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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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Willingess to pay (WTP) perspectives

February 14, 2008 in Economics - General, Experimental | Permalink

Many health economists wonder how much individuals would be willing to pay for a treatment. Since most medical care is paid by third parties (i.e. private insurance companies or the government) we can not use revealed preference econometrics which has been used in other areas of economics. Instead, many economists ask individuals directly these valuation questions. Yet simply asking the question is not enough. Do you ask the person how much they should pay for a treatment for an illness they do not yet have? Or should we only ask patients who have the disease how much they would be willing to pay for their own treatment? In healthcare systems that are run by the government, one may also want to know how much a person would pay for treatment for other people’s diseases.

In order to understand, what perspective should be taken, a paper by Dolan et al. (Health Economics 2003) uses a simple chart to illustrate six different perspectives:

  Ex-ante Ex-post
Personal 0<pp<1; po=0 What value do you attach to treatment being available should you need it? pp=1; po=0 What value do you attach to your own treatment?
Social pp=0; 0<po<1; What value do you attach to treatment being available to others should they need it? pp=0; po=1 What value do you attach to the treatment of others?
Social inclusive personal 0<pp<1; 0<po<1; What value do you attach to treatment being available to a group of people amongst whom you might find yourself pp=1; po=1 What value do you attach to the treatment of yourself and others?
         

The term pp gives of the probability of one’s own need for treatment, and po is the probability that others in society will need treatment.

Why is it important for researchers to keep track of all these different perspectives when measuring willingness to pay (WTP)? Dolan notes that empirically, “real patients often give higher valuations than hypothetical patients.” Yet this need not be the case. If patients, ex-post, have adapted to the disease to a significant degree, than hypothetical patients may have higher valuations that real patients.

Whenever a researcher is investigating WTP measures, they must very cautious as to the perspective under which the question is asked.

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Welfarists vs. Extra-welfarists

February 13, 2008 in Economics - General, Experimental | Permalink

Health economists, policy makers, physicians and public health officials all want to maximize the well-being of society. These groups evaluate different medical treatments or public health interventions and then determine if the benefit is worth the cost.

In an opinion piece by Dorte Gyrd-Hansen in Pharmacoeconomics (2005), two schools of thought are examined. Those who are ‘welfarists’ believe that “the output of healthcare should be judge according to the extent to which it contributes to overall welfare (i.e. the [weighted] sum of individual utilities….’extra-welfarists’ do not define the output of healthcare in terms of preferences for health vis-a-vis other goods, but according to its contribution to health itself, i.e. they wish to maximize health as against overall welfare.”

What does this mean in reality?

“From a welfarist theoretic framework, treating a person who copes well with her disease and thus generates a high level of personal utility despite a poor health state will not be as efficient as treating a person who copes poorly. Extra-welfarists would aim at constructing an outcome measure that would produce equal values for the two strategies thus overriding individual preferences.”

Let’s use a chart to compare these two philosophies:

  Welfarist Extra-Welfarist
Focus Output of medical care should be judged against all other goods Output of medical care should be judged against all other types of treatment
Function to maximize u(x,h(m)); s.t.: x+pm=I h(m); s.t. [h(m)-h(0)]/p>C
Individual heterogeniety Different individuals value the same health state differently Assume that everyone values health states similarly
Analysis Cost-benefit analysis (CBA) Cost-effectiveness analysis (CEA)
Advantage Theoretically superior Easier to implement in practice
     

From the chart we see that welfarists try to maximize [the sum of] individual utilities subject to a budget constraint. Extra-welfarist, try to maximize health which is done by choosing all medical procedures which are more cost-effective than a certain threshold. This threshold, C, is must be chosen by policymakers. Welfarists wisely see that some individuals value health more than others in comparison to other goods. The extra-welfarist assumes all individuals with the same disease are homogeneous. This may seem naive, but in practice, it is very difficult to find each individuals willingness to pay for an increased level of health.

Extra-welfarists often try to elicit willingness-to-pay (WTP) measures for an additional QALY (i.e. quality-adjusted life year). If one applies a single WTP for each QALY, this “will entail overriding individual preferences such as diminishing marginal utility of health and potential differences in the value of increment health across population groups.” If we could rank health on a scale from 0 to 100 where 0 is equivalent to death and 100 is perfect health, economists would argue that under diminishing marginal utility of health that and individual would value an increase in health from 50 to 60 more than they would an increase from 90 to 100.

So is using the extra-welfarist QALY acceptable? While the welfarist camp offers no practical, easily estimable alternative, the do bring out some short comings of using QALYs (e.g., diminishing marginal utility of health, individual heterogeneity in terms of valuation of health against other good). Thus, I think the QALY method is helpful to analyze the benefit of a particular medical treatment, but the cost per QALY should not be the only factor taken into account when analyzing whether or not to adopt a new medical procedure.

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Randomization Bias and the Show-up fee

November 7, 2007 in Experimental | Permalink

Many economists have conducted experiments to analyze the preferences of different populations. In particular, many researchers have attempted to measure the degree of risk aversion or risk loving for a given population. The researcher hopes that his or her subjects are representative of the overall risk aversion composition of the population sampled.

A working paper by Harrison, Lau and Rutström looks at whether or not this will be the case. It is possible that a randomization bias will bias the results. For instance, if there is risk for individuals to be placed into control and treatment groups, more risk averse people will decide not to participate in the experiment. Thus, risk aversion estimates may be too low.

On the other hand, many experiments often give individuals show-up fees which are paid to the participants regardless of what their responses are in the given questionnaire. Harrison and co-authors hypothesize that more risk averse people will decide to participate when there is a guaranteed show-up fee.

To measure risk aversion, the authors use the Holt and Laury (2002) methodology. The find the following results:

  • The average CRRA value for an experiment with a high show-up fee is 0.81 while the average is 0.67 in the experiment with a low show-up fee. Thus, a high show up fee increases the risk aversion of the population.
  • The risk aversion parameters are also stronger when high lottery prizes compared to low ones (0.81 vs. 0.59).

It is important to take into account this randomization bias whenever you are conducting an experiment.

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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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Cure for Cancer: Use an expensive placebo…not a cheap one!

October 22, 2007 in Experimental, Pharmaceuticals | 1 comment

Give a patient a pill and they will feel better. Give the same patient the exact same pill and tell them it was purchased at a wholesale discount, and these same people won’t feel as good.

At least that is what a study by Shiv, Carmon and Ariely (2005) found.

In three experiments, the authors show that consumers who pay a discounted price for a product (e.g., an energy drink thought to increase mental acuity) may derive less actual benefit from consuming this product (e.g., they are able to solve fewer puzzles) than consumers who purchase and consume the exact same product but pay its regular price. The studies consistently support the role of expectancies in mediating this placebo effect.

A question remains, are price and quality related? A study by Riesz (1979) looks for a correlation between price and quality as reported by Consumer Reports for packaged food products. “He concludes that the correlation was near zero, and in cases such as frozen foods, it was even negative.”

Thanks to ‘Undercover Economist‘ Tim Harford for link.

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Analyzing Background Risk with Morgan Dollars

October 9, 2007 in Experimental | Permalink

Their have been much economic research to determine how individuals evaluate risk. Most of this work takes place in a laboratory setting using hypothetical monetary payoffs. Further, the issue of “background risk” is often ignored. For instance, “…mortality risks from alternative occupations tend to be highly correlated with morbidity risks. It is implausible to ask subjects their attitude toward one risk without some coherent explanation as to why a higher or lower level of that risk would not be associated with a higher or lower risk of the other.”

A recent paper by Harrison, List and Towe (Econometrica 2007) attempts to analyze the issue of background risk. The authors attend a 2004 Florida coin show. Individuals attended the show were given a series of binary choices. For each binary choice, those participating in the survey stated their preferred choice. For example, in the money specification, choices include:

Question Option A Option B
1 5/100 of $200; 95/100 $125 5/100 of $350; 95/100 $40
2 10/100 of $200; 90/100 $125 10/100 of $350; 90/100 $40
3 15/100 of $200; 85/100 $125 15/100 of $350; 85/100 $40
… … …

Then the authors decided to give individuals an option of making real world risk judgements. Four coins (denoted coins A, B, C and D) were displayed and the participants again were to choose whether they preferred option A or B in each pair.

Question Option A Option B
1 5/100 of Coin A; 95/100 Coin B 5/100 of Coin C; 95/100 Coin D
2 10/100 of Coin A; 90/100 Coin B 10/100 of Coin C; 90/100 Coin D
3 15/100 of Coin A; 85/100 Coin B 15/100 of Coin C; 85/100 Coin D
… … …

Their are two different treatments using the coins. The first is the graded treatment. Here the Morgan Dollar coins are presented with a 1-to-70 ‘ Sheldon scale‘ rating. This way, respondents can be sure as to the coins’ quality or worth. The second coin treatment is to use ungraded coins. In this case, the coins are presented without any certification as to their quality or grade. This way, the authors can introduce background risk into the game.

Results

Harrison and co-authors find risk aversion distributions (using CRRA utility functions) are very similar between the money payoffs and the graded coin treatments. However individuals are significantly more risk averse when in the ungraded coin treatment. In the authors own words: “the use of artificial monetary prizes provides a reliable measure of risk attitudes when the natural counterpart outcome has minimal uncertainty, but that it can provide an unreliable measure when the natural counterpart outcome has background risk.”

Healthcare Economist comments
One concern I have with the results is that of the lemon’s problem. Respondents may believe that ungraded coins are less valuable. If they were of high quality, why wouldn’t the vendor have paid to have the coins certified. Thus, the respondents may believe that high value ‘Coin C’ is actually of a much lower value. It could be the case that the respondents may select option A more frequently, which would inflate their risk aversion estimates. In the presence of a the lemons problem, the conclusion would be that individuals are game-theoretically rational, and not that they have concerns over background risk.

Nevertheless, I do appreciate that this paper examines risk in a more complex and rich setting than has previously been studied. Also, collecting data from outside the university environment is very useful.

Prospect Theory

July 31, 2007 in Economics - General, Experimental | Permalink

Yesterday, I talked about expected utility theory (EUT). Today I will write about one on the major departures from EUT: Prospect Theory. This theory was developed by Nobel laureate Daniel Kahneman and Amos Tversky (Econometrica 1979). The four key characteristics of prospect theory are:

  1. Individuals use decision weights, π(p), rather than probabilities, p, when making decisions.
  2. The value function is defined as deviations from a reference point. Thus, earning $100,000 this year is perceived differently for an individual earning $50,000 last year compared to one making $1 million last year.
  3. Individuals are risk averse with respect to gains but risk loving with respect to losses. This implies that the value function is concave for gains, but convex for losses.
  4. The value function is steeper for losses than for gains . This means that losses of $1000, hurt more than gains of $1000.

Why is there a need for prospect theory?

Much experimental evidence has shown that EUT does not only hold. Consider the Allais paradox. Which of the following lotteries would you choose:

  • A: ($1m, 1) vs. B: ($1m, .89; 0, .01; $5m .10)
  • C: (0, .89; $1m, .11) vs. D: (0,.90; $5m, .10)

Most people choose A and D. Yet it can be shown that under the EUT, these lotteries are mathematically equivalent and this leads to a preference reversal.

Another example is the following:

  • A: (6000, .45; 0, .55) vs. B: (3000, .90; 0, .10)
  • C: (6000, .001; 0, .999) vs. D: (3000,.02; 0, .998)

The majority of people surveyed here chose B and C. Again these A and C are two are equivalent lotteries as are B and D. The probability of winning in the latter pair is simply dived by 450. Thus, we see a preference reversal according to traditional EUT theory.

Also we see that people treat losses and gains differently.

  • A: (6000, .25; 0, .75) vs. B: (4000, .25; 2000, .25; 0, .5)
  • C: (-6000, .25; 0, .75) vs. D: (-4000, .25; -2000, .25; 0, .5)

Kahneman and Tversky find that 82% of people choose B over A, but 70% of people choose C over D. This implies that individuals are risk averse with respect to gains and risk loving with respect to losses.

Editing

Before utility functions are evaluated, Kahneman and Tversky say that choices are “edited.” The reason for this is 1) it helps to prevent obvious contradictions in which would occur if editing was not included, and 2) the editing process may more accurately reflect the process by which individuals make choices. Here are some of the ways which individuals edit:

  • Coding: Outcomes are perceived as gains and losses with respect to a reference point. The reference point may be the status quo or it may be an expectation. For instance, if my monthly before-tax earnings are $2000 but my after-tax earnings are $1500, I may perceive this as a $500 loss from my expected income rather than a simple $1500 gain.
  • Combination: Identical outcomes are simplified so that (100, .25; 100, .25; 0 .50) = (100, .50; 0 .50).
  • Segregation: Risky components are separated from non-risky components. For instance, (500, .7; 100, .3) is decomposed into a sure gain of $100 and a lottery of (400, .7; 0, .3).
  • Cancellation. This implies that when lotteries are compared, common outcomes are eliminated. “For example, the choice between (200, .20; 100, .50; -50, .30) and (200, .20; 150, .50; -100, .30) can be reduced by cancellation to a choice between (100, .50;-50, .30) and (150, .50; -100, .30).”

Evaluation

After editing, individuals make decisions according to the following utility function:

  • Σ π(p)v(x)

Tversky and Kahneman (J Risk Uncert 1992) show that empirically, the function gives an inverted-S shape (see graph). “…for both positive and negative prospects, people overweight low probabilities and underweight moderate and high probabilities. As a consequence, people are relatively insensitive to probability difference in the middle of the range.” As mentioned earlier, the value x is evaluated with respect to a reference point. It is either a gain or a loss. For gains, v”<0 but for losses v”>0. Also, because the utility function is steeper for losses than gains, v(x)<-v(-x). For a graphical display of a prospect theory value function, see a picture from the U of RI economics website.

Another lottery experiment to support prospect theory is the following:

  • A: (5000, .001; 0, .999) vs. B: 5
  • C: (-5000, .001; 0, .999) vs. D: -5

Of those surveyed, 72% of people choose A over B, but 83% of people chose C over D. This would seem to imply that individuals are risk loving for gains and risk averse to losses. However, the bulk of the evidence has shown that this is not the case. As mentioned above, it seems more likely that people tend to overweight low probability events and underweight high probability events.

While Prospect Theory still is not as popular in mainstream economics as Expected Utility Theory. This is likely due to the added data needed regarding how an individual is editing, and what the individual’s reference point would be. Further, one wonders whether or not individuals become more ‘rational’ in the expected utility sense if they receive feedback from repeated games. Nevertheless, Prospect Theory seems to very accurately explain many of the findings in experimental economics and more work in this area is needed.

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