Natural Interest Rate Bleg

I suppose I should know what the natural rate of interest is, given that I’m a monetary economist.  But I see the term used in two radically different ways, and am not sure which version is correct:

1.  The real interest rate that would exist if the economy were at full employment and stable prices (or on-target inflation).

2.  The real interest rate that would be expected to push the economy back to full employment and stable prices (or on-target inflation).

A recent NY Fed piece used the first definition:

The Laubach-Williams (“LW”) and Holston-Laubach-Williams (“HLW”) models provide estimates of the natural rate of interest, or r-star, and related variables. Their approach defines r-star as the real short-term interest rate expected to prevail when an economy is at full strength and inflation is stable.

The accompanying graph shows their estimate of the natural real rate for the US:

Screen Shot 2018-12-10 at 3.22.38 PM

Obviously, it would have been a disaster if the Fed had set the real rate at that level during the Great Recession. Rather the authors are showing the real rate that would be appropriate in the counterfactual case where the economy was at full employment.

In contrast, an article by Vasco Cúrdia at the San Francisco Fed uses a very different concept when describing the natural rate:

The natural rate of interest is the real, or inflation-adjusted, interest rate that is consistent with an economy at full employment and with stable inflation. If the real interest rate is above (below) the natural rate then monetary conditions are tight (loose) and are likely to lead to underutilization (over-utilization) of resources and inflation below (above) its target.

At first glance, that sounds similar to the New York Fed’s definition, but he later clarifies that this is the rate expected to lead to full employment, and that the natural rate will fall when the economy is depressed:

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