat is likely to be negative.
The coefficient associated with lowsulfur coal price is expected to be positive, while the
sign of the coefficient of highsulfur coal price is ambiguous. Holding the output price constant,
a change in input fuel prices has two substitution effects: the substitution between the two types
16
of coal, and the substitution between lowsulfur coal and allowances.18 When lowsulfur coal
prices increase, both substitution effects raise emission rates. However, when the highsulfur
coal price increases, the two substitution effects work in opposite ways, leaving the sign of Pht
indeterminate.
To estimate the impact of ROR regulations on emissions behavior, I construct two dummy
variables RetailAcessit and Transitit. RetailAcessit takes the value 1 if the state where unit i is
located has begun retail access to industrial customers during year t, 0 otherwise; Transitit takes
the value 1 when unit i is located in a state that is in a transitional period of electricity
restructuring but has not yet started retail access, 0 otherwise. I define a state undergoing
transition to retail competition when any one of the following two events occurs: (1) PUC issues
a final order that contains a date by which all PUCregulated utilities in the state must open their
markets to retail competition; (2) the PUC has required retail restructuring filings from its
regulated utilities in preparation for competition by a particular date, even if it has not yet issued
a final comprehensive order. Based on previous analysis, if deregulated units have higher
incentive to reduce emissions while transitional units are less motivated to bank permits, then the
coefficients of RetailAcessit and Transitit would be negative and positive, respectively.
Zit is a vector of unit specific characteristics that may also determine emission performances,
which include:
SCRUBERit a dummy constructed to be 1 if a scrubber is installed to reduce SO2 emissions.
,
Scrubber can remove up to 90% of SO2 emitted during the production process. The coefficient
associated with SCRUBERit is likely to be significantly negative.
AGEit, the age of the boiler installed, calculated by using the calendar year to minus the year
of initial operation. Given that age and emission performance may not be in a linear relationship,
I estimate the model allowing AGEit to enter with a quadratic specification.
HEATRATEit is a measure of unit efficiency in transferring energy into electricity. It is
calculated by dividing the net kilowatt hours (KWh) of power output by the Btu content19 of the
fuel input. The sign of the coefficient for HEATRATEit is expected to be negative because of the
inverse relationship between heat rate and production efficiency.
CAPi is the design capacity of the boiler expressed in megawatts (MW). The variable is
included to capture possible economies or diseconomies of scale. As suggested by previous
literature (Baumeister et al., 1980; Joskow and Schmalensee, 1987), the underlying
thermodynamic properties of a steam cycle imply that increasing the size of the boiler should
reduce the unit's heat rate, at least within some range. However, the advantage of larger size
tends to deteriorate as scale becomes very large. With this a priori on the effect of boiler scale, I
include the first and second order terms of CAPi in the regression.
18Recall in Appendix A I prove a negative relationship between fuel costs and allowance prices (Eq.[A14]).
Therefore, changes in input fuel costs also changes the allowance prices.
19Btu stands for British thermal unit, a unit of energy frequently used to describe the heat value (energy content) of
fuels.
17
WORKLOADit is the ratio between the actual operating hours during year t and the
maximum working hours of a year (8640 hours). Emission rate may also be affected by operating
conditions. For example, it is generally understood that frequent ramp up and down tends to
increase the level of emissions. I constructed the variable WORKLOADit to capture the impact of
different operating practices between base load and peak load plants on emissions. The
coefficient of WORKLOADit is expected to be negative.
INITIALit is the initial allocation of allowances (tons) issued by the EPA. Although emission
decisions of a pricetaking unit are generally independent of its allowances endowment,
INITIALit can be negatively correlated with the value of convenience yield (it ) when non
negativity constraints are binding. 20 However, since the nonnegativity constraints are
inconsequential during Phase I of the trading program, I expect estimation on INITIALi to be
positive, but the effect is likely to be tenuous.
MUNIi is a dummy equal to 1 when the generating unit is municipally or cooperatively
owned, and 0 otherwise. I interact MUNIi with the measure of electricity price uncertaintyPeit .
An extensive literature has discussed the relative inefficiency of publicly owned facilities. If
MUNIi units are less cost conscious, operational activity of these units will be less responsive to
output price fluctuations. Therefore, I expect coefficient of the interaction term to be positive.
Finally, I also include year and state dummies Tt and Sj. Year dummies can capture year
specific differences in emission performance common to all units, such as secular technology or
productivity shocks. State dummies are included to control timeinvariant state specific
regulatory policies that may influence the crosssectional variation in emissions. For example,
many generating units were subject to sulfur restrictions contained in State Implementation Plans,
which where enforced prior to the Acid Rain Program and are still in effect. Some of these local
regulations are more stringent than those of the Acid Rain Program, and therefore consistently
affect the emission rates of the units in those states.21
An unobservable timeinvariant unit specific characteristic is represented by i and is
assumed to affect emission performance as well. The disturbance term is assumed to be an
idiosyncratic shock to operating performance drawn from an identical and independent
distribution (iid) it ~ N(0, ) . 0 , 2 , ..., 5, and are the coefficients.
2
As a direct analog to Eq.(31), I also test if the percentage change in the amount of
allowances banked between two time periods has any bearing on output price uncertainty (the
dependent variable is [Bt+1 Bt]/Bt). Because allowance banking is negatively related to total
emissions, the coefficients of the above explanatory variables would have similar interpretations
but are expected to have opposite signs.
20For example, when initial allocation increases, a potential stockout is less likely to occur and the convenience
yield becomes less important.
21Specifically, states that have such regulations are Kansas, Michigan, Wisconsin, New York and New Hampshire.
These states had enacted acid rain laws or taken regulatory actions to reduce SO2 emissions that were in effect by
1993 and would observe lower emission levels overall.
18
IV. (ii) Disturbance Term Structure and Alternative Specifications
The regression model (31) is based on the assumption that units are pricetakers in the
allowance market. One potential concern is that the equilibrium allowance price could be
endogenously determined by units that abuse market power. Emission price endogeneity may be
particularly relevant in the first couple of years of the trading program when the market was not
liquid enough and the price determination process might have involved significant interplay of
supply and demand between only a few companies.
To test for the possibility of allowance prices endogeneity, I use the annual average natural
gas wellhead price22 as an instrument for the allowance price. Natural gas and coal are competing
fuels for electricity generation. Fluctuations in natural gas prices have the potential to influence
the market share of coalfired generation, which is a major driving factor of allowance prices.
However, since natural gas prices are generally determined by weather conditions (hot summer
days, cold winter days), the prices of substituting fuel (oil and gasoline), and economic activities,
may not be directly correlated with individual units' emission rates. As robustness check, I
dropped potential noisy observations for the early years (1996 and 1997) and compare the results
of this reduced sample estimation with that of the full sample.
In addition to allowances price endogeneity, the endogeneity of low and highsulfur coal
costs may arise as an issue if coal prices are determined by the demand for coal. A more likely
situation is that because coal is a differentiated product in terms of both quality (sulfur content,
Btu content, moisture content) 23 and location, coal suppliers (producers and carriers) may have
great latitude in formulating prices, while electric generating units are pricetakers in coal
markets,. When pricing decisions are correlated with unobservable factors affecting a unit's
choice for coal and its emission performance, estimations ignoring this correlation would be
biased.
Given the potential endogeneity of coal prices, following Ellerman and Montero (1998), I
use the distance from a unit to the Power River Basin (PRB) in Wyoming and Montana as a
proxy for the prices of the lowsulfur coal available to the units. 24 The rationale for using this
variable is that PRB produces most of lowsulfur coal in the U.S. with the cheapest coalmine
prices, while transportation costs factor importantly into the delivered price of coal.25 A unit's
location in relation to PRB coal will to some extent reflect the actual cost of lowsulfur coal or
other competing coals. However, as Ellerman and Montero (1998) and Montero (1999) point out,
the distance to the PRB coal does not affect lowsulfur coal price uniformly. In particular, low
sulfur coal from central Appalachia becomes more competitive for units 1000 miles away from
Wyoming. To reflect this nonlinear relationship, I included a third degree polynomial to control
for the distance. It is expected that lowsulfur coal price will first increase with the increase of
22Wellhead price is the value at the mouth of the well. In general, the wellhead price is considered to be the sales
price obtainable from a third party in an arm's length transaction.
23Some fuel contracts specify more than a dozen attributes of coal qualities.
24Ideally, to control for the potential fuel price endogeneity, I would estimate hedonic price functions for fuel.
However, it is not possible to identify all of the relevant fuel attributes that might be important in determining fuel
prices, such as the fuel grandability, fuel size or the chemical content of the fuel.
25In fact, for some western coal hauls, transportation costs account for up to 75% of delivered fuel costs. (EIA,
1995),
19
distance to PRB coal and then decrease as more alternative lowsulfur coals become available.
The distance variable and lowsulfur coal price premium are both included as proxies for low
and highsulfur coal prices.
Specifications in (31) establish correlations between state restructuring activity and emission
level. Previous studies (Joskow, 1997; White, 1996) suggest that a major motivation for
electricity restructuring was to remedy the problem of high electricity prices in the Northeast and
California. Under ROR regulation, PUCs set the price of electricity based on the determination
of recoverable costs. If dirty and less efficient coal power plants in the Northeast contributed to
regional high electricity prices by passing on high environmental control costs to consumers,
which in turn induced restructuring, regulatory variables RetailAccess and Transit may be
endogenous to emission rates. A fixed effects model would be able to address the endogeneity
concern. A fixed effects model levels out the inherent variations in unit operation that potentially
correlated with the emission rates, and therefore we can still test how changes in price volatilities
changes emission rates for the same unit across time periods.26
Finally, results could be affected by sample attrition issues due to plants being removed
from the reporting database. In fact, starting in 1998, many plants were divested to nonutilities
and dropped from the sample because cost data of nonutility generating facilities are not reported
to the public. If divestiture decisions were driven by unobservable unit specific characteristics,
which make them systematically different from nondiverstitured plants, for example, if
divestitured plants tend to be more competitive and produce fewer emissions given a level of
output, then the estimation would also be biased. To assess if divestiture creates an attrition bias,
I obtain the estimation results from a balanced subpanel composed of units that remain in the
database through 2004. The sample selection problem would be most severe in this specification
if observations were not missing at random.
The stochastic disturbances in the estimating equations are assumed to be correlated across
observations. 27 To obtain robust standard errors, I adjusted standard errors for clustering by unit
in the following estimations.
IV. (iii) Data
I began construction of the dataset with all privately and public owned Phase I coalfired
generating units. For these units, I constructed a panel dataset beginning in 1996, the first year
for which coal prices are available, and ending in 2004, the last year for which the allowances
trading data were updated. The data are collected and merged from several data sources to obtain
information concerning annual aggregate productions, quality and quantity of coal used, and SO2
26Fixed effects model is not sufficient to avoid endogeneity bias if restructuring policies are adopted in response to
the trend in operating performance. Given that restructuring decisions were generally made before 2000, I conducted
reduced sample estimation based on observations from 2000 to 2004. This alternative specification does not change
the magnitude and significance of the results from the full sample; therefore, suggest that the endogeneity of
regulatory statuses variables may not be a particular concern.
27Estimated average firstorder autocorrelation coefficients indicate uit is likely to be serially correlated. In the
emission rate equation, the coefficient is 0.26 in the fixed effects model; in the percentage change of annually
banked allowance model, the coefficient is 0.38 in the fixed effects model. The likelihood ratio test also shows
evidence of crosssectional heteroskedasticity.
20
emitted during the production process, allowances allocated and banked, electricity prices, input
fuel prices, regulatory statuses and a variety of unitlevel characteristics. This merging process
reduced the sample size, both because of differences in units covered among datasets and
because divestitures removed the plants from the reporting database after 1998. The final dataset
is unbalanced and is composed of 207 Phase I coalfired generating units. All prices are adjusted
to real terms using a 5% discount rate and presented in 1996 dollars. Details of the dataset
collection and construction procedures are described in Appendix D.
Table II presents summary statistics. Table III gives the unityear observations on the
number of units that have been affected by electricity restructuring, installed scrubbers,
experienced fuel switching, or avoided fuel blending. Table III shows that there are rich
variations in fuel inputs and regulatory statuses of the units in both longitudinal and cross
sectional dimensions. In contrast, the number of scrubbers installed remains almost constant
(except for sample attrition that reduces the number) suggesting that changes in emission rates
may not be initiated by the installation of scrubbers.
I also calculate the HerfindahlHirschman Index (HHI) to measure market concentration in
the allowance trading market each year from 1995 to 2004. Generally, the largest seller or buyer
(at the plant level) of allowances has a market share no larger than 3% and the HHI is
consistently lower than 100 across years, which suggests that market power may not be a
significant issue in the allowance market.
IV. (iv) Estimation Results
This section presents estimation results for model (31). I also estimate a number of
alternative specifications to investigate potential endogeneity biases and found that they do not
affect the results.
Table IV reports results from estimating equation (31) using the log of units' annual average
emission rate as the dependent variable (ln[EmissionRate]). Column (1) and (2) report results
from unit fixed and random effects models. A Hausman test suggests that the unobservable error
term i is correlated with at least one of the explanatory variables. Therefore, only the fixed
effects model yields a consistent and unbiased estimation. Nonetheless, the estimated
coefficients of variable Pet are similar and are both negative and statistically significant from
zero. This result is consistent with the theoretical prediction of a negative correlation between
emission rate and electricity price volatility. In particular, based on the fixed effects specification,
a one percent increase in price volatility is associated with a decrease in unit's annual average
emission rate by 0.88%. This means a onestandard deviation increase in electricity price
volatility would induce a sample "average" unit to reduce annual aggregate emissions by 423
tons. With a 95 percent confidence interval, the emission reduction would be anywhere from 383
to 827 tons.
Estimations on the other explanatory variables are generally consistent with prior
expectations. The estimates on SCRUBBER show that the installation of a scrubber would on
average markedly reduce emission rates by 91%. Publicly owned units are less responsive to
electricity price volatilities: the emission rate elasticity of a municipal or cooperatively owned
21
unit is onethird lower than that of an investor owned unit. Estimated coefficient on HEATRATE
shows that inefficient production is associated with higher pollution emissions. Higher allowance
prices, as well as higher electricity prices induce lower emission rates; in contrast, there is a
positive relationship between low and highsulfur coal prices and emission rates. However,
coefficients of these price variables are not statistically significant from zero in the fixed effects
model. AGE does not have a significant impact on emission rates. The reason could be that
HEATRATE depletes all explaining power regarding the effect of production efficiency on
emission performance. Finally, note that different regulatory statuses do not have significant
impact on emission rates, although coefficients of both variables RetailAccess and Transit have
the expected sign.
Column (3) of Table IV presents IV/2SLS estimation results using natural gas wellhead
price as an instrument for SO2 allowance price. The first stage Fstatistics is 22, suggesting that
natural gas price is not a weak instrument. I compare IV/2SLS estimates with those of the fixed
effects model. A Hausman test suggests that allowing SO2 allowance price to enter as an
independent variable yields almost the same estimates as those based on instrumentation. The
statistics is 2(19) = 24.50 and the Pvalue is 0.1775. Therefore, the endogeneity of allowance
price does not seem to be a particular concern. Indeed, using IV/2SLS estimation does not affect
the estimated coefficient of electricity price volatility in either magnitude or statistic significance.
Column (4) of Table IV reports reduced sample estimation. Potentially noisy observations in
the early period of the trading program are dropped. The 2004 data are also excluded from the
analysis. In 2004, the spot price of SO2 allowances, which had been steady at about $200/ton,
were increased by threefold after the EPA proposed the Clean Air Interstate Rule that will
effectively lower the SO2 emission cap by twothirds beginning in 2010. Although the price
response to upcoming stricter limits on emissions provides further evidence on units'
intertemporal optimization behavior, it may swamp the effect of price volatility on emissions
trading. Therefore, regression was restricted to the years 1998 through 2003. This alternative
specification does not qualitatively change coefficient estimation for price volatility although it is
slightly larger than the one received from the full sample year estimation.
To assess if divestiture creates attrition bias, I obtain the estimation from a balanced sub
panel composed of units that remain in the database through 2004. The sample selection problem
would be most severe in this specification if observations were not missing at random. The
results are given in column (5) of Table IV. The estimated coefficient on Pe is quite similar to
those from pervious models, indicating that divestitured units may not be systematically different
from other units regarding the response in emission decisions to price volatility.
As another robustness check, I collect data on the emission rates of Phase I affected units in
1993 as a counterfactual to examine if the change in emission rates can be explained by change
in electricity price volatility. Specifically, I estimate a fixed effects model described by Eq.(33).
With no changes in price volatility, coefficient of price volatility is expected to be zero. About 90
units were not in operation in 1993. Therefore, the sample size is reduced to 118 units in this
regression. The estimated coefficients are reported in column (6) of Table IV. The results are
fully consistent with expectations. The coefficient of price volatility is statistically significant
and is negatively correlated with the emission rate change. To be noted, the coefficient
22
associated with SCRUBBER is much smaller compared to those from other models. This result
again confirms the fact that because most of the scrubbers were installed before the enactment of
the Acid Rain Program, the installation of scrubbers is not a major factor that drives the
decreasing trend in emission rates.
ERTit  ERT93 = 0 + 0 ' RTE93 + 1 lnPeitRTE93 + 2Peit RTE93 + 3Rit RTE93 + 4Zit RTE93
i i i i i i
18 2004
+ Sj +
Tt +it +uit
j=1 t=1996
(33)
Overall, results from alternative specifications closely resemble the basic fixed effects
estimation in column (1). In all cases, the relationship between electricity price volatility and
emission rate, shown in the first row of Table IV, is statistically negative with an estimated
elasticity around 0.8%  0.9%. All four sets of alternative specifications produced qualitatively
similar results on coefficients of other independent variables as well.
The columns in Table V are structured in a manner similar to those in Table IV. Specifically,
the first two columns report the results from the fixed effects and random effects models. A
Hausman test does not reject the null hypothesis that the crosssectional error term uit is not
correlated with the other independent variables. Therefore, both the fixed and random effects
models provide consistent estimations. Nonetheless, in the following, I still report results from
fixed effects estimation, which are not systematically different from those of a random effects
model. Table V shows that the coefficients on price volatility are positive and statistically
distinguishable from zero. Alternative specifications have almost no effect on the estimation
results on the coefficient of price volatility, except for specification in column (5) which
corresponds to estimations of the balanced panel dataset. The lower estimated coefficient of Pe
in column (5) indicates that there could be differences in the elasticity of allowance savings
between divestitured and nondiversitured units. Recall that the size of a unit's allowance bank
(Bi(t+1)) is determined by both levels of emissions (eit) and trading with other units (xit). Given
that the emission elasticities of these two types of units are similar as suggested by Table IV, the
difference in estimated coefficients of Pe could be explained by different trading strategies:
diverstitured units could be more aggressive in purchasing allowances in response to higher
electricity price fluctuations.
Based on column (2) in Table V, a one percent increase in electricity price volatility is on
average associated with an increase of 2.46% in the size of the allowance bank. This implies that
when electricity price volatility increases by a onestandard deviation, a sample "average" unit
will carry an additional 1027 tons of allowances forward to the next period. The 95% confidence
interval is between 137 to 1918 tons. Coefficients of other independent variables generally
remain consistent with prior expectations.
Considering the potential endogeneity of delivered coal prices, I control for units' location
in relation to PRB coal (miles) and the observed price difference between low and highsulfur
coal prices. Table VI reports estimation results for emission rate (columns [1] and [2]) and the
percentage change in annual allowance stocks (columns [3] and [4]) based on these
specifications. Regressions (2) and (4) reported in Table VI also instrument SO2 allowance prices
23
by naturalgas wellhead price. Coefficients of electricity price volatility are consistent with
previous estimations in all models. In addition, the three distance coefficients are individually
statistically significant. The Ushaped profile derived from the distance coefficients echoes the
results from Ellerman and Montero (1998), suggesting that lowsulfur coal prices fall for units
900 miles away from a PRB coal mine.
I use actual price volatility level in 1992 as those that would have prevailed in the absence of
electricity restructuring and compute the corresponding emission rate on the basis of results of
model (1) in Table IV. With expected counterfactual price volatility, extra allowances the
difference between counterfactual emissions and actual emissions is about 11% of the total
banked allowances. Similar values are obtained using coefficients from the models (2) (8).
Following the same exercise but using the average price volatility level during the pre
restructuring period (19901995) as the counterfactual, the increased price volatility can explain
about 8% of the total allowances banked by the sample units during Phase I of the acid rain
program. Similarly, I calculate the counterfactual allowance stock based on estimations gleaned
from model (2) of Table V. I found increased price volatility can explain 6% of the total banking.
Using coefficient estimates from models (1) (8), I found this number will be between 7% to
10%.
V. Welfare Analysis and Policy Implications
To gain further insight into the effects of uncertainty on the timeseries behavior of banking
and emission, I numerically simulate the banking pattern, emission stream and permit price path
over time resulting from different price volatilities and contrast them to the results that would
occur in the absence of uncertainty. Given different social damage functions, I calculate the
potential welfare impact of increased price volatility and discuss the policy implications.
V (i) Simulation of Emission Trading under Different Price Volatilities
In the following, I analyze emission banking from the perspective of the polluting industry
and ignore internal spatial trading within the industry. A representative agent is assumed to
maximize the present discounted value of profit over a planning horizon spanning from 1995 to
2020 based on a production function g = G(lahb) . The permit market is assumed to be perfectly
competitive. The optimization problem is described by Eqs.(17) and (18) in section III. In
addition, I assume the electricity price Pet evolves following a meanpreserving stochastic
process:
Pe + with prob q
Pet = Pe with prob 1 2q
Pe  with prob q
where Pe is the expected mean of the electricity price; q denotes the probability that a price
moves up or down by . Both q and measure the magnitude of uncertainty. To be consistent
with previous analyses, I vary the value of from 0 to 1, while keeping q constant at 0.3. To
24
focus attention on the impact of uncertainty, I have chosen the realized electricity price in each
period to be the same at Pe . Annual initial allocation is 7 million tons in the first five years and is
permanently capped at 3.5 million tons from the year 2000. Production parameters are chosen
with the following values: G = 55, a = 0.6, =0.9. 28Discount ratio is assumed to be 0.95.
Values of the other parameters are chosen as around the sample mean of the empirical data : Pe =
4.8 cents/KWh, ul = 1.64 lb/mmBTU, uh = 4.41 lb/mmBTU, Pl = 120 cents/mmBTU, Ph = 100
cents/mmBTU.29 Permit price is endogenously determined by the operational behavior of the
agent according to Eq.(A8). The process of simulation is discussed in detail in Appendix E.
Numerical analysis produces robust patterns in the response of banking and emission to the
increase in output price uncertainty. Figure II depicts the total amount of banked emission
permits as a function of time. The dashed line corresponds to a scenario in which the price spread
=0.2 and the emission cap remain constant at 7 million tons across all periods. The shaded,
fuzzy line tracks the actual allowance storage through 2004. All the other lines indicate a two
stage schedule of declining emission standards (total emissions are capped at 7 million tons from
1995 to 1999 and at 3.5 million tons after year 2000) with different assumptions about price
volatility ( = 0, 0.2, 0.4, 0.6, 0.8, and 1).
Comparing the dashed line with the other solid lines, it is apparent that when price volatility
is low, tightening environmental standards provide a major incentive for producers to reduce
emissions below the standards in the early years in order to accumulate credits that can be used
when standards are more severe. When price volatility becomes significant ( increases), the
asymmetric impact of uncertainty plays a more important role in determining the optimal size of
bank. As anticipated, a price spread of =1 generates the largest number of banked permits
during Phase I and a zero price volatility generates the fewest. Uncertainty also affects the draw
down rate of the bank. When there is no uncertainty ( = 0 ), the bank is depleted by the year
2008. When =1, the banking period is remarkably extended: the bank continues to grow until
2011.
Of particular interest to the environmental authority is the effect of uncertainty on the
emission stream. The annual emissions flows and the cumulative emissions in each year under
different scenarios of price volatility are plotted in Figures III and IV. As noted, the emission
stream associated with different price volatilities deviate substantially in the beginning and
terminal periods. When prices are volatile, it is optimal to emit less in early periods and more in
later periods. When these uncertainties are high enough, excessive emissions are observed
towards the end.
28Ideally, I would estimate the production functions based on actual data. However, besides observing purchasing
choice over low and highsulfur coal, there are no data on actual inputs of low and highsulfur coal. Production
factor G is chosen to be large enough so that the emission standard imposes a binding constraint on the production
decision. As a sensitivity analysis, I analyze the change in G on the results and find it does not change the qualitative
pattern of the results.
29The price premium of lowsulfur coal, considering the coal blending adjustment cost, is chosen at 20
cents/mmBTU. I examine the importance of the value on the results in the sensitivity analysis.
25
Also noted from Figures III and IV is that the size of early emission reductions is significant.
Based on the numerical analysis, when = 1, producers would have reduced emissions by 48%
more than when = 0 during the first 5 years of the program; with = 0.2 or 0.4, early
emission reductions are at the level of 5% and 14%, respectively, which are in the same order of
magnitude as the elasticity estimated in previous empirical analysis.
Figure V contains the present value permit price path under different price uncertainties.
Permit price equals the marginal abatement cost. Therefore, Figure V corresponds to Figure III in
the sense that the higher the emission level, the lower the permit price. For the high variance
cases, permit prices are extremely high initially and plummet at the end. It is worth mentioning
that the expected price differs from the realized price. Producers bank emission credits so as to
equilibrate expected present value price across compliance periods. However, when uncertainty
is extremely high, banking does little to smooth the actual price series.
The simulation model assumes specific parameter values for the production function and
input and output prices. To test the sensitivity of results to these assumptions, a number of
simulations were run with different values for q, G, a, b, Pl, and Ph. Simulation results on total
banked permits under different scenarios are shown in Table VII. The results indicate that the
qualitative conclusions do not hinge on the specific parameter values chosen. In addition, as
shown in the first two rows of Table VII, emission banking is much larger when the probability
of price movement, q, increases from 0.3 to 0.4, confirming the relationship between uncertainty
and emission banking from another perspective.
V.(II) Welfare Analysis
From the standpoint of economic efficiency, uncertainty shifts emission abatement to the
earlier periods, therefore raising abatement costs because of the discounting effect.
Assume = 0.95, when increases from 0 to 1, the sum of the discounted net payoff is reduced
by 9%; when = 0.85, this number reaches to 20%. Furthermore, high initial compliance costs
generated by high uncertainty would deter new entrants and have a negative impact on the
development of competitive output markets and the emerging environmental markets. Although
it is generally believed that intertemporal trading creates compliance flexibility that reduces
abatement costs and increase efficiency, uncertainty may dampen the cost saving properties of
banking.
In addition to cost considerations, depending on the nature of the pollutants, early abatement
also has different important environmental implications. If the pollutants, such as greenhouse
gases, create stock damage, voluntary early reduction would yield significant environmental
benefits. However, in a finite planning horizon, early abatement increases the degree to which
firms will concentrate emissions to in later time periods and raise the potential of emission spikes.
If the pollutants create flow damages and if the damage function is convex, emission spikes can
impose increased health hazards or even trigger the threshold effect. Emission spikes could also
be associated with periods of market structure change. I simulate an exemplary situation in
which the price spread remains at = 0.4 through year 2002 and declines to 0.2 permanently.
As shown in Figure VI, a sharp emission spike occurs one year before the expected decline in
price volatility.
26
V.(iii) Policy Implications
It is generally concluded that uncertainty about the cost of controlling carbon dioxide
emissions make price instruments preferable to quantity instruments because the cost of limiting
one ton of emissions is expected to rise as the abatement increases, while the expected benefit of
each ton of carbon reduced is roughly constant because climate change is driven by stock effects
rather than flow effects.(Hoel and Karp, 2001; Pizer, 2002).30 However, for a multiperiod
emission control, when marginal abatement costs are also uncertain for regulated sources, a
tradable quota system that allows banking creates incentive for early abatement and generates
substantial higher environmental benefits than a tax schedule. In addition, since the initial caps
on carbon emissions are likely to be relatively undemanding, the expectation of later, more
stringent caps will tend to produce even higher reduction in initial years even when the cap is
nonbinding.31
On the other hand, when the marginal benefits of abatement are steeper compared with the
marginal costs, a quantity instrument without restrictions on the temporal transfer of emissions,
may not necessarily be preferable to a price regulation. This is because a quota system exposes
firms to volatile market prices, which encourages reallocation of emissions in response to
observed uncertainty. When marginal damaging effects increase rapidly along with the increase
of emission flows, a price instrument would be advisable to directly control the marginal social
cost. Another potential solution is to employ a hybrid approach that combines a tradable quota
system with some safety measures, such as restricting the intertemporal trading ratio and/or
applying discounting to banked permits. The government may also consider incorporating
multiple polluting industries into a national trading program so that uncertainties facing one
industry can be diversified, and the importance of building up a bank to buffer unexpected price
strike may be reduced.
VI. Summary and Conclusions
In this paper, I study the theory and empirical behavior of intertemporal emission trading
under uncertainty, and its implications for policy instrument choice and banking regime design.
The theoretical analysis suggests a positive relationship between industrywide uncertainty and
emission banking. In an intertemporal emission trading system, increased output or input price
uncertainty induces larger emission reductions and higher allowance prices. Empirical analysis
based on data from the U.S. SO2 allowance market provides consistent timeseries evidence. The
results suggest that increased price volatility induced by electricity market restructuring could
have contributed to 811% of the extra emission reductions during Phase I of the trading program.
Numerical simulations yield similar elasticity estimates.
30The conclusion follows from Weitzman (1974) that when the slope of the marginal cost function is greater than
the slope of the marginal abatement function, price instruments are preferable to quantity instruments because they
are much more likely to minimize the adverse consequences of choosing the wrong level of control.
31Currently, the transfer of unused allowances from the period 2005  2007 to the first commitment period under the
Kyoto Protocol, i.e. 20082012, is not allowed under an EUwide ban on banking, which from an environmental
point of view, seems to be a troubling decision.
27
Uncertainty affects the pattern of emission levels and abatement costs over time. Its impact
on both economic efficiency and environmental outcomes could be sizable. I estimate and
compare the welfare effects under different output price volatility and provide relevant policy
recommendations.
The future work will be focused on extending the model to reflect other sources of
uncertainty existing in the real world, such as uncertainties over emission cap and interest rate.
For example, emission cap can be endogenously determined by the size of the global carbon
market, i.e. the number of participating countries; Interest rate that reflects countries
macroeconomic policy may also have important implications for the optimal emission decisions.
28
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32
Appendix A
PROOF:
THE MARGINAL VALUE OF ALLOWANCES IS CONVEX IN THE ELECTRICITY PRICE
(A) CobbDouglas Production Function
Rewrite the optimization problem for a representative firm in the industry:
max[Peg(l,h)  c(l,h)]
s.t.
B2 = e(l,h) = (ll +hh) = ll + hh (A0)
where g(l,h) = Glh1  , c(l, h) = Pll+Phh; B2 is the total available emission allowances in the
terminal period.
Define the Lagrangian expression:
L = Peg(l,h)  c(l,h) + (B  ll  hh) (A1)
The necessary firstorder conditions determining a maximum at (l),h),)) are
L/B = ) (A2)
PGl)1h)1  Pl  l = 0
 ) (A3)
e
PG(1)l)h)  Ph  h = 0
) (A4)
e
Crossdividing (A3) and (A4) results in:
Pl + l
) h) )
(A5)
Ph + h
) = 1 l
The expression on the right of (A5) is the marginal rate of technical substation (MRTS) between
the two types of fuel. Eq.(A5) says that at the optimum the MRTS between l and h must be equal
to their price ratio (including the price paid for allowances).
Define the following: dl (1)(Pl + l) and dh (Ph + h) and substitute into (A5)
) )
h) (1)(Pl + l)
) )
= = dl (A6)
l (Ph +h) ) dh
Solving (A6) and (A0), we obtain the conditional factor demand functions
33
l = dh dl B (A7)
dhl + dlh B,h = dhl + dlh
Substituting l and h from Eq.(A7) back into (A4) yields:
Pe = 1 1
G(1) dh dl (A8)
Differentiating (A8) with respect to
= G dh dl
1
> 0 (A9)
Pe hdl + ldh
The inequality (A9) clearly holds for all values of Pe, dh and dl.
Differentiating (A9) with respect to defines the key derivative of the theorem as
2 1
= G(Pe)(
dh dl 2 dl 2 h
Pe 2 hdl + ldh)2 (2hl + (1)2hl +2h (dh ) + (1)2l (ddl )  hl)
(A10)
Letd = dl /dh . Note that the minimum value of 2hd + (1)2l (d ) in the last bracketed term
2 2 1
of (A10) equals 2(1)hl evaluated at d = (1)l .
h
Since by construction, there is d = (1)(Pl + l) (1)l
(Ph +h) > h , then
2hx+(1)2l (1x) > 2(1)hl . Thus
2 2 2 > 0 , which proves the convexity of the
Pe 2
marginal value of permits with respect to electricity price (recalling that is the Lagrangian
multiplier and represents the marginal valuation of a unit of permit).
(B) CES Production Function
Next consider a more general CES production function
1
g = G(l + (1)h ) (A12)
where <1, = 1
1 is the elasticity of substitution. still reflects distribution weight of
lowcarbon fuel.
The first order conditions are:
34
PG(l) + (1)h) ) l)1  Pl  l = 0
11 ) (A13)
e
PG(l) + (1)h) ) (1)h)1  Ph  h = 0
11 ) (A14)
e
Crossdividing (A13) and (A14), the factor proportion at the optimum is determined by
l = ((1)(Pl +l))1 1 dl 1
(A15)
h (Ph +h) (dh )1
As before, solve l and h from (A15) and (A0) and substitute them into (A13)
1
Pe = 1
G(1) ( dl 1 +(1)dh ) 1 (A16)
Taking partial derivative of (A13) with respect to gives
1
= G (dl 1 +(1)dh ) 1
> 0 (A17)
Pe 1 1
(ldl1 + hdh )
1
Apparently, (A17) holds for all values of Pe, dh and dl.
Differentiate (A17) with respect to gives:
1
2 = G (dl 1 +(1)dh ) 1
(A18)
Pe 2 1 1
(1 )(ldl 1 + hdh )
1 2 (Pe )T1
1 1
where T1 dl 1 dh (2h (dh ) + (1)2l (ddl )  2(1)lh)
1 2 dl 2 h (A19)
Note that (A19) has a similar structure to that of the last bracketed term of (A10). Following the
same procedure, we see that because Pl + l l
Ph + h > h , T1 > 0. Then it is sufficient to show that
2 > 0. Therefore, given a more general form of production function, the marginal value of
Pe 2
allowances is still convex in Pe.
35
Appendix B.
PROOF. THE MARGINAL VALUE OF ALLOWANCES IS CONVEX IN INPUT COSTS Pl AND Ph.
Following previous discussion, substitute dl (1)(Pl + l) and dh (Ph + h) into
) )
Eq.(A7) to obtain as an implicit function of Pe
1 1
Pl + l = 1 1
1 [G(1)Pe] (Ph + h) (A13)
Taking partial derivative of (A13) with respect to Pl and gives
=  1 < 0 (A14)
Pl 1
[G(1)Pe] (Ph + h) h + l1
Differentiate Eq.(A14) with respect to
1 1 1 1 2
2 [G(1)Pe] (Ph + h) h
=  > 0 (A15)
Pl 2 1
([G(1)Pe] (Ph + h) h + l)2
1
Pl
The inequality follows naturally. So is also a convex function of Pl . Similarly, we can show
that is convex in Ph . Therefore, increases in the mean preserving spread of Pl and Ph increases
the expected marginal value of permits.
36
Appendix C.
PROOF: In an imperfect electricity market, the marginal value of allowances is also convex
in electricity prices.
Consider the following optimization problem for a firm with market power in electricity market
described presented in the paper (Eq.[20])
V = max[WGlh(1 ) Pll  Phh] (A16)
s.t. B = e(l,h) = (ll +hh) = ll + hh
where = 1, W is the stochastic demand shifter and G is the productivity parameter.
1
The necessary firstorder conditions for a maximum at (l),h),)) are
WGl1h(1 )  Pl l = 0 (A17)
WG(1)lh(1 )1  Ph h = 0 (A18)
The MRT is unaffected by returns to scale and is again described by Eq.(A5). A similar exercise
as in Appendix A provides the following condition where dh and dl are functions of .
W = B1
G(1) dh 1 1 (1 )
dl (hdl + ldh)1 (A19)
Taking partial derivative of (A19) with respect to
(1)  1 (A20)
W = G(1)B1dh dl (hdl + ldh)2 T3
Where
T3 = (1)(hdl + ldh)2 + (1)(hPl  (1)lPh)2 (A21)
When 1, there is still > 0
W
The second order derivative of with respect to W is
2 1 (1)1 2
(A22)
W2 = G(1)B1dh dl (hdl + ldh)1 T3 T4 W
where
37
T4 = T3dldh[2hl + (1)2hl +2h (dh ) + (1)2l (ddl )  hl]+
2 dl 2 h
(A23)
2(1)hldhdl(hPl  (1)lPh)2
Consultation with Appendix A ought to reveal that T4 > 0 because Pl + l l
Ph + h > h , and
2hx+(1)2l (1x) > 2(1)hl. Therefore,
2 2 2 0. Hence when electricity market is
W
imperfect, the marginal value of permits is still convex in the underlying stochastic variable.
38
Appendix D Data Sources
I obtained annual data on allowances initial allocations, holdings, transactions, and
deductions (for emissions compliance purposes) from the EPA's allowance tracking system
spanning from 1995 to 2004 for all 263 Phase I affected coalfired generating units. I merged this
dataset with information collected from FERC Form 767. FERC Form 767 is an annual survey
on steamelectric plant unit operating and design covering the period 19962004, from which I
took annual observations at the generating unit level on unit nameplate capacity, the status of
scrubber installation, electricity generations, load hours, fuel consumption and monthly fuel
sulfur content and heat content, Using information about fuel consumption, fuel heat content,
total generation, along with the emission data derived from the EPA's allowance tracking system,
I computed heat rate, heat input, and emission rate for each unityear observation. Because data
are missing for certain years, and because some units were not operating for an entire year, the
number of observations varies from unit to unit.
The price information on fuel, electricity, natural gas, and allowances are obtained from
different sources. To construct data on prices and input shares for low and highsulfur coal, the
above merged data set was then merged with the Form FERC423 on monthly cost and quality of
coals for electric plants from 1995 to 2004. Form FERC423 records the physical quantity, Btu
content, delivered cost, and carbon content of each fuel transaction at each electric plant. A SO2
emission boundary of 2.5 pounds per million Btu was used to distinguish low and highsulfur
coal. This value was chosen so that the burning of lowcarbon coal meets Phase I standards on
average. Fuel prices are calculated by dividing the delivered cost by the heat content of the fuel.
Fuel prices are missing for some plants when only one type of fuel is purchased (the price of the
other fuel is unobservable). To obtain the cost of fuel that is not purchased by the plant, I use its
price in the previous year as an approximation.
The electricity price data are drawn from the responses from electric utilities survey Form
EIA861 "Annual Electric Power Industry Report." From this data set, I obtained the annual
average industrial price for all years from 1995 to 2004 at the state level. Industrial prices are the
most volatile and least protected by PUC regulation. The volatility of industrial prices is mainly
driven by changes in fuel costs. However, because of the existence of longterm contacts, to use
industrial prices may underestimate the actual price volatility in the spot market. Natural gas
wellhead prices were collected from EIA historical databases. SO2 regulation costs are calculated
as the mean of two monthly price indices of SO2 allowances prices that brokerage firms Cantor
Fitzgerald and Fieldston report to the EPA.
Distance to fuel mines was provided by the EPA's Acid Rain Division. Data on regulatory
status were collected from the Retail Wheeling & Restructuring Report, a statebystate reporting
of regulatory commissions, state legislation, and utilities activities related to retail competition
published quarterly by the Edison Electric Institute. These data are crosschecked with the LEAP
Letter published bimonthly by William A. Spratley & Associates, National Regulatory Research
Institute Web site and EIA's publication on Status of State Electric Industry Restructuring
Activity.
39
Appendix E Stochastic Dynamic Simulation Model Description
Here I present the computational details of the numerical simulation, programming language,
hardware and software used. Consider the following optimization problem
Vt(Pet, Bt) max { Petgt(lt,ht) ct(lt,ht) + Et[V(t+1)(Pe(t+1), Bt )]
+1 (A24)
lt ,ht ,Bt+1
s.t. llt +hht = At + Bt Bt +1
0 Bt At + Bt
+1
where gt = G(lt ht
(1) ) .
This is a multivariate optimization problem with three control variables (l, h, and B). To simplify
the problem, I derive the structural relationship between l, h and B based on firstorder
conditions. This derivation, which involves some tedious calculation,32 leads to the following
specifications:
(1) t is fully characterized by
Pet = (At + Bt  Bt+1)1 
1 1 (1 )
Gs(1) dht dlt (hdlt + ldht)1 (A25)
(2) lt and ht are determined by the following two static optimality equations
lt = dht dlt
dhtl + dlth (At + Bt  Bt+1),ht = dhtl + dlth (At + Bt  Bt+1) (A26)
Noting that now the problem is simplified as we only need to search for the solution for B, and
find optimal choices for l and h using Eqs. (A25) and (A26). Applying a grid search to obtain the
initial guess for B (B* < 20) I then specify a grid of 2001 points between 1 and 20 (million tons)
to compute the value function (A24) at each time t and each state of Pet, beginning with the
terminal value function and working back to period 1 to compute the equilibrium time path for B
and , which jointly determine the optimal choices for lt and ht.
The program needed for the computation of the model was coded in C++ and complied to run on
Windows based machines. The whole simulation runs in one minute. All the code is available
upon request from the author.
32Available from the author, upon request.
40
Figure I
ANNUAL EMISSION CAP, AGGREGATED EMISSIONS AND BANKED ALLOWANCES
41
FIGURE II
AGGREGATE BANKED ALLOWANCES UNDER DIFFERENT PRICE VOLATILITIES
25
=1
20
nces)a 15 = 0.8
low
al
on
(milli 10 = 0.6
Bank
= 0.4
5
= 0.2
= 0
0
5 9 5 7 9 1 3 5 7 9
199 1997 199 2001 2003 200 200 200 201 201 201 201 201
Year
NOTE: The vertical axis describes the total amount of banked permits of the polluting industry in
each year (million tons). is the meanpreserving spread of the stochastic electricity price. The
dashed line corresponds to a scenario that =0.2 and the emission cap remains constant at 7
million tons across all years. The shaded, fuzzy line tracks actual allowance stock in the SO2
allowance market. All the other lines correspond to a twostage schedule of declining emission
standards with total emissions capped at 7 million tons from 1995 to 1997 and at 3.5 million tons
after year 2000.
42
FIGURE III
EMISSION STREAM UNDER DIFFERENT PRICE VOLATILITIES
10
9
8
)snot 7
n 6
ioill
m( 5
snoisis 4
3
mE
2
1
0
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Fixed Cap, =0.2 =0 Year =0.2
=0.4 =0.6 =0.8
=1 Actual
NOTE: The vertical axis describes the aggregate annual emissions of the industry (million tons).
is the meanpreserving spread of the stochastic electricity price. The dashed line corresponds
to a scenario in which =0.2 and the emission cap remains constant at 7 million tons across all
years. All the other lines correspond to a twostage schedule of declining emission standards
with total emissions capped at 7 million tons from 1995 to 1997 and at 3.5 million tons after year
2000.
43
FIGURE IV
CUMULATIVE EMISSIONS UNDER DIFFERENT PRICE VOLATILITIES
120
)snot 100
n
lioil 80
m(
s
onis 60
is
mE
evitalu 40
muC 20
0
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Year
=0 =0.2 =0.4 =0.6 =0.8 =1
NOTE: The vertical axis describes the cumulative emissions in each year (million tons). is the
meanpreserving spread of stochastic electricity price. The dashed line corresponds to a scenario
in which =0.2 and the emission cap remains constant at 7 million tons across all years. All the
other lines correspond to a twostage schedule of declining emission standards with total
emissions capped at 7 million tons from 1995 to 1997 and at 3.5 million tons after year 2000.
44
FIGURE V
PERMIT PRICE PATH UNDER DIFFERENT PRICE VOLATILITIES
5
4.5
4
n)ot/$ 3.5
100*( 3
ceirPti 2.5
2
mreP1.5
1
0.5
0
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Year
Fixed Cap, =0.2 =0 =0.2
=0.4 =0.6 =0.8
=1
NOTE: The vertical axis describes the real term emission price (100 $/ton). is the mean
preserving spread of stochastic electricity price. The dashed line corresponds to a scenario in
which =0.2 and the emission cap remains constant at 7 million tons across all years. The
shaded, fuzzy line tracks actual allowance stock in the SO2 allowance market. All the other lines
correspond to a twostage schedule of declining emission standards with total emissions capped
at 7 million tons from 1995 to 1997 and at 3.5 million tons after year 2000.
45
FIGURE VI
EMISSIONS PATH UNDER CHANGING PRICE VOLATILITY
9
8
7
tons) 6
5
(million
4
ions
3
Emiss
2
1
0
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Year
NOTE: The graphs describes emission path under a scenario in which the price spread = 0.2
from 1995 to 2002 and drops to = 0.4 through 2020.
46
Table I. DEFINITION OF THE SYMBOLS
l lowcarbon fuel input level
h highcarbon fuel input level
g electricity output level
x permits bought (x > 0) or sold (x < 0)
Pe electricity price
Pa permit price
Pl lowcarbon fuel price
Ph highcarbon fuel price
A permits issued by the government (annual)
B banked emission permits
e emission level
carbon content of the fuel
converting rate of carbon to carbon dioxide
carbon dioxide content of the fuel
V value of the firm
discount ratio
r discount rate
ratio of marginal products of high and lowcarbon fuel
shadow value of permits
convenience yield of banked permits( 0)
G productivity factor of electric industry
the share of lowcarbon fuel (0 < <1)
meanpreserving spread of stochastic electricity prices
low and highcarbon fuel's elasticity of substitution parameter
markup coefficient of a unit with market power in a electricity market
( 1)
W exogenous stochastic demand shifter in the electricity market
returntoscale parameter of production technology 1
s allowed return on capital cost under ROR regulation
k previously invested capital of an electric firm
a regulated firm's gross revenue net of operating expenses
Lagrangian multiplier associated with ROR profit constraint. It
reflects the extra profit a firm would get if the profit restriction is
relaxed marginally. 0 < <1 implies profit constraint is effective.
extra return on permits expenditures for a regulated utility
D Pollution damage function
n Convexity of the social damage function
47
Table II
SUMMARY STATISTICS
Variables Obs. Mean Std. Dev. Min Max
Emissionrate(tons/MWh) 1595 .011 .007 .00008 .041
Pe (%) 1595 .050 .037 .014 .170
Pa(dollars/ton) 1595 133 55 80 285
Pe (cents/KWh) 1595 4.21 .95 2.68 9.54
Pl (cents/mmBTU) 1595 127.8 28.0 71.3 279
Ph (cents/mmBTU) 1595 126.7 43.2 76.7 418.6
Png(dollars/thousand cubic feet) 1595 2.97 1.34 1.77 5.45
Vintage 1595 1964 7.8 1949 1978
AGE (years) 1595 36 8.1 18 55
HEATERATE(mmBTU/MWh) 1595 10.23 1.05 2.50 17.90
WORKLOAD (hours) 1595 7253.5 1077.8 792 8760
Initial (tons) 1595 17467 17877 144 192637
Carry (tons) 1595 11187 18472 0 155236
Stock (tons) 1595 29653 27153 343 277612
MUNI 1595 .021 .144 0 1
CAP (MW) 1595 356 254 75 1300
l (lbs/mmBTU)) 1452 1.64 .68 0.41 2.98
h (lbs/mmBTU)) 1452 4.41 1.28 3.00 8.95
DPRB (miles) 1461 1063 327 87 1773
RTE93(lbs/mmBTU) 864 2.32 1.79 .01 8.06
48
TABLE III
YEARLY OBSERVATIONS ON REGULATORY STATUSES, SCRUBBER INSTALLATION AND FUEL
SWITCHING/BLENDING
Year Retail Access Transit Scrubber Switch Noblend
1996 28 165 23 34 21
1997 44 141 23 38 15
1998 58 127 23 35 23
1999 105 83 21 54 8
2000 87 85 21 56 15
2001 55 85 17 40 3
2002 55 84 19 65 11
2003 49 85 16 50 13
2004 49 86 17 36 7
Note: This table shows annual observations on the number of units affected by retail
restructuring, installed scrubbers, switch to lowsulfur coal, or with no fuel blending. After
1998, because many generating units were divestitured to nonutilities and are no longer
reporting fuel purchasing costs to the public, the sample size shrinks, which is reflected by
the decreasing observation numbers of all variables.
49
TABLE IV
DETERMINANTS OF EMISSION RATE (IN LOG FORM)
Variables (1) (2) (3) (4) (5) (6)
Pe .878** .858** .865** .937** .896** .901**
(.401) (.335) (.307) (.365) (.409) (.407)
lnPa .031 .051 1.807*** .024 .196** _
(.065) (.060) (.478) (.038) (.079)
lnPe .269 .249 .221 .234** 153 .305
(.224) (.177) (.163) (.118) (.252) (.222)
lnPl .047 .139* .008 .046 .016 .003
(.086) (.076) (.075) (.100) (.094) (.106)
lnPh .103 .041 .118** .103* .133 .037
(.089) (.058) (.056) (.051) (.091) (.085)
RetailAccess .047 .059 .048 .092 .009 .030
(.051) (.039) (.035) (.046) (.064) (.050)
Transit .069 .073 .073 .054 .083 .005
(.042) (.085) (.079) (.050) (.096) (.061)
SCRUBBER 2.447*** 2.158*** 2.313*** .396** 2.442*** 2.138***
(.036) (.081) (.138) (.068) (.038) (.031)
AGE .023 .006 .023 .008 .003 .012
(.026) (.017) (.019) (.019) (.026) (.035)
AGE2 .00009 .0002 .0001 .0003 .00009 .0004
(.0003) (.0002) (.0002) (.0002) (.0003) (.0005)
lnHEATRATE .163* .271** .133 .247 .234** .231**
(.098) (.114) (.110) (.205) (.094) (.089)
WORKLOAD .053 .085 .059 .092 .013 .139
(.088) (.075) (.070) (.068) (.092) (.095)
INITIAL 1.20e06 1.31e06 1.18e06 3.62e07 8.85e07 1.20e06
(9.33e07) (9.55e07) (8.83e07) (4.04e07) (9.74e07) (1.90e06)
MUNI Pe .245** .113 .245** .135** .236** .104
(.095) (.107) (.112) (.042) (.099) (.077)
CAP _ 1.691 _ _ _ _
(1.846)
CAP2 _ .061 _ _ _ _
(.173)
Constant 7.258*** 264.390*** _ 17.074 11.209*** 4.959***
(.660) (97.189) (4.224) (.858) (1.013)
R2 .930 .717 .929 .961 .859 .944
Observations 1586 1586 1552 1032 1291 871
NOTE: Dependent Variable is Ln(emissionrate). Columns (1) and (2) report results from estimating Eq.(31)
via the fixed effects and random effects models. A Hausman test rejects the null hypothesis that there is
no systematic difference between fixed and random effects estimations. The test statistics are
2(19)=61.84, Pvalue=.0000. Column (3) reports IV/2SLS estimation using natural gas wellhead price
as an instrument for SO2 allowance price. F statistic for the first stage regression is 22.08. Column (4)
reports fixed effects estimation for Eq.(33). The sample is composed of 118 units that were operating in
1993. Column (5) reports estimation results based on a balanced panel dataset, which restricts the sample
to 145 units that were active from 1996 to 2004. Column (6) reports estimation based on sample data
from 1998 to 2003. Standard errors clustered by unit are reported in parentheses. *** indicates significant
at the 1% level; ** indicates significant at the 5% level; * indicates significant at the 10% level. Reported
R2 is the adjusted R2 for fixed effects and random effects models and the centered R2 for the IV/2SLS
model.
50
TABLE V
DETERMINANTS OF ANNUAL PERCENTAGE CHANGE IN ALLOWANCE STOCK
Variables (1) (2) (3) (4) (5)
Pe 2.410** 2.457** 2.358** 2.759** 1.615 **
(1.059) (1.108) (1.088) (1.408) (.509)
lnPa .171 .216* .294** _ .327***
(.113) (.118) (.133) (.093)
lnPe .135 .369 .249 .389 .169
(.416) (.586) (.385) (.671) (.287)
lnPl .235 .110 .327 .073 ..013
(.361) (.206) (.343) (.279) (.093)
lnPh .021 .021 .020 .007 .117
(.114) (.151) (.109) (.199) (.097)
RetailAccess .085 .101 .140 .119 .012
(.120) (.126) (.122) (.358) (.229)
Transit .078 .077 .143 ..051 .117
(.108) (.286) (.154) (.104) (.231)
SCRUBBER .520*** .043 .338** .666*** .491**
(.052) (.126) (.126) (.045) (.050)
AGE .028 .035 .041 .111* .023
(.035) (.041) (.034) (.051) (.033)
AGE2 .0006 .0006 .0005 .002** .00002
(.0005) (.0005) (.0004) (.0008) (.0004)
lnHEATRATE .463 .064 .498 .548** .241
(.300) (.301) (.266) (.216) (.229)
WORKLOAD .541** .240 .518 .105 .579***
(.183) (.227) (.467) (.910) (.137)
INITIAL 2.60e06 2.20e06 2.31e06 3.16e06 1.41e07
(2.30e06) (2.94e06) (2.41e06) (4.09e06) (1.32e06)
MUNI Pe .043 .054 .041 .102 .057
(.049) (.220) (.173) (.071) (.045)
CAP _ 1.767 _ _ _
(2.304)
CAP2 _ .175 _ _ _
(.215)
Constant 1.100 10.89 _ 5.280 4.089**
(1.413) (122.6) (4.782) (1.219)
R2 .226 .046 .228 .301 .201
Observations 1586 1586 1552 1032 1291
NOTE: The dependent variable is (Bi [t+1] Bit)/Bit (%). Columns (1) and (2) report estimation results from
the fixed effects and random effects models. A Hausman test does not reject the null hypothesis; the error
term i is correlated with the other explanatory variables. The test statistics are 2(19) =17.72, P
value=.5412. Column (3) reports IV/2SLS estimation using natural gas wellhead price as an instrument
for SO2 allowance price. Column (4) reports reduced sample estimation between (data from 1998 to 2003).
Column (5) reports estimation results based on a balanced panel dataset, which restricts the sample to 145
units that were active from 1996 to 2004. Standard errors clustered by unit are reported in parentheses.
*** indicates significant at the 1% level; ** indicates significant at the 5% level; * indicates significant at
the 10% level. Reported R2 is the adjusted R2 for the fixed effects and random effects models and the
centered R2 for the IV/2SLS model.
51
TABLE VI
ESTIMATES FOR EMISSION RATE AND PERCENTAGE CHANGE IN BANKING OF ALLOWANCES CONTROLLING
FOR UNITS' DISTANCES TO PRB COAL
Emission Rate Percentage Change in Allowance Stock
Variables (1) (2) (3) (4)
Pe .838** .832** 2.590** 2.642**
(.342) (.348) (1.196) (1.924)
lnPa .043 .002 .234 .836
(.056) (.003) (.122) (2.917)
lnPe .498** .449** .361 .559
(.183) (189) (.641) (.669)
DPRB .003** .003** .002 .002
(.001) (.001) (.002) (.002)
DPRB2 4.02e06** 4.17e09** 1.63e06 1.51e06
(1.50e06) (4.95e10) (2.04e06) (1.72e06)
DPRB3 1.32e09** 1.40e09 4.88e10 4.54e10
(4.97e10) (4.95e10) (6.82e10) (5.75e10)
LSPremium .170** .168** .057 .058
(.060) (.061) (.070) (.063)
RetailAccess .017 350.6** .012 .084
(.041) (113.0) (.317) (.335)
Transit .078 .085 .064 .122
(.085) (.087) (.299) (.313)
SCRUBBER 1.87** 1.87** .097 .101
(.103) (.102) (.143) (.120)
AGE .010 .012 .051 .042
(.016) (.017) (.044) (.041)
AGE2 .0002 .0002 .0008 .0007
(.0002) (.0002) (.0006) (.0005)
lnHEATRATE .349** .344** .111 .078
(.115) (.116) (.318) (.299)
WORKLOAD .099 .092 .235 .150
(.077) (.078) (.245) (.243)
INITIAL 1.21e06 1.23e06 2.08e06 1.63e06
(9.76e07) (9.88e07) (3.23e06) (3.20e06)
MUNI Pe .142 .141 .053 .070
(.104) (.104) (.225) (.196)
CAP 1.988 1.643 2.039 1.770
(1.820) (1.840) (2.544) (2.163)
CAP2 .192 .164 .214 .186
(.173) (.175) (.241) (.204)
constant 242.249** 135.358* 7.913 _
(97.222) (71.532) (136.9)
R2 .710 .708 .049 .050
Observations 1448 1425 1448 1425
NOTE: Columns (1) and (2) report results from estimating determinants of the log of the annual average
emission rates identified in Eq.(30) via fixed effects and IV/2SLS (using natural gas wellhead prices as an
instrument for SO2 allowance price). Columns (3) and (4) report similar regressions with the dependent
variable being the percentage change of annual allowance banking from random effects and the IV/2SLS
model. All estimations use units' distance to PRB coal as a proxy for lowsulfur coal price and include the
lowsulfur coal premium as a repressor. Standard errors clustered by unit are reported in parentheses. ***
indicates significant at the 1% level; ** indicates significant at the 5% level; * indicates significant at the
10% level. Reported R2 is the adjusted R2 for the fixed effects and random effects models and the centered
R2 for the IV/2SLS model.
52
Table VII
Banking Sensitivity Analysis for Values of Production Function Parameters and Input Costs
= 0.2 G=65 = 0.5 Pl=130 Ph=110
* q =0.2 q =0.4 = 0.2 = 0.4 = 0.2 = 0.4 = 0.2 = 0.4 = 0.2 = 0.4
1995 0 0 0 0 0 0 0 0 0 0
1996 1.14 1.19 0.07 0.98 1.04 1.87 1.75 2.34 1.66 2.27
1997 2.44 2.57 0.31 1.9 2.25 3.67 3.6 4.7 3.44 4.59
1998 3.93 4.15 0.84 2.88 3.67 5.62 5.56 7.14 5.33 6.99
1999 5.62 5.9 1.91 4.28 5.3 7.71 7.62 9.65 7.33 9.46
2000 7.5 7.85 3.53 6.04 7.16 9.94 9.78 12.23 9.46 11.99
2001 6.1 6.47 2.13 4.64 5.73 8.8 8.55 11.36 8.19 11.1
2002 4.88 5.28 1.2 3.54 4.5 7.78 7.41 10.56 7.04 10.29
2003 3.84 4.26 0.6 2.72 3.47 6.89 6.37 9.82 5.99 9.52
2004 2.98 3.4 0.22 2.13 2.63 6.11 5.45 9.13 5.05 8.8
2005 2.26 2.68 0.01 1.72 1.95 5.44 4.63 8.5 4.24 8.14
2006 1.7 2.11 0 1.44 1.43 4.86 3.89 7.9 3.52 7.54
2007 1.28 1.65 0 1.23 1.07 4.36 3.26 7.35 2.9 6.99
2008 0.99 1.3 0 1.09 0.82 3.93 2.72 6.84 2.4 6.49
2009 0.78 1.06 0 0.99 0.64 3.56 2.26 6.38 1.97 6.03
2010 0.65 0.89 0 0.91 0.52 3.24 1.89 5.93 1.61 5.61
2011 0.56 0.77 0 0.86 0.44 2.96 1.57 5.52 1.34 5.21
2012 0.5 0.69 0 0.83 0.38 2.72 1.31 5.13 1.12 4.85
2013 0.44 0.63 0 0.8 0.34 2.52 1.12 4.76 0.98 4.49
2014 0.41 0.58 0 0.77 0.31 2.34 0.97 4.39 0.87 4.13
2015 0.38 0.55 0 0.74 0.28 2.17 0.85 3.99 0.77 3.74
2016 0.35 0.52 0 0.69 0.25 2 0.75 3.54 0.68 3.32
2017 0.29 0.46 0 0.61 0.21 1.79 0.65 3.05 0.59 2.86
2018 0.23 0.4 0 0.47 0.15 1.51 0.53 2.51 0.48 2.36
2019 0.11 0.27 0 0.26 0.07 1.08 0.36 1.82 0.33 1.7
2020 0 0.03 0 0 0 0.43 0.1 0.85 0.09 0.78
NOTE: The table shows simulation results for total amount of banked allowances (million tons)
under different parameter values. * corresponds to the base case in which = 0.2 , q = 0.2, G = 55,
53