In this Saturday’s New York Times, in an article titled The Chasm Between Consumers and the Fed, I found the most amazing chart:
Of course I am not a financial journalist, so I have absolutely no understanding of the gigantic amoeba-like-shaded-area in this chart. But it looks very cool and very much like it represents something about which the article has much to say. Sadly, however, the New York Times does not provide the methodology it used in obtaining the amazing fact that six of the points can be grouped together while those other two points are excluded from the party. What astounding mathematical finance model did the Grey Lady use to come up with this plot (I’ll be it involves Ito calculus)?
Frustrated by the lack of transparency, I decided that it would be best if I tried to come up with my own methods and models for obtaining this graph. My first attempt, after scouring the economics literature and using some advance methods (related to integrating over Banach spaces) was the following
As you can see this model seems to pick out the overall rate of return as the defining characteristic. After much great reflection, and reacquainting myself with some obscure results from the theory of hyperbolic partial differential equations and new deep learning techniques from machine learning, I was able to tweak my model a bit and obtained the following
Now this is a beautiful plot, but it clearly does not reproduce the graph from the New York Times. What exactly, was I missing in order to obtain the giant amoeba of correlation?
But then I remembered…I’m not a financial journalist. I’m a physicist. And so, I took a look at the stats notes I took as a physics major at Caltech, quickly plugged in some numbers, and obtained a new, reality based, version of the plot
Well it’s not the New York Time plot. But I like it a lot.
O brave new quantum world!
Dave, this post is awesome. It reminds me of another good one in this regard: http://economistsview.typepad.com/economistsview/2007/07/yet-again-tax-c.html
If I had an undergrad who did crap like this on a homework assignment I would mark it zero.
Nothing to add, just thought this was an awesome post.
Bravo, Dave.
The chart is bizarre. The article was bizarre. And your post was brilliant.
Notably, there was no mention of the difference between real after-inflation returns and nominal returns. For example, in the 1930’s prices were falling at -2.1% per year but the stock market was unchanged, so investors were actually making money (in real terms). Whereas in the 1970’s inflation was rising at 7.1% and stocks were rising at 5.9%, so investors were actually losing money (in real terms) even though their brokerage statements showed them to be making money.
But the one thing that stands out in the text and chart is that it’s fairly rare for the Federal Reserve to actually achieve it’s stated goal of “stable” inflation of 2%! Let’s revisit this in the year 2080 and see if anything has changed.
It seems your fundamental problem was in trying to reproduce the chart quantitatively.
They’re financial journalists – it’s a “guide to the eye.”
Remember, these are the guys who in the height of their quantitative bent believed that Gaussian statistics were totally appropriate for modelling the markets.
I think there is a simple economic explanation for your ‘amoeba’.
The two decades which are not part of the amoeba are the 1930s (aka decade of great depression) and 2000s (financial crisis). It makes sense to exclude these two in a discussion of stock market returns vs. inflation. Inflation is often fueled by high employment, wage pressure, consumer demand – this mechanism broke down in the 1930s and also in the 2000s, I guess.
I think the article makes a similar point.