Incentive contract menu with justification option as a solution to the additionality problem.
Abstract
Joint Implementation/Clean Developement Mechanism projects are accredited in the context of Kyoto Protocol if they provide abatement in excess of what would be achieved without them, that is, are additional. A general incentive contract menu is constructed for implementation of the additionality requirement in the context of asymmetric information (section 2). Residential heating renovation is considered as an application of the proposed theoretical framework (section 3). The current procedures employ self-audit of the project developers to implement additionality, instead of incentive contracting. The option of self-audit (“justification”) is included in the model, which is shown to lead to a situation of mixed equilibria, which is unstable and thus not very desirable as a policy choice (section 4).
1. Motivation: the story of additionality in the context of incentive compatibility.
One of the main issues in the area of flexibility mechanisms under the Kyoto protocol is the additionality requirement. The requirement applies to Clean Development Mechanism (CDM) and Joint Implementation (JI), as well as to the pilot phase projects thereof, Activities Implemented Jointly (AIJ). All these mechanisms imply a firm or government of one country investing in abatement in another country and earning credits towards Kyoto quota on green house gas emissions of their country. The requirement consists in the stipulation that only those abatement units are to be accredited by the international accreditor and thus count towards the respective national quotas that would not be obtained without the flexibility mechanism. In the language developed by the JI/CDM community, the additional abatement is abatement associated with barriers towards its achievement, in particular, the given abatement project shall not be commercially viable (hence “financial additionality” in the World Bank’s terminology). Cost, discount rate, or market demand characteristics make a project commercially non-profitable. There can be further barriers, such as credit unavailability, regulation, or market failures that can potentially make a theoretically profitable abatement project unimplementable and thus additional.
For the purposes of this research, each abatement project is taken to be a source of two types of profit: market profit, accruing due to improved efficiency of the production of the marketable goods, and the profit in the form of abatement credits. There are generically three players in a JI/CDM setting. These are:
Ø Accreditor, or the international agency checking the reports on JI/CDM projects and determining which projects are additional and which are not;
Ø Host enterprise, which often can be assumed not interested in abatement, but this depends on a particular redistribution of credits and market profit between;
Ø Donor enterprise, which is primarily interested in getting abatement credits, but potentially can also have a share of market profits, ensuing from the project implementation.
As long as the interaction and distribution of profits between host and donor are immaterial, the last two players will be called “project developers”.
Define “additionality parameter” as some parameter whose value determines whether the project is additional or not: if an additionality parameter is higher (or lower) than certain value then the project is additional, otherwise not. Additionality parameter can be a common knowledge, or have some expectation value which is common knowledge. In many cases, however, additionality parameter can be known to project developers only, or to the host only, but not to the accrediting agency. Such an additionality parameter will be called “private additionality parameter”, or PAP.
In general, abatement is additional if it is unprofitable. In addition various other barriers can be considered that make a potentially profitable project unimplementable, as long as a flexibility mechanism is not working. This means that such parameters as cost per unit abatement, discount rate on the capital market, and demand for products whose production technology is to be changed, are additionality parameters. It is also possible to consider them as private additionality parameters whenever information on them is available to the project developers and not to (or to lesser extent) the accreditor. In this paper, the simplifying assumption is that abatement cost is considered as the only additionality parameter. Abatement cost is definitely a promising candidate for a private additionality parameter, for one normally needs a lot of local knowledge to figure it out. Also, cost information is often necessary for estimation of other additionality parameters.[1]
The purpose of this paper is to outline an incentive mechanism, optimizing implementation of additionality from the point of view of the accreditor. The Benchmark case, where relationship between the donor and the host are immaterial is based on the classical model of trade-off between informational rent to the low cost type and “undereffort” (or undersupply) of the high cost type (Laffont, Tirole, 1993, Chapter 1). The difference is that here, the principal faces adverse selection rather than moral hazard effects. Next, hierarchical extension is considered and it is proved that abatement credit sharing arrangements between the donor and host are immaterial for the optimality of a contract menu. The most essential assumption in the construction of an incentive contract menu for an abatement project is that the additionality parameter is linked to the size of the project. It is assumed, in the first place, that project developers choose the size of the project, or, in other words, the eventual amount of abatement. Next, it is assumed that a private additonality parameter of the project depends on project size. For example, cost per unit abatement increases with the size of the project, which leads to a fall in marginal market profit from the project. Finally, it is assumed that the level of abatement is observable, in difference from the private additional parameter.
2. Model: Benchmark case.
It is assumed that there is a single piece of asymmetric information, which is a private additionality parameter and is called “marginal cost of abatement”.
Players: accreditor A, project developers PD, that is to say, donor D and host H.
q is the amount of abatement.
PD can be of two types, depending on the marginal cost of abatement for their project: low cost type and high cost type. Marginal cost is assumed twice differentiable.
Marginal cost of the low cost type C1
Marginal cost of the high cost type C2
dCi/dq>0, i=1,2
C1<C2 everywhere except 0, where C1=C2=0
Accreditor believes that it faces low cost type with probability l.
Each project generates market revenue from sale of the product and abatement credits having monetary value r. Thus, an accredited abatement unit brings the total profit of p=p+r. Abatement decreases cost of production (alternatively: increases quality of product, etc) which results in increase of profit from market operation. It is assumed that one unit of abatement increases the profit by p. Then, equating marginal cost and p and p, one can define the following cut-off values of q.
C1(q1)=p<C1(q*1)= p
C2(q2)=p<C2(q*2)= p
Q1 and Q2 are abatement levels of low and high cost type, respectively. These are the variables with respect to which utilities are maximized.
Uaccreditor/PD/donor/host denotes utility of the accreditor/project developers/donor/host, resp.
a and b are shares of the actual abatement which are accredited to, respectively, high and low cost reported type. In other words, if PD abate x units then they receive either ax or bx depending on their reported type. Thus, a and b are respectively, effective tax and subsidy on the project developers.[2]
Uaccreditor= l (Q2 – q2)+(1-l )(Q1 – q1 - R)
where R designates the informational rent that is paid to the low cost type. It is measured in extra abatement units, which makes b>1 whenever incentive compatibility constraint binds.
The notation and relations between parameters can be made better understandable with help of Graph 1.
Graph 1.
r
The game proceeds as follows: A offers a menu of contracts (possibly a single contract) which consists of pair (a,b). If A were able to observe the type, the first best would obtain: .
a=b=1
in case of high cost type Q2= q*2
in case of low cost type Q1= q*1
As long as the types are unobservable, the accreditor may face a binding incentive compatibility constraint in the sense that the low cost type may want to report itself as a high cost type. Potentially losing some of the “efficiency gains” or “market profit”, it may provide low abatement in order to get its non-additional units to be accredited.
This leads us to a second best, which is now to be stated formally. Now we make a not-so-crucial and yet highly convenient assumption: q*1 will be the technologically possible maximal abatement.[3]
The second best solution is based on assuming a binding incentive compatibility constraint for the low cost type. Below, the separating equilibrium is shown.
Accreditor’s utility is a function of four variables:
Uaccreditor= l (Q2 (a) – q2)+(1-l )(Q1 (a,b) – q2 – R(a,b))
a,b (control variables), Q2, Q1(state variables, or control variables of the project developers). The state and control variables (the distinction is rather unimportant) are related in the following way:
Incentive compatibility constraint of the low cost type fixed b as a function of Q2:
Suppose that IC satisfied for the low cost type. Then, if IC binds then b>1.
Further relations (following from profit maximization by the project developers of both types) are:
a(p+p)=C2(Q2) (which gives a as a function of Q2). In particular, because the high cost type never misreports, a£1
b(p+p)=C1(Q1) which means that under truthful reporting Q1= q*1
Only one variable remains in the maximization problem of the accreditor under the assumption that the incentive compatibility constraint for the low cost type binds.
The solution can be rewritten as follows:
FOC: R/Q2=(1-l)/l
SOC: 2R/Q22>0
This means that the optimal “rent”, or credits to the low cost type provided in excess of actual abatement increases with the probability of the high cost type. If l tends to 1, that is to say, only low cost type is present, Q2 is such that rent should be minimal. Intuitively, it pays off to disregard the utility obtained from realization of the high cost project. In this case, a single contract is offered, which is accepted by the low cost, but not high cost type. On the other hand, if the probability of the low cost type is very low (l close to 0), then the contract menu consists of a single contract accepted by both types. Utility to the accreditor in this case is simply
If IC does not bind, this means that the extra abatement credit and market profit accruing from reporting low cost and abating at the respective level make incentive contract menu unnecessary and the first best obtains.
3 Applications
Though the incentive contracts as applied to the additionality problems are widely regarded as impractical the actual feasibility studies at least on certain types of projects do provide the information required for meaningful application of the above ideas. Residential heating is the area for which is incentive contracting seems to be possible. A standard case can be outlined as follows. There are two possible baselines identified, depending on the chances of technological renovation of heating centers. Suppose that there are 100 boilers to be renovated according to the project plan. Renovation brings about a yearly decrease in emissions of some fixed and known size A. The technological lifetime of the project is 15 years. In other words, the maximal abatement credit is 15A. One baseline implies investment to be carried out in 10 years from now, with ensuing abatement of size the proposed project. The other baseline implies the same investment to be carried out in five years. The project, should it be implemented will be accredited according to either five or ten year “project crediting lifetime”, that is to say, the additional abatement is either 5A or 10A. At present, the decision as to which baseline (thus, lifetime) is to be used is made according to the chances of alternative investment plans as assessed by a feasibility study.
The source of asymmetric uncertainty is the NPV of the renovation project, which depends on both the technological cost of renovation and loan conditions. Incentive mechanisms can be created by conditioning accreditation on both the additionality parameter and size of the project. One can consider the size of the project of 100 boilers as possibly false report of “high cost” or low baseline type. In that case, suppose the project developers report crediting lifetime being 10 years (low baseline), with the total size of the project being 100 boilers. Upon receiving this report, the accreditor may find it appropriate to offer the following contract menu: either 100 boilers with crediting time of 10 years and crediting parameter a<1 or 200 boilers with crediting time of 5 years and crediting parameter b>1.
Swiss Thermal Energy Project (STEP) in Buzau and Pascani, Romania\ has been considered from this point of view. The following is a outline of the proposed incentive mechanism, which uses a somewhat stylized version of the mentioned project as data source.
The private additionality parameter, tied to cost considerations, is the business as usual rate of renovation of boilers, which varies due to uncertainty of possibility to obtain a sufficiently cheap loan. This will be called “baseline”. To a certain extent renovation of boilers is profitable, as it raises the welfare of citizens. Town councils (Regies, in Romania) can also benefit from bank loans, in particular EBRD loans. As feasibility study by Ernst Basler+Partners showed, at least up to 15% discount rate allows some renovation to be profitable (abatement per boiler per year Asmall). STEP proposed a higher than profitable level of renovation (abatement per boiler per year Ahigh. However, calculation of actual additional abatement achieved hinges on the assumption of the time when the profitable renovation would start. The reported size of the project is n boilers. There are two possibilities: it can start now or in ten years from now. Suppose that in absence of a JI project, the renovation would start now (the true type is low cost). Then, knowing the level of profit from small renovation (difference in NPV from small renovation and from keeping the status quo, which is in our case 2400 thousand dollars, or 2400/n per boiler, minus loan repayment), one can easily estimate the profit to the low cost type, based on the assumption that the low cost type misreports itself as high cost type. Namely, the actually non-additional abatement over the years from 0 to 10 would count as additional. Given that we know the market value of abatement credits (p), one can easily calculate the monetary value of the rent accruing from misreporting: 10pnAsmall. Total profit disregarding loan repayment from the first ten years will be 10(p-c)nAhigh +USD2,400,000where c is (constant) technological cost per boiler. Next, for the high baseline type (the business as usual abatement starts in the tenth year) there is a maximal profit it can get, which is equal to the maximal number of abatement units under “high baseline” assumption multiplied by monetary value of abatement credit. For the first (controversial) ten years, this will be 10(p-c)nAhigh where c is cost per boiler. The final element is variation of the size of the project. The low baseline type is assumed to benefit from extension of the project geographically, but in absence of incentive correction is deterred from such an extension by the incentive to imitate the high cost type. Maximal extension up to N boilers is therefore such that in absence of incentive correction, the profit forgone by keeping the project small is just exceeded by the profit from misreporting (rent): (N-n)(2,400,000/n+10p (Ahigh -Asmall ) )-REP=10pnAsmall.[4] REP is relevant loan repayment expenditures.