Long run equilibrium and environmental policy in the Nord Pool

Long run equilibrium and environmental
policy in the Nord Pool energy markets: A
macroeconomic perspective
Andrew L. Zaeske∗
Centre for Environmental and Resource Economics
Preliminary: Do Not Cite
November 15, 2012
Abstract
Two major forces that have shaped European electricity markets
since the mid-1990s are deregulation and the development of common
electricity markets, e.g. Nord Pool for the Nordic countries, that cross
national borders. This paper utilizes a modified version of a macroeconomic wholesale energy production model first outlined by Andersson
(1997), combined with the macroeconomic tools of Chari et al. (2007),
which allow us to analyze the effects of market frictions on equilibrium
outcomes. We analytically derive formulas, referred to as ‘wedges,’ to
measure these effects in a number of scenarios, importantly for the
cases of carbon taxation and production specific taxes.
Production specific taxes have unclear effects on the final market
price, although most Nordic taxes and subsidies as currently structured are likely to have no direct effects. However, what this static
model is unable to capture are secondary effects, changes in investment behavior that shift the mix of technology available in the future.
Looking at recent production and price data for Nord Pool shows that
coal and biomass have been the marginal technologies in recent years,
so policies which affect those technologies will be most likely to shift
∗
Contact E-mail: [email protected]
1
the overall market price. Differences in national policy goals and the
need to measure the effects these policies have on firm investment
behavior highlight the need for a dynamic version of this model.
1
Introduction
Deregulation has been a major force in European electricity markets since
the mid-1990s and has run concurrently with the development of common
electricity markets that cross national borders, e.g. Nord Pool for the Nordic
countries. Differences in regulatory policy, primarily terms of direct taxes on
specific types of production and indirect taxes on outputs of certain production processes (e.g. CO2 , SO2 , N Ox ) will not only lead to differing mixes
of power generation technologies being used but may also affect the market
price in all countries. It is crucial to be able to assess what differences in
market structure and tax policy will have on energy prices and the mix of
technologies used in a common market.
This paper utilizes a modified version of a macroeconomic wholesale energy production model first outlined by Andersson (1997) combined with the
macroeconomic tools of Chari et al. (2007) to analyze the effects of market
frictions (e.g. taxes) on equilibrium outcomes. Formulae are analytically derived for gaps in efficiency and prices, referred to in the literature as ‘wedges,’
which provide values for these distortionary effects as functions of model parameters. This paper looks at a number of important scenarios that are seen
in practice, particularly the cases of production and capacity taxes and subsidies.
Examining analytical relationships, we find some fairly standard results.
Cournot competition lowers output and raises prices relative to a competitive market. Due to the price setting mechanism, production specific taxes
will have unclear effects on the final market price. As currently structured,
most Nordic taxes and subsidies are likely to have no direct effects on prices
because they target technologies with marginal costs far below recent market
prices. Accounting for investment targeting policies shows that they should
all increase firm’s desire to invest, although this may not always translate
into investment. Spillovers are all but impossible to account for analytically
without making a myriad of assumptions about the cost structure of the
2
underlying market.
Looking at price and supply data for the Nordic electricity market, Nord
Pool Spot, allows for some basic evaluations of current policies. In recent
years, the marginal production technologies in Nord Pool are either coal
or biomass, with oil and gas being the backstop technologies, the high cost
backups for the types of short term fluctuations this analysis is not concerned
with. This suggests that policies which make these marginal technologies
more expensive, such as carbon or other types of emissions taxes, should cause
an increase in the system price for electricity. Additionally, taxes or subsidies
which discourage future investment in low marginal cost technologies, which
for Nord Pool includes both renewables and nuclear power, would also be
expected to raise the market price, in this case through the restriction of
cheap generating capacity.
Section 2 outlines the model. Section 3 provides a brief background of the
‘wedge’ method and gives some analytical results for the model, while section
4 provides a brief empirical discussion for the case of the Nordic electricity
market. Section 5 concludes.
2
Model
The model utilized by this paper is an adapted version of a wholesale electricity production model first presented in Andersson (1997). This paper makes
two major additions, treating capacity as the result of an investment decision
and not as a fixed exogenous quantity and applying the methods of Chari
et al. (2007) to assess the causes of any deviations from a frictionless perfectly competitive market outcome. This section will discuss the elements
of a wholesale electricity market before outlining the determinants of the
market equilibrium.
2.1
Production
Let there be R regions indexed by r. For simplicity of exposition and
notation, we consider each region to have one firm and use the terms region and firm interchangeably. Results extend to the firm level if we expand this discussion to allow each region to have Ir electricity producing
firms.Additionally time subscripts are omitted whenever possible, which in3
terpretationally is okay because each production decision takes place wholly
within a single period. Therefore, in each period total electricity production
will be
X
E=
Er ,
r
and each firm has a convex cost function associated with its production
decision,
Cr = Cr (Er , Kr ) ,
(2.1)
with Kr denoting total production capacity. This Cr should be thought of as
the ordered composition, from lowest to highest, of individual cost functions,
Crj (Erj , Krj ), for each possible technology j.
Following Raineri and Contreras (2010), investment is considered to be
lumpy, with a schedule of potential projects available to each firm, indexed
by α. Zrα is the indicator variable for whether project α is undertaken
or not, crα represent the per unit of capacity cost of that project and Krα
its capacity size. Each firm is allowed to borrow brt to fund any projects it
wishes to pursue from a perfectly competitive capital market at an exogenous
interest rate, R. This leads to the following law of motion for capacity and
an endogenous borrowing constraint,
X
Zrα crα Krα ,
(2.2)
Kr(t+1) = Krt +
α
brt ≤
X
Zrα crα Krα .
(2.3)
α
The final element that affects the firm’s production decision is the shadow
price associated with production capacity constraints, which will be discussed
in Section 2.3.
2.2
Demand
Demand is viewed at an aggregate level, with a single demand function for
each region. With each region presumably containing a large number of
small electricity consumers, we can safely assume that this market is perfectly
competitive and thus that demand is purely a function of price and aggregate
4
income. This is equivalent to assuming that retail provision of electricity is
competitive. Encapsulating demand in this way allows our model to focus
on production behavior at the expense of being able to account for short run
fluctuations in demand.
With this long run viewpoint in mind, we will have that,
Dr (Pr ) = Sr = Sr0
Pr
Pr0
ηrp
y
p
y
eηr Yrt = βr Prηr eηr Yrt ,
(2.4)
where ηrp is the price elasticity of electricity demand, ηry is the income elasticity of demand and Yrt is regional income. The other parameter, βr , can be a
considered a normalization that is related to the initial level of demand, Sr0
and the initial price, Pr0 . Rearranging this equation, we have the following
expression for prices,
Pr =
2.3
Pr0
Sr
Sr0
1/ηrp
−
e
y
ηr
p Yrt
ηr
y
ηr
=
p
p − p Yrt
βr−1/ηr Sr1/ηr e ηr .
(2.5)
Transmission
Regions do not necessarily need to directly correspond to countries, but each
region is assumed to be completely contained within a country where electricity transmission is run by a state-owned monopoly.1 So if capital expenditures are assumed to be zero, the price charged for transmission will be equal
to the marginal cost of transmission plus the marginal cost of congestion. By
definition, production within a region is equal to the sum of all of its sales2
made to all regions. Similarly, total sales to a region are equal to deliveries
from each region minus any transmission losses. Mathematically, these two
statements say that
X
Er =
Sjr ,
(2.6)
j ∈R
Sr =
X
(1 − δjr ) Sjr ,
(2.7)
j ∈R
δrr = 0, 0 ≤ δjr ≤ 1 ∀j 6= r,
1
2
This is precisely the case within Nord Pool.
A term that will be used interchangeably with deliveries throughout the discussion.
5
where Sjr are sales from a firm i in region j to region r, Sr is total sales
to region r and δjr is the transmission loss for a delivery from region j to
region r. Transmission losses are assumed to be zero within a region and are
allowed to take any value between zero and one for deliveries made to any
other regions. Take note that δjr = 1 would indicate some barrier preventing
electricity sales from j to r, e.g. an embargo or a lack of transmission capacity
linking the two regions, analogous to Mij = 0 in equation (2.8).
Finally, we have to account for the two marginal costs of congestion:
one in transmission and one in capacity. The marginal cost of transmission
congestion is inherited directly from constraints on transmission capacity
between regions, Mrj or Mjr . We have that,
Srj + Sjr ≤ Mrj = Mjr
∀r, j ∈ R
(φrj ) ,
(2.8)
where φrs represents the congestion rent and will also be the Lagrange multiplier associated with this constraint in each firm’s optimization problem.
Similarly, the marginal cost of capacity congestion is derived from the
limit existing capacity places on a firm’s ability to sell (produce),
!
X
(1 − δrj )Srjt × (1 − γr ) ≤ Krt
(λ1rt ) ,
(2.9)
j
where the parameter γ represents a “peak-load premium” to account for
seasonal demand spikes that must be met in reality but will be observed
with the time frame and type of data we hope to utilize. The marginal value
of capacity, λ1t, will be zero as long as there is excess capacity.
2.4
Equilibrium Conditions
Under perfect competition, each producer will solve the following profit maximization problem,
X
T
X
X
t
max
β
Prjt (1 − δjr ) Srjt − Cj (Ej , Kj ) + br(t+1) − Rbrt −
Zrαt crαt Krαt
t=0
α
j
!
+ φjr (Mjr − Sjrt − Srjt ) + λ1t
(1 − γr )Kt −
X
(1 − δjr ) Srjt
j
!
+ µrt Krt +
X
Zrα Krα − Kr(t+1)
α
+ λ2rt
X
α
6
!
Zrαt crαt Krαt − br(t+1)
,
by choosing a set of Srjt , Zrαt and br(t+1) s, given Prjt and all parameter values.
In the case of perfect competition in wholesale electricity production, then
each producer will have the following first order condition for total sales in
region r,
∂Cjr
Pr (1 − δjr ) −
− φjr − (1 − δjr )λ1rt ≤ 0,
∂Ejr
∂Cjr
⇒
+ φjr / (1 − δjr ) + λ1rt ≥ Pr ,
∂Ejr
(2.10)
for all i, j, r ∈ R. So each firm will be willing to provide electricity for any
region as long as the price, adjusted for transmission losses, is at worst equal
to its marginal cost plus any congestion costs.
Additionally, we have the following two shadow prices for capacity, investment and borrowing, respectively.
1
µ − µr(t+1) + ∂K∂C
β rt
r(t+1)
,
λ1r(t+1) =
1 − γr
µrt = cαr (1 + λ2rt ) ,
λ2rt ≤ βR − 1.
The final two conditions combine to provide a bang-bang solution for borrowing; only if R ≤ β1 will the firm will borrow to pay for all new capacity projects
that satisfy Prt > cαr βR. This includes all projects that the firm would desire to invest in regardless of its ability to borrow, plus extra projects that
become desirable because the repayments are lower than the value of added
capacity. In such a case βR, can be thought of as a borrowing “discount” on
capacity.
If we assume perfectly functioning capital markets, then outside investors
would set R = β1 to avoid such “overinvestment.” This implies that λ2rt = 0
and lets us simplify the expression for the shadow price of capacity as follows,
cαr β1 + ∂K∂C
r(t+1)
λ1r(t+1) =
.
(2.11)
1 − γr
Conditional on a lack of congestion, aggregate supply and demand for
the entire system will determine, the price, quantity and set of technologies
7
that are used for production. Crucially, this will identify the technology
used to produce the marginal unit of electricity, or marginal technology,
the cost of which will set the system price according to (2.10). Due to
the structure of individual firm cost functions, this equation generally will
not hold exactly for all technologies for each firm, only for the marginal
technology (or possibly technologies) used. For example, if every method of
production has constant marginal costs, then this equation will hold exactly
for the marginal technology alone.
If transmission or production capacity are insufficient, that is congestion of any type is present anywhere in the system, then the system supply
curve will contain discontinuities and it is possible that there will be different
marginal technologies on either side of any congestion, so there will no longer
be a single price throughout the system. Electricity exporting region prices
will be set purely by their own technologies, while importing regions will
have prices determined by the mix of technologies available after congestion
becomes a factor and the amount of the demand in excess of what can be
delivered without congestion.
3
Analytical Wedge Scenarios
To characterize the inefficiency introduced by a variety of market frictions,
we adopt the wedge method of Chari et al. (2007), originally developed to
describe fluctuations in business cycles as deviations from the outcome of an
efficient (e.g. frictionless) model. Differences between right and left hand
sides of each first order condition are tracked as a new variable, a so-called
“wedge” for the variable that particular first order condition determines. If a
wedge is zero, that simply means that the outcome of our variable of interest
is efficient, in the sense that it is exactly what a social planner would choose
in a frictionless world. Empirically, these wedges are often assumed to be
caused by undetermined market frictions, with possible causes outlined in
any analysis. However, with a more detailed model which assumes particular
policies, it is possible to analytically determine the value wedges will take as
a function of model parameters.
To do this, a market frictions are included directly into the model, i.e.
the assumption of a specific type of tax or subsidy. Examining the first
order conditions, it is often possible to rearrange the result mathematically
8
as either the sum or product of two parts, one being the first order condition
from the case without the friction while the remaining portion is defined as
the wedge. Repeating this process yields an expression for each wedge in
terms of model parameters, which can then be compared to data or assessed
using parameter values from relevant academic literature.
In our case, the wedges can be viewed as production or transmission
frictions as they will affect Sjr , Er or Kr , sales, production and capacity, respectively. The final interpretation depends solely on how the friction enters
the model and through what mechanism it alters producer behavior. One
obvious result from looking at prices, is that if any policy has no effect on the
choice or amount of production of the marginal technology, then it will only
reduce profits of any firm that uses the technology that the policy targets
and not affect quantities produced. Otherwise, the cost of this policy will
be passed on to consumers in the form of higher prices. To further aid with
interpretation, in this paper we also solve each first order condition for the
market price of wholesale electricity whenever applicable. This will generally allow for the expression of the price for any policy scenario to be given
as the competitive price plus a price distortion caused by the intervention.
This price distortion can be can be viewed as a price wedge, a way of viewing the marginal cost of the policy in terms of the change in the amount of
production each firm is willing to engage in.
To provide a simple example of this procedure in a non-policy oriented
context, we examine the wedge that would be caused by the presence of
market power in the case of Cournot competition. With Cournot competition
(simultaneous quantity competition), each region j will have the following
first order condition for total sales in region r,
∂Prt
∂Cjrt
Prt + Sjrt
(1 − δjr ) −
− φjrt − λ2rt = 0,
∂Sjrt
∂Ejrt
∂Prt
∂Cjrt
Prt (1 − δjr ) −
− φjrt − λ2rt = −Sjrt (1 − δjr )
∂Ejrt
∂Sjrt
∂Prt
⇒ ∆jrt
Cournot = −Sjrt (1 − δjr )
∂Sjrt
for all j, r ∈ R. Again we can see that if the wedge is zero, then we simply
have perfect competition, as the left hand side of the last two lines should
be recognizable at the first order condition under perfect competition.
9
In price terms the relationship between Cournot competition and perfect
competition can be expressed as follows,
PrtCournout
=
=
∂C
∂Ejrt
∂Prt
+ φjrt + λ2rt − Sjrt ∂S
jrt
(1 − δjr )
PrtP C
−
∂Prt
Sjrt ∂S
jrt
(1 − δjr )
.
∂Pr
Of particular note in this example is that ∂S
will be negative if as long as
jrk
the price elasticity of electricity demand is negative, so the Cournot wedge is
positive. The price premium due to firm’s market power is equal to the effect
their production has on price times the quantity of their production, with an
adjustment for transmission losses if applicable. A number of studies have
been done to assess market power in Nord Pool,3 but none has yet found
evidence of long-term exploitation of market power. An empirical exercise
with this method provides an alternative method to assess market power,
particularly at the system-wide level.
Now we can provide solutions for and discussions of the wedges for a
number of potential policy interventions related to the electricity market.
Again, time subscripts will be omitted except for the discussion of investment/capacity wedges, since all other effects are static in nature.
3.1
Technology Specific Production Tax/Subsidy
As might be expected, a lump sum tax (i.e. a flat per firm tax) will not
show up in the first order condition and thus only affect the final profits of
the firms and not directly alter the price level. This may shift the preference
ordering of technologies, but only if a firm is driven out of business and this
shifts which technology is the marginal technology. Prices will be unaffected
unless such a scenario occurs.
Alternatively, we can look at per unit production taxes, e.g. a levy of
τrk for each unit of production Erk . This type of taxation will lead to the
following equilibrium price condition,
Prτ = PrP C +
3
τrk
,
(1 − δjr )
See Fridolfsson and Tangers (2008) for a recent survey of these assessments.
10
(3.1)
where the tax increases the price additively and is mitigated by any transmission losses between the sources of energy production (and thus the taxation)
and demand. The magnitude of the tax’s final effect on the system price will
depend on the relative importance of the technology and the producer to the
system supply. It does not just matter how big of a share of total production a particular technology has, but where the technology places, marginal
cost-wise, relative to other technologies.
A per unit production subsidy has a similar effect as a per unit production
tax, with the sign of the distortion reversed.
σrk
Prσ = PrP C −
,
(3.2)
(1 − δjr )
This is not surprising, since subsidies can be viewed as negative taxes.
These policy instruments are particularly useful for analysis because they
do match both past and present policies, e.g. Danish wind subsides and
Swedish nuclear power taxes (Rydén, B., 2006).
3.2
Emissions Taxes
To encapsulate a tax on any specific type of emissions, we further assume
that each firm also has a convex emissions function,
Xr = Xr (Er ) ,
(3.3)
the exact form of which will be dependent on the available production technologies in region r. While this paper will focus on the case of carbon, this
could just as easily be applied to other pollutants such as sulfur dioxide (SO2 )
or nitrogen oxide (N Ox ).
Additionally, let there be an exogenously determined price of carbon,
pCO2 , that each firm will be charged for its emissions- A carbon market such
as the EU Emissions Trading Scheme would be an example of a mechanism
by which the carbon price is set. As long as electricity providers do not
have a large enough share of such a market to set prices, then this reduced
form mechanism would provide a reasonable description of the participation
of electricity producers in that market. These firms have perfect foresight
with respect to production and its effect on emissions and thus they will
with certainty purchase the correct amount of permits ahead of time without
incurring any penalties that may be present in the carbon market.
11
With these assumptions, the carbon price wedge will be,
PrCO2
=
PrP C
+ pCO2
∂Xj
∂Sjr
(1 − δjr )
,
(3.4)
the price times the marginal damage done by an additional unit of production.
Another factor which may be important is that there are some electricity
generating technologies, namely combined heating and power (CHP), which
one would suspect are emissions intensive but which also create an additional
economic good that is sold, heat. The inclusion of a non-separable emissions
function, such as one that interacts with the cost function, may be able
to account for this linkage. It would certainly lead to a more complicated
emissions price wedge, as heating lost through a reduction in CHP would have
to be replaced, perhaps by a process with higher emissions. Such functional
forms should be considered in a more careful empirical exercise.
3.3
Investment/Capacity Interventions
Three common forms of subsidies affecting capacity are direct investment
subsidies, either measured in per unit (σαr ) or lump sum (represented in
normalized per unit terms by `αr ) terms, and preferential interest rates. The
effect on the shadow price of capacity will take the following forms,
1
∂C
cαr βR β − 1
∂Kr(t+1)
rt
λ1r(t+1) = ∆policy
+
,
(3.5)
1 − γr
1 − γr
cαr βR β1 − 1 + ∂K∂C
r(t+1)
λ1r(t+1) =
− ∆rt
(3.6)
lump ,
1 − γr
`αr βR( β1 −1)
1
Rpolicy
rt
with ∆rt
=
−
and ∆rt
. All of
lump
policy = σαr or ∆policy =
1−γr
R
these policies should weakly increase investment in capacity in the targeted
technology, although the policy effect alone may not be enough to push firm
incentives across the threshold for investment.
What is certain, as in the other cases, is that final effects on system
prices and other regions will be unclear. Especially when policies alter the
composition of the system cost curve, as policies of these types likely would,
12
spillovers are inevitable. However, analytically, there is not much that can
be said, due to the complexity of the underlying market.
4
The Nordic Electricity Market in Context
With this mathematical machinery laid out, we now turn to a small empiricalbased discussion. Since switches in technology are crucial in the presented
non-dynamic setting this section undertakers a basic analysis of the Scandinavian common electricity market, Nord Pool. Figure 1 presents the supply
curve for the Nordic market, arranged by ascending marginal costs (a socalled merit order curve).
Figure 1: Nordic Electricity Production
Source: Blesel, et al. 2008
Wind power’s marginal cost is actually negative, because there are per
unit production subsidies in Denmark, where it is primarily produced. Next
are nuclear and hydroelectric, which have roughly equivalent marginal costs,
although each have high initial capital costs and hydroelectric can be subject
to climate and seasonal fluctuations. Finally, we have the thermal methods
of generation, which range from coal up to gas, which is the final backstop
13
technology for the Nordic electricity market. In 2010 the mean price was
0.50 SEK per kWh, corresponding to total system production of 380 TWh.
Since Nord Pool fully integrated the individual Scandinavian markets
in 2000, the most common location for congestion has been the connector
between Denmark and Sweden. Because of the price setting mechanism,
this means that policies on the side with shortages, in this case the Danish
side, are the most likely to affect the final regional price. Crucially, thermal
power sources, such as oil, coal, gas and biomass, make up less than ten
percent of total Nordic electricity production overall, but they make up nearly
75% of Danish production sources (Danish Energy Association, 2009). So
congestion driven shortages in Denmark will lead to shifts towards higher
cost production methods within the country, if available, and possibly lead
to an increase in exports from outside of Nord Pool, in this case Germany.
The mean price for the two Danish regions were respectively 0.443 SEK and
0.544 SEK, with the lower price region having a connection to Norway, in
addition to the separate links to Sweden and Germany that each region has.
The marginal technology in general is thermal, either coal or biomass,
and may even be oil or gas depending on short-term congestion patterns.
This suggests two types of policies that will increase the system price. First,
since the marginal technologies are likely to cause higher emissions than the
lower marginal cost alternatives, this makes them more likely to be affected
by carbon taxation, although that is not strictly the case in every country.
For example, in Sweden wholesale electricity producers are exempt from the
EU ETS. Secondly, taxes or subsidies which discourage future investment in
low marginal cost technologies, which in the case of Nord Pool includes nuclear power, would be expected to raise the market price through restricting
supplies of electricity. In this sense, policies such as Sweden’s nuclear generation tax may have negative effects unless they are counterbalanced with
policies promoting alternative sources of production.
Policies not covered in the analytical exercises, such as Sweden’s plans
to phase out nuclear power, could have large effects as well. If not quickly
replaced by other sources of generation, this would increase Denmark’s reliance on Norway and Germany for balancing power. This could easily be
expected to lead to carbon leakage in addition to having the potential to
shift prices up in the highly populated southern Nord Pool regions of Sweden. Even if this lost nuclear generating capacity is replaced by new plants in
14
Finland, transmission congestion means that these types of effects may still
be present. This further highlights the need for a detailed analysis of the
cross-country effects of future policies, especially since each Nordic country
seems to be focusing on a different type of electricity generation, even if there
is a common overall goal of increasing the share from renewable sources.
5
Conclusion
The existence of energy policy differences across countries that share common
electricity markets requires tools to examine both the national and marketwide effects. This paper modifies the model of Andersson (1997) to allow for
emissions that may be taxed and to make the market price setting mechanism
more concordant with what is observed in common markets such as Nord
Pool. Applying the macroeconomic tools of Chari et al. (2007) to this model,
allows us to show how deviations from a perfectly competitive equilibrium
may be caused by policy interventions. We analytically derive formulae for a
variety of different market distortions to provide measures of their distortions
in terms of model parameters.
Cournot competition lowers output and raises prices relative to a competitive market. Because the technology which produces the marginal unit
of electricity primarily sets the price, production specific taxes will not effect
the final market price unless it affects the marginal technology. Examining current Nord Pool data shows that most Nordic taxes and subsidies as
currently structured are likely to have no direct effects because they target
technologies which cost far below recent market prices to operate.
More than just including such static effects, this model attempts to capture secondary effects, changes in investment behavior that shift the mix of
technology available in the future. Capital subsidies, like Danish subsides
for wind power and some hydroelectric subsidies in Norway and Sweden,
seem likely to have large effects on the availability of technologies, but overall system effects are difficult to parse analytically. This model provides a
solid foundation for an empirical exercise to more deeply explore such issues
and determine the spillover effects that policies have in a common wholesale
electricity market setting.
15
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16