Abstract
The creation of adequate investment incentives has been of great concern in the restructuring of the electricity sector. However, to achieve this, regulators have applied different market designs across countries and regions. In this paper we employ laboratory methods to explore the relationship between market design, capacity provision and pricing in electricity markets. Subjects act as firms, choosing their generation capacity and competing in uniform price auction markets. We compare three regulatory designs: (1) a baseline price cap system that restricts scarcity rents, (2) a price spike regime that effectively lifts these restrictions, and (3) a capacity market that directly rewards the provision of capacity. Restricting price spikes leads to underinvestment. In line with the regulatory intention both alternative designs lead to sufficient investment albeit at the cost of higher energy prices during peak periods and substantial capacity payments in the capacity market regime. To some extent these results confirm theoretical expectations. However, we also find lower than predicted spot market prices as sellers compete relatively intensely in capacities and prices, and the capacity markets are less competitive than predicted.
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Notes
High peak prices could also lead to a flattening of the load curve if demand is sufficiently elastic and shifted from peak to off-peak. While in the experiment we abstract from dynamic pricing in retail electricity markets and the positive effects of demand side learning vis-à-vis high prices, these effects constitute an often used argument to allow for price surges. For an analysis of how elastic demand changes bidding strategies and market outcomes see Borenstein (2005) and Boom and Schwenen (2013).
Henze et al. (2012) examine the network infrastructure investment under three regulatory schemes (a regulatory holiday, forward contracting scheme, and standard price cap regulation). In this setup, the authors focus on the strategic interactions between network operator and users.
In many power markets, especially those without capacity markets, price caps are indeed market-wide. However, caps are sometimes also imposed as firm or unit-specific bid caps, or as offer caps (as in New England where bids are capped but the system operator can allow for a higher price than the cap during stress periods).
See, for instance, the market monitoring reports on the PJM market at monitoringanalytics.com.
For an in-depth analysis of capacity market regulations, containing design examples from Europe and the Americas, the interested reader is referred to Hancher et al. (2015).
See Borenstein et al. (2002) for empirical evidence about convex cost functions in electricity markets.
For a discussion on the nature of fixed and marginal costs in power markets see Crew and Kleindorfer (1979).
Note that, in all treatments, firms are forced to offer all their units to the energy market and withholding can only be implemented via high pricing. In our experimental design, physical withholding cannot be a means to exercise market power. This feature allows us to observe pricing strategies holding initial capacities fixed.
We would like to thank one reviewer for this remark.
Recall that 25 is the maximum demand realization in the energy market. Thus, this regime prevents blackouts or demand rationing even during the most extreme peak demand periods. Inelastic capacity demand has for instance been implemented in the New England capacity auction. Other markets also use elastic capacity demand, as described in FERC (2013) and proposed by Cramton and Stoft (2005) to obtain more stable capacity prices. Note that our capacity market can be understood as a long-term capacity market that incentivizes additional capacity, which would not be built in an energy-only market with too low price caps.
Thus, stage 2 in LowCap and stage 2 in CapMarket are completely identical.
We had only seven markets in the HighCap treatment as compared to eight in the other treatments. Furthermore, we had to dismiss data from the two last rounds in one market as one subject had to leave the experiment unexpectedly.
Instructions and screenshots are provided in the “Appendix”.
We would like to thank one referee to provide this way of formulating the problem that we now borrow in this paper.
Consider \(\bar{q}_{i}=7\; \forall i\). To determine whether this is a subgame-perfect Nash equilibrium we have to compare the expected profit on the equilibrium path to the expected profits that a deviating firm—that decided to hold fewer or more than 7 units—would obtain in counterfactual subgames. Under the assumption that the deviator always sets the market price, the most profitable deviation is a capacity level of 4 units, lowering total capacity from 28 to 25 units. The reason for 4 units being optimal is that (1) the deviator would never be able to sell more than 4 units and (2) relative to holding only 3 units the 4th unit adds a profit in expectation that exceeds the e$7 required for the 4th unit (in both LowCap and HighCap). Whether or not the firm deviates to 4 units has no impact on its profit during off-peak periods, which remain competitive either way. During peak periods the deviating firm sells 2, 3 or 4 units depending on the demand realization. Likewise, the non-deviating firm will sell 2, 3 or 4 units whenever it is asked to set the market price. However, if the four firms tacitly agree to share the burden of setting the market price evenly, the non-deviating firm sells all its 7 units in 75% of the peak periods. Even in LowCap this is so profitable that it easily outweighs the additional capacity cost associated with holding 7 units instead of 4 units.
For this reason we also do not wish to make too much of the fact that Lemma 2 suggests a symmetric outcome for the LowCap treatment and an asymmetric one for the HighCap treatment.
There were 2 peak periods per round, and subjects were able to choose their capacity in 8 rounds (rounds 3-10). With data from eight independent markets we \(2\times 8\times 8=128\) get relevant peak periods.
Pooling the data from all LowCap markets we cannot reject the null hypothesis that the average market capacity in rounds 8–10 comes from a distribution with a mean of 24 units (p value = 0.367).
In fact, the members of one of the two markets experienced the adverse effects of excess supply very badly in round 7 when total capacity spiraled up to 29 units and the market price dropped to e$7 in both peak demand periods of this round. In all subsequent rounds, when market capacity was small, the market price was always e$15 when demand peaked.
There are two variants of the Fisher-Pitman permutation test that we employ in this paper, one for two independent samples and one for paired observations. These tests have the advantage that they make even fewer assumptions than other popular non-parametric tests like the Mann-Whitney-U test or the Wilcoxon signed-rank test, which are both commonly used in the experimental literature. For a more detailed discussion see Kaiser (2007) and Selten et al. (2011).
In addition, there is strategic uncertainty about how many units the other firms decide to hold in a given round since all firms make this decision simultaneously.
The precise level of the marginal cost price depends on the distribution of the firms’ production capacities in the relevant market. For a given level of demand the marginal cost price is lowest when all four firms contribute evenly to meeting that demand; it is highest when capacities are extremely uneven such that the largest firm’s most costly production units need to be dispatched. We did not include any measure of fixed cost so that the marginal cost price refers to short-run marginal costs.
The price drop in HighCap seen in Fig. 5 could of course be a manifestation of more frequent instances of markets without pivotal firms. However, the frequency of markets without pivotal firms does in fact not increase.
The estimates for the confidence intervals were computed by resampling 10,000 times from the empirical distribution of capacity market prices.
Optimal welfare in each period thus equals 30 times the demand realization, minus the lowest possible aggregate generation cost at that demand level. Note that welfare is independent of prices and capacity payments as these merely represent transfers from consumers to producers. However, prices and capacity payments do affect consumer surplus levels, of course.
The difference between HighCap and CapMarket in this respect occurs because the demand levels happen to be somewhat higher in the HighCap treatment by chance.
Crampes and Léautier (2015), however, show that an active demand side may lead to a welfare decrease because of the strong asymmetry between consumers (who have private information on their value for electricity) and firms. Next to flexible energy demand, our assumption on inelastic capacity demand could be relaxed in future works.
Instructions for the other treatments are available from the authors upon request.
References
Abbink, K., Brandts, J., & McDaniel, T. (2003). Asymmetric demand information in uniform and discriminatory call auctions: An experimental analysis motivated by electricity markets. Journal of Regulatory Economics, 23(2), 125–144.
Allaz, B., & Vila, J.-L. (1993). Cournot competition, forwards markets and efficiency. Journal of Economic Theory, 59(1), 1–16.
Boom, A. & Schwenen, S. (2013). Real-time pricing in power markets: Who gains? Scandinavian Working Papers in Economics, No 01-2013.
Borenstein, S., Bushnell, J., & Wolak, F. (2002). Measuring market inefficiencies in California’s restructured wholesale electricity market. American Economic Review, 92(5), 1376–1405.
Borenstein, S. (2005). The long-run efficiency of real-time electricity pricing. The Energy Journal, 93–116.
Brandts, J., Reynolds, S. S., & Schram, A. (2014). Pivotal suppliers and market power in experimental supply function competition. Economic Journal, 124(579), 887–916.
Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. Princeton: Princeton University Press.
Cramton, P., & Stoft, S. (2005). A capacity market that makes sense. The Electricity Journal, 18(7), 43–54.
Cramton, P., Ockenfels, A., & Stoft, S. (2013). Capacity market fundamentals. Economics of Energy and Environmental Policy, 2(2), 27–46.
Crampes, C., & Léautier, T.-O. (2015). Demand response in adjustment markets for electricity. Journal of Regulatory Economics, 48(2), 169–193.
Creti, A., & Fabra, N. (2007). Supply security and short-run capacity markets for electricity. Energy Economics, 29(2), 259–276.
Crew, M. A., & Kleindorfer, P. R. (1979). Public utility economics. London: Macmillan Press.
Diekmann, A. (1985). Volunteer’s dilemma. Journal of Conflict Resolution, 29(4), 605–610.
Diekmann, A. (1993). Cooperation in an asymmetric volunteer’s dilemma game: Theory and experimental evidence. International Journal of Game Theory, 22(1), 5–85.
Engelmann, D., & Grimm, V. (2009). Bidding behaviour in multi-unit auctions: An experimental investigation. Economic Journal, 119(537), 855–882.
Fabra, N., von der Fehr, N. H. M., & De Frutos, M. Á. (2011). Market design and investment incentives. Economic Journal, 121(557), 1340–1360.
Fabra, N., von der Fehr, N.-H. M., & Harbord, D. (2006). Designing electricity auctions. RAND Journal of Economics, 37(1), 23–46.
Feldhaus, C., & Stauf, J. (2016). More than words: The effects of cheap talk in a volunteer’s dilemma. Experimental Economics, 19(2), 342–359.
FERC. (2013). Centralized capacity market design elements. Staff Report: Federal Energy Regulatory Commission.
Goeree, J. K., Holt, C. A., & Smith, A. M. (2017). An experimental examination of the volunteer’s dilemma. Games and Economic Behavior, 102, 303–315.
Hancher, L., de Houteclocque, A., & Sadowska, M. (Eds.). (2015). Capacity mechanisms in EU energy markets: Law, policy, and economics. Oxford: Oxford University Press.
Henze, B., Noussair, C., & Willems, B. (2012). Regulation of network infrastructure investments: An experimental evaluation. Journal of Regulatory Economics, 42(1), 1–38.
Hortaçsu, A., & Puller, S. L. (2008). Understanding strategic bidding in multi-unit auctions: A case study of the Texas electricity spot market. RAND Journal of Economics, 39(1), 86–114.
Joskow, P., & Tirole, J. (2007). Reliability and competitive electricity markets. RAND Journal of Economics, 38(1), 60–84.
Kahneman, D. (1988). Experimental economics: A psychological perspective. In R. Tietz, W. Albers, & R. Selten (Eds.), Bounded rational behavior in experimental games and markets. Berlin: Springer.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291.
Kaiser, J. (2007). An exact and a Monte Carlo proposal to the Fisher-Pitman permutation tests for paired replicates and for independent samples. Stata Journal, 7(3), 402–412.
Kiesling, L., & Wilson, B. (2007). An experimental analysis of the effects of automated mitigation procedures on investment and prices in wholesale electricity markets. Journal of Regulatory Economics, 31(3), 313–334.
Léautier, T.-O. (2016). The visible hand: Ensuring optimal investment in electric power generation. The Energy Journal, 37(2), 89–109.
Le Coq, C., & Orzen, H. (2006). Do forward markets enhance competition? Experimental evidence. Journal of Economic Behavior and Organization, 61(3), 415–431.
Schwenen, S. (2015). Strategic bidding in multi-unit auctions with capacity constrained bidders: The New York capacity market. RAND Journal of Economics, 46(4), 730–750.
Selten, R., Chmura, T., & Goerg, S. J. (2011). Stationary concepts for experimental 2x2 games: Reply. American Economic Review, 101(2), 44–1041.
van Koten, S., & Ortmann, A. (2013). Structural versus behavioral remedies in the deregulation of electricity markets: An experimental investigation motivated by policy concerns. European Economic Review, 64, 256–265.
Vossler, C. A., Mount, T. D., Thomas, R., & Zimmerman, R. (2009). An experimental investigation of soft price caps in uniform price auction markets for wholesale electricity. Journal of Regulatory Economics, 36(1), 44–59.
Wolfram, C. D. (1998). Strategic bidding in a multiunit auction: An empirical analysis of bids to supply electricity in England and Wales. The Rand Journal of Economics, 29(4), 703–725.
Wolfram, C. D. (1999). Measuring duopoly power in the British electricity spot market. American Economic Review, 89(4), 805–826.
Zöttl, G. (2011). On optimal scarcity prices. International Journal of Industrial Organization, 29(5), 589–605.
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We gratefully acknowledge funding from the Swedish Competition Authority and are thankful to the Torsten Söderberg Foundation grant that supported Le Coq’s work under grant E37/13. We are grateful to Roman Bobilev, Pär Holmberg, Elena Paltseva, Giancarlo Spagnolo and Karsten Neuhoff for helpful discussions and comments. We also thank seminar participants at the University of Paris XI, Stockholm School of Economics, UCEI Berkeley, University of Montevideo, University of Basel, as well as conference participants at the IAEE in New York and at the KKV workshop in Stockholm. Finally, we would like to thank Michael Crew and two anonymous referees for making valuable comments.
Appendices
Appendix 1: Instructions for the CapMarket treatment
Welcome! This is an experiment in the economics of decision making.Footnote 31 You will be paid in private and in cash at the end of the experiment. The amount you earn will depend on your decisions, so please follow the instructions carefully.
1.1 General rules
During the experiment you will have the chance to earn “experimental dollars” (e)$,which will be converted into cash at the end of the experiment, using an exchange rate of 60e$ = £1. Thus, the higher your e$ earnings are, the more cash you will receive at the end of the experiment.
There are sixteen people in this room who are participating in this session. It is important that you do not talk to any of the other participants until the session is over.
In this experiment each person in the room represents a firm. During the session four different markets will operate and at the beginning of the session the computer will randomly allocate you to one of these. Similarly, the other firms will be randomly allocated to markets. In your market there will be you and three other firms. Your e$ earnings will depend on your decisions and on the other three firms’ decisions. The firms you are matched with will be the same throughout the session but you will not learn the identity of the persons who represent these firms.
1.2 Rounds and periods
The experiment will consist of a number of ROUNDS and PERIODS. There will be 10 Rounds, and each Round will consist of 6 Periods.
1.3 Description of a period
In each Period of a given Round the computer will buy units of a good from you and your three competitors. By selling units to the computer you can earn e$s.
How many units the computer will demand will vary from Period to Period, but in Periods 1, 2, 3 and 4 the demand will always be LOW and in Periods 5 and 6 the demand will always be HIGH.
When the demand is LOW then the computer will buy either 7 or 8 or 9 units (with equal probability). When the demand is HIGH then the computer will buy either 23 or 24 or 25 units (again with equal probability).
You will be informed about the exact level of demand at the beginning of each Period.
How many of these units the computer will buy from YOU and how many it will buy from the other firms in your market will depend on the prices that you charge and on the prices that your competitors charge. This will be explained in detail below.
Your main task in each Period will be to decide what price you want to charge for each unit you produce. What is important is that you have to pay a production cost for each unit you produce. To be precise, the first unit you produce will cost you 1e$, the second unit you produce will cost you 2e$, the third unit you produce will cost you 3e$, and so on. You can produce up to 9 units.
The following graph illustrates your production costs.
Note that you will pay production costs only for units you sell, not for the other units (for example, if the computer buys 3 units from you, your production costs will be 1e$ + 2e$ + 3e$ = 6e$).
You will decide for each unit separately what price to charge. In principle you can choose your prices freely, but there are a few restrictions:
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You cannot charge a price below the production cost. That is, for Unit 1 you cannot charge a price below 1.00, for Unit 2 you cannot charge a price below 2.00, and so on.
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The maximum price you can charge is 15.00.
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The prices are not allowed to decrease from unit to unit. That is, the price for Unit 2 must not be lower than the price for Unit 1, and the price for Unit 3 must not be lower than the price for Unit 2, and so on. (However, you are allowed to charge the same price for different units.)
This is how the decision screen for a Period will look like at the beginning of the experiment.
You will be able to enter your prices at the top of the screen. The arrow indicates which price you are currently editing. Initially all prices are set to be equal to the production cost of the relevant unit.
There are different ways to modify your prices. You can simply type in a new price using your keyboard, or you can use the PageUp/PageDown keys on your keyboard to change the current price by an amount of +/\(-0.20\) or the normal Up/Down keys to change the current price by an amount of +/\(-0.01\). Little red markers on the screen will illustrate your current choice of prices.
The computer will automatically make correcting adjustments to your prices if your current choice of prices violates any of the three restrictions mentioned above.
You can move from field to field either by clicking on a field, or by using the Tab key on your keyboard:
When you are happy with your choice of prices, please click on the “Submit” button. In each Period you will have 60 s to decide which prices you want to charge. When the 60 s are over the computer will simply take your current selection of prices.
1.4 How your payoffs are determined
Once everybody has submitted their prices (or the 60 s are over), the computer will determine the Market Price and how many units it buys from each firm.
To do this, the computer will first rank all the 36 submitted prices (36 because each of the 4 firms submits 9 prices), from lowest to highest.
The computer will then buy the number of units that it demands in the current Period (which will be 7, 8 or 9 units in Periods 1, 2, 3 and 4 and 23, 24 or 25 units in Periods 5 and 6, as explained above), starting with the lowest-priced unit and then working its way up to the more expensive units.
What is important to note, is that it will buy all units at the same price, the Market Price. The Market Price is the price of the last unit that the computer buys.
An example: Suppose that the demand is 5 units (this will never be the case in the experiment, this is simply an illustration), and the 4 firms have submitted the following prices.
Firm 1 | Firm 2 | Firm 3 | Firm 4 | |
|---|---|---|---|---|
Price for Unit 1 | 4.50 | 3.76 | 2.31 | 3.90 |
Price for Unit 2 | 11.59 | 10.77 | 4.20 | 5.31 |
\(\vdots \) | \(\vdots \) | \(\vdots \) | \(\vdots \) | \(\vdots \) |
The computer then ranks these prices and buys the 5 cheapest units. It buys these units at the Market Price, which is the price of the last (in this case the 5th) unit that the computer buys.
Thus, the Market Price in this example would be 4.50, and the computer would pay 4.50 for each of the 5 units it buys. Firms 1, 2 and 4 would each sell 1 unit and firm 3 would sell 2 units. Firms 1, 2 and 4 would each have production costs of 1 and therefore each make a profit of 3.50. Firm 3 who produces 2 units would also make a profit of 3.50 for its first unit, but would make an additional profit of 2.50 for its second unit (a profit of 6.00 in total).
The case of ties: If there are ties at the Market Price (for example, imagine that Firm 4 had charged 4.50 for its second unit instead of 5.31), it has to be determined which firm gets to sell the last unit. In this case the computer will select a firm at random for each unit where two or more sellers are tied.
At the end of each period your screen will display the Market Price, how many units you have sold and how much profit you have made (You will not see the other firms’ individual prices). Also, you will be able to scroll back to the outcomes of previous Rounds and Periods.
1.5 Description of a round
As mentioned earlier, there will be 10 Rounds, and each Round will consist of 6 Periods of the kind described above. However, from Round 3 onwards one aspect of the experiment will change.
In each Period of Rounds 1 and 2 you are able to produce up to 9 units. In other words, your Production Capacity is 9 units. From Round 3 onwards you will be asked to choose your Production Capacity at the beginning of a Round. How this is done will be explained below, but note that your choice will affect your ability to produce in all 6 Periods of that Round. For example, if you choose a Production Capacity of 2, you can only produce up to 2 units in each Period of that Round.
From Round 3 onwards your Production Capacity will come at a cost: each unit of Production Capacity will cost you 7.00 e$. You can choose to have up to 9 units of Production Capacity at the beginning of a Round. (The 9 units Production Capacity you will have in Round 1 and Round 2, however, will be free.)
The cost of Production Capacity will be deducted from your e$ earnings. However, there is a chance that you receive a compensation payment for your Production Capacity expenses. This is explained in the following.
1.6 How you choose your production capacity
The procedure for choosing your Production Capacity will consist of two steps: Step A and Step B.
Step A: Compensation payments for production capacity
In Step A, before you have made any choice about your Production Capacity, you will make a bid to the computer to request compensation payments for Production Capacity. A compensation payment means that the computer will pay you an amount of e$ as a contribution to your expenses associated with the Production Capacity.
As mentioned above, each unit of Production Capacity will cost you 7.00 e$, but in Step A you can request from the computer any amount between 0.00 e$ and 30.00 e$ for each unit of Production Capacity. You will be able to make separate bids for each unit of Production Capacity, just as you can choose separate prices for your units in the Periods (see above). In other words, you can request different amounts of compensation payments for different units.
Likewise, your three competitors can submit requests for compensation payments like this. The computer will collect all 36 request (36 because each of the 4 firms submits one separate request for each of the 9 units of Production Capacity) and will pay a compensation for the 25 lowest requests.
To determine how much to pay, the computer will use the same procedure as when it determines the Market Price in a Period (explained above). That is, it will compensate the 25 lowest requests and for each of these 25 units it will pay an amount equal to the 25th lowest request. The amount of compensation the computer pays for each of these units can be higher or lower than 7 e$, depending on the submitted requests. It will not pay any compensation for the 11 highest requests in your market.
At the end of Step A your screen will display how much compensation the computer pays for each unit, and for how many units you receive a compensation payment.
Step B: Choosing additional units of production capacity
In Step B you will have the opportunity to choose additional units of Production Capacity. For example, suppose that in Stage A it has turned out that the computer pays you a compensation for 6 units of Production Capacity – this means that in Stage B you now have the option to increase your Production Capacity to 7 or 8 or 9 units (at a cost of 7e$ per extra unit).
However, you cannot reduce your Production Capacity in Step B. That is, you MUST keep all units of Production Capacity for which the computer pays you a compensation! You should also keep this in mind when you submit your requests in Step A.
To assist you with your decisions in Step A and Step B, the software provides an “Analysis Tool”. When you click on the “Analysis” button the screen will display how much profit you have made with each of your units in previous Rounds. (This excludes any compensation payments.)
When you have decided how many extra units of Production Capacity you wish to have, please click on the “Submit” button to start the next six Periods. Note that once you have submitted your choice for the Production Capacity you cannot change it for the current Round!
After you have made your choice, the first Period of the current Round will begin. On the right hand side of the screen the Production Capacity Choices of your competitors will be displayed.
Appendix 2: Screenshots (not intended for publication)
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Le Coq, C., Orzen, H. & Schwenen, S. Pricing and capacity provision in electricity markets: an experimental study. J Regul Econ 51, 123–158 (2017). https://doi.org/10.1007/s11149-017-9324-z
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DOI: https://doi.org/10.1007/s11149-017-9324-z