Journal of Risk and Uncertainty

, Volume 47, Issue 2, pp 147–163 | Cite as

Arrow’s theorem of the deductible: Moral hazard and stop-loss in health insurance

  • Jacques H. Drèze
  • Erik SchokkaertEmail author


The logic of Arrow’s theorem of the deductible, i.e. that it is optimal to focus insurance coverage on the states with largest expenditures, remains at work in a model with ex post moral hazard. The optimal insurance contract takes the form of a system of “implicit deductibles”, resulting in the same indemnities as a contract with full insurance above a variable deductible positively related to the elasticity of medical expenditures with respect to the insurance rate. In a model with a predefined ceiling on expenses, there is no reimbursement for expenses below the stop-loss amount. One motivation to have some insurance below the deductible arises if regular health care expenditures in a situation of standard health have a negative effect on the probability of getting into a state with large medical expenses.


Optimal health insurance Deductible Stop-loss Moral hazard 

JEL Classification



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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.CORE, Université Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of EconomicsKU LeuvenLeuvenBelgium

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