Let's start with Krugman, as he's by far the most articulate of the lot - you can actually understand what he's complaining about. The basic ideas in my post come from two papers, my recent AER article, and this recent working paper. So, I'm not just writing something in a blog that I thought up in the shower. The models I have been working with are built on a Lagos-Wright base. There are good reasons for that. In particular, including credit, collateral, banking, and other key features of financial markets in this type of environment is relatively straightforward. However, not everyone is familiar with Lagos-Wright, so I took some pains to write up some notes based on cash-in-advance. Why cash-in-advance? I think Krugman understands it, since he is clearly a slavish follower of Bob Lucas, and Paul has used cash-in-advance at least once in a paper.
Krugman should love this, for a number of reasons:
1. The key to solving the inefficiency problem that arises in the model is fiscal policy.
2. The underlying problem is that the fiscal authority is doing something stupid.
3. The economy is non-Ricardian - government debt matters.
4. Monetary policy is non-neutral. Indeed, monetary policy can have effects that persist forever.
5. This is all about financial frictions. During the financial crisis, some people seemed to want to tell macroeconomists they had been barking up the wrong tree by paying insufficient attention to such things.
Indeed, if I wanted to, I could probably find something in these ideas that I could link to Keynes's General Theory, call what I do Neo-New-Keynesianism, and start a new fad.
To summarize what is in my cash-in-advance notes, I assume a simple setup where assets other than money play some role in financial arrangements. It's very hard to do collateral constraints (at least it seemed to me it was) in this environment, so I just assume that there are two kinds of transactions - one where you need money, and another where you can use money and bonds. This is to capture the idea that government debt and other safe assets are useful in financial exchange and as collateral. In an equilibrium in which the value of the consolidated government debt is sufficiently small, asset-in-advance constraints bind, and the low quantity of consolidated government debt tends to make consumption and output low, produces an inefficiency wedge, increases the liquidity premium on government debt, and reduces the real interest rate.
In a liquidity trap equilibrium, where the nominal interest rate is zero and open market operations are irrelevant at the margin, if the value of the consolidated government debt is sufficiently low, the inflation rate i is determined by
(1) i = BW - 1,
where W is an inefficiency wedge related to consumption goods - a financial inefficiency wedge - and B is the discount factor. With no financial inefficiency, W = 1. Further, that inefficiency wedge is what is determining the liquidity premium on government debt at the zero lower bound. That is, the low real interest rate is associated with an inflation rate greater than the rate of time preference at the zero lower bound.
Why is this important? Economists have typically associated the zero lower bound with deflation. Thus, once the Fed effectively went to the zero lower bound in late 2008, some people, including Krugman, started to worry about deflation. But the deflation never appeared - indeed, by mid-2011 the inflation rate was running at close to 3% per year. Krugman, faced with a puzzle, argued that wage rigidity explained why inflation was not falling. But you can explain what is going on more satisfactorily, I think, by taking account of the financial inefficiency wedge. At the zero lower bound, as inefficiency increases, the inflation rate rises, and as inefficiency wanes, the inflation rate decreases. Following a financial crisis, it certainly seems useful to explain what is going on in terms of financial factors, and the post-recession path for the inflation rate in the U.S. seems roughly consistent with the story.
So far, dynamics and "stability" don't enter the story. As I show in my notes, the model is fully dynamic, but it actually solves like a static model. Given the fiscal policy rule, the central bank chooses a nominal interest rate period-by-period, and that gives a unique solution for consumption, output, hours worked, and the real interest rate.
But, we could imagine superimposing some policy rule for the central bank on top of this. That's basically what Krugman is up to. The picture he shows you works under the assumption that the "natural rate of interest," which is also the long-run real interest rate, is a constant. You can find a picture like Krugman's in Jim Bullard's Seven Perils paper. Bullard's paper has a useful discussion of the literature related to Taylor rules and their properties. Various people have worried about whether the Taylor rule will induce dynamics that will lead you to the "bad" steady state with deflation, rather than the "good" steady state in which the central bank hits its inflation target. But that's not the issue here. A key difference in my model is that the steady state real rate of interest is not a constant. It will depend on the financial inefficiency wedge, which is endogenous - in particular the financial inefficiency wedge depends on monetary policy. So, you can't draw a simple picture like Krugman's.
However, we can address Krugman's concern, which is that, if the central bank follows a Taylor rule, and the economy is at the zero lower bound, then some small perturbation will send this economy to the "good" equilibrium. Suppose, for example, a typical linear Taylor rule (multiplicative in my notes, but essentially the same thing) of the form
(2) R = max[ai +(1-a)i* - bg + r, 0],
where a > 1, i* is the central bank's target inflation rate, b > 0, g is the central bank's perceived "output gap" - the difference between what the central banker thinks is efficient output, and actual output - and r is the central banker's perceived "natural rate of interest." Then, using equation (1) to substitute in (2),
(3) R = max[a(-s+w)+(1-a)i*-bg+r,0],
where s is the rate of time preference, and w is the log of the financial inefficiency wedge. We'll have w=0 if the financial inefficiency disappears. So, suppose that the central bank has chosen to be at the zero lower bound, which implies, from (3), that
(4) A = a(-s+w)+(1-a)i*-bg+r <= 0. The central banker has been convinced of the wisdom of New Keynesianism, has been reading Paul Krugman, and is convinced that g is high and r is low - he or she thinks there is a large Keynesian sticky-wage and sticky-price inefficiency gap, and a low natural rate of interest. That's why he or she has chosen to peg the nominal interest rate at zero. Now, suppose that the financial inefficiency wedge falls for a period of time. From (1), the central banker will see a falling rate of inflation. That will act to reduce A and make the central banker want to stay at the zero lower bound. Further, if the central banker is a truly committed New Keynesian, falling inflation will make him or her think (through New-Keynesian Phillips curve logic) that the output gap g is increasing, which makes A fall further. For example, if you were Narayana Kocherlakota, you might say:
These low levels of inflation tell us that monetary policy can be useful in increasing the rate of improvement in the labor market.Or, put another way,
The underlying deficiency of demand will call for pedal-to-the-medal monetary policy as a norm.So, there are plenty of good reasons to think that a New Keynesian, living in my model world, could get stuck at the zero lower bound. Under the Taylor rule, the zero lower bound is as stable as a large rock sitting on the open prairie. The quantity A can fluctuate for various reasons, but as long as the inequality (4) holds, the economy stays at the zero lower bound. Note that increasing the inflation target i* does not help, as a>1.
Noteworthy is the fact that the last quote comes from Paul Krugman. He's part of what makes the policy trap a trap.
Three final points:
1. David Andolfatto wonders:
What would the Fed be doing differently if they took this view? Not much, as far as I can see.A key question is: What's the optimal monetary policy in my model? In my cash-in-advance notes, I'm pretty sure that optimal monetary policy is a zero noiminal interest rate under any conditions. That's basically Friedman-rule logic - inefficiency will be minimized when the nominal interest rate is zero, even if the usual Friedman rule is not feasible, as is the case in my model. There are good reasons to think that the standard Friedman rule - which comes out of many monetary models - is missing something important. I have argued (see my AER paper), that there are various costs associated with paper currency - costs of replacing worn-out notes, counterfeiting, fraud and theft, illegal activities. It's efficient to tax that stuff through inflation. There are cheap ways to capture that in the model, without changing anything of significance. Then, it may be the case we would actually be better off with a higher rate of inflation. But we aren't going to get it because the Fed is caught in a policy trap that will keep us at the zero lower bond indefinitely.
2. Paul Krugman thinks that a paper by George Evans has something to do with what I'm talking about. It doesn't - that's about learning in a New Keynesian model. Also, this doesn't have much to do with Kocherlakota either. Kocherlakota was thinking about the world depicted in Krugman's diagram, where the long-run real interest rate is a constant.
3. Some of Nick Rowe's confusion has to do with some holes in his knowledge of dynamics, I think. When I learned macro as an undergraduate (circa 1975), it was common for people to tell pseudo-dynamic stories in static models, probably because they wanted to make these models seem more realistic. For example, I remember an instructor discussing how monetary policy worked in an off-the-shelf Hicksian IS-LM model. The story went something like: M increases, which happens by way of an open market operation, which makes the price of bonds go up and the interest rate go down in financial markets. This increases the demand by firms for investment goods. They buy those goods from other firms, which then find that their inventories are going down. This causes those firms to increase production, and Y goes up. Of course, there are no inventories in the IS-LM model, and no firms producing anything - that's just a story that my instructor made up to make IS-LM more convincing. Actually, she was just doing comparative statics. There's a unique static equilibrium. M changes, the nature of the equilibrium changes, and we can take some derivatives and determine how it changed. But some people took those stories seriously. For example, those people wanted to make arguments such as: If I have this parameter configuration, then when I do the comparative statics I have trouble telling my pseudo-dynamic story. Therefore, that is a parameter configuration I am going to rule out. I think Nick retains some of that thinking, as you can see in the comments on this post.