27 Apr 2009

Taking the Good with the Bad: N. Gregory Mankiw

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I have two negative things to say about the analysis of Greg Mankiw, so let me start off with two positive things. First, check out this hilarious post where he busts the hypocrisy of Ben Bernanke.

Second, reader Stan Kwiatkowski sends me this blast from the past where Mankiw praises Barney Frank for citing Mises and Hayek. (!)

OK but now the bad news. Here I strongly criticize Mankiw’s notorious NYT op ed where he called on the Fed to promise large future inflation as a way to rescue the economy.

Finally, in this post Mankiw epitomizes a trend that really irks me among academic economists. What happens is that they set up a model of the economy that is unrealistic, but they forget that. And then when someone thinks about the economy in an unrealistic but different way, the academic economist pounces as if he has a monopoly on truth–even though the layman’s model’s result might actually be closer to reality!

I’ve criticized David Friedman and Steve Landsburg for this type of thing in the past. For our present example, Mankiw is pooh-poohing a website that offers a simulation of a rollercoaster ride the mimics the Dow Jones Industrial Average from 2007 to 2009. Mankiw comments:

But that can’t be right. Stock prices are approximately brownian motion, which means they are everywhere continuous but nowhere differentiable. In plainer English, “continuous” means that stock prices an instant from now, or an instant ago, are close to where they are now. But “not differentiable” means that the direction they move over the next instant is not necessarily close to the the direction they were heading over the last instant. A roller coaster with that property would be quite a ride.

Hang on a second. First of all, stock prices do not obey Brownian motion. As Mankiw says, Brownian motion is continuous, meaning that if a stock price goes from (say) $100 at 9:30 am to $110 at 9:31 am, then technically the stock price must have hit every intermediate price–$100.01, $100.02, all the way up to $109.99–for some definite time interval in between 9:30am and 9:31am. Obviously that’s not true, and it’s why Hu McCulloch actually favors Mandelbrot’s “stable Paretian” (a non-Gaussian) model of stock price movements, which allows discontinuous jumps (after a bad report on the company, or a war breaks out, for example). (Thomas Bundt and I have an article in the Review of Austrian Economics on this, but I don’t think the issue is online yet? I can’t find it online and it came out pretty recently.)

So sure, Mankiw is right that the rollercoaster simulation is just taking averages of the truly erratic movements in the stock price, but so what? That’s what the Brownian motion approximations used in cutting edge finance models do as well. (And we all know how accurate those models have turned out to be…)

Finally, if I may be a true geek: Is it really the case that a track involving continuous but non-differentiable pieces would be “quite a ride”? I admit that it’s not everywhere non-differentiable, but unless Mankiw lives in a ranch, I bet everyday he traverses a track that is continuous and (at several points) non-differentiable. Yet he probably negotiates it without too much trouble.

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