Challenges in the Era of Globalization - iaabd

Proceedings of the 12th Annual Conference © 2011 IAABD
Basic Model
There are three risk-neutral players in the model: a firm that is eligible to host a carbon reduction project
(hereafter referred to as the `host'), an investor (or financier) and a third party (or the victim). The host
currently uses a technology and/or management practices that involve an inefficiently high rate of
emissions of carbon. However, by adopting an "offset system protocol" (e.g., energy conservation or
afforestation initiatives) at a sunk cost of K, emissions can be significantly reduced. The host must raise
all the requisite funds from the investor. The third party is assumed to suffer financial losses as a result of
the project's inherent risk.
There are three important periods t∈[1,2,3]. For simplicity, we assume no discounting. In period t=1, the
host gets the requisite financing and also negotiates a compensation package with the investor. In period
t=2, the host implements the carbon reduction strategy (at fixed cost K) that lowers carbon emissions
below some baseline level. Every unit reduction in the emissions of carbon below the baseline generates
an emissions reduction credit (ERC). We will denote by R the quantity of ERCs generated by the project
in period t=2. These ERCs are appropriated by the investor, who sells them at a unit price of $1 to the
third party in a perfectly competitive carbon market.
In period t=3, there is a chance that carbon will be released back into the atmosphere, rendering the
offsets spurious and causing a pro rata financial loss (or injury) to the third party. Formally, we assume
that a reversal occurs with probability p and causes an amount z∈Z⊆ℜ+ of carbon to be injected back into
the atmosphere. Since the price of the offsets is unity, z also represents the financial loss potentially
suffered by the third party in the event of a reversal. To capture more simply the combination of
managerial and nonnatural factors in the make up of carbon releases, we let z= z + ε − e , where e∈[0,∞)
is reversal-avoidance managerial effort that the host supplies and ε ~ N(0,σ 2 ). The density function of z is
denoted ϕ(z,e). Effort causes disutility C(e,ω), where ω is a cost parameter, a firm’s type, that is unknown
to the investor. Type can be interpreted as a productivity parameter that reduces cost, all else equal. To
keep the problem mathematically tractable, we shall assume that the disutility structure is multiplicatively
separable in that C(e,ω)=ωψ(e), where ψ′(e)>0 and ψ′′(e)>0.
While the host knows exactly the value of its cost parameter ω from the outset, the investor's knowledge
of ω is limited. The investor knows, however, that the cost parameter ω belongs to some closed connected
set Θ⊂ℜ₊. Without loss of generality we take Θ = [ ω,
ω ] . Following the Bayesian approach, we assume
that the investor has some subjective a priori probability on Θ, which is associated with a continuous
probability density function f(ω)≡dF(ω)/dω, where F(ω) is the distribution function of ω. Denote by ω
the most efficient type possible. As is standard in the incentive literature, we assume the following with
respect to F(ω):
Assumption 1. The distribution of types F(ω) satisfies the monotone hazard rate property:
∂ 1 − F(
ω)
∂ F(
ω)
≤ 0,
>
∂ω
f ( ω)
∂ω
f ( ω)
0.
We assume that to motivate the host to supply effort, the investor implements linear incentive scheme that
comprises only a reward structure. More specifically, the investor offers a transfer of the form
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