On the positive correlation property in competitive insurance markets

Most competitive models of insurance markets under asymmetric information predict a positive relationship between coverage and the accident probability. This paper derives the conditions under which this prediction holds true in a general setting involving multiple loss levels and fixed administrative costs. If there is one loss level, this prediction holds necessarily true only if all equilibrium contracts offer strictly positive coverage. With multiple loss levels, the positive relationship between coverage and the accident probability may not hold true even if all contracts offer strictly positive coverage and administrative costs are zero. These results have important implications for empirical testing.