1. 1 Geographic Integration, Transmission Constraints, and Electricity Restructuring * Pennsylvania State University and The Brattle Group, respectively. The authors can be contacted at ank1@psu.edu and james.reitzes@brattle.com.ank1@psu.edujames.reitzes@brattle.com March, 2005 Not for Quotation without Authors’ Permission Andrew N. Kleit James D. Reitzes*

2. 2 Topics for Discussion Ž How to Estimate Arbitrage Costs Ž How to Modify the Arbitrage Cost Model for Electricity Markets in Order to: Estimate the Impact of ISO formation on Electricity Trading Costs Assess the Prevalence of Binding Transmission Constraints under Different Transmission Organizational Regimes ●How to Estimate the Shadow Value of Adding Further Transmission Capacity All with easily available data!

3. 3 Arbitrage Cost Estimation Basic Methodology

4. 4 Arbitrage Cost Estimation – Basic Methodology Ž The basic “arbitrage cost” model was developed by Spiller and Wood (1988), who examined integration of regional gasoline markets. Ž Other papers using a similar model include: Sexton et al. (1991) for celery; Kleit and Palsson (1996, 1999) for Canadian cement; and Kleit (1998) in natural gas.

5. 5 Arbitrage Cost Estimation – Basic Methodology (cont.) Ž Use maximum likelihood techniques to distinguish two regimes: (a) Arbitrage (Unconstrained Trade) - inter-regional price differences represent marginal trading costs. (b)Autarky - inter-regional price differences most likely reflect differing regional supply and demand conditions. Under autarky, (i) no trade occurs, or (ii) trade occurs on a long-term contract basis but does not respond to short-term arbitrage opportunities.

6. 6 Arbitrage Cost Methodology Ž Assume a (stochastic) cost of “arbitrage” – the cost of shipping a good from Region 1 to Region 2 (or vice versa). The price difference between the two regions cannot exceed arbitrage costs.

7. 7 Basic Arbitrage Cost Model Ž Let P 1 = price of the good in Region 1, Let P 2 = price of the good in Region 2, Let Y= P 1 -P 2. Ž Without the threat of arbitrage, the price difference between the two regions is determined by the autarky relationship  P N =  + , (1)  = constant;  ~ N(0,  2 ).

8. 8 Basic Arbitrage Cost Model (cont.) Ž If price in Region 1 becomes “much” higher than price in Region 2, buyers in 1 will arbitrage the difference by buying the good in 2 and shipping to 1. Ž Now define the arbitrage (i.e., trading) cost of sending the good from Region 2 to Region 1 T 1 = T 1 +  1, (2)  1 ~ N(0,  1 2 ), truncated from below at -T 1 Ž The reason for the truncation from below is that arbitrage costs must be nonnegative, (i.e., T 1 >0).

9. 9 Basic Arbitrage Cost Model (cont.) Ž Now, an observed price difference, Y= P 1 -P 2 >0, could result from two possible states: (1)autarky (i.e., the absence of arbitrage), implying that arbitrage costs exceed the observed price difference:  P N =Y and T 1 >Y. (2) arbitrage, implying that the price difference would be larger under autarky T 1 =Y and  P N > Y.

10. 10 Basic Arbitrage Cost Model (cont.) Ž The likelihood of observing a particular value of Y is therefore as follows: L(Y i ) = Likelihood (  P N =Y i and T 1 >Y i ) + Likelihood (T 1 =Y i and  P N >Y i ),(3) L(Y i ) = f(  P N =Y i )(1-F(T 1 =Y i )) + f(T 1 =Y i )(1-F (  P N =Y i )),(4) where f = pdf, F=cdf. This is a variant of Tobit with stochastic limits.

11. 11 An Extension to the Basic Arbitrage Cost Model Ž Autarky price differences should be related to structural factors (i.e., cost and demand conditions) in each regional market. (7)

12. 12 Electricity Restructuring and Market Integration

13. 13 Electricity Restructuring and Market Integration Ž ISOs were designed to facilitate wholesale electricity trading by lowering trading costs and mitigating incentives to manipulate the transmission system. --- Has this occurred? Ž Hardly any analysis has been performed on this question. Ž Thus, we examine the impact of forming the PJM ISO on electricity trading costs between PJM and New York and between PJM and the ECAR Reliability Region.

14. 14 Modified Arbitrage Cost Model Adding Quantity-Constrained Trade

15. 15 Adjusting the Arbitrage Cost Estimator for Electricity Markets Ž Since transmission capacity limits and institutional impediments may constrain the quantity of electricity that can be traded between regions, we modify the traditional arbitrage cost model to consider three possible equilibrium states: (1) autarky (2) arbitrage (i.e., unconstrained trade), and (3) quantity-constrained trade.

16. 16 Quantity-Constrained Trade Ž Quantity-constrained trade represents a state where trade takes place up to some “capacity limit”, and no more. Ž Capacity limit can be a physical or institutional trading barrier..

17. 17 Quantity-Constrained Trade Ž We express the price differential between regions 1 and 2 under quantity-constrained trade as: C i = A i - FLOW i +  = Z i ′ θ - FLOW i +  (9) Ž Thus, the quantity constrained price difference equals the autarky price difference, less FLOW 1, where FLOW 1 represents the change in the price difference induced by the flow of electricity from one region to another up to the available quantity limit.

18. 18 Likelihood Function with Quantity-Constrained Trade L + (Y i ) = Likelihood (  P i N =Y i and T 1i ≥ Y i ) + Likelihood (T 1i =Y i and  P i N > Y i ≥ C 1i ) + Likelihood (C 1i =Y i and  P i N > Y i >T 1i ). (10)

19. 19 Modified Trading Cost Equation Ž We add indicator variables to estimate the impact on trading costs of: (a) the formation of the PJM ISO (April 1, 1998) (b) PJM’s switch from cost-based to market-based bidding (April 1, 1999) Ž Revised trading cost specification is: T 1 = T 1 + β 98 I 98 + β 99 I 99 +  1, (2') where I 98 =1 after April 1, 1998; else 0 I 99 =1 after April 1, 1999; else 0  1 ~ N(0,  1 2 ), truncated from below at -(T 1 + β 98 I 98 + β 98 I 99 )

20. 20 Calculating Regime Probabilities – Using Bayesian Updating ● From (10), we obtain: Recall Pr(A|B) = Pr (A∩B)/Pr(B). Writing in “likelihood space”, Pr(Autarky|Y i ) = L + (Autarky∩Y i )/L(Y i ) We calculate probabilities similarly for the unconstrained and constrained trading states.

21. 21 Institutional Detail and Data

22. 22 Institutional Detail Ž Our analysis focuses on arbitrage costs involving: PJM - New York PJM – ECAR Ž On April 1, 1998, the PJM “exchange” market began with only “cost-based” bidding permitted. However, no explicit mechanism existed for monitoring compliance with costs. PJM members were allowed to supply electricity at “market- based” rates outside of PJM’s service territory (and through bilateral transactions within PJM’s territory).

23. 23 Institutional Detail (cont.) Ž After April 1, 1999, “market-based” bids were allowed within PJM’s service territory. Ž We use indicator variables to distinguish 3 periods: (i) before April 1998; (ii) between April 1998 and March 1999; (iii) April 1999 and after.

24. 24 Data Time period January 1997-July 2002 --- 1350 observations Dependent variable daily electricity prices (PJM, NY, ECAR) --- volume-weighted averages of the contract prices for pre-scheduled, day-ahead 1x16 electricity blocks (Power Markets Week)

25. 25 Data (cont.) Demand shifter temperatures (PJM, NY, ECAR) --- summer and winter degree days calculated from NOAA temperature data Cost shifter fuel costs --- Henry Hub gas prices

26. 26 The Results PJM – New York

27. 27 Autarky Parameters: PJM/NYISO (t-stats in parentheses) Constant 11.27** (3.42)  38.66** (4.84) Price of Natural Gas -3.32** (-3.80) (Δ Cooling Degree Days) -2.79** (-3.21) (Δ Cooling Degree Days) 2 0.217** (8.07) (Δ Heating Degree Days)1.18 (1.36) (Δ Heating Degree Days) 2 0.00413 (0.15)

28. 28 Transaction Costs: PJM/NYISO (t-stats in parenthesis) Transaction Cost to PJM from NYISO Transaction Cost to NYISO from PJM Constant -18.07** (-3.91) -10.67** (-2.71) April 1998 Indicator 1.31 (0.34) -4.05 (-1.17) April 1999 Indicator -4.00* (-1.91) 14.48** (3.74) σ 1 8.84** (14.83) 4.84** (16.18) Flow ParametersTo PJM 72.86** (11.26) To NY 72.69** (11.72)

29. 29 Mean Transaction Costs: PJM/NYISO ($/MWh) Mean Transaction Cost To PJM from NYISO To NYISO from PJM Before April, 1998 3.251.70 April 1998 – April 1999 3.401.36 After April, 1999 2.973.78

30. 30 Expected State Probabilities: PJM/NYISO PJM Price > NYISO Price NYISO Price > PJM Price Autarky12.1% 6.3% Unconstrained Trade80.1%88.3% Quantity-Constrained Trade 7.8% 5.4%

31. 31 Conclusions: PJM-NYISO Ž Transaction costs fell to PJM from NY, subsequent to formation of PJM ISO. Ž Transaction costs to NY from PJM rose by more than $2/MWh after PJM switched from cost-based to market-based bidding. Explanation – (1) more inward focus by PJM suppliers after market-based bidding; (2) differing ISO protocols, perhaps. Ž Prevalence of quantity-constrained trade similar in each direction for PJM-NY, but results will be different for PJM- ECAR!

32. 32 The Results PJM – ECAR

33. 33 Autarky Parameters: PJM/ECAR (t-stats in parentheses) Constant 43.77** (7.39)  56.79** (3.18) Price of Natural Gas -0.540 (-0.36) (Δ Cooling Degree Days) -0.312 (-0.29) (Δ Cooling Degree Days) 2 0.0833** (2.98) (Δ Heating Degree Days) -0.527 (-0.59) (Δ Heating Degree Days) 2 0.0398* (1.96)

34. 34 Transaction Costs: PJM/ECAR (t-stats in parenthesis) Transaction Cost to PJM from ECAR Transaction Cost to ECAR from PJM Constant 2.00** (4.61) -3.41 (-0.54) April 1998 Indicator -2.11** (-2.75) -3.01 (-0.75) April 1999 Indicator 4.44** (6.60) -0.325 (-0.14) σ 1 3.29** (72.44) 5.47** (4.48) Flow ParametersTo PJM 148.34** (12.93) To ECAR 41.37** (7.39)

35. 35 Mean Transaction Costs: PJM/ECAR ($/MWh) Mean Transaction CostTo PJM from ECAR To ECAR from PJM Before April 1998 3.503.34 April 1998 – April 1999 2.592.70 After April 1999 4.942.64

36. 36 Expected State Probabilities: PJM/ECAR PJM Price > ECAR Price ECAR Price > PJM Price Autarky 3.3% 7.3% Unconstrained Trade92.9%65.4% Quantity-Constrained Trade 3.8%27.3%

37. 37 Conclusions: PJM-ECAR Ž Transaction costs to PJM from ECAR fell by nearly $1/MWh after formation of PJM exchange market. Improved price discovery, perhaps. Ž Transaction costs to PJM from ECAR rose by more than $2/MWh after PJM switched from cost-based to market-based bidding.

38. 38 Conclusions: PJM-ECAR (cont.) Ž High prevalence of quantity-constrained trade when ECAR has higher prices than PJM is striking, given apparent lack of binding physical transmission constraints moving from PJM into ECAR. Ž Results suggest that significant efficiencies in transmission usage may arise from PJM’s westward expansion and the formation of an effective MISO.

39. 39 The Value of Expanding Transmission Capability

40. 40 Estimating the Shadow Cost of Quantitative Trade Constraints Ž Little research has attempted how to estimate the efficiency losses imposed by existing quantity constraints on electricity flows. Ž Estimating the “shadow cost” of quantity constraints in terms of their marginal contribution to inter ‑ regional price differences represents a means of assessing the value that additional transfer capability (e.g., transmission capacity) could provide.

41. 41 Estimating the Shadow Cost of Quantitative Trade Constraints A two-stage process is used to estimate the “shadow cost” arising from quantity constraints on electricity flows. (1) We take the observed price difference on each day and subtract our estimated mean transaction cost, assuming constrained trading. Assuming quantity-constrained trade, an incremental increase in electricity flows from a lower ‑ priced to a higher-priced region will reduce energy costs by the observed price difference, less the transaction cost. (2)The amount in (1) is multiplied by the estimated probability that the observed inter-regional price difference on that day is associated with quantity-constrained trade.

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45. 45 Estimated Annual “Shadow Cost” of Quantity Trade Constraints ($/MW) Ž Annual Shadow Cost = (Total Shadow Cost)/5.33 years. Ž Total Shadow Cost = Σ [(Actual Daily Observed Price Difference - Estimated Mean Transaction Cost) * (Probability That Observed State Is Quantity-Constrained Trade)]. To: From: PJM NYISO PJM ECAR PJM Value$6,182$1,638$2,389$18,961

46. 46 Conclusions – Value of Increased Transmission Capability Ž Additional transmission capability has substantial “peak load” value. Most of shadow value is derived from lessening price spikes in summer months. Ž Highest shadow value of increased transmission capability is to ECAR from PJM (nearly $19,000 per MW year), which may not be a physical transmission constraint but rather an institutional constraint.