Friday, May 22, 2015

On Foolish Correlations

James Montier and Paul Krugman are in a bit of a spat over how much interest rates matter. Krugman put forth data from FRED (Federal Reserve Economic Data) showing a strong correlation between interest rates and housing starts. But, says Cullen Roche, he left out 40% of the data, putting his whole thesis into question. A simple regression of the all the data yields an R-squared of just 0.0453 (in other words, interest rates predict about 4.53% of the variation in housing starts).

But the ultimate problem isn't the missing data but the premise. If monetary policy is effective, we shouldn't see much of a correlation between interest rates and housing starts because, by the nature of the Fed, interest rates should be low during recessions. That's one of the jobs of the Federal Reserve: keep unemployment low.

There's any number of appropriate variables you can pick to factor in market conditions but let's look at the big one: civilian unemployment. Here's the graph with civilian unemployment thrown in:

Unfortunately, it's hard to tell much from this but a regression can help. With change in interest rates AND unemployment predicting housing starts, we get:
  • Unemployment
    • Coefficient: -100.6
    • T-Stat: -11.48 (statistically significant)
  • Interest rate
    • Coefficient: -22.7
    • T-Stat: -5.91 (also statistically significant)
  • R-squared: 0.202 (now we're explaining over 20% of the variation!)
Here's the interesting bit about this regression: Krugman transformed interest rates to be negative. Graphically, this makes it easier to see the relationship: when both lines are increasing, that means a negative correlation. Lower interest rates mean more new construction.

I didn't remove that transformation when I ran the regression. Thus the negative coefficient means positive correlation between interest rates and housing starts. So despite the incomplete approach by his critics, Krugman still appears to be wrong.

But don't throw out the demand curve just yet. New housing starts don't just respond to monetary policy; monetary policy responds to new housing starts. It is the classic causation problem that comes up in statistical analysis, especially regressions.

This is why theory is so important; it just makes too much sense that as interest rates fall, people will want to borrow more. Untangling all the effects to demonstrate that is indeed the case--and to what degree that's the case--cannot be done with something as simple as a correlation coefficient.