Risk Aversion

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Risk aversion and health behaviors

December 5, 2008 in Experimental | No comments

Are risk averse individuals less likely to engage in unhealthy behaviors?  According to Anderson and Mellor (JHE 2008), the answer is yes.  Using a Holt and Laury (AER 2002) methodology to measure risk aversion, the authors find that individuals who are risk averse are less likely to smoke, drink, be overweight or drive over the speed limit.  Risk averse individuals are more likely to use a seat belt.

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Risk Aversion in the Laboratory

August 26, 2008 in Experimental | Permalink

Many experimental economists have been interested in measuring the level of risk aversion as well as the determinants of risk aversion. These studies often take place in a controlled, laboratory setting and designing an experiment which will elicit responses which are true to life is essential.

In “Risk Aversion in the Laboratory,” Harrison and Rutström review some of the techniques used to elicit risk aversion preferences. We will review 5 of these techniques: multiple price list (MPL), random lottery pairs (RLP), ordered lottery selection (OLS), Becker-DeGrot-Marschak (BDM) and trade-off (TO).

  • Multiple price list (MPL). In this type of lottery, subjects are given a list of binary lottery choices to make all at once. The most famous example of MPL is the Holt and Laury (2002) study. MPL is probably the most widely used method to elicit risk preferences, but do suffer from the problem of framing. In the Holt & Laury study, subjects may have tended to choose a switching point in the middle of lottery list even if their actions in the real world would not have reflected this choice.
  • Random lottery pairs (RLP). Under RLP, subjects face binary lottery choices in a sequence and must choose the preferred lottery. Hey and Orme (1994) used this methodology to test expected utility predictions. The experimenters’ elicited the subjects preferences over 100 pairs of lotteries, where the outcome values were fixed (£0, £10, £20, £30) but the probabilities for each outcome changed among the 100 lottery pairs.
  • Ordered lottery selection (OLS). In this methodology, the subject chooses one lottery from an ordered set. For instance, Barr (2003) allowed villagers in Zimbabwe to choose from the following 50/50 lotteries: (100; 100); (90, 190); (80, 240); (60, 300); (20, 380); (0, 400). The OLS structure can help to answer questions about risk preferences, but since all lotteries are 50-50, they can not answer questions regarding higher order risk preferences (e.g., prudence, temperance). Further, this method does not allow for the analysis of any Kahneman and Tversky-style probability weighting.
  • Becker-DeGrot-Marschak (BDM). In the words of Blavatsky & Köhler (2007), “Under the BDM procedure, individuals are asked to state their minimum selling price for a risky lottery. The experimenter then draws a random number between the lowest and the highest outcome of the lottery. If the price that the individual states is lower than or equal to the drawn number, she receives the drawn number as her payoff. Otherwise she has to play the risky lottery.” The benefit of BDM is that if preferences satisfy the independence axiom, then the bid will be the individuals exact certainty equivalent. However, it assumes that individuals do not make errors and understand the fairly complex nature of the game.
  • Trade-off (TO). The trade off design gives subjects choices over lotteries and these lotteries are endogenously defined in real-time by prior responses of the same subject. This can lead to a more precise measure of the certainty equivalent, but does the lotteries played will vary by subject.

With any of these experiments it is important to pay real money for the subjects answers. Otherwise, many of the results will suffer from hypothetical bias (see Camerer and Hogarth, 1999).

  • Cox and Harrison (2008), “Risk Aversion in the Laboratory,” Risk Aversion in Experiments, Research in Experimental Economics, volume 12.

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How to present your lottery in an economic experiment

August 8, 2008 in Experimental | Permalink

How should you present a lottery to a subject of an economic experiment? Is a pie chart the best? What about a Holt & Laury style chart?

I have compiled a document (“Lottery Presentation Styles“) to give you some suggestions.

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Would you give up some life expectancy to know the day you will die?

July 11, 2008 in Academic Articles | Permalink

  • “The best-laid schemes o’ mice an’ men. Gang aft agley” – Robert Burns

The only certainty in life is uncertainty. Individuals make plans for their future without knowing how long they will live in reality. Retirement planning, for instance, is very difficult due to uncertain life expectancy. Would you be willing to trade some of your life expectancy in order to be more certain of the date you will perish?

This is the question Ryan Edwards attempts to answer in his 2008 NBER working paper. Countries such as the U.S. and France have a relatively high variance of life expectancy while Sweden and Japan have very low levels of life expectancy variance.

He calculates that “one less year in standard deviation is worth about half a mean life year.” Further, “health inequality must be larger between rich and poor countries than is implied by life expectancy alone, since life-span uncertainty is surely higher in developing countries.”

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Risk Aversion, Impatience and Cognitive Ability

March 6, 2008 in Economics - General, Experimental, Labor Economics | Permalink

Are smart people risk averse? Are dumb people impatient?

This is what Thomas Dohmen, Armin Falk, David Huffman, Uwe Sunde explore in their 2007 Discussion paper. Using data from a choice experiment of 1000 German adults, the authors tested for risk aversion using a Holt & Laury framework, and for impatience by varying the annual rate of return for a €100 investment. It is necessary to test the risk aversion and impatience parameter separately because in expected utility theory (EUT), a more concave utility function will cause more impatient choices, holding constant the discount rate. Cognitive ability was measured using questions similar to those on the Wechsler Adult Intelligence Scale (WAIS).

The authors found that individuals with higher cognitive abilities are less likely to be risk averse. Further, those who scored higher on the WAIS are significantly less impatient. This finding is true even after controlling for income, education, and credit constraint co-variates.

According to the authors:

“The paper also points to a different interpretation of reduced form models that have been estimated in the literature on cognitive ability and labor market outcomes. These models have typically included a measure of cognitive abilities, but not risk aversion or impatience, as explanatory variables (e.g., Cawley et al., 2001). Outcomes such as educational attainment or wages may by affected by risk aversion and impatience, and thus part of the impact of cognitive ability may reflect the correlation with these traits. In other words, our findings point to a potentially important source of omitted variable bias in this type of estimation.

Given that cognitive ability is known to be transmitted from parents to children, our findings could also be relevant for the literature on intergenerational transmission of preferences and socio-economic status.”

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Survey Measures of Risk Aversion and Prudence

November 1, 2007 in Current Events, Econometrics, Experimental | Permalink

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”).

  • η(w)=A(w) + {(10-z)-1 + [2z/(100+z2)]}*∂z/∂w
  • Ï?(w)=w*η(w)

The term η(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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