Environmental Policy under Imperfect Information: Incentives and Moral hazard A. Xepapadeas (1991)
Introduction Env.Policy Implementation can be achieved through di erent instruments (control agency). Any implementation system can be assessed according to a number of criteria: 1 Static E ciency 2 Maintain a predetermined set of env. standards when changes in exogenous parameters take place 3 Provide incentives to the adoption of new clean technologies 4 Satisfaction of distributional or ethical notions 5 Informational requirements for the use of the implementation system 6 Cost of monitoring whether potential polluters comply with the given system and cost of enforcing the system in the presence of violators
Environmental Policy under Imperfect Information: Incentives and Moral hazard A situation implies Moral Hazard when: Each discharger s net emissions or abatement e orts are not observable, while the outcome of all discharger s combined e orts is observed. Objective of the paper: Design instruments (CONTRACTS) for achieving environmental targets when there is limited information with respect to individual net emissions or abatement e orts.
Environmental Policy under Imperfect Information: Incentives and Moral hazard Terms of the contract: The dischargers as a group are subsidized for abating pollutants The amount of subsidy depends on: the deviations between the desired concentration levels and the measured levels at the receptor point. The smaller the desviations the greater the subsidy to be distributed When the desired standard is exceeded one or more dischargers are liable for a ne, while the rest receive subsidies Problems: Collective penalties might place nancial strain on the whole group of rms.
Model A Dynamic Optimal Allocation Model Consider an economy with i = 1,..., n producers Producer i produces output using labor and capital (only one good) Output production generates pollution Good can be consumed or accumulated as capital in output production or pollution abatement processes
Model A Dynamic Optimal Allocation Model Y i (t) = total output by producer i at time t c(t) = per capita consumption at t Ki P (t), K a i (t) = total capital employed in output production and pollution abatement respectively L p i (t), La i (t) = total labor L(t) = i (L p i (t) + La i (t)) Ii P (t), I a i (t) = gross investment P i (t) = total pollution A i (t) = total pollution abated E i (t) = P i (t) A i (t) = net emission of the pollutant W (t) = ambient concentration of the pollutant Q(t) = index of environmental quality at t N(t) = population in the economy at t d = exponential depreciation rate of the capital stock γ = exponential natural pollution decay rate h = exponential rate of population growth
Model Producers output: Y i (t) = f i [Ki P (t), L p i (t)] 8i (Concave twice di erentiable and time invariant) Producer i s net capital formation is. K P i = Ii P (t) K P i (t), Ki P (0) = K P0 i 8i. K a i = Ii a (t) K a i (t), K i a (0) = K a0 i 8i Lower bounds for gross investment undertaken by any producer 0 Ii P (t) I P i 8i 0 Ii a (t) I a i 8i
Model Total output is located among consumption and gross investment (Y i (t) I P i (t) I a i (t)) N(t)c(t) 0 Total labor force is a constant fraction of total population L(t) = αn(t) = αn(0)e ht Assuming Labor mobility among processes, αn(t) i (L p i (t) + La i (t)) 0 Producer i s output production generates pollution according to a strictly increasing convex and twice di erentiable function, P i (t) = P i [Y i (t)] 8i
Model Pollution can be abated according to an abatement function independent of the ambient concentration of the pollutant A i (t) = A i [K a i (t), La i (t)], 8i (A i has positive rst derivatives, is concave and twice di erentiable) Net emission at time t i E i (t) = i fp i [Y i (t)] A i [K a i (t), La i (t)]g Ambient concentration of the pollutant at each t W (t) = W (0)+ R t 0 [ i E i (τ) γw (τ)] dτ The ambient concentration should never exceed some exogenously predetermined level W W (t) 0 The economy s criterion function over a given time horizon, R t 0 e st N(t)U[c(t), Q(t)]dt
Solving Max Problem
Solution Optimal investment policy: If P j i (t) = µ(t), then bi j i (t) 2 [0,I j i ] 8i, j If P j i (t) > µ(t), then bi j i (t) =I j i 8i, j If P j i (t) < µ(t), then bi j i (t) = 0 8i, j Society s valuation of optimal abatement is SB(t) = λ(t) i ba i (t) Society s valuation of optimal net emissions is SC (t) = λ(t) i be i (t)
Limited Information and E cient Contracts when individual monitoring is not possible, the agency observes only W (t), which could be compared to the optimal path cw (t).deviations cannot be attributed to a speci c discharger. Solution: E cient Contracts E cient: It induces the dischargers to adopt optimal abatement policy in the absence of e ective monitoring. Total subsidy: b i (t) = SB(t) i TR = RSB The discharger s pro t: Π i (b i, A i ) = Π 0 i + b i C i (A i )
Condition for e cient contracts Condition for e cient contracts: A system of subsidies bb i, i=1,...,n is PO if there do not exist subsidies bi and abatement levels Ai such that: Π i (b i, A i ) Π i (bb i, ba i ) 8i Note that Ai 2 [0, ba i ) denote the cheating abatement and ba i = (ba 1,..., ba i 1, ba i+1,..., ba n )the vector of optimal abatement levels of i PO implies that Ω = Π i (b i, A i, ba i ) Π i (bb i, ba i, ba i ) < 0 8A i 2 [0, ba i ) and λ(t) W ( ba i, ba i ) A i = C ( ba i ) A i where W (ba i, ba i ) = cw
Condition for e cient contracts In the presence of deviations, a contract that does not involve nes but only subsidies is not e cient. Contract A: The discharger receives the full amount of subsidy if ambient concentration standards are met; if not, the subsidy is reduced according to the valuation of excess concentration of the pollutant. if W (t) = cw (t), then b i = bb i (t) = φ i RSB(t) where b A i φ i = i ba i if W (t) > cw (t), then b i = bi (t) = φ i [RSB(t) + Γ(t)] where Γ(t) = λ(t)(w (t) cw (t)) E ciency requires [C (ba i ) C (A i )] + φ i Γ(A i, ba i ) < 0 In words, the cost saving from cheating is lower than the subsidy losses However, if the opposite happens then the discharger will never follow the optimal policy
Condition for e cient contracts Contract B: The discharger receives the full amount of subsidy if ambient concentration standards are met; if not, the subsidy is reduced according to the valuation of excess concentration of the pollutant. if Γ(t) = 0, then b i = bb i (t) = φ i RSB(t) where φ i = i ba i if Γ(t) < 0, then b i = b i (t) = F i whit probability ξ i 2 (0, 1) bb i + φi 0[ φ bb m + F m + Γ(t)] whit probability 1 ξ i [RSB(t) + i Γ(t)] For Γ(t) < 0, i b i (t) = F m+ i bb i + i φ 0 i [ bb m + F m + Γ(t)] = RSB + Γ(t), i 6= m. The contract exhausts the available amount. b A i
Condition for e cient contracts Pareto Optimality requires Since Ω i is strictly decreasing function of F i, there should be a ne bf i 2 (0, + ) such that Ω i (bf i ) < 0. Therefore Contract B is e cient.
Discussion If the contract scheme is supplemented by sample monitoring of individual dischargers, then the ne could be lower. However, the e ciency of the contract does not depend on catching the violator As long as the ne are su cient to make expected pro ts under cheating lower than under optimal abatement, the contract is PO Therefore, the e ciency depends upon making suboptimal abatements levels unpro table.