Free EUAs and fuel switching

Energy Economics 35 (2013) 14–21

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Free EUAs and fuel switching Paolo Falbo a,⁎, Daniele Felletti b, Silvana Stefani b a b

University of Brescia, Department of Quantitative Methods, C.da S. Chiara 48b, 25100 Brescia, Italy University of Milano Bicocca, Department of Quantitative Methods for Economic and Business Sciences, U7, Piazza Ateneo Nuovo 1, 20126 Milano, Italy

a r t i c l e

i n f o

Article history: Received 16 January 2011 Received in revised form 18 December 2011 Accepted 18 December 2011 Available online 24 December 2011 JEL classification: Q40 Q42

a b s t r a c t This paper focuses on the impact of EUAs on the optimal policy of a competitive electricity producer. The effect of grandfathering is consistently shown to introduce significant distortions to the system. It is theoretically shown that there is a threshold value of carbon price so that, for prices above this, the EUA becomes an incentive for reduced production rather than a penalty for inefficient producers. These theoretical results are supported by the data of one producer from Italy and one from Germany. Furthermore, the empirical evidence concludes that the high level of free allowances may generate a shift in production from less to more polluting technologies. © 2011 Elsevier B.V. All rights reserved.

Keywords: Emission markets Electricity production Renewable resources EUA Green Certificates

1. Introduction Under the Kyoto Protocol, the EU has committed itself to the reduction of GHG emissions by 8% compared to the 1990 level, by the years 2008–2012. To this end, the European Union has adopted a European Union-wide Emission Trading Scheme (EU ETS) in order to reduce CO2 emissions by companies from the energy and other carbon-intensive industries. The trading system started operating officially on January 1st, 2005. The EU ETS envisaged three time phases: Phase I (2005–2007), a “warm up” period, Phase II (2008–2012), which coincides with the Tokyo commitment period, Phase III (2013–2020), the post-Tokyo commitment period. At the beginning of each phase, each country has to present a national allocation plan defining how many EUAs each (major) emitter will get in this phase. For all emissions produced each year, the emitter must have the corresponding allowances. Therefore, he can decide whether to abate emissions in-house or to buy allowances on the market. The expected result of this system is to limit CO2 emissions by introducing a penalty for each ton of CO2 emitted over the agreed quantity. For the origins and motivations of the trading scheme refer to Abadie and Chamorro (2008), Benz and Trück (2009) and Convery (2009).

⁎ Corresponding author. Tel.: + 39 030 2988 531; fax: + 39 030 2400 925. E-mail addresses: [email protected] (P. Falbo), [email protected] (D. Felletti), [email protected] (S. Stefani). 0140-9883/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.eneco.2011.12.007

During Phases I and II, at least 95% and 90% of allowances respectively were generously grandfathered, i.e., distributed free of charge, to polluting industries based on historical data on emissions or fuel use. According to this scheme, carbon intensive plants received more free certificates than “cleaner” natural gas plants (see for example Jaehn and Letmathe (2010) and Pahle et al. (2011)). As discussed in Böhringer and Lange (2005), Bode (2006), Convery (2009) and, especially, Markussen and Svendsen (2005), carbon-intensive industry lobbies strongly conditioned the final design of the ETS. This is confirmed by Yu-Bong (2008), who develops a theoretical analysis based on a two stage lobbying game. He finds that when the ratio of initial permits to the total permits is high, the industries will support grandfathering rather than auctioning. Grandfathering has been criticized on different grounds. First, it has been consistently shown that the energy industry, especially emitters of a carbon intensive technology mix, has profited from emissions due to the consequent increase in electricity prices which has penalized downstream industries and private consumers (Bode, 2006; Jaehn and Letmathe, 2010; Lee et al., 2008). Second, it has been argued that grandfathering is equivalent to a government subsidy that creates an artificial incentive for market participants to keep operating older or less efficient plants (Clò, 2010). Third, as Pahle et al. (2011) have pointed out, grandfathering can be the basis of a considerable number of new coal power plants, i.e. plants that are more polluting than “cleaner” gas plants, added to Germany power mix between 2005 and 2009 or planned for the future. This is a puzzling result with respect to the EU ETS general objectives, especially if the

P. Falbo et al. / Energy Economics 35 (2013) 14–21

inclusion of alternative clean resources is considered an important way to achieve emission reduction. Quite surprisingly, there is relatively little literature focusing on the direct effects of grandfathering on the electricity producers policy and the possible effects on the decision to convert to less polluting technologies. Using qualitative arguments, Cramton and Kerr (2002) show that auctioning is preferred to grandfathering because, among other things, it provides greater incentives to innovation. Similar conclusions are also reported in Woerdman et al. (2008). Pahle et al. (2011) develop a macro-economic analysis and introduce an NPV based decision model to invest in different technologies (lignite, hard coal and gas). By a numerical analysis they show how such a preference depends heavily on three alternative ways to allocate EUAs: NAP1 (the current allocation rule), NAP2 (the more restrictive allocation planned for the 2nd phase), and AUC (a full auction allocation). By a linear programming model, Klingerhofer (2009) shows that in general, even without grandfathering, tradable permits have several effects on investments and do not always encourage environmentally beneficial projects. This paper models the expected profit of a producer generating electricity from a fossil resource, including the option of non-producing and selling the unused allowances on the market. The expected profit does not depend monotonically on the price of EUAs and a threshold emission price pA* exists that turns the EUA into an incentive to polluting producers, since, for emission prices pA > p*, A a rise of pA increases the polluter's profit (due to the sale of unused EUAs). pA* is an individual parameter, since it depends on the pollution coefficient k and on the efficiency of each plant. The dependence of pA* on k is negative, that is the higher k is, the lower pA* becomes. This implies that the range (p*,+ ∞) in which an intensive CO2 emitter enjoys is A wider. The same distortion occurs for high levels of grandfathering: increasing the amount of free allowances lowers the value of p*. A Again, the range (pA*,+ ∞) in which an intensive CO2 emitter enjoys is wider and such economic distortion occurs more frequently. Remember, that in Phases I and II at least 95% and 90% of allowances were grandfathered. Furthermore, as an empirical application and refinement of the theoretical analysis, we consider the case of an electricity producer comparing different generation technologies, conventional and renewable (i.e. gas, coal, wind). These are analyzed to decide whether switching to less polluting technologies is a profitable investment alternative. The aim is to establish whether renewable plants, endowed with incentives (Green Certificates at price pGC), mitigate the extensive use of polluting plants and if the ETS with grandfathered EUAs motivates a switch to renewables. The cases of two different electricity producers, one in Italy and one in Germany are analyzed, for different degrees of grandfathering (from a grandfathering quota α = 0 to α = 92%). In some cases the three technologies generate the same expected profit, so the use of renewables or cleaner fossil production (gas) can be more profitable for some pairs (pA, pGC). However, this does not occur under conditions of strong grandfathering (α = 92% like in Phase II). Both for Italy and for Germany, gas plants are no more profitable and production from coal predominates. Renewables are more convenient in a limited price range. This paper is organized as follows: in Section 2 the theoretical model for an electricity producer from a conventional source is set out. In Section 3 the definitions in Section 2 are extended to the wind plant and generalized to include the Green Certificates. The empirical application based on the German and Italian electricity markets follows in Section 4. Section 5 is the conclusion. 2. The model 2.1. The profit function Consider the profit function of a thermal plant with nominal capacity Q. The producer is supposed to receive, free of charge, a

15

number of emission permits equal to αQ, that is a percentage of his production capacity. Let p be the unit price of electricity (€/MWh) fixed on the electricity market. Assuming an affine cost function, the production of 1 MWh has a variable cost equal to c €/MWh (mainly represented by fuel) and a fixed operational and maintenance hourly cost of cm €/MWh (€/h per MW of nominal capacity). When the plant is turned on, it emits k tons of CO2 per MWh (or CO2 equivalent green-house gases). As a consequence of the cited European directive, all the emissions must be “covered” by a corresponding number of EUAs, so, for every unit of energy, the producer must buy a quantity of emission allowances equal to (1 − α)k. The price of an emission certificate (pA) is quoted daily on the market. Let's assume here that at a macro-economic level there is no influence of pA on p, which is debatable. Particularly in the electricity sector where the level of competition is low. However such an assumption can be acceptable as long as some friction exists in transferring the variations of production costs to sale price, at least when the price changes are relatively small. Depending on the daily economic conditions, the producer decides whether it is convenient to activate his plants or not. The cost of switching the plant on and off and the physical limits of the ramp rate are not included here. The producer assesses these two alternatives: • if he decides to activate the plants his profit is Q ðp−c−ð1−α ÞkpA −cm Þ • if he decides to keep his plants off line, he saves the cost of fuel and can sell the unused certificates. So his profit is Q ðαkpA −cm Þ: Thus the decision to activate the plant can be reduced to p−c−ð1−α ÞkpA > αkpA that is p > c þ kpA :

ð1Þ

Such a decision is nothing but a specification of what is called a “clean spark spread” option (in the particular case of an electricity producer using gas plants, or “clean dark spread” in the case of coal), that is the option to start production only when it is profitable (Falbo et al., 2010). Note that such a decision is not affected by the level of α. With respect to the classical formulation, the term kpA introduces a specific analysis of the impact at a micro-economic level of the EUA system. Regarding Eq. (1), since kpA is positive, the plant will be kept shut off more often than not in the absence of an EUA market. This is true even when p is affected by pA. The gross profit (G) function is ( G¼

Q ðp−c−ð1−α ÞkpA −cm Þ Q ðαkpA −cm Þ

if p > c þ kpA ¼ if p≤c þ kpA

ð2Þ

¼ Q ðαkpA þ maxðp−c−kpA ; 0Þ−cm Þ: In the specification of the gross profit let's observe the typical payoff of the previously mentioned call option on the spark/dark spread p–c corrected by the effect of carbon price. The producer charges the consumer for the full cost of CO2, which is just partially absorbed by the price of electricity, according to the allotment of market power among the producers. Since the demand curve of electricity is almost rigid, the carbon price is fully reflected in the price of electricity both when the market is driven by agents with strong market power (this is obvious) and also when it is very competitive. The reason is that, in the latter case, the market price

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of the electricity is close to the marginal cost of the marginal plant, which includes the full carbon cost (as shown by condition 1). 1

E[G]

2.2. Some considerations The average hourly profit of the plant is the expected value of the hourly profit in Eq. (2): E½G ¼ Q ðαkpA þ E½maxðp−c−kpA ; 0Þ−cm Þ

ð3Þ

pA is stochastic like p and c because EUAs are continuously traded on several markets, anyway pA is considered as a constant parameter in the following. If the derivative of E[G] is analyzed with respect to pA (see Appendix A), it appears not to be always negative, as could be expected: dE½G ¼ Qkðα−P ½ p > c þ kpA Þ dpA

ð4Þ

where P[⋅] is the probability of event [⋅]. For the purposes of this analysis, there is no need to specify a particular form for P. The assumption that it is continuous in its arguments suffices. The event considered in Eq. (4) coincides with that in Eq. (1), that is the economic condition required to activate the production. Let pA* be the price of emission certificates so that   α−P p > c þ kpA ¼ 0: As shown in Fig. 1, pA* is the point of minimum for Eq. (3) because the profit function is convex: d2 E½G 2 ¼ Qk ρðc þ kpA Þ≥0 dp2A where ρ(p) is the probability density of the electricity price. Hence pA = pA* is the most unfavorable condition for the producer. The profit function has economic consistency only if it is decreasing wrt pA because otherwise the allowances mechanism becomes an incentive instead of a disincentive for polluters (and, as a consequence, an indirect incentive for renewables and CO2 efficient productions). Therefore α−P ½p > c þ kpA ≤0 should be desirable. This condition occurs whenever pA ≤pA*. Then, • when pA b pA*: the higher pA, the higher the penalty for polluters and the penalty is higher for lower efficiency plants since they need a higher amount of allowances; • when pA > pA*: the higher pA, the higher the advantage and the advantage is higher for low efficiency plants because they have more exceeding allowances to sell. The persistence of such a condition vanishes the incentive to fuel switch. The expected profit function is lower bounded by the line Q(kαpA − cm) which represents the profits from the sale of the assigned EUAs (i.e., no production). For large pA, the expected profit function is clearly asymptotic to such a line: the higher pA is, the lower the time the plant is on. pA* is an individual parameter, since it depends on the pollution coefficient k and on the efficiency of the plant (which affects both k and c). These parameters are different for each producer. Let F ðxÞ ¼ P ½ p−c≤x 1 Clearly, if an inversion in the order of merit of the technologies occurs (i.e., the marginal technology changes), the “new” marginal technology fixes the price of electricity: e.g., without carbon penalty, let technology 1 be marginal at cost c1 and the less polluting technology 2have cost c2 > c1. If pA is high enough to have c2 + k2pA b c1 + k1pA, so that technology 2 is marginal now, the price of electricity in a perfectly competitive scenario rises from c1 to c2 + k2pA (not simply to c1 + k1pA), so that k2pA b Δp = k2pA + (c2 − c1) b k1pA. Δp includes not only the carbon cost of the less polluting technology (k2pA), but also the gap of production costs (c2 − c1). However, it is less than the carbon cost of the more polluting technology (kpA).

pA*

pA

cm Fig. 1. Expected profit as a function of pA. When the EUA price is above pA*, the profit of the polluting producer increases when pA increases. With no grandfathering there is no positive p*. A

be the probability function of p. It is clearly non-decreasing (let us assume it is strictly increasing so that F − 1 is its inverse). pA* must solve the equation    F −1 ð1−α Þ   : P p > c þ kpA ¼ 1−F kpA ¼ α⇔pA ¼ k

ð5Þ

Eq. (5) clearly shows the inverse relation between pA* and both k and α (since F− 1 is an increasing function). Fig. 2 depicts the negative dependence between α and p*. A Besides it shows that the previous qualitative consequences still hold when the probability distribution of electricity prices ρ(p) is altered by the presence of EUAs (i.e., ρ(p) = ρ(p ;pA)).2 Some consequences: • big polluters (high values of k, due indifferently to the kind of fuel or to the low efficiency of the plant) face smaller pA*; • higher fuel costs c, due indifferently to the kind of fuel or to the low efficiency of the plant, imply smaller pA*; • higher quotas α of the certificates distributed free of charge reduce pA*; • lower energy prices or higher fuel costs reduce pA*. All the previous considerations but the last one come directly from Eq. (5). The last one comes from the following reasoning: consider two probability functions F1, F2 for the spread p − c with F2(x) > F1(x) (at least for ordinary values of x). Under F2 low spreads occur more likely (either because p is lower, or because c is higher). This implies F2− 1(1− α) b F1− 1(1− α). Hence (see Eq. (5)) pA* are lower in markets where electricity prices are lower and/or fuel costs are higher. The first two consequences depend largely on the technology adopted by the producer (even though the second one is also market driven), the third one depends on political choices, the last one is market driven and has some degree of interdependency with the market price pA of EUAs. For a given value pA, all the producers facing a pA* b pA are long in EUAs, while all the producers facing a pA* > pA are short. The market will fix an intermediate pA so that it is an incentive for high polluters while it is a penalty for low polluters, which can lead to relevant economic distortions because electricity consumers are charged at least for part of production costs. Instead, no distortion can occur when α = 0. This discussion shows that the intended objective of reducing CO2 emissions in the sector of electricity production through the creation of the EUA market, at least during the grandfathering phase, is thwarted 2 The demand curve of electricity (which is non-increasing) is not changed by EUAs, while the supply curve is eventually shifted toward higher prices. Then, for the same values of c, k and pA, for any x the event p > x occurs with a smaller probability (because this occurs when the demand is greater than a certain value, which is greater for p2A > p1A ⇒∀xP p2 ðp > xÞ≤P p1 ðp > xÞ⇒ A   A  . positive pA ). More generally: ⇒P p2 p > c þ kp2A ≤P p1 p > c þ kp2A ≤P p1 p > c þ kp1A A

A

A

P. Falbo et al. / Energy Economics 35 (2013) 14–21

17

4. Evaluating the convenience of switching to renewables or less polluting plants

Fig. 2. Increasing the value of α reduces p*. A

under quite normal circumstances. The analysis confirms the common belief that the EUAs distributed free of charge to the electricity industry have not contributed to the renewal of the carbon intensive plants, rather they have generated free profits for the pocket of electricity generators. 3. Investing in conventional and renewable plants The analysis is now extended to three different technologies to generate electricity: coal, gas and wind. An electricity producer is evaluated for the expected profits resulting from an investment in one of the three alternatives. The profit function from renewable resources includes the incentives. This analysis allows an evaluation whether and under which conditions it is profitable to switch to less polluting technologies. 3.1. The profit functions While EUAs are supposed to be a penalty for emitting CO2 into the atmosphere, Green Certificates (GC) are incentives to promote electricity production through renewable resource plants (RES-E). The inclusion of GC into the equation of profits has either a positive or negative impact depending on whether a producer meets an established minimal percentage target (αGC) of RES-E production. GCs (worth 1 MWh each) are traded on the Green Certificates Market (or by direct agreement) by parties with deficits or surpluses of generation from renewables. 3 The hourly profit, per MW of capacity installed, of a fossil fuel producer can be set as: G ¼ αkpA þ max½ p−c−kpA −α GC pGC ; 0−cm where pGC is the unit price of a GC, αGC is the GC percentage target. The equation shows that the GC program amounts to a cost proportional to production. For a production based on RES-E plants only, the hourly profit, per MW of capacity installed, is: G ¼ γ ðp þ pGC Þ−cm

Consider a producer who bases his decisions only on expected profits, that is in a risk neutrality setting. To keep the initial investment constant among the three alternatives, the producer can scale down the capacity of each plant. In other words, it is assumed that the cost of a plant depends linearly on its nominal capacity (in MW). Taking the investment required to install a 1 MW gas plant as a reference, the 1 MW gas plant is compared to Φc MW coal plant and Φw MW wind plant since Φc and Φw (the “conversion factors”) express the capacities of a coal and a wind plant which can be acquired with the same amount of capital investment in alternative to a 1 MW gas plant. The hourly profit generated by the three kinds of plants will depend on fuel costs (c), the cost (or profit) of EUAs and GCs, and the operation and maintenance (O&M) fixed costs (cm). The hourly profits generated by the three choices are: h i Gg ¼ αkg pA þ max p−cg −kg pA −α GC pGC ; 0 −cmg Gc ¼ Φc ðαkc pA þ max½p−cc −kc pA −α GC pGC ; 0−cmc Þ Gw ¼ Φw ðγðp þ pGC Þ−cmw Þ

ð6Þ

where: • Gg, Gc and Gw are the profits of the gas, coal and wind plant respectively, • kg and kc are the emission intensities of the gas and the coal plant respectively, • αGC is the mandatory quota for renewable production defined through the Green Certificate program, • pGC is the price of one GC, • cmg, cmc and cmw are the unit O&M costs (per MW) of the gas, coal and wind plant respectively, • γZ is the hourly “efficiency” of the wind plant (related to the wind speed). The problem of optimally diversifying an investment uniquely based on the expected values of profits is linear, so the solution is of the “bang-bang” type: it consists in investing all the capital in one single alternative offering the highest expected profit. The following analysis compares two different producers, one from Italy and one from Germany (year 2006). Regarding wind technology, a small Italian wind park was considered while the entire production of a big German wind company (EON) was analyzed, resulting in a substantially higher intermittence on the part of the Italian wind plant. However, the average activity (hours per year) is the same: ~ 19% for both countries. The parameters of the model are reported in Table 1. 5 Italian law established a quota α GC ¼ 2% þ 0:35% ðyear−2004Þ of renewables, that is αGC = 2.7% for 2006. The same quota was used in the German case, which is an “as if” analysis, since the incentives for wind generation in Germany are not supplied by GCs. German producers receive another form of incentive (i.e., feed-in tariffs), which favors RES-E plants but does not directly penalize fossil fuel

where γ is the hourly efficiency parameter of the plant. 4 3 A producer adopting RES-E plants can apply to be in a project for CO2 reduction, in which case he can receive a certain quota of CERs (similar to EUAs). However, in this case he should give up any other form of incentive. This is usually very unfavorable, so the assumption is that the incentive of renewables is supplied only by GCs. 4 This “efficiency” parameter is different from the efficiency of a fuel plant (which is the ratio between the electric energy produced and the thermal energy generated by fuel burning and is a constant parameter). Most RES-E plants suffer intermittence and are subjected to random production. A 1 MW wind plant will produce γ MWh of electricity in a certain hour according to the intensity of the wind in that hour. γ is stochastic and clearly varies in the interval [0 ; 1].

5 Sources: ICE UK Natural Gas one day forward price and the DES ARA index were used for gas and coal prices (source: Datastream). Efficiencies of 50% and 25% were assumed respectively for gas and coal technology to convert the prices into €/MWh. Investment and O&M costs come from CESI report (2004). EEX (Germany) and IPEX (Italy) day ahead prices were downloaded from the relative websites of the power markets (www.eex.com/en and www.mercatolettrico.org). The Italian power market also publishes CGs prices. Bluenext EUAs prices (www.bluenext.eu) were used as a reference. The emission intensities kg and kc were computed by the low heating value of gas and coal, assuming the above mentioned efficiencies for the plants and using the proper energy conversion factor (to obtain the unit t/MWh).

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Table 1 Parameters of the model: conversions factors (Φ), fixed costs (cm) and emission intensities (k) for gas (g), coal (c) and wind (w) plants. Conversion factors

O&M costs

Carbon intensities

cmg = 4 €/h

kg = 0.40392 kc = 1.36224

Φc ¼

1000 €=kW 5 ¼ 1200 €=kW 6

cmc = 4 €/h

Φw ¼

1000 €=kW 2 ¼ 1500 €=kW 3

cmw = 3.5 €/h

plants (Falbo et al., 2008). All other things being equal, the replacement of the current incentives instead of the “as if” analysis would possibly shift the results to favor coal plants than what we obtained. Fig. 3 shows some contour plots of the expected profits versus pA and pGC for different values of α (the assigned grandfathered quota of EUAs) for the Italian and German producers. α = 0 corresponds to the full auctioning (not grandfathering); α = 92% is approximately the grandfathered allocation of Phase II. Darker areas refer to lower profits. The three colors (yellow, red and green) represent the most profitable technology (gas, coal or wind). 4.1. Impact of Green Certificates and EUAs For increasing values of pGC the expected wind plant profits increase linearly, while the fossil fuel plant profits decrease because of the increased production cost caused by pGC. However GCs lessen the penalty of EUAs, since their presence reduces the probability of having the plant turned on (see Eq. (6)), that is: either the thermal producer should buy fewer EUAs or he should sell more of them. The impact of pA is different: wind plant profits do not depend on pA, 6 but fuel plant profits change in the non-monotonic way described above. As pA increases, the probability of having to turn on the fuel plant decreases. At the same time the profit from selling unused EUAs increases as well. For large values of pA, production is strongly reduced and consequently a great profit from the sale of the redundant EUAs occurs (except in the case α = 0). The gas and coal plants have different profit functions (because the distributions of the fuel costs differ and kg ≠ kc). The boundaries of the different areas correspond to the pairs (pA, pGC) making the choice indifferent among the technologies.

Finally, in some cases, the pair (pA, pGC) which makes the three technologies generate the same expected profit is not unique. Graphically, this can be seen in Fig. 3 (first column α = 0): the pair (pA, pGC) is found at the intersection of the three regions. In other cases (e.g., for α = 92%) no pairs exist so that the technologies are substitutable. These “indifference” prices are the solution to the following equations in pA and pGC for an assigned level of α: h i E Gg ðpA ; pGC Þ ¼ E½Gc ðpA ; pGC Þ ¼ E½Gw ðpGC Þ:

ð7Þ

The indifference prices without grandfathering are reported in Table 2 In other words, 4.63 €/MWh and 140.05 €/MWh are respectively the “fair” prices of EUAs and GCs that make the three technologies generate the same expected profit without grandfathering. Table 2 clearly shows the different situations between the two markets. Wind production is significantly higher in Germany than in Italy and German electricity prices are lower (the 2006 average electricity price is 74.75 €/ MWh in Italy versus 50.79 €/MWh in Germany). This, in turn, reduces the economic advantage of fossil fuel plants, so the indifference pGC is much lower in Germany. Since the indifference pGC and pA can substitute each other to keep the same level of expected profit, the indifference price of EUAs in Italy is lower than in Germany. Finally, the expected profits of Italian producers are more than three times those of German ones. 4.3. Impact of pA and pGC on profits. The role of pA* The equilibrium wind/fossil fuels is mainly affected by pGC, while pA drives the equilibrium gas/coal. This is seen observing the derivatives of the expected profits with respect to the prices of the incentives, which determine the sensitivities of the profit: h i3 2  h i 3 ∂pA E Gg kg α−P p > cg þ kg pA þ α GC pGC h i5 ¼ 4 h i 5 ∂pGC E Gg −α GC P p > cg þ kg pA þ α GC pGC " #  ∂pA E½Gc  Φc kc ðα−P ½p > cc þ kc pA þ α GC pGC Þ ¼ −Φc α GC P ½p > cc þ kc pA þ α GC pGC  ∂ E½Gc  " pGC #  ∂pA E½Gw  0 : ¼ Φw E½γ ∂pGC E½Gw 

2 4

∂p E½G

4.2. Impact of grandfathering For both the Italian and the German producers, the increase of α (i.e. the quota of grandfathered EUAs ) has the effect of reducing the preference for wind plants: the green area reduces passing from α = 0 to α = 92%. At the same time, coal plants become preferable to gas plants. This is due to the (relatively) higher amount of EUAs grandfathered to coal plants. This trend reinforces when pA is large. In general, wind plants are more profitable for the German producer than they are for the Italian producer. This is mainly explained by the average price of electricity which is lower in Germany than in Italy. This, in turn, makes gas and coal production too expensive for the German producer so that wind plants remain the only source to generate profits.

6 Actually p is affected by pA (and pGC), so ETS affects the profit of the wind plant. However it is assumed here that consumers are not charged for carbon costs.

In the case α = 0, for conventional fuels we have ∂p A E½G ¼ αkGC . This GC

ratio is about 14.26 for gas and 50.45 for coal, so that the expected profit is significantly more sensitive with respect to pA than to pGC. This fact remains true also when α ≠ 0, unless  α  α e 1 þ GC P ½ p > c þ kpA þ α GC pGC eP ½p > c þ kpA þ α GC pGC : k

ð8Þ

This condition holds when α is close to the probability of activating the plants. In turn, such a condition holds when pA epA − αkGC pGC , that is: when pA minimizes the expected profit of the fuel plant. Note the differences between the potential effect of the two types of incentives (i.e. EUAs and Green Certificates): as was previously shown, when α ≠ 0, the derivative of the expected profit with respect to the price of EUAs becomes positive for sufficiently high values of pA, while the derivative with respect to the price of Green Certificates is always negative, as is expected from an economic point of view. Since GCs add a cost and lower the probability of turning on the fuel plant, they increase the chances of spoiling the mechanics of EUAs.

P. Falbo et al. / Energy Economics 35 (2013) 14–21

α = 20%

α=0

19

α = 50%

α = 92%

PGC

PGC

PGC

PGC

240

240

240

240

180

180

180

180

120

120

120

120

60

60

60

60

30 60

I

30 60

PA

30 60

PA

PA

PGC

PGC

PGC

PGC

240

240

240

240

180

180

180

180

120

120

120

120

60

60

60

60

G

30 60

PA

30 60

PA

30 60

PA

30 60

PA

30 60

PA

Fig. 3. Expected profits vs pA and pGC for several values of α, in the Italian market (I) and in the German market (G). Darker areas represent lower profits. The color shows the most profitable technology: gas is yellow, coal is red, and wind is green.

Fig. 4 shows p~ A , the EUA price of minimal expected profit, for gas and coal plants in Germany and Italy as a function of α for different values of pGC. p~ A ¼ pA − αkGC pGC plays the same role as pA* (described in Section 2) in the presence of GCs. Such a price is clearly negatively related to α, since larger quotas of EUAs increase the expected profit (by slowing production and selling EUAs). In other words: the theoretical results discussed in Section 2 are confirmed even in the presence of GCs. The four graphs remain basically unchanged for large variations of pGC (pGC = 0, 100, 200, 300). It is concluded therefore that GCs play a negligible role in the fuel switch. p~ A is significantly lower for a German producer than it is for an Italian producer, which is a “local” distortion of the ETS: the same coal plant can be EUAs long in Germany, while short in Italy. But, even worse, for α = 92%: the p~ A of the more polluting Italian coal plant is higher than that of the less polluting German gas plant. This means that, eventually, German gas plants would be “shut off” before Italian coal plants! Finally, observe that for α = 92%, p~ A varies from a few euros per ton (German coal plant) up to about 20 euros per ton (Italian gas plant with no GC). These values are consistent with ordinary prices of EUAs.

Table 2 Indifference pairs (pA, pGC) and expected profits for the Italian and German cases.

pA pGC E[G]

Italy

Germany

4.63 €/MWh 140.05 €/MWh 26.22 €/MWh

9.91 €/MWh 34.73 €/MWh 7.83 €/MWh

5. Conclusion This paper contributes to the discussion and the criticism against the grandfathering of EUAs. An analytical model of the expected profit of a competitive electricity producer is developed within the ETS system. Under quite general conditions, such a function is not monotonically decreasing with respect to the price of the emission certificates, and it is possible to identify a point of minimum expected profit. Indeed, if the current price of EUAs happens to increase over such a threshold, the inefficiency of the producer is rewarded instead of penalized. This unlucky event occurs because the producer can sell the unused EUAs he received free of charge. Besides the more carbon inefficient a producer is, the greater the amount of unused EUAs he owns. Furthermore, this threshold is decreasing with respect to the percentage of quota distributed free of charge (grandfathered) to the producer. This implies that such a distortion is more likely to happen with a higher level of grandfathering. These results show that grandfathering severely spoils the expected effect of the entire ETS system: heavy CO2 emitters will find it unprofitable to convert their plants to technologies with low or no-emission. On the contrary, they will obtain substantial profits keeping their most polluting plants in place and selling the grandfathered EUAs. Such results are perfectly in line with several theoretical and empirical findings available in the literature. This model includes the impact of Green Certificates on the expected profits of a producer comparing wind, gas and coal plants. The results give further ground to the literature against grandfathering. The level of grandfathering and the price of emission certificates have a relevant impact on the order of preference based on the expected profit (per MWh) of the three types of plants.

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P. Falbo et al. / Energy Economics 35 (2013) 14–21

~ pA

~ pA

80

80

pGC=0

60

60 40

40

pGC =300

20

20

20

40

60

80

α

20

40

60

80

α

60

80

α

~ pA

~ pA 80 60

pGC=0 pGC =300

80

pGC=0

60

pGC =300

40

40

20

20

20

40

60

80

pGC =300

α

pGC=0

20

40

Fig. 4. p~ A (in €/MWh) as a function of the assigned percentage α of EUAs for different values of pGC: 0, 100, 200, 300 €/MWh.

Such theoretical results are reinforced through an empirical application based on current data of production and market prices. The analysis of German and Italian producers gives different results. The German producer finds it profitable to invest in renewables for a (pA, pGC) range wider than the Italian producer. This is due to the high differential of electricity prices between the two countries. The price of electricity is lower in Germany than in Italy, and this makes coal production too expensive, so that wind plants become the residual technology source to generate profits. What is particularly striking is that the high quotas of free allowances (about 92% in Phases I and II) more probably generated a shift from clean production (wind) to the most polluting production (i.e., coal) rather than vice versa. This is true both in Germany, where a significant portion of electricity is generated by renewables, and in Italy, where renewables are still low. The grandfathering of EUAs frustrates the aim of the incentives for renewables (Green Certificates). The results obtained so far are based on the comparison of expected profits, with no explicit reference to risk implications. Volatility of prices in the electricity sector is severe, so an extension of this analysis in the direction of encompassing risk is a basis for future research. Appendix A A.1. Proof of Eq. (4) An intuitive proof of Eq. (4) is illustrated here. So the probability measure of (p, c) is assumed to be absolutely continuous with respect to Lebesgue measure on R2 and its Radon–Nikodym derivative ρ(p, c) is a function regular enough to allow the derivative and the integral

operators to commute (step 4) and the use of Leibniz integral rule (step 5) ∂pA E½G ¼ þ∞

ð1Þ

þ∞

¼ ∂pA ∫ dc ∫ ðQ ðαkpA þ max½p−c−kpA ; 0−cm ÞÞρðp; cÞdp ¼ 0" 0 # þ∞

ð2Þ

þ∞

¼ Q∂pA ðαkpA −cm Þ ∫ dc ∫ ρðp; cÞdp þ þ∞

þ∞

0

0

þQ ∂pA ∫ dc ∫ max½p−c−kpA ; 0ρðp; cÞdp ¼ 0

0

þ∞

ð3Þ

þ∞

¼ Q∂pA ðαkpA −cm Þ þ Q∂pA ∫ dc ∫ ðp−c−kpA Þρðp; cÞdp ¼ 0 þ∞

ð4Þ

þ∞

cþkpA

¼ Qαk þ Q ∫ dc∂pA ∫ ðp−c−kpA Þρðp; cÞdp ¼ 0

ð5Þ

¼ Qαkþ2 þ∞

þ∞

0

cþkpA þ∞

cþkpA

3

þQ ∫ dc4 ∫ −kρðp; cÞdp−kððc þ kpA Þ−c−kpA Þρðc þ kpA ; cÞ5 ¼ þ∞ ð7Þ ¼ Qαk−Q k ∫ dc ∫ ρðp; cÞdp ¼ Q k½α− Probðp > c þ kpA Þ:

ð6Þ

0

cþkpA

When Green Certificates are considered in the profit function, the formula becomes

∂pA E½G ¼ Q k½α− Probðp > c þ kpA þ α GC pGC Þ:

P. Falbo et al. / Energy Economics 35 (2013) 14–21

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