Tuesday, October 12, 2010

Are misconceptions worse if they're about facts or concepts?

In a post on Marginal Revolution called "Economic Misconceptions," Alex Tabarrok says:

Students typically come to an economics class with many misconceptions, not just random errors but systematic biases.
He gives several examples from a 2009 study by a macroeconomics professor who surveyed his students. For instance:
When asked about profits as a percentage of sales the median student guessed 30% (actual rate, closer to 4%).
In each example, the "misconception" is a guess about a specific fact, which is always in the form of a percentage. But I wonder if this is such a good way to tell whether someone has "misconceptions" about economics. The implication is that we should be good at estimating percentages on the spot.

But why would you think the human mind was well-equipped to do that? Maybe economics professors have some misconceptions about how people think or how they should think.

I notice that all the questions asked of the students (at least the ones given in the blog post), the correct answer was either a tiny or huge percentage. For instance, in the example I quoted, the correct answer is tiny — 4% — and in another question, the correct answer is huge — 248% (in case you're wondering, that's the increase in American incomes since 1950).

By contrast, the median wrong answers the students gave were 35%, 30%, 11%, and 25%.

The students might not have had any fundamental misconceptions about how the world works — maybe people are just bad at guessing percentages. So they gravitate toward mid-range ones like 25%, 30%, 35% because they feel like these are relatively safe guesses. They really have no idea, but they don't want to be too far off.

I've also seen polls asking what percentage of Americans are Jewish. I can't find these now, but I remember the answers being around 25% or 30%. The correct answer is between 1% and 2%.

But again, does this represent a serious problem that should be corrected? Anyone who needs to know the actual statistic can easily look it up. Beyond that, is it so bad if people intuitively imagine a given minority group as making up a much larger chunk of the population than it actually does?

I'm more convinced by this New York Times column by Robert H. Frank, which focuses not on people's success or failure at guessing statistics but on their understanding or misunderstanding of basic concepts. And Frank targeted not just economics students but economics professors:
Consider, for example, the cost-benefit principle, which says that an action should be taken only if its benefit is at least as great as its cost. Although this principle sounds disarmingly simple, many people fail to apply it correctly because they do not understand what constitutes a relevant cost. For instance, the true economic cost of attending a concert -- its ''opportunity cost'' -- includes not just the explicit cost of the ticket but also the implicit value of other opportunities that must be forgone to attend the concert.

Virtually all economists consider opportunity cost a central concept. Yet a recent study by Paul J. Ferraro and Laura O. Taylor of Georgia State University suggests that most professional economists may not really understand it. At the 2005 annual meetings of the American Economic Association, the researchers asked almost 200 professional economists to answer this question:

''You won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Tickets to see Dylan cost $40. On any given day, you would be willing to pay up to $50 to see Dylan. Assume there are no other costs of seeing either performer. Based on this information, what is the opportunity cost of seeing Eric Clapton? (a) $0, (b) $10, (c) $40, or (d) $50.''

The opportunity cost of seeing Clapton is the total value of everything you must sacrifice to attend his concert -- namely, the value to you of attending the Dylan concert. That value is $10 -- the difference between the $50 that seeing his concert would be worth to you and the $40 you would have to pay for a ticket. So the unambiguously correct answer to the question is $10. Yet only 21.6 percent of the professional economists surveyed chose that answer, a smaller percentage than if they had chosen randomly.

Some economists who answered incorrectly complained that if people could apply the cost-benefit principle, it did not really matter if they knew the precise definition of opportunity cost. So the researchers asked another group of economists to answer an alternative version of the question in which the last sentence was revised to read this way: ''What is the smallest amount that seeing Clapton would have to be worth to you to make his concert the better choice?'' Again, the correct answer is $10, and although this time a larger percentage got it right, a solid majority still chose incorrectly.

When they posed their original question to a large group of college students, the researchers found that exposure to introductory economics instruction was strikingly counterproductive. Among those who had taken a course in economics, only 7.4 percent answered correctly, compared with 17.2 percent of those who had never taken one.

Teaching students how to weigh costs and benefits intelligently should be one of the most important goals of introductory economics courses. The opportunity cost of trying to teach our students an encyclopedic list of technical topics, it seems, has been failure to achieve that goal.

7 comments:

Ed Dolan said...

Good post. Opportunity cost is hard to understand and full of paradoxes. Here is one I sometimes try on my students:

Suppose La Pavilion is way above your usual choice of restaurants. Dinner there will cost you $150. It is good, but you would never, never go there on your own account.

So, which birthday present would give you the most pleasure?

1. A nonrefundable gift certificate for a meal at La Pavilion

2. A gift certificate at LP that you can turn in for $150 in cash if you choose

3. A check for $150, paper-clipped to a review of the glories of LP, hinting that you should spend the money on a meal there.

My answer is "1". Why? Because there is no opportunity cost to using the nonrefundable gift certificate. Your enjoyment of the meal is pure pleasure, no regrets. With 2, and even more with 3, while you are eating, you are thinking about what else you could have spent the money on instead, so the pleasure you would have gotten from the other uses is mentally being subtracted from the pleasure of the meal even while you sip your Paulliac.

Furthermore, looking back, you remember the nonrefundable meal with pure fondness. With option 2 or 3, every time you are short of cash, you look back on the meal at LP with regret that you didn't take the $150 instead.

Nonetheless, every econ textbook will tell you the gift of cash gives maximum utility. The moral: don't ask an economist for a recommendation when you are trying to think of what to give your beloved for his/her birthday!

John Althouse Cohen said...

Interesting thought-experiment. I agree that "1" seems best, although "2" and "3" are tempting.

As you mentioned, economists can easily dismiss the value of traditional gift-giving. Joel Waldfogel came out with a book last year called Scroogenomics. His pitch said:

When we buy for ourselves, every dollar we spend produces at least a dollar in satisfaction, because we shop carefully and purchase items that are worth more than they cost. Gift giving is different. We make less-informed choices, max out on credit to buy gifts worth less than the money spent, and leave recipients less than satisfied, creating what Waldfogel calls "deadweight loss."

I notice that even the first blurb quoted on his own promotional page did not give unambiguous praise:

"Leave it to an economist to make an impassioned argument for why we shouldn't give gifts, especially during the holidays."--Los Angeles Times

Here's a PDF of an academic economics article by Waldfogel, where he made a similar case. You mentioned cash gifts, and Waldfogel analyzes these as an alternative that often has higher utility (though he says it depends on who gives them). Of course, if everyone gave each other cash gifts, the value would partly or even entirely cancel out. I know of a brother and sister who used to give each other presents for Christmas but apparently weren't too enthusiastic about the exchanges. Then, one Christmas, they each decided to give each other cash -- in the same amount. They stopped exchanging Christmas presents after that. Yet Waldfogel would presumably consider this an optimal outcome, since he thinks gift-giving tends to waste value, unlike individuals buying things for themselves in conventional market transactions (in which the giver and receiver each value what they get more highly than what they give up).

I got those links from this NYT blog post by Harvard economics professor Edward Glaeser, who defends gift-giving against Waldfogel's attack. Glaeser has the insight that "value" isn't the only relevant economics concept; there's also "signaling":

Signaling has many virtues, and it is hard to think of anything more valuable than showing affection for others. In the schooling context, signals allow the matching of people to jobs. In the context of gift-giving, providing presents increases the welfare of others by giving them the sense that they are loved.

Similarly, the first commenter on the NYT post demolished the Scroogenomics thesis in a single sentence:

Joel Waldfogel completely misses the point by viewing the annual holiday tradition of gift-giving as a mere transfer of goods rather than a more complex process of emotional connection between those people who care about each other.

The economist's devaluing of gift-giving seems to ignore our "revealed preferences": we keep giving gifts year in and year out. Now, one could impute this to blind, irrational tradition. But many people would be genuinely distraught if we all stopped giving gifts. This suggests there's something limited about economics. The old saw that economists "know the cost of everything but the value of nothing" is too simplistic. Perhaps economists can take into account subjective value. But I don't know of any way to do this that wouldn't be highly ad hoc.

BJP said...

Ed, really? Doesn't the fact that you would never, never go to LP on your own account indicate that $150 cash is worth more to you than the dinner? So, 3 would give the most pleasure; burn the review without reading it, cash the check, and spend the $150 on whatever alternate thing is better than the LP dinner.

If you can't do that because burning the review would be impolite, then the three options don't have the same dollar value because you have failed to account for the cost of cashing in.

Assistant Village Idiot said...

I think the corrective that people are not good at estimating, and want to make a safe guess, is reasonable. However, the general topics are much in the national discussion. The questions measure current events knowledge, especially in relation to economics. For that reason, I would be less concerned if students were making safe guesses, but in the right direction. With 0% inflation, I'm not worried if they are afraid to guess an extreme like zero and guess 3%. Guessing 11% does concern me. Similarly, had the students guessed that incomes since 1950 had almost doubled, I would not be concerned that they didn't get anything like 248%. (We also get into a modern history general knowledge problem, wondering if they know it was just after WWII and what the economy was then.)

Grobstein said...

The bad figures plausibly stand for conceptual misunderstandings. For example, economics students should know that profits are generally competed away -- this is a consequence of the one micro model everyone should understand. Grasping the concept should lead students to guess a small figure for profits; 30% is a large figure (and half of students guessed more). (Now, in real life, businesses do seem to earn profits sometimes. Perhaps this highlights a limitation of the very simplest models. Perhaps some students guessed 30% because they grossly overestimated the share of firms that are in monopolistic markets, or something. But the simpler interpretation of the data, I think, is that most of them just didn't get it.)

I think your remark about tiny vs. huge percentages undermines your general thesis here. Students needn't be able to estimate exact figures closely, but they should know conceptually whether a quantity is likely to be huge or tiny -- and that is all that was asked of them here. It is a conceptual error to give a "mid-range" guess when your theoretical background suggests the number should be approximately zero. Like you say, they reveal that "they really have no idea" about the underlying mechanisms that should guide their answers.

The survey of economists on opportunity costs is disturbing.

John Althouse Cohen said...

I think your remark about tiny vs. huge percentages undermines your general thesis here. Students needn't be able to estimate exact figures closely, but they should know conceptually whether a quantity is likely to be huge or tiny -- and that is all that was asked of them here. It is a conceptual error to give a "mid-range" guess when your theoretical background suggests the number should be approximately zero. Like you say, they reveal that "they really have no idea" about the underlying mechanisms that should guide their answers.

I don't know that this undermines my thesis. My thesis might still be wrong, but I think what I've said is at least internally consistent. I'm saying people are simply, across-the-board bad at estimating percentages. When they give guesses like "25%," they don't actually mean much at all. That could be code for: "OK, you got me — I can't even come close to getting this right, but I don't want to be embarrassed, so I'll just stick with something in the middle so I'll have something to say."

The fact that they're bad at answering these questions is, by definition, less-than-ideal. But it's not obvious why this is such a bad thing. Instead of bemoaning economics students' "conceptual errors," why don't we just accept that this is a trivial glitch in a lot of people's thinking and focus on the ways people are good at thinking?

Here's an example. One of the questions is how many people are earning the minimum wage. The median answer is 35%. The correct answer is "2.3% of hourly-paid workers and a smaller share of all workers." As the first comment on the post says, it's not clear why we should even care about students botching this question, when the question itself seems almost designed to throw them off:

I have to say that I find the % working at minimum wage highly misleading. As a student, I never knew anyone who worked at exactly minimum wage. Instead, it was minimum wage + 50cents or the like. When minimum wage rose, so did their wages. I think if you measured how many people's wage rates depend directly on the minimum wage, you would get a far more relevant answer.

In the real world, how often does one need to be able to give a close guess about an arcane statistic off the top of one's head? My theory is that this is a skill that's not very useful or common. So if you try to test this skill, you'll get people desperately clinging to the middle range between, say, 10% and 90%, rather than guessing a figure that seems "extreme." People just aren't inclined to pull figures like 0.1% or 1,000% out of the blue. I don't see why this would impede them from doing a good job of thinking about such numbers if they actually come up in a concrete situation.

David Schwartz said...

Cost benefit analysis is really not all it's cracked up to be.

I offer you either a free Mars bar or a free Snickers bar. You value the Mars bar at $1. You value the Snickers bar at $1.

While any rational person would see this as a pure win, anyone with an understanding of economics would see this as the nightmare scenario.

To take the Mars bar, I must give up the opportunity to have a free Snickers bar, that's break even. To take the Snickers bar, I must give up the opportunity to take a free Mars bar. So neither bar is worth taking. And taking neither bar gives up only two opportunities each with a net value of zero. So taking neither bar is just as good as taking either bar.

Really.