Department of Economics Discussion Paper 2007-05
Informational Efficiency and Interchange Transactions in Alberta’s Electricity Market* Apostolos Serletis Department of Economics University of Calgary Calgary, AB T2N 1N4 Canada and Mattia Bianchi Dipartimento di Ingegneria Gestionale Politecnico di Milano Piazza L. da Vinci 32 20133 Milano Italy
This paper can be downloaded without charge from http://www.econ.ucalgary.ca/research/research.htm
Informational Efficiency and Interchange Transactions in Alberta’s Electricity Market1 by Apostolos Serletis2 Department of Economics University of Calgary Calgary, Alberta T2N 1N4 Canada and Mattia Bianchi Dipartimento di Ingegneria Gestionale Politecnico di Milano Piazza L. da Vinci 32 20133 Milano Italy
Forthcoming in: The Energy Journal
JEL classification: C22, L91, L94 Keywords: Granger causality; Electricity markets; Market power; Hurst exponent
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We would like to thank the Editor and four referees for comments that greatly improved the paper. We also thank Paul Dormaar, Melvin Hinich, Aryeh Rosenberg, Jason Vaccaro, and Kenneth Wyllie for useful comments. 2 Corresponding author. Phone: (403) 220-4092; Fax: (403) 282-5262; E-mail:
[email protected]; Web: http://econ.ucalgary.ca/serletis.htm.
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Abstract This paper aims to investigate the informational efficiency of the Alberta electricity market and also the issue of whether interchange transactions (power flows between markets) are becoming increasingly significant factors in electric power markets. In doing so, we use hourly data for all hours, peak hours, and off-peak hours over the period from January 1st, 1999 to July 31st, 2005. In testing the efficiency of the Alberta power market, we use a statistical physics approach --- namely the ‘detrending moving average (DMA)’ technique, introduced by Alessio et al. (2002) and further developed by Carbone et al. (2004a, 2004b), and recently applied to energy futures markets by Serletis and Rosenberg (2007). In analyzing the relationship between power imports and exports and pool prices, we assess whether regulatory changes have modified the causal relationship between import/export volumes and the pool price. According to our results, the electricity market in Alberta is highly inefficient and cross-border trade of electricity between Alberta and neighbouring jurisdictions helps predict the price dynamics in Alberta’s electricity market.
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1. Introduction This paper aims to investigate the informational efficiency of the Alberta electricity market and also the issue of whether interchange transactions (power flows between markets) are becoming increasingly significant factors in electric power markets. Although our paper is only about Alberta --- a relatively isolated market with only two links to external systems and only one of them of much market importance --- the issues it addresses are of importance to Regional Transmission Operators (RTOs) in the United States and to the discussion of power market liberalization in Europe --- see, for example, Hobbs et al. (2005), Neuhoff (2003, 2004), and Neuhoff and Newbery (2007). In deregulated electricity markets, the pool price is determined by competitive market forces, the laws of supply and demand. Being components of supply and demand, imports and exports do influence electricity prices in Alberta’s deregulated wholesale electricity market. Import and export volumes play an important role in ensuring system reliability and security in Alberta. In conditions of scarcity of supply and/or excess of demand, power must be imported via the inter tie-lines that connect the Alberta electric grid system with the neighbouring jurisdictions. The Alberta Interconnected Electric System (AIES) is connected, on the west side, to the British Columbia (BC) grid by the 800 MW Alberta-BC inter-tie, while it is linked on the east side to the Saskatchewan power system by a 150 MW DC interconnection. Since the total available capacity of the inter-ties represents about 11% of the Alberta maximum peak load (9,438 MW in 2005), the tie lines may have a considerable impact on the pool price (a wholesale market price). It has been argued that this fact, in combination with Alberta’s steep supply curve and inelastic demand even at high prices, has given importers and exporters significant market power, which has raised concerns among market participants. As the Market Surveillance Administrator (2005) of the Alberta electric system recently put it, “the role and influence of imports and exports into/out of Alberta via the BC interconnection has long been a contentious issue amongst industry stakeholders. A recent issue that has been expressed by some participants concerns the occurrence of imports that appeared to be unprofitable based on economics using the appropriate market index prices. The concern was not so much that the observed imports were unprofitable, but rather that the motivation behind the import behaviour was a desire to influence Pool prices --- in this case, to push Pool prices down.” In order to understand the role that imports and exports have played in the Alberta power pool, we consider the rules implemented over the last six years that have affected the ability of interchange transactions to influence power prices. Prior to December 15th, 2000, importers and exporters were allowed to offer and buy power at whatever price
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maximized their profit. The Pool Price Deficiency Regulation (PPDR), introduced on December 15th, 2000, stated that imports and exports to and from Alberta were no longer allowed to set the pool price. However, under this scheme, importers were paid what they offered through an uplift charge. Since the uplift rule was extremely unpopular with pool participants, at the end of 2001, the Power Pool of Alberta implemented the Intra Day Market (IDM). This last arrangement revoked the uplift charge and forced imports and exports to be price takers. In this paper we investigate the efficiency of the Alberta power market, using a statistical physics approach, namely the ‘detrending moving average’ method, introduced by Alessio et al. (2002) and further developed by Carbone et al. (2004a, 2004b), and recently applied to energy futures markets by Serletis and Rosenberg (2007). Moreover, we analyze the relationship between power imports and exports and pool prices in Alberta’s electricity market. In particular, we assess whether regulatory changes have modified the causal relationship between import/export volumes and the pool price. In doing so, we use hourly data on prices, imports, exports, and load for all hours, peak hours, and off-peak hours over the period from January 1st, 1999 to July 31st, 2005. The paper is organized as follows. Section 2 provides a detailed discussion of Alberta’s power market and interconnection capacity while Section 3 describes the data used in the paper. Section 4 investigates the efficiency of the Alberta power market, using the ‘detrending moving average’ method and Section 5 presents and interprets the Granger causality test results. The final section concludes the paper. 2. Alberta’s Power Market and Interconnection Capacity The Demand for Power in Alberta Alberta is a Canadian province that lies between the 49th and 60th parallels. It is bounded on the east by Saskatchewan, on the west by British Columbia, on the south by the state of Montana, and on the north by the Northwest Territories. The Alberta electricity market is a member of the Western Electricity Coordinating Council (WECC), which is the largest and most diverse of the ten reliability councils that form the North American Electricity Reliability Council (NERC). The WECC is responsible for coordinating and promoting electric system reliability and for facilitating the formation of Regional Transmission Organizations in various parts of the western North America --see Bianchi and Serletis (2007) for more details. Electricity demand in Alberta is comprised of four primary groups: residential, farm, commercial, and industrial. The industrial load is over 50% of all electric sales while the residential load is only 15%. This provides a very stable load curve all over the
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year, which helps reduce the frequency of price spikes. The main contributors to the fluctuations of demand are residential and small commercial customers (CERI, 2004). Electricity demand in Alberta is also cyclical in nature, with demand being lower in the spring and fall than in summer and winter. In general, Alberta has higher winter consumption, due to lower temperatures that cause increased heating and shorter daylight hours --- in fact, in 2005 the summer peak load was approximately 90% of that in the winter. Moreover, winter hourly load in Alberta has two distinct peaks. Demand is low in the early morning hours and begins to increase through the morning hours, with a first peak around nine o'clock. During this interval, load can increase by 1500 MW. The other peak is around dinnertime, six-seven o'clock. The peaks in the day tend to float depending on the number of daylight hours. Demand also follows a weekly cycle and tends to be higher on weekdays than during the weekends. Finally, demand for power is relatively inelastic in Alberta. There is no requirement for load to bid in the price they are willing to pay for the energy. Hence, unbid load is treated as a price taker into the merit order of the Alberta's power market and must pay the hourly pool price for the energy consumed during that hour. Only a small percentage (around 4%) of the load is bid into the market. According to AESO, there is around 300 MW of price responsive demand; some large industrial customers agree to be curtailed at high pool prices, introducing some price sensitivity at higher price levels. Market Fundamentals and Power Prices In deregulated marketplaces, competitive market forces --- the laws of supply and demand --- guide electricity price formation. Factors affecting demand, like temperature and time of day, and factors affecting supply, like gas prices and unit outages, determine the pool price. As demand increases, more expensive generation must be dispatched to serve load causing electricity prices to rise. Imports and exports are also components of supply and demand, respectively. Export deliveries act as additional demand and imports act as additional supply. If cheap imports are available, more expensive generating units can be dispatched off. Import capability depends on the situation in the exporting market --- plant failures, maintenance outages, and weather conditions may reduce electricity supply. For example, little precipitation can make low priced hydro generation unavailable. Moreover, the available transmission capacity is essential --- if transmission congestion happens, importers which could supply at lower prices may not be able to move their power. Other factors can strongly impact on electricity prices as well. First, import prices may reflect the opportunity cost of selling into other high priced markets. This happens when a market is connected to different regions and thus can strategically choose whom to sell to. Also, the relative size of trading markets matters. Prices in the smaller market 5
are responsive to trade volumes within the bigger market, but the opposite may not be true. Also, a higher number of players on the tie-line, acting as exporters or importers, may increase competition in the market, limiting market share and thus potentially market power. Market dynamics are not the only forces that play in competitive electricity markets. Electricity prices are highly sensitive to regulatory policies and intents. In Alberta, for example, rules have disallowed exports or imports setting the market clearing price. Imports and exports become price takers. When such rules introduce constraints to the free operation of market forces, they may discourage power traders from participating in the market. Finally, power prices reflect the strategic behaviour of market players, as they pursue different pricing strategies in order to maximize their profits. Alberta’s Interconnection Capacity The Alberta electricity market has two links to external systems, with only one of them being of much market importance. In fact, the interconnection capacity as a percentage of peak load is lower in Alberta than any other province in Canada (approximately 12% in Alberta compared to about 40% in British Columbia). Also, Alberta electricity imports and exports are low compared to other provinces --- in fact, Alberta has the lowest import/export capacity among major Western Electricity Coordinating Council (WECC) utilities. Finally, it should be noticed that Alberta is generally a net importer of electricity; only in 2001 exports exceeded imports, due to lower prices in Alberta compared to neighbouring markets. The Alberta electric grid system is connected, on the west side, to the British Columbia (BC) electric system via the Alberta-BC interconnection and, on the east side, to the Saskatchewan (SK) electric system. The 800 MW Alberta-BC tie line supports commercial import and export activity through providing Alberta the access to the North American electric grid and the U.S. Pacific power markets, members of the Western Electric Coordinating Council. The Alberta-BC interconnection is comprised of one 500 kV transmission line and two 138 kV lines. However, the inter-tie is effectively limited to the capacity of only the 500 kV line at most transfer levels. The British Columbia portion of the tie-lines is owned by BC Hydro and operated by the BC Transmission Corporation (BCTC), while the Alberta portion of it is currently owned by AltaLink and operated by the Alberta Electric System Operator (AESO). With regard to electricity flowing from BC to Alberta, the WECC approved Path Rating for the BC to Alberta path (i.e. west to east) is 1200 MW. However, this level of transfer would lead to excessive load shedding in Alberta in case of contingency and is rarely an acceptable operating condition for Alberta operators. Normally, the total transfer capacity for the BC to Alberta inter-tie is 760 MW while the firm transfer limit is 6
set at 545 MW. Conversely, the WECC approved Path Rating for the flow of electricity from Alberta to BC inter-tie (i.e. west to east) is 1000 MW. However, most of the time there are limitations inside Alberta which prevent operation at this level. The BC limitation on the transfer from Alberta to BC is currently 600 MW. The reasons for the operational limits on the tie-line available transmission capacity are twofold. With regard to imports to Alberta, it lies on the single contingency reliability criterion which limits the capacity of the interconnection to the largest single capacity contributor from time to time. Regarding exports from Alberta, voltage acts as a constraint with Alberta, due to insufficient transmission reinforcement during high peak load periods. The AESO and BC Hydro are parties of an Interconnection Agreement that establishes the conditions for operating the Alberta-BC Interconnection. BC Hydro has been designated by the WECC as the Path Operator for the interconnection. Scheduling of power flows on the inter-tie is coordinated between BCTC, which is responsible for the interchange transactions on the BC side, and the AESO, which is responsible on the Alberta side. The scheduling process of interchange power flows is more complicated on the Alberta side than on the BC side. While AESO manages a competitive market where several market participants have the opportunity to trade on the tie-line, BC Hydro has almost exclusive access to its transmission system. The market share of BC Hydro on the Alberta-BC interconnection is about 69% (including Alberta’s market players). In Alberta, imports and exports must be submitted before hh:30 in order to be included in the inter-tie schedule for the next hour. Those submitted after hh:30 may or may not be approved by the AESO, which can refuse the dispatch in the next hour. Between hh:30 and hh:40, the scheduling information is transferred to BCTC and at hh:40 the AESO and BCTC confirm the net interchange schedule, the ramp start time and the ramp duration for the next scheduling hour --- see Christian and Hughes (2004). Due to less ‘dispatchability’ of imports, changes on the interchange scheduling are not permitted except for security reasons or for emergency. The Alberta power market is also connected through BC to the U.S. Pacific markets, such as, for example, the Mid Columbia (Mid C) market. Mid C is an electricity market hub in the United States, referring to an area containing five significant public hydro projects along the Columbia river, overlapping Chelan, Douglas, and Grant counties in central Washington State. Mid C is the market hub most commonly referenced in the Pacific North West. California Oregon Border (COB) is another trading hub, located along the Pacific AC inter-tie, which connects the electric grid of California and Oregon. On the east side, Alberta is also linked with the Mid-Continent Area Power Pool (MAPP) via Saskatchewan by a 150 MW DC interconnection. The total available transmission capacity of Alberta (with BC and Saskatchewan) represents about 11% of the Alberta peak demand (9,438 MW, in 2005). In 2004 Alberta generating capacity was 7
about 12,100 MW, while in British Columbia it was 13,500 MW. With regard to electricity power sources, British Columbia relies almost entirely on their rich hydropower resources (94%). Alberta and Saskatchewan, conversely, rely more on conventional thermal and combustion turbines, given their large coal and natural gas reserves. The different market structures constitute an impediment to the full utilization of the Alberta-BC interconnection. The interrelationship between Alberta’s pool price, prices in neighboring markets, and the flow on the transmission interconnections is complicated by the fact that Alberta’s two closest jurisdictions are not deregulated markets. The electricity market design is very different between the provinces and the connected U.S. western states. Alberta is the first Canadian wholesale and retail competitive marketplace, having a pool market that is dispatched on a minute-by-minute basis. The pool price for buyers and sellers alike is not known until after the fact. British Columbia and Saskatchewan are each a single buyer market, where the single buyer purchases a planned amount of power from competing independent power companies. On the other hand, Mid C and COB have completely different market structures than the above jurisdictions. Mid C is a bilateral market where buyers and sellers seek each other out in order to complete a transaction. The spot market for power is a decentralized over-the-counter market --- prices are negotiated by traders at various utilities, not in a centralized market. The electric grid presents difficult coordination problems among scattered injection and delivery points on a complex network. In these markets, prices are known prior to delivery of the energy and most trades are transacted day ahead over on- and off-peak strips. There is also a liquid hourly market required by participants to make adjustments to circumstances occurring in real time. Moreover, the Mid C market is on an hourly schedule that matches the hourly schedules of the BC tie line. The Alberta-BC interconnection, by virtue of its size, gives rise to the majority of concerns in terms of tie line impact on the Alberta market. On the supply side, the Alberta-BC tie line works as a very large generating unit, supplying power energy to Alberta. Being larger than any generating plant in Alberta, it has the potential to affect the pool price (Alberta MSA, 2005). As already noted in the introduction, the ability of power marketers to significantly influence the price dynamics through import/export trading tactics have raised many concerns among Alberta’s domestic industry stakeholders. 3. Data and Regulatory Regimes The data used in the analysis consist of hourly data on power prices, imports, exports and load for all hours, peak hours, and off-peak hours, over the period from
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January 1st, 1999 to July 31st, 2005 for Alberta’s spot electricity market. With regard to power prices, we use the hourly real time pool prices (volume weighted) posted by the AESO. This price is the average of sixty (every minute) system marginal prices that are based on the price of the highest bid that must be dispatched to meet pool demand. Prices are in Canadian dollars per megawatt-hours. Imports, exports, and load are also available on the AESO website. Imports refer to the hourly amount of electricity imported to the Alberta power pool. This power is sold in the Alberta pool but is produced in external jurisdictions. On the other hand, exports represent the hourly amount of electricity that is delivered outside of Alberta, though being produced by Alberta generators. Both imports and exports represent interchange transactions; that is, power flows between regions. Cross-border electricity trade happens through the transmission interconnection of the Alberta Interconnected Electricity System (AIES) with any electric system in a jurisdiction bordering Alberta. Finally, load is the hourly total amount of electricity demand. Imports, exports, and load are all in megawatthours. For the purposes of our analysis we create three data sets: all hours, peak hours, and off-peak hours. The reason why on- and off-peak series are used is to group similar patterns of energy use. The on-peak is characterized by higher energy consumption and higher power prices. As Alberta is connected to the Western Electricity Coordinating Council, we adopt the official WECC definition for peak and off-peak periods. The official WECC definition for peak hours is the hour ending (HE) 8:00 to the HE 23:00 Monday through Saturday inclusive. The official definition of the off peak hours is the remaining hours Monday through Saturday and Sundays. To investigate the relationship between imports and exports of electricity and power prices in Alberta’s market, we also conduct our analysis over three different time periods: from January 1st, 1999 to December 14th, 2000, from December 15th, 2000 to December 20th, 2001, and from December 21st, 2001 to July 31st, 2005, in order to deal with the regulatory changes affecting the import/export transactions in the Alberta’s power market.3 In fact, over the period of analysis, three regulatory regimes have existed, as discussed in more detail below. Ability of Import Offers and Export Bids to set Alberta’s Pool Price The first regulatory scenario existed from January 1st, 1999 to December 14th, 2000.4 Prior to December 15th, 2000, imports and exports contributed in the formation of 3
Data for November 1999 and December 1999 are not included in the sample due to unavailability of data on imports and exports over these two months. 4 Actually, it was in effect from January 1st, 1996 but we use data from January 1st, 1999. Data in our sample go from January 1st, 1999 due to the unavailability of imports and exports volumes on earlier periods.
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the system marginal price. The system marginal price is the price of the most expensive offer of energy supply (intra Alberta generated energy or imported energy) required to be dispatched to serve demand. The pool price is the average of the 60 one-minute system marginal prices (SMPs) in a given hour. All the generators dispatched (domestic or external) receive the pool price and all loads (domestic or external) pay this pool price. This mechanism is simply known as merit-order dispatch: it minimizes the total cost of generation by dispatching the least expensive units needed to meet demand. It does not discriminate between imported power and power produced by Alberta generators. During the year 2000, power prices in Alberta increased dramatically, as a consequence of the tight supply and demand balance, the boom of natural gas prices in North America, and the low rain precipitation in the Pacific North West that dramatically reduced hydro power supply. Thus, the Alberta government introduced in late 2000 a set of rules designed to protect consumers from high import costs and high prices of external markets. The Pool Price Deficiency Regulation (PPDR) This rule was in effect from December 15th, 2000 to December 20th, 2001. The PPDR, approved by the Government of Alberta in November 2000 and implemented on December 15th, 2000, directed the Power Pool of Alberta not to include energy imported or exported from the province in the calculation of the power pool price. The aim of the regulation was to protect Alberta’s electricity consumers from high power prices of external markets. According to this rule, imports and exports to and from Alberta were no longer allowed to set the pool price. However, imports received an uplift payment if they received an energy market dispatch at an offer price higher than the pool price. Thus, there were two components for the settlement of supply. The first component included all energy supplied, which was settled at the pool price. The second component made an adjustment to settlement for importers by adding an uplift. This was an additional energy payment to importers when dispatching an import that was in merit but whose offer price was above the price of the last ‘intra Alberta’ price block that was dispatched. In order to recover the costs of imported energy’s uplifts, uplift recovery rules applied in a three tiered scheme: uplift was first charged to any participant that was importing and exporting in the same hour (simultaneously). The rationale was to make a market participant pay the same amount to export that it received to import. This removed an immediate arbitrage opportunity. The remaining uplift up to an amount equal to the export volume was allocated to exporters (not involved in direct sales) on a pro rata basis. When uplift payments were not fully recovered from exporters, the remaining pool purchasers (all metered load and exports with a direct sale) received an increase to their energy charge. 10
The PPDR aimed to attract importers into Alberta’s market (offering higher payments through uplifts) while insulating the pool price from the prices of external markets. Nonetheless, the PPDR introduced regulatory risk and investor uncertainty and caused the Alberta’s pool price inability not to provide a clear and univocal price (Power Pool of Alberta, 2001). The introduction of PPDR was considered to be interference in the marketplace by pool participants and an obstacle to the deregulation process in Alberta’s electricity market. On December 13th, 2001 the Power Pool of Alberta Council approved the rule changes associated with the Intra Day Market and Interconnection Scheduling initiative.
The Intra Day Market (IDM) and the Interconnection Scheduling Initiative This last arrangement came into force on December 21st, 2001 and is still in effect. The main objective of IDM is to give pool participants the ability to hedge price risk as close to real time delivery as possible. Such instrument, almost in real time, created synergies to external market timelines which use firm hour ahead instruments for trading instead of day ahead instruments. Additionally, the IDM allows importers and exporters to align themselves in the real time market similarly to other suppliers and loads. In particular, the following changes were introduced on December 21st, 2001. The uplift was removed from the settlement calculation and thus no longer paid to importers nor charged to purchasers. Imports assets had one block of energy with a price of $0.00, while exports assets had one block of energy with a price of $999.99. In other words, imports remain price takers and are offered into the AESO at zero dollars to ensure dispatch. Exports remain price takers, who bid into the AESO at the maximum price (price cap) to ensure that they are dispatched to supply external contracts. Imports and exports are set to be price takers because they are generally scheduled one hour in advance and cannot respond to inter-hour market dispatches. Data Overview In Table 1 we report summary statistics for each variable, over the whole sample from January 1st, 1999 to July 31st, 2005, and over each of the three regimes; that is, from January 1st, 1999 to December 14th, 2000, from December 15th, 2000 to December 20th, 2001, and from December 21st, 2001 to July 31st, 2005. Figures 1-9 present the (all hours, off-peak hours, and peak hours) hourly data for Alberta pool prices over each of the three subperiods of our analysis. Figures 1-9 demonstrate the fact that the Alberta power market is a very volatile market --- the hourly prices are characterized by frequent spikes with excursions to the
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$1,000 level, which is the price cap in Alberta’s electricity market. According to Table 1, the first subperiod shows the highest prices and volatility, mainly due to the tight supply and demand balance, high natural gas prices, and the effects of the Californian electricity crisis in 2000. Prices in the second subperiod are still affected by the post-crisis effects until July 2001. Nonetheless, they show a low level of volatility (this is also due to small sample size). In the third subperiod, price spikes and excursions to the price cap are much less frequent; prices are lower, though in 2002 prices were driven up by high natural gas prices, robust demand growth, several plant outages, and limited imported capability. As shown in Table 1, Alberta is overall a net importer of electricity. In the first subperiod, the gap between imports and exports is significant, with imports being about four times larger than exports, which are very volatile. In the second subperiod, the situation is the opposite, with Alberta exporting power twice more than it imports. In the third subperiod, imports are slightly higher than exports and have similar volatility. The level of imports has decreased from the first to the second subperiod while it has increased from the second to the third subperiod. Conversely, the level of exports has followed the opposite path. It is also to be noted that Alberta load has grown steadily over the period of analysis and its volatility has remained stable. Electricity demand is cyclical in nature. Load varies from winter to summer seasons. Alberta has higher winter consumption, due to lower temperatures that cause increased heating and shorter daylight hours. Moreover, demand is lower in the spring and fall than in summer and winter. 4. Informational Efficiency of the Alberta Power Market We start by testing the efficiency of the Alberta power market. In doing so, we use a statistical physics approach --- namely the ‘detrending moving average (DMA)’ technique, recently introduced by Alessio et al. (2002) and further developed by Carbone et al. (2004a, 2004b). The DMA method is an improvement over the ‘detrended fluctuation analysis (DFA),’ introduced by Peng et al. (1994) for the detection of multiscale autocorrelations in various types of data, including financial, geophysical, and physiological signals. In particular, the DMA method detrends a series by subtracting a continuous function, the moving average, thereby being more accurate since the moving average is a better low-pass filter when compared to the polynomial filter used for DFA. To illustrate the DMA algorithm, consider the time series x(t) with t = 1,…,N. Denote the n-th order moving average of x(t) by
1 n −1 x n (t ) = ∑ x(t − k ). n k =0
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The series x(t) is detrended by subtracting x n (t ) , and the standard deviation of x(t) around the moving average, x n (t ) , is calculated as follows
σ DMA =
1 N − nmax
N
∑ [x(t ) − x
t = nmax
(t )] , 2
n
where nmax refers to the maximum value of n. The Hurst exponent is obtained by graphing σ DMA and n on a log-log plot and computing the slope. In fact, Arianos and Carbone (2007) show that
σ DMA ∝ n H , where H is the Hurst exponent. A linear relationship between σ DMA and n on a log-log plot indicates the presence of power law (fractal) scaling. Under such conditions, the scaling exponent H can be used to identify long-range dependence in the data. In particular, if 0.5 < H < 1, then x(t) is a persistent process (a process that maintains a trend). That is, if x(t) increased (decreased) in the past, it will most likely increase (decrease) in the future. If 0 < H < 0.5, then x(t) is an anti-persistent (or mean reverting) process. In this case, if x(t) increased (decreased) in the past, it will most likely decrease (increase) in the future. Finally, H = 0.5 corresponds to uncorrelated Brownian motion and we treat it as a necessary condition for the efficient market hypothesis to hold in the Alberta power market. The detrending moving average analysis functions, σ DMA , denoted in Figures 1-9 by F (n) , are shown in each of the figures for n = 50. Clearly, F (n) has a non linear form in double logarithmic coordinates, indicating a multifractal structure. Moreover, the Hurst exponents are all statistically significant at conventional significance levels and well below the value of 0.5 that corresponds to an efficient market. We conclude that the Alberta power market displays anti-persistence (or mean reversion). Therefore, we fail to find evidence for the weaker form of the efficient market hypothesis. Although it is difficult to distinguish between the three different successive regulatory regimes in Alberta’s electricity market based on the DMA method, it should be noted that in the current regime which requires exports to be bid into the pool price at $999.00 per MW per hour and imports at zero, the Hurst exponents are the lowest, followed by those in the early regime (before December 15, 2000) which allowed imported power to be bid into the pool and set the pool price directly in the event that it was the marginal supply. The Hurst exponents seem to be the highest in the second
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regime which precluded imports from setting the pool price but paid an uplift charge to imports where these were required to balance supply and demand. 5. The Role of Imports and Exports
In this section we use the Granger-causality method to test the hypothesis that imports and exports are causal factors in Alberta power pool prices. In doing so, we assume that the relevant information is contained in the present and past values of these variables and use a multivariate autoregressive representation. It is to be noted that we interpret causality merely in terms of predictability and not as implying underlying structural economic relationships. The first step in testing for causal relationships is to test for the presence of a stochastic trend (a unit root) in the autoregressive representation of each individual time series over each subperiod. A time series that has a stochastic trend is said to be nonstationary. Most economic and financial variables that exhibit strong trends, like GDP and price levels, are non-stationary and thus have a unit root. In many cases, the first difference of a non-stationary time series is stationary. When this is true, the time series is said to be integrated of order one [or I(1) in the terminology of Engle and Granger (1987)]; a stationary time series is integrated of order zero, or I(0). In order to test for the existence of a stochastic trend, we use the augmented Dickey-Fuller (ADF) test --- see Dickey and Fuller (1981). Thus, we test the null hypothesis of a stochastic trend by estimating the following ADF regression equation k
∆xt = α 0 + α 1t + γxt −1 + ∑ β∆xt − j + ε t j =1
where x represents the variable under consideration, ∆ is the difference operator, and k is the optimal lag length, determined using the AIC+2 rule suggested by Pantula et al. (1994). Tables 2-4 present the results for each of the three subperiods; that is, from January 1st, 1999 to December 14th, 2000, from December 15th, 2000 to December 20th, 2001, and from December 21st, 2001 to July 31st, 2005, respectively. The tests are applied to the levels of the series. In panel A of each table we report results for all hours, in panel B for peak hours, and in panel C for off-peak hours. In each table, the first column reports the optimal value of k in the ADF regression equation, the second column reports the tstatistic for the null hypothesis γ = 0, and the third column shows the p-value of the tstatistic. Finally, the fourth column summarizes the outcome of the test for each variable, that is whether the relevant series has a unit root or not. Clearly, the null hypothesis of a unit root is rejected (at conventional significance levels) for all series over each subperiod. 14
Because of this result, we proceed to test for Granger causality using the levels of the variables, in the context of the following model r
s
q
p
j =1
j =1
j =1
j =1
Pr icet = α 0 + ∑ α j Pr icet − j + ∑ β j Im portst − j + ∑ γ j Exportst − j + ∑ δ j Load t − j +ε t (1) where α0, αj, βj, γj, and δj are all parameters and εt is a white noise disturbance. In the context of equation (1), causality from (say) Imports to Prices can be determined by first fitting equation (1) by ordinary least squares and obtaining the unrestricted sum of squared residuals, SSRu. Then by running another regression equation under the null hypothesis of no causality (all the coefficients of the lagged values of Imports are zero), the restricted sum of squared residuals, SSRr, is obtained. The statistic ( SSRr − SSRu ) / s SSRu /(T − r − s − q − p − 1)
has an asymptotic F-distribution with numerator degrees of freedom s and denominator degrees of freedom (T – r – s – q – p – 1), where T is the number of observations. If the null hypothesis cannot be rejected, then the conclusion is that the data do not show causality. If the null hypothesis is rejected, then the conclusion is that the data do show causality. In Table 5 we report Granger causality tests for all hours, peak hours, and offpeak hours for each of the three subperiods; that is, from January 1st, 1999 to December 14th, 2000 (in panel A), from December 15th, 2000 to December 20th, 2001 (in panel B), and from December 21st, 2001 to July 31st, 2005 (in panel C). We computed the optimal lag length (reported in the first column) using the Akaike Information Criterion (AIC) with a maximum value of 15 for each of r, s, q, and p. That is, we run a maximum of 50,625 regressions and selected the one that minimizes the AIC. η1 (in the second column) is the asymptotic F-test statistic for the null hypothesis that Imports do not cause power prices, when the coefficients of Exports and Load are not restricted to equal zero. η2 (in the third column) is the asymptotic F-test statistic for the null hypothesis that Exports do not cause power prices, when the coefficients of Imports and Load are not restricted to equal zero. η3 (in the fourth column) is the asymptotic F-test statistic for the null hypothesis that Load does not cause power prices, when the coefficients of Imports and Exports are not restricted to equal zero. Finally, η4 (in the fifth column) is the asymptotic F-test statistic for the null hypothesis that Imports and Exports jointly do not cause power prices when the coefficients of Load are not restricted to equal zero.
15
Panel A of Table 5 shows that, over the period from January 1st, 1999 to December 14th, 2000, there is evidence of a causal relationship between power imports, exports, and load to power prices during all hours. However, we do not find evidence of causality from exports to prices during peak hours (the p-value is 0.732) and from imports to prices during off-peak hours (the p-value is 0.896). In the former case of exports not causing prices, the reason may be the significantly low volume of exports over this first period; the average exports volume during peak hours was 12.54 MWh, which is extremely low when compared to the corresponding average load of 6,312 MWh. In the case of imports not causing prices, the interpretation of the findings is not as straightforward, as the average imports volume was higher than the exports volume. According to the results reported in panel B of Table 5, there is evidence of a causal relationship between power imports, exports, and load to power prices during all hours and peak hours over the period from December 15th, 2000 to December 20th, 2001. However, there is no evidence of causality from exports to prices during off-peak hours (the p-value is 0.064). This is perhaps due to the fact that exports were very stable over this period due to higher prices in the US markets that made exports from Alberta extremely profitable, while prices were highly volatile, since they still reflected the postCalifornian-crisis effects. Finally, according to the results reported in panel C of Table 5, there is significant causality from power imports, exports, and load to power prices over the period from December 21st, 2001 to July 31st, 2005. 6. Conclusion
We have investigated the efficiency of Alberta’s power market using a statistical physics approach --- detrending moving average --- and argued that the electricity market in Alberta is highly inefficient. We have also investigated the causal relationship between power imports and exports and power prices in Alberta’s power market by running Granger causality tests. According to our results, cross-border trade of electricity between Alberta and neighbouring jurisdictions helps predict the price dynamics in Alberta’s electricity market. The volumes of imported or exported energy across the Alberta-BC and Alberta-SK inter-tie have a significant causal effect on the pool price. Therefore, a comprehensive analysis of the price performance of Alberta’s power market must take account of the exchange of energy with interconnected markets. In particular, our results show that strong bidirectional causality exists between the variables over each of the three subperiods, from January 1st, 1999 to December 14th, 2000, from December 15th, 2000 to December 20th, 2001, and from December 21st, 2001 to July 31st, 2005. This means that the overall effect of the regulatory changes implemented by the AESO --- that is, the Pool Price Deficiency Regulation and the Intra
16
Day Market --- whose objective was to remove the ability of imports and exports to set the pool price, might have been limited. That is, irrespective of the rules applied, casual relationships exist from imports and exports to power prices over each of the three regulatory epochs. As already noted, we interpret causality in terms of predictability and not as implying underlying structural economic relationships. Hence, although we report evidence that power flows between regions Granger cause power prices, we do not claim that such interchange transactions influence power prices. Our results are also consistent with the evidence recently reported by Serletis and Shahmoradi (2006) who estimate a multivariate GARCH-M model of natural gas and electricity prices and report evidence of bidirectional (linear and nonlinear) causality between these prices, meaning that natural gas prices could also help forecast power prices. Hinich and Serletis (2006), however, test for randomly modulated periodicity in Alberta’s electricity market using signal coherence spectral analysis, and detect very unstable cycles in prices, meaning that forecast errors will have a high error variance. Thus, our results challenge the weak form as well as the strict form of the efficient market hypothesis --- the hypothesis that prices fully reflect available information. The efficient market hypothesis has its roots in the work of Bachelier (1900) and Cootner (1964), and was explicitly formulated by Samuelson (1965) and Fama (1953) for storable commodities. In this respect, Fama (1991) defined three types of (informational) capital market efficiency, each of which is based on a different notion of exactly what type of information is understood to be relevant. In particular, markets are weak-form, semistrong-form, and strong-form efficient if the information set includes past prices alone, all public information, and any information public as well as private, respectively. Finally, it is to be noted that we have not been able to successfully address the market power issues and the potentially undesirable practices mentioned in the introduction that have led to controversy within the Alberta power market. Economic issues of interchange transactions have been addressed in different ways in the literature -- see, for example, Hobbs et al. (2005), Neuhoff (2003, 2004), and Neuhoff and Newbery (2007). These papers, however, focus on explicit coordination between power markets, the general issues of arbitrage, and the effects of rules on power flows between markets. This approach, however, is not possible in the Alberta context as Alberta is bordered by ‘non-market’ power systems. Hence, addressing the market power issues in the Alberta context is an area for potentially productive future research.
17
References
Alberta Market Surveillance Administrator Report. “A Review of Imports, Exports, and Economic Use of the BC Interconnection.” (January 10, 2005). Alessio, E., A. Carbone, G. Castelli, and V. Frappietro. “Second-Order Moving Average and Scaling of Stochastic Time Series.” The European Physical Journal B 27 (2002), 197-200. Arianos, S. and A. Carbone. “Detrending Moving Average Variance: A Derivation of the Scaling Law.” Physica A (forthcoming, 2007). Bachelier, L. ‘Théorie de la spéculation’ [Ph.D. thesis in mathematics]. Annales Scientifiques de l' Ecole Normale Supérieure 17 (1900), 21-86. Bianchi, M. and A. Serletis. “Cointegration Analysis of Power Prices in the Western North American Markets.” In A. Serletis (ed.), Quantitative and Empirical Analysis of Energy Markets. World Scientific (2007). Cootner, P.H. The Random Character of Stock Market Prices. Cambridge MA: MIT Press, 1964. Canadian Energy Research Institute (CERI). “Electric Power Industry Fundamentals & the Role of the AESO.” (2004). Carbone, A, G. Castelli, and H.E. Stanley. “Time-Dependent Hurst Exponent in Financial Time Series.” Physica A 344 (2004), 267-271. Carbone, A., G. Castelli, and H.E. Stanley. “Analysis of Clusters Formed by the Moving Average of a Long-Range Correlated Time Series.” Physical Review E 69 (2004), 026105. Christian, J. and K. Hughes. “The BC-Alberta Intertie: Impact of Regulatory Change.” (June 16, 2004). Dickey, D.A. and W.A. Fuller. “A Likelihood Ratio Test for Autoregressive Time Series with a Unit Root.” Econometrica 49 (1981), 1057– 1072. Engle, R.F. and C.W.J. Granger. “Cointegration and Error Correction: Representation, Estimation, and Testing.” Econometrica 55 (1987), 251– 276. Fama, E.F. “Efficient Capital Markets: A Review of Theory and Empirical Work.” Journal of Finance 25 (1953), 383-417.
18
Fama, E.F. “Efficient Capital Markets: II.” Journal of Finance 46 (1991), 1575-1617. Hinich, M.J. and A. Serletis. “Randomly Modulated Periodic Signals in Alberta's Electricity Market.” Studies in Nonlinear Dynamics and Econometrics 10 (3) (2006), Article 5. Hobbs, B.F., F.A.M. Rijkers, and M.G. Boots. “The More Cooperation, The More Competition? A Cournot Analysis of the Benefits of Electric Market Coupling.” The Energy Journal 26 (2005), 69-97. Neuhoff, K. “Effect of Integrating Dutch and Belgium Electricity Market on Dutch Prices.” DAE, University of Cambridge, July 25, 2003. Neuhoff, K. “Coupling Transmission and Energy Markets Reduces Market Power.” Discussion Paper, University of Cambridge , January 21, 2004. Neuhoff, K. and D. Newbery. “Integrating Energy Markets: Does Sequencing Matter?” Utilities Policy (forthcoming, 2007). Pantula, S.G., G. Gonzalez-Farias, and W.A. Fuller, W.A. “A Comparison of Unit Root Test Criteria.” Journal of Business and Economic Statistics 12 (1994), 449– 459. Peng, C.-K., S.V. Buldyrev, S. Havlin, M. Simmons, H.E. Stanley, and A.L. Goldberger. “Mosaic Organization of DNA Nucleotides.” Physical Review E 49 (1994), 685-1689. Power Pool of Alberta Discussion Paper. “Assessment of Pool Price Deficiency Regulation and Intra Day Market – Next Steps.” (October 4, 2001). Samuelson, P.A. “Proof that Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review 6 (1965), 41-45. Serletis, A. and A.A. Rosenberg. “The Hurst Exponent in Energy Futures Prices.” Physica A (forthcoming, 2007). Serletis, A. and A. Shahmoradi. “Measuring and Testing Natural Gas and Electricity Markets Volatility: Evidence from Alberta’s Deregulated Markets.” Studies in Nonlinear Dynamics and Econometrics 10 (3) (2006), Article 10.
19
Table 1
Data Summary
1/1/99-31/7/05
1/1/09-14/12/00
15/12/00-20/12/01
21/12/01-31/07/05
A. Prices (Can$/MWh) Observations
56,232
15,672
8,904
31,656
Mean
67.12
90.83
77.12
52.57
Standard deviation
89.08
131.87
64.38
61.66
B. Imports Observations
56,232
15,672
8,904
31,656
Mean
161.11
217.06
106.53
148.76
Standard deviation
166.82
183.02
98.67
166.05
C. Exports Observations
56,232
15,672
8,904
31,656
Mean
123.36
57.58
267.66
115.33
Standard deviation
175.43
125.30
212.12
161.78
C. Load Observations Mean Standard deviation
56,232
15,672
8,904
31,656
6,690
5,972
6,218
7,177
825.46
546.74
549.05
649.84
Figure 1. All Hours Prices for January 1, 1999 to December 14, 2000 1,000.00 0 H = 0.2382 (s.e. = 0.0254)
900.00 -0.2 log F(n)
800.00
700.00
-0.4
600.00
-0.6
500.00
-0.8 0
400.00
0.5
1
1.5
2
log (n)
300.00
200.00
100.00
0.00 1
715
1429 2143 2857 3571 4285 4999 5713 6427 7141 7855 8569 9283 9997 10711 11425 12139 12853 13567 14281 14995
Figure 2. Off Peak Prices for January 1, 1999 to December 14, 2000 -0.2
1,000.00
H = 0.2144 (s.e. = 0.0146)
900.00
log F(n)
-0.4
800.00
-0.6
700.00 -0.8 0
600.00
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
log (n)
500.00
400.00
300.00
200.00
100.00
0.00 1
251 501 751 1001 1251 1501 1751 2001 2251 2501 2751 3001 3251 3501 3751 4001 4251 4501 4751 5001 5251 5501 5751 6001 6251 6501
Figure 3. Peak Prices for January 1, 1999 to December 14, 2000 0
1,000.00
H = 0.2332 (s.e. = 0.0145)
900.00
log F(n)
-0.2
800.00
-0.4
700.00 -0.6
600.00 -0.8 0
500.00
0.5
1
1.5
2
log (n)
400.00
300.00
200.00
100.00
0.00 1
333 665 997 1329 1661 1993 2325 2657 2989 3321 3653 3985 4317 4649 4981 5313 5645 5977 6309 6641 6973 7305 7637 7969 8301 8633
Figure 4. All Hours Prices for December 15, 2000 to December 20, 2001 -0.4
1000
H = 0.3311 (s.e. = 0.0175 ) -0.6 log F(n)
900
-0.8
800 -1
700
-1.2 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
log (n)
600
500
400
300
200
100
0 1
322 643 964 1285 1606 1927 2248 2569 2890 3211 3532 3853 4174 4495 4816 5137 5458 5779 6100 6421 6742 7063 7384 7705 8026 8347 8668
Figure 5. Offpeak Prices for December 15, 2000 to December 20, 2001 0 1000 -0.2 H = 0.4025 (s.e. = 0.0101) 900 log F(n)
-0.4
800
-0.6 -0.8
700 -1 600
-1.2 0
0.5
1
1.5
2
log (n)
500
400
300
200
100
0 1
139 277 415 553 691 829 967 1105 1243 1381 1519 1657 1795 1933 2071 2209 2347 2485 2623 2761 2899 3037 3175 3313 3451 3589 3727
Figure 6. Peak Prices for December 15, 2000 to December 20, 2001 -0.4
1000
H = 0.2074 (s.e. = 0.0106)
900 log F(n)
-0.6 800
-0.8
700
600 -1 0 500
0.5
1
1.5
2
log (n)
400
300
200
100
0 1
185 369 553 737 921 1105 1289 1473 1657 1841 2025 2209 2393 2577 2761 2945 3129 3313 3497 3681 3865 4049 4233 4417 4601 4785 4969
Figure 7. All Hours Prices for December 21, 2001 to July 31, 2005 1000
900 0
800
H = 0.1847 (s.e. = 0.01841)
-0.1 700 log F(n)
-0.2
600
500
-0.3 -0.4 -0.5 -0.6
400 -0.7 0
300
0.5
1
1.5
2
log (n) 200
100
0 1
1393 2785 4177 5569 6961 8353 9745 11137 12529 13921 15313 16705 18097 19489 20881 22273 23665 25057 26449 27841 29233 30625
Figure 8. Off Peak Prices for December 21, 2001 to July 31, 2005 -0.2
1000
H = 0.2099 (s.e. = 0.0097 ) -0.3 log F(n)
900
-0.4
800 -0.5
700
-0.6 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
log (n)
600
500
400
300
200
100
0 1
598
1195 1792 2389 2986 3583 4180 4777 5374 5971 6568 7165 7762 8359 8956 9553 10150 10747 11344 11941 12538 13135
Figure 9. Peak Prices for December 21, 2001 to July 31, 2005 -0.2
1000
H = 0.1645 (s.e. = 0.0098) 900 log F(n)
-0.3
800
-0.4
700 -0.5 600 -0.6 0
500
0.5
1
1.5
2
log (n) 400
300
200
100
0 1
796
1591 2386 3181 3976 4771 5566 6361 7156 7951 8746 9541 10336 11131 11926 12721 13516 14311 15106 15901 16696 17491
Table 2
ADF Unit Root Test Results: January 1st , 1999 to December 14th, 2000 k
∆xt = α 0 + α 1t + γxt −1 + ∑ β∆xt − j + ε t j =1
Series
Number of lags
t-statistic
p-value
Decision
A. All Hours Prices
50
-11.673
< 0.001
I(0)
Imports
50
-8.750
< 0.001
I(0)
Exports
50
-8.992
< 0.001
I(0)
Load
50
-9.773
< 0.001
I(0)
B. Peak Hours Prices
35
-10.388
< 0.001
I(0)
Imports
35
-8.280
< 0.001
I(0)
Exports
35
-11.285
< 0.001
I(0)
Load
42
-6.410
< 0.001
I(0)
C. Off-peak Hours Prices
24
-10.090
< 0.001
I(0)
Imports
33
-8.214
< 0.001
I(0)
Exports
38
-6.688
< 0.001
I(0)
Load
38
-5.616
< 0.001
I(0)
Table 3
ADF Unit Root Test Results: December 15th, 2000 to December 20th, 2001 k
∆xt = α 0 + α 1t + γxt −1 + ∑ β∆xt − j + ε t j =1
Series
Number of lags
t-statistic
p-value
Decision
A. All Hours Prices
41
-9.903
< 0.001
I(0)
Imports
39
-9.595
< 0.001
I(0)
Exports
31
-7.364
< 0.001
I(0)
Load
41
-8.181
< 0.001
I(0)
B. Peak Hours Prices
34
-8.017
< 0.001
I(0)
Imports
34
-7.456
< 0.001
I(0)
Exports
34
-7.030
< 0.001
I(0)
Load
34
-7.687
< 0.001
I(0)
C. Off-peak Hours Prices
15
-10.944
< 0.001
I(0)
Imports
11
-12.637
< 0.001
I(0)
Exports
23
-6.508
< 0.001
I(0)
Load
31
-6.728
< 0.001
I(0)
Table 4
ADF Unit Root Test Results: December 21st, 2001 to July 31st, 2005 k
∆xt = α 0 + α 1t + γxt −1 + ∑ β∆xt − j + ε t j =1
Series
Number of lags
t-statistic
p-value
Decision
A. All Hours Prices
57
-15.268
< 0.001
I(0)
Imports
52
-12.997
< 0.001
I(0)
Exports
63
-13.443
< 0.001
I(0)
Load
63
-8.968
< 0.001
I(0)
B. Peak Hours Prices
52
-12.485
< 0.001
I(0)
Imports
52
-10.742
< 0.001
I(0)
Exports
50
-13.917
< 0.001
I(0)
Load
51
-8.639
< 0.001
I(0)
C. Off-peak Hours Prices
25
-15.135
< 0.001
I(0)
Imports
48
-12.950
< 0.001
I(0)
Exports
48
-12.289
< 0.001
I(0)
Load
48
-8.163
< 0.001
I(0)
Table 5 Granger Causality Test Results
Optimal lag (r, s, q, p)
η1 (βj= 0 for all j)
η2 (γj= 0 for all j)
η3 (δj= 0 for all j)
η4 (βj= γj= 0 for all j)
A. January 1st , 1999 to December 14th, 2000
All Hours
(15, 2, 15, 15)
< 0.001
< 0.001
< 0.001
< 0.001
Peak
(15, 15, 1, 15)
< 0.001
0.732
< 0.001
< 0.001
Off-peak
(10, 1, 10, 10)
0.896
< 0.001
< 0.001
< 0.001
B. December 15th, 2000 to December 20th, 2001 All Hours
(24, 2, 20, 24)
< 0.001
< 0.001
< 0.001
< 0.001
Peak
(24, 2, 9, 18)
< 0.001
< 0.001
< 0.001
< 0.001
Off-peak
(23, 3, 4, 12)
0.001
0.064
< 0.001
< 0.001
C. December 21st, 2001 to July 31st, 2005 All Hours
(14, 14, 1, 14)
< 0.001
0.008
< 0.001
< 0.001
Peak
(15, 13,15, 15)
< 0.001
< 0.001
< 0.001
< 0.001
Off-peak
(15, 15, 8, 11)
< 0.001
< 0.001
< 0.001
< 0.001
