Optimal contract with moral hazard for Public Private Partnerships

Abstract

Public–Private Partnership (PPP) is a contract between a public entity and a consortium, in which the public outsources the construction and the maintenance of an equipment (hospital, university, prison ...). One drawback of this contract is that the public may not be able to observe the effort of the consortium but only its impact on the social welfare of the project. We aim to characterize the optimal contract for a PPP in this setting of asymmetric information between the two parties. This leads to a stochastic control under partial information and it is also related to principal-agent problems with moral hazard. Considering a wider set of information for the public and using martingale arguments in the spirit of Sannikov, the optimization problem can be reduced to a standard stochastic control problem, that is solved numerically. We then prove that for the optimal contract, the effort of the consortium is explicitly characterized. In particular, it is shown that the optimal rent is not a linear function of the effort, contrary to some models of the economic literature on PPP contracts.

Keywords:

• Public Private Partnership
• stochastic control under partial information
• HJB equation
• moral hazard

Acknowledgements

We thank Guillaume Carlier, Ivar Ekeland, Dylan Possamaï, Nizar Touzi, Stéphane Villeneuve, Hao Xing and Junwei Xu for interesting and helpful discussions and comments. We also thank the referee for his constructive remarks.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author C. Hillairet was supported by the research programs Chaire Risques Financiers of Fondation du Risque, and Investissements d’Avenir [ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047].