## Friday, October 30, 2015

### Did the Natural Rate Fall***?

Paul Krugman describes the natural rate of interest as "a standard economic concept dating back a century; it’s the rate of interest at which the economy is neither depressed and deflating nor overheated and inflating. And it’s therefore the rate monetary policy is supposed to achieve."

The reason he brings it up-- aside from obvious interest in what the Fed should do about interest rates-- is because a recent paper by Thomas Laubach of Federal Reserve and San Francisco Fed President John Williams has just provided updated estimates of the natural rate for the U.S. Laubach and Williams estimate that the natural rate has fallen to around 0% in the past few years.

The authors' estimates come from a methodology they developed in 2001 (published 2003). The earlier paper noted the imprecision of estimates of the natural rate. The solid line in the figure below presents their estimates of the natural real interest rate, while the dashed line is the real federal funds rate. The green shaded region is the 70% confidence interval around the estimates of the natural rate. (Technical aside: Since the estimation procedure uses the Kalman filter, they compute these confidence intervals using Monte Carlo methods from Hamilton (1986) that account for both filter and parameter uncertainty.) The more commonly reported 90% or 95% confidence interval would of course be even wider, and would certainly include both 0% and 6% in 2000.
 Source: Laubach and Williams 2001
The newer paper does not appear to provide confidence intervals or standard errors for the estimates of the natural rate. As the figure below shows, the decline in the point estimate is pretty steep, and this decline is robust to alternative assumptions made in the computation, but robustness and precision are not equivalent.
 Source: Laubach and Williams 2015

Note the difference in y-axes on the two preceding figures. If you were to draw those green confidence bands from the older paper on the updated figure from the newer paper, they would basically cover the whole figure. In a "statistical significance" sense (three stars***!), we might not be able to say that the natural rate has fallen. (I can't be sure without knowing the standard errors of the updated estimates, but that's my guess given the width of the 70% confidence intervals on the earlier estimates, and my hunch that the confidence intervals for the newer estimates are even wider, because lots of confidence intervals got wider around 2008.)

I point this out not to say that these findings are insignificant. Quite the opposite, in fact. The economic significance of a decline in the natural rate is so large, in terms of policy implications and what it says about the underlying growth potential of the economy, that this result merits a lot of attention even if it lacks p<0.05 statistical significance. I think it is more common in the profession to overemphasize statistical significance over economic significance.

1. What if the FED raises its Funds Rate when the economy is really, really, not very perky? Does the cost of borrowing go up in lockstep anyway? For instance, it people's desire to buy houses wanes significantly, do mortgage rates go up nonetheless? From the above, maybe not, but can the effect be estimated?

2. It is super important to have a real time measure of potential real GDP to get a good measure of the natural rate of interest.

Here is my post that talks about that.
http://angrybearblog.com/2015/10/lw-not-see.html

Look at indicators of the growth of potential. It is positive, not negative. But it is much lower than it used to be.

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