A couple of weeks ago Larry Summers held a widely praised speech on the difficulties ahead for economic stabilization policy. As far as I can tell, not much of it was really new, as also pointed out by e.g. Krugman, but that does not mean it wasn’t a great speech, and one that seems to have had considerable influence on the policy debate. In essence it boils down to the problems we face due to the zero lower bound on nominal interest rates, and what happens in a world where the real interest rate required to establish full employment, sometimes also called the natural real interest rate, is negative, as it almost certainly is right now. Yet from the regression’s I have been running, it would seem that the equilibrium real interest rate was already considerably lower than in previous periods even before the crisis started. In other words, even before the crisis struck, monetary policy already had considerably less room to maneuver than in the decades preceding the the 2000s. To recap, let’s again take a look at a fairly simple Taylor rule one might use to describe Fed policy in the 2000s, more precisely from the first quarter of 2000 to the second quarter of 2009, which is roughly around the time when the zero lower bound started binding.

Conceptually, a Taylor rule such as the one above has two straight-forward offsets: the equilibrium interest rate and the inflation rate in period t. Econometrically it is impossible to estimate both separately, meaning that one has to be held constant in order to achieve a meaningful separation directly through the regression. In my case the choice was easy, as I was basically trying to do ex-post estimations of what Fed policy was like during a given period of time, meaning I have accurate data on the inflation rate in period t, leaving only r* unknown.

The interest lag introduced to the Taylor rule essentially represents a third, also time-variant offset that has to be taken into consideration. Conceptually, even if both the unemployment gap and the inflation gap are 0, i.e. the central bank fully achieves its targets, the nominal interest rate it sets will still be determined not only by its estimate of the equilibrium real interest rate and the current (i.e. target) level of inflation, but also to a certain degree by the nominal interest it set in the previous period. Long story short, given the Taylor rule stated above, if we assume the central bank does not consistently miss its targets (which it doesn’t over my sample), we can calculate the approximate equilibrium real interest rate as implicitly assumed by the central bank by taking the intercept value (the estimated offset of the recession) and adding to it the weighted interest smoothing term.

The graph above represents this implicit equilibrium real interest rate over the period in question. Note that this is not strictly speaking *the* natural real interest rate, which is notoriously difficult to calculate, but rather reflects the *beliefs* held by the central bank (as derived from an estimated Taylor rule that describes the actual behavior of the central bank in a sufficiently accurate way) with regards to what it assumed the equilibrium real interest to be. The apparent fact that this rate fluctuates considerably provides plenty of room for interpretation by itself. And even though there is considerable uncertainty regarding the precise values, the mean value for the example in question is pretty interesting: it is roughly 1.34%. As a comparison, the original Taylor rule paper assumed an equilibrium real interest rate of 2%, while Judd et al. (.pdf) for instance estimated a value of around 2.82% for the Greenspan years up to 1997. No matter how I specify the Taylor rule, I always get results that lie considerably below the 2% mark often simplistically assumed as being a kind of “historic average”.

Why does this seem to be the case? My guess is as good as yours, yet it is of vital importance for policy discussions. If the real equilibrium interest rate is lower, a lower nominal interest rate is needed to achieve the same level of inflation. Put differently, given a fixed inflation target, the likelihood of running up against the zero lower bound on interest rates is higher the lower the real interest rate is. In other words: not only was monetary policy in a tough spot because it faced an economic crisis bigger than any other seen since the great depression, it was also from the very start more constrained by the zero lower bound than in previous decades, limiting its ability to stimulate the economy at a time when we needed stimulus the most.

Your equation confuses me. Shouldn’t there be i_{t} (the interest rate at time t) on the left-hand side? And why do you have the inflation rate twice on the right-side?

I’m not convinced that what you are plotting is the natural interest rate. You are taking the estimated intercept of the Fed’s Taylor rule (which is a constant) and add to it more or less the current nominal interest rate. So what you are plotting is, well, the Federal Funds Rate minus a constant.

Was in London over the weekend, sorry for the late response.

You are right that a t is missing. The * simply symbolizes it’s essentially the nominal rate “target”, the optimal value at which the central bank would like to set rates, which, for simplicity, it just does. I have two times inflation of the right because that’s just what a Taylor rule looks like, essentially. You can, of course, collect terms, which in general you need to do to arrive at the Taylor principle (i.e. the central bank changes interest rates by more than 1% if inflation changes by 1%), but in general the idea is that, if all targets are met, the central bank sets nominal rates = real equilibrium interest rate + its inflation target. Just the way the rule is specified basically.

As to the second point, I am not fully convinced either, but as far as I see it it’s merely an issue of identities. The two “basic” offsets of the formula are r* and pi_t. It would seem that the inflation smoothing term is nothing else than another offset: if the central banks targets are met, it will set nominal interest rates as real equilibrium interest rate + its inflation target + beta_0*i_{t-1}, which, of course, would tend to converge over time to the “classic” rule if beta_0 < 1. In any case, if I include no offset in my OLS regression, the intercept that R gives me is essentially some constant + the inflation target. In my mind, however, this intercept does not include beta_0*i_{t-1} since strictly speaking this is not a constant in the way that the others are yet should be treated in that way. It would seem that intercept + beta_0*i_{t-1} = real equilibrium interest rate, since the intercept does include (or more accurately exclude) the inflation target, but not the interest rate lag term. Put differently, I see the "naked" (without pi_t as an offset) intercept = r* + pi_t – beta_0*i_{t-1}. I only have one unknown variable there, which is what I plotted. The "clean" intercept is a negative number,and one that I cannot reconcile with anything that could meaningfully interpreted as the real equilibrium rate. So yes, I am essentially plotting the Fed Funds – a constant, but I think that is exactly what I want to be plotting. Gotta run to university, but will give it some more thought later.

If you stumble over a fault in my logic while reading this, I'd very much appreciate it though.

I’m not really up on the Taylor Rule literature, so please excuse my ignorance. I accept that what you are plotting is the Fed Funds Rate which we would have seen if the Fed had met its inflation and unemployment targets in every period. But I don’t accept this as an approximation of the natural real interest rate, because the Fed Funds Rate is a nominal rate. So it can only be equal to the natural real rate if you have zero inflation. But that’s of course not the case.

Well, the thing is I am not plotting the nominal Fed funds rate. To be exact, I am plotting -0.9238 + 0.6789*(FedFunds at t-1). The first term is the intercept I get from the regression, the second is the interest smoothing term with the weight I estimated.

This could very well be completely wrong, but at a first glimpse the line I am plotting is roughly 1.5% below the nominal Fed Funds rate on average. Over the entire period I am plotting the line I have roughly 1.8% inflation on average, so at least the ballpark number seems to be right.