时间：2022-08-07 12:46:07
Abstract: This paper adopts Besley and Ghatak’s and HalonenCAkatwijuka’s framework to analyze how public goods should be owned. It weakens BG’s assumptions and takes indispensability and complementarities as well as spillovers of human capital into account.
Key words: public good; human capital; indispensablity; complementarity; spillover
I The Model
Assume that there are two agents and : has lower valuation for the public good whereas has higher valuation. and produce the public good together. Both agents invest in project-specific human capital and their investment levels are and , respectively. Benefit the agents can get from the project is . The agents value the public good differently, the valuation parameter of agent is and that of agent is ; . Costs of the project are functions of the agents’ investments in project-specific human capital: for . The timing of the project is:
1. Two agents sign a contact on the ownership of the public good;
2. Both agents invest in project-specific human capital;
3. Two agents bargain over the surplus of the project and produce the public good.
If bargaining breaks down and agent becomes the owner, benefit from the project turns to . Producing the public good together is assumed to be more efficient than bargaining breaking down, that is, Let and
Furthermore, we assume the following specific functional forms:
where is degree of complementarities of the agents’ human capital, is the indispensability of agent when she is not the owner, is a measurement of spillover, Agent
and are symmetric and they have the same level of importance of investment. The key assumption of Besley and Ghatak (2001) is:
We weaken BG’s key assumption following HalonenCAkatwijuka (2008):
II First Best
We are facing the same situation as BG’s model: in reality, there is no complete contract, that is, the agents’ investment levels are not specified in the ex ante contract. Therefore, we have to find under which ownership the joint surplus is highest (the second-best investments).
III Ownership and Incentives
The agents’ optimal investment levels do not solely depend on her relative valuations of the public good, other factors of human capital such as spillover, indispensability of the non-owner and degree of complementary are also determinants.
IV One Investment
If there is only one investing party, and the other agent is indispensable, the low-valuation agent’s ownership gives better incentive; if the other agent is dispensable, higher incentive occurs under the high-valuation agent’s ownership. If there is only one investing party, and there is no spillover from her investment, the agent has better incentive under the low-valuation agent’s ownership; if there is full spillover from her investment, the high-valuation agent’s ownership gives better incentive.
V Two Investments
When two agents invest in the project and both of them are indispensable, ownership of the low-valuation agent is optimal. If only the high-valuation agent is indispensable, when there are no complementarities between the agents’ investments, each agent has better incentive when she is the owner. When complementarities are maximal and there are no spillovers from the agents’ investments, the high-valuation agent’s ownership is optimal; when there are full spillovers, the low-valuation agent should be the owner. When both agents are dispensable, ownership of the high-valuation agent is optimal. But if there are full spillovers, two individual ownerships are indifferent. If only the high-valuation agent is dispensable, when there are no complementarities between the agents’ investments, agents have better incentives under the other one’s ownership. When complementarities are maximal and there are no spillovers, the high-valuation agent should be the owner; when there are full spillovers, ownership of the low-valuation agent gives better incentives.
When there are no spillovers from the agents’ investments, ownership of the high-valuation agent is optimal. When there is full spillover from the low-valuation agent’s investment, each agent has better incentive if she owns the project herself, but when there are no complementarities between investments, and the agents are indispensable to each other, the high-valuation agent has better incentive under the low-valuation agent’s ownership. When there are full spillovers, ownership of the low-valuation agent is optimal; but if two agents are dispensable to each other, their incentives under both types of individual ownership structures are the same. When there is no spillover from the low-valuation agent, agents have better incentives under the other one’s ownerships except when complementarities are maximal and agents are dispensable to each other, the high-valuation agent has better incentives when she is the owner.
VI Joint Ownership
When only the low-valuation agent invests, and the other agent is indispensable, her ownership and joint ownership give the same incentive. If the other agent is dispensable, joint ownership gives her better incentive. If only the high-valuation agent invests, when the other agent is indispensable, the low-valuation agent’s ownership gives better incentive; when the other agent is dispensable, the high-valuation agent’s incentive is higher when she owns the project.
If only the low-valuation agent invests, and there is no spillover from her investment, her incentive is no different under the high-valuation agent’s ownership and under joint ownership. If there is full spillover, joint ownership gives her higher incentive. If only the high-valuation agent invests, and there is no spillover from her investment, she has better incentive when she owns the project; when there is full spillover from her investment, the latter’s ownership gives her better incentive.
In case of two investments, if they are indispensable, joint ownership provides better incentive for the low-valuation agent and the high-valuation agent has better incentives when she is the owner. If the low-valuation agent is dispensable, and there are no complementarities between the investments, her ownership and joint ownership are indifferent, high-valuation agent still has better incentive when she is the owner. If complementarities are maximal and there are no spillovers, it is optimal for the high-valuation agent to be the owner. If there are full spillovers, joint ownership gives higher incentive to the low-valuation agent and the high-valuation agent has better incentive under the other agent’s ownership. If two agents are dispensable, and there are no complementarities, joint ownership gives better incentive to the low-valuation agent, and the high-valuation agent has better incentive under her own ownership. If complementarities are maximal and there are no spillovers, it is optimal for high-valuation agent to be the owner. If there are full spillovers, joint ownership gives better incentive to the low-valuation agent and incentive of the high-valuation agent depends on her valuation for the public good, better incentive could occur under single ownership, joint ownership, or these two types are indifferent to her. If the low-valuation agent is indispensable, and there are no complementarities, joint ownership gives higher incentive to the low-valuation agent, and the high-valuation agent has better incentive under the other agent’s ownership. If complementarities are maximal and there are no spillovers, ownership of the the high-valuation agent and joint ownership are both optimal. If there are full spillovers, joint ownership gives better incentive to the low-valuation agent and the high-valuation agent has better incentive under the low-valuation agent’s ownership.
For spilloevers, when there are no spillovers from two agents’ investments, ownership of the high-valuation agent is optimal. When there is full spillover from the low-valuation agent’s investment with no complementarities between the investments, both joint and the low-valuation agent’s ownership provide the same levels of incentives for low-valuation agent. If complementarities are maximal and agents are indispensable to each other, the low-valuation agent’s ownership and joint ownership are indifferent to the agents. If agents are dispensable, joint ownership gives better incentive to the low-valuation agent and the high-valuation agent has better incentive when she owns the project herself. When there are full spillovers, joint ownership gives better incentive to the low-valuation agent, and the high-valuation agent has better incentive under the other one’s ownership. But if the agents are dispensable, the high-valuation agent has better incentive under single ownership. When there is no spillover from the low-valuation agent’s investment, with zero complementarities and indispensable agents, the low-valuation agent is no different under the high-valuation agent’s ownership and joint ownership, and the high-valuation agent has better incentives when the other agent is the owner. If two agents are dispensable, the high-valuation agent’s ownership is optimal.
VII Leadership
With an indispensable high-valuation agent and a dispensable low-valuation agent with zero spillovers, if the complementarities are maximal, the high-valuation agent should be the leader. When both agents are dispensable, complementarities are maximal and there are no spillovers from their investments, the high-valuation agent should lead the project. When there is a dispensable high-valuation agent and an indispensable low-valuation agent, if complementarities are maximal and there are no spillovers from their investments, there is no difference between the high-valuation agent being the leader and the agents leading the project jointly.
If there are no spillovers from the agents’ investments, the high-valuation agent should be the leader. If there is a high-valuation agent with no spillover and a low-valuation agent with full spillover, complementarities are maximal, and the agents are indispensable to each other, the low-valuation agent being the leader and two agents leading the project jointly are indifferent. When there are full spillovers and there are no complementarities between the agents’ investments, they should lead the project jointly. If there is full spillover from the high-valuation agent’s investment, zero spillover from the low-valuation agent’s investment, complementarities are maximal, the agents are dispensable, the high-valuation agent should lead the project.
VIII Applications
According to BG, NGOs have higher valuations for the public good than governments, and the two agents have holdup problems due to incomplete contracting in practice. NGOs with higher valuations for the public good should be the provider of the public good. NGOs’ higher incentives occur when they own the project because of their relatively high valuations for the public good and for governments as low-valuation agents, they have better incentives if they provide the public good with NGOs jointly.
In less developed regions the government is indispensable to NGOs. NGOs are high Cvaluation agents with small spillovers from their investments. It is optimal to provide the public goods and services jointly when there is an indispensable low-valuation agent.
IX Conclusion
We not only examined the effects of agents’ spillovers when they are not the owners, but also the effects of indispensability of each agent on their incentives. So the conclusions are partly different from what BG have suggested. Having better incentive under high-valuation agent’s ownership for high-valuation agent and under joint ownership for low-valuation agent is not always the case. In addition, with consideration of degree of complementarities, we have found different results comparing to Halonen-Akatwijuka’s. There are some empirical results supporting BG’s, Halonen-Akatwijuka’s and our theoretical predictions.
References
[1] Besley, T. and M. Ghatak, (2001), “Government versus Private Ownership of Public Goods”, Quarterly Journal of Economics, 116, 1343-72.
[2] Besley, T. and M. Ghatak, (2004), “Public Goods and Economic Development”, mimeo, London School of Economics.
[3] Besley, T. and M. Ghatak, (2007), “Reforming Public Service Delivery”, Journal of African Economics, 16, 127-156.
[4] Farrington, J. and A. Bebbington, (1993), Reluctant Partners: NGOs, the State and Sustainable Agricultural Development, London: Routledge.
[5] Farrington, J and D. Lewis, (1993), Non-governmental Organizations and the State in Asia: Rethinking Roles in Sustainable Agricultural Development, London: Routledge.
[6] Halonen-Akatwijuka, M., (2008), “Nature of Human Capital, Technology and Ownership of Public Goods”, mimeo, University of Bristol.