During my recent research I thought it would be interesting to look at what different central banks say they target and what they really target. To anyone that does not study economics and reads this, you might think about skipping it. It’s probably going to get somewhat technical. Also, this is as much to find out if what I’m doing makes sense as it is to actually present some of the stuff I’ve stumbled upon.

As many papers have showed, different forms of Taylor rules have worked pretty well in the past in describing particularly the behavior of the Fed in an ex-post fashion. Taylor rules, in term, are essentially nothing else than a formula that describes a central bank’s attempt to minimize deviations from its targets. Tinkering around a bit, the following form of the Taylor rule seems to be able to explain around 95% of Fed behavior (which seems too good to be true, but combing through econometrics books has so far not forced me to assume I did something coming up with my regression results):

This isn’t too different from the basic Taylor rule. The only thing it adds is an interest rate lag, essentially the simplest way to take interest smoothing behavior into account, which has been shown many times to be important in describing Fed policy decisions. As a side note, this interest rate smoothing behavior makes it so the Taylor rule no longer obeys the Taylor principle: a rise in inflation of 1% is no longer countered by a rise in the interest rate of more than 1%. The new rule also replaces the output gap with the unemployment gap, in line with the Fed’s official mandate. Let me throw out some graphs for you below the fold. Excuse the somewhat unaesthetic presentation, I’m still coming to grips with R.

The red line represents actual FED funds over the period I decided to analyze. The Blue line is the Taylor rule I estimated using the formula described above. The fit is indeed fascinatingly accurate. But where it starts getting interesting is when I try to interpret what this means. For instance, introducing a dummy to account for the Zero Lower Bound proves to be not significant, which I interpret as meaning that, given the estimated Taylor Rule that seems to accurately describe Fed policy from 2000-2013, they ZLB did not play a relevant role in limiting monetary policy action. But even more fascinating: neither the unemployment gap (nor the output gap if you use that) is significant. In other words, it would seem as if, ex-post, the Fed’s behavior is best described as that of a central bank that has a simple inflation target, and does not care about anything else. In terms of interest setting, this seems to be the case.

The green line is probably even more interesting. It’s essentially a counter-factual scenario where I modified the weights in the estimated Taylor Rule so that unemployment and inflation is targeted equally. In essence, this is what the Fed says it does. Yet, clearly, the ZLB gets in the way, which forced the Fed to abandon its dual mandate and switch to a simple inflation targeting regime as far as interest setting is concerned. Prior to the crisis, it seems like it would not have made much of a difference whether the Fed used its dual mandate or a simple inflation mandate, underlining the common finding that (in general) a stable inflation rate makes everything else fall in place nicely as well. Yet in the crisis, this is the point where QE comes in – QE is the Fed’s attempt to target unemployment in times where it cannot decrease interest rates any further. If it were happy just targeting inflation, the ZLB would not have played a role at all until now.

Great work!

But I think your interpretation of the results is seriously flawed. The Taylor rule with equal weights on inflation and unemployment (the green line) appears to give a very good fit until the interest rate hits zero in 2009. Afterwards, the ZLB binds, so the interest rate stays constant while unemployment soars. Hence it is absolutely no surprise that you don’t find a significant effect of unemployment on the interest rate over the whole sample. It’s insignificant because of the ZLB!

Also, I think your ZLB-dummy variable test isn’t any good. I would do a breakpoint test to see whether there has been a change in the relationship between interest rates, inflation and unemployment around the time the interest rate hit zero (Chow test, Wooldridge p. 449-450). And I bet you’ll find such a structural break!

Exactly the response I was hoping for!

A Chow-test breaking the sample in two where the ZLB starts binding indeed rejects the null hypothesis, meaning (if I understood that correctly) there is a structural break.

That basically means that it’s useless to estimate a Taylor rule over the whole sample, right? And here I had spent 2 hours of my life formatting the tables for my Taylor rules in LaTeX…also, how would you explain the dummy variables not being any good? Clearly the Chow test has proven to be superior, but shouldn’t they do something similar?

I can feel your pain, Flo! LaTex really is a pain in the ass when it comes to table formatting.

Well, yes, if the Chow test is in the rejection region, that’s evidence for a structural break. And in my view that’s as good a piece of evidence as you can get that the ZLB has been a real constraint on the Fed’s policy.