WP 2012-11 Willingness to Pay for Insurance in Denmark

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Published in 2016 in The Journal of Risk and Insurance, Volume 83, Issue 1.

AUTHORS: Jan V. Hansen, Rasmus H. Jacobsen, and Morten I. Lau

ABSTRACT. We estimate the maximum amount that Danish households are willing to pay for three different types of insurance: auto, home and house insurance. We use a unique combination of claims data from the largest private insurance company in Denmark, measures of individual risk attitudes and discount rates from a field experiment with a representative sample of the adult Danish population, and information on household income and wealth from registers at Statistics Denmark. We assume that households maximize expected inter-temporal utility subject to an inter-temporal budget constraint with several possible states of nature, where all uncertainty is realized in the initial period and any loss incurred by an accident is subtracted from initial wealth. The estimated willingness to pay is based on annual claims and should thus be considered as an annual premium. Since there is some uncertainty about the estimates of risk attitudes and discount rates, there is some uncertainty about the estimated willingness to pay. We use a randomized factorial design in our sensitivity analysis where each simulation involves a random draw from independent normal distributions of the estimated risk and time preferences. The results show that the willingness to pay is marginally higher than the actuarial fair value under Expected Utility Theory. However, the estimated willingness to pay is significantly higher under Rank-Dependent Utility Theory, and for some households it may be up to 600% higher than the actuarial value of the insurance claims.