# "Zero" Reactions

#### The Fed's reaction function changes at the zero lower bound, and with nominal interest rates

This post is a response to Karl Smith, who I think raised some important points in a post I found via Scott Sumner:What we disagree about is whether the Fed’s reaction function changes significantly in the presence of the zero lower bound. Indeed, that might be an interesting paper...[possibly] the Fed’s inflation weighting simply rises as it hits the zero lower bound. I don’t have an immediate explanation for this apart from the hypothesis above, but we should consider that something odd simply happens in the minds of central bankers as they bump up against the zero lower bound. The evidence suggests this.Smith raises all sorts of other intriguing possibilities which might explain if the Fed's reaction function changes at the zero lower bound on nominal interest rates, presuming that change exists -- asymmetric weights on Keynesian and non-Keynesian easing and "hysteresis in policy making" were two in particular.

I've done some research into, and thinking about, monetary policy reaction functions that I've published in the past on this blog -- see here and here; someday I hope to get these ideas published for real. To summarize so that I can use some of the concepts and shorthand developed in those two posts, I empirically determined the relative weights central banks put on deviations in real growth and inflation at different times -- their "loss functions" -- interpreting the consistent discretionary choices of policymakers as NGDP-style rules, with additional weights on real growth or inflation. I further combined the two weights into a single measure which I called an H-value; a positive H signifies a policy which is intolerant of inflation deviations relative to real growth deviations, a negative H signifies the opposite, and an H of zero is an NGDP rate target.

Applying this research, my perspective was to rephrase Karl Smith's question as: Does the Fed's H-value change at or near the zero lower bound?

The answer I got was yes, and the effect is substantial. For every percentage point the nominal federal funds rate falls, the Fed becomes 17 percent more sensitive to deviations in inflation relative to deviations in real output. And for reasons I will get into momentarily, I think a more sophisticated analysis would show that the change in the H-value as interest rates fall is of even larger magnitude.The obvious negative slope of the line of best fit brings us to the conclusion written above; the 17 percent number comes from the inverse of the slope. This correlation stretches from now all the way back to 1954, which is the earliest data for the effective federal funds rate I could find on FRED. *(I say that because if anyone has reliable data from the 1920s and the Great Depression, I'd really, really want to run my H-value test on them to see if policymakers were zero lower bound-averse then.)*

I don't know why this is happening, just that it is, in regards to the second part of Karl Smith's question. One possibility I would consider is that if policymakers know high interest rates are costly, and that inflation is also costly, and so if inflation ever jumps, they will raise rates quickly to kill the smallest outbreak, because they don't want to be forced into a situation of rising inflation and expectations bringing about higher rates than would be required if they responded harshly and immediately. An aversion to high interest rates, in other words, would explain the high-H values at low interest rates. And this story seems to work very well with the Fed's past.

My first answer presumes that the Fed's loss function changes linearly with nominal interest rates. But there are good reasons to think that the relationship could be nonlinear, as Smith suggested -- as a central bank sees that it's nearing the zero lower bound, it could suddenly shift to not caring about inflation. Is that what we see going on in the data?

I took the three episodes of interaction, or near-interaction with the zero lower bound -- in the late 1950s, and from 2000 until today -- and looked at that subset of our data. What I found is that a linear function no longer does a qualitatively good job of describing the relationship between the H-value and the nominal interest rate.Instead, it looks like there's a "bend" in the loss function right when the federal funds rate hits 1 percent, which makes sense that it's at this point when the zero lower bound suddenly looks like a likely possibility, and there's a cognitive break in the minds of central bankers.

The reason why this nonlinear relationship is obscured in the larger dataset is because there appears to be some "drift" of the function to the up and right and to the down and left (perpendicular to the function) as Fed policy evolves. When you take drift away by looking at a more limited sample, you see that the original function is not linear.