Wednesday, March 15, 2006

Cognitive reflection and decision making

Whether you would prefer $1,000 for sure or a 90% chance of $5,000 depends on your risk-aversion. Whether you would prefer $100 now to $120 in 3 months time depends on your time preference. Economists typically accept different levels of risk aversion or time preference without explanations. But Shane Frederick, in a recent Journal of Economic Perspectives, tries to understand why people answer as they do in terms of their cognitive skills.

Answers to the following simple test seem to explain a lot:
1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?
2) If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?
3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?
This cognitive reflection test measures ability to solve math problems and the willingness to reflect on and check answers. The questions here all have intuitive but wrong answers - you have the advantage of being warned!

Frederick gave this test to 3500 respondents, mostly students at US universities. Participants also answered a survey about how they would choose between various financial payoffs and time-oriented questions like how much they would pay to get a book delivered overnight.

Getting the math problems right predicts nothing about most tastes but high scorers - those who get all questions right - do prefer taking risks even if, on average, it hurts them. So, for example, a third of high scorers preferred a 1% chance of $5,000 to a sure $60. These smarty-pants are also more patient. Particularly when the discount rate, is large. Choosing $3,400 this month over $3,800 next month implies a discount rate of 280%. Yet only 35% of low scorers - those who missed every question - said they would wait, while 60% of high scorers preferred the later payoff.

Men and women show different results. Being smart makes women patient while it makes men take more risks. High-scoring women show slightly more patience than high-scoring men but differences in risk-taking are much larger. High-scoring women are about as willing to gamble as low-scoring men, while low-scoring women are even more risk-averse. Thus 80% of high-scoring men would choose a 15% chance of $1 million over a sure $500, compared with only 38% of high-scoring women, 40% of low-scoring men and 25% of low-scoring women.

The connection between cognition and risk preferences challenges the prospect theory of Daniel Kahneman and Amos Tversky. They observed that people would accept larger risks to avoid losses than to achieve gains, even when the two choices were mathematically equivalent. The same person might take a sure $100 instead of a 50% chance of $300, yet prefer a 50% chance of losing $300 rather than a sure $100 loss. This result is a major finding of behavioral economics. But according to Frederick prospect theory works for the low-scoring group but high scorers treat potential gains and potential losses about the same.

The general idea is that time preference and risk attitudes measure cognitive ability. Preferences are not arbitrary but can be understand in terms of cognitive ability. In my own work on substance abuse I have noted that people who consume narcotics have high levels of impulsiveness and take unreasonable risks with their lives.

This survey of the Frederick paper is based on Virginia Postrel in the New York Times. The full paper in JEP is good reading. The correct answers to the test are given in the comment below.


hc said...

The correct answers are 5 cents, 5 minutes and 47 days.

Sam Ward said...

Nobody should be taking the 1% chance of $5000 over the guaranteed $60. Your expected return is $50 vs $60. These are the same people who play the lottery. (And the same people who provide me with my living)

hc said...

I agree Sam its weird. The 'smart' people went for risky options even when 'on average' it hurts them so its not just a matter of overcoming irrational risk aversion.

I am doing some work on economics of gambling, so I should post on this to see what you think.

rabee said...

Suppose that you did the following experiment:

You ask people to answer the same question:

1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

If they get the right answer, then you give them a hundred dollars. Otherwise, they get nothing.

How many people will get it right? I suspect that most people will get it right.

Asking a people to waist their time answering silly questions for free is simply going to give you information about how much people value their time.

People who do waist their time and answer correctly
don't valued their time as much as a person who pays little attention to the survey.

Further people who don’t value their time are more likely to be risk takers. That is pretty obvious.

conrad said...

I'd take the 1% chance of $5000 (particularily if I don't have to pay anything to get it). If I get $50 without having to do anything, its no big deal (to me at least). Alternatively, $5000 I wouldn't mind at all. Thus the real worth of the money is exponential too me. With $50, I can't do much, but with $5000, I can really do something I want to. Thus the effective worth is more than 50 * 100.

A similar principle can be used to understand why I hate enforced superanuation and why I didn't pay my HECS loan off at the cheaper lump sum rate.

It is because the effective value of the money at different stages of my life is different (more then and less now) -- thusI assume that I will enjoy the same amount more now than later.

Now, is that really a cognitive bias, or is it a sensible evaluation ?

hc said...

Rabee's point worries me and I will check out if they controlled for it. It applies also to the verbal tests of 'opportunity costs' discussed a few weeks ago. Here economics PhDs were found to have poor understanding of economics. Again it could be that they couldn't be bothered putting effort into answering an unrewarded question. In a post on Crooked Timber one interviewee said as much.

When I did the first of the 3 questions I got it wrong - partly because I didn't take it seriously and was only half-concentrating. When I found I was wrong I felt silly and put more effort in - and got the last two correct.

I don't concentrate all the time - I'll tune out if I feel the stakes are low.

Anonymous said...

This research is pathetically sexist. Men seem more "cognitively reflective" than women. I guess it's not surprising - Amos Tversky was extremely sexist and a pathological womanizer. His legend lives on.

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