There is a long-standing debate over the difference between the social sciences and the physical sciences. It’s clear that economics is a social science. As such, many of the tools that we use in the physical sciences will simply not work. One of the tools is the bell-shaped curve or normal distribution.
Normal distribution is an appropriate way to measure a natural phenomenon. For instance, let’s say we put 50,000 adult, American males in a football stadium. Using normal distribution, it would be appropriate to say that the height of those adult males would be distributed around 70 inches with a standard deviation of plus or minus two. Weight and height would be normally distributed, too, among the males in the stadium.
However, if we decided to measure wealth, and Bill Gates was in the stadium, it simply would not work to apply a normal distribution. It wouldn’t work to say he is an outlier. He would completely blow the distribution because he’s likely to have more wealth than everybody else in the stadium put together. So, normal distribution modeling or bell-shaped curves work for natural phenomenon. They do not work for economics, a man-made phenomenon and social science. It’s important to understand the distinction.
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I think the point you are making is a good one, Carl. Economics is indeed a social science. I have seen many assumptions that appear to be rooted in the thought that it is a physical science and that certainly can lead to big misperceptions.
I don't go so far as to say that a bell-shaped curve can never apply in the social sciences, however. You give an example of Bill Gates and his wealth being so far out of the norm that his one case would throw everything off. Fair enough. But what if you left Bill Gates out of it? My guess is that there is some sort of normal distribution of wealth among earners. Is it not the case that there are a small number who earn large salaries, a small number who earn low salaries, and a larger number that earn salaries in the middle of the two extremes? I don't know the percentages. It just seems to me that the normal distribution concept to a considerable extent applies.
How about with saving? Again, my guess is that there are a small number who save large amounts, a small number who save zero, and a larger amount that save amounts somewhere in the middle.
I like the point you are raising. I would like to see it explored in more depth. But intuitively it would seem to me that there would be some application of a bell curve concept in the social sciences.
Rob
Weight, stadium, Bill Gates, normal — looks like this is “borrowed” from Nassim Taleb. Why don't you replicate the entire original argument with references to Mediocristan and Extremistan. At least his version is more entertaining.
Rob, Wealth and income follow what is called as a power law – eg the number of people with 2x the money is 5x smaller. This is very different from a normal distribution.
If the post had included the entirety of the original argument by Nassim Taleb instead of just extracting a little bit, then you would have gotten the full picture. See about an hour and 10 minutes into the audio at this site: http://www.econtalk.org/archives/2007/04/taleb_...
Come on…
I am a huge fan of Taleb's but I didn't know that he invented the example of the stadium. In fact I don't recall him using it so I am glad you provided a reference but to say that I “borrowed” it from him is certainly a stretch.
If I had to give attribution to everyone that used the height and stadium example then I would have to include my high school stats teacher, Mandelbrot, and Wikipedia.
If Taleb was the first and only one to use this example, my apologies for not being clear, but if you have read much of my stuff you know that two things are true:
[1] Much of my thinking is influenced by others
[2] I try to be careful about giving credit where credit is due.
Wealth and income follow what is called as a power law – eg the number of people with 2x the money is 5x smaller. This is very different from a normal distribution.
Thanks, Santa. I understand the distinction and it makes sense to me.
Are you able to say whether there are cases in the social sciences in which a normal distribution does apply? I'm no statistician. My thought is that there might be some circumstances in which a normal distribution applies and other circumstances in which a normal distribution would not apply. Perhaps a normal distribution cannot be assumed but should not be ruled out as a possibility either.
Rob
I think a middle ground makes sense, as I wrote in a posting about being all gaussied up.
Rob-
The point I was trying to make here is that in the case of measuring “risk”
and “return” of asset prices trying to make the “fit” into a bell shaped
curve just does not work. It is generally accepted that normal distributions
(the bell curve) happen among natural phenomena and not man made.
This gets back to the claim that Andrew Lo makes that economists have
“physics envy”, always looking for a simple model that will explain this
very complex structure. Returns/risk do not seem to fit into a simple model.
When you realize that risk & return are not normally distributed that has
broad implications because that core assumption (which is wrong) is the
foundation of so much of what we do in the investment and financial planning
worlds.
Carl:
Thanks for the helpful back-and-forth. All of the thoughts below are tentative ones.
I understand the point about “physics envy” and to a large extent I agree. I certainly have seen cases where those in the investing field have attempted to make their “findings” appear more scientific than they are and thereby to make them more persuasive. So I see value in this point.
I have doubts (but remain open to the possibility of being persuaded) about the idea that risk and return do not fit a bell-shaped curve. My guess is that what happened here is that the people doing the checking failed to make adjustments for valuations. The sort of bell-shaped curve that you would see starting from a time when stocks were insanely overvalued is going to be very different from the sort of bell-shaped curve that you are going to see starting from a time when stocks are priced insanely low. The range of returns at both times might be bell-shaped, but the bell would have different starting and ending points. A huge problem with most of the research done during the Passive Investing era is that it fails to adjust for valuations and thus sends us down all sorts of dead ends. I am not saying that I am certain that this is such a case. I am saying that it seems possible to me that this is such a case.
Your sentence “It is generally accepted that normal distributions (the bell curve) happen among natural phenomena and not man made” is certainly worthy of exploration but I am not sure what it signifies here. Long-term stock returns come from the productivity of the economy. Is economic productivity a man-made phenomena or a natural phenomena? I am not entirely sure.
How about the irrationality that causes volatility? If investing were a 100 percent rational endeavor, I believe that the return on stocks would be roughly 6.5 percent real per year. Economic ups and downs would not affect the annual return because investors would look ahead to when bad times would turn good and to when good times would turn bad. So I think it is fair to say that just about all volatility is caused by investor emotion. Is investor emotion man-made or a natural phenomenon? Again, I am not entirely sure.
Intelligence follows a bell curve, does it not? (I am not sure of this but this is my impression.) If intelligence follows a bell curve, it seems to me possible that the investor emotion that causes stock volatility might follow a bell curve too (and that stock returns might follow a bell curve once the adjustment for the starting-point valuation level was made).
My sense is that the root question here is whether last year's price crash should have been a surprise. There certainly are many who were surprised by it. I have heard some refer to it as a “black swan” event. But those who follow valuations had been predicting it for some time. For example, Shiller predicted it in 1996. My experience is that, when valuations are taken into consideration (as they always must be if we are to examine stocks from a rational perspective, in my view), many of the mysteries that appear before us when we use the Passive Investing model to analyze things disappear.
I certainly agree that we need to be careful about assuming that returns follow a bell curve. But I think it is a mistake to reach hasty conclusions re this point. My personal sense is that bell curves might apply in some circumstances if we made the necessary adjustments for valuations (which we have gotten out of the habit of doing during the Passive Investing Era).
Again, these are tentative thoughts. I certainly feel comfortable saying that this is a topic that needs to be explored in far more depth than it has been explored in the past.i certainly see value in the discussion, which has forced me to think about some things that I have not thought through carefully before.
Rob
want the differences between economic as a science and the physical science
i said i want the difference between economic as a science and the physical science
want the differences between economic as a science and the physical science
i said i want the difference between economic as a science and the physical science
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