## Monday, December 2, 2013

### Noah's Complaint

I was waiting for Noah to chime in eventually, on this post, and I'm ready for him. Noah's complaint is that the the same character (yours truly) who is now telling everyone that the Fed is stuck in a low-inflation policy trap used to be concerned that the Fed would send us to a bad high-inflation path. Did that goofball have some revelation, abandon his old models, and come up with some new wacky stuff, or what? Who would want to believe a silly nut who changes his mind like he changes his socks?

Back in days of yore, my concern was that we could indeed get higher inflation. How? I had thought that the Fed had the ability to control inflation, but when push came to shove, they wouldn't do it. Once people caught on to that idea, we could get on a high-inflation path that was self-sustaining. Of course, since I said that, I've continued to work on these problems, and stuff has been happening. In particular, we're not seeing that high-inflation path. How come? That's what my previous post is about.

So, recall how the model in my cash-in-advance notes works. Now we'll have to worry about what happens away from the zero lower bound in a steady state. The inflation rate will satisfy

(1) i = -s + w1

Equation (1) is standard. The inflation rate is equal to minus the rate of time preference s plus an inefficiency wedge w1 related to goods purchased with money. As well, in the model I wrote down, the nominal interest rate is

(2) R = w1 - w2,

where w2 is the inefficiency wedge associated with goods purchased with bonds. The real interest rate is

(3) z = s - w2,

so the inefficiency wedge w2 is associated with a lower real rate. Now, remember the Taylor rule from my previous post:

(4) R = max[ai +(1-a)i* - bg + r, 0]

The idea is that this is the rule followed by a New Keynesian central banker, who lives in my model world, but doesn't understand how it works. The NK central banker perceives an output gap g, thinks the "natural rate of interest" is r, and has an inflation target i*. In my last post, we thought about what happens at the zero lower bound, and why the NK central banker could get stuck there. Here, we'll think about the other equilibrium in Krugman's picture. Using (1), (2), (3), and (4), the inflation rate in a positive-nominal-interest-rate equilibrium satisfies

(5) i = i* + [1/(a-1)]bg + [1/(a-1)](z-r)

There's a complication here, relative to Krugman's picture, for example, in that the real interest rate z is endogenous, so this is not closed form. In any case, recall that a > 1. So, to the extent that the NK central banker is perceiving a NK output gap that is not there (the NK banker is thinking about the wrong inefficiency), or perceives a natural rate of interest that is lower than the actual real rate, the inflation rate exceeds the central bank's target interest rate. That is, the same errors that cause the NK central banker to get stuck in the liquidity trap equilibrium will make inflation higher than the central banker's target in the other equilibrium.

So, that all comes out of the same model. We can be stuck in a liquidity trap equilibrium where the inflation rate declines as the liquidity premium on safe assets falls, or we could be in a self-sustaining equilibrium where we get inflation higher than the central banker's target.