Using Incentive Preserving Rebates to Increase Acceptance...

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Using Incentive Preserving Rebates to Increase Acceptance of Critical Peak Electricity Pricing Robert Letzler January 29, 2008 The views expressed in this paper are those of the author and do not nec- essarily represent the views of the Federal Trade Commission or any individual Commissioner. An earlier version of this paper – with more discussion of the background – appeared as Center for Study of Energy Markets Working Paper 162. I would like to thank my advisers Lee Friedman, Severin Borenstein, John Morgan, Rob MacCoun, and Geno Smolensky as well as Michael Baye, Nina Bubnova, Pete Fishman, Karen Herter, Teck Ho, Lily Hsueh, Pat McAuliffe, David Meyer, Karen Notsund, Matt Rabin, David Schmidt, Catherine Waddams, Brian White, and Charlie Whitmore for comments, advice, sugges- tions, documents, data, and support. Thanks also go to seminar participants at the FTC, UC Energy Institute, UC Berkeley, and RAND. Contents 1 Introduction: The economics and psychology of dynamic electricity pric- ing 4 1.1 Implementation .................................. 6 2 Background: Improved electricity pricing can deliver significant savings 7 3 Psychological explanations of customer resistance. 8 3.1 Evidence about behavioral interventions’ effectiveness ............. 10 3.2 Similar interventions to improve decision making by addressing biases are possible for electricity pricing .......................... 10 4 Improving the presentation while preserving incentives 11 4.1 Using fixed credits and fixed charges to offer rebates while preserving CPP’s marginal incentives and annual total bills .................... 12 4.2 Bundling rights with power purchases ...................... 14 4.3 Preserving incentives through account-level revenue neutral rebates ..... 15 4.4 Psychological evidence about consistent rebates ................ 17 1

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Using Incentive Preserving Rebates to IncreaseAcceptance of Critical Peak Electricity Pricing

Robert Letzler

January 29, 2008

The views expressed in this paper are those of the author and do not nec-essarily represent the views of the Federal Trade Commission or any individualCommissioner. An earlier version of this paper – with more discussion of the background– appeared as Center for Study of Energy Markets Working Paper 162. I would like tothank my advisers Lee Friedman, Severin Borenstein, John Morgan, Rob MacCoun, andGeno Smolensky as well as Michael Baye, Nina Bubnova, Pete Fishman, Karen Herter, TeckHo, Lily Hsueh, Pat McAuliffe, David Meyer, Karen Notsund, Matt Rabin, David Schmidt,Catherine Waddams, Brian White, and Charlie Whitmore for comments, advice, sugges-tions, documents, data, and support. Thanks also go to seminar participants at the FTC,UC Energy Institute, UC Berkeley, and RAND.

Contents

1 Introduction: The economics and psychology of dynamic electricity pric-ing 41.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Background: Improved electricity pricing can deliver significant savings 7

3 Psychological explanations of customer resistance. 83.1 Evidence about behavioral interventions’ effectiveness . . . . . . . . . . . . . 103.2 Similar interventions to improve decision making by addressing biases are

possible for electricity pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Improving the presentation while preserving incentives 114.1 Using fixed credits and fixed charges to offer rebates while preserving CPP’s

marginal incentives and annual total bills . . . . . . . . . . . . . . . . . . . . 124.2 Bundling rights with power purchases . . . . . . . . . . . . . . . . . . . . . . 144.3 Preserving incentives through account-level revenue neutral rebates . . . . . 154.4 Psychological evidence about consistent rebates . . . . . . . . . . . . . . . . 17

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5 Revenue neutrality and incentive preservation proofs 175.1 A formal overview of CPP-IPR . . . . . . . . . . . . . . . . . . . . . . . . . 175.2 The equivalence of incentive-preserving fixed credits to rights to regular priced

power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.3 Account-level revenue equivalence . . . . . . . . . . . . . . . . . . . . . . . 18

6 CPP-IPR Compared to Other Rates 196.1 Managing Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196.2 IP rebates avoid the economic flaws in baseline-rebate rates . . . . . . . . . . 206.3 Baseline-Rebate Rates: Field Experience . . . . . . . . . . . . . . . . . . . . 22

7 The political, organizational, and financial feasibility of CPP-IPR: Evi-dence from California Customers 227.1 Economic constraints: consistent rebates, inframarginal bundled rights, and

revenue neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237.2 Implementing CPP-IPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

7.2.1 Offer existence, predictability, and administrative feasibility . . . . . 247.2.2 Making offers to broad categories of customers . . . . . . . . . . . . . 267.2.3 Optimization algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 267.2.4 Performance of Optimal Group and Categorical Rates . . . . . . . . . 27

7.3 IP rebates are a rate feature, not a whole rate . . . . . . . . . . . . . . . . . 29

8 IP rebates and seasonal bill variations 31

9 Conclusion 31

A Design Details to Ensure Revenue Neutrality 38A.1 A clever calendar can help ensure account-level revenue neutrality . . . . . . 38A.2 Ensuring that customers get the rights they paid for . . . . . . . . . . . . . . 38

B The general case: dealing with customers who do not buy all of the offeredrights 38

B.0.1 Bundling rights with the first units of power never creates a deadweightloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

C Generalizing IP Rebates to other markets 40C.1 This two period generalization performs worse than three-period CPP-IPR . 42C.2 Benefits of offering credits selectively . . . . . . . . . . . . . . . . . . . . . . 42

D Graphical Comparison of Rates’ Incentives 43

E Percentage of Customers for Whom Consistent Offers exist 43E.1 Predicting consistent offers using readily available information . . . . . . . . 49E.2 Optimal offers to each of the 16 groups. . . . . . . . . . . . . . . . . . . . . . 51E.3 Offers that are not consistent are typically fairly close to being consistent . . 51

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E.4 Robustness of these offers to changes in weather, economic conditions, andcustomer characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

F Appendix: Notation 54

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Abstract

Low consumer opt-in rates prevent dynamic electricity pricing programs, like Criti-cal Peak Pricing (CPP), from achieving their potential. This project uses insights frombehavioral economics to understand consumer resistance and to propose Incentive Pre-serving Rebates that address it without changing CPP’s economic properties.

Dynamic pricing programs set prices each hour that are closer to the fluctuatingcost of generation than conventional, time-invariant rates. CPP programs designateseach hour as being offpeak, peak, or “critical” and price them accordingly. CPP isa common approach to offering dynamic pricing to customers who use only a modestamount of power. Customers in CPP pilot programs used less power during high-priced periods than did customers on traditional, time-invariant rates. CPP customersreported high satisfaction levels, tend to stay on dynamic pricing, and often saved 10%or more. Yet, roughly 99% of customers reject opportunities to switch to CPP.

The psychology literature documents a set of decision making heuristics that peopleuse to choose among options with uncertain payoffs. This paper describes the evidencethat one or more of these heuristics explains customer reluctance to opt-in to CPP.It then suggests Incentive Preserving Rebates that change the presentation of CPPto address these heuristics. Incentive Preserving Rebates reframe scarcity “events” asopportunities to get rebates rather than as periods of extremely high prices. IncentivePreserving Rebates change the presentation, but change neither marginal incentivesnor each customer’s total annual payments. The paper then explores the implicationsof Incentive Preserving Rebates for customers who participated in a California pilotprogram.

1 Introduction: The economics and psychology of dy-

namic electricity pricing

Low consumer opt-in rates prevent dynamic electricity pricing programs, like Critical PeakPricing (CPP), from achieving their potential. This project uses insights from behavioraleconomics to explain consumer resistance and to propose Incentive Preserving Rebates thataddress it without changing CPP’s economic properties.

Most customers are on time-invariant pricing that charges the same price per unit of powerduring high and low cost hours. Dynamic rates vary prices to reflect temporal patterns incost. “Real time” electricity pricing sets hourly prices that reflect the marginal cost. Signingup every residential customer for real time pricing could deliver an estimated $6-12 billionin annual social benefits.1

CPP is a simpler dynamic rate. Typical CPP rates announce a schedule of peak andoffpeak periods and prices. CPP allows utilities to designate about 1% of all hours as critical,scarcity periods which invoke a significantly higher rate. CPP makes prices reflect somevariations in the marginal social cost of power. Policy makers consider CPP an attractive

1American residences spent $116 billion on electricity in 2004.(http://www.eia.doe.gov/cneaf/electricity/epm/table5 2.html ) Borenstein (2005) reports that realtime pricing could yield 5-10% annual savings on energy over the long term. There are – to the best of myknowledge – no academic papers that estimate the potential benefits of CPP and compare those to realtime pricing.

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rate for residential and small commercial customers. This project proposes features that canbe added to CPP rates without affecting their incentives or revenue properties.

CPP works. Residential customers who switch to CPP reduce their usage during higher-priced, peak periods and the highest-priced, critical periods. CPP customers report high sat-isfaction levels. Indeed, the majority of customers who received $175 to participate in a Cal-ifornia CPP experiment chose to stay on CPP at the conclusion of the experiment.(Faruquiand George, 2005; Charles River Associates)

Consumers, however, resist signing up for CPP. Mailings offering Florida customers aCPP rate that saves participants an average of $90 a year get a 1.3% opt-in rate (White,2006). Customers are more receptive to baseline-rebate programs that create similar incen-tives by rewarding customers whose critical-period power use is below a “baseline” level.Calculating baselines from a customer’s use can perversely reward increases in energy con-sumption during baseline-setting periods with increased rebates. Customers who resist CPPbut are open to rebate programs with the same average bill appear to have preferences aboutelements of the presentation that affect neither incentives nor total bills.2

Residential CPP will generally be an opt-in program until it develops a track record thatjustifies making it the default. Presenting the rate in a way that helps customers to makebetter enrollment choices may both increase participation in opt-in programs and generatefield experience to support discussions of making dynamic pricing the default rate. Hence,this project seeks to present CPP in a way that elicits good enrollment choices when shownside by side with the status-quo time invariant rate.3

A growing literature documents heuristics people often use to make economic choicesand situations in which these heuristics lead to systematic, predictable deviations from theexpected utility maximizing choice.4CPP presents good incentives in a way that biases severalheuristics toward choosing not to enroll. CPP delivers subtle savings by lowering prices mostof the time. Its critical events inflict visible losses by notifying customers that it is raisingprices so much that customers spend more on power or get less power during the criticalperiod than they would had it been an ordinary period. California customers reduced usage12% when the CPP pilot experiment events more than doubled prices.(Faruqui and George,2005; Charles River Associates; Herter et al., 2007) Thus, during the 1% of all hours thatwere events, many customers paid more for power despite conserving. CPP reduced mostparticipating customers’ total annual bills because the savings from small price reductionsnights, mornings, and weekends more than offset any bill increases during the rare, butvisible critical events. People’s heuristic decision making procedures are likely to noticeand overweight the high priced periods and either not notice or underweight the gains.Concentrating losses in a few high cost months and diffusing gains over the calendar repels

2It is rational for consumers to prefer time-invariant pricing to CPP if CPP’s transaction costs or higherprices during peak periods reduce the consumers’ overall utility. Consumers who use a smaller-than-averageproportion of their electricity during weekday afternoons could save money under CPP without changingtheir consumption patterns. Yet, the majority of these structural winners do not sign up.

3CPP’s initial opt-in status is a political reality, but the strand of literature that suggests that IP rebatesmight work also reports that changing defaults or forcing people to decide can lead to considerably betterchoices in retirement savings. See Choi et al. (2003) for an overview. Wood (2002a,b) discusses the potentialof making dynamic pricing the default to increase participation.

4For reviews of this literature, see e.g. Rabin (1998); DellaVigna (2007) while Kahneman and Tversky(2000) collects many classic articles.

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loss-averse customers if they “narrowly bracket”, meaning that they consider bills one cycle– or even one day – at a time, rather than over the long term (Thaler, 1999; Read et al.,1999). CPP also repels customers who believe it is unfair to charge very high prices forair conditioning when they need it the most (Kahneman et al., 1986). Incentive PreservingRebates change the presentation of CPP to avoid these biases.5,6

IP rebates present critical events as opportunities to earn rebates through sacrifice. IPrebates change neither the total annual bill nor marginal incentives.7 IP rebates add a fixedamount to each month’s CPP bill. This monthly payment buys the customer rights to buy afixed quantity of power at the usual price during critical events. If customers use less powerthan they had rights to during an event, they get a rebate for the value of the unused rights.

We can see how this works in practice by considering a rate that sets the opportunitycost of a kilowatt hour (kWh)8 during a critical event at 60 cents and charges 24 cents perkWh during normal peak periods. A customer who has the right to buy one kWh during acritical event for the normal price of 24 cents can use the right for either 36 cents worth ofpower or for a 36 cent rebate. We can offer a customer the right to 8 kWh at the usual priceduring each of 15 events if we charge the customer $3.60 (which buys 10 kWh of rights) eachmonth. A customer who exhausts their rights during an event has to pay the full price of 60cents per kWh.

Psychological and economic factors are important throughout the life cycle of a dynamicpricing program. This project focuses on psychology at the opt-in stage and on creating theright incentives at the participation stage. This prioritization reflects evidence that decisionmaking heuristics cause mistakes at the opt-in stage.9 By contrast, participant consumptionand exit decision patterns seem consistent with neo-classical choice.

Increasing the IP rebate credit size does not affect annual utility revenue or the consumer’stotal annual payments, but loss-averse customers prefer rebate opportunities to high pricesduring events. This project aspires to offer most customers a rebate during any month withan event.

1.1 Implementation

There is good reason to think that the IP rebates are feasible. IP rebates add revenue neutralcharges and credits to an underlying rate that regulators can tailor to meet local needs.

5IP rebates can work with a wide family of dynamic pricing programs. This project presents them in thecontext of CPP because CPP is a simple, illustrative, and policy relevant application. Section C describesthe generalization.

6Adding IP rebates to CPP may slightly change the amount of power that customers buy because IPrebates charge a few extra dollars during some months and return those dollars as bill reductions in othermonths which creates income effects.

7This project, like much of the policy-oriented behavioral economics literature, assumes that consumererrors and biases are a common but not universal problem and thus seeks interventions that improve biasedconsumers’ choices without affecting rational consumers’ choices. (c.f. Camerer et al. (2003) “Regulation forConservatives: Behavioral Economics and the Case for ‘Asymmetric Paternalism’” and Sunstein and Thaler(2003) “Libertarian Paternalism is Not an Oxymoron”)

8A kWh is enough energy to run a 100 watt light bulb for 10 hours, or a central air conditioner for about15 minutes.

9Many customers suffer “projection bias” which causes them to overestimate how difficult a new situationwill be to get used to (Loewenstein et al., 2003).

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This project proposes a rate that asks customers to pay for their rights through a smallmarkup on a fixed number of units of power per month. This creates a trade off between thecustomer’s likelihood of getting rebates and their ability to pay for their rights. For example,a rate might work well for a customer if they used fewer than 20 kilowatt hours during eachfive hour event and used at least 300 kilowatt hours per month.

An IP rebate policy has to decide whether to address the challenge of making an appro-priate offer to each customer by offering each customer a customized offer or by splittingcustomers into categories and making one offer to each category. Making offers to broadcategories of customers defined by use and geography can perform adequately and has com-pelling advantages over individualized offers. Specifically, assigning rebate eligibility bycategory seems fair since neighbors who live in superficially similar houses will generally getthe same offer. Offers to categories of customers facilitate analysis and discussion amongutilities, regulators, and advocates who may be able to use categories already in use forother regulatory purposes. Categorical offers reduce the likelihood that customers will de-mand extra power in a (misinformed and fruitless) attempt to profit by becoming eligiblefor more rebates. An analysis of California data shows that we can make adequate offers tothe vast majority of customers even if we crudely split up customers using readily observablecharacteristics like climate zones and monthly summer electricity usage.

This paper proceeds in two stages. The first stage describes the economic case for im-proved electricity pricing, the behavioral challenges to implementing it, and proposes Incen-tive Preserving (IP) Rebates. The second stage explores whether IP rebate deployment isfeasible by simulating IP rebates’ impacts on a set of California CPP customers.

2 Background: Improved electricity pricing can de-

liver significant savings

Providing better incentives for customers to shift power use away from periods of electricityscarcity has the potential to save billions of dollars, to deliver significant environmentalbenefits in some markets (Holland and Mansur, 2005, 2006), and to facilitate the integrationof wind generation into electricity systems.

Most consumers are on time invariant rates, which do not depend on when the customeruses the power. Time invariant rates offer customers no incentive to shift use away fromhigh cost periods. The combination of time-invariant rates and the need to meet demandminute by minute creates extremely inelastic demand and can give suppliers a great deal ofmarket power. These factors require electric system operators to maintain extra generatingcapacity that they only use when extreme weather or equipment problems tax the system afew hours a year. Joskow (2000) discusses the background in detail while Borenstein (2005)discusses the background and estimates the potential benefits of dynamic pricing.

Few utilities have successfully implemented dynamic pricing – largely because they havestruggled to present dynamic pricing in ways that consumers find attractive (Barbose et al.,2004). Many have not done a good job of risk management, marketing, and implementation.Most implementations have struggled to get customers.

For example, field experience in Florida and Illinois shows that residential resistance

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is a serious problem.10 Gulf Power offers GoodCents Select residential CPP in Florida.Gulf Power and its parent, the Southern Company, are considered leaders among utilitiesin marketing and customer service. The Community Energy Cooperative’s Energy-SmartPricing Plan offers Illinois residences “real time prices” based on the hourly market rate.Both notify customers of high priced periods. The two retailers report that most customerswho sign up save significant amounts of money, are satisfied, and stay enrolled. But bothprograms get sign up rates of only about 1%.

Some consumer resistance is rational. Customers who use a large proportion of theirpower during peak periods would pay more under CPP. The transaction costs of respondingto price signals could deter some customers. Practitioners and scholars are working to ad-dress both issues (see e.g. Borenstein (2006); Wright et al.). Gulf Power’s Good Cents Selectprogram creates winners by saving participants an average of $90 a year (White, 2006), andreduces transaction costs by providing a computerized “set it and forget it” thermostat thatautomatically shifts air conditioning away from critical periods (Gulf Power). However, con-ventional economic reasons cannot explain the high rejection rate among customers who usea larger-than-average proportion of their power off peak and would save money on CPP evenif they did not respond to price signals. Customer retention and customer recruiting arerelated, but fundamentally different challenges. Retention involves customers who have ex-perienced CPP. They know the program’s implications for their total bills, lifestyles, decisionmaking heuristics, and preferences. Recruiting involves decisions by customers who knowsignificantly less. Further, retaining customers requires 1) that responsive customers savemoney under the new program which is a function of the CPP rate; 2) that the program beexplained clearly and that customers know when they are saving money; 3) that respondingnot be too onerous – which requires thinking carefully about whether to include eveninghours in events and whether to call events on consecutive days; and 4) – potentially – thatthe program use something like IP rebates to present critical events in a way that mesheswith the way people make decisions. Gulf Power, the Community Energy Cooperative, andCalifornia’s Statewide Pricing Pilot have high customer retention rates. Field experiencesuggests, however, that recruiting is a harder, unsolved problem. This project concentrateson designing CPP rates that facilitate recruiting customers.

This project tries to address the recruiting challenge by designing policies that overcomepsychological resistance to efficient policies among consumers who stand to gain from signingup for them.

3 Psychological explanations of customer resistance.

CPP delivers subtle benefits by modestly lowering prices most of the time while it occasion-ally inflicts visible losses during critical events when the average customer uses less power,but pays more in total for it. A variety of psychological theories suggest that presentingsubtle gains and visible losses will repel consumers.

10Large commercial and industrial customer resistance is also a problem. Commercial and industrialcustomer are beyond the scope of this project because large consumers should hire analysts and otherwiseanalyze economic decisions in different ways than small customers do. Large customers may also sufferprincipal agent problems.

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• “Narrow bracketing” consumers base their decision on short term outcomes like abilling period or an afternoon rather than the appropriate long term outcomes (Thalerand et. al., 1997; Read et al., 1999). Narrow bracketing is necessary for most of thepsychological findings below to explain resistance because many customers will comeout ahead on CPP in the long run.

• A reference dependent, loss averse customer codes outcomes as gains or losses relativeto an anticipated (“reference”) outcome. These consumers consider that losses relativeto the reference point loom larger than gains. (Kahneman and Tversky, 1979) A criticalevent that leads the average customer to pay more to buy less than they would on theirreference, non-critical day would seem quite painful.

• Studies of choice under risk suggest that consumers not only exhibit something akin toloss aversion, but also often consider just the worst case rather than the whole outcomedistribution. (March and Shapira, 1987; Lopes, 1987)

Field evidence is consistent with these factors playing a role:

• “A number of [RTP] program managers suggested that”...“the vast majority of eligiblecustomers view the risks of RTP as too great and/or the potential benefits as toosmall.” (Barbose et al., 2004)

• “Customers were already prepared to spend the current amount each month.... So,they were not strongly motivated to ... lower it [i.e. their bill]. At the same time, amuch higher monthly bill would become a serious problem, one that customers werestrongly motivated to avoid. That mentality [often drove] ... the decision to refuseparticipation.” (Focus Pointe, 6,22)

• “The Super Peak rate period was especially anxiety producing.” It “created strongapprehensions about the size of the monthly energy bills .... ” (Focus Pointe, 6,22)

Customers sometimes appear to choose the option with the greater number of attributesthat compare favorably (Redden and Hoch, 2005). Two of the three periods in a typicalCPP rate are more expensive than the time invariant price but account for less than 20%of all hours. Gulf Power’s decision to use four CPP periods that sets two off-peak prices –“medium” and “low” – lower than the time invariant price – might be effective because itaddresses this customer decision-making heuristic.

Many consumers find it unfair to raise prices to deal with a shortage stemming from ashock that has increased their demand for a product. Critical periods often raises priceswhen heat maximizes air conditioning demand. This is a summer analog to Kahneman et al.(1986)’s finding that most consumers found it unfair to raise the price of snow shovels duringa blizzard. Many customers consider conventional, efficient pricing an unfair way to dealwith shortages (Kahneman et al., 1986). Gulf Power (Gulf Power) assures customers thatits Critical Peak Pricing price levels “[R]eflect the actual cost of producing electricity duringthose periods.”

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3.1 Evidence about behavioral interventions’ effectiveness

Scholars have proposed interventions which, like IP rebates, change presentation; informationflows; and the timing of decisions, costs, and benefits. Studies show that these interventionsimprove consumer choices in areas like retirement savings and investment choices. For exam-ple, the “Save More Tomorrow” program increased employee savings at companies by askingthem to precommit to increase their retirement savings rate the next time they got a raise.This timing sidesteps loss aversion. (Thaler and Benartzi, 2004) A series of lab experiments(Gneezy et al., 2003; Thaler and et. al., 1997; Gneezy and Potters, 1997) show that cus-tomers invest more in riskier, but higher expected return instruments when experimenterssend them aggregated information which forces them to broadly bracket. This reduces thelikelihood that subjects will learn of temporary losses, which reduces resistance from refer-ence dependent loss aversion. Most of the increase in risk taking happened as soon as thesubjects learned that they will be getting aggregated feedback but before they experiencedthe aggregated reports (Gneezy and Potters, 1997) which offers hope that merely promisingto reduce the experience of losses can recruit customers.

Marketers frame costs as gains by presenting sales below a “regular” reference price orby offering rebates. They use deferred payments to deliver benefits now and costs later. Bycontrast to marketers, public policy designers should seek behavioral interventions that notonly change outcomes, but also reduce self-destructive mistakes.

Behavioral economists suggest seeking interventions that improve biased consumers’choices without affecting rational consumers’ choices because errors and biases are com-mon, not universal (Sunstein and Thaler, 2003; Camerer et al., 2003). This project sharesthat outlook.

Interventions like changing the presentation of choices and information flows and thecombination of CPP and IP rebates (CPP-IPR) proposed here reflect the emerging idea thatwe should address problems by not only using good incentives – like CPP – but also bypresenting incentives in ways that reflect how consumers decide.

3.2 Similar interventions to improve decision making by address-ing biases are possible for electricity pricing

Assigning customers property rights that allow them to earn rebates and come out aheadduring critical peak events can sidestep resistance from all of these heuristics:

• Rebate opportunities can transform the presentation of critical events into opportuni-ties to earn rebates through sacrifice rather than obvious losses when customers paymore to get less.

• Rebates address narrow bracketing by providing monetary gains during the criticalevents that create incentive for consumption sacrifices.

• Rebates during critical periods and low prices during off peak peak periods may meanthat customers who count lower priced periods will think that two of three price periodscompare favorably to the status quo, time invariant rate.

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• A rebate program seems fair because customers have the right to use power duringshortages and the program pays willing customers to conserve, rather than makingcustomers face the likelihood of paying more to get less during each event.

• The property rights that creates rebate opportunities will typically improve outcomeson both the costliest days and costliest months11 which will make the offer more attrac-tive to customers who focus on the worst case. As 8 describes, CPP-IPR is particularlyeffective in reducing the worst monthly outcomes in climates where customers use themost power the season of scarcity.

Rebate programs seem popular with consumers. Members of a residential customer focusgroup considered conventional real time pricing and a similar rate presented with rebates.When asked to name rate features they liked, most customers mentioned rebates. (King andHarper-Slaboszewicz, 2006)

We need to worry that using IP rebates to reframe critical events as opportunities ratherthan threats will make customers more willing to sign up, but less responsive to criticalevents. A series of experiments have documented an “endowment effect” that makes cus-tomers demand far more to give up mugs that they have just been handed than they arewilling to pay for mugs that they do not have, so there is reason to be concerned that tellingcustomers that they own the right to low priced power will make them less likely to giveit up. Anaheim customers shifted a significant amount of consumption away from criticalperiods to earn rebates in a pilot test of a a critical peak rebate program (Wolak, 2006). ACPP-IPR program that created an endowment effect might still deliver more benefits than aCPP program with no endowment effect, if the CPP-IPR program got a higher participationrate than the CPP program.

The remaining challenge is to develop an intervention along these lines that preservesCPP’s incentives and is feasible to implement.

4 Improving the presentation while preserving incen-

tives

Psychology suggests a need to change the presentation of dynamic pricing to make criticalevents into opportunities to gain and to do so without imposing fixed fees. This section seeksways to deliver that presentation in a way that preserves marginal incentives and chargeseach customer a total annual bill identical to what would have been charged under CPP.

CPP rates are a simple way to create time specific incentives. Their marginal incentivesare independent of the customer’s power usage in this time period or a previous time pe-riod. Preserving marginal incentives is important because Wolak (2006) reports that manycustomers exploited the incentives in Anaheim’s rebate program. A senior regulator charac-terized these customers as “mini-Enrons” when she discussed his findings at the Universityof California Energy Institute POWER Conference in March 2006.

11Critical events happen disproportionately when the average customer is using the most power and payingthe most for it. CPP-IPR dampens seasonal variations for these customers. Some customers’ usage does notfollow these patterns.

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4.1 Using fixed credits and fixed charges to offer rebates whilepreserving CPP’s marginal incentives and annual total bills

Incentive preserving rebates transform the presentation of CPP while preserving CPP’s rev-enue streams and generally preserving its marginal incentives.

IP rebates make critical events into opportunities for customers to gain by selling eachcustomer rights to a block of power at the regular price during critical events and offeringrebates for the value of any unused credits. The rebate value per kWh gives customers theright incentives to choose between using their rights and cashing them in. Each customerpays a fixed monthly fee to buy these rights. For example, a customer might pay $5 a monthto buy the rights to $4 worth of power during each of 15 events a year. So the customerpays a total of 12 ∗ $5 = $60 per year to get credits worth $60.12

The essential insight here is that fixed transfers of cash or property rights can adjust billswhile maintaining the right marginal incentives. Versions of this insight underlie the CoaseTheorem, hedging in financial markets, and policies like cap-and-trade pollution permitsystems. Since CPP defines the number of events per year and the prices during the criticalevents the value of rights to use power during each event is clear and there is no reason tocharge a risk premium. Hence, there is a well defined price of the property rights to power,so transfers of cash are identical to transfers of property rights.

We can make these transfers of rights revenue neutral for each customer – every pennythey put in they get back either as power or as a rebate.13 This revenue neutrality meansthat it is impossible for a customer to profit by strategically manipulating the number ofrights that the utility assigns to them. Hence, the only new economic incentive that a CPP-IPR program creates is the desired incentive to shift use away from peak and critical periods.Revenue neutrality makes it costless for designers to offer customers rights to more (or less)power than they would have used in the absence of dynamic pricing. Designers can use thisfreedom to ensure that most customers get rebates and to make the same offer to a broadclass of customers. Cross subsidies, where some types of electricity customers pay more thantheir share of total system costs, while other types of customers pay less than their share,are a ubiquitous flaw of electricity rates.14 Revenue neutrality means that there are no crosssubsidies in the rebate program, making CPP-IPR as transparent and as equitable as theunderlying CPP rate. Further, it means that the rebate program should deliver revenue thatis identical to CPP revenue – so none of the design parameters that the rebate programdictates lessens the utility’s revenue stream or makes revenues harder to predict.15

12The rate in Table 1 has customers contribute 2.5 cents ∗ 450kWh = $11.25 per month, which is $135 peryear, and offers them $9 ∗ 15 events = $135 per year

13Achieving true revenue neutrality requires paying interest on contributions to equate the net presentvalue of the dollars each customer pays to the net present value of the rights that they get later in thatcalendar year. I omit this straightforward but small and tedious adjustment for brevity.

14Going to real time pricing that sets a price of power each hour is a necessary, but not sufficient conditionto eliminate cross subsidies. Critical peak pricing reduces cross subsidies.

15CPP and CPP-IPR raise identical revenue assuming that customers behave identically under them.Section 3.2 discusses endowment effects that might cause CPP-IPR customers to use more critical periodpower. This might cause the kind of shift in revenue that would reflect the relationship between the CPPprice’s critical price and the cost of providing power during those times. If utilities charged a critical priceequal to the marginal cost of critical-period power, then this change would also be (net) revenue neutral.

12

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Figure 1: Presenting IP rebates as the right to choose between power at the usual price ora rebate during each event is equivalent to presenting it as a fixed credit during each criticalevent. Both presentations keep the marginal incentives equal to the critical peak price.

We have a great deal of flexibility in how to describe the rights that the customers own.One attractive way to do so is to describe it as a property right to access a set number ofunits of power at the reference price during each critical event. Customers can cash in theunused rights to a kWh for the value of access to a kWh of critical period power at the peakprice, which is the difference between the peak and critical prices. Customers on the ratein table 1 get $9 worth of rights during each critical event, which lets them access up to 25kWh of power for 24 cents each instead of 60 cents and cash in the unused part of theserights for a rebate of 36 cents per kWh. Figure 1 shows the equivalence of the fixed creditand regular-priced-units presentations while section 5.2 proves their equivalence.

Presentation matters: Loss-averse customers may be more receptive to the “usual-price”explanation (used in the sample rate in table 1 on page 16) than to the “fixed-credit”presentation. Customers who have rights to buy all of their critical period power at the usual,peak price (likely, the reference price) experience no losses in mental spending. Presentingeconomically identical incentives as a high price and a fixed credit creates offsetting gainsand losses, but loss-averse customers put more weight on losses than gains and will perceive

Rates are often marked up to recover fixed costs and regulators deal with shifts in demand on a regularbasis.

13

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the offsetting gains and losses as a net loss.16,17

This presentation of IP rebates preserves CPP’s marginal incentive by keeping the sumof the price of the marginal unit and any foregone rebate equal to the CPP price for thattime period. It is efficient and fair that all customers face the same CPP incentives to usepower regardless of whether the customer is eligible for a rebate. The critical rate presentedin table 1 achieves this by having customers with no rights left pay 60 cents per kWh, whilethose with rights face a 60 cent opportunity cost because they pay 24 cents and forgo a 36cent rebate for each kWh.

4.2 Bundling rights with power purchases

Selling customers a fixed, monthly block of rights for a fixed fee is a simple, effective fundingmechanism that does not change customers’ incentives. The marketing literature reportsthat customers are averse to paying fixed fees. An alternative approach is to bundle rightswith the first few units of power that customers use each month and to increase the priceof those units by the value of the bundled rights. This creates incentives mathematicallyidentical to declining block pricing – but, in strong contrast to past utility declining blockpricing, the markups on the initial block of power buy the customer rights that they will latercash in rather than covering fixed costs of the shared infrastructure. Further the marketingliterature shows that customers who resist fixed fees are more receptive to almost identicalincentives and charges presented through declining block prices (Ho and Zhang, 2004). Forexample, instead of using the $5 a month example in section 4.1, we bundle 2.5 cents ofrights with each of the first 200 kWh of power the customer used.

Bundling does not change the consumer’s incentive to buy power since IP rebates’ revenueneutrality means they return every cent that customers pay through it.18 We aspire to haveeach customer buy all of the power with bundled rights each month in order to ensure thateach customer buys the rights their rate promised. If the rate fails to offer a customer therebates that it promised because the customer did not fully purchase their rights, customersmay experience the kind of unexpected loss that the rate structure is designed to avoid.

It is desirable to keep offpeak power that is bundled with rights less expensive than thetime invariant rate so 3-period CPP-IPR rates compare favorably to time invariant ratesduring both off peak and critical periods. This is attractive to customers who simply countthe number of periods during which one rate outperforms another (Redden and Hoch, 2005).It also lets marketers claim that CPP-IPR offers lower prices more than 80% of the time –as Gulf Power does.

Collecting money for rights each month and returning it during critical events reschedulea significant part of CPP’s savings. CPP delivers savings in a subtle way year round duringoffpeak times. CPP-IPR delivers many of those benefits in a visible way during criticalevents. Table 2 compares the proportion of customer bills that come from peak, offpeak,and critical periods under time invariant, CPP, and CPP-IPR rates. This change in the

16We could use a model like Koszegi and Rabin (forthcoming) to formalize this.17Prospect theory suggests that customers will have diminishing marginal sensitivity to gains which will

further diminish the perceived difference in size between the gain from the full credit of presented by thefixed-credit presentation and the smaller rebate emphasized by the usual-price presentation.

18Section B.0.1 proves this.

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timing of charges over the year may cause small income effects, but these effects are likelyto be negligible.

Table 1 provides an example of how CPP-IPR works in practice and how offer lettersmight explain it to consumers.19 In this example rate, customers on the time invariant ratepay 14.6 cents per kWh regardless of when they use it. Customers on CPP pay more – a24 cent per kWh “high rate”– during non-holiday weekday afternoons. Customers on CPPpay less – a 12 cent per kWh “low rate”– during the remaining, “off peak,” periods. Morethan 85% of all hours are offpeak. The utility can notify customers that a (typically peak)period will be a critical period, raising prices 36 cent per kWh.20 Roughly 1% of all hoursare critical.

The CPP-IPR example rate is identical to CPP with three modifications:

1. The customer’s first 450 kWh per month are bundled with 2.5 cents worth of rights.

2. The customer has the right to access up to 25 kWh of power during an event at theusual price (typically the high price) for that period. If the customer uses less than25 kWh during the event that lasts 5 hours or less, he also earns a 36 cent per kWhrebate for the difference between their 25 kWh of rights and their actual use. Forexample, a customer who used 20 kWh during a critical afternoon would get a rebateon 25kWh of rights− 20kWh used = 5kWh, for a total of a $1.80 rebates.

3. CPP puts a ceiling of 1% on the proportion of hours in which the utility can invokecritical prices, while CPP-IPR requires the utilities to offer customers rebate opportu-nities equivalent to declaring 1% of all hours as critical periods. Section A.2 discussesthis in more detail.

4.3 Preserving incentives through account-level revenue neutralrebates

IP rebates aspire to provide an appropriate level of rights to each person without creatingperverse incentives. Charging customers a dollar for every dollar of rights they get ensuresthat the marginal change in total annual bills with respect to a change in rights levels is zero.This strict revenue neutrality makes customers and utilities economically indifferent abouthow many rights they get and preserves CPP’s marginal incentives. Achieving account-level revenue neutrality requires vigilance about policies for things like rights purchased inanticipation of events never called and customer entrance and exit. Appendix A discussessome of these details.

Customers’ electricity use is an important – but manipulable – signal about the quantityof rights a customer needs to avoid bill increases from critical peak events. Any mechanism

19The CPP rate in table 1 is based on Pacific Gas and Electric’s “low ratio” experimental CPP rate(Pacific Gas & Electric, a). These CPP and CPP-IPR rates would raise the same amount of money as thetime invariant rate did from the customers on time-invariant rates in California’s Statewide Pricing Pilot.California has some of the highest electricity prices in the country.

20Structuring critical periods as costing 36 cents per kWh more than the normal price for that time periodfacilitates creating a system that means that the utility to can call critical events with the usual rebateprovisions and revenue implications during offpeak periods should the need to do so ever arise.

15

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Table 1: Examples of rates. The IP rebate offer here is appropriate for a high use customerwith air conditioning in a hot climate.

Price per kWhPricePeriod

Times in effect TimeInvariantRates

CPP CPP-IPR

initial price beyond 450kWh/mo.

Low weekdays before2PM; after 7PM;all day weekends &holidays

14.6 cents 12 Cents 14.5 cents 12 cents

High Weekdays 2:00PM-6:59PM

14.6 cents 24 Cents 26.5 cents 24 cents

Critical Announced with atelephone call atleast 24 hours inadvance

14.6 cents 60 Cents First 25KWh: 24 cents; 36cent rebate for every kWhyou save. Additional kWhafter the first 25: 60 cents

Table 2: Bills by time of electricity use. CPP and CPP-IPR generated lower bills thantime-invariant rates would have for these California CPP customers. IP rebates rescheduledsavings into critical periods. Data: California State Wide Pricing Pilot CPP customers,described in section 7.2.1, CPP-IPR benchmark offers described in section 7.2.4.

offpeak peak critical annual total billTime Invariant 84.6% 14.1% 1.3% $939

(% of bill and total kWh’s used)CPP 71.4% 23.8% 4.8% $909

CPP-IPR 77.6% 24.9% -2.4% $909

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that uses consumption to adjust the number of rights that customers get must adjust thenumber of rights that they purchase by an identical amount to avoid distorting the incentivesto consume power. Section 6 provides details.

4.4 Psychological evidence about consistent rebates

If customers dislike paying critical prices or experiencing bill spikes, then we can sell cus-tomers enough rights to ensure that most customers receive rebates during each billing cyclecontaining an event.21 The IP rebate design means selling customers more credits will notreduce utility revenue or distort incentives. Thus, we aspire to provide most customers with“consistent rebates”.

Maximizing the number of customers getting rebates has potential downsides. IP rebatesmay induce customers to accept improved air conditioning management incentives, but re-duce their awareness of air conditioning’s costs. Customers might misinterpret consistentrebates as a sign of low peak use.22

Good rates offer most customers a level of rights that deliver consistent rebates and thatthe customer buys through bundled purchases and keeps marked up offpeak power cheaperthan the time invariant price. Section E.1 finds offers that meet these criteria for mostCalifornia customers.

5 Revenue neutrality and incentive preservation proofs

This section proves that IP rebates are revenue neutral and preserve marginal incentives forthe well behaved case in which customers buy all the bundled rights their rate offered, whileappendix B extends the proofs to the general case.

Consider a CPP rate with three periods: low-priced, offpeak periods (denoted “L”),higher-priced, peak hours (“H”), and the highest-priced, critical hours (“c”). The quantityof power that the customer uses during period i is Qi.

23 The rate sets prices for each period,denoted PH , PL, and Pc.

24 The total monthly bill, TCCPPm , under this rate is:

TCCPPm = PcQc + PLQL + PHQH

5.1 A formal overview of CPP-IPR

IP rebates change the presentation of CPP by adding charges and credits that sum to zeroand that retain CPP’s marginal incentives.

21Analogously, the US income tax system is tuned so that many citizens withhold too much and get refundswhen they file rather than writing large checks.

22Ranking each customer’s rebate size might avoid this misinterpretation by sending messages like “7 outof 10 of your neighbors earned significantly bigger rebates than you did last month.”

23Characteristics that vary by customer – like quantity consumed, Qi – appear in sans serif.24Rate characteristics like PL and miscellaneous entries appear in the math typeface. Rate characteristics

reflect local system costs and this document generally takes them as given in designing an IP rebate system.Section F lists the notation used in this document.

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Consider a rate that calls Nc critical events per year and a month m in which the utilitycalled Nm ≤ Nc events. The rate bundles rights with the first QB kWh that increase theirvalue and price by markup M.25

5.2 The equivalence of incentive-preserving fixed credits to rightsto regular priced power

Fixed credits are an attractive way to change outcomes while preserving incentives. Section4.1 offers rationale for offering customers rights to rebates or power at the usual price duringevents. This section proves that these two approaches have identical bill and incentiveimplications.

The rights offer customers up to qR of power at the normal price, typically PH , duringa critical event. Further, if they use a quantity qe < qR they get a rebate of Pc − PH perunit for any unused rights, qR − qe. Writing this out and multiplying through shows thatthis is mathematically equivalent to offering each customer a fixed credit that reduces billsby R = (Pc − PH)(qR) during each event.

TCCPP−IPRe = PHqe − (Pc − PH)(qR − qe)

= PHqe − PHqe + Pcqe − (Pc − PH)(qR) (1)

= Pcqe − (Pc − PH)(qr)

= Pcqe −R (2)

Equation 2 makes it clear that CPP-IPR customers face the same price, Pc, during anevent as CPP customers do, but get a lower bill because they receive a fixed credit of R.Equation 1 shows that the two formulations are equivalent because the sum of the usualprice PH and the forgone rebate, Pc − PH is equal to the critical price, Pc.

26

The balance of this analysis describes IP rebates as providing a fixed credit of R to bothsimplify its notation and emphasize the preservation of the marginal incentive.

5.3 Account-level revenue equivalence

This section shows that CPP-IPR generates total annual total bills identical to the underlyingCPP rate in the well-behaved case where customers buy Qm ≥ QB kWh in each month m,buying all the rights the rate offers them, namelyMQB worth per month.27. These customerspurchase power rights worth R during each of Nc events. Revenue neutrality requires that

25IP rebate designers choose values for the variables listed in bold, including QB, R, and qR.26Customers who use qe > qR pay Pc for their marginal power use. That equivalence proof is analogous

and omitted for brevity.27IP rebates change seasonal bill patterns by raising CPP bills by up to MQD each month and returning

that money during (typically summer) months with events. A section below discusses how impacts onseasonal bill patterns vary by region. Most areas’ highest use season coincides with the California summerpeak, but usage in other regions peaks during the winter.

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the amount the customer pays through the purchase of marked up units equal the value ofthe rights the customer gets back, formally that 12MQD = NcR.28

Appendix B considers the analogous general case that maintains revenue neutrality evenif customers buy less than the planned MQB worth of rights in some months.

This customer’s total monthly bill, TCCPP−IPRm , will be:

TCCPP−IPRm =MQD −NmR + TCCPP

m =MQD −NmR + PcQc + PLQL + PHQH

The total annual CPP-IPR bill, TCCPP−IPRa , is simply the sum of the monthly CPP bills,

TCCPPm , plus exactly offsetting rights and charges. We can see this by computing the total

annual CPP-IPR bill, rearranging terms, and recalling that 12MQD = NcR and that thetotal number of critical events Nc =

∑12m=1Nm, as follows:

TCCPP−IPRa =

12∑m=1

[MQD −NmR + PcQc + PLQL + PHQH]

= 12MQD −NcR +12∑

m=1

[TCCPPm ]

= 0 +12∑

m=1

[TCCPPm ]

6 CPP-IPR Compared to Other Rates

This section compares CPP-IPR to other rates, especially to baseline-rebate rates that alsouse rebates to improve incentives.

6.1 Managing Volatility

Customers accept time invariant rates and baseline-rebate rates. These, like CPP-IPR,include features that dampen bill volatility by default. The dynamic rates customers rejectgenerally make risk management optional.29 Borenstein (2007) reports that RTP leads tosignificant increases in bill volatility, but that simple hedges can control that volatility. Itmakes sense to make risk management that uses well defined property rights part of the

28For simplicity, I present these examples without calculating interest, but equating the two values in netpresent value is technically correct and failure to account for interest creates small incentive distortions andsmall wealth transfers.

29The rights that IP rebate customers buy have bill-volatility reduction effects that are akin hedging bybuying ahead on the futures market, but differ from conventional hedging in that there is no unknown stateof the world that affects the realization of the price of the commodity when the customer uses their forwardrights, although there is uncertainty about the number of critical events in each billing period and about thecustomer’s demand during events.

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default rate.30,31 Time invariant rates and baseline-rebate rates do not manage volatilitythrough well defined property rights and thus create flawed incentives. For example, timeinvariant rates include a built in mandatory hedge that gives customers a use-it-or-lose-itright to as much cheap power as they want. Customers use too much power during periodswhen wholesale power is expensive and they would prefer to sell their rights for their truecost. Time invariant rates and CPP-IPR ask customers to contribute toward insuranceagainst critical events year round, while plain CPP does not – so IP rebates are a moreincremental change from the time invariant status quo than CPP would be. Baseline-rebaterates bundle a “free” hedge with electricity purchases during baseline setting periods.

6.2 IP rebates avoid the economic flaws in baseline-rebate rates

Utilities have used baseline-rebate rates that use rebates to incent customers to reduce useduring high cost periods. Baseline-rebate rates calculate a personalized, baseline demandlevel from each customer’s consumption history and then offer rebates to customers whouse less than their baseline level during critical events. Baseline rebate programs, unlike IPrebates, often create troubling cross subsidies and flawed incentives both during ordinaryand baseline setting periods. Diagrams in appendix D illustrate the incentives discussed inthis section.

Baseline rebate mechanics in a peak load management context: These ratesgive rebates to customers who consume less than their baseline level, which is a functionof their “normal” usage during similar, non-critical periods.32 The baseline amount, Q̄bt,is generally the customer’s average use, qt−i, during a set of Nb weekday afternoon or peakperiods, t−Nb · · · t− 1, before the event at time t.

Q̄bt =1

N

n∑i=1

qt−i

The customer’s total bill under a baseline rebate plan is:

TCbaseline = PLQL + PH(QH + Qc)− PB max{0, ncQ̄bt − Qc} (3)

30Zero expected cost risk management or month-to-month volatility reduction make customers happier forbehavioral and neoclassical reasons. IP rebates are in this category since they provide features that reducemonth to month bill volatility at zero cost to the consumer while their dynamic pricing lets customers reducetheir overall bill. Rational customers, however, should be willing to pay only a very small risk premium toreduce the risk of a bill spike of a few tens of dollars (Rabin, 2000).

31Making a revenue-neutral volatility dampening mechanism or actuarially fair hedge the default is at-tractive. Including the hedge by default reduces the transaction costs of protection against fairly small billshocks. People often refuse to choose when they face too many choices (Iyengar and Lepper, 2000; Dhar,1997); and are strongly influenced by default offers (Choi et al., 2003). Economically rational customerswill generally be nearly indifferent about the exact number of rights purchased under revenue neutral billvolatility reduction strategy; and not have particularly high willingness to pay for one hedge that has zerobill impact in expectation over another.

32Baseline-rebate rates create asymmetric information games in which customers know their demandfor electricity, but the utility only learns how much they used. It is generally difficult to design efficientmechanisms to get customers to reveal their demand. In the absence of mechanisms designed to minimizedistortions, customers have incentives to strategically misrepresent their demand during baseline-settingperiods.

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Baseline-rebate rates create perverse incentives during baseline-setting peri-ods. Baseline-rebate rates bundle free baseline rights with power during baseline settingperiods. This makes power artificially cheap and gives customers incentives to increase us-age during baseline setting periods. To see this, substitute the formula for Q̄bt into thebaseline-rebate bill formula, 3, and take the partial derivative with respect to the quantity ofpower used during the baseline-setting period assuming, for notational simplicity, that thecustomer gets a rebate:33

∂TC

∂Qi

= PH − PB

∑i∈Bt

1

N

This distortion becomes small (large) as the baseline setting period gets large (small).Using a long baseline-setting period, however, is likely to include cooler weather in thebaseline and thus to make it a less accurate estimate of what people would have been doingon the critical day in the absence of an incentive to conserve.

These bundled baseline rights create significant changes in incentives. For example, SanDiego Gas and Electric’s proposed baseline-rebate rate offers a 65 cent rebate for every kWhthat a customer’s period use is below a baseline set by the customer’average use on the fivenon-event weekdays preceding the event day (Gaines, 2006). This means that San Diegocustomers get another roughly34 1

5kWh of baseline rights, worth 13 cents, bundled with

every baseline-setting kWh. Residential customers in San Diego pay between 4 and 18 centsper kWh of power (San Diego Gas and Electric).35 The bundled rights can be worth evenmore if one day sets the baseline for more than one critical event. Anaheim offered a 35cent rebate and used the average of the consumption during the three highest use non-eventweekdays of the summer season as its baseline for every event. Since a single additional kWhconsumed on a baseline-setting day increases the baseline by 1

3kWh over 12 events, this unit

that costs either 6.75 or 11.07 cents comes bundled with rights worth $1.40 to a customergetting rebates (Wolak, 2006, 14).

This distortion often increases demand when wholesale power is moderately scarce andexpensive.

During events, baseline-rebate rates offer unlimited power at the usual priceand give customers not earning rebates no extra incentive to reduce usage onthe margin. Baseline-rebate rates, like time invariant rates, implicitly include the cost ofmandatory, unlimited critical period price insurance in the price of basic electric service.

Baseline-rebate programs are expensive, create cross subsidies and force un-comfortable trade offs: Baseline-rebate rates are not revenue neutral for individual cus-tomers which means that baseline-rebate programs create unpredictable rebate costs that

33There is no distortion for customers who will never get rebates. And there is a tedious, unenlighteningcorner case for customers who switch from no rebates to rebates as they use more during the baseline period.

34San Diego’s proposes to set its baseline by multiplying the average consumption during the baseline-setting period by a scaling factor, namely the ratio between the system wide demand on baseline-settingdays and the critical day. This lets them correct for differences in demand – especially in weather-driven airconditioning demand – between the baseline-setting and critical days.

35Most California utilities – including San Diego Gas and Electric and Anaheim Public Utilities – use anincreasing block rate structure that offers the first few kWh per month at a low price, then increases themarginal price as customers use more.

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utilities need to recover. Utilities recover rebate program costs by increasing rates, oftencreating inequitable cross-subsidies. Baseline levels can be mistakes since, unlike IP rebates’choice of qR, they transfer cash among customers and create incentives, 36. Hence, the idealbaselines is the amount the customer would have used without the rebate opportunity. Thelimited data availability and normal usage variation lead many customers’ to deviate frombaseline predictions even in the absence of rebate opportunities.37 Thus, IP rebates avoidflaws in baseline rebate designs.

6.3 Baseline-Rebate Rates: Field Experience

Utilities have fielded baseline-rebate rates. Wolak (2006) analyzes an experiment with abaseline-rebate dynamic pricing program in Anaheim, California and reports that consumersreduced use during critical periods but many customers exploited poor incentives. San DiegoGas and Electric proposed making a similar “Peak Time Rebate” rate the default for itscustomers.38. California utilities offered a “20/20” during the electricity crisis that offeredcustomers a 20% rebate on their electricity bill if they reduced their total summer electricityuse 20% below their baseline, namely, use the previous summer. California Utilities’ “10/20”baseline rebate program during a Winter 2005-06 natural gas price spike offered a 20% rebatefor reducing gas consumption at least 10% below the previous winter. Many utility staff andregulators are disatisfied with baseline rebate rates.

Baseline-rebate programs often get universal participation, unlike opt-in dynamic pric-ing, because utilities generally describe baseline-rebate plans as containing only rewards forconservation.39

7 The political, organizational, and financial feasibility

of CPP-IPR: Evidence from California Customers

CPP-IPR implementations need to meet administrative and financial constraints. Data froma California CPP pilot study shows that most customers meet the financial constraints onCPP-IPR. The central, interlocking feasibility issues are:

• Economic feasibility. CPP-IPR works well if we can assign each customers a revenue

36The underlying CPP rate creates the incentives in CPP-IPR; IPR’s simply presents those incentives ina more palatable way.

37San Diego Gas and Electric also reports that more than a quarter of their customers had usage in absenceof the critical event that would have either given them a rebate or have given them a baseline that wouldrequire them to reduce usage 15% before they got a rebate.

38The Anaheim and San Diego rate designs comply with the AB1X prohibition on raising certain rates inCalifornia.

39Baseline-rebate programs that claim to provide only rebate opportunities – carrots without visible sticks– often recover rebate costs by raising rates later. A PG&E proposal reads, “[T]he 10/20 Winter Gas SavingsProgram is forecasted to pay out $200 million in rebates...PG&E proposes that these costs...be recovered inresidential and small commercial customers’ transportation rates during the summer gas season...” (PacificGas & Electric, b, 4). Thus, some customers would have done better had they been able to opt out of boththe rebate program and the responsibility to pay for it.

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neutral pair of a rights size, qR, and a number of units bundled with rights, QB, thathas the attractive properties described below.

• Administrative and political feasibility. CPP-IPR should coexist with existinganalytic categories, be an incremental change from existing rates and let regulatorsaddress equity concerns.

This section proceeds as follows:

1. Section 7.1 introduces properties that are desirable in CPP-IPR implementations andshows that offers exist meeting these criteria for most customers.

2. Section 7.2.1 discusses reasons why implementations may make broad categories ofcustomers a single offer rather than individualizing offers.

3. Section 7.2.2 shows that using 16 existing categories from the California StatewidePricing Pilot CPP field experiment performs 86% as well as making omniscient indi-vidualized offers and that the 16 offers can be reduced to 3, by optimally assigningthose 16 categories to small, medium, and large groups.

4. Section 8 discusses CPP-IPR’s tendency to smooth seasonal variations by having cus-tomers purchase rights each month and then applying those rights to bills during thehighest use months.

5. Section 7.3 IP rebates are a revenue neutral, marginal incentive-preserving featurethat can be added to any CPP rate. Providing most customers consistent offers,however, requires that the difference between offpeak and time-invariant prices – theupper bound on the quantity of rights that can be bundled with each kWh – be “largeenough.”

7.1 Economic constraints: consistent rebates, inframarginal bun-dled rights, and revenue neutrality

IP rebates make each customer an offer, (qR, QB), which specifies the quantity of rightsthat the customer gets during each event, qR, and the number of kWh the declining blockmarks up each month, QB. It is desirable for offers to meet the following constraints for asmany customers as possible:

i. Consistent rebates: The offer includes enough kWh at the usual price so that thecustomer gets a (weakly positive) rebate during each month with an event, or qR ≥ q̄c.In other words, the number of protected kWh, qR, has to be at least as great as thecustomer consumed during the average event in the customer’s highest average-event-use month q̄c = maxm∈M{Qc/Nm} .

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ii. Consistent purchases through inframarginal declining blocks: Customers buyall of the rights that the offer promised only if the declining block marks up less powerthan the customer uses each month40, or QB ≤ Qm.

iii. Customer-level revenue neutrality: each customer makes payments for rightsequal to the value of the rights they receive. If the customer consistently purchasesQB per month (constraint ii) then, this becomes 12MQB = NcqR(Pc − Ph).

Satisfying the revenue neutrality constraint is necessary to avoid creating transfers andflawed incentives that customers can exploit. IP rebates aspire to do so while making offersthat are consistent because they provide consistent rebates (i) and consistent purchases ofbundled rights (ii) to as many customers as possible.41

Substituting the first constraints i and ii into constraint iii, reveals a criterion that de-termines whether a consistent offer exists, namely:

12MQm ≥ 12MQB = NcqR(Pc − Ph) ≥ Ncq̄c(Pc − Ph) (4)

Dropping the middle, revenue neutrality, terms creates a feasibility criterion that dependsonly on customer characteristics and characteristics of the rate that we take as given. Thecriterion implies that a consistent offer exists only if:

12MQm ≥ Ncq̄c(Pc − Ph) (5)

Figure 2 visualizes the three constraints and their implications by plotting the use duringevents on the x-axis and monthly use on the y-axis.

7.2 Implementing CPP-IPR

7.2.1 Offer existence, predictability, and administrative feasibility

Providing most customers consistent offers requires that, for most customers, consistentrights levels (satisfying 4) exist and be feasible to predict. There is no field experiencewith CPP-IPR, so data on customer behavior on economically-similar CPP rates providesthe best available evidence about the feasibility of CPP-IPR. California’s Statewide PricingPilot (SPP) collected data on 500 CPP customers who experienced 27 CPP events (CharlesRiver Associates, 20) from summer 2003 into fall 2004. The example CPP-IPR rate in table

40I assume that qR and QB stay the same year round. Making seasonal changese to the declining blocksize, QB, may be an important way to provide consistent offers. Requiring extra contributions early inthe year could provide a reserve fund to cover under contributions later. It may be particularly natural toconsider seasonal variations in QB orM in electricity systems that already seasonally adjust rates. Seasonaladjustments, however, make rates harder for customers to understand.

41This project focuses on maximizing the probability of getting a consistent offer during each customeryear. Since Qmand q̄care a minimum and a maximum, respectively, so the more observations they consider,the more extreme results they will report. It is more relevant to rate design to know that a family’s annualvalues of Qm and q̄c supported consistent offers in 19 of 20 years than to know that taking the same extremesfrom the Qm’ and q̄c’ over 20 years discovers outlying values – like an extended vacation and running thedryer during a critical period – for which there are no consistent offers.

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Figure 2: Visualizing constraints 1-3.

1 is adapted from the CPP rate described in an SPP Welcome Kit (Pacific Gas & Electric,a), .

Appendix E uses SPP data to estimate that for the example rate 97% of customersstatewide have demand patterns that satisfy feasibility criterion 5; shows that aggregatedsummer electricity use is strongly correlated with the number of rights that a customerrequires to get consistent rebates, and calculates the percentage of customers for whomconsistent offer exist under other rates. That analysis shows that CPP-IPR meets the basicfeasibility criteria. The balance of this section summarizes results from Letzler (2007b) andLetzler (2007a) about whether IP rebates can perform well under tougher contraints that wemake offers to categories of customers.

IP rebate implementations either make each customer a customized offer or make offersto categories of customers.

• Category level offers seem fair because they typically offer neighbors and other (su-perficially) similar customers identical rebate opportunities. (An IP-rebate programthat has no effect on total annual bills is unlikely to be objectively unfair, but it isimportant that customers perceive it as fair regardless of whether they understand thisdetail.)

• Making broad categories of customers identical offers is unlikely to give customers the(wrong) notion that they can profit through strategic consumption distortion to getmore rights.

• Offers to categories are less likely to generate calls to customer service about the originof the rebate levels and simplifies answering those calls.

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• These properties help CPP-IPR reduce peak usage even if some customers understandonly that CPP-IPR makes it advantageous to reduce power use weekday afternoons,and especially during critical events.

• It is easier for the regulatory process to analyze and discuss a few categorical offers,especially if the regulatory process already classifies customers into those categories.

Rate implementers need to predict a consistent offer for each customer using availableinformation – like data on total use per billing cycle – that may not report the customer’sneed for peak period power rights. Many utilities install “interval” meters that capturedisaggregated usage data only for dynamic pricing customers. The analysis in appendix E.1below shows that aggregate use, account type, and geographic data predict consistent offerswell enough to support implementation while the analysis below categorizes customers byaggregate use and climate zone.

7.2.2 Making offers to broad categories of customers

Employing categories that rate designers already use would facilitate the implementation ofCPP-IPR. This section tests the feasibility of taking that approach using the SPP’s catego-rization of customers. Its analysis shows that making offers to as few as 3 broad categoriesof customers defined by use and geography can make consistent offers to a large percentageof customers. The SPP divided the state into 4 climate zones and each climate zone intothree groups: apartments, high use single family houses, and low use single family houses.It classified customers’ use levels as high or low using consumption from the summer beforethe experiment began. The ceiling on the low use category varies from 16 kWh per day inthe coolest climate zone to 28 kWh per day in the hottest zone.

The SPP’s original low use and apartment categories in the hottest climate zones con-tained a set of customers too diverse for a single IP rebate offer to fit well. Simplifying bydiscarding the distinction between apartments and single family homes converts the original12 groups to 8 groups. Subdividing those groups at the median use level yields 16 groupsthat allowed us to make consistent offers to the vast majority of customers.42 This yieldedvery low use, low use, high use, and very high use categories in each of the four climate zonesfor a total of 16 groups.

7.2.3 Optimization algorithm

The analysis calculated the optimal offer to each of the 16 groups and then repeated thatanalysis to find the optimal offer for each possible assignment of 16 groups to 1, 2, 3, 4 and5 categories as described in Letzler (2007b).

43

The optimal offer calculation algorithm proceeded as follows:

42Most apartments were low use. Retaining and subdividing the apartment category yielded 24 cells, someof which were unacceptably small in the 500 customer SPP database. All else equal, subdividing a categorybefore computing optimal offers for each category will improve the offers’ fit.

43Determining the optimal assignment of groups to broader, category level offers requires (potentiallyimplicit) weights capturing the relative benefits of making consistent offers to the average customer in eachgroup. The optimization reported here chose weights so that the optimal category-level offer maximized

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• It calculated the range of offers, [qR,imin,qR,i

max], that satisfies feasibility criterion 4for each customer, i. This is the range from the smallest offer that provides consistentrebates, qR,i

min = q̄c, to the largest offer that the customer can consistently buy,

qR,imin =

12MQm

Nc(Pc−Ph).

• It used each customer’s optimal range [qR,imin,qR,i

max] to calculate the proportion ofall customers in each group who would get a consistent offer for each value of qR. Thisyields the kind of objective step function in figure 4. The set of optimal offers comprisethe “plateau” on top of function.

7.2.4 Performance of Optimal Group and Categorical Rates

Appendix E.2 describes the optimal offers to each of 16 groups.44 It contains table 6 sum-marizes the 16 optimal offers and their performance in providing consistent offers and figure10 that displays identical information about the optimal offers but not about their perfor-mance. The balance of this paper will use this 16-offer CPP-IPR rate as a benchmark incalculating the impacts of CPP-IPR.45 We can get from 16 to 9 categories without makingany compromises by merging groups with similar rights needs.

Group-level performance Calculating the offer that is consistent for the greatest weightednumber of people in each group yields a set of offers listed in table 6 and visualized in figure10. These are consistent for 86% of all customers statewide regardless of whether a feasibleoffer exists for that customer. This number reflects a 92% consistent offer rate in the moretemperate climates zones 1 and 2 and a 77% rate in the hottest climate zones 3 and 4.Five percent of zone 3 and 4 customers’ demand patterns violate criterion 5, so no feasibleconsistent offers exist for them.

Appendix E.3 reports analysis showing that most offers that are not consistent are withina few dollars of being consistent, which is substantively small when the average total annualbill is about $900.

Category-level performance The optimal category-level offer analysis is equivalent torunning the above algorithm on every possible combination of the 16 groups into between 1

deadweight loss reduction benefits. It proceeds under assumptions, documented in Letzler (2007b), implyingthat any increase in the probability that a customer gets a consistent offer leads to some increase in theprobability that they sign up. Letzler (2007b) converts estimates of the peak-period, energy use impact ofexposing each of the 16 groups of customers to peak and critical prices from Letzler (2007a)into a scalarestimate of each category’s summer season, average deadweight loss reduction value.

The category-level offer analysis rounded feasible ranges to .25 kWh increments to reduce the number ofsubstantively similar options to search.

44The 16 analysis groups contain both apartment and single family customers. The analysis weightedobservations of apartment and single family SPP customers to calculate optima for the mix of housing stockin each usage and climate zone cell.

45These results and the results below modify the example rate in table 1 by moving from the 15 events peryear that the CPP promised to the 18 events that it in fact called during the 12 months from October ’03through September ’04. It reallocates the fixed credits by offering 15/18 of the Rvalue per event – reducingthe critical price from 60 cents to 54 cents. This is a very small implicit CPP rate reduction

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60

70

80

90

10

0p

erf

orm

an

ce a

s %

of o

ptim

al 1

6 g

rou

p o

ffe

r

1 2 3 4 5number of offers

optimal categorization 1 offer per climate zone

1 offer for zones 1-2; another for zones 3-4

Optimal Offer Performance by Categorization

Figure 3: The performance of the optimal category-level offers, plus the performance of theoptimal hot and cold climate zone offers and the optimal offer to each of the four climatezones.

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Table 3: The optimal assignment of 16 groups to three categories and the level of rights thatprovide consistent offers to the greatest number of customers. This reports the percentageof customers who would get consistent offers under the optimal 16 group offer who still getthem under the optimal 3 category offer.

Optimal 3 category offersize class zone 1 zone 2 zone 3 zone 4 offer

very low84.0% 88.0% 99.5% 100.0% Category 3Cat. 3 Cat. 3 Cat. 3 Cat. 3 6.5 kWh/event

low92.6% 88.6% 100.0% 100.0% Category 2Cat. 3 Cat. 3 Cat. 2 Cat. 2 14.25 kWh/event

high100.0% 92.5% 97.1% 89.2% Category 1Cat. 2 Cat. 2 Cat. 1 Cat. 1 25.75 kWh/event

very high91.3% 100.0% 94.6% 100.0%Cat. 1 Cat. 1 Cat. 1 Cat. 1

and 5 categories.46 Doing so reveals that collapsing these groups into three categories basedon consumption and geography performs 96% as well as making an optimal offer to each ofthe 16 groups. Using three optimal categories far outperforms one- and two-category offers.47

Four and five category offers perform modestly better than the three category offer.Respecting energy consumption differences in aggregate, historical usage within climate

zones improves performance and lessens the appeal of categorizing by broad geographiccategories alone.48,49

The optimal three-category offer makes “consistent” offers to between 75% and 90% ofthe customers in most groups50 which reflects both limits on the predictability of electricityconsumption and the diversity within categories that cut across California’s extraordinarilydiverse climates and building stock.

7.3 IP rebates are a rate feature, not a whole rate

IP rebates are a revenue neutral feature that can be added to any CPP rate without affectingits marginal incentives. Implementing IP rebates as a feature that coexists with a wide va-riety of rates preserves CPP rate designers’ freedom to strike compromises between pricingnear marginal cost, meeting revenue requirements, maintaining simplicity, making incre-mental changes to the status quo, treating rate payers equitably, and addressing other local

46It uses a heuristic described in Letzler (2007b) that runs the full optimization algorithm only on cate-gorizations that might outperform the best categorization found so far.

47This paper identifies and reports the characteristics of the optimal one-size-fits-all offer. We cannot ruleout the possibility that there is a two category offer that uses a better way to assign customers to categoriesthat performs as well as the best three category offer that collapses the 16 groups.

48The 500-customer SPP data set lacks size to evaluate the effectiveness of making narrow geographicoffers that are specific to e.g. ZIP codes or subdivisions.

49When energy consumption data are not available, a proxy like the building’s size, age, and neighborhood,or a previous tenants’ use might be useful proxies for it.

50No consistent offer exists for about 3% of all customers. Even an omniscient system would be unable tomake these customers a consistent offer, so they are not in the denominator here.

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Figure 4: The proportion of very high use customers in climate zone 3 for whom each possibleoffer is consistent.

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concerns. CPP rate designers’ choices of rate periods and prices have reasonably transparentimplications – unlike, for example, the choice of baseline-rebate parameters.

While IP rebates can be added to any underlying CPP rate, the number of customerswho get consistent offers is sensitive to the size of the difference between offpeak and time-invariant prices because that difference is the upper bound on the markup, M ≤ Pu − PL.Increasing the markup bundles more rights with each kWh and expands the set of consistentoffers by relaxing criterion 7.

8 IP rebates and seasonal bill variations

Consumers and policy makers express a preference for bill levels that are consistent frommonth to month. Many utilities offer balanced payment or “flat bill” plans. Flat bill planscharge customers their expected total monthly bill plus a roughly 10% risk premium chargesregardless of the customers’ usage.

IP rebates reduce CPP bills during critical periods and increase CPP bills during thefirst QB hours each month. This shifts bills among months since the monthly contributionsare spread evenly around the year, while most critical periods take place during the summer.Thus, IP rebates reduce seasonal variations in bills for customers whose total use peaksduring the season with the largest number of critical events. IP rebates can amplify seasonaldifferences in regions where electricity use peaks in a different season from the majority ofthe electricity use in their system.

Figure 5 shows how these possibilities play out in California’s most temperate and hottestclimate zones. The top three lines on the graph show that CPP-IPR smooths the air-conditioning-driven, summer bill peak in the desert (zone 4). CPP-IPR amplifies the modestwinter bill peak in zone 1’s temperate climate. Seasonal patterns in the two intermediatezones – the Foothills (zone 2) and Central Valley (zone 3) – lie between the zone 1 and zone4 extremes.51

9 Conclusion

Efficient incentives can be an important part of improving public policies. But the obvious,natural implementations of efficient policies often repel customers who use flawed behavioraldecision making heuristics.

The evidence from this project and from a line of behavioral field experiments suggeststhat behavioral insights can provide insights about the source of behavior that serves neitherindividuals nor society well and suggest levers for interventions that address this behavior.Using economics and psychology to guide the design of improved incentives can often yieldimplementations that preserve the important economic properties of a policy while helpingsome consumers make significantly better choices.

51Looking at customer-level bill volatility – as Borenstein (2007) did – yields qualitatively similar results:IP rebates reduce each customer’s month-to-month bill volatility relative to CPP in climates that hit theirpeak consumption season when the system does and increase each customer’s month-to-month bill volatilityin regions where residential use peaks in a different season than the statewide system does.

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Figure 5: IP rebate rates (diamond) smooth a high summer peak in the climate zone 4 (desert)at the top of this graph but exacerbate modestly winter peaking bills in climate zone 1 (thetemperate fog belt; largely the San Francisco Bay Area) at the bottom of the graph.

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Incentive Preserving Rebates are an example of an intervention that preserves incentivesand revenues while changing the presentation of incentives to address a significant set ofpsychological and implementation concerns. The behavioral considerations drive five con-straints, while implementation challenges add requirements like using a small number ofexisting categories.

The evidence suggests that IP rebates are administratively feasible and that coarse,categorical offers can meet the needs of most customers. Most customers will fully fundrights that deliver them consistent rebates. Those who do not fully fund their rights or whodo not get get consistent rebates experience deviations in the form of payments at the criticalprice or reductions in rights from the promised level that are typically less than 1% of theirtotal annual bill.

IP rebates smooth bills and reduce volatility relative to conventional CPP. IP rebates aresomewhat sensitive to customer diversity, but not nearly as sensitive as baseline rebate ratesare.

Changing the framing of prices is a well recognized tool in marketing. This applicationto public policy may be the first of many important potential applications to help peoplemake better choices in areas like the purchase of energy efficient appliances and vehicles orchoices between owning a car and using public transportation.

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Anthony C. Wilson. Application of the Potomac Electric Power Company for approval ofthe tariff and meter to be used in a small customer smart meter project. Formal Case1002 Public Service Commission of the District of Columbia, June 2006.

Frank Wolak. Residential customer response to real time pricing: The anaheim critical peakpricing experiment. Working Paper, presented at the POWER conference, March 2006.ftp://zia.stanford.edu/pub/papers/anaheim cpp.pdf.

Lisa Wood. The new vanilla: Why making time-of-use the default rate for residential cus-tomers makes sense. Fortnightly’s Energy Customer Management, July/August 2002a.

Lisa Wood. Effective demand response programs for mass market customers. Presentedat the NYSERDA Time Sensitive Electricity Pricing Workshop. Albany NY, October 32002b.

Paul Wright et al. Demand-responsive electrical appliance manager website.http://dr.berkeley.edu/dream/index.htm.

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A Design Details to Ensure Revenue Neutrality

A.1 A clever calendar can help ensure account-level revenue neu-trality

Flawed policies to handle under-contribution or mid-year customer exit could break theaccount-level revenue neutrality. Concentrating events at the end of the fiscal year can ensurethat customers pay for property rights before they use them. A requirement that customersbuy rights before using them prevents customers from profiting by strategically entering forjust the peak season, claiming rebates, and then exiting the program. Clustering events atthe end of the fiscal year also ensures the feasibility of reducing credit sizes if customersuse too little power during a month and prevents customers from using rights during thesummer and then underpaying for them in the fall. A calendar that makes customers wholeave eligible to cash in their unused rights is often administratively preferable imposing feeson exiting customers or adding the value of rights that were used, but never purchased toutility’s revenue requirement.52 A standard fiscal year facilitates making equitable, revenueneutral program revisions since everyone would experience new charges or benefits at thesame time.

A.2 Ensuring that customers get the rights they paid for

CPP-IPR can handle year to year fluctuations in the number of times that weather andequipment problems justify critical events by returning the fixed credits for any unusedevent days. In other words, the customer would get the rebate they would have received ifthe critical periods had been called and the customers used zero power during the period.The requirement that the utility redeem rights for unused event days gives utilities exactlythe same incentives to call critical events in a CPP-IPR program as would a CPP rate witha hard cap on the number of events it could call. By contrast, allowing utilities to pocketcredits from unused event days would create an incentive to not call events.

B The general case: dealing with customers who do

not buy all of the offered rights

This section generalizes the discussion above to allow customers to buy less than QB kWhof power in some months, which means that they did not purchase a full MQB worth ofrights. It maintains revenue neutrality by only selling customers the rights they have paidfor, R̂.53 Selling customers only the number of rights that they pay for is consistent withtreating this bill volatility control strategy as a well-defined property right – which section 6discusses further. The customer buys rights bundled with the lesser of QB and their actualconsumption, Qm each month which are worth Mmin{QB,Qm}

52Standardizing the fiscal year requires a provision for customers who joined after current fiscal yearstarted, like calling fewer critical events for them.

53Equivalently, we could return to the original plan by marking up more than QBunits of power andbuying the missing units in a later month.

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Customers thus own rights worth R̂c during event c customers to purchase their rights,formally:

Nc∑c=1

R̂c =M12∑

m=1

min{QB,Qm}

Strategies to restore account-level revenue neutrality reduce bills relative to the full con-tribution scenario during the months when the customer contributes too little and increasesbills during months in which the customers get a reduced credit of R̂c < R. Reference de-pendent people may perceive these adjustments as a gain and a loss of the same size, whichthey would take as a net loss since they weigh losses more heavily than gains.54

The cumulative deficit, δm, in month m, is a deficit in a customer’s purchases of rights forfuture events relative to the value of rights that the rate slated for the customer. The deficitgrows when monthly consumption is too low, Qm < QB, and shrinks when the customer getsfewer rights during an event.55 Formally, the definition is:

δm = min {0, NmR− δm−1 −M(QB −min{QB,Qm}} (6)

Formula 6 defines the cumulative deficit as the sum of that month’s deficit and theprevious deficit, less any amount of the deficit that can be applied to reduce the value of therights offered during events in that month.

We can ensure budget balance by offering rights each month worth

NmR̂ = max {0, NmR− δm−1 −M(QB −min{QB,Qm}}

This reduces to the full contribution case above if the customer buys at least QB kWheach month, so δm−1 = 0, min{QB,Qm} = QB, and R̂ = R.

B.0.1 Bundling rights with the first units of power never creates a deadweightloss

Bundling rights with the first units of power a customer buys each month never creates adeadweight loss, unlike similar declining block rates. It avoids deadweight losses becauseevery extra dollar that a customer pays for through this rate’s markup, M, returns to thecustomer as an extra dollar of rights.56

Typical declining block rates can create deadweight losses by increasing the marginal costof a customer’s marginal unit.

54Customers may be equally frustrated that issues in the fine print of their offer letter are costing themmoney.

55This algebra, for simplicity, closes the entire deficit at the first available event. Equivalent, perhaps morepalatable, approaches attempt to spread the reduction over several events.

56Customers may not notice this subtle connection, but the markup is still unlikely to cause significantdistortions because many customers are unaware of whether the quantity they have consumed so far duringa month means they are paying a markup on the margin and because demand at the offpeak and peak pricesis quite inelastic. All we really need customers to know for CPP-IPR to work well is that there is someeconomic reason for them to shift power use away from weekday afternoons, and stronger reason to shiftpower use when the utility notifies them of a critical period.

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Formally, consider the marginal incentives for a customer to buy one more unit of powerduring period i ∈ {c,H, L} for a month m when Qm < QB. Taking the derivative withrespect to the total annual bill:

∂TCa

∂Qm= Pi +M− ∂δm

∂Qm= Pi +M−M = Pi

C Generalizing IP Rebates to other markets

IP rebates can be used to implement dynamic pricing and improve incentives over uniformpricing for products which have underlying costs that fluctuate over time. Generalized IPrebates offer customers:

• rights to buy a block of the product at the usual nominal price during high pricedperiods,

• rebates for unused rights, and

• product purchase opportunity costs closer to the cost of production during high andlow cost periods.

Further, an IP rebate implementation will often cause a smaller change to the customer’suniform pricing annual bill patterns than a conventional implementation of dynamic pricingwould.57

The uniform pricing that we seek to improve can generally only survive in the context ofexclusive, long term relationships with a single supplier for perishable products. Customerswho choose suppliers frequently would purchase from firms with dynamic pricing during lowcost seasons. Inexpensive storage smoothes cost differences over time. It is common forcompanies to provide difficult-to-store products through long term, exclusive relationshipsin utilities, in telecommunications, and in services like shipping, answering phone calls, ortechnical support.

I simplify this discussion by assuming that the firm prices at average marginal cost plusa uniform markup. The uniform markup makes the firm indifferent between selling high costand low cost units of the product.58,59 This assumption makes “high cost periods” and “highprice periods” interchangeable terms below.

57This IP rebate approach will not change a customer’s uniform pricing bill patterns at all if the customerhas zero demand elasticity and consumes the average ratio of peak to off peak product. In other words, thecustomer who sees no bill impact is neither gaining nor losing from the price insurance inherent in uniformpricing. By contrast, consider a customer who buys during the lowest cost season, meaning she buys anytimeunder uniform pricing. She would see a larger change under IP rebates than they would under conventionaldynamic pricing. Under both pricing schemes, this customer will shift all of their spending to the low costseason. Under an IP rebate scheme that marks up the product and then returns those markups during thehigh cost season, her bill increase (decrease) would be larger during the low (high) cost seasons than underthe conventional dynamic pricing approach.

58Adams and Yellen (1976) show that pricing that makes the firm indifferent between selling two differentproducts can be part of an optimal bundling strategy.

59Changing to either kind of dynamic pricing will generally change the total quantity that the firm sellsand often change the seller’s profits. I ignore the profit issue here because utility regulators can adjust ratesto ensure that the utility earns its rate of return despite the change in quantity and because any welfareimproving change in pricing creates a potential Pareto improvement that can increase firm profits.

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Intuition: Uniform pricing marks up products during low cost periods to cover othertimes’ higher costs. We can set opportunity costs that better reflect production cost duringeach period. Divert the markups the customer pays to buy credits that he can either eitheruse to buy the product during high cost periods or keep as a rebate. These markups canpreserve the nominal prices during low cost seasons and they sell customers rights to aquantity of the product at the usual nominal price during high cost seasons.

Proof: We can decompose the uniform price paid during low priced periods into the lowcost and the markup, then applies the total markup paid to buy an equal value of refundablerights to buy a fixed quantity of product at the uniform price during the high priced period.Specifically:

Consider a market with low and high cost sets of time periods with prices P̄L and P̄H

respectively. The high price can be decomposed into the low price plus a price increase,formally P̄H = P̄L + ∆P .

Let fH be the fraction of all consumption at uniform prices Pu that takes place duringhigh cost hours. Then, setting a uniform price of Pu = P̄L + fH∆P will raise the sameamount of revenue as would selling the same amount of product during each time period,but charging P̄L and P̄H for it. LetMu = fH∆P be the markup that customers pay duringlow priced periods to offset the cost of the expensive product. Then customers who buy thepopulation average proportion of the product, fH , during high cost periods pay in exactlyas much in markups as they get back in reductions of the price of the high cost product.

We can move prices closer to costs by setting each customer’s peak period opportunitycosts to P̄H and converting each customer i’s payment of Qi

LMu into a bill credit of Rthat the customer gets regardless of his critical period use. An IP rebate style description

would present this as rights to buy qR =Qi

LMu

P̄H−P̄uunits at the uniform price of P̄u where

QiL is the customer’s consumption during low priced-periods. Offering a rebate P̄H − P̄u for

each unused unit makes the opportunity cost P̄H . This approach also implicitly lowers theopportunity cost of consuming off peak to PL because the customer gets back every cent theypay through the markup of Mu. This moves opportunity costs closer to true costs whilemaintaining nominal prices.

The high and low cost periods can be subdivided into any number of subsets so long asthe customer pays markups during low priced periods that equal the value of the rights thecustomer gets during high priced periods, or:∑

i∈L

MiuQ

iL =

∑h∈H

Rh

if L(H) represents the set of low (high) cost periods. It generalizes to a single high andsingle low price period (e.g. CPP with just low and critical price periods), cases with a fewperiods per subset (e.g. CPP with low, high, and critical periods), and to cases with a verylarge number of price periods per subset (e.g. real time pricing that charges the market priceevery hour).

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C.1 This two period generalization performs worse than three-period CPP-IPR

This two period generalization will not offer consistent rebates and is harder to explain tocustomers than the three-period CPP-IPR approach.

• Each customer gets rights as a function of their usage, causing fluctuations in rightslevels that may confuse customers.

• This approach leaves the nominal price during low-cost periods at Pu. It may bedifficult to explain that customers pay Pu = PL +Mu, but that the opportunity costis PL since the customer gets Mu back. Customers who do not understand that theopportunity cost has dropped to PL may consume as if the opportunity cost werePL +Mu.

• The two period implementation does not offer most customers consistent rebates.Customer-base wide revenue neutrality implies that, in the absence of demand elastic-ity, the average customer in the population would get rights to exactly as much poweras they use during high priced periods. Customers who use a greater than averageproportion of their energy during high priced periods will not get a rebate and will paythe high price on the margin. However, demand elasticity will increase the number ofcustomers getting rebates by increasing purchases bundled with rights and decreasingpurchases that use rights.

C.2 Benefits of offering credits selectively

CPP-IPR works well when it splits high cost periods into “high” priced periods withoutrights and “critical” periods with rights. Offering rights selectively is a generally applicablestrategy that frees up cash to offer more customers consistent rebates, to reduce nominaloffpeak prices, or to bundle rights with a fixed initial units per month.60

60I have made no assumptions about the proportion of unhedged hours in the unhedged high price bin –so it is not clear how much cash is available to fund consistent rebates for more customers or to move to adeclining block implementation.

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D Graphical Comparison of Rates’ Incentives

Figures 6 and 7 graphically compare their incentives to CPP and CPP-IPR.

E Percentage of Customers for Whom Consistent Of-

fers exist

Figure 8 plots constraints in the style of figure 2 with real data. SPP data suggest that97% of customers statewide have demand patterns that satisfy feasibility criterion 5 for theexample rate.

The rectangular region above the diagonal line is the single offer that provides consis-tent rebates to the largest number of customers. The rectangle encloses the largest set ofcustomers who get consistent rebates under a single-optimal offer. One size does not fit all.It is not surprising that a coastal apartment’s monthly usage bundled with M in rights perkWh is insufficient to provide a big desert house consistent rebates.

We can generalize this analysis to a family of CPP-IPR rates by rearranging feasibilityconstraint 5 as a relationship between characteristics of customers and characteristics ofrates, namely:

12MNc(Pc − Ph)

≥ q̄c

Qm(7)

The left (right) side of this equation describes rate (customer) characteristics. The leftside is the ratio of the rate’s ability to raise money to the cost of providing each kWh ofrights during each event. The right hand side is the ratio of the the number of rights requiredto offer the customer consistent rebates to the greatest number of bundled rights they couldconsistently purchase.

Figure 9 shows the cumulative distribution of the right hand side of the rearrangedcriterion, 7, q̄c

Qmto see the percentage of customers who could get consistent offers under the

IP rebates that could be added to a variety of CPP offers. Figure 9 suggests that IP rebateswork well with three-period rates. IP rebates struggle with a two-period rate proposed byPepco for Washington DC customers for the reasons outlined in section C.1. The figure alsoshows that mindlessly implementing this IP rebate approach struggles with Ameren’s fourperiod rate and is less than ideal for Gulf Power’s four period rate, because they both splitthe low priced period into a low priced rate and an intermediate, shoulder rate that is quiteclose (.9 cents in Gulf Power; 0.14 cents for Ameren) to the time invariant rate. Markups thatkeep the shoulder rate less expensive than the time invariant rate often generate no consistentoffers. Either imposing a larger markup (a four cent markup would keep prices lower 64% ofthe time under Ameren’s rate) or sacrificing some economic efficiency by reducing the priceduring the shoulder period (perhaps by adding more low priced hours to it) could addressthese problems.

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Figure 6: These diagrams compare the plans’ marginal incentives during critical events andpeak periods, including the peak periods that may set baselines for the critical events.

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Figure 7: These diagrams compare the plans’ pricing of rights to access low cost power duringevents.

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Figure 8: Most California’s SPP customers’ demand patterns are above the diagonal linedefined by feasibility criterion 5, so consistent offers exist for them. But the single offer thatprovides consistent rebates and rights purchases for the greatest number of customers doesnot perform particularly well, so we should consider more customized offers.

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Figure 9: Offer feasibility under a variety of rates: Rearranging criterion 5 to 12MNc(Pc−Ph)

≥q̄c

Qmlets us compute the percentage of California CPP customers for whom consistent offers

exist for real CPP-rates. This approximation assumes negligible demand elasticity. Table 4describes the rates pictured here.

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# crit. uniform peak off critical

Source of Rate rate hrs price price peak price 12(Pu−PL)Nc(Pc−Ph)

(State) pds. 5Nc Pu PL price PH Pc

Pepco (DC) 2 60 7.92 6.81 6.81 63.98 .019Ameren (MO) 4 32 7.64 7.5, 4.8 16.75 30.0 .020Gulf Power (FL) 4 87.6 8 7.1, 5.9 11.7 32.6 .029SPP Low Ratio(CA)

3 75 PU PU − 1.2 PU + 9.8 PU + 41.8 .030

Example, Table1

3 75 14.6 12 24 60 .058

SPP High Ratio(CA)

3 75 PU PU − 5.09 PU + 11.64 PU + 60.91 .083

Table 4: The table describes the CPP rates plotted in figure 9. They have 2-4 rate periods.Two-period rates have just normal and critical periods. The two period rate presented hereis designed to generate identical average bills to the time-invariant rate and its IP rebatemodification looks like the one proposed in section C and suffers the shortcomings of takingapproach to a two period rate that are described in section C.1. Three period rates haveoffpeak, peak, and critical rates. Four period rates further subdivide the offpeak period intoa low rate and a “shoulder” rate that contains hours during the transition between the peakand offpeak periods. The four-period rates struggle to fund rights because the shoulder rateis quite close to the uniform price. Adjusting the rate to expand the shoulder period andreduce its average price or changing the IP rebate markup structure would improve theirperformance. For example, basing a markup on Ameren’s lowest price of 4.8 cents per kWhwould yield prices that are lower during 64% rather than 90% of all hours, but would yielda 12(Pu−PL)

Nc(Pc−Ph)of .39 – which performs so well as to be off this chart. The SPP called 5 hour

events, so NC counts events assuming that they lasts 5 hours. I calculate the number of“5-hour events” that other rates call by dividing number of hours of events that they callby 5. This table reports the summer prices of seasonally varying rates. (Sources: Wilson(2006); Pepco; Voytas (2006); Ameren; Gulf Power; Pacific Gas & Electric (c); San DiegoGas & Electric)

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E.1 Predicting consistent offers using readily available informa-tion

Rate implementers need to be able to identify consistent offers but often lack customer-levelhot weekday afternoons power use data, which bound the level of rights customers need toget consistent rebates. Many utilities install “interval” meters that capture disaggregatedusage data only for dynamic pricing customers. Firms may want to use existing data tomake initial CPP-IPR offers. The analysis below shows that aggregate use, account type,and geographic data predict consistent offers well enough to support implementation.

In order to estimate the desirable offers using a conventional approach, we need to iden-tify an optimal offer from the set of consistent offers. Most customers’ use patterns meanthat criterion 4 defines a range of consistent offers between the smallest qR that providesconsistent rebates and the largest QB that the customer can buy each month. For the pur-poses of this analysis, I selected the consistent offer, (qR

∗,QB∗), that satisfies criterion 4 in

a way that is robust to the largest number of dollar deviations in total ability to buy rights,12Qm, and the needs for rights, Ncq̄c(Pc − Ph).61

This analysis proceeded in three steps:

i. I constructed an optimal offer qR,′04i∗ for each customer. It specified the set of of-

fers that would be consistent for that customer-year, typically the year October ’03-September ’04.62

ii. I ran the following OLS regression: qR,′04i∗ = α+β1∗useSummer02 +β2∗ClimateZone+

β3 ∗ apartment + ε where useSummer02 is the customer’s average kWh per day duringthree summer months the year before the experiment began, apartment is 1 if theaccount is in a multifamily building and zero if the account is a single family home,and ClimateZone is a set of dummies indicating whether the account is located in eachof four mutually exclusive climate zones. Fog-belt zone 1 largely near San Francisco(the omitted category) is the coolest. The zones get progressively hotter and culminatein desert zone 4. Table 5 shows that regressing the optimal offer calculated from a 12month period in 2003-04 (qR

∗,QB∗) on total summer usage in 2002 explains 76%

percent of the variation and that adding readily available variables about the climateand whether the account is at a single or multifamily building improves the fit toexplain 78% percent of the variation.63

61The optimal offer should minimize the likelihood that random variation would prevent the offer fromproviding consistent rebates or purchases. This requires knowing the within-customer standard deviations ofrights needs,q̄c, and of the ability to purchase rights, Qm. The SPP data only tracks 27 events over 15 months,so there are too few years and too little variation in exogenous factors like weather, economic conditions,appliance upgrades, and family configuration changes to calculate meaningful standard deviations.

62I focus on the last 12 months of the 15 month sample where possible because the experiment enrolledcustomers gradually, but ended abruptly, so looking at the initial 12 months would yield different date rangesfor different subjects. Using each customer’s first 12 months would make the results harder to understand,especially because usage is heavily weather driven.

63This approach sometimes performs worse than the optimal offer range for each group calculations inpart because the range optimization used data on each customer’s whole range of consistent offers ratherthan representing the range with a single point.

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iii. I used the results of that regression to predict a consistent offer, q̂i∗R,′04, for each cus-

tomer and determined whether it was consistent in the sense of satisfying criterion 4 forthe values of (Qm, q̄c) for that year. The full regression predicts consistent offers thatsatisfy criterion 4 for 80% of all customers for whom a consistent offer exists. Manyq̂i∗

R,′04 that were not consistent offers were close. Half were less than 2.4 kWh of rightsaway from the nearest consistent offer. That size of deviation customers would forcecustomers with too few rights to buy high-priced power costing no more than $1.44per event.

iv. I tested a model from one summer’s ability to predict appropriate offers for anothersummer. Most California scarcity events take place in the summer months of Julythrough September, and the SPP called 21 of its 27 events during those months. The15-month experiment contained the important part of 2 years. This allows us tomake some preliminary investigations of how well parameters developed from one yearpredict for a different year. I went out of sample to check whether q̂i∗

R,′04 calculatedfrom the year containing Summer 2004 (namely October 2003-September 2004) wasa consistent offer that satisfied criterion 4 using the customers’ consumption patterns(Qm,03, q̄c,03) for the year including Summer 2003, namely July 2003-June 2004. Theout of sample universe contained 61% of customers. These customers had to be in thesample for two summers, and had to have (Qm,03, q̄c,03) that was different from (Qm,04,q̄c,04). This implies that either or both their their highest event use that set q̄cor theirminimum consumption that set Qmhad to occur between July and September.64 Theout of sample prediction of q̂i∗

R,′04 was a consistent offer that satisfied criterion 4 using(Qm,03, q̄c,03) for 82% of the out of sample universe.

64The SPP CPP treatment started in July 2003 and ran through September 2004. California’s electricitydemand (and scarcity) peaks during the summer, so we observe two separate summers but not two separateyears. A significant proportion of Zone 1, fog-belt customers used more during the winter events than duringany summer events. These customers set their their rights needs, q̄c, during the winter and thus get droppedfrom the out-of-sample analysis which used summer 2004 data to predict summer 2003 needs.

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Table 5: Using an OLS regression to predict the optimal IP rebate offer in kWh per eventworks well. Standard Errors in parentheses.

usage only model usage, climate, account type modelavg. daily use .78*** .80***Summer 2002, kWh (.028) (.031)climate zone 2 .84

(.621)climate zone 3 -.45

(.668)climate zone 4 -2.95***

(.869)apartment -1.47**

(.466)intercept 2.62*** 2.91***

(.452) (.644)

N 482 482R2 0.764 0.781

E.2 Optimal offers to each of the 16 groups.

We can get from 16 to 9 categories without making any compromises by merging groupswith similar rights needs. Most often, these involve combining usage categories from thesame region or combining the same usage level in neighboring regions.65

E.3 Offers that are not consistent are typically fairly close to beingconsistent

Offers that are not consistent are generally pretty close to being consistent and exposecustomers to only a few dollars per year of either exposure to critical pricing or of reducedrebates. Specifically:

• The majority of the 9.3% of customers who did not get consistent rebates paid thehigh marginal price in just one month. The weighted median (mean) customer whodid not get consistent rebates paid for 4.67 (8.23) kWh at the full critical price, whichcost $2.80 ($4.94).

• The rate marked up more power in at least one month than customers bought for 3.9%of all customers. The mean amount of rights that these customers were supposed tobuy, but did not was a total of $3.65 per year.

• To put this in perspective, this sample of customers spent a weighted average of $898.71on power over the course of the year under the example CPP or CPP-IPR rates.

65Specifically, we can make offers from the following offer ranges to each of the following sets of categories{3VH, 4VH: offer 31.42-31.46 kWh of rights per event}, {3H, 4H, 1VH, 2VH: 25.83-26.00}, {1L, 2L, 1H:10.15 - 12.79 }, and {3VL, 4VL: 6.13-6.36}. The four other groups would get their own offers, as listed in 6.

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Table 6: Optimal group offers: the range of rights values that provides consistent offers tothe greatest number of customers. This reports the number of number of customers gettingconsistent offers as a percentage of the number of consumers whose demand patterns satisfyconsistent offer existence criterion 5.

proportion getting optimal range:climate zone, use type consistent offers optimal range: lower end upper end1 very low use .93 3.19 3.282 very low use .87 4.97 5.173 very low use .84 6.00 6.364 very low use .87 6.13 7.551 low use 1.00 7.61 14.212 low use 1.00 10.15 12.794 low use .81 14.30 15.133 low use .84 17.98 19.421 high use 1.00 9.65 18.042 high use 1.00 18.38 18.983 high use .85 24.15 26.004 high use .96 23.49 27.181 very high use 1.00 17.13 27.432 very high use 1.00 25.83 28.303 very high use .97 28.82 31.464 very high use .88 31.42 31.82

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Figure 10: Optimal Offers by Group: consistent offers for higher use customers and cus-tomers in hotter climates provide more rights.

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• Customers in hot climates 3 and 4 were roughly twice as likely to have too few rightsor to contribute too little as customers in more temperate climates 1 and 2.

E.4 Robustness of these offers to changes in weather, economicconditions, and customer characteristics

Good rights offers need to work not only for the summer and customer-base that they weredesigned for, but also for summers that have differing weather and economic conditions andfor an unexpected subset of the customers. A thorough exploration of these issues meritsa paper in its own right, but the results from some simple tests suggest that the offers arereasonably robust. One promising way to understand the robustness of the offers is to lookfor evidence about the engineering and social limits on power consumption. If a customerwould get consistent rebates despite running their air conditioner flat out and turning onanother major appliance like an oven or dryer, their offer is quite robust. And if the customeris either never home to activate the other major appliance or is paying enough attention tonot do so during a critical event, then their offer also seems to be robust.

• 72% of all customers would get consistent rebates even if every event matched theirhighest use event over the 15 month study. The other customers who got consistentrebates did so by averaging an extreme event with lower-use events over the course ofa month.

• 47% of all customers would get consistent rebates even if they equaled their maximumuse weekday afternoon over the 15 month study. These customers appear to haveengineering or social limits that are likely to prevent them from using more powerthan they have rights to.

• The median customer uses only 49.1% of their rights to get consistent rebates and gets adeclining block that marks up only 57.1% of the power that they use in their lowest usemonth. Similarly the 75th percentile customer has only 71.3% of their power markedup in their lowest use month and needs only 71.4% of their hedge to get consistentrebates. Most customers get significant cushions that make their IP rebate offers fairlyrobust to variations in conditions. Once we reach the 90th percentile, however, thecushions largely disappear and customers have 93.7% of their use marked up in theirlowest use month and need 99.0% of their hedges to get consistent rebates. It’s likelythat some of the marginal customers in the SPP experiment who needed the greatestrights levels joined the experiment to contribute to knopwledge and earn $175 but werenot responding to price signals and would not opt in CPP-IPR.

F Appendix: Notation

• Characteristics that vary by customer – like quantity consumed, Qi – appear in sansserif.

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• Rate characteritics like PL and miscellaneous entries appear in the math typeface.Rate characteristics reflect local system costs and this document generally takes themas given in designing an IP rebate system.

• Variables that IP rebate designers choose – most notably QB, R, and qR– appear inbold.

object source notationbasic objectsPrice exogenous Pquantity per month varies Qi

quantity per critical orbaseline-setting peakperiod

varies qi

time periods – sub-scripts and setsmonths exogenous mset of months exogenous Mcritical peak events –e.g. use during anevent

exogenous c, set is C

baseline setting pd exogenous b, Brate of interest exogenous r

CPPcountsnumber of criticalevents, per year

exogenous rate design Nc

number of criticalevents, this month

exogenous rate design Nm

number of days inbaseline setting period

exogenous Nb

rate period sub-scriptsoffpeak - low exogenous rate design Lpeak - high exogenous rate design Hcritical exogenous rate design ctime invariant,uniform

exogenous rate design u

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what? source notationIPR featuresvalue of rights / credit IPR Rnumber of kWh perevent protected byrights / credit

IPR qR

IPR rebate rate IPR PR

baseline-rebate rebaterate

baseline-rebate PB

declining blockmarkup

IPR/exogenous M

number of kWhmarked up by thedeclining block

IPR QB

bills Note that B abbrevi-ates baseline, not bill.

CPP Bill implication TCCPP

CPP-IPR Bill implication TCCPP−IPR

Customer Charac-teristicsminimum monthlyconsumption /ability to buy ahedge, shorthand forminm∈M{Qm}

customer level Qm

maximum con-sumption duringan event / hedgeneed, shorthand for

maxm∈M{∑

cinCMqc

Nm}

customer level q̄c

deficit / cumulativeundercontribution

customer level δm

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