Performance-Based voluntary group contracts for nonpoint source water pollution control

even if there exists a risk of free riders as long as the contract offers them economic gains compare with the default command and control regime. Peer pressure (PP) has two enforcement tools: 1) Future income loss, 2) Social sanctions. If an agent gets caught as shirking, he will have these two penalties from the group members by leaving him out of the group. These two kinds of punishments can play a very important role in the success of this kind of mechanism. However, which one is more effective depends on the size or effect of these punishments. In societies where the social ties are very strong, social sanctions can be very effective even if future income loss is not so high, or vice versa. One of the nice features of this mechanism is that the peer pressure does not have to be all monetary (future income loss) or nonpecuniary (social sanctions). Depending on the region, the mechanism can be arranged. In other words, it is very flexible. If a region is weak in terms of peer monitoring and social sanctions, this problem can be overcome if future income loss for the agents are high enough. *( )qγ is increasing in q, because the higher (lower) the bonus payment, the higher (lower) an agent’s incentive to monitor his peers since shirking any of them will decrease the group success and getting the bonus payment. Therefore, as the bonus payment increases the required peer monitoring increases, too. 99 Another way of interpretation is that if an agent chooses to exert high effort, there is a chance that all other agents can exert low effort (worst possible situation). In this case, his abatement cost will be high but his expected utility will go down dramatically as the level of fixed payment goes down and bonus payment (q) goes up that is because the probability of group’s success and getting that bonus payment is very low. On the other hand, if the agent chooses to exert low effort and the rest high effort (best possible situation), the agent’s abatement cost will be low and his expected utility will go down slower since everybody in the group except the agent himself exerts high effort, i.e., probability of group’s success and getting that bonus payment is very high. This may lead an agent to shirk. To deter the agent from shirking the group needs higher peer monitoring. *( )qγ is increasing in ( )H LC C− , because the higher the difference between the abatement cost when the agent exerts high effort and the abatement cost when the agent exerts low effort, the higher the required peer monitoring effort in order to prevent the moral hazard. High abatement costs give disincentive to the agents to exert high effort. That is why, agents with high abatement costs will have more tendency to shirk. In order to stop/ease that, more peer-monitoring is needed. *( )qγ is increasing in 1 1 1 1 )(Pr Prn nL H H LA A− −− , because the higher the difference in probabilities, the higher the agent’s incentive to shirk since exerting low effort will provide higher expected payoff, and, therefore, the higher the required peer monitoring effort to prevent this. These probabilities are affected both by the agents’ actions and weather uncertainty. As the number of shirkers in the group increases the probability of 100 group success decreases dramatically. Also, the group size (n) is also important in probabilities. I assume that as n increases the effect of each agent on total outcome is decreases. For example, think about a group of two vs. a group of ten. When one agent in these groups shirks, in a group of two agents, one agent’s weight on total outcome is very high, compare to a group of ten agents. If one agent shirks, it is very difficult for the other agent to compensate his peer’s portion by producing more abatement himself. So in this case, the probability of success as a group is very low. However, if there are ten agents in the group, shirking of only one agent can be easily compensated by the other high effort agents. That is, the probability of success as a group is much higher in this case. By the same notion, the probability of success is much lower when there is only one agent who exerts high effort in a group of ten agents compare to a group of two agents. That means the difference between 1 1Pr nL HA − and 1 1Pr n H L A − gets larger as group size gets bigger. Keeping this in mind and considering the equation (3.5), required peer monitoring is higher as the group size increases. Since as 1 1Pr nL HA − gets bigger, expected utility from shirking himself and working others increases, too. So agents will have more incentive to shirk in large groups. In order the agents to refrain that, more peer monitoring and peer pressure is needed. This is reasonable and intuitive. In group lending, it is preferable not to have large groups in order to control free riding problems (Armendariz de Aghion, 1999). In other words, as the bonus payment increases the agents’ payment depends more and more on their peers’ action. This will induce the peer monitoring. If peer monitoring is not big enough, the agents will have incentive to shirk. 101 Peer Monitoring and Payment Structure In order to explain and show the relationship between required peer monitoring and the level of fixed payment/bonus payment, let’s recall the agent’s expected utility functions when he choose to exert high effort and low effort, respectively. (3.6) max *[ Pr ] ( )i j i j t A H L H L H A A A EU F B C a = = + −∑ (3.7) max *[ Pr ] ( )j i j i t A L H L H L A A A EU F B C a PPγ = = + − −∑ Where (1 ) and b bF q pa B qpa= − = Now let’s suppose that the principal offers a contract with all fixed payment and no bonus payment (q=0). Then the agent’s expected utilities become: (3.8) ( )i jH L HEU F C a= − (3.9) ( )j iL H LEU F C a PPγ= − − In this case, the agent’s expected utilities from this contract are completely independent from his peers’ actions. Only thing he is concerned is the cost of his action, i.e. cost of abatement. Rationally he is going to choose low effort (shirk) to avoid high abatement costs if there is no or little peer monitoring and peer pressure. I assume that even though it is all fixed payment, the agents’ still have incentive to monitor their peers. This incentive can be induced by the principal punishing or threatening the whole group to lose any future payments from this contract plus any government subsidies they are 102 getting from the other programs if the group misses the target, such as two years in a row. This approach is parallel to the ones proposed by Segerson and Miceli (1998), and Alberini and Segerson (2002). They have shown that this kind of background threat (regulatory threat or the stick approach) can lead to more participation and efficiency gain under certain conditions in voluntary environmental agreements. In micro-finance group lending also the bank lends money to each borrower who is jointly liable at the beginning of the season, i.e. all fixed payment, and threatens them with losing future financing if they do not pay back. This induces the borrowers who are jointly liable with each others’ loan to monitor his peers and use social sanctions who strategically default. With all fixed payment, in order to induce an agent to exert high effort the required peer monitoring/peer pressure has to be: (3.10) ( ) ( ) ( ) ( ) i j j iH L L H H L H L EU EU F C a F C a PP PP C a C a γ γ ≥ ⇒ ⇒ − ≥ − − = − Now let’s change the situation where this time there is no fixed payment and all bonus payment (q=1). In this case, the agent’s expected utilities not only depends on his action but also depends on the actions of his peers and weather. If he exerts high effort he not only spends more on abatement costs but also he can lose the bonus payment if the group fails. This will make the agent more cautious about exerting high effort. In order to induce the agent to exert high effort the group needs to have larger penalty on shirking agent. So increasing bonus payment increases required peer pressure and peer 103 monitoring. Consider again the agent’s expected utilities in equations (3.6) and (3.7). When it is all bonus payment (q=1), expected utilities become: (3.11) max Pr ( )i j i j t A H L H L H A A A EU B C a = = −∑ (3.12) max Pr ( )j i j i t A L H L H L A A A EU B C a PPγ = = − −∑ In order for an agent to choose high effort, required peer monitoring/peer pressure has to be: (3.13) max max max ) Pr ( ) Pr ( ) (Pr Pr ( ) ( ) i j j i i j j i t t j i i j t H L L H A A H L L HH L A A A A A A A L H H L H L A A A A EU EU B C a B C a PP PP B C a C a γ γ = = =   − +   ≥ ⇒ − ≥ − − ⇒ ≥ − ∑ ∑ ∑ Comparing the above equation (3.13) with equation (3.10), it is clear that to satisfy the dominant strategy, i.e. even if everybody else shirks the agent is still better off if he exerts high effort, required peer monitoring and peer pressure in equation (3.13) is larger than in equation (3.10) since the probability of group success when the agent shirks and everybody else exerts high effort is much higher than the probability of group success when the agent exerts high effort and everybody else shirks max max 1 1 1 1Pr Prn n t t A A L H H L A A A A A A − − = =   >  ∑ ∑ . 104 Without Peer Monitoring Cost Let’s first assume that peer monitoring is endogenous but it does not have any cost on the agents. Under such an assumption, the agents will make the decision of peer monitoring. Since it is costless and monitoring his peers provides benefits to him by decreasing the shirking and increasing the probability of meeting target as a group, one can expect that everybody in the group would choose the highest possible monitoring level in this case. Let’s assume that peer monitoring is perfect ( 1γ = ), i.e. it is definite that if an agent shirks he will get caught by his peers. Now equation (3.4) becomes: (3.14) max 1 1 1 1 ) ( ) ( )(Pr Prn n t A L H H Lb L H A A A A qpa C a C a PP− − =   − ≤ − +  ∑ Rearranging equation (3.14): (3.15) ( ) max 1 1 1 1 ) ( ) ( )(Pr Prn n t A L H H Lb H L A A A A PP qpa C a C a− − =   ≥ − + −  ∑ Even though everybody in the group has 100% peer monitoring, is it still possible to have moral hazard in the group? The answer to this question is yes. Because if the group does not have enough penalties or punishment (peer pressure) for the shirking agents, an agent can still join the contract and shirk even if he knows that he will certainly get caught. If he knows that joining the contract one time and shirking, and staying out of it for the rest of the periods will make the agent better off than exerting high effort and staying in the group for all periods, he will obviously choose the former one. In order for an agent to stay in the group and exert high effort, required peer pressure is to have a penalty for shirking at least as big as the benefit of shirking (first term of 105 equation 3.15 on the right hand side) and additional cost of abatement stems from exerting high effort (second term of equation 3.15 on the right hand side). So peer pressure can provide coercion if and only if it is strong enough. This is again shows how peer monitoring and peer pressure works together. If one is very high but the other is very low and cannot make the agent choose the high effort, then this contract does not work. The important point is that combination of both has to be high enough to discourage agents to shirk. Group size effect and Peer monitoring cost Group size in group lending can involve up to as many as 15 borrowers. As for the nonpoint source pollution, group size can also go up to 15 easily in a watershed. Examining the effects of group size on both the agents and the principal’s payoffs can be helpful. In this section, I will attempt to analyze the issue of group size and the influences of peer monitoring costs on both the agents and the principal’s decision making. I assume mutual monitoring structure, whereby each agent monitors all his peers. Let’s first examine an agent’s decision whether to exert high effort or low. Recall equation (3.4) that agent k will choose high effort if and only if: (3.4) max 1 1 1 1 ) ( ) ( )(Pr Prn n t A L H H Lb L H A A A A qpa C a C a PPγ− − =   − ≤ − +  ∑ Following the model of Armendariz de Aghion (1999), where 1 2 1 11 (1 )(1 )...(1 )(1 )...(1 )k k nγ α α α α α− += − − − − − − is the probability of the agent k being monitored by at least one of his peers. 1α denotes the probability that agent 1 monitors 106 agent k; 2α the probability that agent 2 monitors agent k; 3α the probability that agent 3 monitors agent k; and so on8. (1 )iα− is the probability of the agent k not being monitored by the agent ‘i’. Now let’s turn our attention to find out the optimal monitoring effort of each agent. Given ( )qγ is the probability of peer monitoring spent by all the other agents on the agent k, each agent has to decide the effort level of peer monitoring to spend on the agent k. For example, given the monitoring effort of other agents on agent k, the minimum required monitoring effort that must be spent by the agent 1 on agent k in order to deter the agent k shirking must be such that: 1 2 1 1( ) 1 (1 )(1 )...(1 )(1 )...(1 )k k nqγ α α α α α− += − − − − − − , that is: (3.16) 1 2 1 1 1 2( ) 1 ( )1 (1 )...(1 )(1 )...(1 ) 1 ( )1 (1 ) k k n n i i k q q γ α α α α α γ α α − + = ≠ − = − − − − − − = − −∏ Assuming identical agents and symmetric monitoring ( 1 2 3 ....... nα α α α= = = = ), optimal monitoring for each agent can be written as follows: (3.17) 1 2 1 1 * 1 * 1 ( ) 1 (1 )(1 )...(1 )(1 )...(1 ) (1 ) 1 ( ) 1 1 ( ) k k n n n q q q γ α α α α α α γ α γ − + − − = − − − − − − − = − = − − 8 Armendariz de Aghion (1999) has considered the three agent case, and I have extended his approach to ‘n’ agent case. 107 Now let’s examine an agent’s monitoring decision, given the fact that all the agents are being mutually monitored. Assume that cost of monitoring is linear and equal to wα , where w is the marginal cost of monitoring. As the peer monitoring effort (α ) increases one unit, the cost of monitoring increases by w unit. An agent will choose the optimal monitoring effort *( )qα if and only if the following condition is met. Otherwise he will simply choose not to monitor at all (α =0). (3.18) max max * 1 1 *( ) ( ) ( )Pr Pri j i j t t A A H L H LH H A A A A A A F B C a w q F B C aα+ − = = + − − ≥ + −∑ ∑ Let * 1 1Pr i jH LA + − be the probability of group success when the agent decides to monitor, and Pr i jH LA be the probability of group success when the agent decides not to monitor. Left hand side of equation (3.18) is the agent’s expected utility when he exerts high effort for his abatement and decides to monitor his peer. As usual, he is going to get the fixed payment (F) no matter what. He is going to get bonus payment (B) if the group is successful. In this case, since he is going to monitor his peer, his peer is not going to shirk and this will increase the number of agents who exert high effort (Hi+1) and decrease the number of agents who exert low effort (Li-1). As the number of agents who exert high effort increases the probability of group success will increase too. However, monitoring his peer is costly for the agent ( wα ). 108 Right hand side of equation (3.18) is the agent’s expected utility when he exerts high effort for his abatement but decides not to monitor his peer. In this case, he is not going to have any cost of monitoring but his probability of getting the bonus payment will be lower, since his peer is going to shirk. The agent will choose to monitor if the payoff from exerting high effort and monitoring is more than exerting high effort but not monitoring. That is, if the increase in probability of group success and payoff are more than the cost of monitoring, then the agent will choose the monitoring level with probability *( )qα . Namely, rewriting equation (3.18), agent 1’s decision to monitor agent k will depend on whether: (3.19) max * 1 1 *) ( )(Pr Pri j i j t A H L H L A A A A B w qα+ − = − ≥∑ This inequality simply says that the benefit of monitoring (left hand side) has to be greater than or equal to the cost of monitoring (right hand side). To show this more clearly, let’s differentiate equation (3.19) with respect to α . Again I assume that probability of success (PrHL) is an increasing function of α , i.e. PrHL(α ). This means any increase in peer monitoring effort will increase the number of agents who exert high effort, and that will increase the probability of success. The optimal monitoring rule is where marginal cost of monitoring (w) equals to the marginal benefit from monitoring. Namely, first derivative of equation (3.19) with respect to α is: (3.20) max * 1 1 )(Pr Pri j i j t A H L H L A A A A B w α + − =  ∂ −   = ∂ ∑ 109 By the same token, given bB qpa= , plugging in *( )qα from equation (3.17) into equation (3.19), the maximum bonus payment (q) that the principal can offer is the one that satisfies the condition (3.19) with equality, namely: (3.21) ( ) max * 1 1 1) 1 1 ( )(Pr Pri j i j t A H L H Lb n A A A A qpa w qγ+ − − = − = − −∑ This equation simply says that the principal can increase the bonus payment and decrease the fixed payment up to the point where the agent’s cost of monitoring (right hand side) equals to the agent’s benefit from monitoring (left hand side). As the group size (n) increases, the cost of monitoring another agent becomes smaller (right hand side of equation (3.21), given that such a cost is shared among an increasingly large number of peers. On the other hand, as discussed under equation (3.5), as the size of the group becomes larger ( )qγ gets bigger, too. That means each agent becomes increasingly fearful about shirking of his peers. In order to eliminate free riding problem that rises with group size, required monitoring needs to be higher. This shows that having lower cost of monitoring in larger groups is mitigated by the need of higher monitoring effort. Having higher peer monitoring ( )qγ increase the cost of monitoring for an individual agent, i.e. right hand side of equation (3.21) goes up. 110 Principal’s Problem: Optimal level of bonus payment The principal is a point source polluter. Point source polluters have government emission regulations. So each point source has a maximum pollution limit. However, they can make trades between point sources or between point source and nonpoint sources. The basic idea behind this trade is to transfer abatement costs from higher to lower sources. This will lead to pareto improvement for each party. In this model, pollution trade is between point source and farmers as nonpoint source polluters. The principal’s objective is to save as much money as she can by letting the low cost farmers abate on his behalf. The principal will be better off since she will pay less than she could if she had to produce herself. Farmers will be better off as well since they will get more than their abatement costs. The lower the price of abatement is the better for the principal. The principal’s objective function can be written as: (3.22) max 0 0 1 0 ( * ) * ( )( )]Pr Pr [ t n n t A A H L H L t A T A T q AA A A mc B A mc mc p A A FMax − ==    − + − − − −   ∑ ∑ 1 1 1 1 Where: (1 ) (1 ) n n b b T k k k k n n b b T k k k k B B qpa nqpa F F q pa n q pa mc p = = = = = = = = = − = − ≥ ∑ ∑ ∑ ∑ Subject to: 1) Equation (3.17) in order to ensure that the agents will not shirk; 2) Equation (3.19) so as to induce peer monitoring with probability *( )qγ [a lower 111 monitoring effort would indeed result in the agents shirking]; and 3) 1q ≤ , that is portion of bonus payment from the total payment to an agent has to be less than or equal to one [ one refers to all bonus payment and no fixed payment]. Recall equation (3.5): (3.5) max 1 1 1 1 * ) ( ) ( ) ( ) (Pr Prn n t A L H H Lb H L A A A A qpa C a C a q PP γ − − =   − + −   = ∑ This is optimal level of peer monitoring spent on an agent by all the other agents in the group. Now recall equation (3.17): Optimal level of individual peer monitoring spent on another agent. (3.17) * 11 1 ( )n qα γ−= − − We can substitute equation (3.5) into equation (3.17), and we obtain: (3.23) max 1 1 1 1 * 1 ) ( ) ( ) 1 1 (Pr Prn n t A L H H Lb H L A A A A n qpa C a C a PP α − − = −    − + −     = − −      ∑ Equation (3.19) can be rewritten as follows: (3.24) max * 1 1 *) ( ) 0(Pr Pri j i j t A H L H Lb A A A A qpa w qα+ − = − − ≥∑ 112 Substituting Equation (3.23) into Equation (3.24), we obtain: (3.25) max 1 1 1 1 max * 1 1 1 ) ( ) ( ) ) 1 1 0 (Pr Pr (Pr Pr n n t i j i j t A L H H Lb H L A AA H L H L A Ab A A n A A qpa C a C a qpa w PP − − + − = − =      − + −      − − − − ≥          ∑ ∑ Maximizing the principal’s objective function subject to equation (3.25), and letting λ denote the corresponding Lagrangian equation can be written: (3.26) max 0 0 max 1 1 1 1 max * 1 1 1 0 1 ( * ) * ( )( )] ) ( ) ( ) ) 1 1 Pr Pr [ (Pr Pr (Pr Pr t n n t n n t i j i j t A A H L H L t A T A T AA A A L H H Lb H L A AA H L H L A Ab A A n A A L A mc B A mc mc p A A F qpa C a C a qpa w PP λ − − + − − == = − =    = − + − − − −         − + −     + − − − −         ∑ ∑ ∑ ∑          Now let’s differentiate equation (3.26) with respect to q: (3.27) max max * 1 10 max 1 1 1 1 1 [ ) 1) ] 0 ( 1) (1 ( )) Pr (Pr Pr (Pr Pr i j i jn t t n n t A A H L H LH Lb b b A A A A A A A A L H H Lb A A nnA A L npa npa pa q w pa PP n q λ γ + − − − = = − = ∂ = − + + − ∂      − − ≥     − −    ∑ ∑ ∑ Rearranging equation (3.27), we get: (3.28) max max * 1 10 max 1 1 1 1 1 1 1 [ ) 1) ] 0 ( 1) (1 ( )) Pr (Pr Pr (Pr Pr i j i jn t t n n t A A H L H LH Lb b A A A A A A A A L H H Lb A A nnA A q npa pa w pa PP n q λ γ + − − − = = − =   = ⇔ − + −        − − ≥     − −    ∑ ∑ ∑ (See Armendariz De Aghion, 1999 for the derivation of the formula for the joint responsibility component) 113 For w PP sufficiently small that, max max * 1 1 1 1 1 1 1 1) ) ( 1) (1 ( )) (Pr Pr (Pr Pri j i j n n t t A A H L H L L H H Lb b A A A A nnA A A A wpa pa PP n qγ + − − − − = =      − > −     − −    ∑ ∑ then q*=1. That means it is optimal for the principal to offer all bonus payment, no fixed payment, whenever w PP sufficiently small. That means, if the cost of monitoring (w) is low enough or peer pressure (PP) is high enough, the principal can set the q=1. Given the peer pressure, if the cost of monitoring gets lower each agent will have more incentive to monitor his peers. By setting the q=1, the principal can induce agents to higher peer monitoring level and get more benefit out of it. On the other hand, given the cost of monitoring if peer pressure gets higher, the agents will have less incentive to shirk. So as PP gets larger, the principal can increase the bonus payment and decrease the fixed payment to the agents. After some point q can be one. This shows that depending on the cost of monitoring and peer pressure, bonus payment can be full or partial. SUMMARY In this chapter, I have analyzed the endogenous peer monitoring in joint liability group contracts. Peer monitoring is costly and agents have to decide the monitoring level depending on the payment mechanism offered by the principal. First, I have derived the optimal peer monitoring level in equilibrium from the agent’s incentive compatibility constraint. That shows the peer monitoring and bonus payment (q) are positively correlated, i.e., as the agents’ payoff is more dependent on bonus payment and less on fixed payment, they will have more incentive to monitor the 114 peers. However, peer monitoring and peer pressure are negatively correlated, any increase in peer pressure makes the required monitoring lower. That means, even though peer monitoring is not perfect and there is a chance that an agent can shirk and get away with that, this contract can still work as long as the group has enough peer pressure to prevent that. By the same token, even if the peer monitoring is perfect an agent can still tend to shirk if peer pressure is very weak. High abatement costs induce agents to shirk because if they exert high effort and do not meet the target as a group it will cause him lower payoff. In order to induce high abatement cost agents to exert high effort, the group needs higher peer monitoring level. In addition, the agents who exert high effort and have high abatement costs will have more incentive to monitor their peers since their loss will be high in case where peers shirk and the group does not meet the target. In addition, it shows that as the group size increases the agents have more incentive to free-ride. However, I have shown that as the group size increases peer monitoring increases because more agents are committed to monitoring, and cost of monitoring per agent decreases since it is shared among larger number of peers. These two effects can counteract against free-riding and minimize it. Finally, I have examined the optimal bonus payment (q) for the principal. She prefers higher bonus payment and lower fixed payment in order to induce peer monitoring and high effort. She can set the bonus payment portion (q) equals one, full bonus payment (no fixed payment), only if w PP is sufficiently small. That is, if the cost of monitoring is low enough or peer pressure is high enough that each agent has enough 115 incentive to monitor or punish his peers, then the principal can simply set the bonus payment level to full (q=1). This shows that depending on the cost of monitoring and peer pressure, bonus payment can be full or partial. 116 CHAPTER 4 SUMMARY AND RESULTS SUMMARY In this study I have attempt to design a joint liability group contract for nonpoint source pollution (specifically runoff from agricultural land) that uses peer monitoring and peer pressure as enforcement tools within the group. Unlike current nonpoint source pollution control programs, this contract is based on the performance of the group. That means, the measure is directly to do with the contribution of the polluters to the surface water quality, not based on what technology or input they use. I believe that using this kind of approach will create flexibility for farmers to choose whatever technology or input to use. Since they have usually more knowledge and information about the environment they are living and each farmer has its own way of operation and environment, they are more likely to choose “the best technology” available for them, rather than some third party assigning what best works for them. In addition, having this flexibility and having performance-based payment mechanism will encourage innovation amongst farmers to find the best, the most efficient and the cheapest technology and input possible. This will lead to efficiency gain, and off course better surface water quality. This contract will be voluntary. Anybody who is willing to contribute the water quality and believes that he can make money out of this will join the contract. The performance-based contracts proposed by Segerson (1988) and Xepapadeas (1991) say 117 nothing about participation to the program they offer. Considering their contract mechanism, it is doubtful that those kinds of mechanisms can work under voluntary settings because of their payment mechanism (severe penalty and random penalty). The mechanism Pushkarskaya (2003) offered is also voluntary but the structures are different. She uses association type group forming and participation while I use individual participation and assume auction type bidding mechanism to select and form the group. This contract is joint liability group contract that uses subsidy only, nonbudget balancing type payment mechanism with enforcement tools of peer monitoring and peer pressure. It is very common in literature to use joint liability concept for this kind of group contracts and joint productions. Many economists have used this concept in their papers (Holmstrom, 1982; Segerson, 1988; Xepapadeas, 1991; Pushkarskaya, 2003). However, some adopted budget balancing type payment mechanism (Xepapadeas, 1991; Pushkarskaya, 2003), some non-budget balancing type payment mechanism (Holmstrom, 1982; Segerson, 1988). I used non-budget balancing type contract only because it can alleviate moral hazard problems within the group under such asymmetric information cases. However, unlike Segerson’s (1988) payment mechanism I used subsidy only payment mechanism in order to attract farmers to join the contract and delegate the enforcement to the farmers themselves by introducing the peer monitoring and peer pressure concepts The main contribution of this study lies in these peer-monitoring and peer-pressure concepts. This study is a first and modest attempt at analyzing important aspects of these two enforcement tools in the design of a nonpoint source group contract. Under NPS pollution settings, the effect of peer monitoring and peer pressure on moral hazard, cost 118 of monitoring, and group size effect had not been explored before. However, these two enforcement tools commonly used in real life and have been studied in other areas (especially micro finance group lending) and successfully implemented in many developing countries. All these facts have stipulated me to apply this approach for nonpoint source pollution. The underlying idea to delegate monitoring and enforcement to the agents themselves stems from the problem of identifying individual contribution and monitoring costs for the principal. By doing that the principal will save from the monitoring costs plus will alleviate the moral hazard problem. RESULTS Results show that having fixed payment can increase the participation but also increase the agent’s incentive to shirk. If the group has big enough peer pressure and peer monitoring, the principal can offer a payment mechanism with some fixed payment. If the group doesn’t have any or very low peer monitoring and peer pressure, agents will revert to low effort level (shirking) since their incentive compatibility constraints are not satisfied. Under such conditions this kind of contract cannot be implemented successfully. However, if the group has big enough peer monitoring (exogenous or endogenous) and peer pressure, agents will have incentive to exert high effort no matter what. This will make this contract work. Peer monitoring and peer pressure substitutes each other. If one is higher, the requirement for the other is lower. So if peer monitoring is not perfect, and there is a chance of free-riding, this contract can still work if peer pressure is high enough to revert agents’ to exert high effort. Also by the same token, social sanctions and future income 119 loss, which are two components of peer pressure, can substitute each other. If social sanctions are low in a watershed, but future income loss is high enough for an agent, then he still wouldn’t have incentive to shirk. The results also shows that depending on the peer pressure, peer monitoring, and cost of monitoring, the principal can set the bonus/fixed payment level between zero and one. If PM and PP is high or cost of monitoring is low, the principal prefers higher bonus and lower fixed payment to get more benefit out of it. Group size is also important. I demonstrated that given mutual monitoring structure, as the size of the group gets larger the agents have more incentive to shirk, but also the cost of monitoring gets lower and level of peer monitoring gets bigger for each agent. As a result decrease in cost of monitoring and increase in peer monitoring counteracts with free-riding, and this can help to have larger group size. FUTURE RESEARCH DIRECTION This study proposes some new aspects and features for policy makers. If this kind of contract can be applied in real life, this can help to improve water quality by reducing the pollution specifically coming from nonpoint sources. More importantly, this can enhance the trade between point and nonpoint source polluters, which is very rare today in market. The main difficulty of this trade today is because of current nonpoint source programs that only focus on the abatement technology. By switching the performance/output, point-nonpoint sources can directly trade based on final output, which makes the trade easier. 120 Since this is a first attempt to some of the concepts. This study is very basic and needs to be extended to more complicated and realistic cases. For example, agent’s utility function can be change to risk-averse case, or the principal can be social planner (government entity) instead of point source of polluter. Also, target level and abatement price can be internalized as decision variables for the principal, and optimal level of them can be found. This study has dealt with one period static model. In practice, this puts an obvious limit to the implementation of the contract. This needs to be extended to the more period of times and dynamic model should be examined. Especially, it will be interesting if future income loss for a shirking agent can be an endogenous variable with time period. In addition, different peer monitoring structures (such as rotating pyramid) can be analyzed and the best structure can be recommended. Studying correlated risk amongst the agents can be very interesting too. Since they are usually engaged in similar production activities and work under the same environmental condition, we expect a positive correlation amongst abatement productions, too. 121 APPENDIX A: Possible Incentive Compatibility Constraints for an Agent Let’s recall the expected utility functions of agent k. Depending on his effort level and effort levels of his peers he has different expected utilities. When Agent k himself exerts ‘high’ effort max *[ Pr ] ( )i j i j t A H L A A A H L H k k k k kEU F B C a = = + −∑ When Agent k himself exerts ‘low’ effort max [ * ] ( )Prj i j i t A L H L H L k k k A k k k A A EU F B C a PPγ = = + − −∑ We know that the principal always wants the agent to exert high effort. In order for an agent to choose high effort, the expected utility from it must be greater than the expected utility from choosing low effort. To illustrate this assume that the group size is three, and the agents are identical. Incentive compatibility constraints for an agent, say agent k, are: 1. Everybody high effort vs. Everybody low effort max max 3 0 3 0* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 122 * Notice: 1) Left hand side is always agent k exerting high effort, and right hand side agent k is always exerting low effort. 2) Fixed payments (Fk) in both sides of expected utilities cancels out each other. 2. Everybody high effort vs. two low and one high efforts max max 3 0 2 1* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 3. Everybody high effort vs. one low and two high efforts max max 3 0 1 2* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 4. Two high and one low efforts vs. everybody low effort max max 3 02 1* * ( )Pr ( ) Pr t t A A L HH L L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 5. Two high and one low efforts vs. two low and one high efforts max max 2 1 2 1* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 6. Two high and one low efforts vs. one low and two high efforts max max 2 1 1 2* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 7. One high and two low efforts vs. everybody low effort 123 max max 3 01 2* * ( )Pr ( ) Pr t t A A L HH L L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 8. One high and two low efforts vs. two low and one high efforts max max 1 2 2 1* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ 9. One high and two low efforts vs. one low and two high efforts max max 1 2 1 2* * ( )Pr ( ) Pr t t A A H L L H L A k A k k k A A A A H k k k B C a PPB C a γ = = − −− ≥∑ ∑ This last one is the one that dominates the other incentive compatibility constraints. Because when the only agent k himself exerts high effort and the rest shirks (left hand side of equation 9), the probability of meeting the target and getting the bonus payment is very low plus.cost of abatement is high. So the expected utility of agent k is lowest in this case if there are no peer monitoring and peer pressures. On the other hand, when the only agent k himself shirks and the rest exerts high effort (left hand side of equation 9), the probability of meeting the target and getting the bonus payment is much higher plus.cost of abatement is low. 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