Private provision of environmental public goods: Household participation in green-electricity programs: Comment

Arnab Mitra1,2 Department of Economics Portland State University

This comment refers to the study of Kotchen and Moore (2007, JEEM; 53, 1-16) on private participation mechanisms in green energy programs. The authors develop a framework for the voluntary contribution mechanism (VCM), the flexible green tariff mechanism (FGTM) and the all-or-nothing green tariff mechanism (A/NGTM) under symmetric Nash Equilibria, and empirically test some predictions using household data on participants and nonparticipants. I show that the presented theory of the A/NGTM should be modified and should ideally include a more restrictive constraint than what the paper discusses. A generalization of the restrictive constraint yields important insights, contrasting to what one would presume otherwise. As the number of participants increases, the green energy premium should continually decrease to generate a (small) positive provision under the symmetric equilibrium.

JEL Classification: H41; Q42

1

Email address: [email protected] The author thanks Michael Moore and Tom Lyon for numerous helpful discussions on the broader subject of green energy and for their comments on this note. Matthew Kotchen’s comments also helped improve this note. 2

Private provision of environmental public goods: Household participation in greenelectricity programs: Comment

In an insightful and well cited study, Kotchen and Moore (2007) (henceforth, KM07) discuss household level voluntary participation in green energy programs. In the first part of their study, a framework is developed for private participation under pure and impure public good provision mechanisms, which include the VCM (pure), the FGTM (impure) and the A/NGTM (impure). The framework generates three important theoretical results. The first two results (page 5) describe how the VCM and the FGTM compare, and the third result (page 6) describes the performance of the A/NGTM vis-à-vis the other two mechanisms. The theoretical results are illustrated with two related examples of a two-participant economy under symmetric Pure Strategy Nash Equilibrium (henceforth, SPSNE). The examples are cornerstones for the theory. The theory of the A/NGTM is entirely based on equation (7) (page 6). Unfortunately, this equation is slightly erroneous, as I establish below. As a consequence of this, (i) the associated result, (ii) Example 2 of the study and (iii) Figure 1, should be modified to improve our theoretical understanding of the mechanism. To motivate the idea, I begin with the example. The equilibrium level of provision in Example 2 is given as

(E2)

The authors derive the constraint

using a simplified version of equation (7),

which, suppressing other parameters for brevity, can be restated as

(7) Note that the strategy profile under the left and the right hand side of inequality (7) is symmetric because the framework in the paper invokes SPSNE. Corresponding to the positive provision in (E2), the ith individual’s provision and expenditure on (x & y) will respectively be

and With this setup, I focus on the error involved in (E2). The authors inadvertently ignore another criterion that must be satisfied in order for (E2) to be regarded as equilibrium. This criterion requires the ith individual’s indirect utility of switching to the strategy of not be greater than the same from the symmetric strategy profile of must be greater than or equal to

must which means

. This can be restated as

(*) The above inequality can be simplified to

(**) Since

a correct version of (E2) will involve the more

restrictive constraint.

(E2 corrected)

For a numerical example, consider m = 10 and π = 1 ≤ (2m – 1). According to (E2), this will result in 10 units of provision, whereas according to (E2 corrected), there will be no provision. In view of the constraint (**), Figure 1 of the paper is corrected and reproduced at the end.

A generalization of the framework to an ‘n-participant’ economy yields two crucial theoretical insights that deserve our attention. Without the first insight, we shall be at risk of an incorrect notion of the theory of the A/NGTM. (i) Consider the number of participants in the program to be n ≥ 2. If one were to generalize the example (E2) to include n participants using equation (7), one would obtain

This implies the ith individual’s indirect utility from the symmetric strategy profile of

must be greater than or equal to the same from the symmetric

strategy profile of

The above expression reduces to

It follows that

with an increase in the number of participants, the energy premium may rise in a concomitant manner leading to (a) a sustenance of positive provision and (b) an increase in the magnitude of provision, under the SPSNE. Unfortunately, this is an incorrect notion embedded in the theory presented in KM07. For a correct notion, consider the same setup and a modified version of (*). To prevent individual deviation from the symmetric strategy profile of

to the strategy of

it must be that

which simplifies to

(***) Note that (a) (***) reduces to (**) when n = 2 and (b) if n → ∞, π → 0. This implies that as the number of participants increases, the green energy premium should continuously decrease in

order to generate a positive provision under the SPSNE. This is directly opposite to the notion rooted in KM07. (ii) Assuming (under SPSNE) π → 0 when n → ∞, the limiting level of provision is given by

In the above expression k > 0 is a positive finite constant. It follows that if at all, the SPSNE can generate only a limited amount of revenue even if the number of participants increases under the A/NGTM3. In the light of the discussion above, the existing result on the A/NGTM (page 6, KM07) can be modified to: Only when the green energy premium is sufficiently low, the all-or-nothing GTM can generate a positive provision, which can either be higher or lower than the provision under the VCM or the flexible GTM. With an increase in the number of participants, the premium must continuously decline to support a positive provision under the SPSNE. I conclude with three observations. First, perhaps the potential reason for the error in KM07 is that the results on the VCM and the FGTM are outcomes of a standard utility maximization exercise involving derivatives, and by definition, such outcomes are automatic candidates for SPSNE. In contrast, the result on the A/NGTM is based on corner solutions, and therefore the incentive for individual deviation from the symmetric strategy profile of needs to be carefully considered, which the authors have missed. Second, from the specific theoretical standpoint discussed above, the A/NGTM will likely result in no provision.

3

In a work-in-progress, Mitra and Moore find that the feature of limited revenue generation under SPSNE also extends to the VCM and the FGTM.

However, the fact that some programs (such as the Traverse City Light & Power’s “Green Rate” program discussed in the paper) indeed result in actual provision alludes to alternative household preferences, which may include egoism, warm-glow attitude, environmentalism etc. Third, from an energy supplier’s perspective of revenue generation, perhaps the strategy of creating multiple participant strata and limiting the number of participants within each stratum has some merit. Reference M.J. Kotchen, M.R. Moore, Private provision of environmental public goods: Household participation in green-electricity programs, Journal of Environmental Economics and Management. 53 (2007) 1-16.

Figure 1 (Corrected): Aggregate Provision under Different Participation Mechanisms