Participating insurance contracts and the Rothschild-Stiglitz equilibrium puzzle

We show that an equilibrium always exists in the Rothschild-Stiglitz insurance market model with adverse selection when insurers can o¤er either nonparticipating or participating policies, i.e. insurance contracts which may involve policy dividends or supplementary calls for premium. The equilibrium allocation coincides with the Miyazaki-Spence-Wilson equilibrium allocation, which may involve cross-subsidization between contracts within subgroups of individuals. The paper establishes that participating policies act as an implicit threat that dissuades deviant insurers who aim at attracting low risk individuals only. The model predicts that the mutual corporate form should be prevalent in insurance markets or submarkets where second-best Pareto e¢ ciency requires cross-subsidization between risk types. Stock insurers and mutuals may coexist, with stock insurers o¤ering insurance coverage at actuarial price and mutuals cross-subsidizing risks. It is also shown that deferred premium variations may act as a substitute to policy dividend or supplementary call with similar strategic e¤ects. Ecole Polytechnique, Department of Economics; Email: [email protected]