Allo cating Emissions Permits in Cap-and-trade Programs: Theory and
Evidence
Preliminary. Please do
not cite without p ermission
Comments very welcome
February 2010
Meredith Fowliey
Abst ract
The allo cation of emis sion s p ermits in
ontentiou s p olicy d esign is su e. Re ce
ncy an d distributional imp lic ations of a
ermits in d etail. This p ap er te sts wh e
the s tan dard theory. I de velop a s imp
oretical re lationsh ips b e twee n p e rm
uction de cision s. Data gathe red f rom
us ed to analyze the se relation ship s e
f or explicit e nvironm ental compliance c
emissions ) in their short-ru n s up ply d
resp ondin g to the le ss s alient pro d uc
e rmit allo cation u p dating.
I th an k Step hen Holland , E rin Mans ur, and
iversity of California, Berkeley, th e Un ive rsity of M
elpfu l comme nts an d d is cus sion. I grate fu lly a
th rou gh grant SE S-0922401, the UC En ergy Ins
University of Michigan. Erik John son provide d e x
yDepartment of Agric ultural and Resou rce Econ o
Berkeley CA, 94720. em ail: fowlie@b erkeley.ed u
1 Intro duction
1Billions
of dollars worth of tradable emissions p ermits are allo cated each year to U.S. industrial
pro ducers regulated under emissions "cap-and-trade" programs.In theory, how these p ermits
are allo cated can have signi cant implications for who will b ear the costs and how e¢ ciently the
mandated emissions reductions will b e achieved. Permit allo cation has thus emerged as one of
the more contentious issues in p ermit market design.
Regulatory agencies have b een allo cating tradable emissions p ermits under the auspices
of lo cal, regional, and nationwide cap-and-trade programs for over a decade. Over this time p
erio d, theoretical analyses of the e¢ ciency and distributional implications of p ermit market
design choices have grown increasingly sophisticated. However, we know relatively little ab out
how p ermit allocation design a/ects rm decision-making in real world settings. This pap er brings
evidence to b ear on a rst-order empirical question: are rms resp onding to p ermit allo cation
incentives as standard theory predicts?
Traditionally, p olicy makers have chosen b etween two general approaches to allo cating
emissions p ermits: auctioning and grandfathering. Under an auction regime, emissions p ermits
are sold to the highest bidder. In contrast, "grandfathered" p ermits are freely distributed to
regulated sources based on pre-determined, rm-sp eci c characteristics. In the absence of other
market failures, this choice b etween grandfathering and auctioning should have no b earing on p
ermit market e¢ ciency in the short-run (Montgomery, 1974).
2Many
economists favor auctioning on the grounds that revenues can b e used to o/set
distortionary taxes (Crampton and Kerr, 2002; Goulder et al.,1999). 3However, in practice, p olicy
makers have routinely chosen to forego auction revenues in favor of handing p ermits out for free
to regulated entities.The ability to make concessions to adversely impacted and p olitically p ow1The
value of p e rmits allo cate d to emittin g f ac ilitie s und er the NOx Bud get P rogram and the Acid Rain
Program each year is rough ly $1.4 B and $4.5B, resp ectively. The U.S . Environ mental Prote ction Agenc y (EPA)
has estimated th at th e value of allowan ces allo cated an nu ally un der prop ose d Fe deral climate le gislation
would exce ed $200 b illion (US E PA, 2008) .
2Oth er e ¢ cien cy-re lated argume nts in f avor of auc tioning p e rtain to the mitigation of p re -existin g regu latory
distortions an d distrib ution al con cerns . For examp le, Dinan and Rogers (2002) an d Parry (2004)? emp hasize th
e p otential distribu tion al implic ations of th e allo cation d esign choice, de mons tratin g that high income ind ividu
als are like ly to gain more f rom f re ely allo cate d allowanc es th an are low inc ome ind ividu als,
3A ma jority of p e rmits are distrib uted f ree ly to re gu late d e ntitie s in Sou th ern California s RE CLAIM
program,
1
erful stakeholders via grandfathering has arguably b een as imp ortant a factor in the widespread
adoption of emissions trading programs as the promise of cost minimization and gains from trade.
More recently, a third design alternative has emerged. Under a "contingent allo cation"
regime, up dating rules established ex ante are used to determine how a rm s p ermit allo
cations will b e p erio dically up dated over the course of the trading program. Allo cation up
dating is typically based on a rm s pro duction choices (such as output levels or fuel inputs). The
incentives created by contingent allo cation rules are quite di/erent from those asso ciated with
grandfathering or auctioning b ecause up dating creates an incentive to increase whatever activity
determines future emissions p ermit allo cations.
4In
a theoretical, " rst-b est" setting, it is straightforward to demonstrate that p erio dically up
dating rms future p ermit allo cations based on present pro duction choices will undermine the
e¢ ciency of p ermit market outcomes b ecause the implicit subsidy conferred by allo cation up
dating encourages rms to increase output to economically ine¢ cient levels. (Bohringer and
Lange, 2005; Sterner and Muller, 2008).However, contingent up dating can welfare dominate
more standard p ermit allo cation approaches when there are additional, pre-existing distortions to
contend with. For example, the theory literature has explored how allo cation up dating can b e
used reduce ine¢ ciencies resulting from the exercise of market p ower (Fischer, 2003; Gerbasch
and Requate, 2004; Neuho/, Martinez, and Sato, 2006), tax interaction e/ects (Fischer and Fox,
2007), and emissions leakage (Bernard et al., 2007; Quirion and Demailly, 2006). Allo cation up
dating can also b e used to address p olitical concerns ab out the incidence of a cap-and-trade
programs (Jensen and Rasmussen, 2000).
5Political
supp ort for contingent allo cation up dating is increasing. Industry groups endorse it as
a "common sense way to promote e¢ ciency, fairness, and environmental protection".Policy exp
erts concede that it may o/er the most pragmatic approach to mitigating the adverse e/ects of
environmental regulation on domestic industry comp etitiveness when emissions regulations are
the Eu rop e an Un ion s Emiss ion s Trading Program, th e nation -wide Ac id Rain Program, and the re gion al NOx
Bu dget Trad in g Program.
4Here, " rst-b es t" ref ers to a regulatory environ ment in wh ich th e only market d is tortion or imp e rf ection is th e
environme ntal exte rn ality that the emissions regulation is de signed to internalize.
5"Advantages of Allo cating E missions Credits Based on E ¢ cienc y." Th e Clean E nergy Group . May 15, 2009.
http ://www.thec le an en ergygrou p.com/lsgbrie n gs .as p
2
6incomplete.7Federal
climate legislation passed in June 2009 by the House of Representatives
includes provisions for allo cation up dating as a means of comp ensating trade exp osed emitters
for compliance costs incurred.8In California, legislators are considering allo cation up dating as a
means of mitigating impacts on consumer prices and reducing emissions leakage to unregulated
entities (CPUC-CEC, 2008).
9Can
p ermit allo cation design b e e/ectively used to achieve these kinds of p olicy ob jectives?
This dep ends in large part on whether rms resp ond to p ermit market incentives as standard
theory predicts. In p olicy debates, stakeholders questioned the extent to which the implicit
subsidy conferred by up dating will b e factored into rms "real world" pro duction
decisions.Others contend that these subsidy e/ects will b e mitigated by pre-existing regulatory
and market constraints (NCEP, 2008). Finally, past research has demonstrated that gain-loss
asymmetries, asymmetric pass-through of op erating costs, and heuristic approaches to dealing
with cognitive constraints can all a/ect how rms p ercieve and resp ond to di/erent kinds of pro
duction incentives (see, for example, Duxbury and Summers, 2004; Hirshliefer, 2001 ; Zachmann
and von Hirschhausen, 2008). If these kinds of institutional factors and/or b ehavioral phenomena
a/ect rms environmental compliance decisions, p ermit allo cation rules may not have the
intended e/ect.
This study makes three contributions to b oth the academic literature and the ongoing p olicy
discourse. First, a static analytical mo del is used to illustrate the essential short-run implications
of the p ermit allo cation design. In an e/ort to clarify the terms of the p olicy debate, these
implications are sometimes over-simpli ed to the p oint of misrepresentation. For example, a
recent and in uential rep ort that seeks to "clear up misp erceptions, common among many
stakeholders, ab out how allo cation decisions do and do not a/ect the way an emissions trading
program works in
6Se
e, f or example, th e testimony of Richard Morge ns te rn of Re sources f or the Future. Competitiveness and Cl
imate Pol icy : Avoiding Leakage of Jobs and Emissions : Hearings before the Committee on Energy and Commerce
U.S. House of Representatives. March 18, 2009
7The ju sti cation for contin ge nt u p dating in this c ontext re sts on th e con cern th at rms would dive rt n ew inve
stments and pro d uc tion to manuf acturin g facilities lo c ated in c ountries withou t commen surate regulations .
Continge nt allo cation up datin g, inten de d as a s top -gap me as ure, comp en sates rms for the c omplian ce c
osts incu rred so as to mitigate adverse comp e titive nes s imp ac ts.
8The d esign re commen dation s of b oth the Calif orn ia Pu blic Utilitie s Comm is sion an d th e WCI in clud e th e
minimization of the impacts of carb on re gu lations on cons ume rs and the mitigation of leakage as ob jec tives of
the allo cation pro ces s. In th is context, allo c ation u p dating h as eme rge d as a p olitically palatable option.
9Se e, for example, RGGI, 2004.
3
practice" asserts that [a]lo cation a/ects the distribution of b ene ts and burdens among rms and
industry sectors; it do es not change program results or overall costs (NCEP, 2007)." In fact, this
conventional wisdom do es not hold when future p ermit allo cations are contingent up on current
pro duction choices. The simple mo del presented in this pap er intuitively demonstrates how p
ermit allo cation design can signi cantly a/ect rms short-run pro duction choices (and thus
aggregate so cial costs).
Second, the study provides insight into how di/erent p ermit market incentives are
a/ecting rms short-run pro duction decisions. An emerging literature examines the relationships
b etween p ermit price series and wholesale electricity price series (Bunn and Fezzi, 2007; Fell,
2009; Sijm et al., 2006 ; ). Given the complexity of interactions b etween p ermit markets and
wholesale electricity markets, it has b een di¢ cult to deduce rm-level b ehaviors from wholesale
market price dynamics. This pap er examines rm-level resp onses to changing p ermit market
conditions in unprecedented detail.
1 0Finally,
the pap er o/ers some of the rst empirical evidence of how contingent allo cation up
dating is working in practice. Previous attempts to study the e/ects of contingent p ermit allocation
up dating, and revenue recycling more generally, have b een unable to convincingly separate the
e/ects of the implicit subsidy from the overall e/ect of the environmental regulation.I exploit an
unusual p olicy setting in which the implicit subsidies conferred by a regional emissions trading
program vary systematically across pro ducers and across seasons. Much of this variation is
exogenous- in an econometric sense- to rms short-run pro duction decisions.
The empirical analysis b egins by demonstrating that statistical relationships in the data are
generally consistent with standard theoretical predictions regarding pro ducers resp onse to p
ermit allo cation incentives. I then derive a tractable reduced form mo del of the underlying data
generating pro cess that can b e implemented empirically using a discrete choice framework.
Conditional on
1 0Sterne
r and Is akss on (2006) ? we re the rs t to e mpirically inves tigate th e e/e cts of reve nu e re cyc lin g in
the context of marke t-base d emiss ions regu lation. Th ey an alyze a Swe dish program in which e missions charge
s are refu nd ed to p ollu ting rms in p rop ortion to outp ut. Becau se reb ate s do not vary across rms or acros s
time , the authors c an not sep arate the e/e ct of the tax fro th e e/ect of th e re cycled revenue s. In a more rec ent p
ap er, Sj im et al. (2006) en counter s im ilar d i¢ c ultie s in their analysis of how se qu entially gran df ath ere d p e
rmits in the E U ETS imp ac ts electric ity market outcomes . The lack of clarity s urroun ding how cu rrent p ro du
ction d ecisions will in uen ce fu tu re p ermit allo c ations in the Eu rop e an Un ion s E mis sions Tradin g System
comp lic ates th eir analysis of how th is implic it u p dating h as a/ec ted rm de cision makin g.
4
the assumptions of the mo del, this provides a basis for investigating causal relationships b
etween p ermit allo cation design features and rms short-run pro duction decisions. I provide
evidence to suggest that rms are accounting for the explicit compliance costs (i.e. the costs of
holding p ermits to o/set emissions) in their short-run pro duction decisions. The data also indicate
that pro ducers in allo cation up dating regimes are resp onding to the implicit subsidy. I fail to
reject the hyp othesis that pro ducers are equally attentive to the p ollution disincentive and pro
duction incentives conferred by allo cation up dating.
The pap er pro ceeds as follows. Section 2 develops a simple theoretical mo del that is used
to intuitively demonstrate the rst order implications of alternative p ermit allo cation designs.
Section 3 intro duces the NOx Budget Program. Section 4 discusses the data collected from this
program. Section 5 discusses the underlying data generating pro cess and lays out an empirical
strategy. Section 6 summarize the estimation results. Section 7 concludes.
2 Allo cating emissions p ermits: Theory
The analytical framework intro duced in this section serves two purp oses. The mo del is rst used
to demonstrate the most essential partial equilibrium implications of the p ermit allo cation design
choice and then to motivate the empirical analysis. The mo del is intentionally simple. Many of the
institutional details and market imp erfections captured by mo dels found elsewhere in the
literature (such as pre-existing tax distortions, the exercise of market p ower, or incomplete
regulation) have b een stripp ed away. Eliminating some of the complexities of real p olicy
settings helps to highlight the most basic trade-o/s b etween static pro duction e¢ ciency, static
allo cative e¢ ciency, and distributional concerns.
The analysis will fo cus on short-run relationships exclusively. To the extent that allo cation
up dating is seen as a way to smo oth the transition to auctioning regimes, these short-run
relationships will b e very imp ortant. Also, a clear characterization of short-run interactions is an
essential rst step towards understanding longer-run outcomes and implications.
5
2.1 A static partial equilibrium framework
Pro duction of a homogeneous go o d generates harmful p ollution. Industry pro duction in time t
is denoted Qt. Let qitdenote the quantity pro duced by rm i in time t. Pro ducers are characterized
by increasing marginal cost technologies; Ci(qi) and cdenotes the unit-sp eci c total cost function
and marginal cost, resp ectively. E¢ cient factor markets are assumed. Marginal op erating costs
thus re ect the true opp ortunity cost of allo cating inputs to pro duction in this industry. Emissions
rates eiiqitare constant p er unit of output. Demand is characterized by an a¢ ne inverse demand
function Pt= a bQt. To keep the mo del transparent and tractable, only two price taking rms are
represented. A
more general mo del with N > 2 is easily formulated but more di¢ cult to intuitively interpret. The
two rms are indexed c (denoting the relatively "clean" pro ducer) and d (denoting the relatively
"dirty" pro ducer). For the purp ose of this example, I assume emissions rates are negatively
correlated with op erating costs: ; ec< ed, cc> cd1 1:
Industry emissions are regulated under a cap-and-trade program; aggregate emissions in p
erio d t cannot exceed an exogenously determined cap E: The time path of p ermitted emissions
(i.e. E1; E2t; :::) is set by the regulator ex ante. To comply with the program, rms must o/set
uncontrolled emissions with p ermits. These p ermits are tradable in an emissions p ermit market.
There are no spatial or temp oral restrictions on p ermit trading. I assume that rms acts as price
takers in b oth the p ermit and pro duct markets.
This short-run analysis conditions on existing pro duction technology and op erating
characteristics; emissions rates and op erating costs are exogenously determined and xed.
Emissions reductions can thus b e achieved in two ways: through increasing the share of the
market served by the relatively clean pro ducer or reducing the quantity consumed.
In existing and planned cap-and-trade programs, p ermits are allo cated via auctioning,
grandfathering, symmetric "output-based" up dating, or asymmetric up dating. Stylized
representations of all four approaches are considered b elow.
1 1This
assu mption n ds emp irical sup p ort in the e missions market I cons id er he re. Un it-leve l f ue l op erating
c osts and NOx emiss ion s rates are n egatively corre lated in the data analyz ed in the sub seque nt s ection.
However, the re are ce rtainly examples of low-e mitting f acilities with re latively low op erating costs, and high-e
mitting f acilities with relatively high op e rating cos ts .
6
2.2 The b enchmark case
Outcomes under alternative allo cation rules will b e compared against a " rst b est" b enchmark
that maximizes total economic surplus S (Q) sub ject to technology op erating constraints and
the constraint that aggregate emissions do not exceed the exogenously set cap:
: S (Qt) = Z P (Qt)dQt Cc(qct) Cd(qdt) (1)
Qt
0
max
qct;qdt
s:t: ecqct +
edqdt
qc + qdt = Qt:
= Et
t
Note that the welfare measure S (Qt) re ects the utility asso ciated with total consumption less pro
duction costs but do es not capture the b ene ts asso ciated with emissions reductions. Because
aggregate emissions are held constant at E across all scenarios, changes in S (Q t) across
scenarios will re ect changes in absolute welfare vis a vis this b enchmark.
The rst order conditions for this maximization problem imply:
P (Q t)
tei = 0; i = c; d: (2)
ciq it
P cdP is the shadow value of the emissions constraint at time t.
ccqq d cmaximize economic surplus sub ject to the constraint.
where t
Rearranging these rst order conditions (and omitting
clarity) yields:
= edec: (3)
edFigure
1 helps to illustrate this result. The downward sloping line, representing the emissions
constraint, connects all allo cations of pro duction across the two rms that exactly satisfy the
emissions cap. The slop e of this line isec: The economic surplus function S (Q) is also pro jected
into this space. The level sets of the surplus function app ear as concentric iso-surplus curves.
The slop e of an iso-surplus curve measures the rate at which pro duction at the clean rm can b
e substituted for pro duction at the dirty rm while holding total economic surplus constant. The
7
so cially optimal allo cation of pro duction o ccurs at the p oint where the emissions constraint is
just tangent to an iso-surplus curve. All other p oints that exactly satisfy the emissions constraint
are asso ciated with lower levels of economic surplus.
Two e¢ ciency prop erties of this equilibrium are worth highlighting: Property 1 : Marginal
abatement costs (measured in terms of foregone pro ts p er unit of emissions reduction) are set
equal across pro ducers:
P
=P
: (4)
ceddq d ceccq c
This assures that abatement activities have b een e¢ ciently allo cated among pro ducers. Given
pro duction level Q , the cost of meeting the emissions constraint E is minimized.
Property 2 : Emissions abatement activities are allo cated e¢ ciently across the supply and
demandside of the pro duct market:
@ S @ccq c cd : (5)
E=
ed
ecq d
Intuitively, the derivative of the welfare function with resp ect to the emissions constraint
captures the marginal cost of reducing emissions via conservation measures on the demand side
(i.e. through a reduction in consumption). The marginal abatement cost on the supply side is the
cost of reallo cating pro duction from the low cost, high emitting pro ducer to the high cost, low
emitting pro ducer so as to incrementally reduce emissions. Equation [5] implies that an optimal
balance is struck b etween the two short-run abatement options. This result is derived in App
endix 1.
Returning to Figure 1, the broken line connects all p oints asso ciated with an aggregate
production level Q : Pro duction allo cations on the emissions constraint lying strictly ab ove (b
elow) the optimal outcome are asso ciated with more (less) consumption than is consistent with
compliance constrained economic surplus maximization, thus requiring higher (lower) levels of
supply-side abatement to achieve compliance.
2.3 Grandfathering and auctioning regimes
8
I now consider a p erfectly comp etitive industry sub ject to a market-based emissions
cap-and-trade program. Let Aitrepresent the rm s p ermit allo cation in p erio d t. Under
grandfathering, the numb er of p ermits the rm receives (free of charge) from the regulator each
p erio d is determined at the outset of the program. Under auctioning, A it= 0 8 i: Under either
scenario, rms future p ermit allo cations are indep endent of their pro duction decisions going
forward.
Let trepresent the p ermit price (an endogenously determined parameter). The rm s
compliance costs (i.e. the cost of holding p ermits to o/set uncontrolled emissions) are t(Ait
eiqit): The pro t maximization problem faced by price taking rm i in time p erio d t is thus:
max : it = Ptqit C (qit) + t(Ait eiqit); i = c; d: (6)
Assuming price-taking b ehavior in b oth the p ermit and pro duct markets, the rst order
conditions for this pro t maximization problem are given by [2]. Thus, the e¢ ciency prop erties [4]
and [5] are satis ed under b oth grandfathering and auctioning.
2.4 Output-based up dating
Under a contingent up dating regime, the total quantity of emissions p ermits to b e allo cated in
each p erio d, and the rules sp ecifying how rms pro duction decisions will determine future p
ermit allo cations, are determined at the outset of the program. An output-based up dating
regime de nes a rm s p ermit allo cation in p erio d t as a function of the rms pro duction
decisions in the preceding p erio d or p erio ds. I consider the simplest of output-based allo
cation rules: a rm s p ermit allo cation in p erio d t + 1 is determined by its market share in p
erio d t:
Ait+1 =
qit stqit: (7)
Et+1Qt
The size of the subsidy conferred by output-based up dating will dep end on the total numb
er of p ermits allo cated in the future p erio d E, how the rm discounts future revenue
streams i(t), the future p ermit price t+1t+1, and total industry pro duction Qt: Contingent-up dating
adds
9
an additional argument to the rm s pro t function.:
max : it = Pitqit C (qit)
teiqit + i(1)
t+1stqit: (8)
Some additional assumptions further simplify the
analysis. Unrestricted banking and b orrowing of p
ermits, rational exp ectations, and zero arbitrage
together imply that p ermit prices are constant in
present value terms. If all rms discount future p erio
d gains at the market rate and take total sector
output Qas given, the implicit subsidy p er unit of pro
duction in p erio d t simpli es to st1 2.tOmitting t
subscripts for simplicity, the rst order conditions for
pro t maximization under output-based up dating are:
0P (Q)
(ei s ) = 0; i = c; d (9)
ciq0 i
The subscript denotes equilibrium outcomes under
non-contingent p ermit up dating. Rearranging [9]
yields:
ed s ec s
P cdP =
ccqq0 d0 c :
This
equilibrium outcome { q0 c, q0
d
13
12
t tAt+1qt
Q2 t
tim e t + 1 p er s hare of ou tput Qt
13
10
g lies strictly ab
ove the optimal outcome on the emissions constraint
line and is asso ciated with a level of total economic
surplus that is strictly less than S (Q) (see gure 1):
Intuitively, the implicit pro duction subsidy increases
each rm s willingness to supply vis a vis
grandfathering or auctioning. At higher levels of pro
duction, more supply-side abatement is required to
comply with the emissions cap. Consequently, the
market share of the relatively clean pro ducer
increases relative to the rst b est b enchmark.
App endix 2 demonstrates that the equilibrium p
ermit price will b e unambiguously higher than ,
re ecting higher supply-side marginal abatement costs.
Consumption levels exceed that asso ciated with
optimal compliance, so there is a transfer of surplus
from pro ducers to consumers vis a vis grandfathering.
Alte rn atively, rms could take into accou nt how the ir own p
ro du ction dec is ion s a/ec t aggre gate pro d uction levels (an d
thus th e s iz e of the imp licit s ubs id y). Th is would re duc e th e
p e rce ive d p ro du ction su bsid y by: Intu itively, if the rm in
crementally in crease s pro duc tion in time t , it d ecrease s the
nu mb er of p e rmits allo cated in
, alth ough it is n ow entitled to
an ad dition al s hare .
Making s imilar distribu tion al comparis ons with auc tionin g is
c om plic ate d by the f ac t that con sum er and pro-
2.5 Asymmetric contingent allo cation
In practice, the implicit pro duction subsidy intro duced by contingent up dating is often
asymmetric. For p olitical and practical reasons, the s parameter often varies across units
based on technology typ e, fuel e¢ ciency, or other observable op erating characteristics. To
accommo date asymmetric up dating, the rm s ob jective function is mo di ed slightly to allow
the implicit pro duction subsidy to vary across rms. Omitting the t subscripts for simplicity,
the rst order conditions for pro t maximization are:
00P (Q)
(ei + si) = 0; i = c; d (10)
ciq00 i
I assume that the up dating parameters are de ned such that the total numb er of p ermits allo
cated through up dating do es not exceed the total cap. This implies that the average up dating
parameter cannot exceed the average emissions rate. In this asymmetric case, the equilibrium
p ermit price is no longer equal to the economic cost of redispatching pro duction activity in
order to incrementally reduce emissions. If the implicit pro duction subsidy favors the relatively
dirty (clean) rm, the p ermit price must rise ab ove (fall b elow) the true marginal abatement
cost in order to counteract this asymmetry in compliance incentives. The equilibrium p ermit
price is:
= cedcq
qd
cd + (sc
) : (11)
ecc
sd
0
0
The e¢ ciency and distributional implications of asymmetric up dating vis a vis rst b est will
dep end on the ratio of the up dating parameters scand sdsd. If the implicit subsidy p er unit of p
ollution is exactly equal across rms (i.e. implying thatsc=edec), the rst b est quantities and pro duct
price are achieved (see App endix 3). If the subsidy p er unit of emissions is larger for the
relatively clean rm (as is the case with output based up dating), the outcome will o ccur at a p
oint on the emissions constraint ab ove the optimal outcome. This would result in to o little
conservation on the demand side and to o much abatement on the supply side. Conversely, if the
subsidy p er unit of emissions is larger for the more p olluting rm, consumer prices will increase
and consumption levels will fall relative to rst b est. A larger share of the mandated emissions
du cer s urplus und er auc tioning will de p end on how au ction re venues are allo cated.
11
reductions will b e achieved on the demand-side.
2.6 Motivating the empirical exercise
sConditional
on the assumptions outlined ab ove, contingent allo cation up dating will distort
outcomes away from the e¢ cient short-run equilibrium in a rst b est setting (except in the very sp
ecial case wheresij=eeij; 8 i 6 =; j ). Abatement e/orts will b e ine¢ ciently allo cated across
producers and consumers, and across rms with di/erent pro duction technologies and cost
structures. General equilibrium mo dels calibrated to sp eci c p olicy contexts have b een used to
quantitatively estimate the p otential magnitude of these distortions. In several instances, ine¢
ciencies induced by allo cation up dating have b een found to b e economically signi cant
(Burtraw et al. (2005), Jensen and Rasmussen (2000), Neuho/ et al. (2005)). Much of the theory
literature is devoted to extending this kind of analytical exercise to more complicated, second-b
est settings. In cases where the implicit subsidy can b e used to mitigate one or more pre-existing
distortions or imp erfections (such as the exercise of market p ower in the pro duct market, or
incomplete emissions regulation) contingent allo cation up dating may welfare dominate
grandfathering and auctioning.
This entire literature is predicated on the assumption that compliance cost minimizing rms in
cap-and-trade programs accurately account for all p ermit market incentives in their supply
decisions However, there are several reasons why this assumption might not hold in practice.
First, the b ehavioral nance literature o/ers evidence to suggest that rms may fo cus on
information that is more readily accessible and easy to understand at the exp ense of information
that is more opaque or that requires more resources to pro cess (Hirshleifer, 2001; Sarin and
Web er, 1993). It is arguably much easier for plant managers to translate p ermit prices into
compliance costs p er unit of pro duction, versus the exp ected future subsidy p er unit of current
pro duction. Particularly when allo cation up dating rules are convoluted or confusing.
Second, researchers have found evidence of gain loss asymmetry (whereby agents place
more emphasis on minimizing losses versus maximizing gains) in private sector decision-making
(Fiegenbaum, 1990). A recent study do cuments asymmetric cost transmission in p ermit
markets, whereby
12
rms pass op erating cost increases through to customers at a di/erent rate than they pass any
cost reductions (Zachmann and von Hirschhausen, 2008). To the extent that these b ehavioral
elements a/ect rms environmental compliance decisions, managers may discount- or ignorethe implicit pro duction subsidy.
Finally, if there is any uncertainty regarding how the cap-and-trade regulation will b e
implemented or mo di ed in the future, managers may discount the implicit pro duction subsidy to
re ect this regulatory risk.
In sum, whereas it is standard to assume that the explicit compliance cost and implicit pro
duction subsidy are weighted equally in rms pro duction decisions, this may not b e the case in
practice. The obligation to hold p ermits to o/set uncontrolled emissions may a/ect short-run
compliance decisions di/erently than the implicit subsidy conferred by p ermit allo cation up
dating. If rms discount- or ignore- the implicit subsidy conferred by contingent allo cation up
dating, p ermit allo cation incentives will not have the intended e/ects on market outcomes.
3 Empirical application: The NOx Budget Program
The data in this study come from a ma jor U.S. emissions trading program: The NOx Budget
Program. In 1998, the U.S. Environmental Protection Agency (EPA) determined that 23 eastern
states were contributing signi cantly to ozone non-attainment problems. These states were issued
"NOx budgets" and required to design and implement regulations that would reduce seasonal
NOx emissions to budget levels. Although states had exibility in cho osing their compliance
strategies, they were invited to meet their compliance obligations by joining an EPA-administered
cap-and-trade program. All states accepted the invitation.
1 4States
in the NOx Budget Program (NBP) were required to accept program design features
outlined in a mo del rule that was issued by the EPA. These features include p ermit trading proto
cols and emissions rep orting standards. For instance, throughout the program, a NOx p ermit
authorizes the holder to emit one ton of NOx during "ozone season" (i.e. May to Septemb er).
1 4Compliance
is on ly re qu ired in th e sp ring and su mmer wh en ave rage temp eratu res rise an d NOx emiss ion
s contribu te to smog f ormation .
13
1 5At
the end of each season, all regulated source must hold su¢ cient p ermits to o/set ozone
season emissions.There are no spatial trading restrictions in the NBP; p ermits are freely traded
among all participating sources in all participating states.
1 6The
mo del rule also required standardization of intertemp oral trading restrictions across
participating states. Emitters cannot b orrow against future allo cations. Emissions in year t must
b e o/set using p ermits of vintage t or earlier. Permits can b e banked, although the use of
banked p ermits is sub ject to a "progressive ow control" (PFC) constraint designed to
discourage the excessive use of banked p ermits in a particular year.
3.1 Permit allo cation in the NBP
1 7In
the pro cess of designing the NBP mo del rule, the US EPA commissioned an ex ante
analysis of p ermit allo cation design alternatives. A detailed numerical simulation mo del of the
electricity sector was used to evaluate various allo cation regimes, including grandfathering,
output-based allo cation up dating, and fuel input-based allo cation up dating (US EPA, 1999).
Simulation results indicated that the p ermit allo cation design choice would appreciably a/ect
market outcomes. Consumer electricity prices were pro jected to b e 3.4 p ercent lower in an allo
cation up dating regime as compared to grandfathering. This amounts to a transfer from pro
ducers to consumers of $1.25 billion. The study also indicated that emissions leakage to neighb
oring, unregulated states would b e reduced under allo cation up dating; simulated electricity pro
duction in regulated jurisdictions was 10 p ercent higher under up dating as compared to
grandfathering. With fewer emissions reductions coming from demand-side
conservation/substitution and/or substitution of imp orts for domestic pro duction, more of the
mandated emissions reductions had to come from regulated
1 5If
a facility s emiss ion s excee d its p erm it allo cation , th e facility mu st p urch ase add itional NOx p e rmits in
the p ermit marke t. Complian ce h as b ee n ne arly p erfec t ove r the duration of the p rogram; the f ew c as es of
noncomp lianc e h ave b e en attrib uted to accounting errors.
1 6By law, if th e nu mb e r of p ermits in th e re gion- wid e bank prior to ozone s eason exce eds 10 p erce nt of the
total (i.e . p rogram -wide) cap for that s eason, a non -lin ear disc ou nt factor is ap plied. Th e P FC ratio is comp
uted as 10 p e rce nt of th e season al cap divid ed by the size of the ban k. This ratio d e n es the f raction of b anked
p e rmits th at can b e us ed to o/set a ton of p ermits that se ason. Th e remaining p ermits can b e use d to o/s et
only a h alf ton.The disc ount factor is ap plie d at the f ac ility level. For example, if a single rm hold s 100 p erm its
and th e ratio in year t is d e n ed to b e 0.5, that rm can us e 50 b an ked p ermits to o/set e missions in year t on a
on e f or on e b asis.
1 7Bec ause ove r 90 p e rc ent of emis sion s re gulate d un der th is p rogram c om e from e le ctricity p ro du cers,
EPA analys is fo cu sed exclus ively on the electric ity s ector. This an alysis ac counted f or b oth short and long-run
re sp on ses to p ermit allo cation ince ntives.
14
pro ducers. Supply-side abatement costs were pro jected to b e 18 p ercent higher under up
dating versus grandfathering, largely due to an increased share of electricity supply provided by
relatively clean- and relatively more costly- natural gas units.
1 8Whereas
many imp ortant program design features were de ned at the federal level, states
were ultimately given broad exibility with regards to p ermit allo cation design. The EPA
recommended allo cation up dating based on heat inputs, but states were free to deviate from this
recommendation.Several states chose to pursue alternative approaches; p ermit allo cation rules
vary signi cantly in terms of overall regime choice (i.e. grandfathering, or contingent up dating),
the frequency of allo cations, and the basis for distributing the allowances.
4 Data
1 9I
use data from the rst four years of the NOx Budget Program (i.e. 2003-2006) and fo cus
exclusively on electricity pro ducers serving restructured wholesale electricity markets in the
eastern United States (i.e. the New York, New England , and Mid-Atlantic or "PJM" markets).Data
sources and details are provided in App endix 4.
State-level permit al location regimes Table 1 rep orts state-level NOx budgets (which were
pre-determined and do not change over the study p erio d) and information regarding state-sp
eci c p ermit allo cation design choices. Whereas smaller states chose grandfathering (due in part
to the management resources required to administer a more complex p ermit allo cation up dating
pro cess), a ma jority of states chose some form of contingent allo cation up dating based on
either output or fuel inputs.
1 8Fu
el-bas ed u p dating was ch osen over outpu t-base d u p dating primarily b ecau se, h is torically, emiss ions
regulation s h ad b e en de ne d in te rms of m as s e mis sions p er un it of he at in put.
1 9Elec tricity gen erating fac ilitie s (E GUs) comp rise 87 p erce nt of the e mis sions s ou rc es and over 90 p ercent
of the NOx em is sion s regulate d un der the NBP (EPA, 2007). E GUs re gulate d un der the NBP op e rate in a
variety if elec tricity marke ts . W he re as u nits in the samp le s upp ly res tru ctured wholesale electric ity markets,
oth er f ac ilitie s in the p rogram are rate-regulated p ro du cers se rving vertically inte grated, econ omic ally regu
lated electric ity marke ts , while oth er un its are own ed and op erated by p ub lic entities and op erate on a n on-p
ro t basis. Pro duc tion at rate -re gulate d plants an d pu blic entities are more c entrally co ord in ate d and in ue
nce d by an array of ec on omic, regulatory, an d in stitu tion al fac tors. I cho ose to fo cus on restructu re d electric
ity markets b e caus e EGUs in th ese marke ts are more like ly to h ave sh ort-run ob jec tives con sistent with pro t
maximization.
15
Unit-level operations and attributes
2 0Table
2 summarizes some imp ortant unit-level op erating characteristics by p ermit allo cation
regime. Two op erating attributes that are particularly relevant to this analysis are the NOx
emissions rate (i.e. p ounds of NOx emitted p er MWh electricity pro duced) and heat rate (i.e.
btus of fuel burned p er kWh of electricity pro duced).It is fairly standard in the empirical literature
to treat these unit-sp eci c p erformance parameters as immutable features of the pro duction
technology. However, emissions rates and heat rates can b e a/ected by op erating decisions
made by the plant manager, including the choice of fuel characteristics, utilization rates, and
combustion tuning. Purely exogenous factors (such as ambient temp erature) can also play a
role.
2 1To
construct unit-sp eci c summary measures of these op erating characteristics, separate
seasonal regression equations are estimated for each unit. This estimation exercise, describ ed in
more detail in App endix 5, obtains unit-sp eci c, season-sp eci c p oint estimates of emission
rates and heat rates under average op erating conditions.Capacity-weighted summaries of these
estimates are presented in Table 2. The supp ort of the distributions overlap considerably across
allo cation regimes, which facilitates an empirical comparison of short-run pro duction decisions
made by similar units facing di/erent p ermit allo cation incentives.
Emissions permit prices NOx p ermits are actively traded in a liquid p ermit market.2 22 3Brokers
facilitate the ma jority of arms length transactions, administer escrow accounts, and provide
market analysis. A variety of transaction structures exist in the market, including forward
settlements, calls, puts, comp osite structures such as straddles, and vintage swaps. Table 3 rep
orts average sp ot NOx p ermit prices by vintage (in nominal dollars p er ton). NOx p ermit prices
are falling over the sample p erio d, largely due to abatement costs that proved to b e lower than
anticipated, and lower than exp ected temp eratures in the early years of the program.This table
also helps to illustrate the e/ect of
2 0A
u nit s h eat rate me as ures the e¢ c ie nc y with wh ich the un it trans forms fue l into electric ity. The lower th e
he at rate, the more fu el e¢ c ie nt th e gen erator.
2 1Sp eci c ations that allow rates to vary acros s years are also e stimate d.
2 2In 2007, th e volume of "ec onomically signi cant" immed iate settlement trade s (i.e. trade s b e twee n versu s
within rms ) re ache d 247,000 tons (EPA 2008).
2 3Evolution M arkets LLC p rovide s inf ormative month ly an alyses of th e NOx B udge t Program p e rmit marke
t.
16
2 4the
progressive ow control (PFC) constraint on p ermit prices. As early as 2003, p ermit market
participants correctly anticipated that the PFC constraint would start to bind in 2005. This explains
the large vintage 2004/2005 spread in 2003 and 2004..
Compliance costs and production incentives
2 5To
estimate the cost of purchasing p ermits to o/set the emissions asso ciated with generating a
MWh of electricity, each unit s NOx emissions rate is multiplied by the NOx p ermit price. Table 4
summarizes these unit-level cost estimates. On average, explicit compliance costs amount to a 7
p ercent increase in total variable (i.e. fuel, op erating and maintenance) costs.However, among
units with particularly high emissions rates, this increase can exceed 40 p ercent.
Estimating the implicit pro duction subsidies conferred by contingent up dating is more
complicated. The size of the pro duction subsidy varies with state p ermit allo cation rules, statesp
eci c NOx budgets, annual pro duction levels, and unit-level heat rates (in input-based up dating
regimes). Individual states allo cate their resp ective NOx "budgets" (listed in Table 3) using
formulas of varying complexity.
For each unit, an estimate of the numb er of future p ermits earned p er unit of current pro
duction is constructed using the corresp onding state budget Es, average ozone season pro
duction (or heat input) aggregated across NBP sources in the state, and the sp eci c details of
states p ermit allo cation up dating proto cols. For example, if NOx p ermits in state s are allo
cated based on the average heat input in the preceding L years, the e/ect of an incremental
increase in current pro duction at rm i in year t on future p ermit entitlements is assumed to b e
hi measures the fuel inputs required to generate a unit of output at unit i , and HstEHss t ;where
himeasures the total quantity of fuel inputs used by NBP sources in state s over the course of the
ozone season in year t. An imp ortant-and plausible- assumption is that rms take the size of the
p er-MWh
2 4In
years when th e PFC cons traint bind s, ban ke d p ermits trade at a con siderable disc ount. The PFC ratio was
0.25 an d 0.27 in 2005 an d 2006, resp ectively. In b oth ye ars, p ermits we re use d to o/se t e missions at a d is
counted rate (4,168 and 1,950 p e rmits in 2005 and 2006, re sp e ctive ly). In M arch of 2005, th e EPA re le as ed its
new Clean Air Interstate Rule (CAIR), inten ded to su bsu me th e NBP in 2009. CAIR e liminated progres sive ow
control.
2 5Unit-sp e ci c e stim ate s of variable f ue l op eratin g c osts are ob tain ed by multip lying the u nit-le vel heat rate
(se e ab ove) by the corres p ond in g fu el p rice. E stimate s of un it- le ve l variable, non -fu el op eratin g and
mainten ance costs (not inc lu ding e nvironme ntal comp lianc e cos ts ) are obtain ed from Platts .
17
2 6subsidy
as given.Column 3 of Table 4 summarizes these estimated subsidies, in terms of future
p ermits allo cated, p er MWh of electricity generated.
In present value dollar terms, the estimated implicit subsidy conferred under this input-based up
dating regime is:
= Ll =1X i(l ) Ll hitHEt s ; (12)
28
sit
where
l
27
26
st
27
i(l
)l
28
is the exp ected p ermit price in l years and
(l ) is the discount rate applied to b ene ts
accruing l years in the future.In the nal column of Table 4, net compliance costs (i.e. explicit
compliance costs less the implicit subsidy p er MWh) are summarized.These incentives vary
signi cantly across facilities. Notably, for several units in allo cation up dating regimes with
relatively low emissions rates, the estimated implicit subsidy exceeds the estimated explicit
compliance cost such that the net e/ect of the NBP on variable op erating costs is negative.
5 Empirical framework
The unique design of the NBP provides several p otentially useful sources of variation. First, the
delegation of p ermit design to state-level agencies has yielded signi cant interstate variation in p
ermit allo cation rules and related incentives. From a research design standp oint, p ermit allo
cation design features would ideally have b een randomized across electricity pro ducers.
Although states choice of p ermit allo cation regime was not random, interstate variation in p
ermit allo cation design is arguably exogenous, in an econometric sense, to rms short-run pro
duction decisions. State level p ermit allo cation design decisions were determined by a variety of
factors, including the institutional capacities of the implementing agency and the preferences of p
olitically p owerful
A rm with a d omin ant marke t p os ition wou ld want to accou nt for the f act th at inc re asing its fue l c onsu
mption wou ld inc re ase Hand thus d ecrease th e size of the s ubs id y it rec eived for all of its p ro du ction . Thus
we would exp ec t the p erceived sub sidy wou ld b e dec re asing in m arket sh are .
To c onstruct an es timate of the se implicit s ub sidies, th e fu tu re s pric e of p e rmits issu ed l years in th e fu
ture is us ed to es timate : In c ases wh ere p ermits did n ot trad e far en ou gh into the f uture, the market price f or
the p e rmit vintage farthes t in the fu tu re was ap plied to all su bse qu ent vintage s..
Rather th an as sume an arb itrary discou nt rate, th ese c alc ulations p res ent un disc ou nte d estimate s of th
e imp licit pro duc tion s ubs id y. Plant man age rs p re sum ab ly disc ount the valu e of fu ture p ermit allo cations,
so thes e es timates sh ould b e inte rpreted as ge nerous .
18
constituents. Conditional on pre-determined industry and pro duction technology characteristics,
the factors that shap ed a state s choice of allo cation regime should not directly impact unit-level
short-run pro duction decisions.
Second, the seasonal nature of the program s compliance requirements generates useful
intertemp oral variation. There is considerable overlap in the distribution of hourly load levels, and
other observable market conditions across ozone season and o/-season (see Table 5). This
makes it p ossible to observe unit-level pro duction decisions in hours that di/er in terms of ozone
compliance requirements, but are otherwise similar.
Third, a subset of NOx emitting pro ducers supplying the New England electricity market are
exempt from the NBP for meteorological reasons. Most counties in Maine, Vermont, and New
Hampshire were already in compliance with the ozone standard. Prevailing wind and weather
patterns ensure that emissions from p oint sources in these states do not contribute signi cantly to
U.S. non-attainment problems. The distributions of op erating characteristics that determine
shortrun pro duction decisions in the exempt and NBP regulated sub-p opulations overlap
considerably (see Table 2), making these exempt units a p otentially useful control group.
2 9Finally,
a ma jority of states chose to adopt the EPA s recommended p ermit allo cation
approach: heat input based up dating. Under this regime, the pro duction subsidy varies
signi cantly with fuel e¢ ciency. Input-based up dating thus generates interfacility, intra-market
variation in pro duction incentives that is indep endent of variation in explicit compliance costs p
er unit of pro duction.
5.1 Mo deling the data generating pro cess
The mo del develop ed in section 2 serves as a go o d starting p oint for a mo del of the data
generating pro cess. However, a preliminary lo ok at observed hourly electricity pro duction
decisions suggests that some mo di cations are needed. First, physical capacity constraints
routinely bind at the unit-level in the short-run. Interior solutions are no longer assumed. Second,
the vast ma jority of variation in hourly heat rates o ccurs across (versus within) units (see App
endix 5). I therefore
2 9The
corre lation co e¢ c ie nt b etwe en u nit-level f uel e ¢ cienc y measu re s and NOx e mis sions
rates.is 0.69.
19
assume constant unit-level marginal costs. Once these two mo di cations are made, the mo del
closely resembles mo dels used to simulate wholesale electricity market outcomes in comp etitive b enchmark analysis (see, for example,
Borenstein, Bushnell, and Wolak, 2002 and Wolfram, 1999) and environmental p olicy simulations
(examples include US EPA, 1999 and Burtraw, Palmer and Kahn, 2005). This mo del predicts
that pro t maximizing electricity pro ducers follow an on-o/ strategy, pro ducing at full capacity
whenever price exceeds a reservation price set equal to the unit s marginal op erating cost. In
theory, the intro duction of the NBP increases this reservation price by an amount equal to the
unit-sp eci c net compliance cost p er MWh.
3 0Are
observed pro duction decisions consistent with this prediction? Figure 2 is generated using
a small subset of the data collected from a representative unit over a short (three day) p erio d in
the ozone o/-season.3 1The left panel plots capacity utilization and hourly wholesale electricity
prices over these 96 hours. The horizontal line represents the estimated marginal o/-season op
erating cost of $49/MWh sp eci c to this unit and time p erio d (i.e. the reservation price). The right
panel plots capacity factor as a function of the wholesale electricity price less variable op erating
costs. The thick black step function plots the relationship predicted by the mo del. The thin S-shap
ed curve is a lo cal p olynomial smo oth of the observed data. Note that observed hourly pro
duction decisions at this unit deviate systematically from the predictions of the simple, static mo
del.
3 2Figure
3 conducts a similar exercise using the complete data set. The vertical axis measures
capacity factor. The horizontal axis measures price less variable op erating costs (not including
NBP compliance costs). The solid line in each panel plots the lo cal mean smo oth of hourly,
unitlevel capacity utilization rates on hourly, unit-sp eci c price-cost margins in the ozone
o/-season.
These functions are generated separately for grandfathering and contingent up dating regimes,
3 0I
chos e a p erio d in the ozone o/-s eason in which the wh ole sale e le ctricity p rice was vasc illating aroun d this
un it s the oretical res ervation price (i.e . the pre vailing fu el pric e multiplie d by the u nit s f uel e¢ c ie ncy rating
plus variable , n on-f ue l op erating c os ts).
3 1The se su pply d ecisions are obse rved in the ozon e o/-seas on. The ave rage ne t comp lianc e cost in curre d by
this un it du ring ozone s eason is es timated to b e $3.16. Th e thick re d line illustrate s how the intro d uc tion of the
emiss ion s trading p rogram shou ld , in theory, a/ec t the unit s h ou rly pro duc tion dec is ion s.
3 2To ge nerate thes e gu res , I us e an E pane ch nikov we ight fu nction and a rule- of -thumb band wid th es
timator. The smo oth is evaluated at 50 p oints. Pric e cos t margin s are calculated by su btracting a un it s f ue l c os
ts and non -fu el variab le op erating costs p er MW h f rom th e h ou rly real- time wholesale electric ity p rice.
20
resp ectively. The broken lines plot the same relationships using data from ozone season (i.e.
May to Septemb er) when units are required to hold p ermits to o/set their NOx emissions.
On average, we should exp ect that the ozone-season supply functions will lie to the right of
their o/-season counterparts. Because the average net e/ect of the NBP on variable op erating
costs is substantially higher among units op erating in grandfathering regimes (see table 4), we
exp ect that the NBP-induced shift in the supply curve will b e larger in the right panel. The data
app ear to b e consistent with the rst prediction, less so with the second.
These gures suggest that the simple, static mo del p o orly approximates the underlying
data generating pro cess. On average, plant managers are willing to op erate in hours when
prices fall b elow marginal op erating costs, and are slow to resp ond when the prices rise ab ove
cost. Much of this b ehavior can b e attributed to technological and system op erating constraints
that are omitted from this static mo del. At the unit level, ramping limits, start up costs, minimum
run times, and other intertemp oral op erating constraints can signi cantly a/ect how a plant resp
onds to changing market conditions. At the system-level, transmission constraints,
system-security requirements, and other op erating proto cols can a/ect which units get called up
on to run in a given hour. Intertemp oral op erating constraints
The true data generating pro cess involves a complex, multi-p erio d optimization problem.
This so-called "unit commitment" problem (i.e. the dynamic scheduling of electricity pro duction
over hours in a day.) has b een extensively analyzed in the op erations research and p ower
systems literature. The problem is di¢ cult to solve b ecause of its large dimension, non-linearity,
and large numb er of constraints (Sheble and Fahd 1990). One formulation of the unit
commitment problem, intro duced in App endix 5, helps to convey the complexity of the dynamic
optimization faced by plant managers and system op erators each day.
Previous work has demonstrated the p erils of ignoring unit commitment idiosyncrasy when
simulating short-run wholesale electricity market outcomes in the context of comp etitive b
enchmark analyses (Harvey and Hogan, 2002(Harvey & Hogan 2002); Mansur, 2008). Ignoring
unit commitment constraints will also b e problematic in this setting, although for di/erent reasons.
The extent to which the solution to the unit commitment problem departs from the static mo del
21
of pro t maximization is likely correlated with factors that determine a plant s resp onse to p ermit
allo cation incentives. Ignoring unit commitment constraints could bias estimates of rms resp
onse.
Sp ecifying a fully structural econometric mo del of unit commitment would b e
computationally intensive and would require critical assumptions ab out the nature of b oth the
system-level and unit-level op erating constraints and proto cols. Given the limitations of the
available data, two complementary empirical strategies are pursued. The rst approach is
grounded in economic theory only to the extent that theory identi es which variables should
a/ect rms supply decisions. The second fo cuses on one sp eci c dimension of the larger unit
commitment problem- the decision to b egin op erating conditional on b eing shut down- and
derives a reduced form that can b e implemented empirically as a discrete choice problem.
5.2 A descriptive mo del of short-run supply decisions
In theory, price-taking pro ducers cho ose output levels based on historic, current, and forecast
electricity market conditions, op erating costs, and intertemp oral op erating constraints. My ob
jective with the rst empirical exercise is to assess extent to which statistical patterns in the data
are consistent with the standard theory. I de ne the following short-run supply function:
t e( ei s+ si) + "it; (13)
cfit = i + X0 iti + O
Zt
where i indexes the electricity generating unit, t indexes the time p erio d, and cf is the capacity
factor (i.e. the p ercentage of maximum capacity at which the unit is op erating). The deterministic
comp onent is comprised of two parts. The rst is a exible function that predicts a rm s op
erating capacity, given Xiti+ X0 itwhen the cost of emissions is zero. Let f cfitirepresent this
conditional predicted value. The matrix X includes observable variables that a/ect short-run supply
decisions but are unrelated to the NBP (including fuel prices, day ahead and real time electricity
prices, temp erature, etc.). The second deterministic comp onent in [13] allows predicted pro
duction levels to deviate system22
atically from f cfit as the NOx price deviates from zero. The binary variable D _O Zit
i
and si
s
e
it
33
34
Let Hi
33
35
34
35
23
eq
uals one during ozone season and zero otherwise. The NOx p ermit price is .
Unit-level emissions rates and implicit subsidies (in terms of future p ermits earned p
er unit of electricity generated) are represented by e, resp ectively. The co e¢ cients
allow for asymmetric weighting of the explicit compliance costs and implicit pro duction
subsidies. We should exp ect to b e negative and to b e p ositive. The error term "is
intended to capture the e/ects of unobserved determinants of the op erating decision
(including unanticipated deviations from least-cost system dispatch and unit level pro
ductivity sho cks).
This descriptive mo del can b e used to assess whether the statistical
relationships in the observed data are qualitatively consistent with the theory.
However, b ecause the assumed linear conditional mean sp eci cation has not b een
formally derived from the underlying unit commitment problem, any attempts to draw
causal inferences will require additional assumptions.
5.3 A reduced form mo del of the participation decision
The second approach is more directly tied to the underlying theory. Consider the unit
commitment problem faced by a single electricity generating unit (see App endix
5).The advantage of the second approach is that, conditional on the assumptions of
the mo del, there is a basis for investigating causal relationships b etween p ermit allo
cation design features and rms short-run pro duction decisions. The disadvantage is
that, by conditioning on b eing inactive, only a fraction of the available data are used to
estimate the mo del.
denote the relevant time horizon (measured in hours) for the unit
commitment problem solved by unit i . Because most electricity generating units are
incapable of resp onding quickly to changing market conditions, pro duction levels in
one hour will constrain pro duction p ossibilities H >0 hours into the future.
This es timation fram ework is s im ilar to the ap proach us ed by Man sur (2008) to m o d el the s
hort- run pro d uction de cisions of e le ctricity gene rating u nits in the PJM wholesale market.
Here I as sume th at hou rly s up ply de cisions are controlled by p lant managers in sofar as th ey c
an sub mit b id s to the in dep end ent system op e rator to achieve their de sired pro duc tion le vels.
Among the most n imble u nits, H = 0 and the pro d uction d ecision red uc es to th e static b e
nchmark mo de l.
Let qmeasure the output level at unit i at the b eginning of hour t. The control variable
dititmeasures the change in output at unit i in hour t. The transition equation that determines the
evolution of the state variable qitover time is thus qit+ dit= qit+1: Let D de ne the decision space.
The set of p ossible pro duction level changes available to unit i in hour t, D, will dep end on
time invariant parameters of the op erating constraints iitand the state variable qit(qit; i: The
family of unit-sp eci c constraint sets is fD)g. Pro ts earned from the sales of electricity
generated at unit i in hour t are:it
it
= (Pit
ci
t
tei + s
tsi)(qit + dit) Uiyit
Fi; dit 2 f Dit(qit; i)g (14)
i
;
);
t
;
X
F
0 included to allow rms to weigh explicit compliance costs and
where the parameters
are
implicit subsidy asymmetrically
in their pro duction decisions. The X0 itmatrix includes stat
d
variables observed byi b oth
plant manager and the econometrician, including fuel pric
i the
ermit prices, day
ahead
and
real
time electricity prices.
(
t
t
Note that the contemp
oraneous
p ermit price tsis used to proxy for rms exp ectations
q
regarding future p ermit prices in [14]. This implies that managers value future p ermit allo
cations at contemp oraneous p ermit prices and employ a discount rate of zero. This
simplifying assumption solves a multicollinearity problem; current and future p ermit prices
are highly correlated. However, rms presumably use a non-zero discount rate when valu
b ene ts accruing in future p erio ds. Moreover, Table 2 illustrates how futures prices can
deviate from sp ot prices in this p ermit market. Consequently, captures b oth a discount
factor and the average exp ected di/erence b etween current and future p ermit prices.
i in [14] equals 1 if the unit turns on in hour t; otherwise y
The binary variable yit
and Fi
it; dit
it= 0.
Startup costs and xed costs are represented by U, resp ectively. The plant manager s ob
jective is to maximize multi-p erio d pro ts (q0; X0i0; d) =HiX) sub ject to the transition function T (q)
and the constraint set Dit(qit; it=0F (qit; X0 it; dit): Within this framework, theory makes clear
predictions ab out when an inactive unit should
24
st
ar
t
pr
o
d
u
ci
n
g.
A
pr
o
t
m
a
xi
m
izi
n
g
m
a
n
a
g
er
wi
ll
c
h
o
o
s
e
to
in
c
ur
th
e
c
o
st
s
of
in
iti
at
in
g
o
p
er
at
io
n
s
if
th
e
pr
o
ts
fr
o
m
d
oi
n
g
s
o
e
xc
e
e
d
th
e
pr
o
ts
a
ss
o
ci
at
e
d
wi
th
re
m
ai
ni
n
g
o
ut
of
th
e
m
ar
k
et
.
F
o
c
u
si
n
g
e
xc
lu
si
v
el
y
o
n
th
e
p
ar
tic
ip
at
io
n
m
ar
gi
n
(a
n
d
th
u
s
c
o
n
di
ti
o
ni
n
g
o
n
qit
=
0)
gr
e
at
ly
si
m
pl
i
e
s
th
e
d
er
iv
at
io
n
of
a
n
e
sti
m
a
bl
e
re
d
u
c
e
d
fo
r
m
m
o
d
el
.
L
et
j
to
in
d
e
x
th
e
p
ar
tic
ip
at
io
n
c
h
oi
c
e
sit
u
at
io
n
a
n
d
t
in
d
e
x
th
e
h
o
ur
s
re
le
v
a
nt
to
th
e
p
ar
tic
ip
at
io
n
d
e
ci
si
o
n:
t
=
0:
::
H:
I
d
e
n
e
c
h
oi
c
e
s
p
e
ci
c
v
al
u
e
fu
n
cti
o
n
s
v
(y
;
X
00
ji3
6)
to
c
a
pt
ur
e
th
e
e
x
p
e
ct
e
d
pr
o
ts
a
ss
o
ci
at
e
d
wi
th
p
ar
tic
ip
at
io
n
c
h
oi
c
e:
v (1;
X00 j)
= E0
H t=1 F
[
; (1) ; X00 j) +
(1) ;FX00 j) + X (qt d t
1 j]
(15)
(
0
;
d
0
The X00
atri
x
incl
ude
s all
stat
t
v (0; X00 j) = E0 [F (0;
0; X00
j; ) +
t
=
1
X
H
F
(
q
t
;
d
t
m
(0) ; X00 j) +
j:
ij
0
e
vari
abl
es
rele
van
t to
the
part
icip
atio
n
cho
ice
ma
de
in
hou
r 0.
The
se
incl
ude
fuel
pric
es
and
p
erm
it
pric
es
(wh
ich
do
not
var
y
ove
r
the
tim
e
hori
zon
H ),
the
real
tim
e
ele
ctric
ity
pric
e in
hou
r0
and
the
day
ahe
ad
fore
cas
t
ele
ctric
ity
pric
es
in
hou
rs
1::
H.
The
opti
mal
pro
duc
tion
cho
ice
in
hou
rt
con
diti
ona
l on
the
initi
al
part
icip
atio
n
cho
ice
y is
d(y
). A
dec
isio
n
sp
eci
c
sho
ck
yca
ptur
es
the
e/e
cts
of
uno
bse
rve
d
fact
ors
a/e
ctin
g
exp
ect
ed
retu
rns
to
eith
er
star
ting
to
pro
duc
e or
rem
aini
ng
ina
ctiv
e.
The
se
fact
ors
cou
ld
incl
ude
pla
nt
e¢
cie
ncy
sho
cks,
uns
che
dul
ed
out
age
s,
or
op
erat
or
erro
rs. I
ass
um
e
the
se
sho
cks
are
add
itive
and
ind
ep
end
entl
y
dist
ribu
ted
N(0
, ).
T
o
c
o
m
pl
et
e
th
e
m
ot
iv
at
io
n
of
th
e
e
c
o
n
o
m
et
ri
c
m
o
d
el
,I
d
e
n
e
a
la
te
nt
v
ar
ia
bl
e
yt
o
m
e
a
s
ur
e
th
e
di
/e
re
n
c
e
in
th
e
s
e
c
o
n
di
ti
o
n
al
v
al
u
e
fu
n
cti
o
n
s:
y = v (1;
ij
X00 ij
The
xe
d
e/e
ct i
cap
ture
s
unit
-sp
eci
c
star
t-up
cos
ts,
xed
op
erat
ing
cos
ts,
and
oth
er
uno
bse
rve
d,
tim
e-in
vari
ant
fact
ors
in u
enc
ing
the
part
icip
atio
n
dec
isio
n.
The
set
of
ele
ctric
ity
pric
e
co
e¢
cie
nts
P t,
t=
0
:::H
;
cap
ture
the
p
erio
d
by
p
erio
00 ij)
=
i
v (0; X)
+
Ht=0 P ij
X
tP t
c ijcij
e
je i
+
s
jsi
+
ij
(16
)
d
di/e
ren
ces
in
opti
mal
out
put
lev
els
(co
ndit
ion
al
on
the
part
icip
atio
n
dec
isio
n
ma
de
in p
erio
d 0)
for
a
part
icul
ar
unit
and
cho
ice
situ
atio
n:
P t=
(qt(
1) +
d t(
1))
(qt(
0) +
d t(
0)).
Let
ijm
eas
ure
the
e/e
ct
of
the
part
icip
atio
n
3
6
T
h
e
i
s
u
b
s
c
r
i
p
t
s
h
a
v
e
2
5
b
e
e
n
d
r
o
p
p
e
d
f
o
r
e
a
s
e
o
f
e
x
p
o
s
i
t
i
o
n
.
:
decision on pro duction over the time horizon Hi
c;
e;
and
ij
=
Ht=1X(qij(1)
h
+d
ij h(1)
ij,
qij h
t i ij
ij h(0) d
, and s i ij
i
s
ij
t(y
0
j
)g . The random state variable
and 1
ij
j
00
ij
i
j H
t=0
P ij
tPt
c ijcij
e
je
+
s
jsi!
; (17)
serves as an
y j
ij
Pr(yij
(0)). The reduced form parameters co e¢ cients are de ned as ; resp ectively. Note that
the values vary b oth across units and across the Jchoice situations faced by a given unit i .
This is b ecause fuel prices, p ermit prices, and electricity prices will vary across choice
situations, and this will have implications for the tra jectories of optimal pro duction choices f
dis assumed to b e normally distributed (arising from the di/erence b etween ): The observed
binary choice variable y> 0 : y= 1fy ij 1g: The probability that an inactive unit i facing choice
situation j will b egin to op erate is given by:
i
= 1jX ; ) =
i
+X
where is the cumulative distribution function of the standard normal distribution.
6 Estimation
3 7Explanatory
variables and sto chastic comp onents o ccur at nested micro (i.e. unit-hour) and
macro (i.e. electricity generating unit) levels. Each individual unit is observed making pro duction
decisions over several thousand hours, so there are su¢ cient data to carry out a unit-by-unit
analysis of relationships b etween short-run supply choices and changing electricity market
conditions. However, indep endent variation in p ermit allo cation-related incentives exists only in
very limited quantities at the micro-level.The empirical analysis must therefore exploit
macro-level variation in unit-level op erating characteristics and state-level p ermit allo cation
design choices. Estimation strategies are designed to make e¢ cient use of these hierarchical
data without incurring large computational costs.
3 7The
re is some with in -un it variation in emiss ion s rates and he at rates (and thus p er-M Wh comp lianc e costs)
across ye ars. This variation is extreme ly limited as c ompare d to the signi c ant cross- sec tional variation in e
missions rate s and implicit pro d uction s ubs idies.
26
6.1 Estimating the descriptive mo del of unit-level pro duction decisions
The iparameters in equation [13] are likely to vary signi cantly across pro duction technologies
and op erating proto cols. There are su¢ cient data to estimate these parameters separately for
each unit. This could b e done in one step using fully p o oled OLS, but this is cumb ersome b
ecause it would involve thousands of interactions b etween the variables in Xitand unit-sp eci c
dummy variables. Estimating the mo del in two steps is computationally easier and has exp
ositional advantages.
6.1.1 First stage of estimation
The primary purp ose of this rst stage is to obtain unit sp eci c estimates of the ico e¢ cients.
Unit-sp eci c equations are estimated using micro-level data:
cfit = 1 i + X0 iti + i t D _O + "it: (18)
Zt
The dep endent variable measures unit-level, hourly capacity factor (on a scale of 0-100). The Xit
matrix includes 28 covariates: marginal op erating costs, wholesale price (contemp oraneous and
two lags), forward price (contemp oraneous and two leads), daily average price (contemp
oraneous and lagged), and year xed e/ects. With the exception of the xed e/ects, these
variables enter as third-order p olynomials.
3 8To
address p otential endogeneity concerns, ISO-sp eci c hourly demand forecasts are used to
instrument for electricity prices. Lo cal marginal electricity prices may b e endogenous if
unobserved supply sho cks a/ect b oth market clearing prices and unit-level supply decisions. Day
ahead demand forecasts should b e indep endent of unobserved supply sho cks but highly
correlated with realized demand conditions and thus electricity prices in a given hour. Serial
correlation is another concern given the time series nature of these data. Newey-West auto
correlation consistent standard errors are estimated assuming a twelve hour lag.
3 8Note
that th is error structu re do es n ot accou nt for contemp oraneou s correlation across the un it-le ve l
equations.
27
6.
1.
2
S
e
c
o
n
d
st
a
g
e
of
e
sti
m
at
io
n
In
th
e
s
e
c
o
n
d
st
a
g
e,
th
e
fo
ll
o
wi
n
g
e
q
u
at
io
n
is
e
sti
m
at
e
d
u
si
n
g
a
fe
a
si
bl
e
g
e
n
er
al
iz
e
d
le
a
st
s
q
u
ar
e
s
(F
G
L
S)
e
sti
m
at
or
:
The estimated
b
0
i
i
0=
e+
i
ei s+ si
i
+ i: (19)
o
e¢
cie
nts
are
regr
ess
ed
on
a
con
sta
nt,
a
me
asu
re
of
the
unit
-sp
eci
c
NO
x
emi
ssio
ns
rate
e;
and
the
unit
-sp
eci
c
imp
licit
pro
duc
tion
sub
sidy
s.
Emi
ssio
ns
rate
s at
3
9
40
c
unit
s
exe
mpt
fro
m
the
NO
x
Bud
get
Pro
gra
m
are
set
to
zer
o
and
the
vari
abl
e is
de
me
ane
d
suc
h
that
the
con
sta
nt
ter
m
cap
ture
s
the
ave
rag
e
rela
tion
shi
pb
etw
een
an
incr
em
ent
al
cha
nge
in
the
NO
xp
erm
it
pric
e
and
op
erat
ing
cap
aciti
es
am
ong
unit
s
with
ave
rag
e
NO
x
emi
ssio
ns
rate
s.In
mor
e e
xibl
e
sp
eci
cati
ons
,
the
co
e¢
cie
nts
are
allo
we
d to
var
y
with
obs
erv
abl
e
unit
cha
ract
eris
tics.
T
h
e
s
e
c
o
n
d
st
a
g
e
re
si
d
u
al
s
c
o
nt
ai
n
tw
o
c
o
m
p
o
n
e
nt
s:
a
s
a
m
pl
in
g
er
ro
r
c
o
m
p
o
n
e
nt
(i.
e.
th
e
di
/e
re
n
c
e
b
et
w
e
e
n
th
e
tr
u
e
v
al
u
e
of
th
e
e
sti
m
at
e
d
d
e
p
e
n
d
e
nt
v
ar
ia
bl
e
a
n
d
th
e
tr
u
e
v
al
u
e)
a
n
d
th
e
id
io
sy
n
cr
at
ic
v
ar
ia
ti
o
n
th
at
w
o
ul
d
h
a
v
e
o
bt
ai
n
e
d
re
g
ar
dl
e
ss
of
w
h
et
h
er
th
e
d
e
p
e
n
d
e
nt
v
ar
ia
bl
e
w
a
s
e
sti
m
at
e
d
or
o
b
s
er
v
e
d
di
re
ctl
y.
If
th
e
s
a
m
pl
in
g
v
ar
ia
n
c
e
di
/e
rs
a
cr
o
ss
u
ni
ts
,
th
is
c
o
m
p
o
n
e
nt
wi
ll
b
e
h
et
er
o
sk
e
d
a
sti
c.
T
o
a
d
dr
e
ss
th
is
is
s
u
e,
a
F
G
L
S
e
sti
m
at
or
is
u
s
e
d
to
in
c
or
p
or
at
e
in
fo
r
m
at
io
n
a
b
o
ut
th
e
v
ar
ia
n
c
e
st
ru
ct
ur
e
re
s
ul
te
d
in
th
e
r
st
st
a
g
e
e
sti
m
at
io
n
(
H
a
n
u
s
h
e
k,
1
9
7
4)
.T
h
e
w
ei
g
ht
in
g
m
at
ri
x
u
s
e
d
in
th
e
s
e
c
o
n
d
st
a
g
e
is
gi
v
e
n
b
y:
2
N k (21)
X ) 1b
+ tr
This is a dis ad vantage of es timating rst s tage re gres
i sion e qu ations sep arately.
GX
I treat un it- le ve l emiss ion s rates as xe d. No attemp t is mad e to ac count for the sto ch astic p rop e rties
of the se unit-sp eci c op eratin g param eters (se e App end ix 4). Future work will e xp lore alternative app roach
es to incorp orating this variation . For e xamp le , Joskow and S ch male nse e (1985) demon strate a cons is te nt
(ad ju sted least-s qu ares ) te ch niqu e f or uesing e stimated plant op erating charac teristics as ind ep en de nt
variab le s in c ross sec tion regre ssion an alysis.
4 0A more common app roach to adj usting s tan dard e rror e stimate s wh en th e d ep e nde nt variab le is e stim
ate d involves weighting sec ond s tage ob se rvation s u sing the invers e of th e es timated s tan dard error of the
de p end ent variable (S axonh ouse , 1976). However, this ass umes th at th e total residu al is h eteroskedas tic
(versu s j ust the comp on ent that is explain ed by s amplin g error).If th e varian ce du e to s ampling e rror ac
counts f or a relatively small fraction of th e total res id ual varian ce in the se cond s tage, this rewe ightin g can ge
nerate m is le ad ing s tan dard error es timates .
28
b
=
b
2
=
P
i
b
G
+
2I
; (20)
39
2
i
b
Pi
where bG is the variance covariance matrix from the rst stage, e2 iare the rst stage standard
errors of the estimated co e¢ cient that serves as the dep endent variable in the second
stage, iare the residuals from an OLS estimation of the second stage, k is the numb er of
regressors in the second stage and X is the matrix of regressors. This estimator weights more
precise rst stage estimates more heavily, but only to the degree that sampling error is an imp
ortant comp onent of the overall second stage residual. Standard errors are also clustered at the
facility level to account for the fact that the idiosyncratic comp onent of the error term may b e
correlated among b oilers lo cated at the same facility.
6.1.3 Results
Table 6A summarizes results from estimating [18] using 2SLS. For ease of exp osition, this
table rep orts summary statistics for only a subset of the co e¢ cient estimates: the unit-sp eci c
constants, fuel costs ($/MWh), hourly wholesale electricity market price ($/MWh), and the NOx
price interacted with the ozone season indicator ($/ton). Corresp onding standard errors are also
rep orted.
4 1These
rst stage results lo ok sensible. The marginal cost co e¢ cient is negative on average,
the co e¢ cient on (instrumented) electricity price is p ositive.The co e¢ cient on the NOx p ermit
price interaction is also negative on average.
Table 7 rep orts results from the second stage of the estimation. The dep endent variable is
the unit-sp eci c NOx price co e¢ cient obtained in the rst stage. The most restrictive sp
eci cation (1) includes only the demeaned NOx emissions rate and a constant. The intercept is
not statistically signi cant at the 10-p ercent level, suggesting that there is no statistical
relationship b etween observed pro duction decisions and ozone season NOx prices among NBP
units with average NOx emissions rates. This is surprising; we should exp ect these units would
pro duce less (more) when increases (decreases) in NOx p ermit prices increase (decrease)
marginal op erating costs.
The NOX emissions rate co e¢ cient is statistically signi cant and negative at the 1-p ercent
4 1The
wh ole sale electric ity pric e co e¢ cie nt is p articularly di¢ cu lt to inte rp ret b ec ause th is variab le is h igh ly
corre lated with the lagged prices , day ahe ad lead pric es, an d h igh er ord er te rms that are alos includ ed in the
regre ssion. M arginal costs als o ente r as a third order p olynomial.
29
elevel,
suggesting that the relationship b etween NOx p ermit prices and hourly output is
signi cantly more (less) negative among units with higher (lower) emissions rates. Adding the
implicit subsidy variable (sp eci cation 2) marginally improves the t of the mo del. The co e¢ cient
on the implicit subsidy is p ositive (as exp ected) but very imprecisely estimated. The co e¢ cient
b ecomes more negative (as exp ected), but not signi cantly so.
4 2Column
(3) investigates the extent to which these co e¢ cient estimates vary systematically with
observable unit characteristics (namely NOx emissions rates and op erating capacity).Because b
oth the NOx emissions rate variable and the pro duction capacity variables are demeaned, the
constant term now estimates the conditional mean value of iamong units with average NOx
emissions rates and pro duction capacities. Of the interaction terms, only the quadratic emissions
rate term is signi cant, suggesting a negative and convex relationship. Patterns of statistical
signi cance, and most p oint estimates, are not signi cantly changed when p otentially
endogenous wholesale electricity prices are used in the rst stage versus instruments (see
Column 4).
The last four columns are intended to address concerns ab out p otentially spurious
correlation. Note that [13] mo dels the e/ect of a change in NOx prices on hourly capacity factor
somewhat crudely as a vertical shift inf cf it4 3. This shift should only o ccur in hours when a unit is
close to the margin. Otherwise, an incremental change in the p ermit price should have no e/ect
on short-run pro duction decisions (see Figure 2). For many units in the sample, price-cost
margins are far b elow or ab ove zero in ma jority of hours. In these cases, we should exp ect
to nd a very weak or non-existent relationship b etween p ermit price variation and unit-level
capacity factor (averaged across all hours). Inclusion of these non-marginal observations biases
estimates toward zero. If unit-level price-cost margins are correlated with emissions rates or
implicit subsidies, this would confound the interpretation of the estimation results.
I take two complementary approaches to assessing this issue. First, unit-sp eci c averages of
squared price-cost margins are added to the mo del (columns 5 and 6). Estimated co e¢ cients
4 2Se
veral alte rn ative s p ec i cation s we re tried but n one imp roved the t of th e mo de l. For example, NOx
emiss ion s rate s and implicit sub sidies were also interac te d with heat rate s an d S O2 e mis sions rates.
4 3The corre lation c o e ¢ cient b etween un it-leve l NOx rate s an d a unit-sp eci c meas ure of squared hourly pric e
cos t margin s is 0.55. Th e corre lation co e¢ c ie nt b e tween the implicit sub sidy measu re an d the pric e cost
margin meas ure is 0.38.
30
are not signi cantly a/ected. Second, the mo del is re-estimated using a data set that omits
observations asso ciated with price cost margins that are large in absolute value (i.e. greater than
$50/MWh or less than -$50). These estimates are rep orted in columns (7) and (8). As exp ected,
all co e¢ cient estimates are larger in absolute value. Taken together, these results suggest that
the negative NOx emissions rate co e¢ cient and the p ositive subsidy co e¢ cient are not a result
of spurious cross-sectional variation in price-cost margins.
4 4To
put these results in context, consider a fairly small change in the NOx price of $100/ton (the
average NOx price over this p erio d is $2837/ton; the standard deviation is $1437). For a unit
with an average NOx emissions rate in a grandfathering regime, this NOx price change would
increase ozone-season op erating costs by approximately $0.22/MWh.For a unit of average op
erating capacity op erating in a grandfathering regime, this incremental NOx price change is asso
ciated with a decrease in op erating capacity of 7% . If this unit is in an up dating regime and
receives 2.9 lbs worth of p ermits p er MWh generated (the average subsidy observed in the
data), this decrease falls to 3%. Using the more limited data set that omits hourly observations
that are far from the margin, these estimated decreases are on the order of 10% and 5%, resp
ectively.
sIn
sum, the statistical patterns found in these data are generally consistent with standard theory.
The estimated NOx emissions rate co e¢ cient is negative and consistently statistically signi cant
across all sp eci cations. This is consistent with the hyp othesis that plant managers will account
for environmental compliance costs in their short-run pro duction decisions. The coe¢ cient on the
implicit pro duction subsidy is p ositive, somewhat smaller in absolute value, and less precisely
estimated. The statistical signi cance of the eco e¢ cient is not robust to all sp eci cations. These
results o/er relatively weak supp ort for the hyp othesis that the implicit subsidy conferred by allo
cation up dating will mitigate the negative e/ects of environmental compliance costs on short-run
pro duction decisions. Finally, whereas the value of svaries systematically with unit capacity and
emissions rate, attempts to explain variation in the co e¢ cient are largely unsuccessful.
4 4This
.
31
in crease is very small relative to average variable op erating c osts wh ich exc eed $80/MWh
6.2 Estimating the reduced form mo del of the participation decision
To estimate the reduced form mo del of the participation decision, all unit-hours in which a unit b
egins an hour with a capacity factor ab ove zero are dropp ed from the data set. This amounts to
omitting more than 80 p ercent of observations at coal- red units, approximately 25 p ercent of
observations at natural gas red units, and 14 p ercent of hourly observations at oil- red units.
Electricity generating units in the study sample vary signi cantly in terms of the pro duction
technologies they use and the wholesale electricity markets they serve. This variation presumably
b egets variation in residual variances and the ijPparameters. The large quantity of data makes it
p ossible, in principle, to consistently estimate the reduced form , ; and cco e¢ cients in
[17]separately for each unit. Estimation in two stages is much easier to implement, although this
relative simplicity comes at a cost of b eing unable to account for contemp oraneous correlation
across the unit-level equations.
In the rst stage, unit-sp eci c probit equations are estimated:
j
yij = 1f i + Ht=0 P Pt c icij
1i
D _O + ijg :
X it
Zj
In the second stage, unit-sp eci c estimates of 1 iare regressed on a constant, unit-level
emissions rates (interacted with an NBP indicator variable) and estimated implicit subsidies. An
FGLS estimator is used to incorp orate information ab out the variance structure obtained in
the rst stage.
Interpretation of these second stage estimates is complicated by two p otential identi cation
problems. The rst is inherent in all discrete choice mo dels: parameters are identi ed only up to a
scale factor (Maddala 1983). Consequently, comparisons of co e¢ cient estimates across units
confound the magnitude of the regression co e¢ cients with residual variation. The second
identi cation problem p ertains to the structure of the reduced form estimating equation. Permit
price co e¢ cients are confounded with the ijparameters:4 5If resp onsiveness to p ermit allo
cation in4 5The
ratio of the marginal cost an d NOx p e rmit price c o e ¢ cient is id enti ed in prin ciple; s cale parameters an
d parameters canc el ou t. One ap proach wou ld involve u sing th is ratio as th e dep end ent variab le in th e sec
ond s tage in orde r to overc ome th ese identi cation p roblems . Howe ver, th is is di¢ cu lt to imp le ment in p ractice
. Bec ause the distrib ution of b oth c o e ¢ cients inclu de z ero, s ome e stim ate s of th is ratio can b e in n itely
large.
32
centives varies across units with di/erent emissions rates and/or di/erent implicit subsidies in ways
that are correlated with the unobserved residual variances from the rst stage and/or
the ijparameters, co e¢ cient estimates may b e biased. In this section, I present some alternative
sp eci cations and auxiliary tests which are generally supp ortive of the identifying assumptions.
4 6Table
6B summarizes the estimation results from the rst stage. These estimates are generated
using a sp eci cation that assumes a time horizon of six hours.Hourly demand forecasts are used
as instruments for real time and day ahead electricity prices. As exp ected, estimated marginal
cost co e¢ cients are negative on average. Estimated wholesale electricity price co e¢ cients are
of the same order of magnitude and are p ositive on average. The average NOx price co e¢ cient
estimate is also negative and highly variable across units.
6.2.1 Results
Estimation results from the second stage are presented in Table 8. The dep endent variable is the
estimated 1 ico e¢ cients from the rst stage. The most restrictive sp eci cation includes only a
constant and demeaned NOx emissions rate. Here again, the constant term is not statistically
signi cant. This implies that an incremental change in the NOx price has no statistically signi cant
e/ect on the latent value y as de ned in [16] among units with average NOx emissions rates. The
NOx emissions rate co e¢ cient is negative and statistically signi cant, as exp ected. This implies
that the e/ect of a change in the p ermit price on the latent y value is signi cantly more (less)
negative among units with relatively high (low) emissions rates.
A less restrictive sp eci cation (2) allows the NOx price co e¢ cient to vary with the implicit
subsidy intro duced by contingent allo cation up dating regimes. The emissions rate co e¢ cient
increases slightly in absolute value and remains highly statistically signi cant. The co e¢ cient on
the subsidy variable is p ositive as exp ected, but imprecisely estimated and not statistically
signi cant at a 10 p ercent con dence level.
4 6The
choice of a six h our time horiz on was inf ormed by an in form al analys is of ramping con straints . Un it-s p
ec i c ram p rates were c ru dely es timated by lo okin g at hou r-to-h our changes in pro d uction, e xp re ssing th ese
change s as a p ercentage of installe d capac ity, an d d e n in g th e ramp in g c onstraint to b e th e 95th p erc entile
hou rly chan ge. The mean ramp ing constraint is 50%, m eaning that th e average p lant is c ap able of increasin g
outp ut by half its installed c apacity over the spac e of one h our. The vast ma jority of estimate d ramp rates excee d
16 p e rc ent.
33
Several alternative sp eci cations were estimated so as to allow the NOx rate and subsidy co
e¢ cients to vary with observable unit-level characteristics. One of the sp eci cations that b est t
the data allows these co e¢ cients to vary with installed capacity (column 3). Results indicate that
pro duction decisions of larger emitting pro ducers are more resp onsive to a change in emissions
p ermit prices (and thus compliance costs) as compared to smaller pro ducers. With the addition
of these interaction terms, the subsidy e/ect b ecomes statistically signi cant at a 5 p ercent
con dence level. This suggests that larger pro ducers are also more likely to resp ond to the
implicit subsidy.
Columns (4), (5), and (6) explore the robustness of these results to varying assumptions ab
out the endogeneity of rst stage covariates and the assumed time horizon. Column (4) rep orts
results obtained when electricity prices are assumed to b e exogenous in the rst stage. Columns
(5) and (6) rep ort results under varying assumptions ab out the time horizon. The NOx rate co e¢
cient is negative and highly statistically signi cant across all sp eci cations. The statistical
signi cance of the implicit subsidy and the interaction terms are somewhat less robust to these sp
eci cation changes.
In order to use these results as a basis for causal inference regarding the impacts of unit-level
emissions rates and subsidies on the relationship b etween p ermit prices and short-run
participation decisions, I intro duce some additional assumptions. I assume that the residual
variance and the ij4 7parameters are distributed indep endently of p ermit allo cation incentives.
If this is not the case, strong correlations b etween NOx price co e¢ cients estimated in the rst
stage and emissions rates or implicit subsidies could b e spurious.To investigate this p
ossibility, additional sp eci cations are estimated. Although the ijparameters and residual
variances are not observable, variables that are plausibly strongly correlated with these factors
are observed in the data. For example, fast ramp rates should b e asso ciated with
smaller parameters. Larger op erating capacities should b e asso ciated with
larger ijijparameters. Columns (7) and (8) constitute indirect tests of these indep endence
assumptions. Ramp rates
parameters, are added to
and unit capacity, two variables plausibly correlated with the ij the
4 7For
e xamp le , if the
ij
34
parameters are system atically smalle r among units with h igh er e mis sions rates , th is wou ld resu lt in a n
egative NOx emis sion s rate c o e ¢ cient in th e s econ d s tage that has noth in g to do with a cau sal relations
hip b e twee n h igh emiss ion s rate s an d the nature of pro duc ers resp on se to chan gin g NOx p ermit pric es.
mo del in (7). Although b oth have the exp ected sign, only the ramp rate co e¢ cient is statistically
signi cant. The other co e¢ cient estimates are not substantially a/ected.
Residual variances could b e exp ected to vary across regional electricity markets with
di/erent dispatch proto cols and pro cedures. Indicator variables for the New York and New
England market are added to the mo del in (8). The New York co e¢ cient is p ositively and
weakly signi cant. This could b e a result of smaller residual variance among units supplying New
York, or it could b e capturing the average e/ect of the state s input-based allo cation up dating
regime. The other co e¢ cient estimates are not signi cantly a/ected. Taken together, these results
provide weak supp ort for the aforementioned indep endence assumptions.
Conditional on my additional identifying assumptions, the estimation results suggest that
electricity suppliers do resp ond to b oth explicit compliance costs and implicit pro duction
subsidies asso ciated with the intro duction of this cap-and-trade program. The NOx emissions
rate co e¢ cient is negative and strongly statistically signi cant across all sp eci cations. The p oint
estimate of the e/ect of the implicit subsidy is consistently p ositive and smaller in absolute value.
Taken at face value, these p oint estimates are roughly consistent with a discount rate of 10-15 p
ercent (p ermit allo cations are up dated with a three to four year lag on average). However,
based on these fairly noisy estimates, the hyp othesis that plant managers ascrib e equal weight
to the implicit subsidy and the explicit compliance costs in their short-run pro duction decisions
cannot b e rejected.
7 Conclusions
Policymakers, industry representatives, and other stakeholders are increasingly interested in
understanding how the design of p ermit allo cation proto cols a/ects p ermit and pro duct market
outcomes. A growing theoretical literature o/ers insights into how rms should resp ond to di/erent
p ermit allo cation rules, including "up dating" regimes that simultaneously p enalize emissions
while rewarding pro duction. Empirical evidence has thus far proved elusive. This pap er analyzes
the pro duction decisions of hundreds of electricity generators in a large emissions trading
program that is particularly well suited to a study of the short-run impacts of p ermit allo cation
design.
A simple partial equilibrium mo del demonstrates the theoretical, short-run implications of
35
contingent up dating vis a vis more traditional p ermit allo cation designs (i.e. auctioning and
grandfathering) and serves to motivate the empirical work. Two complementary empirical
strategies are used to assess whether the detailed hourly data collected from electricity
generators in the NOx Budget Program are consistent with standard theory. The rst investigates
statistical relationships in the data. I nd that an increase in the emissions p ermit price is asso
ciated with larger (more negative) changes in the short-run pro duction decisions of units with
higher emissions rates. I also o/er somewhat weaker evidence that the relationship b etween NOx
price changes and short-run supply decisions is less negative among units that implicitly receive a
pro duction subsidy via p ermit allo cation up dating. These results are generally consistent with
our theoretical understanding of how p ermit allo cation incentives a/ect market outcomes.
The second strategy imp oses more structure so as to provide a basis for causal inference. I
fo cus exclusively on the participation margin of the unit commitment pro cess that presumably
generates the observed short-run supply decisions. I derive and estimate a reduced form mo del
of electricity pro ducers decisions to resume op erations conditional on b eing inactive.
Estimation results provide further, robust evidence in supp ort of the hyp othesis that pro ducers
account for b oth the explicit emissions tax and the implicit pro duction subsidy conferred by this
emissions trading program. I fail reject the hyp othesis that negative emissions incentives and p
ositive production incentives conferred by allo cation up dating are weighed equally in short-run
pro duction decisions.
This analysis is not without its limitations. Precise estimation of the welfare implications of the
p ermit allo cation design decisions I analyze is b eyond the scop e of this pap er. A burgeoning
literature endeavors to predict welfare impacts of p ermit allo cation design choices in a range of
counterfactual p olicy contexts using detailed, theory-based simulation mo dels. Although the
results of these studies cannot b e con rmed or refuted based on evidence presented here, the
empirical ndings lend supp ort to some pivotal assumptions underpinning these simulation
exercises.
Finally, an imp ortant motivation for this study is to inform future p ermit market design
decisions, particularly those that will determine how hundreds of billions of dollars worth of carb
on
36
credits will b e allo cated under prop osed Federal climate change legislation. The pap er provides
empirical evidence that rms are resp onding to the relatively mo dest p ermit allo cation
incentives conferred by the NOx Budget Program. We might exp ect this resp onse to carry over
to a larger greenhouse gas emissions trading program where the stakes will likely b e much
higher. However, the regional emissions trading program analyzed in this pap er and prop osed
Federal program designed to limit greenhouse gas emissions di/er along a numb er of imp ortant
design dimensions. Additional research is needed b efore we can de nitively anticipate how rms
will resp ond to p ermit allo cation incentives in the next generation of cap-and-trade programs.
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40
Fig
ure 1 : Emi ssions constrained social welfa r e maxi mizing outc ome
Notes : The downward sloping solid li
ne represents the emissions constraint. The soci
ally optimal allocation of production o
ccurs at the point where the emissions constraint is just tan gen t to a leve
l set of the economic surplus function. This point is intersecte
d by the vector from the origin. The broken line , with a slope of -1, conne
cts all poin ts that correspo nd to an aggregate output qua
ntity equal to that associated with th e optimum outco me. Points l y
ing on the emissions constraint above (belo w ) th
e optimal point are associated with more (less) consu
mption and more (less) supply side abatement tha n is consisten t with w elfare maximi
zation .
41
Figure 2 : Hourly Producti on
0 .2 .4 .6 .8 1
0 20 40 60 80
0 12 24 36 48 60 72 84 96hour
Decisi ons
wholesale electricity price
0 .2 .4 .6 .8 1
-20 -10 0 10 20 30price-cost margin
at a Repr ese nta tive Unit
capacity factor
capacity factor
Notes : Hourl y production decisions at a single uni
t (measured as capacity factor) and th e corresponding hourly wholesale electrici t
y price over a four day peri od are plotte
d in the left panel. The horizontal li ne represents the theoret
ical reservation price duri ng these off - season hours (i.e. th e unit’s constan
t marginal ope r ating cost). This cost of $ 49/MWh is e s timated using th
e fuel input pri ces that prevailed in this four day period, the unit- spe
cific heat rate, and other variable (no n - fuel) operations costs. The thin black li
ne in the right pan el plots these same data in capa city fa ctor, price- co
st margin (i. e . the hourly wholesale electri city pri c
e less the marginal operating costs incurred) space. This is a mean smooth of c
apacity factor on price - cost margins. The thi ck bla ck line represents the on off producti on protocol implie d by th e benchmark model of a profit maxi mi
zing, pri ce taking produce r . Comparing these two functions he
lps to illustrate how observed production decisions deviate systematica
lly from the predictions of the simple, static model. Finally, the thick red liner
epresent th e expected impact of the NBP on thes e short- run supply f unctio
ns. In theory, the uni t’s reservation pri ce should increase by an amount equa
l to the net compliance co sts per MWh .
42
Capacity
season
factor
Ozon
Grandf ather i ng
Regimes
Contingent Upd at i ng Regimes
Figure 3 : Electricity Supply Decisi ons in Grandf ath e ring and Contingent All
ocation Updati ng Regimes
Notes : Th ese figures plo t a local mea n smooth of hourly, unit - level capaci
ty factors on hourly, unit - specific pri ce - cost margins
, where costs include fuel costs and other variable operating costs but excl
ude any costs or implici t subsi dies associated with the NOx Bu
dget Program. The shaded regions represent 95 percent confidence intervals. The
se graphs are ge n e r a te d usi ng hourly from almost 600 electrici ty generati
ng units over the study time period (2003- 2 006), excludi
ng the top and bottom fiv e per centiles of observations. I use an Epane chni
kov weight function and rule- of- thu m b b a
ndwidth estimator. The right panel s ummarizes the produ ctio n de
cisions at 73 units operating in states where NOx permits are grandfathere
d. The lef t panel summar i zes producti
on decisions at 515 units operating in states where permit alloca tions are peri
odically u pda ted based on lagged inpu t or output choices.
-150 -100 -50 0 50 100Price-cost margin
($/MWh)
43
($/MWh)
Off
season
0 .2 .4 .6 .8
0 .2 .4 .6 .8
-150 -100 -50 0 50 100Price-cost margin
Off season95% CI Ozone
season
95% CI Ozone
season
Table 1 : Permit allocati on regim e chosen by New York, New Eng l and , and Mi d- Atl
antic states
State Annu al state NOx bu
Chosen perm
Electricity
dget for Electricity ge nerating uni
it allocation regime
market
ts
(tons NOx)
CT 4,253 Outp ut - based up datin g MA 12,861 Outp ut - based up datin
N
g ME N/A N/A NH N/A N/A RI 936 Grandfatheri ng VT N/A N/A
e
New York
NY 30,405 Inpu t - based updati ng
w
PJM DC 233 Grandfatheri ng
DE 4,463 Grandfatheri ng MD 14,520 Grandfatheri ng NJ 8,200
Outp ut - based up datin g
E
PA 47,244 Inpu t - based updati ng VA 17,091 Inpu t - based updati ng
n
Notes: Annual, state- level NOx b udge ts do not chan ge over the s tudy
. Amongg states that chose contin gen t u pdatin
l
g, implementation
details vary considerably. For example, whereas so
a
me states update annually, others u pdate in thre e or four year blocks.
n
d
44
period
Table 2 : Operating summ ary statistics by per m it all ocati on regi
me : CENSUS
# Units
Summer
Off - seas
Hea
Allocati on
Capacit
on capacit
t rate* (b
y
y
tu/kW h)
regime
(MW)
factor
11,384 (
2,444)
353 155 (206)
Outp ut - based updati ng
Grandfatheri ng
Exe m pt
140 134 (176)
69 200 (182)
18 181 (234)
0
0
5
$
0
3
$ 2 2
7
4 3 2
2 0 0
$ 1
8
3
12,080 (
3,447)
3.07 (
3.60)
1.57 (4.67)
19% (26%)
10% (18%)
21% (26%)
23% (29%)
$
5
2
0
0
6
8
4
3 6 8 2
2 0 0 4
$ 2 1 8
0 5
$ 2
$ 2 7 7 1
$ 2 9 5 1
2
2 0 0
2.01 (
2.04)
2.82 (
4.54)
Notes: Standard deviations in pare nth e ses. Su mmar y statistics are gen
erated using da ta fr om 610 fossil
fuel - fired ele ctricity gener a ting units su
pplying the New York, New En gland, or PJM mark ets durin
g the study period (2003- 2006). Self ge nerati ng and co - ge
nerating units are exclude d from the sample. * Emissions rate and hea
t rate summary statistics are weighted by installed ca
pacity.
Table 3 : NOx Allowance Prices
2003- 2
006 (Nominal $/ton)
Permi t vintage Transac tion year 2003 2004 2005* 2006*
2
-
NOx rate* (lbs
NOx/MWh)
12,857 (
3,090)
11,5
92 (5,388)
Inpu t - based updati ng
Ozone season
$ 1 9 0 6
$ 3 1 6 3
0
$ 1
2 0 4
$ 1 5 0 7
$ 3 0 1
7
$ 2 6
6
2
$
1 7 5 0
2 0 0 8
$ 2 7 0 5
$ 2 2 9 9
$ 1 5
7 0
2 0 0 9
$ 2 3 1 4
$ 2
2 3 2
$ 1 5 1 8
Notes: This table reports average an
nual permit prices by NOx permi t vintage. Conte
mporaneous permit pri ces appear in bold. Th
e asterisk denotes years in which the progressive flow control
(P FC ) constraint wa s bindin
g. The PFC ratio was 0.25 and 0.27 in 2005 and 2006, respec
tively; ban ked permits are traded at a discoun t in these years.
45
5
7
0
5
$
Table 4 : Es ti mate d NBP compliance c o sts an d prod uction incentives by alloc
a tion regim e
(1)
(2)
(3)
(4)
NOx permi
(1) as a perce ntag Future permi
Estim ated ne
t costs per M e of off ts allocated (tot compliance co
Wh
season
ns)
pest
Allocati
r
MWh
genera
generated
variable
oper
per MWh*
on regime
ted
ating costs
Inpu t based updati
ng
Out
p ut
bas
ed
upd
ati
ng
Grandfatheri
ng $6.49 ($9.03)
$4.89 (
$4.69)
$
7
.
4
6
6.4% (
6.0%)
6.5% (
5.9%)
0.001 (
0.001)
0.002
(0.0
01)
$1.40 (
$4.69)
$1.45 ($8.15)
(
$
8
.
2
4
)
8.1%
(6.8%)
0
$6.49
($4.01)
Notes:
Stand a rd deviations in
parenthe ses. Summar
y
statistics
are generate d using
data
fr om 580 fossil fuel fired ele ctricity
gen e r a ting uni
ts
supplying
the New York,
New
England,
or PJM markets duri
ng
the
study
period
(2003- 2006). Self
g e nera ting and co generati ng
units
are e xcl uded
from
the sample
.
Averages across unit - year
s are reported; standard deviations are in paren thes
es.
* To
calculate net complia nce
costs, future permi
ts
allocated
per unit
of output are valued using
futures
perm
it
prices. This
value
is
then
subtra cted from the
expli
cit compliance
cost per MWh
(i .e.
the
prod uc t
of the
specific emissions rate and the spot NO x permit pri ce).
Exe m pt $0 -- 0 $0
46
uni t -
Table 5 : Regi onal whol esa l e elec tricity prices
ectricity dem and by seas on
Ho urly el ectr icity dem
an d
and el
Wholesale el
ectricity pric e
($/MWh)
Regio
nal
(MW)
el
ectricity mar
ket
Off - seas on
New Engla
nd (NEPOOL)
New York
(NYISO)
Ozone season Off - seas
on
14,603 (
15,344 (
2,513)
3,416)
17,547 (
2,768)
19,151
(3,936)
$60.88 ($
29.34)
Ozone seaso
n
$57.98 ($
34.88)
$68.00 (
$96.97)
$52.03 (
$33.84)
Mid- Atl antic (PJM) 29,214 (8,787) 31,694 (9,957)
Notes: Standard deviations in pare nth e ses. Th is tabl
e summarizes observed pri
ces and load levels over the 32,748 hours in the data. Both
ad levels are simi larly distribu ted across seasons.
47
prices and lo
$70.74 (
$78.17)
$55.41
($43.34)
Table 6A : Summary of first stag e es ti mate s:
Dependent variable is hourly capacity factor
Covariate
Average poi
Standard
Average standard e
n t estim
rr or
ate
deviation
- 9.24 12.93 4.18
U n i t l e v e l
c o n s t a n t
2 5 . 2 4
9 3 . 4 9
p e r a t i n g
c o s t
( $ / M W h )
3.04 17.76 9.39
Local whol
esale marginal
price ($/MWh)
6 2 . 6 6
M a r g i n a l
- 0.003 0.25 0.0008
15,087
NOx price * Ozone
indicator ($/to
n)
Average # obs
e rvati ons /unit
Note s:
The unit of analysis is a unit -hour. The dependent va r i a b l e is the cap a c i ty factor (measu
red on a scale of 1 - 100). For ea se of exposition, only th e higher order cost and price variable
s, lagged prices, futu res prices, and year dummies are omitted from this table.
Table 6B : Summary statis tics for the fi rst stag e e s ti mate s
Note s:
The unit of analysis is a unit -hour. The dependent va r i a b l e is the bin a
ry participation indicator. Each unit - level regression includes: a un it
-level fixed effect, marginal operating costs, contemporaneous wh
olesale price , hourly forward prices for 1 through 6 hours forward, the NOx permit pric
e interacted with the ozone season indicator and year fixed effects. Real time and day
d electricity prices are instrumented for using hou r ly demand forecasts.
48
Covariate
- 2.98 1.78 1.69
l e v e l
Marginal ope r ati n
g cost ($/MWh)
Local whol
esale marginal
price ($/MWh)
NOx price * Ozone
indicator ($/to
n)
Average # obse
rvati ons /unit
Average poi
n t estim
ate
c
o
Standard
Average
rr or
deviation
U n i
n s t a n
- 0.14 0.03 0.02
0.06 0.09 0.05
- 0.0004 0.018 0.0001
13,945
t
t
-
standard e
ah e a
o
Table 7 :
Des c riptive model :
Second stage es tima ti on resul ts
Specification (1) (2) (3) (4) (5) (6) (7) (8) Constant - 0.00 (0.02) - 0.02 (0.02) - 0.05 (0.03) - 0.03* (0.02) 0.03 (0.02) - 0.07** (0.03) - 0.05 0.03 - 0.10*** (0.03)
NOx ra
te
14.56**
16.27***
30.02***
28.46***
15.68***
31.35***
35.83***
61.87***
(5.65)
(5.59)
(10.90)
(7.24)
(5.87)
(11.75)
(12.87)
(17.84)
10.82 (9.84)
23.42**
17.06**
13.41
26.00**
27.14
31.52*
Estimated
(11.00
(7.96)
(9.
(11.46
(17.
subsidy
)
54)
)
(18.72)
45)
Pri ce cos
t margi
n
2
(NOx
0
0
*
d
rate
1
rate
3
1
727.62)
Estimate
.
2
5
7
0
0.09*
(
(0.05)
0
0
2
7
.
1
7
*
1413.27***
*
2225.61*
.
9
)
.
8
0
0
.
8
(
550.55 (1359.16)
First stage
V
Y
N
Y
.
0
5
5
-
)
(
0.06 (0.06)
0.05
553
N
0
1297.7
1
8
635.06 (1
-
0
.
0
0.05
553
0.03
553
Y
N
Y
N
N
N
0
.
-
5
0 8
0 .
(
2
)
0.07 (0.09)
0.09
553
0.02
550
R
N
.
0
(0.001)
938.23 (7718.3
6)
0
8
0.02 (0.05)
0.02
553
0
5
8
)
0.02
553
(
0
.
0.0001 (0.0003) - 0.05 (0.03) 0.001
2
-
subsidy
NOx rat
e * ca
pacity
Estimated
subsid
y * c
apacity
2
0
)
1
7
9
8
2
5
.
6
467.35 2033.56 (887.56)
)
NOx
0
3
N
N
Y
0.03
550
Y
Y
Y
I
Re s t ricte
d sample?
Note s:
The unit of analysis is an electricity gen e rating un it. The depend
ent variable is the estimated NO x price effect (during ozone season ) from the unit -le v e
l linear regression estimation. In the first stage, forecast demand is used to instrument for loc
al marginal electricity prices un less otherwise indicated. Emissions rates (d emean e
d) and estimated subsidies are measured in tons of NO
x per MWH. Production capacity (also demeaned ) is measured in MW. Th e price-cost margin va
r i a b l e is constructed by computing th e average squared pric e
-cost margin for each unit (across all hours). FGLS standard errors (in parentheses) are clustere
d at the facility le v e l . To estimate specifications (7 ) an d (8 ), all un it -hours in wh i c
h the estimated price margin is greater th a n $50 or less than -$5
0 are dropped in the first stage. See text for details.
* Statistically significant at the 10 per
c ent level. ** Statistically significant at th e 5 perc
0
*
0
*
ent level.
49
***
Statistically
significant at the 1
perc ent le v e l .
Table 8 :
Ho w do NOx permit prices
on resul ts
af fect the participation deci sion? Second stage es tim ati
Specification (1) (2) (3) (4) (5) (6) (7) (8) Constant 0.000 (0.000) - 0.003 (0.002) - 0.004*** (0.001) 0.002 (0.001) - 0.002 (0.002) - 0.002 (0.002) 0.002 (0.002) - 0.005* (0.001)
NOx rate
(tons /
2.21***
2.44***
3.04***
2.05***
2.87***
2.97***
2.73***
3.09***
MWh)
(0.80)
(0.82)
(0.44)
(0.49)
(0.54)
(0.65)
(0.52)
(0.45)
1.69 (1.23)
1.92***
1.45*
1.48*
1.47
1.69**
1.65**
(0.
(0.
(0.99)
(0.71
(0.75
Estimated
(0.70)
76)
84)
)
)
subsidy
(tons / MWh)
NOx rat
e * ca
pacity
*
*
2
)
0.014*** (0.01)
0
.
0
Estimated
subsid
y * c
apacity
0
1
(
0
.
0
0
4
0.004) 0.004 (0.004)
R
a
0
1
C
.
)
m
0
.
0
0
(
0
.
0
- 0.002 (0.003) - 0.003
8
0
(0.004) -
*
0.010***
)
0.007*
p
(
r
0.007*
(0.00
4)
0.003
0.008**
(0.005)
(0.003)
(0.003)
0.001
(0.005)
a
t
e
-
0
a
0
p
0
N
3
a
.
*
c
0
*
i
t
0
.
0
.
0
0
0
y
0
0
E
(
N
.
(
0
.
0
0
.
0
0
2
0
1
)
Y
0
2R
0
0
0.09
.
First
stage
0
1
0.08
553
6
IV?
*
(
0.10
0
0.06
0.12
0.12
553
550
550
550
550
6
3
)
0.11
0.10
550
N
Assume
d time horiz
on (hours )
0
2
550
6 2 8 6 6
6
Y
Y
Y
N
Y
Y
Y
Notes:
The unit of analysis is an electric ity generating unit. The de
pendent variable is the coefficient on the inte
raction between the NOx permit price and ozone season indicator from
irst stage of the estimation. First stage probit equations also include a
nt, unit- specific marginal op erating cos t , year indicato rs, and instrume
nts for current and future wholesale electric
the f
consta
ity prices (unless otherwise indicated). These first stage equations are estimate
d under different assumptions about the relevant time horizon (me a s u re
d in hours). Emissions rates (demea ned) and estimated subsidie
s are measured in to n s of NOx per MWH. Prod uction capaci ty (als
o demeaned) is measured in MW. FGLS standa
rd errors (in parentheses) are clus te re d at the facili ty le ve
l. See text for de tails
* Statistically
ent level.
50
***
significant
Statistically
at the
10 perc ent level.
significant at the 1
**
Statistically significant
perc ent le v e l .
at th e
5 perc
A
p
p
e
n
di
x
1
U
si
n
g
th
e
sy
st
e
m
of
rs
t
or
d
er
c
o
n
di
ti
o
n
s,
s
ol
v
e
fo
r
e
q
ui
li
br
iu
m
q
u
a
nt
iti
e
s
a
n
d
p
er
m
it
pr
ic
e
in
te
r
m
s
of
th
e
m
o
d
el
p
ar
a
m
et
er
s:
+e
c +
c
ae
+
e
q c = bE
ecbe2 c
2+
E
dec
d
q
d
= bE
edbe2 c
d
d
+ e2 cced d aece+
be
+ e2 dcc + be2 d
2 cc
+Ee
+ e2 dcaeced2
+ e2 d
dcc
2+
d
d
be
2 dd
c
2
c
c
d
c
c
+
ae
(2)
(
c+
3)
Q
dced 2ae
=E
eccb d bE e 2bec
ed2 c 2bedc bE e
2beeccec
c) 2
+ e+ E edcc + ae2dc+
d
ae2 d
(1)
2 dcc
e
c)
cc
E (bcc2 c+ bcd +
+e
cc
(4)
cccd
d
+ e2 ccd
d=
d
+ ) b (e e
c
Substituting these expressions
into the economic surplus function and di/ere
c
ect to the emissions
a
constraint:
c
)
(
e
c
c
@ S@
E=
y equation [??] ,
b
E
(
c
) b (e ed2)+ e2 d
+
a
+e
= : (5)
ccc (eccd
is also
B the marginal cost of reducing emissions on the supply side. Thus, in the rst b est case,
marginal abatement costs are set equal across all pro ducers and across the supply and
demand side of the pro duct market.
App endix 2 :
Pro t maximization under symmetric up dating yields lower consumer prices and higher supply
side abatement costs as compared to the rst b est case. To see this, I solve for the equilibrium
quantities and p ermit price in terms of the mo del parameters:
51
=E
eccbed2 c
S_U
PQ
2be
+
be2 d
2b
ec
ce
d
d
d
2aeccc
2
2
cc
d
dc
c
+
+ e2 + e2
be2 d ccd
dcc
ced seced + E eccd+ ae2 d
+
+ ae
se2 d
c d seced + E
2 c
+
c
2c
c
edcc
se2 c
d
e
= bE ec secc bE2be se be2
= bE ed
ed
ae aed c
qS _ U P
2be
c
q
S_UP
d
+
bcd
2
S_U
P
A
ss
u
m
in
g
th
e
i
m
pl
ici
ty
pr
o
d
u
cti
o
n
s
u
b
sE c ced
sE cc+de+ E edcc
e
+ ae2 c+
+e
ae2 d
(7)
e 1+
d
be2 d
2+
e2
+e c
c
>
(8)
1ccd
bE e
+ cccd) + s
(e
2) + e c + e2
2 2c1
= a (ecc + edd
d
) E (bccc ) b (e e
c
c+ ecc
d
(9)
si
d
y
is
st
ri
ctl
y
gr
e
at
er
th
a
n
z
er
o,
th
e
p
er
m
it
pr
ic
e
u
n
d
er
u
p
d
at
in
g
(a
n
d
th
u
s
th
e
m
ar
gi
n
al
a
b
at
e
m
e
nt
c
o
st
o
n
th
e
s
u
p
pl
y
si
d
e)
is
hi
g
h
er
u
n
d
er
u
p
d
at
in
g
v
er
s
u
s
th
e
b
e
n
c
h
m
ar
k
c
a
s
e.
It
c
a
n
al
s
o
b
e
s
h
o
w
n
th
at
c
o
n
s
u
m
pt
io
n
le
v
el
s
wi
ll
b
e
hi
g
h
er
u
n
d
er
sy
m
m
et
ri
c
u
p
d
at
in
g:
2c
+ E edcc 2aeced + ae2 c+ ae2 d
s
E
c
+ E edcc
2ae
2be2)cceed
(a (e
c
+ ae2 c
+
sE cc
(11)
c
d
a
e
+
+ e c + e2
d dcc
be2 d
d
cd
2 d
2
c
dc
c
seccd
sedcc
2
c
be 2bece + be2 +
c
e c +e
d
2d
S_U
Q
PQ
= s (e
d
e
=E
(10) E e
eccbed2 c
) E (bcdcc +
+ bEc + acccd)) (12)
d
edcc
@ S+ edcc) E (bcd + bEc d + acccd > 0): Thus, QO B A > Q :
a ( eccd+ ed
52
d+ cc+ ccc
Note that (a (eccd
=))
>0
if
the
emi
ssio
ns
con
stra
int
bin
ds
in
the
@E
dcc)
c
bE (
c)2+ e2 cc
2 dc c
rs
tb
est
cas
e (b
eca
use
) b( e
e+ ed
A
p
p
e
n
di
x
3
Pr
o
t
m
a
xi
m
iz
at
io
n
u
n
d
er
sy
m
m
et
ri
c
u
p
d
at
in
g
yi
el
d
s
lo
w
er
c
o
n
s
u
m
er
pr
ic
e
s
a
n
d
hi
g
h
er
s
u
p
pl
y
si
d
e
a
b
at
e
m
e
nt
c
o
st
s
a
s
c
o
m
p
ar
e
d
to
th
e
r
st
b
e
st
c
a
s
e.
T
o
s
e
e
th
is,
I
s
ol
v
e
fo
r
th
e
e
q
ui
li
br
iu
m
q
u
a
nt
iti
e
s
a
n
d
p
er
m
it
pr
ic
e
in
te
r
m
s
of
th
e
m
o
d
el
p
ar
a
m
et
er
s:
2
+ e2
+ e2
dcc
d ccd
ce
d
d
+E
ecc
= bE ec
bE
edbe2 c
qA_ U P c
s+
+ e2
d ae2 d dsc
aece + E ed
2be
aecdce
d
+
qA_ U P d = bE ed
2
2bece
csd d
b (ed
b
e
be2 +
d e2 ccd
ed +
c
d
bE
ecbe2 c
c
(14 eced
) dsc
a
e
2+
d
e2 dcc e e
+ e2
cs
(15
)
+e c +e c
d
cdb
d
c
(e+ edcc) E cd+ bcc 2c+d cccd) + becsc
(bcd ec2)dsc+ be
+ e2 c
+ edccsd
ccd
(17
)
c
c2
c cc
= a (ecc (16) be be e2)dsd+ es+ ec
A_ U P
A_ U PQ
=
c
+
sd ;
= E eccd + E edcc 2aebec2 + ae2 c+
ae2 d
2c
ced+ be
note that e2 dsc = ecedsd and e2 csd= ecedsc
d+
e2 csd
2be
d
+ e2
dsc
ecedsc
ecedsd
(13
)
cedsd
ec
ed
sc
2 dsc
2
c
s
d
: Thus, if the pro duction subsidies are set such thatI the subsidy p er unit of emissions are
f equal, the rst-b est pro duction quantities and pro duct price is achieved. Although the pro duct
price in this case will b e equal to P;note that the p ermit price will exceed (to comp ensate for
the relatively high subsidy paid to the more p olluting rm). If the subsidy p er unit of p ollution is
2+
d
e+ e
hig
. Alternatively, if the subsidy p er unit of p ollution is higher for the more p olluting rm, the
her
reverse will b e true.
for
cle
App endix 4 :Data set construction
an
er
rm
State-level permit al location regimes Permit allo cation design parameters were collected from
s state-level implementing agencies. All states have do cumented the sp eci c algorithms and
(as
equations used to determine facility-sp eci c p ermit allo cations in detail. Agencies were
iscontacted directly when implementation details were unclear or could not b e found in the
the
public record.
ca
se
Unit-level operations and attributes
wh
en
pro
1Hourly, unit-level emissions, heat input, and output data were obtained from the US EPA
duContinuous Emission Monitoring System (CEMS).Continuous emission monitoring and rep
ctiorting
on
1Coal un its rep ort hourly gross an d n et u nit load (in MWe ). Combined -cycle un its are require d to re p ort
su th e
bsi
53
die
s
are
sy
m
me
tric
),
e>
e;
e>
ece
dsc,
an
d
co
ns
um
pti
on
ex
ce
ed
s
rst
b
est
lev
els
2requirements
for EGUs regulated under EPA s Acid Rain Program (ARP) and/or the NOx Budget
Program require monitoring of hourly sulfur dioxide mass emissions, carb on dioxide mass
emissions, NOx emission rates, heat input, and other op erating conditions.
3I
exclude nuclear, hydro, and renewable electricity generators b ecause these zero emitting pro
ducers are categorically excluded from the NOx Budget Program. Small pro ducers (i.e. less than
10 or 15 MW) are also excluded from the NBP. Finally, I exclude any units for which wholesale
electricity generation is not the primary pro duction activity (such as self generating units). This
leaves 580 electricity generating units in the cleaned data set and 15,455,067 hourly
observations.
Emissions permit prices NOx p ermits are actively traded in a liquid p ermit market.4Brokers
facilitate the ma jority of arms length transactions, administer escrow accounts, and provide
market analysis. A variety of transaction structures exist in the market, including forward
settlements, calls, puts, comp osite structures such as straddles, and vintage swaps. Daily p ermit
price data were purchased from Evolution Markets LLC.
Electricity market data Hourly data summarizing electricity market conditions (including realized
and forecast load,
real time prices, and day ahead prices) were collected from the New England, New York, and
PJM Indep endent System Op erator websites. Hourly weather station data were obtained from
the National Oceanic and Atmospheric Administration. Additional op erating characteristics
(including pro duction capacities and fuel characteristics) were obtained from Platts Basecase
database.
Fuel price data
su m of all loads as so ciate d with all c yc le s (steam and electric ) on a cons is te nt bas is . This s ometimes
involves converting steam load to an equivale nt e le ctrical load or vice -versa.
2Only those un its that p articipate in b oth th e NB P an d th e th e Acid Rain P rogram are require d to re p ort h
ourly op eration s year round . Un its regulate d und er the NBP on ly nee d n ot re p ort ou ts id e of ozon e s eason .
Hourly data are also n ot rep orte d whe n plants are take n o/-line f or sche duled outtage s or mainten ance . In total,
th e analysis samp le includ es 15.5 million hourly ob servation s.
3The
d ata set in clud es April 2003 th rou gh Dec emb er 2006. Th e maximu m numb er of ob servations on a single
un it is 32,748 . Th e average numb er of obs ervations p e r un it is much lower (26,646) b e caus e several un its rep
ort only du ring oz on e s eason .
4In 2007, th e volume of "ec onomically signi cant" immed iate settlement trade s (i.e. trade s b e twee n versu s
within rms ) re ache d 247,000 tons (EPA 2008).
54
5Daily
sp ot prices of New York Harb or No. 2 and No. 6 heating oils were obtained from the
Energy Information Administration. Daily natural gas sp ot prices were obtained from Platts.
6The
OTC NYMEX "Lo ok-Alike" contract, the most actively traded coal pro duct, is used as a
measure of coal prices.
App endix 5 : Unit-level op erating characteristics The data set used in estimation contains
15,455,067 hourly observations for 580 units. Table A1 decomp oses the observed variation in
hourly heat rates (a measure of fuel e¢ ciency) and NOx emissions rates into within and b etween
unit comp onents. To generate this table, all observations in which a unit is running at or b elow 5
p ercent capacity factor are dropp ed. When electricity generators are ramping up or down and
are op erating at low capacity factors, plants run inef ciently and NOx emissions rates can b e
much higher than they are when the plant is running e¢ ciently. Because emissions rates and
heat rates observed at these low capacity factors are not go o d indicators of units average op
erating characteristics, they are dropp ed.
Table A1 : Decomp osing the variance in unit-level op erating characteristics
5For
Ne w En gland I us e the n atu ral gas sp ot p rices for Algonquin City Gates an d Ten nes see , zon e 6. For
New York gas prices I u se Dominion, n orth p oint. For P JM I use the Transc o Zone 6 non- Ne w York pric es.
6The NYME X lo ok-alike pric e is based on trading us in g th e sp e ci cations in the NYME X f utures contract. Origin
ally, NYME X was pred omin antly traded "phys ic al" with c omp anies engaging in bilate ral agre ements. Now a ma
jority of NYMEX trad es are trans acted OTC then "given up" to the e xchange for c le aring, wh ich allows marke t
partic ip ants to m an age cred it risk over a larger p o ol of c ounte rp arties.
55
NOx emissions rate Heat rate (lbs
NOx/MWh) (btu/kWh)
Mean 2.79 11,206
Between 5.06 4,952 standard deviation % variation
93% 84%
Within 1.42 2,955 standard deviation % variation 7%
16%
Observations 5,043,876 5,043,876
Units 580 580
Although the vast ma jority of the observed variation is b etween units, there is some within-unit
variation in b oth op erating attributes. This within-unit variation can b e a result of pro duction
choices made by the plant manager (i.e. choice of fuel characteristics, the capacity at which the
plant is running, combustion tuning, etc.) or it can b e a/ected by purely exogenous factors
(such as ambient temp erature). Unit-sp eci c, season-sp eci c (i.e. ozone season or o/-season)
measures of these two imp ortant op erating parameters are obtained by estimating regression
equations separately for each unit and season. The following general sp eci cation is estimated:
= is + X0 its is + "its;
can b e interpreted as the
i
unitzits
56
where zi
is the op erating characteristic of interest (i.e. heat rate or emissions rate) and X is a matrix of
variables that a/ect a unit s op erational p erformance (ambient temp erature and capacity
factor). Because the variables in X are demeaned, the intercept a
sp eci c. season-sp eci c value of z under average op erating conditions for unit i: These
equations are estimated using all available data and data from hours when units capacity factors
exceeded 5%. Unit sp eci c p oint estimates are summarized in table 2.
App endix 6 : The Unit Commitment Problem
The unit commitment problem (UCP) confronting electricity system op erators has b een
extensively studied in the op erations research literature. The problem obtains decisions for a
sequence of time p erio ds (typically 24 hours of a day). What happ ens in one hour a/ects what
can happ en in subsequent hours; optimal unit commitment in one hour is not indep endent of
solutions in other hours. The following UCP sp eci cation was adapted from Hobbs et al. (2001)
8i; t
min Xiqit= Dts:t: Xitir8t
it+ X qitci it+ X yitUi
Xqitit= S D zitt8tM I
NizitFi
qit + rit
zitM AXi
8i; t
rit
zit M AX S
8i; t
Pi
q it 1 + M xI N Cii 8i; t
qit
it 1
8i; t
+ M xD E C
q
qit
zit 1
+ yit 8i; t
zit
= xit
zit
zit 1 ak i(qit8i; t X) M xF l 8 k ; i ;
owit
t
where the decision variables are:
57
qitthe MW pro duced by unit i in hour t ritthe MW of spinning reserves itA binary variable indicating whethe
provided by unit i in hour t zitA binary variable indicating whether unit binary variable indicating whether u
i is dispatched in hour t: y
T
h
e
p
a
r
a
m
e
t
e
r
s
o
f
t
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p
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e
:
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ct
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p
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tt
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of
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at
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ni
ti
in
p
er
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t
(
m
e
a
s
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in
$/
h
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).
cit
V
ar
ia
bl
e
o
p
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at
in
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c
o
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s
at
u
ni
ti
in
p
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(
m
e
a
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d
in
$/
M
W
h)
.
Ui
tT
h
e
c
o
st
s
of
st
ar
ti
n
g
u
p
u
ni
ti
(
m
e
a
s
ur
e
d
in
$)
.
M
A
X
T
h
e
m
a
xi
m
u
m
pr
o
d
u
ct
io
n
c
a
p
a
ci
ty
of
u
ni
ti
.
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I
Ni
iT
h
e
m
in
i
m
u
m
pr
o
d
u
ct
io
n
c
a
p
a
ci
ty
of
u
ni
ti
(a
s
s
u
m
e
d
to
b
e
0
fo
r
al
li
)
M
xI
N
Ci
M
a
xi
m
u
m
ra
m
pu
p
ra
te
fo
r
in
cr
e
a
si
n
g
pr
o
d
u
ct
io
n
at
u
ni
ti
M
x
D
E
C
M
a
xi
m
u
m
ra
m
pd
o
w
n
ra
te
fo
r
d
e
cr
e
a
si
n
g
pr
o
d
u
ct
io
n
at
u
ni
ti
.
ak
iiL
in
e
ar
iz
e
d
c
o
e
¢
ci
e
nt
re
la
ti
n
g
b
u
s
i
in
je
ct
io
n
to
li
n
e
k
o
w
.
M
x
Fl
o
wi
t
M
a
xi
m
u
m
M
W
o
w
o
n
li
n
e
k
in
p
er
io
d
t.
In
th
e
re
st
ru
ct
ur
e
d
el
e
ct
ri
ci
ty
m
ar
k
et
s
c
o
n
si
d
er
e
d
in
th
is
p
a
p
er
,
m
ar
k
et
p
ar
ti
ci
p
a
nt
s
s
u
b
m
it
bi
d
s
7t
o
a
n
in
d
e
p
e
n
d
e
nt
s
y
st
e
m
o
p
er
at
or
(I
S
O
).
U
ni
t-l
e
v
el
pr
o
d
u
ct
io
n
a
ct
iv
iti
e
s
ar
e
c
o
or
di
n
at
e
d
vi
a
a
t
w
os
et
tl
e
m
e
nt
m
ar
k
et
s
y
st
e
m
.
A
d
a
y
a
h
e
a
d
fo
r
w
ar
d
m
ar
k
et
s
c
h
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ul
e
s
re
s
o
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e
s
a
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d
d
et
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in
e
s
h
o
ur
ly
pr
ic
e
s
fo
r
th
e
fo
ll
o
w
in
g
d
a
y;
a
b
al
a
n
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n
g
m
ar
k
et
e
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s
ur
e
s
th
at
s
u
p
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m
e
et
s
u
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in
g
d
e
m
a
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re
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ti
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e.
O
n
c
e
g
e
n
er
at
or
s
h
a
v
e
s
u
b
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e
d
th
ei
r
s
u
p
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s,
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d
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u
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c
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it
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e
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b
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to
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s
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d
s
of
u
ni
t-l
e
v
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a
n
d
s
y
st
e
m
-l
e
v
el
o
p
er
at
in
g
c
o
n
st
ra
in
ts
.If
r
m
s
a
ct
a
s
pr
ic
et
a
k
er
s,
s
u
b
m
itt
in
g
bi
d
s
th
at
re
e
ct
tr
u
e
c
o
st
s
a
n
d
o
p
er
at
in
g
c
o
n
st
ra
in
ts
is
a
li
k
el
y
to
b
e
a
pr
o
t
m
a
xi
m
iz
in
g
st
ra
te
g
y
(
G
ro
s
s
a
n
d
Fi
nl
a
y,
1
9
9
6)
.
R
e
f
e
r
e
n
c
e
s
B
.
H
o
b
b
s
,
M
.
R
ot
h
k
o
pf
,
R
.
O
N
ei
ll,
a
n
d
H
.
C
h
a
o.
2
0
0
1.
T
h
e
N
e
xt
G
e
n
er
at
io
n
of
El
e
ct
ri
c
P
o
w
er
U
ni
t
C
o
m
m
it
m
e
nt
M
o
d
el
s.
Kl
u
w
er
.
7T
h
e
d
i/e
re
nt
re
gi
o
n
al
e
le
ct
ric
ity
m
ar
ke
ts
re
q
ui
re
g
e
n
er
at
or
s
to
su
b
mi
t
bi
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s
in
di/
e
re
nt
f
or
m
s.
F
or
ex
a
m
pl
e,
th
e
N
e
w
Y
or
k
IS
O
s
e
p
ar
at
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s
e
n
e
rg
y
b
id
s
int
o
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ar
tu
p
co
st
cu
rv
es
a
n
d
a
n
e
n
er
gy
cu
rv
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hi
ch
ca
n
b
e
a
th
re
e
p
ar
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or
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6
s
e
g
m
e
nt
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ec
e
wi
se
lin
e
ar
c
ur
ve
.
5
8
G.Gross and D.J. Finlay, 1996, Optimal bidding strategies in comp etitive electricity
markets, Pro ceedings of Power Systems Computation Conference (PSCC 96), Dresden, August
19-23, 1996, pp.815-823).
59