## Healthcare Economist

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## Survey Measures of Risk Aversion and Prudence

Written By: Jason Shafrin - Nov• 01•07

Can we estimate risk aversion and prudence using a survey question for the general public? This is what a paper by Eisenhauer and Ventura attempts to do.

Methods

In the 1995 Survey of Italian Households’ Income and Wealth, one question asked:

You are offered the opportunity of acquiring a security permitting you, with the same probabilities, either to gain 10 million lire [5165€] or to lose all the capital invested. What is the most you are prepared to pay for this security?

Assuming, the respondents answer honestly and precisely (which is a big assumption to make), the authors can create and individual’s utility function:

• U(w)=0.5U(w-z)+0.5*U(w-z+10)

The variable w represents initial wealth and z is the amount individual would pay for a security. Using a Taylor expansion, we can create an estimate of absolute risk aversion.

• 2U(w)=U(w)-zU'(w)+0.5z2U”(w) + (10-z)U'(w) + .5(10-z)2U”(w), or
• [(50-10z+z2)/(10-2z)]*U”(w)=-U'(w)
• A(w)=[(10-2z)/(50-10z+z2)]
• R(w)=A(w)*w

The term A(w) represents the Arrow-Pratt measure of absolute risk aversion while R(w) is equal to relative risk aversion. If we differentiate the second equation above with respect to initial income, w, we can calculate a measure of prudence (-U”’/U”).

• Î·(w)=A(w) + {(10-z)-1 + [2z/(100+z2)]}*âz/âw
• Ï?(w)=w*Î·(w)

The term Î·(w) measures absolute prudence while Ï?(w) measures relative prudence.

Results

Since the authors have information regarding each individual’s initial earnings and various sociodemographic factors, they can analyze which type of people are risk averse.

• Relative risk aversion is between 7.18 and 8.59.
• Relative prudence is between 7.32 and 8.65.
• The most risk averse groups are those in poor health and those with only an elementary school education.
• The least risk averse are the college educated and those with health insurance.
• Those with risk assets such as stocks or loans are less risk averse.
• The authors claim that generally R(w)<Ï?(w)<R(w)+1 and risk aversion and prudence are highly correlated.

Healthcare Economist critique

Finding that people are risk averse and prudent is unsurprising, but the levels of risk aversion and prudence are very high compared to other studies. While having a vast array of sociodemographic information is important, simply eliciting a willingness to pay for a risky gamble is likely not a precise estimate of risk aversion. Likely, most people will respond to the question categorically (5 million lire, 4.5 million lire, 4 million lire, etc.). Further, finding that people with health insurance are less risk averse is counter-intuitive. One explanation is that having health insurance may be a proxy for wealth. Thus people with heath insurance in general could be more risk averse, but since this group of people is also richer (and more affluent people are generally less risk averse) we could have opposing effects.

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