How risk averse are you?

Economists have long been interested in trying to figure out people's tolerance for risk.  Such information is useful in predicting, for examples, which crops farmers will plant, which stocks investors will buy, how much insurance is bought, how much of a premium one is willing to pay for organic food, and how fast people drive.  Of course, we don't expect all people to have the same risk preferences, so for decades economists have sought to identify tools and methods that will allow them to discover different people's levels of risk aversion.

One of the most popular techniques is the so-called Holt and Laury (H&L) multiple price list (MPL) based on this paper in the American Economic Review.  As of this writing, the paper has been cited 3,900 times according to googlescholar, making it one of the most cited economic papers published in the last 15 years.  The approach requires people to make a choice between a relatively safe lottery (e.g., 10% chance of $2 and a 90% chance of $1.60) and a relatively risky lottery (e.g., 10% chance of $3.85 and a 90% chance of $0.10).  Then, the subject repeats the choice except the probability of the higher payoffs increases.  This process is repeated again and again about 10 times until one gets to the very easy choice between 100% chance of $2 and 100% chance of $3.85 (If you don't know which of those you prefer, give me a call.  We need to talk).  One very crude measure of risk aversion is simply the number of times a person chooses the relatively safe lottery over the relatively risky lottery.  

The H&L method is relatively easy to use, which goes a long way toward explaining it's popularity.

With all that as a backdrop, I'll point you to a new paper I published with Andreas Drichoutis in the Journal of Risk and Uncertainty. We point out an important problem with using the H&L method as a measure of risk aversion and propose a new, yet equally easy to use, MPL that helps solve the problem.  If you're not an academic economist, the rest of this may get a bit wonky, but here goes:

In what follows, we show that H&L’s original MPL is, perhaps ironically, not particularly well suited to measuring the traditional notion of risk preferences — the curvature of the utility function. Rather, it is likely to provide a better approximation of the curvature of the probability weighting function. We then introduce an alternative MPL that has exactly the opposite property. By combining the information gained from both types of MPLs, we show that greater prediction performance can be attained.

Here is one of the main critiques of H&L, which relates to whether people weight probabilities non-linearly (the parameter γ is a measure of the extent to which probabilities are "distorted").

Now, consider a simple example where individuals have a linear utility function (i.e., they are risk neutral in the traditional sense), U(x) = x. With the traditional H&L task, a risk neutral person with U(x) = x and γ = 1 would switch from option A to B at the fifth decision task. However, if the person weights probabilities non-linearly, say with a value of γ = 0.6, then they would instead switch from option A to B at the sixth decision task. Thus, in the original H&L decision task, an individual with γ = 0.6 will appear to have a concave utility function (if one ignores probability weighting) even though they have a linear utility function, U(x) = x. The problem is further exasperated as γ diverges from one. Of course in reality, people may weight probabilities non-linearly and exhibit diminishing marginal utility of earnings, but the point remains: simply observing the A-B switching point in the H&L decision task is insufficient to identify the shape of U(x) and the shape of w(p). The two are confounded. While it is possible to use data from the H&L technique to estimate these two constructs, U(x) and w(p), ex post, we argue that more information is contained about w(p) than U(x) in the original H&L MPL.

The other problem we point out with the H&L approach is that it provides very little information about the shape of U(x) as only four dollar amounts are used in the design (and only two differences are uniquely identified).  Instead, 10 different probabilities are used, which provides much more information about the shape of γ.  What can one do about this if they truly want to know about the shape of U(x)?  We suggest a new kind of payoff-varying MPL.

Given the preceding discussion, one might ask if there is a simple way to use a MPL that yields more information about U(x) and, at least in some special cases, avoids the confound between w(p) and U(x)? One can indeed achieve such an outcome by following an approach like the one used by Wakker and Deneffe (1996) in which probabilities are held constant. Using this insight, we modify the H&L task such that probabilities remain constant across the ten decision tasks and instead change the monetary payoffs down the ten tasks.

I'm under no allusion that our new MPL will become nearly as popular as the original H&L task.  But, if we even get one-tenth their number of citations, I'll be thrilled.