Willingness to Pay for Insurance in Denmark

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. † Danish Insurance Association (Hansen); Department of Economics, Copenhagen Business School, Denmark (Jacobsen and Lau); and Department of Accounting and Finance, Durham Business School, Durham University, United Kingdom (Lau). E-mail contacts: [email protected], [email protected], and [email protected]. We thank the Danish Social Science Research Council for research support under project #24-02-0124 and #27508-0289, and the Danish Insurance Association and Tryg A/S for the provision of household data on insurance claims. -2There is no simple way to measure the economic value of insurance products because the primary use of these products deals with the control of risk. Some studies attempt to estimate the willingness to pay for insurance products using contingent valuation or stated choice methods that are based on hypothetical questions, while other studies attempt to estimate risk preferences from data on insurance claims and deductible choices (Einav and Cohen [2007]). Contingent valuation and stated choice methods are based on survey questions with no real purchase or consumption consequences for the participants. These methods may thus attract a “hypothetical bias,” which measured as the divergence between the real and hypothetical willingness to pay. There is widespread evidence of participants in contingent valuation studies to overstate the amount they are willing to pay for an incremental unit of private goods (Cummings, Harrison and Rutstrom [1995]; List and Gallet [2001]; Murphy, Allen, Stevens and Weatherhead [2005], and Blumenschein et al. [2008]. We estimate the willingness to pay among Danish households for three types of insurance using a unique combination of claims data from the largest Danish insurance company, Tryg A/S, register based data from Statistics Denmark, and measures of individual risk attitudes and discount rates from a field experiment with a representative sample of the adult Danish population. These field experiments were carried out under the auspices of the Danish Ministry of Economic and Business Affairs, and the incentives in these experiments are comparable to the average claims on auto, home and house insurance products that we consider in this study. The estimated willingness to pay for insurance is based on a decision problem in which the decision maker maximizes expected inter-temporal utility subject to an inter-temporal budget constraint. The model is calibrated to claims data in 2004 from the customer database at Tryg A/S, and this data is mapped to information at Statistics Denmark on annual household income and financial wealth. Since potential insurance claims may be substantial in comparison to annual income, and the probability of filing a claim is relatively small, it is appropriate to allow for consumption smoothing over a longer time period and thereby reduce the impact of an accident on consumption in the short term. We use experimental data from a field methodology developed by Harrison, Lau, Rutström and Sullivan [2005] to elicit both risk and time preferences from the same respondents. The experimental procedures build on the risk aversion experiments of Holt and Laury [2002] and the 1 See Harrison and Martinez-Correa [2012] for a systematic overview of the literature on behavioural insurance.