Moral hazard, risk sharing, and the optimal pool size∗ Frauke von Bieberstein,y Eberhard Feess,z José F. Fernando,§ Florian Kerzenmacher,{ and Jörg Schillerk September 7, 2016 Abstract In risk pools, the effective share of the own loss borne is the sum of the direct share (the coinsurance rate) and the indirect share borne by the residual claimant. In a model with n identical risk-averse individuals and moral hazard, we derive two main results: First, for all mixed risk averse utility functions, the effective share required for incentive compatibility for the high effort increases in the pool size. This is a downside of larger pools as it, ceteris paribus, reduces risk sharing. Second, however, we find that the optimal pool size nevertheless converges to infinity as the positive effect from better diversification of the risk borne by other individuals always outweighs the negative effect from the larger risk of own damage. In our basic model, we restrict attention to two effort levels, but we show that our results extend to a model with continuous effort choice. Keywords: risk sharing, moral hazard, mutuals, partnerships JEL Classification: D81, G22 ∗We thank Harris Dellas, Marc Möller, Martin Nell, Richard Peter, and Harris Schlesinger for valuable comments. yUniversity of Bern, IOP, Engehaldenstr. 4, 3012 Bern, Switzerland,
[email protected]. zFrankfurt School of Finance & Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany,
[email protected]. §Universidad Complutense de Madrid, Facultad de Matemáticas, Departamento de Álgebra, Plaza de Ciencias, 3, 28040 Madrid, Spain,
[email protected] {Frankfurt School of Finance & Management, Sonnemannstr. 9-11, 60314 Frankfurt, Germany,
[email protected].