It’s easy to find a correlation between two macro variables, as the same sort of factors (inflation, output growth, interest rates) tend to affect all sorts of financial and macro variables. For that reason, one of the most useful statistical tools is time-varying correlations.
For example, when I studied the Great Depression I recall reading a year end summary of the 1931 stock market in the New York Times. They summarized the US stock market month by month, and mentioned German problems in all the summaries of the last 7 months, but none of the first 5 months. And sure enough, during the last half of 1931 the price of German war bonds was highly correlated with US stock prices.
But how can one prove cause and effect? Lots of things might have affected both German war bond prices, and US stock prices. For example, signs of a strong economic recovery worldwide might boost the value of both assets. On the other hand, if German problems were depressing US equity markets, then you’d expect a strong correlation between German war bond prices and US equity prices during periods when there were lots of problems in Germany (late 1931), but essentially no correlation during periods when German problems were not particularly significant (early 1931.) And that’s exactly what I found. Or to take another example, Steve Silver and I found that US industrial production became negatively correlated with nominal wages after 1933, precisely when New Deal programs began to artificially raise nominal wages.
Almost a year ago David Glasner mentioned that he was working on a similar study, this time estimating the time-varying correlation between US inflation expectations and US equity prices. He has frequently sent me very significant results, but I held back from mentioning them in order to let him get the project completed before publicizing the results. He has now placed the paper at the SSRN web site, where others can read it. In the meantime I notice that others have observed this pattern, indeed the commenter Gregor Bush recently mentioned some similar results.
It is well known that there is normally little correlation between US inflation expectations and US stock prices. Higher inflation might boost stock prices if associated with growing aggregate demand, but higher inflation can also lead to expectations of tight money, or higher taxes on capital, since capital income is not indexed. Indeed the high inflation of the 1970s seems to have depressed real stock and bond prices. In general, the stock market seems content with the low and stable inflation of recent decades, at least judging by reactions to changes in inflation expectations.
David looked at 8 years of data, from January 2003 until December 2010, and divided the sample up into 10 sub-periods. He found almost no significant correlation between inflation expectations (TIPS spreads) and stock prices (S&P 500) until March 2008. (Actually, there was a modest positive correlation during the first half of 2003, another period when people worried about excessively low inflation.) After March 2008, the correlation was highly significant, and positive. Right about the time where the US began suffering from a severe AD shortfall, the stock market began rooting strongly for higher inflation. And it still is, even in the most recent period. Money is still too tight.
There is no way to overstate the importance of these these findings. The obvious explanation (and indeed the only explanation I can think of) is that low inflation was not a major problem before mid-2008, but has since become a big problem. Bernanke’s right and the hawks at the Fed are wrong.
Arnold Kling noted that the AS/AD approach can sometimes verge on the tautological. When inflation and output both fall, demand-side economists are likely to infer that AD is lower. And they are also likely to claim that the fall in AD caused both the drop in inflation and the drop in output. Of course that’s not the only evidence demand-side economists have, but in many cases it’s hard to find definitive evidence of causation.
In my view the time-varying correlations between inflation expectations and stock prices are one of the most important pieces of evidence we have that AD became a problem after mid-2008. It will be interesting to see if those economists who are skeptical of demand-side explanations can come up with a plausible alternative explanation for this pattern.
PS. If anyone knows how to estimate a continuous time-varying correlation, it would be interesting to find out precisely when in 2008 US equity markets started rooting for higher inflation.
PPS. I’ve been asked to comment on the very weak performance of NGDP and the very strong performance in final sales during 2010:4. If I had any confidence in the government numbers I would comment. Let’s wait a few more quarters, look at lots of different data, and see where we are. Again, my test of a policy is its effect on expected NGDP, not the actual movements in NGDP (which reflect all sorts of factors.)