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markets: A macroeconomic perspective Andrew L. Zaeske∗ Centre for Environmental and Resource Economics Preliminary: Do Not Cite November 15, 2012 Abstract Two major forces that have shaped European electricity markets since the mid-1990s are deregulation and the development of common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 References Andersson, B. (1997). Essays on the Swedish Electricity Market. PhD thesis, Stockholm School of Economics. Chari, V. V., Kehoe, P. J., and McGrattan, E. R. (2007). Business Cycle Accounting. Econometrica, 75(3):781–836. Danish Energy Association (2009). Danish Electricity Supply ’08. Statistical survey. Fridolfsson, S.-O. and Tangers, T. (2008). Market power in the nordic wholesale electricity market: A survey of the empirical evidence. Working Paper Series 773, Research Institute of Industrial Economics. 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