Academic journal article Journal of Risk and Insurance

Demography of Risk Aversion

Academic journal article Journal of Risk and Insurance

Demography of Risk Aversion

Article excerpt


This article uses life insurance data to estimate the Pratt-Arrow coefficient of relative risk aversion for each of nearly 2,400 households. Attitudinal differences toward pure risk are then examined across demographic subgroups. Additionally, differences in speculative risk-taking are examined across demographic groups based on survey responses and compared with the results on pure risk aversion.


In the mid-1960s, John Pratt and Kenneth Arrow introduced the now-familiar measure of relative risk aversion, along with the hypothesis that relative risk aversion increases with wealth. Since that time, numerous researchers have attempted to estimate the magnitude of relative risk aversion for subsets of the population using a variety of techniques, and others have conducted empirical tests of the increasing relative risk aversion (IRRA) hypothesis. Most recently, attention has turned to comparing risk aversion across different demographic subgroups, particularly men and women. [1] Remarkably, these efforts have been largely independent of one another. Some of those seeking to estimate risk aversion parameters, for example, assumed a utility function exhibiting constant relative risk aversion (CRRA), effectively precluding tests of the IRRA hypothesis. On the other hand, most studies examining the relationship between risk aversion and demographic or wealth variables infer differences in risk aversion parame ters rather than calculating the parameters explicitly. Many use either hypothetical questions or experimental gambling data, and most restrict attention to forms of risk in which both gains and losses are possible.

In the present study, the authors integrate and extend these three strands of research. First, the authors derive a reduced form equation for the Pratt-Arrow measure of relative risk aversion without imposing prior assumptions on the shape of the utility function. The authors then estimate the risk aversion parameter empirically for individual households using survey data on life insurance purchases. This gives us more than 2,300 numerical measurements of the Pratt-Arrow coefficient. These measurements are then used to examine differences in relative risk aversion across demographic groups based on age, gender, education, nationality, race, marital and parental status, religion, health and behavioral indicators, and employment status, income, and wealth. The availability of wealth data also allows us to test the IRRA hypothesis. Finally, the authors examine attitudes toward a second type of risk, by studying survey responses to a hypothetical question regarding employment and income risk.

The first section briefly reviews the prior research. The second and third sections present the authors' theoretical model and empirical results, respectively, pertaining to relative risk aversion in the context of mortality risk. The fourth section discusses results pertaining to speculative risk, and the article ends with a brief conclusion.


For a concave utility function U defined over wealth of W, Pratt (1964) and Arrow (1965) suggested the elasticity of marginal utility with respect to wealth, or R(W) = -WU"(W)/U'(w), as an appropriate measure of relative risk aversion. Arrow showed that this measure is directly related to one's insistence on favorable odds when putting some fraction of wealth at risk, and Pratt demonstrated that R(W) is proportional to the insurance premium one is willing to pay to avoid a given risk. Both Pratt and Arrow hypothesized that R(W) increases with W; the hypothesis implies that at higher levels of wealth, individuals become less willing to subject a given percentage of wealth to risk. Subsequent empirical research has addressed three central questions: the magnitude of R(W), the IRRA hypothesis, and the relationship between risk aversion and demographic variables.

Among the earliest empirical estimates were those by Friend and Blume (1975), who studied the demand for risky assets and concluded that R(W) generally exceeds unity and is probably greater than 2. …

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