The paper examines the economic impact of space weather by drawing on hourly data from the PJM power grid over the period 1 June 2000 through 31 December 2001. The PJM grid is one of the largest power pools in North America. As of 31 December 2001, its service area had a population of approximately 22 million and included all or part of Pennsylvania, New Jersey, Maryland, Delaware, Virginia, and the District of Columbia. Market prices are determined for every hour of the day. As of June 2000, there are actually two markets for energy: a real-time market in which market participants can buy and sell electricity in “real time” and a day ahead market that allows participants to enter into transactions one day ahead of time. The existence of these two markets allows us to disentangle the effect of space weather conditions from other factors (such as fuel prices and expected demand) that affect the baseline price (as established in the day ahead market) for wholesale electricity. Several econometric analyses are conducted. The first examines the contribution of space weather to transmission congestion within the power grid. Building on the first analysis, the second analysis constructs an econometric model that examines the impact of space weather on the real-time market. Factors considered in the model include the outcome in the day ahead market, the level of generation utilization, unexpected demand, generation outages, unexpected transmission outages that are believed to be terrestrial in origin, and space weather. The results indicate the presence of space weather effects on the real-time price even after controlling for the other factors. A third model examines whether these space weather impacts affect subsequent prices in the far larger day ahead market.
“It's not utter nonsense…” Ben Damsky of the Electric Power Research Institute on the hypothesis that the wholesale price of electricity is affected by space weather conditions [Lee, 2001]
 While some of the economic impacts of adverse space weather conditions such as the 1989 collapse of Hydro Quebec are fabled within the space weather community, to date no one has systematically documented and quantified the true economic costs. (On 13 March 1989 a space weather–induced transformer failure on one of the main power transmission lines in the Hydro Quebec system led to a collapse of the entire power grid. Six million people lost electrical power for 9 or more hours. For more information on the 1989 collapse of Hydro Quebec, see Kappenman et al. .) This paper will begin to rectify this shortcoming by offering an initial assessment of space weather's economic impact on the electricity market using standard econometric techniques.
 Although skeptics in the power industry dismiss the economic impacts, given the deleterious effects of space weather on transmission and the high degree of reliance that the electricity market places on the transmission of power, it would be surprising if these events did not have any market impact. Adverse space weather conditions can affect the reliability, that is, the effective capacity, of the transmission system and thus can increase the average wholesale price of electricity within a power grid by constraining the flow of low-cost power.
 The paper is organized as follows. Section 2 briefly discusses the physics of space weather and its possible ramifications for the electricity market. Section 3 provides a brief overview of the PJM market, whose data are employed in the paper's empirical analyses. Section 3 also presents some anecdotal evidence concerning the impact of space weather on the transmission of electricity. Section 4 presents an econometric analysis that explores whether space weather contributes to transmission congestion. Section 5 considers the market impact of space weather. In section 5 a simple economic model is used to develop two hypotheses. The first is that adverse space weather events can be expected to increase the level of price dispersion within a power control area. The second hypothesis is that adverse space weather events can be expected to increase the system-wide weighted average price. Section 6 presents the framework of an econometric model to test the latter hypothesis, taking into account other determinants of price such as the demand for power, generation outages, etc. The model focuses on explaining the real-time price of electricity. It is hypothesized that a portion of the variation in the real-time price can be attributable to adverse space weather conditions.
Section 7 presents a methodological note on multivariate regression analysis, the quantitative technique that will be employed to test these hypotheses. Section 8 tests the latter hypothesis using data from the PJM control area. To test for threshold effects, space weather conditions are incorporated into the model as a series of binary variables. Section 9 refines the basic model, taking into account the results of section 8. Section 9 also presents the estimated impacts of space weather in terms of dollars per megawatt-hour. Section 10 considers the impacts of other electricity markets within PJM. Section 11 summarizes the paper and considers the direction of future research.
2. Connection Between Space Weather and the Electricity Market
 The fundamental reason why space weather may adversely impact the performance of the power grid is because the transmission of electricity is vulnerable to geomagnetically induced currents (GICs). Specifically, the power transmission grid acts as an “antenna” of sorts, picking up geomagnetically induced currents from depths of hundreds of kilometers. The GICs are the result of electric currents high in the atmosphere of Earth (at ionospheric altitudes), produced by geomagnetic storms and substorms as the magnetosphere interacts with disturbances in the solar wind. The primary cause of severe geomagnetic storms is sporadic ejections of magnetic structures from the Sun, coronal mass ejections (CMEs), that travel to Earth in a few days [e.g., Gosling, 1993].
 Why is the power transmission grid susceptible to GICs? From basic physics we know that the power loss in a conductor is proportional to the square of the electric current flowing in it; therefore utilities minimize that loss by transmitting electricity at high voltages (hence at reduced current). But at the starting point of the transmission grid, the electricity generators, only lower voltages are generated, so transformers are required to “step up” the voltage. At the final endpoint of the transmission grid, other transformers “step down” the voltage to make it available for distribution to users. During a space storm, GICs will enter these transformers. As GICs enter these transformers, they produce half-cycle saturation, which disrupts voltage regulation. Because geomagnetic storms can have continental-size footprints, multiple transformers can be affected, and the grid can collapse unless operators undertake compensatory actions by reducing the flow of electricity. Operators monitor local conditions relevant to their portion of the grid by use of magnetometers, and they receive alerts and warnings from national agencies monitoring space environmental conditions such as the National Oceanic and Atmospheric Administration's (NOAA) Space Environment Center in the United States as well from commercial vendors such as Metatech Corporation. The upshot is that space weather storms reduce the effective safe operating capacity of the transmission system. Several authors have addressed this phenomenon from a technical viewpoint [e.g., Kappenman, 2001; Lanzerotti, 1979, 1983; Pirjola, 1983; Pirjola et al., 1999; Boteler, 1994]. In this paper, it is the market impact of such storms that is considered.
 We begin by noting the research of Kappenman [2001, Figure 10] that the reactive power losses in a transformer as measured in megavolt-amperes-reactive (MVARS) are proportional to the GIC levels passing through the transformer. (Kappenman also points out that the reactive power loss increases with the voltage of the transformer.) These losses increase the likelihood of transmission congestion. These GIC-induced impacts will be reflected in the market price in those electricity markets where prices reflect the actual operating conditions of the power grid. Moreover, given that the reactive power losses are proportional to the GIC levels, we would not be surprised to find that even modest levels of GICs have a market impact.
 Ideally, an empirical analysis of space weather's impact on the electricity market would employ actual GIC data as the measure of geomagnetic activity. A suitable proxy for GIC would be measurements from a ground-based magnetometer network covering the grid under study. Unfortunately, neither of these data sets was available. Global indices of space weather conditions that are readily available include AE (an hourly determination of the high-latitude auroral electroject), Ap or Kp (calculated every 3 hours at midlatitudes), or Dst (calculated hourly from equatorial stations). In this analysis, GICs are proxied by the Dst (disturbance storm time) index, which was developed by Sugiura . This index is a direct measure of the hourly average of the variations of the globally symmetrical equatorial electrojet. Large negative perturbations are believed to be indicative of an increase in the intensity of the ring current. While this index may not be an ideal proxy for actual GIC data, the fact that it is reported hourly does makes it a better match for the electricity market data than either the Ap or Kp indices, which are reported on 3-hour intervals. For a summary of the various geomagnetic indices, see http://nssdc.gsfc.nasa.gov/space/model/solar/geomagnetic_indices.html.
3. PJM Market
 As of 31 December 2001, the PJM Interconnection had a peak load-generating capacity of over 54,000 MW, which makes it one of the largest centrally dispatched electric power grids in the world (Table 1). The PJM Interconnection has over 8000 miles of high-voltage transmission lines and 560 generating units. As of 31 December 2001, its service area had a population of 22 million and included all or part of Pennsylvania, New Jersey, Maryland, Delaware, Virginia, and the District of Columbia. (Its name is derived from those first three states.)
Table 1. Peak Load Capacities of Various Power Gridsa
 The PJM Interconnection was divided into 10 zones over the period of study (in early 2002, PJM was expanded to 12 zones). The zones correspond to the service territories of the following electric utilities: Atlantic Electric, Baltimore Gas and Electric, Delmarva Power and Light, Jersey Central Power and Light, Metropolitan Edison, PECO Energy, Pennsylvania Electric, Potomac Electric Power, PPL Electric Utilities, and Public Service Electric and Gas. In contrast to some power grids that use “postage stamp” pricing (such as Nordpool in Scandinavia), PJM allows the price of electricity to vary across zones; that is, PJM uses locational pricing.
 In contrast to the power market in California the PJM market is widely viewed as a success. Indicative of this, the United States Federal Energy Regulatory Commission has directed PJM and the other power pools in the northeast United States to form one northeast regional transmission organization based on PJM's platform (see http://www.pjm.com/contributions/news-releases/2001/20010920-rto.pdf). Further evidence of PJM's success is provided by R. J. Sutherland (Estimating the benefits of restructuring electricity markets: An application to PJM, unpublished manuscript, Center for the Advancement of Energy Markets, 2003), who has estimated that end use consumers within PJM saved over three billion dollars in 2002 as a result of the competitive environment provided for by PJM. With respect to the August 2003 blackout it should be noted that while the grids to both the north and the west of the PJM power grid were blacked out, only about 7% of the PJM service territory was affected (see http://www.pjm.com/contributions/news-releases/2003/20030815_power_outag.pdf). In any event, the market transparency provided for by PJM provides for an almost ideal framework in which to examine the impact of space weather on the electricity market.
 As discussed in section 1, PJM operates two markets for electricity, a day ahead market and a real-time market. PJM also operates markets for capacity credits, ancillary services, and financial transmission rights. The real-time electricity market is based on current day operations. Real-time locational marginal prices (LMPs) are calculated at 5-min intervals on the basis of the actual operating conditions of the system. For this reason the real-time market is probably the most important indicator of current operating conditions. The day ahead market is a forward market that market participants can use to insulate themselves from the price volatility in the real-time market. In this market, day ahead LMPs are calculated for each hour of the next operating day on the basis of generation offers, demand bids, and bilateral transactions submitted in the day ahead market. PJM accepts bids and offers for electricity for the next operating day until 1200 PJM local time (LT). Up until 1200 LT, PJM receives bids and offers for the next day. Between 1200 and 1600 LT the bids and offers are evaluated by PJM. The day ahead prices are released at 1600 LT. On the basis of the bids and offers, expected demand, and the requirements and known limitations of the transmission system, PJM determines the LMPs for the next operating day. In terms of the volume of transactions the real-time market in 2001, the year that accounts for the vast proportion of the sample period, accounted for approximately 21% of the average load while the day ahead market accounted for about 15% [PJM, 2002, p. 3]. Indicative of the growing importance of these markets, in 2002 the share of load accounted for by the real-time and day ahead markets was 38% and 32%, respectively [PJM, 2003b, p 3]. PJM operates a two-market settlement process such that day ahead transactions are also reported as real-time transactions. For this reason the net share of the load accounted for by the real-time market was approximately 6% in both 2001 and 2002.
 Demand-side participants can also meet their needs by purchasing energy in either real-time or day ahead import markets. They can also self supply or enter into bilateral agreements with the owners of generators or market intermediaries. In the case of a bilateral agreement the seller and a buyer of electricity bypass the electricity pool and instead enter into a direct contracting relationship. While the terms of these contracts are generally confidential, there is little doubt that they are heavily influenced by the outcomes in the real-time and day markets. In the words of PJM's 2001 state of the market, “The PJM day-ahead and real-time prices are key benchmarks against which market participants measure the result of other types of transactions” [PJM, 2002, p. 4].
 In section 2 it was hypothesized that space weather reduces the effective safe operating capacity of the transmission system. The western portion of PJM's control area (largely central and western Pennsylvania) is a net exporter of electricity while the eastern portion (the Philadelphia region and New Jersey) is a net importer. As the electricity flows from west to east, it flows through three interfaces: the western transfer interface, the central transfer interface, and the eastern transfer interface. Each of the three interfaces comprises three to five 500 kV power lines. Transfer limits (measured in megawatts (MW)) describe the reactive and voltage criteria used to safely operate the system. According to PJM's transmission operations manual, PJM's “…dispatching staff performs online security analysis studies to determine Transfer Limits for the use in real-time operations” [PJM, 2001a, pp. 3–11]. In addition, the dispatchers continuously monitor and control the actual megawatt flows on each transfer interface so that the flows are less than or equal to the transfer limits. The purpose of this is to ensure that no single contingency loss of generation or transmission causes a voltage loss drop greater than 5% [PJM, 2001a, pp. 3–13]. It is not unusual for transfer limits to change hour by hour over the course of the day. For example, during the months of June, July, and August of 2000 and 2001 the average transfer limit for the western interface was 5969 MW at 1600 UT (1200 local time) and varied about 2% during other periods of the day. The limits also vary by month. For instance, over the period June 2000 through August 2001 the transfer limits on the western interface averaged 5979 MW in the month of July but were only 5317 MW in the month of October.
 Do space weather conditions affect these limits? PJM's emergency operations manual indicates that the system's limits are reduced upon receipt of information, either from NOAA or from sources within PJM, that a “severe” geomagnetic disturbance is either imminent or in progress [PJM, 2004, p. 38]. Figure 1 suggests that this policy is actually practiced. Figure 1 reports on transfer limits and flows on PJM's eastern interface and the Dst readings on 15 July 2000. As Figure 1 reveals, between the hours of 1900 and 2200 UT the Dst index plunged from −43 to −289. (Negative Dst values indicate that a magnetic storm is in progress. The greater the negative value, the more intense the magnetic storm. For more on the index, see http://sprg.ssl.berkeley.edu/dst_index/Dst_index.html.) Over this same period the transfer limit plunged by over 900 MW, a decline of more than 20%. Grid operators apparently reacted to the geomagnetic storm by limiting the flow of electricity through the interface just enough to avoid exceeding the limits. Figure 2 shows data for a similar event that occurred on 31 March 31 2001.
4. Space Weather and Transmission Congestion: An Empirical Analysis
Section 3 suggests that adverse space weather conditions affect the safe operating limits of the PJM transmission system. The aim of this section is to examine whether adverse space weather conditions lead to transmission congestion. We define transmission congestion to be the inability to deliver low-cost power to the demand location because of transmission constraints. Over the sample period, there were more than 2300 instances in which a power line, transformer, or interface within PJM was determined to be congested in that it was unable to accommodate all of the desired power flow. While many of these events had duration of only an hour or so, others were almost as long as an entire day. Analysis of all of these events is beyond the exploratory nature of this research effort. Instead, the analysis will focus on major congestion events such as congestion on the interfaces, the 500 kV power lines, and the 500 kV transformers.
 The starting point of the analysis is the premise that the probability that an interface, transmission line, or transformer or group of transformers is congested, that is, unable to accommodate all the desired power flow, is primarily a function of load. At higher levels of load the probability of congestion is presumed to be higher. It is also hypothesized that the probability of congestion will be higher when space weather conditions are more adverse. Given that the dependent variable in this case is binary, that is, the transmission component is either congested or it is not, it would be inappropriate to estimate these events using a linear least squares regression since it would not guarantee that the predicted fraction is between 0 and 1. This inadequacy can be avoided by employing the Probit estimation technique that imposes the normal cumulative density function to estimate the model's parameters. In this way, the predicted probability of the dependent variable is strictly bounded between zero and one. For more on the Probit model, see Greene .
 Using the Probit approach, the estimating equation for transmission congestion events is
where P(Ck,t) is the probability that the transmission element k is congested during time period t; Φ is the standard normal density function; Lt is the system-wide load of PJM for period t; WDst,t is the absolute value of the Dst index for hour t when Dst < 0 (it is equal to zero otherwise); k is congestion on PJM's eastern interface, congestion on PJM's western interface, congestion on one or more of PJM's 500 kV transmission lines, and congestion on one or more of PJM's 500 kV transformers; and c, β1, and β2 are parameters to be estimated. The congestion and load data were obtained from the PJM Web site. The Dst data were obtained from the World Data Center for Geomagnetism in Kyoto, Japan (http://swdcdb.kugi.kyoto-u.ac.jp).
 The estimation results are presented in Table 2. While the overall explanatory power of the regressions is low in terms of their R squares, the model correctly forecasts congestion/no congestion over 95% of the time. The coefficients on both Lt and Lt * WDst,t are both positive and statistically significant in four out of the five regressions. For each regression the predicted values of the dependent variable were calculated. An event was classified as “space weather related” if more than 50% of the predicted value could be attributed to the variable Lt * WDst,t. Under this procedure, 20 of the 437 hours (approximately 4.6%) of congestion on the eastern interface were classified as space weather related. For the 500 kV transformers, 75 of the 416 hours of the reported congestion events (18%) could be classified as space weather related. The incidence of space weather-related events was considerably lower for the remaining categories of congestion. Table 2 also reports the average value of Dst for those congestion events deemed to be space weather related. For example, average Dst level for congestion on the eastern interface to be classified as space weather related is −141. Using the 50% criteria discussed above, the model classifies the reported congestion on the eastern interface between the hours of 2000 UT on 15 July 2000 and 0200 UT on 16 July 2000 as being space weather related. This is reassuring given that Dst ranged from −61 to −301 over these hours as well as the fact that the system was operating under emergency procedures during these hours because of a major storm that has come to be known as the Bastille Day storm. (On Bastille Day of 2000, that is, 14 July 2000, NOAA's Geostationary Operational Environmental Satellites (GOES) and the orbiting Solar and Heliospheric Observatory (http://sohowww.nascom.nasa.gov) recorded one of the most powerful solar flares of solar cycle 23. For more information on this storm, see http://science.nasa.gov/headlines/y2000/ast14jul_2m.htm.) The average Dst level for a 500 kV transformer congestion event to be classified as being space weather related is −67. This appears to be consistent with Kappenman's [2001, pp. 16–17] hypothesis that high-voltage transformers are especially sensitive to GICs. In any event, the results of this section indicate that space weather is a contributing factor to transmission congestion. The results of this analysis will be employed in later sections. Specifically, the reported non-space weather congestion events, that is, those hours where congestion is reported but the criteria for the event to be classified as space weather related are not met, will be included as explanatory variables in a multivariate regression model that seeks to disentangle the market impact of space weather from other factors that influence price.
Table 2. Probit Estimation Results of Electricity Load and Space Weather on Transmission Congestion
Voltage Constraint on the Western Interface
500 kV Transformer
500 kV Power Lines
Statistically significant at the 1% significance level.
Statistically significant at the 5% significance level.
Number of congestion events that are space weather related
Average value of Dst for those congestion events that are believed to be space weather related
Scaled R squared
5. Economics of Space Weather and the Electricity Market
 We know from basic physics and from the published operating procedures of PJM that there are reasons to believe that adverse space weather conditions can inhibit the transmission of electricity. Employing data from PJM, the analysis in section 4 has presented empirical evidence consistent with this hypothesis. This section develops a simple model of the electricity market to consider the impact of these space weather-induced transmission constraints on the market equilibrium price.
 Consider a hypothetical electricity grid with two distinct zones, zone 1 and zone 2. Assume that the operator of the grid has instituted zonal pricing. Under this arrangement, prices can deviate between the two zones, depending on the presence of transmission constraints. Assume that the demand and supply for electricity in each zone can be represented by the functions Di and Si, i = 1, 2, as depicted in Figure 3. The hypothetical supply curves Si, i = 1, 2, are upward sloping, indicating that the quantity of electricity supplied to each market increases as price increases. The demand curves Di, i = 1, 2, have a negative slope, indicating that the quantity of electricity demanded declines as price increases.
 In equilibrium, the quantity demanded equals the quantity supplied, and thus if the two zones were not connected, then the equilibrium price of electricity in zone 1 would be P1 while the price in zone 2 would be P2. At these prices, zone 1 would both produce and consume Q1 units of electricity, while zone 2 would both produce and consume Q2 units of electricity.
 However, production need not equal consumption within each zone if there are no constraints on the flow of electricity. In the absence of transmission constraints, market participants have the incentive to transmit electricity to the high-price zone from the low-price zone. This has the effect of increasing the price in zone 1, the low-price zone, while reducing the price in zone 2, thereby narrowing the price differential between the zones. If there are no transmission constraints or variable costs associated with transmission, the equilibrium price differential will be zero; that is, the equilibrium prices in the two zones will be equal. Consumers will pay the same price regardless of whether they reside in zone 1 or in zone 2. This system-wide price will be determined by total system-wide supply S1 + S2 and total system-wide demand D1 + D2, as shown in Figure 4. In this case the equilibrium price in both zones is P3, which is between P1 and P2. At the system-wide price of P3, zone 1 produces Q1S amount of electricity while only consuming Q1D amount of electricity. Zone 2 consumes Q2D while only producing Q2S. Observe that this solution entails the transmission of Q1S − Q1D amount of electricity from zone 1 to zone 2.
 Our hypothesis is that space weather can impact the above solution by curtailing the transmission of power between the zones. For instance, suppose the operators of the grid reduce the flow of electricity between zones 1 and 2 to Q′ in reaction to a geomagnetic storm (Figure 5). In this case the effective demand for power in zone 1 is D1′ (equal to D1 + Q′). Given zone 1's supply of S1, the equilibrium price of electricity in zone 1 will be P1′, which is below P3, the unconstrained system-wide price. With respect to zone 2 the effective supply with the transmission constraint is S2′. Given zone 2's demand of D2, the price in zone 2 will equal P2′. This price is above the unconstrained system-wide price of P3. Observe that the transmission constraint has caused the price to vary across zones. While Figure 5 does not show this, the weighted average price over the entire grid has increased. The reason for this is that while the price in zone 1 has declined, the output of the low-cost zone has also decreased (as represented by the movement from point E to point F along S1). In contrast, the output of electricity from the more costly zone, zone 2, has increased (as represented by the movement from point A to point B along S2). Accordingly, the overall weighted average price over both zones must rise. In summary, this analysis suggests that adverse space weather conditions will increase both the dispersion in prices across zones and the system-wide average price, all else being equal.
6. Determinants of the Real-Time Price of Electricity
 In estimating the economic costs of space weather, this paper focuses on the determinants of the outcome in the real-time market. In this way the effect of space weather on the market can be properly disentangled from the effect of other factors. It is hypothesized that the real-time market outcome will vary on the basis of the following factors.
 1. The outcome in the day ahead market: The day ahead market can be expected to reflect all public information and expectations pertinent to the next day's operating conditions. Accordingly, it will or should reflect the market prices of the fuels used to produce electricity. It should reflect known generation outages. It should also reflect known transmission constraints. Finally, it should reflect the expected load. Given the importance of these factors, it is virtually impossible to overstate the contribution of the day ahead market outcome in explaining the variation in the real-time price. The reason for this is quite simple. Market participants can choose to participate in either market. They can be expected to base their choice on their expectations of the two prices. Thus, if the day ahead price is high, it is reasonable to expect that the real-time price will also be high. In contrast, a high standard deviation in the day ahead prices may lead to a lower real-time price as suppliers respond to the high zonal dispersion in prices by increasing their real-time offerings in the zones with above average day ahead prices.
 2. Capacity utilization of the generators: The marginal cost of electricity is generally recognized to be both relatively low and constant at low levels of generation utilization. Marginal cost will eventually rise as utilization increases given that high-cost peaking units must be dispatched when utilization is high. Given that marginal cost rises as utilization increases, all things being equal, increases in utilization can be expected to increase the real-time price. The association between capacity utilization and the relative degree of price dispersion across zones can also be expected to be positive given that transmission congestion is more likely to occur when utilization is high.
 3. Unexpected demand: For any given day ahead price, the real-time price will depend on whether actual demand for electricity is less than, equal to, or greater than expected demand. In the case of actual demand greater than expected, high-cost “peaking” generating units may have to be dispatched that otherwise might have remained idle if the actual demand had been known in advance. Production from intermediate load generation plants may have to be curtailed when actual load is less than expected. Given these considerations, the market impact of higher than expected demand may not be symmetric with that of lower than expected demand: Unexpected positive demand could lead to a sharp increase in the real-time price, while negative unexpected demand may only exert moderate downward pressure on the real-time price. It also seems safe to presume that the market impact of a deviation between actual and expected load will be larger the higher the level of system load: The deviation between actual and expected load may have a minimal impact when the utilization of the generators is low but a large impact when utilization is high.
 4. Unexpected generation outages: Depending on the level of utilization, unexpected generation outages may increase the system-wide price. When utilization is low, there may be little, if any, price impact given that there are alternative generation units that can be readily dispatched. However, the price may increase substantially if an outage occurs when utilization is high.
 5. Unexpected transmission constraints that are terrestrial in origin: Events such as the damage to a power line from falling trees can impede the transmission of power from low- to high-cost zones and thus can increase both the average system-wide prices as well as the degree of dispersion across zones. The econometric analysis in section 7 will attempt to account for the market impact of these constraints on the basis of the Probit analysis reported in Table 2.
 6. Space weather: Like transmission constraints that are terrestrial in origin, space weather is hypothesized to impede the transmission of power from low-cost to high-cost zones and thus to increase the dispersion in prices across zones as well as the average price over all zones. These hypothesized impacts are consistent with the July 2000 Bastille Day storm as depicted in Figures 6 and 7. Figure 6 suggests that the sharp increase in the real-time standard deviation in zonal prices, relative to the day ahead standard deviation in zonal prices, was associated with the storm. Consistent with the view that the market impact of space weather is largely unanticipated, observe that the day ahead price does not appear to have been directly affected by the storm. Likewise, Figure 7 suggests that the sharp increase in the real-time weighted average price across all 10 zones within PJM, relative to the day ahead average price, was also the result of the storm. Specifically, at hour 1900 UT the Dst index stood at −43, and the real-time and day ahead prices were $18.50 and $18.51 per MWh, respectively. Over the next 3 hours the Dst index plunged to −289, its lowest level in over a decade, and the real-time price surged to $66.53, almost 4 times the corresponding day ahead price. While the market impact of this major storm is almost undeniable, it seems reasonable to presume that there may be a “threshold” negative level of Dst that needs to be realized before there is a market impact. To test for this, the negative values of Dst in section 8 will be represented as a series of binary variables: very low negative Dst (DstVLN), low negative Dst (DstLN), medium negative Dst (DstMN), medium high negative Dst (DstMHN), high negative Dst (DstHN), extreme negative Dst (DstEN), and very extreme negative Dst (DstVEN). The statistical significance and pattern of the coefficients should indicate the magnitude of the space weather's market impact as well as whether there is a threshold negative value of Dst.
 There is also the issue of Dst > 0 to consider. While the consensus view is that positive values of Dst are indicative of relatively benign space weather conditions (for example, see http://sohowww.nascom.nasa.gov/spaceweather/), an anonymous reviewer has cited a possible example to the contrary. The day in question was 24 March 1991. Over the hours of 0100 through 0500 UT, Dst went from −7 to 63. Dst was nonpositive and largely declining over the remaining hours of the day. According to PJM's support desk a solar magnetic disturbance induced PJM into reducing its transmission transfer limits over the time interval of 0408 through 0834 UT. We are grateful to a reviewer for informing us of this possible example in which operations may have been impaired as a result of Dst > 0.
 To test the conjecture that the positive values of Dst have a market impact, the positive values of Dst above the 75th percentile will be represented as a series of binary variables: medium positive Dst (DstMP), medium high positive Dst (DstMHP), high positive Dst (DstHP), extreme positive Dst (DstEP), and very extreme positive Dst (DstVEP). The category where Dst is positive but less than the 75th percentile of the positive values will therefore be captured in the constant term. The statistical significance of these binary variables should provide some insights on how to assess the consequences of Dst > 0.
7. Multivariate Regression Analysis: A Methodological Note
 This paper seeks to estimate the market impact of space weather using multivariate regression analysis. Although this is a common methodology in the field of economics, many readers of the Space Weather Journal may benefit from a review of this technique, including its limitations. For an excellent introduction to multivariate regression analysis as applied to the physical sciences, see Bevington and Robinson . For an introduction to multivariate regression analysis as applied to economics, see Pindyck and Rubinfeld  or Wooldridge .
 Multivariate regression analysis is sometimes equated with the estimation of correlations. However, they are not the same. The correlation between two variables, say, X and Y, is defined as follows:
where ρX,Y is the correlation coefficient, σX,Y is the covariance between X and Y, σX is the standard deviation of X, and σY is the standard deviation of Y.
 The estimated correlation coefficient reports on the strength of the linear association between X and Y. It is easily demonstrated that −1 ≤ ρX,Y ≤ 1. If ρX,Y > 0, then X and Y are positively associated in the sense that higher than average values of Y are associated with higher than average values of X. Likewise, if ρX,Y < 0, then X and Y are negatively associated in the sense that higher than average values of Y are associated with lower than average values of X. One weakness of this statistic is that it says absolutely nothing about the direction of causation between X and Y. It may also be the case that the association is spurious in the sense that another variable Z may “cause” both X and Y. An equally if not more important limitation is that the simple correlation between X and Y ignores the possibility that Y may depend on X as well as other variables such as Z. In the case before us, namely, the relationship between space weather and price, the estimated simple correlation between Dst and the real-time PJM price is −0.0275 over the period 1 June 2000 through 31 December 2001. Some may be tempted to cite this statistic as evidence that the hypothesized relation is not supported by the data. However, this temptation should probably be resisted given that the statistic does not take into account that there are factors other than space weather (such as the demand for electricity) that also affect price.
 In contrast to correlation analysis, multivariate regression analysis starts with a model. This is a critical step. Assume that the correct specification of the model is that the variable Y is a linear function of k exogenous variables X1, X2, X3…Xk:
The variable Y is the dependent variable, the Xs are the independent variables, and ɛ is the error term. In terms of notation, Xj,i represents the ith observation of the explanatory variable Xj.
 In the classical linear regression model, the above linear specification is assumed along with the following additional assumptions: (1) The Xs are nonstochastic, and there is no exact linear relationship between two or more of the independent variables. (2) The error term ɛi has an expected value equal to zero and a constant variance; that is, E(ɛi) = 0 (where E is the expected value operator) and E(ɛi2) = σ2. In this case the error term is said to be homoscedastic. (3) The random variables ɛi are statistically independent. Thus E(ɛi, ɛj) = 0 for i ≠ j. (4) The error term is normally distributed.
 The fitted equation is
where is the predicted value of Y and j is the fitted value of b (j = 1, 2, 3, …k). From equations (3) and (4) the error sum of squares is
which reduces to
The method of least squares entails choosing values of b0, b1, b2…bk that minimize the error sum of squares. The first-order conditions for minimization are
Solving these k + 1 conditions yields parameter estimates 0, 1, 2 …k, where j represents the estimated impact, all other things being equal, of Xj on Y, that is, j = ∂/∂Xj. According to the Gauss-Markov theorem, the coefficients will be the best (minimum variance) linear unbiased estimators of b0, b1, b2,…bk. In summary, least squares estimation allows a researcher to arrive at an unbiased estimate of the impact of Xj on Y even when Y is affected by other variables.
 From the central limit theorem, j will be asymptotically normal. This means that one can conduct hypothesis tests as to whether the observed value of j is statistically different from zero (or some other value).
 As one might suspect, violations of the classical least squares assumptions can have serious consequences. For instance, if the variance of the error term is heteroscedastic (a violation of assumption 2 above) in the sense that the error terms associated with “large” values of the independent variables may have a greater variance, then the variances of the estimated parameters will be biased, which can lead to an erroneous conclusion when a hypothesis test on j is performed. If the error terms are serially correlated in the sense that the error term for time period t is correlated with the error term from the preceding period (a violation of assumption 3), then the standard errors of the estimated parameters will be downward biased, which can lead to an erroneous conclusion when a hypothesis test on j is performed. If the independent variables are stochastic (a violation of assumption 1), then j will be a biased estimator of bj if the Xs are correlated with ɛ. While these and other violations of the classical least squares assumptions can lead to faulty analysis, there are, fortunately, a number of statistical procedures, some of which will be employed in this paper, that can used to arrive at estimators that are consistent and, for large samples, asymptotically efficient. (Consistency is the property where the probability limit of j is equal to bj as the number of observations approaches infinity.)
8. Space Weather and the Real-Time Price of Electricity: An Econometric Analysis
 In section 5 it was hypothesized that adverse space weather conditions increase the zonal variability in prices across zones as well as the system-wide average price, all things being equal. This section attempts to test the latter hypothesis using multivariate regression analysis. (The testing of the former hypothesis is reported in Appendix A.) As discussed in section 7, this methodology enables space weather's impact to be disentangled from the impacts of the other factors that affect price.
 Following the discussion in sections 5 and 6, the system-wide load weighted real-time price is hypothesized to be a function of the day ahead price, two measures of the dispersion in zonal day ahead prices, the level of unexpected load for the system as a whole, the magnitude of a generation outage interacted with the utilization rate of the generators, the existence of real-time transmission constraints believed to be terrestrial in origin, and space weather. More specifically, the regression equation is
coefficient to be estimated;
α0, α1, α2,…α6
coefficients to be estimated;
βk, δ1, δ2, δ3,…δ12
coefficients to be estimated;
the natural logarithm of the real-time system-wide load weighted average price for hour t;
the natural logarithm of the day ahead system-wide load weighted average price for hour t;
a binary variable that is equal to 1 if the standard deviation in the zonal day ahead prices for hour t is positive;
the standard deviation in the zonal day ahead price in hour t;
the utilization rate of the generators located within PJM in hour t;
the absolute value of the deviation between actual and expected load in hour t multiplied by expected load in hour t when actual load exceeds expected load (it is zero otherwise);
the absolute value of the deviation between actual and expected load in hour t multiplied by the expected load in hour t when the actual load in hour t is less than projected (the value is 0 otherwise);
the positive change in forced capacity, forced capacity being capacity that is not available to be dispatched, multiplied by the utilization rate;
a vector of binary variables representing transmission constraints that are believed to be terrestrial in origin for hour t.
The index k refers to the specific congestion event as follows: congestion on one or more of PJM's 500 kV transmission lines, 500 kV transformers, congestion on the eastern interface, congestion on the western interface, or a voltage constraint on the western interface. Each of the variables has a value of 1 if k was constrained because of terrestrial-based factors during hour t. Each variable is 0 otherwise. Events were classified as terrestrial as opposed to space weather related on the basis of the Probit results presented in Table 2.
DstMP is a binary variable that is equal to 1 if 11 < Dst ≤ 16, where 11 represents the 75th percentile for the positive values of Dst over the sample period and 16 represents the 90th percentile. It has a value of 0 otherwise.
DstMHP is a binary variable that is equal to 1 if 16 < Dst ≤ 21, where 21 represents the 95th percentile for the positive values of Dst over the sample period. It has a value of 0 otherwise.
DstHP is a binary variable that is equal to 1 if 21 < Dst ≤ 35, where 35 represents the 99th percentile for those observations where Dst > 0. It has a value of 0 otherwise.
DstEP is a binary variable that is equal to 1 if 35 < Dst ≤ 41, where 41 represents the 99.5th percentile for the positive values of Dst over the sample period. It has a value of 0 otherwise
DstVEP is a binary variable that is equal to 1 if Dst > 41. It has a value of 0 otherwise.
DstVLN is a binary variable that is equal to 1 if −9 ≤ Dst < 0, where −9 represents the 25th percentile for the negative values of Dst over the sample period, that is, 25% of the negative values of Dst have an absolute value that is ≤9. It has a value of 0 otherwise.
DstLN is a binary variable that is equal to 1 if −19 ≤ Dst < −9, where −19 represents the 50th percentile for the negative values of Dst over the sample period. It has a value of 0 otherwise.
DstMN is a binary variable that is equal to 1 if −33 ≤ Dst < −19, where −33 represents the 75th percentile for the negative values of Dst over the sample period. It has a value of 0 otherwise.
DstMHN is a binary variable that is equal to 1 if −56 ≤ Dst < −33, where −56 represents the 90th percentile for the negative range of Dst over the sample period. It has a value of 0 otherwise.
DstHN is a binary variable that is equal to 1 if −83 ≤ Dst < −56, where −83 represents Dst's 95th percentile over the sample period for those observations where Dst < 0.
DstEN is a binary variable that is equal to 1 if −205 ≤ Dst < −83, where −205 represents the 99.5th percentile for the negative values of Dst over the sample period. It has a value of 0 otherwise.
DstVEN is a binary variable that is equal to 1 if Dst < −205. It has a value of 0 otherwise.
 The dependent variable in equation (7a) is the natural logarithm of the real-time price. The day ahead price is also represented in terms of its logarithm. This specification was chosen following a preliminary analysis that indicated that the relationship between the two prices was not linear but could be represented as being linear in the logarithms. One might wonder why the standard deviation in the zonal prices was not also represented in terms of its natural logarithm. Such a specification would have been ill advised given that 3740 of the observations entailed a standard deviation in the zonal day ahead prices equal to 0.
 The data series on PJM's expected load were obtained from the consulting firm Itron (www.Itron.com), which provides day ahead forecasts of PJM load for every hour of the day. (PJM does not archive its day ahead load forecasts.) These forecasts are available prior to the 1200 PJM local time closing of the day ahead market, and thus this information can be expected to be incorporated into the day ahead prices. All the other data were obtained from the PJM Web site.
Equation (7a) was estimated over the period 1 June 2000 through 31 December 2001 using hourly data. Because of data issues, 226 observations were dropped from the sample. One observation was dropped because the price was negative, which is incompatible with the logarithmic form. One hundred twelve additional observations were dropped because of missing data. Each of these 113 observations required the dropping of an additional observation because the procedure used to correct for autocorrelation requires sequential observations. It should also be noted that there were 117 hours in which prices were zero. These prices are believed to reflect market conditions during the hours in question. Because of the method used to calculate the autocorrelation term, dropping these observations would effectively reduce the sample by 234 observations. To avoid dropping these observations, the arbitrary constant of .00001 was added to all the day ahead and real-time prices before the logarithmic transformation was performed.
Equation (7a) was estimated using generalized least squares with corrections for both heteroscedasticity and serial correlation. The estimation results are presented in Table 3. As expected, the coefficient on the day ahead price is positive and highly statistically significant, indicating that the average real-time price will be higher the higher the day ahead price. This is not surprising given that the day ahead price represents the market's assessment of what the real-time price will be. The coefficient on σDA+, the binary variable representing whether the standard deviation in the day ahead zonal prices is positive, is statistically insignificant. Likewise, the coefficient on the standard deviation itself is negative but is statistically insignificant. The coefficient on Ut is positive and highly statistically significant, indicating that the real-time price is higher when utilization is higher.
 The coefficient on U(L)+ is positive and highly significant, indicating that higher than expected demand for electricity has a positive impact on the real-time price. In contrast, the coefficient on U(L)− is statistically insignificant. These results suggest that there is an asymmetric price response to load-forecasting errors. Underprediction of demand, that is, forecasted load less than actual load, leads to higher prices above and beyond the impact of higher utilization on price, while overprediction of demand, that is, forecasted load greater than actual load, has no impact on price other than through the impact of lower Ut on price. One possible reason for the asymmetry is that higher than expected demand may require the use of high-cost peaking units that might not have had to be dispatched had demand been accurately forecasted. In contrast, lower than expected demand can probably be accommodated by simply taking the highest-cost generating unit off-line. One implication of these results is that there may be considerable economic benefits from improving the accuracy of load forecasts. Specifically, on the basis of the positive and highly significant coefficient on U(L)+, prices would be generally lower if the magnitude of the underprediction errors, that is, the magnitude of the load forecasting errors where demand is higher than expected, could somehow be reduced through making better use of the available weather forecasts and/or through improved weather forecasting.
 Only two of the five coefficients on the terrestrial transmission constraint variables are positive and statistically significant. Specifically, the coefficients on the terrestrial constraint variables for 500 kV lines (CL) and 500 kV transformers (CT) are positive and statistically significant. The coefficients on the other terrestrial transmission constraint variables, namely, constraints for the eastern interface (CEI) and western interface (CWI) and voltage constraints for the western interface (CWIV), are statistically insignificant. One possible explanation for these results is that the first two variables may reflect the intended supply-side considerations while the latter three variables reflect demand-side influences that are being captured in other variables such as Ut.
 The coefficient on O was hypothesized to be positive. The estimated coefficient is negative but is statistically insignificant. One possible explanation for this is that a substantial portion of the variation in this variable might be attributable to planned outages whose market impact should be reflected in the day ahead price. Moreover, there is evidence that routine maintenance is scheduled for those periods when utilization (and thus, in turn, prices) is expected to be low. According to PJM [2003a, p 16], “…planned outages usually occur during those seasons of the year when peak demand on the power System is lowest.”
 Let us now consider the estimated space weather/price relationship. Table 3 reveals that the coefficients on all the binary variables representing moderate to very extreme positive values of Dst, namely, DstMP, DstMHP, DstHP, DstEP, and DstVEP, are statistically insignificant. This is consistent with the widely accepted view that positive values of Dst represent benign space weather conditions.
 Recall the second hypothesis advanced in section 5 that more adverse space weather conditions lead to higher prices, all things being equal. Consistent with this hypothesis, the coefficients on DstVLN, DstLN, DstMN, DstMHN, DstHN, DstEN, and DstVEN are all positive. In terms of statistical significance the coefficient on DstVLN is statistically insignificant while the coefficients on the other space weather coefficients are all statistically significant. This suggests there is a threshold level of Dst, that is, that space weather only impacts the market when the severity of the storm is above the level associated with DstVLN. Moreover, consistent with the space weather/price hypothesis, the estimated coefficients increase with the severity of the Dst category, indicating that larger storms have larger impacts on the system-wide load weighted average real-time price.
 A restricted version of the model was also estimated. In this version all of the binary variables representing space weather are excluded from the estimating equation. Comparison of the two sets of parameter estimates should provide insight into the robustness of the model. The estimating equation is
The estimation results for equation (7b) are also reported in Table 3. With the exception of the constant term, all of the estimated parameters are similar in magnitude and statistical significance. For example, the estimated coefficient and t statistic for Ut in equation (7a) are 4.257 and 6.279, respectively; the corresponding values in equation (7b) are 4.149 and 6.185. Likewise, the coefficient and t statistic for ln PDA in equation (7a) are 0.407 and 3.279, respectively; the corresponding values in equation (7b) are 0.409 and 3.282. The only notable exception is that the coefficient on U(L)−, which was insignificant in equation (7a), is marginally significant in equation (7b).
 The estimation of equation (7b) enables us to assess the joint significance of the binary variables representing space weather in equation (7a). The appropriate test statistic is the F statistic
where R7a2 is the R2 corresponding to equation (7a), R7b2 is the R2 corresponding to equation (7b), q is the number of variables whose statistical significance is under consideration, k is the number of independent variables in the unrestricted version of the model, and N is the number of observations. In this case, Fq,N−k equals 1.865. This exceeds the critical value of F at the 5% level, and thus one can reject the null hypothesis that space weather, as measured by the series of binary variables, has no effect on the real-time price of electricity. (Given that all the coefficients on the binary variables representing positive values of Dst are insignificant, one could argue that a more appropriate test would involve an F statistic based on the difference in the R2 between a regression that excludes these variables and the regression equation (7b). The calculated F statistic in this case is 2.898, which is statistically significant at the 1% level. For more on the use of the F statistic in testing hypotheses involving more than one coefficient, see Pindyck and Rubinfeld [1991, pp. 110–115].)
 While this result indicates that space weather has a market impact, it does not quantify its contribution in accounting for the variation in the market price. Fortunately, space weather's contribution to the explained variation in ln PRT can be assessed by comparing the R2 associated with equation (7b), the equation that only considers terrestrial supply and demand considerations, with the R2 associated with equation (7a), the equation where both terrestrial and space weather considerations are incorporated. Inspection of Table 3 reveals that the R2 for equation (7a) is 0.508322, indicating that the unrestricted model can account for approximately 50.83% of the sample variation in ln PRT. The R2 for equation (7b), 0.507579, is marginally less than this, indicating that the vast proportion of the explained variation in ln PRT is accounted for by terrestrial supply and demand considerations.
 These results suggest that one can estimate a satisfactory econometric model to explain the real-time price of electricity without accounting for the impact of space weather. It is therefore not entirely surprising that previous analyses of the real-time versus day ahead market appear satisfied with their findings. A recent study by Longstaff and Wang  of the University of California, Los Angeles, examined the relationship between PJM's real-time and day ahead prices over the same sample period considered in this paper. They find that the day ahead price contains a significant risk premium. Specifically, with the exception of early morning hours, their results indicate that the median day ahead price is higher than the median real-time price. They suggest that this premium represents compensation for the risks of “rare but catastrophic shocks” in the real-time price. They suggest that these shocks can be attributed to equipment failures and the vagaries of terrestrial weather. Nevertheless, the results of this section of the paper indicate that including space weather in the analysis marginally improves the explanatory power of the model. As will be shown in section 9, however, the economic significance of space weather is nonnegligible.
9. Further Analysis
 Using binary variables to represent space weather conditions, the empirical results in section 8 indicate that space weather conditions more severe than the Dst levels associated with DstVLN can lead to higher real-time prices, all things being equal. Appendix A presents corollary results when a measure of price dispersion across zones is the dependent variable. This section seeks to build on these findings and to recast the model using Dst as a continuous variable. Given the statistical insignificance of the binary variables representing Dst > 0 and DstVLN as reported in section 8, the analysis will only use values of Dst in excess (in absolute value) of the range defined by DstVLN (−9 ≤ Dst < 0).
 The estimating equation is
where DstR is the absolute value of the negative values of Dst less than −9, where −9 is the lower bound associated with the binary variable DstVLN. With this formulation the marginal impact of Dst over the range −9 ≤ Dst < ∞ is assumed to be zero. Econometric models of this type are known as spline functions. For more about spline functions, see Suits et al. .
 Before proceeding, it is probably useful to consider the properties of equation (8). One might expect that the marginal impact of space weather on price is dependent on the load level. For instance, it seems reasonable to suppose that a geomagnetic storm that strikes Earth at 0300 local time when the system-wide load is low would have a substantially smaller market impact than an otherwise identical storm that strikes at 1500 local time on a hot muggy afternoon when system-wide utilization is high. We can demonstrate that equation (8) has this property. To address this issue, take the antilog of both sides of equation (8). Now differentiate this expression with respect to the variable DstR. Observe that the sign of this derivative corresponds to the sign of the parameter δ. Now take the derivative of this expression with respect to Ut. Observe that the sign of this cross derivative has the same numerical sign as the coefficient on U(α3) multiplied by the coefficient on DstR(δ). Thus the cross derivative will be positive if both α3 and δ are positive as expected. Accordingly, equation (8) does not presume that the marginal impact of space weather on price is independent of other factors. Instead, it is in accord with the expectation that the marginal impact of space weather on price will be larger when utilization is high (assuming that both α3 and δ are positive). A similar line of reasoning applies to equation (7a) except that one cannot use calculus to make the point given that the space weather is represented by a series of binary variables.
Equation (8) was estimated using generalized least squares with corrections for both heteroscedasticity and serial correlation. The results are presented in Table 4. Observe that the coefficients on the variables that were included the analysis reported in section 8 (such as Ut and U(L)+) are similar in magnitude and statistical significance to those reported in Table 3. Also observe that the model is capable of accounting for over 50% of the variation in ln PRT as indicated by the R square of 0.508. While this degree of explanatory power is not impressive, recasting the explanatory power in terms of PRT itself, as opposed to its logarithm, yields an R2 of 0.735, a value that most econometricians would find acceptable (see Wooldridge [2000, pp. 202–204] for the procedure used to calculate the R2 of the variable Y when ln Y is the actual dependent variable). More importantly, note that, consistent with the space weather/average price hypothesis discussed in Section 5, the coefficient on DstR is positive and highly statistically significant.
 To provide a better basis upon which to assess the “credibility” of the model, consider its performance during a period in which the PJM market was subjected to extreme stress. The period in question was 6–11 August 2001. Because of very hot and humid weather, a new record peak load of 53,071 MW was established at hour 2100 UT on Tuesday, 7 August. This record was short lived when a new record peak of 53,531 MW was established at hour 2100 UT the very next day. On Thursday, 9 August a new record was again established when demand reached 54,014 MW at hour 1900 UT, approximately 2400 MW higher than the peak experienced during the July 1999 heat wave [PJM, 2001b]. Figure 8 reports on the day ahead price, the real-time price, and the model's predicted real-time price over this turbulent week. As Figure 8 reveals, the real-time price went from approximately $50 per MWh to over $800 per MWh over the course of 4 of the 6 days. While the price predicted by the model does not attain the heights attained by the real-time price on 3 of these days, it does account for a large proportion of the variation in the real-time price. (There can be a bias when the parameters from a regression model are used to predict Y when ln Y is the dependent variable. Fortunately, there are well-established procedures to remove this bias. The procedure used here follows directly from Wooldridge [2000, pp. 202–204].) Specifically, the correlation between the predicted and actual real-time price is a respectable 0.884 over the 6–11 August 2001 period. While a skeptic might note that some of the forecasting errors are over 10%, we would point out that these errors pale next to the forecasting errors associated with using the day-ahead price as a predictor of the real-time price.
 With respect to the impact of space weather on price, Figure 9 reports on the values of the Dst index, the model predicted real-time price, and actual real-time prices for 15–16 July 2000. As previously depicted in Figure 7, observe that the spike in the real-time price is coincident with the plunge in the Dst index. Figure 9 also depicts the estimated space weather effect on the basis of the parameters reported in Table 4. Consistent with the fact that PJM declared an emergency off cost operations (redispatching) because of the geomagnetic storm, Figure 9 indicates that a substantial portion of the price spike can be attributed to space weather. Figure 9 indicates that the impact of the storm was approximately $30 per MWh at its peak. Further inspection of Figure 9 reveals that the model initially underestimated the actual real-time price over hours 2100 through 2300 UT, and in subsequent hours it overestimated the real-time price. We suspect that that these errors may be related to our use of Dst, a global measure of geomagnetic activity, as a proxy for local geomagnetic conditions. In any event, the correlation between the model predicted real-time price and the actual real-time price over this 2-day period equals 0.80. This is substantially higher than the corresponding 0.35 correlation between the day ahead and real-time price over this time period.
Figure 10a reports on the values of the Dst index, the actual real-time price, model predicted real-time price, and the estimated price impact of space weather on 8 September 2000. Inspection of Figure 10a reveals that the real-time price rose over the course of the morning as Dst declined and reached a local maximum at hour 1600 UT as the Dst index reached its nadir of approximately −44. While the increase in the price is nominal, some might even say trivial, this interpretation of events is consistent with the simultaneous increase in the standard deviation in the real-time price across zones to over $17 as reported by Figure 10b. On the basis of this interpretation, the estimated impact of space weather attained a value of $3.30 per MWh at hour 1600 UT. With respect to the subsequent spike in the real-time price at hour 1900 UT, comparison of the actual and model predicted real-time prices suggests that it is not space weather related.
Figure 11a reports on the values of the Dst index, the actual real-time price, the model predicted real-time price, and the estimated price impact of space weather on 12 September 2000. Figure 11a reveals that Dst declined to −73 from −2 over the hours of 0900 through 2000 UT. Over the same period of time, prices rose, reaching a peak value over $150 per MWh at hour 2100 UT. On the basis of the parameter estimates, the impact of space weather peaked at approximately $25 per MWh at hour 1900 UT. Consistent with this interpretation, the standard deviation in the zonal prices increased from approximately 0 in hour 1800 to over $19 in hour 2000 UT (Figure 11b).
Figure 12a reports on the values of the Dst index, the actual real-time price, the model predicted real-time price, and the estimated price impact of space weather on 24 and 25 November 2000. Figure 12a reveals that the Dst index declined to −33 from 11 over the hours of 1900 and 2300 UT. Over this same period the real-time price increased by over $100 per MWh. While it may seem implausible that a modest storm such as this could account for a price increase of this magnitude (in fact, the estimated space weather impact is only $4.93 per MWh at its peak), the hypothesis that space weather had a role to play in the price increase is consistent with the observed increase in the standard deviation in zonal prices from approximately 0 in hour 1900 UT to almost $20 in hour 2100 (Figure 12b).
Figure 13a reports on the values of the Dst index, the actual real-time price, the model predicted real-time price, and the estimated price impact of space weather on 31 March 2001. Inspection of Figure 13a reveals that the Dst index declined by almost 200 between the hours of 0600 and 0800 UT. Over this same period the real-time price more than doubled to over $43 per MWh, while the standard deviation in the zonal prices increased to $15 per MWh (Figure 13b). While prices initially declined as the storm ebbed, they subsequently increased to over $83 per MWh by hour 1400 UT (900 local time) as the morning demand increase of over 5000 MW most likely exacerbated the impact of the storm. (Recall that the marginal impact of space weather can be expected to be conditional on load.) On the basis of the estimated parameters reported in Table 4, the estimated impact of space weather reached a peak value of approximately $37 per MWh at hour 1500 UT.
 A skeptic could take issue with the above graphical depictions by pointing out that in some cases the real-time price was no higher on the above days than on similar days when space weather was not a factor. For instance, one could point out that the real-time price on 8 September 2000 as reported in Figure 10a was actually generally lower than the prices observed on “similar” days, namely, 1 week prior (1 September 2000) and 1 week after (15 September) the storm. At first glance, such an observation would appear to seriously undermine the analysis of this paper. However, careful consideration of the empirical findings suggests that this potential criticism is without merit. The findings do not assert that the real-time price will be unconditionally higher on days of adverse space weather conditions. Instead, the analysis indicates that real-time price will be higher if the dominant factors that affect price, namely, terrestrial supply and demand, are held constant. In this context, it is worth observing that the model indicates that the prices on 1 and 15 September 2000 were higher than on 8 September 2000 because of terrestrial supply and demand considerations. Indicative of this, the model is capable of accounting for a large portion of the variation in prices over these 3 days in that the correlation between the actual real-time price and the model predicted real-time prices on 1, 8, and 15 September equal 0.79, 0.83, and 0.88, respectively.
 On 29–30 October 2003 the Earth experienced a storm that will probably be regarded as one of the largest storms of the current solar cycle. Figure 14 reports on the Dst levels and the real-time prices for these 2 days. Observe that there were three major declines in Dst index over these 2 days. The first occurred at hour 1000 UT on 29 October when Dst sank to −180. The second occurred at hour 0100 UT on October 30 when Dst, having recovered somewhat from the first decline, plunged to −363, and the third occurred at hour at 2300 UT on 30 October when Dst fell to −401. Consistent with both the economic model of section 5 and the empirical evidence presented in this paper, prices spiked in the PJM market at approximately the same hours. Recall that space weather can be expected to lead to increases in both the average price as well as in the likelihood that prices will vary across zones; that is, the standard deviation in zonal prices will exceed 0. Close inspection of Figure 14 suggests that the events of the 28–30 October time period are consistent with these hypotheses.
 A skeptic could also question why the magnitude of the price spike on 30 October 2003 was so modest (approximately $54 per MWh) given that Dst reached −401. We suspect that low capacity utilization may have been a factor: Load was less than 40,000 MW (out of a capacity of over 70,000 MW as of that point in time, PJM having undergone a major geographic expansion in 2002) at the time of the storm. This is important if one recalls the discussion earlier in this section where the properties of equation (8) were discussed. In this discussion the marginal impact of Dst is shown to depend on the level of capacity utilization. Another consideration is that PJM may have taken into account the space weather advisory issued by NOAA's Space Environment Center on 28 October that warned of a G5 storm over the next 48 hours. This warning would seem to have been highly credible given the events of 29 October. The warning can be viewed at http://www.sec.noaa.gov/advisories/200310281800_bulletin.html.
 In conclusion, Table 5 provides a summary of the estimated impact of space weather on the real-time price. For the range −19 < Dst < −9 the estimated average impact is $0.50 per MWh. As expected, the impact is higher during those periods of more adverse space weather. The estimated impact is $1.52, $2.66, $5.07, $7.93, and $19.02 per MWh for the categories DstMN, DstMHN, DstHN, DstEN, and DstVEN, respectively. Over all observations, including those cases where Dst was above the threshold of −9, the estimated average impact is $1.1679 per MWh or approximately 3.67% of the average real-time price. As with all estimates, there is a degree of uncertainty. The typical approach to presenting this uncertainty is to calculate a confidence interval. On the basis of the estimated parameter on DstR and its associated standard error, the 99% confidence interval for the coefficient is 2.91E-3 ± 1.5794E-3. This translates into a confidence interval for the price impact of $1.1679 ± $0.002 per MWh. While the narrowness of this confidence internal is reassuring, one should note that there are other elements of uncertainty, including, but not limited to, the uncertainty in the price impact associated with using Dst as a proxy for local geomagenetic conditions. Since the marginal impact of DstR on price is not independent of other factors such as utilization, there is also the issue of the parameter uncertainties in these other coefficients.
Table 5. Estimated Impact of Space Weather on the PJM Real-Time Price Over the Period 1 June 2000 Through 31 December 2001
−19 ≤ Dst < −9
−33 ≤ Dst < −19
−56 ≤ Dst ≤ −33
−83 ≤ Dst < −56
−205 ≤ Dst < −83
Dst ≤ −205
Number of hours
Estimated impact of space weather in dollars per MWh
Estimated percentage impact
10. Impact on Related Markets
Section 9 presents strong empirical support for the hypothesis that adverse space weather events affect the outcome in the real-time market. However, the net share of the overall electricity market accounted by real-time transactions was around 6% over the sample period. Accordingly, the economic impact of space weather on the overall market will be almost inconsequential unless its impact on the real-time market spills over into other markets. In this section we consider this issue.
10.1. Linkage Between the Real-Time and Day Ahead Markets
 The starting point of the analysis is that market participants are free to choose between the real-time and day ahead markets. The extent to which a firm participates in one market relative to the other can be expected to depend on how the outcomes of the two markets compare. Specifically, real-time prices that are above their respective day ahead prices may signal to purchasers (sellers) that the real-time market is a more expensive source of supply (relatively more lucrative outlet for sales). The purchasing firm in this case would have the incentive to reduce its future reliance on the real-time market vis-à-vis the day ahead market. At the same time, sellers of electricity would have the incentive to increase their future offers to sell in the real-time market and reduce their future offers to sell in the day ahead market. These revisions in strategies effectively reduce (increase) the future demand for electricity in the real-time market (day ahead market) and increase (reduce) the future supply in the real-time market (day ahead market). These changes in both future supply and future demand can be expected to increase future day ahead prices. Following this logic, a market outcome whereby the real-time price is greater than the day ahead price on a particular hour and day, because of space weather or any other reason, may impact the day ahead prices that are observed in subsequent days. The essential argument is that the real-time and day ahead prices are cointegrated in the sense that there is an equilibrium relationship between the two prices. To test for this, each series was tested for the presence of a unit root using the augmented Dickey-Fuller test. Both tests indicated that the hypothesis of a unit root could be rejected. Given these results, the two series were then subjected to the Engle-Granger cointegration test. The results of this analysis indicated that the hypothesis of no cointegration could be easily rejected. These results are available upon request. For a tractable exposition of these tests, see Wooldridge .
 To test the hypothesis that outcomes in the real-time market influence future outcomes in the day ahead market, consider an econometric model of the day ahead price for hour k (1 ≤ k ≤ 24), where the first explanatory variable is the natural logarithm of the forecasted load for hour k. The next explanatory variable is the spot price of natural gas. While natural gas represents a smaller share of PJM's energy inputs as compared with, say, coal, electricity from natural gas can play an important role in the price determination process given that plants that burn this fuel are oftentimes the last generating units to be dispatched, coal and nuclear plants typically satisfying base load demand. (For evidence regarding this point, see R. Gilkey, Natural gas market fundamentals and potential impact on PJM electric pricing, Powerpoint presentation, May 2003, available at http://www.pjm.com/committees/working-groups/dsrwg/downloads/20030529-natural-gas-gilkey.pdf.) The price of natural gas ranged from $2.03 to almost $20 per GJ over the sample period (the average was approximately $5.25). Given this volatility and its role in the price determination process, there is probably considerable merit to including it as an explanatory variable.
 The model also includes as explanatory variables the lagged differences between the real-time and day ahead prices. The concept is that these lagged differences may affect the day ahead price for hour k. In estimating this model, one needs to take into account that the day ahead market closes at hour 1200 local time. Consequently, deviations between the real-time and day ahead price after hour 1200 local time of the previous day but before the hour k of the day in question cannot be expected to impact the day ahead price in hour k. For example, if the hour in question is hour 2100 local time (k = 21), then there is a 33-hour gap in which the deviation between real-time and day ahead price cannot affect the day ahead price in hour 2100, the day ahead market having been closed 33 hours earlier. If the subsequent deviations affect bidding behavior, it is presumed that the impact will be reflected over the following week, that is, the subsequent 168 hours.
 On the basis of the discussion above, the model to be estimated is
where c, α1, α2, and βt are coefficients to be estimated; PDAk is the average day ahead price for hour k; ln E(L)k is the day ahead load forecast for hour k; Pgas is the previous day's closing spot price of natural gas in Transco zone 6, which is a market center for natural gas covering a six-state area from Virginia to New York City (data series obtained from the trade publication NGI Daily Gas Price Index); PRT is the average real-time price for hour t, where t < k; and PDA is the average day ahead price for hour t, where t < k.
 If previous market outcomes have no effect on the day ahead price, that is, market participants view the deviations between the real-time and day ahead prices as aberrations of no consequence in terms of future bidding behavior, then the sum of the coefficients on the lagged differences between the real-time and day ahead price, that is, ∑β, will not be statistically different from zero. Alternatively, if events in the real-time market spill over fully into the day ahead market such that a $1.00 differential between the real-time and day ahead price during a particular hour and day leads to a $1.00 increase in the day ahead prices observed during future days, then ∑β will not be statistically different from unity.
Equation (9) was estimated for the local time hours of 0700, 0900, 1100, 1200, 1300, 1500, 1700, 1900, 2100, and 2300 over the period 1 June 2000 through 31 December 2001. The times in question are in local time so as to adequately control for the period in which the market is closed. (Recall that the day ahead market closes at hour 1200 local time. Accordingly, the gap between the closing of the market and hour k of the subsequent day would vary depending on whether daylight savings time or standard local time was in effect.) The sample is identical to that considered in the earlier analysis for the real-time market except that here the analysis focuses on prices for specific hours of the day. Because of this, there are far fewer observations in each estimation than in the estimation of equations (7a), (7b), and (8). The results are reported in Tables 6a and 6b. In terms of overall explanatory power the estimated equations can account for between 46% and 71% of the variation in the day ahead price. The coefficient on the variable ln E(L) is positive and highly statistically significant, indicating that the price will be higher for those hours when forecasted demand is higher. With the exception of the equation for hour 1500 local time the coefficient on the spot price of natural gas is both positive and statistically significant, indicating that higher prices for natural gas increase the day ahead price of electricity. With respect to the lagged price differences, each equation contains 168 lagged real-time/day ahead price deviations, and thus space considerations limit us to reporting the sum of the coefficients. To aid in the interpretation of the results, the standard error of ∑β is reported in parentheses immediately below the point estimate.
Table 6a. Estimation Results for Equation (9) for the Local Time Hours of 0700, 0900, 1100, 1200, and 1300
 Several points are in order. In all 10 cases the sum of the coefficients on the lagged price differences, that is, ∑β, is greater than zero. In the case of hour 1100 local time the sum of the coefficients equals 1.07, which is more than 3 times the associated standard error, indicating that the hypothesis of no spillover from the real-time market to the day ahead market can be rejected at the 1% significance level. The null hypothesis of no spillover can also be rejected for hour 2300 at the 1% significance level. For the local time hours of 0900, 1200, 1700, 1900, and 2100 the sum of the coefficients is more than twice the associated standard errors, indicating that the hypothesis of no spillover from the real-time market to the day ahead market can be rejected at the 5% significance level. The null hypothesis can be rejected at the 10% level for the local time hours of 0700, 1300, and 1500. In summary, in all 10 cases the estimates indicate that the null hypothesis of no spillover from the real-time market to the day ahead market can be rejected.
 But is the spillover partial or complete? In other words, does a $1.00 positive difference between the real-time and day ahead price increase future day ahead prices by, say, $0.10? Or is the spillover complete in the sense that a $1.00 positive differential between the real-time and day ahead price alter bidding behavior such that future day ahead prices are $1.00 higher? To address this issue, note that the sum of the estimated coefficients ranges from a low of 0.67 to a high of 1.71. Also note that the difference between these values and unity is either less than or approximately equal to the associated standard error. For example, ∑β = 0.67 when k = 7. The difference between this value and 1 is 0.33, which is less than the standard error of 0.35. Accordingly, while one can reject the hypothesis that ∑β = 0, one cannot reject the hypothesis that ∑β is unity at standard significance levels. This indicates that the hypothesis that ∑β equals unity cannot be rejected at standard levels of statistical significance in any of the 10 cases. On the basis of these results, it appears that the impact of space weather on the electricity market is not confined to the real-time market. Instead, the results indicate that when the real-time price is above the day ahead price, whether induced because of space weather considerations or any other factors, market participants revise their bidding behavior so as to increase the day ahead price in future periods.
10.2. Other Market Arrangements
 In addition to the real-time and day ahead markets, market participants in PJM have other institutional arrangements through which they can buy and sell energy. Load-serving entities such as local distribution companies can meet their needs through self-supply, bilateral purchases from generation owners, or market intermediaries. These contracting relationships can be short term or multiyear in duration. The contractual price can be indexed to either the day ahead or real-time market. Alternatively, the participants can enter into fixed-price contracts. In the former case the spillover effect of space weather on the contractual price is obvious: Prices for those days when there are space weather effects simply get averaged into the index used to calculate the contractual price. The spillover effect in the latter case, that is, the case where there is a fixed-price contract, is no less real but is less apparent at first glance. To see this, let us first acknowledge that the contractual price in a fixed-price contract will reflect, in part, the prevailing market conditions when the agreement was entered into. The terms of a fixed-price contract that was signed in, say, late July of 2000 will reflect the turbulent market conditions of the Bastille Day event as well as the other much less significant events that occurred over the period that each of the two parties deem relevant in determining the net economic gains from the contractual relationship. Accordingly, while a local distribution company may be able to insulate itself from the direct price effects of space weather that occur during the period covered by the contract, those effects can be expected to be factored into the price when the terms of the contract are renegotiated.
 There is reason to believe that the parties in a fixed-price bilateral contract are impacted by space weather events even over the period the contract is binding. The reason for this is that under PJM's rules all bilateral transactions must specify both a source location, where the producer delivers the energy, and a sink location, that is, where the buyer is receiving the energy, and the two parties are billed congestion charges equal to the difference in the source/sink locational marginal prices. (See PJM 101: The Basics—Part 1, p. 96. This document can be obtained at http://www.pjm.com/services/training/train-materials.html.) If the bilateral transaction is a scheduled transaction, the billed congestion cost per megawatt would be equal to the difference in the day ahead locational marginal prices corresponding to the source/sink. In the case of an unscheduled transaction, the billed congestion cost per megawatt would be equal to the difference in source/sink real-time locational marginal prices. Given that the empirical evidence presented in this paper indicates that space weather contributes to these zonal differences in prices (see Appendix A for an analysis of space weather's impact on the zonal variation in the locational marginal prices), it is probably not safe to presume that the parties in a fixed-price bilateral contract are immune from the cost of space weather.
 The analysis in this paper has produced empirical evidence that space weather conditions have affected the wholesale market for electricity. Using Probit analysis, we have provided empirical evidence that adverse space weather conditions have contributed to congestion on the PJM transmission system. We also presented an econometric model of the determinants of the real-time price of electricity. Explanatory variables in the model included the outcome in the day ahead market, the level of generation utilization, unexpected demand, generation outages, unexpected transmission outages that are believed to be terrestrial in origin, and space weather. After controlling for other factors that influence price, the results indicate that even relatively minor storms can affect the real-time price. Subsequent analysis indicates that these impacts can be expected to be reflected in future day ahead prices.
 While some have dismissed space weather's impact on the market, the analysis presented here indicates that estimated average impact is a nontrivial 3.3% of the real-time PJM price. While the Dst/price relationship was found to be robust, the precise estimate should be treated with a relatively high degree of caution given that econometric modeling is not an exact science as well as the fact that the measure of space weather may be a poor proxy for GICs. With these caveats in mind the economic impact of space weather works out to be approximately $500 million based on the hourly prices and loads (over 400 million MWh) over the sample period (1 June 2000 to 31 December 2001). This presumes that the impact of space weather is not confined to just the real-time and day ahead markets. The estimated impact is about $100 million if one assumes that bilateral transaction prices are not influenced by space weather activity. We believe this case to be implausible given our expectation that rational negotiators in a potential bilateral fixed-price contract will use historical market prices as a benchmark in assessing the benefits of the contractual relationship. However, we freely concede that we have not demonstrated this point.
 Are the findings reported here representative of the price impact for other power grids? Only analysis of other power grids will tell. Potential candidates for analysis include the New York independent system operator (ISO), the New England ISO, California, the National Grid of England and Wales, Nordpool (Scandinavia), the Ontario independent market operator, and possibly even the New Zealand power market. Some preliminary results have been obtained for the New York ISO. The results are qualitatively similar to the results presented here, but data on variables such as utilization and transmission congestion need to be collected and incorporated into the analysis. In addition to the analysis of more power grids, local magnetometer data are needed so as to ensure that the space weather variable accurately reflects the actual grid conditions. Dst is a global index of geomagnetic conditions, and thus it is probably a less than ideal measure.
 While much has been learned during the course of this research effort, there remains much territory to be explored. For instance, one facet of the current study examined the relationship between space weather and the probability of five different types of transmission congestion (congestion on the 500 kV transformers, congestion on the eastern interface, etc). A statistically significant relationship was found in four of the five cases. There are numerous other congestion events that we did not examine. Examples include congestion on the 345 kV transformers, the 230 kV transformers, the 138 kV transformers, and the 69 kV transformers. Analysis of the space weather contribution to congestion on these transformers would substantially increase our knowledge of space weather's impact on the transmission infrastructure and, in turn, the market.
 This research effort focused on flows of electricity within a given control area. While the results presented here indicate that this was the logical place to begin the analysis, it seems likely that space weather also affects the flows of electricity between grids. There is anecdotal evidence from the Hydro Quebec 1989 collapse that this is indeed the case.
 Another aspect we might consider is the following: There are different “types” of geomagnetic storms. Do they have different impacts on the electricity market? During certain times of the solar cycle, there are recurrent, somewhat milder, disturbances every 27 days that have limited duration (we have not seen that in our study period). But the most significant storms are caused when CMEs strike, and they can last for more than a day (e.g., 15 July 2000). It may be the case that storms have a cumulative impact on the grid and hence price, that is, that the impact of current space weather conditions on the grid might be conditional on the severity and duration of the storm in question.
 Another potential fruitful area of analysis is whether forecasts of space weather mitigate space weather's economic impact. One might expect that the economic impact of space weather would be substantially lower if market participants had credible forecasts of the storms. However, this may not necessarily be the case if there is very little that can be done by grid operators to mitigate the impact. Inclusion of a variable in the estimating equation that represents historical forecasts of space weather activity may shed some light on this issue.
Appendix A:: Space Weather and Price Dispersion Across Zones
 Following the discussion in sections 5 and 6, the level of price dispersion in the real time market, as measured by the probability that the standard deviation in zonal prices is nonzero, is hypothesized to be a function of conditions in the day ahead market, the utilization rate of the generators, the level of unexpected load for the system as a whole, the relative magnitude of generation outages, the existence of real-time transmission constraints believed to be terrestrial in origin, and space weather. More specifically, the regression equation is
where σRT is the real-time standard deviation in zonal prices; P(σRT) is the probability that σRT is nonzero during time period t; and Φ is the standard normal density function.
 For approximately 47% of the observations, σRT, the standard deviation in the real-time price across zones, was equal to 0; that is, the grid was entirely uncongested in the sense that prices were equal across all zones. The method of least squares can potentially lead to seriously biased estimates under these circumstances. To avoid this bias, equation (A1) was estimated using the Probit maximum likelihood procedure. See Green  for a discussion of shortcomings of least squares under these circumstances as well as how these shortcomings can be avoided through the use of the Probit procedure.
 The estimation results are presented in Table A1. As expected, the coefficient on the day ahead price is positive and statistically significant, indicating that the higher the day ahead price, the higher will be the probability that the standard deviation in the real-time zonal prices will be positive. The coefficient on σDA+ is also positive, indicating that a positive standard deviation in the day ahead price makes it more likely that the standard deviation in the real-time prices will also be positive. The empirical results also indicate that the size of the standard deviation in the day ahead price also matters, as evidenced by the positive and statistically significant coefficient on σDA.
Table A1. Probit Analysis of the Standard Deviation in Zonal Real-Time Prices
Number of observations where the standard deviation of the zonal prices exceeds zero
 The coefficient on Ut is positive and highly statistically significant, indicating that the standard deviation in zonal prices is more likely to be positive when the utilization rate of the generators is higher. The coefficient on U(L)+ is negative and highly significant, suggesting that higher than expected demand for electricity reduces the likelihood of price dispersion across zones. In contrast, the coefficient on U(L)− is both positive and statistically significant. One possible reason for the asymmetry in the coefficients on unexpected load is that higher than expected demand can typically be satisfied through the use of peaking units that are located in close proximity to end-users. In contrast, reductions in the amount of generation that is dispatched will usually affect intermediate load power plants that tend to be more distant from end-users. The positive and statistically significant coefficients on the five terrestrial transmission constraint variables (CL, CT, CEI, CWI, and CWIV) indicate that transmission congestion that is terrestrial in origin increases the probability that there will be variation in the zonal prices.
 The coefficient on O is negative and statistically significant. This is an unexpected result. One possible explanation is that a substantial portion of the variation in this variable might be attributable to planned outages where the plant in question is taken out of service for routine maintenance. Since these outages are planned, it seems reasonable to suppose that they are planned for periods when utilization and hence the variation in zonal prices are low.
 Let us now consider the estimated space weather/standard deviation relationship. Table A1 reveals that the coefficients on all the binary variables representing moderate to very extreme positive values of Dst, namely, DstMP, DstMHP, DstHP, DstEP, and DstVEP, are statistically insignificant. This is consistent with the widely accepted view that positive values of Dst represent benign space weather conditions.
 Recall the first hypothesis advanced in section 5 that more adverse space weather conditions lead to greater dispersion in prices, all things being equal. Consistent with this hypothesis, the coefficients on DstVLN, DstLN, DstMHN, DstHN, DstEN, and DstVEN are all positive and statistically significant. The only outlier is the coefficient on DstMN, which is negative and highly insignificant. Leaving aside this one case, the estimated coefficients generally increase with the severity of the Dst category, indicating that the probability of transmission congestion, as measured by the probability of σRT being nonzero, is larger the larger the severity of the storm. Using the Tobit procedure, the determinants of the level of the standard deviation in the zonal prices was also modeled. The results of this analysis (available upon request) are generally consistent with the Probit analysis reported in Table A1. The only exceptions concern the statistical significance of the coefficients on DstVLN, DstLN, and DstHN. In the Probit analysis, which examines the probability that σRT is positive, these coefficients are statistically significant. In the Tobit analysis, which examines the magnitude of σRT, taking into account that the lower bound of σRT is 0, these coefficients are insignificant. Our interpretation of these differences is that minor storms affect the probability that σRT will be positive but not its magnitude, while larger storms affect both the probability that σRT will be positive and its level of magnitude.
 This material is based on work supported by the National Science Foundation under grants 0318582 and 0127213. The authors would like to thank Sally Lou, Matt Austin, and Elaine Einfalt for their excellent research assistance. The authors would also like to thank the World Data Center for Geomagnetism in Kyoto, Japan, the Dst stations, and the persons who derive the index for providing us with the Dst data series, the staff of PJM L.L.C. for providing access to their data series, the consulting firm Itron for providing archived day ahead forecasts of electricity demand for the PJM control area, and Jose Villar of the Energy Information Administration for his guidance on natural gas pricing data. Thanks also go to Ernest M. Zampelli for his suggestions on the econometric modeling. Preliminary results were presented at the 2002 URSI meetings in Maastricht, Netherlands, the 2003 Allied Social Science Association meetings in Washington, D. C., the April 2003 International Industrial Organization meetings in Boston, Massachusetts, and the 2003 Space Weather Week meetings in Boulder, Colorado. Thanks go to the participants of these sessions for their constructive criticism and helpful suggestions. In particular, we have benefited from fruitful discussions with David Boteler, John Felmy, David Fugate, Henry Hertzfeld, Matt Lackay, Louis Lanzerotti, Udi Helman, Ernest Hildner, John Kappenman, and Ray Williamson. Any errors remain the full responsibility of the authors.