Monitoring and Privacy in Automobile Insurance Markets with Moral Hazard

1. Monitoring and Privacy in Automobile Insurance Markets with Moral Hazard ARIA August 6, 2007 Quebec City

2. Automobile insurers record data about • distance traveled • frequency of trips • when (time of the day, rush hour) • duration of trips, stopovers • where (type of road, speed limits) • speed • accelerations and braking • space measuring • usage of seatbelts • airbag-functioning • collision data • tire pressure

3. Related literature • imperfect exogenous signals: • Holmström (1979), Shavell (1979), Harris / Raviv (1979) • endogenous monitoring: • random sampling - Townsend (1979), Dye (1986), Lambert (1985) • endogenous precision of the signal - Singh (1985), Meth (1996), Kim / Suh (1992)

4. Contract schemes (1) • conditional monitoring • only the indemnities (I) depend on the monitoring signal

5. Contract schemes (2) • no restrictions on monitoring • both (B) the premiums and indemnities depend on the monitoring signal

6. General setting of the model • perfectly competitive market with risk-neutral insurers • risk-averse individuals • two possible outcomes: Loss (W-L) and No Loss (W) • two effort levels, with probabilities of NO Loss • insurance contracts • monitoring with comprehensiveness of data • individuals’ utility • with and

7. General setting of the model • monitoring technology • generates a binary signal

8. Conditional monitoring – endogenous precision (1) • maximization problem

9. Conditional monitoring – endogenous precision (3) with without privacy costswith privacy costs • IC: • zero-profit constraint: • expected contractual utility

10. Conditional monitoring – endogenous precision (4) without privacy costs with privacy costs • marginal effect of precision

11. Conditional monitoring – endogenous precision (6) • generally, when i increases: • the signal becomes more informative of effort • incentives on effort improve • risk-sharing improves • expected contractual utility increases • privacy costs: • lead to an interior solution for i unless privacy costs increase too fast • reinforce the incentives on effort • improve the allocation of risk • increase the expected contractual utility • decrease the total expected utility

12. Conditional monitoring – endogenous precision ex post • precision ex post • effect is as if the level of precision was not observable • additional incentive constraint: with respect to precision • risk sharing is worse • ex post flexibility of monitoring decreases the efficiency of the contract

13. Comparison of the contract schemes • without privacy costs: • Unrestricted monitoring (B) is more efficient than conditional monitoring (I) for any level of precision i. • with privacy costs: • B lacks the positive incentive and risk sharing effects of privacy costs (indirect effects) • with B the expected privacy costs are larger than with I (direct effect) • I is better than B, if • the efficiency of effort is high, • the efficiency of the monitoring technology is low, • the probability of loss is small • the privacy costs with B are large

14. Summary • without privacy costs: • B with maximum amount of data is optimal • with privacy costs: • unless privacy costs increase too fast, insureds will choose some monitoring with any contract scheme • with conditional monitoring (I) • privacy costs have an incentive and a risk sharing effect, • the expected utility of net wealth increases, • however total expected utility decreases, • I gains advantages due to direct and indirect positive effects of privacy costs. • I can be more efficient than B • ex post precision is inefficient

15. Thank you!