A person’s decision to make risky choices can be explained by a structural model that incorporates probability distortions, a model distinguished by greatly overweighting small probabilities, and risk aversion.
The authors examine household data on choices of insurance deductibles to develop and estimate a structural model of deductible choice that incorporates standard risk aversion and generic probability distortions. For each household, the authors observe the choices of deductibles for auto collision, auto comprehensive, and home insurance. They find that probability distortions play a key role in explaining the choices that households make regarding deductibles. They also demonstrate that Koszegi and Rabin’s (Quarterly Journal of Economics 2006; American Economic Review 2007) loss aversion and Gul’s (Econometrica 1991) disappointment aversion cannot explain the probability distortions.
How Is This Research Useful to Practitioners?
The examination of how people evaluate risk is pertinent to many areas of business. The authors’ findings are part of a growing investigation into better descriptive models of decision making. Reliance on an expected utility model to explain risk aversion to moderate-stakes risk has problems because the model implies an implausible degree of risk aversion over larger-stakes risk. Although prospect theory modeling has a value function that describes how people value outcomes and a probability weighting function that describes how people evaluate risk, most behavioral research has not focused on probability weighting.
When the authors estimate their model, which includes probability distortions, there is far less standard risk aversion. They find that large probability distortions play a statistically and economically significant role in explaining household choices of insurance deductibles.
Although this research is focused on insurance deductibles, it may be applicable to other areas. The authors suggest that additional research on decision making under uncertainty should have a strong focus on probability weighting.
How Did the Authors Conduct This Research?
The authors use a dataset from a large US property and casualty insurance company that contains information on more than 400,000 households. The authors select household deductible choices in three lines of coverage: (1) auto collision, (2) auto comprehensive, and (3) all-perils home insurance. They consider only the initial deductible choices of each household, and they also restrict the dataset to households that (1) hold both auto and home policies and (2) purchased their policies from the company in the same year, either 2005 or 2006. After screening the dataset, a core sample of 4,170 households is used.
The authors begin with an expected utility model of deductible choice that incorporates standard risk aversion. They generalize the model to allow for probability distortions. Their choice of deductible data enables them to separately identify standard risk aversion and the probability distortion. In their baseline analysis, they assume homogeneous preferences (each household has the same standard risk aversion and probability distortion), and then they expand the model to permit heterogeneous preferences.
They address the issue of moral hazard and believe it to be minimal because most deductibles are small relative to the overall level of coverage. They note that households have a duty to report claimable events under the terms of the insurance contract and have incentives to file claims no matter what the size. But because the possibility of nil claims could bias their results, the authors make the larger $1,000 deductible more attractive and find the model is also robust for nil claims. Finally, they consider the potential of noise affecting household deductible choices and find that noise is important but not dominant.
The authors’ use of field data from an insurance company to estimate nonstandard probability distortions (without imposing a parametric form) is an important piece of behavioral modeling research. By necessity, the authors must make various assumptions and implement data limitations. It would be interesting to see how the model performs in years outside of the 2005–06 research period; Hurricane Katrina hit the US Gulf Coast in August 2005, and news coverage may have affected consumer choices of deductibles. It would also be appropriate to conduct similar research with sample data from outside the United States to confirm the model’s explanatory power in risk-averse cultures. The authors urge caution when applying their analysis, which is based exclusively on insurance deductibles, to other domains. Further exploration and research into different industries is warranted.