Signaling versus endogenous certification with two quality levels

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Domestic Regulation under Asymmetric Information

Consider the scenario where the government in country i is uninformed on both the cost parameters of domestic firms and the demand parameters of other countries β−i = (β1, . . . , βi−1, βi+1, . . . , βn). We now look for a Bayesian-Nash equilibrium in which coun-tries non-cooperatively choose their own domestic regulation. Remind that such a regula-tion consists of a price pi at which permits are traded on the domestic market, a quantity of such permits (which of course is equal to the total emissions Ri = Ei), and a subsidy τi. Those instruments are chosen so as to maximize domestic welfare given the set of regulatory instruments chosen elsewhere.

Domestic Incentive-Feasibility

Firms are privately informed on their abatement cost parameter βi. Because of arbitrage on the market for permits, all firms have to trade permits at the same price and thus no screening is possible. A firm whose parameter is θ can thus pretend to have the worst efficiency parameter θ. Doing so, it produces and emits the same amount than this inefficient type, pockets the same subsidy but reduces its abatement effort by θ − θ. Adopting this strategy, this firm earns some information rent worth (θ − θ)pi. For future reference, we notice that, aggregating over the whole distribution of domestic firms, the total amount of information rent left to domestic producers in country i is worth Δpi.
A domestic regulation (pi, Ri, τi) must also ensure that all types of firms obtain more by running their business under those regulatory constraints than what they get in the BAU scenario. With our previous normalization, this reservation payoff is normalized at 0. This participation constraint is of course more stringent for the least efficient firms θ. This participation condition determines the level of subsidies that firms receive. Of course, firms with more efficient abatement technologies would be ready to participate rather than opting for the BAU scenario even with lower subsidies. Imposing participation for all possible values of the abatement costs thus requires: Ui(θ) = max riq − 1 (q − e + θ)2 − pi(e − Ri) + τi ≥ 0. (q,e) 2 Using the expressions of the volume of pollution permits and the domestic price given in (1.2), (1.3) and (1.5), this condition becomes: pi(D(βi + pi) − Δ) − 1 (1.6) 2pi2 + τi ≥ 0.

International Environmental Agreement: Information Shar-ing

Taking a normative perspective, we now examine the design of an international regula-tion. The goal of such hypothetical mechanism would be to make it possible for each country to internalize the impact of its own emissions on the rest of the world. Such an international regulation should be viewed as a proxy for the best outcome that any In-ternational Environmental Agreement between countries could reach given the existing informational constraints that prevail both within and across countries.
More precisely, an hypothetical central regulator supersedes domestic regulators in each country by recommending a collection of domestic regulatory mechanisms (pi, Ei, τi)i {1,…,n}.
For each country, such a regulation stipulates a price pi at which permits are traded on the local market for pollution permits, a number of permits Ei that are distributed equally among domestic firms, and as before a lump-sum subsidy τi which is paid by domestic consumers to those firms. The novel instrument available to foster worldwide cooperation and make each coun-try internalize the impact of its own emissions on others is a set of budget balance com-pensatory transfers from and towards each country. Those transfers stem for all kinds of financial compensations that a given country may receive for implementing the requested price for carbon. The possibility of incorporating monetary contributions into environ-mental treaties is, indeed, often made explicit. To illustrate, Article 11 of the Kyoto Con-vention allows for the possibility of transfers from developed to developing countries under the aegis of an International Green Fund. Compensatory payments may also be given a broader interpretation and be viewed as the benefits or costs that countries expe-rience when climate negotiations are linked to negotiations on other issues such as R&D technology transfers, sovereign debt, and trade agreements (Barrett, 2003).
We first envision a complete information scenario and assume that, although domes-tic firms in each country keep private knowledge of their abatement costs, the central regulator and all countries know the whole collection of demand shock parameters β = (β1, . . . , βn) that hit those countries. In other words, an international agreement makes it possible for all countries to credibly disclose information on what they know on local con-ditions. Although highly hypothetical, this scenario allows us to investigate the highest bound on welfare that such an agreement could achieve.
This informational structure has two consequences. First, any domestic regulation, even if suggested by this central regulator, is still bound to satisfy the domestic firms’ incentive constraints and the requirement for acceptance by both domestic consumers and domestic producers. Henceforth, a by-now familiar domestic incentive-feasibility constraint will apply in each country. This condition is similar to that which applies when only domestic regulations are possible. It is also different because the fall-back option is no longer the BAU scenario as before but instead what happens when each country is free to choose a regulation on its own without any constraint being imposed externally by an agreement. Second, the central regulator can now condition the domestic regulation in country i on demand shocks that affect emissions abroad to facilitate coordination if needed. Indeed, international coordination may certainly benefit from such information sharing. COMPENSATORY TRANSFERS. At the Bayesian-Nash equilibrium of domestic regulations, country i’s emissions were shown to be E(pn(βi), βi). This quantity takes into account the local negative externality suffered in country i, but ignores the negative externality exerted on other countries j = i. Those countries may want to pay country i so that it reduces its own emissions. To illustrate, if country i reduces its emissions to E(pi, βi) = D(βi + pi) − pi + θe instead of E(pn(βi), βi), country j’s welfare (for j = i) increases by n1 (E(pn(βi), βi) − E(pi, βi)). Country j is thus ready to pay i up to that amount so as to have i reduce its emissions. Overall, country i thus receives from all other countries j = i an aggregate contribution worth n − 1 (E(pn(β ), β ) − E(p ,β )). (1.13).


International Environmental Agreement: Asymmetric In-formation

We now consider a scenario in which countries participating to an agreement keep pri-vate information on their domestic demand. This two-tier information structure is thus the same as in the Bayesian-Nash scenario. Countries have now not only imperfect infor-mation on the abatement costs of their domestic producers but also on the demand shocks elsewhere in the world. Following the tradition of the mechanism design literature (Myerson, 1982), we thus envision any International Environmental Agreement as an incentive mechanism that elic-its private information held by countries. Borrowing an approach that was pioneered by Myerson and Satterthwaite (1981)’s analysis of bargaining problems, such incentive mech-anism should be viewed as a metaphor for the dynamic bargaining and communication process that takes place in the framework of international negotiations. While in Section 1.3, the sole role of the central regulator was to coordinate and enforce the cooperative regulation implementing different carbon prices and enforcing compensatory payments across countries, this regulator acts now also as a mediator communicating with privately informed countries and recommending which domestic carbon prices they should adopt. Again following Myerson and Satterthwaite (1981), we assume that the uninformed reg-ulator’s objective is to maximize ex ante efficiency, giving thus an equal weight to each country in his welfare criterion.
An allocation that arises at the equilibrium of any bargaining protocol must actually satisfy a set of constraints. First, and as in the analysis of Section 1.3, any mechanism must be accepted by both domestic consumers and producers. It means that such mech-anism is bound to respect a domestic incentive-feasibility condition that applies within each country. Whenever the mechanism is not ratified by country i, this country shifts to its dominant strategy and opt for the Bayesian-Nash domestic regulation.
Second, each country must now also be induced to reveal information on its own de-mand shock. Such information is necessary to assess the externality that its emissions will exert on the rest of the world and thus the magnitude of any compensation it should receive to reduce such emissions. INCENTIVE MECHANISMS. The central regulator still proposes a set of domestic regula-tions that stipulate the price for carbon in each country and the possible compensatory payments that this country receives from others. From the Revelation Principle (Myerson, 1982), there is thus no loss of generality in viewing such regulation as a set of direct revela- ˆ ˆ tion schemes {pi(β), zi(β)}i∈{1,…,n} with prices and compensatory payments in each coun- ˆ ˆ ˆ try i being a priori contingent on the whole vector of announcements β = (β1 , …, βn). In fact, and by the same reasoning as that made in Section 1.3, the separability of the global welfare function into a sum of functions that each only depends on domestic carbon prices and demand shocks implies that there is no loss of generality in looking at simpler mech-anisms where the carbon price in country i depends only on this country’s announcement βi, namely pi(β) ≡ p(βi). Yet, payments may be more general as we will see below.
In order to facilitate comparison with the analysis in the previous section, we will sometimes invoke the Taxation Principle (Rochet, 1985) and view a mechanism as a non-linear schedule that stipulates a compensation payment Zi(pi) as a function of the carbon price pi chosen by country i. The benefit of this approach is that it captures the idea that the choice of those prices can actually be delegated to the level of countries where the relevant information on domestic shocks is known. Expressing expected payments in terms of the underlying contribution, the following identity should hold Zi(pi(βi)) = Eβ−i (zi(βi, β−i)). (1.20).

Signaling versus exogenous costly disclosure

We first consider a similar setting as Daughety and Reinganum (2008a). A monopolist si-multaneously chooses between two options: either paying for a certification or signaling its quality level with price. The certification consists in a fee K(θ) and reveals the exact quality level to consumers. Of importance, I assume that this fee reflects the verification cost incurred by the third-party performing the certification. We consider several struc-ture of fee, reflecting different types of verification cost, and study how this affects the monopolist’s choice.
With the certification, the monopolist gets the full information profit minus the fee: πm(θ) − K(θ) = (pm(θ) − θ) (1 − F (pm(θ) − v(θ))) − K(θ), ∀θ ∈ θ, . (2.7).
Using the envelop theorem, (2.1), and noting ˙ ( ) the derivative of the certification fee, K θ the derivative of (2.7) with respect to quality level writes: (θ) − K(θ) = (1 − F (p (θ) − v(θ))) ( v˙(θ) − 1) − K(θ). π˙ m ˙ m ˙ (2.8).

Table of contents :

1 The Law of One Carbon Price 
1.1 The Model and some Relevant Benchmarks
1.2 Domestic Regulation under Asymmetric Information
1.2.1 Domestic Incentive-Feasibility
1.2.2 Equilibrium Characterization
1.3 International Environmental Agreement: Information Sharing
1.3.1 Domestic Incentive-Feasibility
1.3.2 Optimal International Environmental Agreement
1.4 International Environmental Agreement: Asymmetric Information
1.4.1 Domestic Incentive-Feasibility under Asymmetric Information .
1.4.2 International Incentive-Feasibility under Asymmetric Information .
1.5 Conclusion
1.6 Appendix
2 Third-Party Certification and Price Signaling 
2.1 Model and Benchmarks
2.1.1 Full information equilibrium
2.1.2 Signaling equilibrium
2.2 Signaling versus exogenous costly disclosure
2.3 Signaling versus endogenous certification with two quality levels
2.3.1 Set of incentive-feasible contracts
2.3.2 Existence of an incentive-feasible contract and audit costs
2.3.3 For-profit certifier
2.3.4 Industry certifier
2.4 Extension: certifier as a standard setter
2.5 Conclusion
2.6 Appendix
3 The Two Middlemen 
3.1 Model and benchmarks.
3.1.1 Full information equilibrium.
3.1.2 Separating signaling equilibrium.
3.1.3 Exogenous disclosure.
3.2 Endogenous disclosure with one middleman
3.2.1 For-profit middleman
3.2.2 Industry middleman
3.3 Endogenous disclosure with two middlemen
3.3.1 For-profit label owner
3.3.2 Industry label owner
3.3.3 Potential extensions with a monopoly
3.4 Extension Duopoly.
3.4.1 Exogenous disclosure
3.4.2 Separating signaling equilibrium
3.4.3 Comparison of the realized profits in the two equilibrium
3.5 Conclusion
3.6 Appendix


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