Arnold Kling  

Expressing Economic Ideas

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Although it's a painful download, Tyler Cowen's talk on economics blogging is really outstanding. It runs quite counter to the angst that seems to be showing up lately on Greg Mankiw's blog.

One question that Tyler addresses is, "Why economics?" Why doesn't blogging take place so much in other academic disciplines?

There probably are many answers. I would frame my answer in terms of supply and demand.

There is an audience demand for clear writing about intellectual developments in many fields. In the natural sciences, however, my guess is that the cost of providing this sort of writing tends to be quite high. Only some extremely talented individuals are up to it. For now, their most remunerative outlets are books and other traditional publications, but perhaps some day an educational foundation will provide support for science blogging.

Another question Tyler poses is whether blogging leads to a "dumbing down" of economics. For now, my answer would be that on the contrary, the social utility of the papers that get play on blogs is higher than that of papers that go into journals but are ignored on blogs. So I think that blogging could be a force for positive change.

I can think of only one economic idea that I have never been able to express satisfactorily in non-mathematical terms. That is the Portfolio Separation Theorem, which says that the optimal market portfolio does not depend on individual risk preferences. When I discussed CAPM, I talked around that theorem. I still cannot come up with a good way to explain it. (The conditions under which the theorem holds may or may not apply in practice. That is not the issue here. My point is that I cannot convey the intuition behind the theorem.)

In general, results in economics fall into three categories:

a. Results that I am not aware of or have made no effort to understand.

b. Results that I do not think are important.

c. Results that I can explain without resorting to math.

The Portfolio Separation Theorem is the one result that I can think of that falls outside of those categories.


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COMMENTS (17 to date)
Josh H writes:

I'm really partial to this kind of post, because as a non-economist I'm always wondering what I don't know because I never did the coursework. I like to read economist's blogs because the best ones are extremely accessible and well-written and they give me a handle on what I know and what I don't know. So, thanks Arnold.

Fly Fisher writes:

Arnold,

Your approach to explaining economics is responsible for my considerable interest in the topic. I have advanced degrees in engineering, and I don't shy away from mathematics. But you've made the topic much more interesting for me.

We should never be afraid to 'dumb down' a topic to a level that is accessible to non-experts. For instance, see this Chronicle column
with the following quote:

Richard Feynman, the late Nobel Laureate in physics, was once asked by a Caltech faculty member to explain why spin one-half particles obey Fermi Dirac statistics. Rising to the challenge, he said, "I'll prepare a freshman lecture on it." But a few days later he told the faculty member, "You know, I couldn't do it. I couldn't reduce it to the freshman level. That means we really don't understand it."
neal hockley writes:

Arnold wrote:

In the natural sciences, however, my guess is that the cost of providing this sort of writing tends to be quite high

Why is this? Are you suggesting that nat scientists' opportunity costs are higher? why?

I wonder if the difference lies on the demand side. Perhaps few natural science subjects are so provocative of discussion? - advances in medicine are obviously extremely important, but we don't feel the need to discuss them.

dearieme writes:

Some Natural Science subjects can't be discussed without your risking being sacked. Elementary, my dear Watson.

Daublin writes:

The guy Mankiw quotes writes the following:


The hazard - and this applies as well to disciplines beyond economics - is that extraordinarily talented individuals may end up, like lab mice drinking sugar water, spending more time blogging than they should, even though their comparative advantage is smaller in blogging than it is elsewhere.

What I wanted to post on Mankiw's blog, but could not, is that his comparative advantage is huge. He explains things well, and he maintains an excellent tone of discussion. May econ bloggers post crap economics and put all their energy into clever turns of phrase.

To contrast, I have no clue what his comparative advantage is with economics research. I have long worried, though, about the concept of the best guys in a field putting all their energy into furthering the field, and none into spreading the findings to the wider population.

eric frankenstein writes:

Tobin's Portfolio Separation Theorem is the least intuitive part of modern portfolio theory. But I think the difficulty in explaining it reflects a deeper problem: it is based on the mean-variance preferences. Given preferences are linear in the variance, and opportunity sets are linear in volatility, you the highest sloping set of feasible portfolios gives you access to the highest utility, which is the line that originates at the Risk Free rate and then kisses the tangency of the convex hull of risky portfolios.

But I never understood why preferences for risk and return should even be approximately linear in variance. I understand why they are more tractable that way from a modeling perspective, but intuitively, most investors are familiar with volatility, knowing that the volatility of a stock is 35%, or that the volatility for the US stock market is about 17% on average. This is the annualized standard deviation of returns for a portfolio, meaning that 67% of all observation are within one standard deviation of this number. So a portfolio with a volatility of 5% will be the expected return +/- 5%. Variance, is the square, so saying the variance is 2% is kind of confusing, because this implies your annualized return will be the expected return +/- 2%^.5, or 14%. No one I know thinks this way. Sharpe ratios, or Information Ratios, which are ubiquitous in asset management, look at volatilities, not variance, because the intuition is much more straightforward.

Further, assuming preferences are linear in variance, means that moving from 5% to 10% volatility, is just as painful as moving from 20% to 22% volatility (square the numbers, the differences are the same). This is kind of bizarre, not obvious at all.

FMB writes:

This is the best argument I've heard to motivate the relevance of variance as a linear term when determining the cost of risk. I recognize this is hand-wavy in places and perhaps more mathy than necessary, but certainly most readers should be able to follow.

outside of a casino, you would normally need to be paid to bet some material amount on a coin flip.

a) Say you would want x to bet $1k on a coin flip.

b) How much would you want to commit up front to do it twice in a row? Seems like 2x should be about right (assuming $2k wouldn't come close to bankrupting you).

c) Now how much would you want to bet $2k on a single flip? Call that y.

d) Suppose you flipped a coin to decide whether to play game c -- heads you do nothing, tails you receive y but must flip another coin for $2k. Since you're neutral about c, this should require no additional compensation.

d is (just about) equivalent to accepting y/2 to flip 2 coins for $10k, so consistency suggests that y/2 = 2x -> y = 4x. In other words, doubling the size of the wager on a coin flip should lead you to demand 4 times the compensation for risk. Anything materially different is likely internally inconsistent; certainly demanding compensation linear in standard deviation is not possible as a reasonable utility function.

General Specific writes:

I've always thought economic blogs are popular because economics is ideological and political. It's not called political economy for nothing. And consider the ideological and substantive disagreement between economists. The differences between physicists would not interest people on a day to day basis. But economists have opinion differences that impact day to day policy and regulation. People are interested in that.

Sociology also comes to mind, but I think economists have probably pre-empted sociological discussions, e.g. the freekonomics and caplan-esque approach to economics.

I think that's what makes economics blogs popular.

Note: Global warming blogs are also popular. As is peak oil or other energy blogs. Also note that people with money fund economic blogs for legitimate communication and for more questionable propaganda purposes.

9160 writes:

I agree with Josh, reading economist’s blogs are so very interesting because they talk about the different views on certain topics. And because I do not know near enough about economics these blogs help me to better understand complex concepts that need a thorough examination and explanation by professional economists. Sometimes I may not completely understand what some of these economists are talking about, but because they seem so passionate about it I feel the need to research in more depth.

And yes, there are people out there blogging about things that they know nothing about, but does it really bother anyone? I mean just skip over there blog, don’t read it, and don’t respond. I don’t think that people blogging about economics is in anyway leading to a “dumbing down” of economics.

Matt writes:

Google physics blogs and economic blogs. The number that is reported is not all that different. Both searches used .22 seconds. My bookmark list is expanding, thanks for the reminder.

eric frankenstein writes:

FMB: but if you are indifferent to c, then the probability of the coin in d is immaterial: 0.5, 0.005, 1, which gives an infinite number of answers.

FMB writes:

EF: the coins are all presumed fair, that's a condition for a-c. In d, you would be indifferent to the p for the first coin since you're neutral about both heads and tails, but the 2nd coin had better be the same as in c, i.e. fair: if not then d is no longer equivalent to b, betting twice.

The math as given applies if all coins are fair and there's only one answer. If you change the fairness of the coins, you need to make sure that the asserted equivalence still applies.

An equivalent but messier example with a (WLOG) 2:1 coin, where you risk $1k on the unlikely side to win $2k would look something like this:

a) demand x to play that game, or the reverse (yes I've added an assumption that skew is irrelevant).
b) demand 2x to play it twice.
c) demand y to play for twice the stakes

The payoff of playing it twice, b, is:
1/9 $4k (win twice)
4/9 $1k (win once, lose once in either order)
4/9 $-2k (lose twice)

This is equivalent to:

1/3: risk 2k to win 4k on a 2:1 coin (the top payoff plus half the bottom payoff)
2/3: risk 2k to win 1k on a 1:2 coin (the middle payoff + half the bottom payoff)

So y/3 + 2x/3 = 2x
y = 4x, the same answer as before. Replacing 1/3 with p throughout (including in particular rephrasing bet twice as some combination of no bets, betting 1 unit, and betting 2 units) leads to getting the same result independent of p.

Or did you mean something else I'm missing? Note that I'm definitely ignoring a bunch of possible higher order effects. This is intended as (strong) motivation for a position, but not quite a proof.

FMB writes:

Where I said:

In d, you would be indifferent to the p for the first coin since you're neutral about both heads and tails, but the 2nd coin had better be the same as in c, i.e. fair: if not then d is no longer equivalent to b, betting twice.

I meant: In d, you would be indifferent to the p for the first coin since you're neutral about both heads and tails, but the 2nd coin had better be the same as in c, i.e. fair. AND if the first coin IS NOT fair, then d is no longer equivalent to b, betting twice on a fair coin.

The example provided should make this (tolerably) clear to anyone still with this thread.

eric frankenstein writes:

fmb: well, I have to say your example is at the least, not 'easy'. If you are indifferent to the fairness of the coin flip in d, it is unnecessary, so I don't see how it adds to your logic.

fmb writes:

Sorry, I was going off on a tangent trying to motivate the relevance of variance (instead of stdev) as the proper measure of risk in a utility function in response to your first comment. I did not mean to cite this as especially easy, though it's the easiest argument I know. Based on the obvious rhyme for your handle I also went faster than I would have for a general audience.

The point of the first coin flip in D was to make the payoffs and chances equivalent to B and therefore the utility the same, without that flip the payoffs are not the same. To sum up: betting one stake twice (B) is equivalent to a 50% chance of betting twice the stake (D), i.e. they both have a 25% chance of winning 2 stakes, a 25% chance of losing 2 stakes, and a 50% of no money changing hands. So betting twice the stake should be 4 times the (negative) utitility of betting 1 stake. If the negative utility due to risk is not linear in variance, then you can construct 2 different coin flip games with the same payoffs but different utilities.

eric frankenstein writes:

fmb:"The point of the first coin flip in D was to make the payoffs and chances equivalent to B and therefore the utility the same, without that flip the payoffs are not the same"

This is where I lose you. *if* you assume the probability of D is 0.5, you get mean variance preferences in your initial example. But D could be anything bounded by 0 and 1 because you are indifferent to C, in many cases not generating mean variance preferences. Does that also prove those preferences exist? I get the sense you are saying that as X+Y=Z, because Y=0, if X is 7, this proves Z is 7. QED. But if X is 8, Z is 8, etc. So you really aren't showing how these preferences arise out of some deeper, more intuitive preference, just how a sequence of bets is equal to a single bet assuming mean-variance preferences.

fmb writes:

Can you elaborate on how a non-0.5 probability in D leads to non-mv preferences? As I see it, when p != 0.5, there's no relationship that allows you to solve for the utility of a $2k bet (y) as a function of the utility of a $1k bet (x), so there's no conclusion available to draw about the nature of utility (where you seem to say that you can draw a conclusion that utility is *not* linear in variance). If, as in a previous comment, you shuffle enough other p's around so that there is a relationship, then it leads back to the utility growing as the square of the scale of the wager.

Happy to continue this offline if you want: fbaseggio hotmail. I'm apparently not following your critique, but remain interested in working out where the misunderstanding lies.

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