..the Fed does not engage in reflective equilibrium. It rejects the conclusions of what I regard as the standard Patinkin-style existing model of Krugman (1999). But it does not propose an alternative model. There seems to me to be no theoretical ground, no model even considered as a filing system, underpinning the "orthodox" modes of thought that the Fed believes. And it does not seem to feel this absence aaa a problem. I find that somewhat disturbing.It's unfortunate that Brad's post distracted me, as I was busily engaged in reflective equilibrum, but what the heck. I thought I would check out Krugman's 1999 article, to refresh my memory. As I thought, the meat of the thing isn't actually a "Patinkin" model, it's a simple Lucas cash-in-advance model. As far as I remember, this thing has not been rejected where I work, though some of my colleagues might object to the CIA constraint as being insufficiently grounded in theory. Further, out here in flyover country (or the pond, as it's come to be known in recent days), we take offense when people call our models "orthodox," and if someone suggested we think of our theories as "filing systems," we would likely scream and run away.

Oh, by the way, here's something interesting. Let's take Brad seriously and look at the implications of Krugman's (1999) model. There's a representative, infinitely lived agent, with discount factor

*B*and utility function

*u(c),*where

*c*is current consumption. There is a fixed endowment of perishable consumption goods each period, which must be purchased with money, which is supplied by the central bank. We can flesh out the details of transactions, for example there can be many households which sell their endowment and purchase output each period, or output could be grown on "Lucas fruit trees," with consumers owning shares in the trees. But those are details that are irrelevant for the equilibrium. As well, money could be injected by way of lump-sum transfers, or through open market operations. Again, the details don't matter for what we'll do here. Let

*R(t)*denote the nominal interest rate,

*i(t)*the inflation rate, and

*M(t)*the aggregate money stock.

Consider deterministic equilibria in which the central bank sets policy as a sequence of nominal interest rates

*R(0), R(1), R(2),*... . Then, intertemporal optimization implies

(1)

*i(t+1) = B - 1 + BR(t)*,

for

*t = 0, 1, 2, ... .*The central bank then supports the sequence of nominal interest rates in a rational expectations equilibrium through the appropriate series of money growth rates m(1), m(2), m(3), ..., where

(2)

*m(t) = M(t)/M(t-1) - 1*,

and the sequence of money growth rates required to support the interest rate policy is

(3)

*m(t+1) = B - 1 + BR(t).*

Basically, Krugman's model is a purely Fisherian model of inflation - there's no liquidity effect, only a Fisher effect, so the nominal interest rate always reflects only anticipated inflation. So if the central bank thinks inflation is too low and wants it to go up, what should it do? Equation (1) says it must

*raise the nominal interest rate.*

So, I'm pleased to report that Brad is a neo-Fisherian. Seemingly, so is Paul.