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Green Electricity Markets as Mechanisms of Public-Goods Provision: Theory and Experimental Evidence

Environmental and Resource Economics volume 71, pages 45–71 (2018)Cite this article

Abstract

Utility-based green electricity programs provide market opportunities for consumers to reduce the carbon footprint of their electricity use. These programs deploy three types of public-goods contribution mechanisms: voluntary contribution, green tariff, and all-or-nothing green tariff (Kotchen and Moore, 2007). We extend the theoretical understanding of the all-or-nothing green tariff mechanism by showing that an assumption of warm-glow preferences is needed to explain widespread participation in programs deploying this mechanism. We conduct the first experimental test to compare the revenue generating capacity of a pure public good (based on the voluntary contribution mechanism) and an impure public good (based on the green tariff mechanism). In experimental play, the voluntary contribution mechanism raises 50% more revenue than the green tariff mechanism. With the all-or-nothing green tariff, experimental play and regression estimates show that a warm-glow preference positively affects participation, as predicted by the theory.

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Notes

  1. These markets complement state-based regulatory programs for reducing \(\hbox {CO}_{2}\) emissions from electricity generation. As of 2017, the federal government does not regulate \(\hbox {CO}_{2}\) emissions from power plants, although such regulations are being developed by the U.S. Environmental Protection Agency.

  2. The VCM conforms to the theoretical framework of a privately provided public good (Bergstrom et al. 1986). The GTM and A/NGTM apply the theory of a privately provided impure public good (Cornes and Sandler 1984, 1994). Kotchen (2006, 2009) extends these theoretical frameworks to analyze markets for green products and carbon offsets, for which green electricity programs are commonly used as a motivating example.

  3. Unlike Kotchen and Moore (2007) who developed a three-good framework, we construct a two-good model. Two-good models are particularly useful for testing empirical validity of the predictions through laboratory experiments.

  4. In the paper, we interchangeably use the words contributions, provision, and revenues. This reflects the context of public-goods theory along with the practical setting of raising revenue to finance green electricity capacity.

  5. Rose et al. (2002) used laboratory experiments to study a public-good provision point mechanism to analyze subjects’ participation in and willingness to contribute to a green electricity program.

  6. Studying the VCM in a laboratory experiment follows a tradition of experiments on contributions to a pure public good (e.g., Andreoni 1995a, b). Similar to our work on the GTM and A/NGTM, recent research uses laboratory experiments to study contributions to an impure public good (Munro and Valente 2009; Engelmann et al. 2011). However, using laboratory experiments to compare the pure and impure public good mechanisms is novel.

  7. Equations (2) and (3) can be derived by using the standard Lagrange Multiplier Method of utility maximization. The symmetric Nash equilibrium is characterized by \(\left( {y_i^*,g_i^*} \right) =\left( {y_j^*,g_j^*} \right) \,\forall \, i,j=1,\ldots ,n\) and \(i\ne j\). Existence of a Nash equilibrium is ensured by applying Brouwer’s Fixed Point Theorem on individual best response functions \(g_{i}^{*}\).

  8. There is a threshold level for the green tariff \(\left( {\pi _L } \right) \), below which an individual maximizes her utility by paying the green tariff on her entire consumption of the private good (corner solution). Put differently, when \(\pi <\pi _L \), the constraint \(\alpha _i \in \left[ {0,1} \right] \) binds at \(\alpha _i^+ =1\). As long as \(\pi <\pi _L \), total contributions \((g^{+}=nM/\left( {P_Y /\pi +1} \right) )\) continually rise with \(\pi \), however, they also stay lower than the same under the VCM or the GTM with an interior solution. If \(g^{*}\) represents the total contributions to green electricity at the symmetric Nash equilibrium under the VCM or the GTM with an interior solution, then the solution to \(\pi _L \) is given by \(g^{*}/g^{+}=1\), which implies \(g^{+}\left\{ {{\begin{array}{l} {<g^{*}{} \textit{ if }\pi <\pi _L } \\ {=g^{*}{} \textit{ if }\pi \ge \pi _L } \\ \end{array} }} \right. \).

  9. For an excellent discussion, see Andreoni (1989).

  10. Note that the marginal per capita return (MPCR) from the public good at the SNE under the VCM (or GTM with interior solutions) is given by: \(\textit{MPCR}=\hbox {C}\sqrt{\hbox {ng}_{\mathrm{i}}^{*} }=\sqrt{120\hbox {n}/\left( {\hbox {n}+1} \right) }\), (assuming \(\hbox {C}=\hbox {P}_{\mathrm{Y}} =1\) and \(\hbox {M}=120)\). Now if \(\hbox {n}=4,5,6\) or 7, then \(\hbox {MPCR}=9.80,10,10.14\) or 10.25. This formulation is in complete accord with treatment #3 (that states altering \(\hbox {n}\) also alters MPCR) on page 182 in Issac and Walker (1988). We thank an anonymous referee for bringing our attention to this insightful paper.

  11. The parameters used for Fig. 2 are: \(C=P_Y =\pi =1\) and \(M=120\). As in Example 3(i), the warm-glow component in the utility function is assumed to be \(0.5\sqrt{g_i }\). With these specifications, individual contributions under the VCM and GTM are given by: \(g_i^*=g_i^+ =\left[ {120\left( {0.5+\frac{1}{\sqrt{n}}} \right) ^{2}} \right] \Big /\left[ {1+\left( {0.5+\frac{1}{\sqrt{n}}} \right) ^{2}} \right] \).

  12. Economists have long entertained the idea of experimental scrutiny of mechanisms that predict equal revenue generation in theory, particularly in the context of auction theory. Experimental studies, for example, on the equivalence of the Dutch auction and the first-price sealed-bid auction (Cox et al. 1982; Lucking-Reily 1999), and on the English auction and the second-price sealed-bid auction (Kagel et al. 1987), developed a deeper insight into participants’ decision making. In view of this literature, and also due to the lack of appropriate revenue data from naturally occurring markets, we investigate the predictions of the pure and the impure public good provision mechanisms (VCM and GTM) using experimental techniques.

  13. In the context of the experiment, “participant” refers to a subject in the public-good games. In the theoretical models, in contrast, “participant” refers to an individual who makes a positive contribution to the public good.

  14. We deliberately choose M = 120 (and not 100). The choice of 100 is “focal” and can potentially lead a participant to a focal 50–50 allocation of her budget between \(y_i \) and \(g_i \). See Goeree and Holt (2005) for a similar approach.

  15. The instructions given to participants are available upon request from the corresponding author.

  16. Note that despite a finite repetition of the game, application of the backward induction principle will lead to the unique subgame perfect Nash equilibrium in each game which is identical to the unique Nash equilibrium in the one-shot game.

  17. We let the participants choose numbers with decimal digits under the VCM because a corresponding percentage choice with a whole number under the GTM may actually result in a contribution with decimal digits.

  18. In principle, cooperation among the participants can be one of the reasons (but certainly not the sole reason) behind greater than Nash equilibrium contributions in a public good game, as has been indicated in many studies, such as Andreoni (1995a, b). Indeed, if the participants in an experimental public good game have warm-glow preferences (which our results are indicative of), cooperation is likely to occur (Andreoni, QJE, 1995). While it is difficult to completely remove the possibility of cooperation in a public good game that is repeated for multiple rounds, an experimenter can potentially nullify the impact of cooperation by adopting strategies that may include (i) a stranger matching protocol, (ii) limiting the number of rounds of play, (iii) comparing the first round data across the treatments, which does not result from any cooperative behavior, and examining evidence of any treatment effect during that first round, and (iv) in our context, running a questionnaire on environmental issues and examining whether more environmentally conscious participants contribute more to the environmental public good. Finally, after all these checks, if there still exists a doubt about the impact of cooperation, an experimenter may put forward a counter argument. If cooperation were to impact the outcome, it would impact each experimental game on a symmetrical basis, provided the sample size for each game is large. Therefore, any difference in the outcome across the experimental games should be attributable to the built-in features of those games.

  19. The Altruism scale should not be confused with the concept of pure altruism discussed earlier. The Altruism scale reflects generosity of an individual in reference to social issues.

  20. As suggested by use of the tobit estimator, the OLS estimator might be inconsistent due to the bounds on contributions. Note, however, that the estimated marginal effects on the individual variables are quite similar in magnitude and significance across the three regressions. This suggests that any inconsistency is not severe.

  21. When the number of individuals increases under the A/NGTM, individuals characterized by pure altruism are expected to contribute zero, whereas individuals with warm-glow or egoistic preferences are expected to contribute a positive amount. In contrast, under the VCM/GTM, individuals characterized by pure altruism are expected to lower their contributions along a continuous curve due to a similar increase in the number of individuals (\(g_{i}^{*}\) or \(g_{i}^{+}\) is a continuous function of n). Therefore, the nature of preferences plays a more tangible role under the A/NGTM.

  22. Each of the experimental sessions discussed in Sect. 6 was comprised of four practice rounds, followed by 12 decision rounds. Since participant confusion is a common phenomenon in experimental public-goods games (see Ferraro and Vossler 2010), the practice rounds were meant to promote clarity in participants’ understanding of the process of game playing and payoff calculation in each round.

  23. \(f\left( n \right) \) is continuous in n because \(n\pi M\) and \(\left( {n-1} \right) \pi M\) can be conceived as \(M^{\prime }\) and \(M^{{\prime }{\prime }}\), which basically represent two rescaled levels of income.

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Author information

Authors and Affiliations

  1. Department of Economics, Portland State University, 1721 SW Broadway, Portland, OR, 97201, USA

    Arnab Mitra

  2. School of Natural Resources and Environment, University of Michigan, 440 Church Street, Ann Arbor, MI, 48109, USA

    Michael R. Moore

Authors
  1. Arnab Mitra
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  2. Michael R. Moore
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Correspondence to Arnab Mitra.

Additional information

The authors thank Jim Andreoni, Erin Krupka, Tom Lyon, Christian Vossler, and two anonymous referees for insightful suggestions. Dana Jackman and Emily Ceran provided excellent research assistance. Financial support from the Erb Institute for Global Sustainable Enterprise at the University of Michigan and from the Portland State University is gratefully acknowledged.

Appendices

Appendix

Proof of Propositions

Proposition 1

In the symmetric Nash equilibrium, \(\frac{dg_i^*}{dg_{-i}^*}=-1\).

Noting that \(g^{*}=g_i^*+g_{-i}^*\), Eq. (3) can be rewritten as

$$\begin{aligned} \frac{\partial U_i \left( {y_i^*,g_i^*+g_{-i}^*,C_i } \right) }{\partial y_i }=P_Y \frac{\partial U_i \left( {y_i^*,g_i^*+g_{-i}^*,C_i } \right) }{\partial g_i } \end{aligned}$$
(13)

Differentiating both sides of (13) w.r.t. to \(g_{-i}^*\) one obtains

$$\begin{aligned} U_{y_i y_i } \frac{dy_i^*}{dg_{-i}^*}+U_{gy_i } \left( {\frac{dg_i^*}{dg_{-i}^*}+1} \right) =P_Y \left[ {U_{g_i y_i } \frac{dy_i^*}{dg_{-i}^*}+U_{gg_i } \left( {\frac{dg_i^*}{dg_{-i}^*}+1} \right) } \right] , \end{aligned}$$

where \(U_{y_i y_i } =\partial ^{2}U_i /\partial y_i^2 \), \(U_{gy_i } =\partial ^{2}U_i /\partial g\partial y_i \), \(U_{g_i y_i } =\partial ^{2}U_i /\partial g_i \partial y_i \) and \(U_{gg_i } =\frac{\partial ^{2}U_i }{\partial g\partial g_i }\). Noting that \(y_i^*=\left( {M-g_i^*} \right) /P_Y \) and simplifying the above equation one obtains

$$\begin{aligned} \left( {-\frac{1}{P_Y }U_{y_i y_i } +U_{g_i y_i } } \right) \frac{dg_i^*}{dg_{-i}^*}+\left( {U_{gy_i } -P_Y U_{gg_i } } \right) \frac{dg_i^*}{dg_{-i}^*}=-\left( {U_{gy_i } -P_Y U_{gg_i } } \right) \end{aligned}$$
(14)

If we differentiate both sides of (13) w.r.t. to \(y_i \) and rearrange terms, we find

$$\begin{aligned} -\frac{1}{P_Y }U_{y_i y_i } +U_{g_i y_i } =0 \end{aligned}$$

Using the above information in (14) and rearranging terms one obtains

$$\begin{aligned} \frac{dg_i^*}{dg_{-i}^*}=-\frac{\left( {U_{gy_i } -P_Y U_{gg_i } } \right) }{\left( {U_{gy_i } -P_Y U_{gg_i } } \right) }=-1 \end{aligned}$$

Proposition 2

(also an illustration for subsection 2.3.1) Consider the FRDC as a function of n:

$$\begin{aligned} f\left( n \right) =V\left( {\frac{M}{\left( {P_Y +\pi } \right) },\frac{n\pi M}{(P_Y +\pi )}} \right) -V\left( {\frac{M}{P_Y },\frac{\left( {n-1} \right) \pi M}{(P_Y +\pi )}} \right) \end{aligned}$$

Since indirect utility functions are continuous in M, \(f\left( n \right) \) is continuous.Footnote 23 Now it must be that

$$\begin{aligned} f\left( 1 \right) =V\left( {\frac{M}{\left( {P_Y +\pi } \right) },\frac{\pi M}{(P_Y +\pi )}} \right) -V\left( {\frac{M}{P_Y },0} \right) >0, \end{aligned}$$

because there must be at least one participant in the A/NGTM program. Now consider the limit:

$$\begin{aligned} \mathop {\lim }\limits _{n\rightarrow \infty } f\left( n \right)= & {} \mathop {\hbox {lim}}\limits _{n\rightarrow \infty } \left[ {V\left( {\frac{M}{\left( {P_Y +\pi } \right) },\frac{n\pi M}{(P_Y +\pi )}} \right) -V\left( {\frac{M}{P_Y },\frac{\left( {n-1} \right) \pi M}{(P_Y +\pi )}} \right) } \right] \\= & {} V\left( {\frac{M}{\left( {P_Y +\pi } \right) },\infty } \right) -V\left( {\frac{M}{P_Y },\infty } \right) <0 \end{aligned}$$

Since \(f\left( n \right) \) is continuous and \(f\left( 1 \right) >0\) and \(f\left( \infty \right) <0\), by the intermediate value theorem, there must exist a critical value of \(n>1\), given by \(n_C \left( \pi \right) \), such that if \(n\ge n_C \left( \pi \right) \), \(f\left( n \right) <0\).

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Mitra, A., Moore, M.R. Green Electricity Markets as Mechanisms of Public-Goods Provision: Theory and Experimental Evidence. Environ Resource Econ 71, 45–71 (2018). https://doi.org/10.1007/s10640-017-0136-5

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Keywords

  • Impure public good
  • Laboratory experiment
  • Voluntary environmental program
  • Warm-glow altruism

JEL Classification

  • C92
  • D01
  • H41
  • Q42