Incentivizing Energy Efficiency under Private Information: The Social Optimum.

• Author: Wirl, Franz

1. INTRODUCTION

   The objective of the paper is to scrutinize on theoretical grounds what energy efficiency programs can achieve given an energy efficiency gap, external costs of energy use, and private information of consumers about their willingness to pay for efficiency. Energy efficiency (in the following often only efficiency) has been a public policy objective for decades. At the beginning, regulatory and economic efficiency aspects were the raison d'etre, while the current justification is that energy use is inevitably associated with environmental harms. Increasing energy efficiency is not only seen as an important but also as a 'low cost - no regret' option to mitigate climate change. This claim is based on the so called efficiency gap, i.e., consumers bypass profitable energy efficient appliances, Gerarden, Newell and Stavins (2017). Based on this claim, conservation has a high priority in all C[O.sub.2] mitigation strategies, e.g., the European Union (EU) committed to a 20% reduction in energy consumption due to higher efficiencies until 2020 (European Commission, 2006, 2011) and the International Energy Agency (IEA 2014) considers energy efficiency an important source of energy.

   Almost all conservation incentives are linked to energy efficiency improvements and " hundreds of studies have evaluated energy efficiency policies" according to Gillingham, Keyes and Palmer (2017). Utilities were considered to play a special and helpful role because "energy markets do not operate properly... utilities can help to overcome these barriers and do so at low cost" quoted from Hirst (1992). This position is still upheld, e.g. in Bertoldi et al. (2013, p. 337) and some (e.g., Lovins, 1985) even claim that utilities can "make gigabucks with negawatts." However, the role of utilities as conservation angel is questionable, because "a butcher is asked to sell fish" (Ruff, 1986). Indeed, Cicchetti and Hogan (1989) show that such programs are only profitable if the regulated price were below the marginal cost, which is unlikely in today's liberalized electricity markets.

   Eliminating the efficiency gap should target consumers instead of intermediaries like utilities, which make their money from selling kWhs. Therefore, it is assumed that a benevolent government designs conservation initiatives for consumers, who are characterized by an efficiency gap and private information, and faces costs of public funds. Although an individual consumer's willingness to pay for efficiency is a 'known unknown' as no outsider can know my willingness to pay, for example, for a hybrid car, only very few papers account for private information, which is the focus of this paper. Lewis and Sappington (1992) and Chu and Sappington (2012, 2013) assume private information of a utility facing passive consumers (but Chu and Sappington (2013) account for the rebound), recently, Blonz (2018) on the misrepresentation of conservation by utilities (a similar point was already made in Wirl, 1995), while Wirl (1999a, 2016) allows for strategic consumer actions similar to the analysis below. In this paper, private information is linked to the claim that consumers apply too short payback times when evaluating the energy efficiency of an appliance, which accounts for one of the distortions. E.g., a consumer demands that an investment is paid back in two years if ten years were the appropriate payback time. The second potential distortion is that the external costs of fossil energy are not internalized. In the language of Allcott, Mullainathan and Taubinsky (2015), the efficiency gap is due to an internality and an externality. In order to isolate the conservation potential due to the payback gap, a second scenario is considered in which all external costs are internalized and the energy tax revenues are returned to consumers. This leads to a nonstandard mechanism design problem because it is necessary to account for aggregates. The technique (developed in an Appendix) is applicable to other areas like labor contracts that account not only for individual but also for team performance.

   The existence of an efficiency gap can justify public interventions even if private information is taken into account. This assumption is not only realistic, albeit by and large ignored in the conservation literature, but also important because it turns the design of incentives upside down. More precisely, the efficient types receive higher subsidies, although the efficiency gap is higher for the inefficient types. Due to this implicit free riding, actual conservation will be meagre relative to the proclaimed efficiency gap. The program induced conservation is further reduced if the government internalized the external costs. In this case, the efficient types do not conserve anything (given complete internalization, they chose already the first best) but must receive the highest subsidies. As a consequence, conservation initiatives are uneconomical for not too large payback gaps but even for large gaps if the costs of public funds are substantial or if consumers with large payback gaps are less likely.

2. FRAMEWORK

   Only market distortions and failures justify interventions like efficiency programs and standards that are both part of an EU Directive for 2020 (EED, 2012). The justifications are: First, economic agents choose energy inefficient appliances; Gerarden, Newell and Stavins (2017) survey the so called efficiency gap. Second, the external costs of fossil fuels are not, or at least not sufficiently, internalized, because "politicians are reluctant to impose taxes, standards or permits," Gillingham, Keyes, and Palmer (2017).

   2.1 Demand for Energy and Efficiency

   The following partial equilibrium framework of demand accounting for distortions is based on Wirl (1997, 1999a). The first distortion is that boundedly rational consumers apply too low payback times (defined below) when choosing the energy efficiency of an appliance. Too short payback times result from consumers using either too high discount rates and/or too short planning horizons. Empirical studies since Hausman (1979) claim that consumers use too high implicit discount rates when buying appliances. Secondly, consumers base their decisions on energy prices that do not incorporate all external costs. Although often labeled as a market failure, the lack of Pigouvian taxes is a failure of politics.

   The crucial assumption is that services matter and not kWhs. Service s is the product of the energy efficiency [eta] (expressed in terms of the amount of service s delivered per unit of energy, e.g., miles per gallon) and energy e:

   s = e[eta].

   Service benefit u(s) satisfies the standard assumptions: increasing, concave and the Inada conditions ensure s > 0.

   The consumers make two choices: First, they buy an equipment with efficiency [eta] at the price K([eta]), K' [greater than or equal to] 0 and K" > 0. Second, they choose their service level in each period by buying the necessary amount of energy e at the unit price p; the consumer price, p, may or may not include environmental taxes and the latter case provides the second reason for an efficiency gap.

   The analysis must start from the back. The ex post optimal choice of energy conditional on the ex ante chosen efficiency [eta] determines the flow of surplus (w) depending on efficiency and the price of energy,

   [mathematical expression not reproducible]. (1)

   In the first stage, a consumer chooses the energy efficiency that maximizes the net present value (NPV) of surplus w minus the investment expenditure,

   [mathematical expression not reproducible]. (2)

   The NPV factor (t),

   [mathematical expression not reproducible], (3)

   denotes the subjective payback time based on a consumer's subjective discount rate (r) and planning horizon (L) less or equal to the lifetime of the equipment; the upper bound [bar.t] is the socially correct payback time that is based on the social rate of discount ([rho] [less than or equal to] r) and the full (economic) lifetime of an equipment ([LAMBDA] [greater than or equal to] L). Therefore, [bar.t]--t is called the payback gap.

   Absent incentives (this scenario is identified by [subscript.sub.0]) consumers' efficiencies [[eta].sub.0](t) are based on the maximization in (2). The corresponding necessary (and sufficient) optimality condition is that the marginal benefit must be equal to the marginal annuity (based on t) for efficiency investment

   [mathematical expression not reproducible]. (4)

   Substituting (4) into (2) determines the NPV of a consumer's surplus,

   [U.sub.0](t):=tw([[eta].sub.0](t))-K([[eta].sub.0](t)). (5)

   Any voluntary program must guarantee each consumer at least the reservation price [U.sub.0](t), which is increasing due to the envelope theorem and, economically, because a larger t increases the net present value of benefit.

   2.2 Payback Time Versus Discounting

   Since the payback time t defined in (3) is a monotonically declining transformation of the subjective discount rate (holding L fixed), nothing changes at the conceptual level if the private information is linked to discounting: making distributional assumptions about r implies the distribution for t and vice versa. However, there are crucial advantages for the use of the payback time. First, t is measured in years, which is a more convenient measure than the rate of exponential discounting.

   Second, the payback time depends on two factors: discounting and planning horizon. Consider two examples that also demonstrate the private nature of this information: A Ph.D. student, who is characterized by a low subjective discount rate, e.g., 3%/a, expects to enter the job market in 3 years. Therefore, the student's payback time is t(L = 3,r = 0.03) = 2.87 if buying a new refrigerator to replace a broken one. Parents of small children have a long planning horizon (say the full lifetime of the refrigerator) but apply high discounting (say 30%) due to financial constraints, then...