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If he's wrong, why are we stuck in a liquidity trap?

Jim: see my other posts. Because the Fed hasn't communicated the right policy. But that's not the point of this post. I'm just trying to clarify what PK meant.

How is the fed supposed to know the 'magic number' target inflation rate for the good equilibrium?

Nick:

The IS curve is plotted in the Y-i coordinates, not the unemployment-inflation plane. I am sure you know that better than me.

Besides, Krugman's Phillips is vertical at 5% unemployment. Is it just sloppy, or intentional?

If mathy stuff is used in this manner, a number of bells start ringing in my mind.

Andrew: It doesn't. It has to guess. But as long as it doesn't guess too low, it will be alright. Because it can raise the nominal interest rate if it promises too high inflation, and so overshoots the good equilibrium on the upside.

vjk: as I said in the post, we normally draw the IS curve in {r,Y} space. But that's not a problem, If inflation is a negative function of r (it is, given i=0%), and if u is a negative function of Y (standard keynesian assumption), we can re-draw the IS curve in the new space.

vjk: Krugman deliberately drew the Phillips curve vertical higher up. That's not sloppy. It's standard. Whether it's vertical at exactly 5% unemployment, who knows.

Nick:

What is the empirical evidence of the P-curve being vertical at a certain unemployment rate ? Zimbabwe ?

"The good equilibrium is unstable."

What, exactly, is an "unstable equilibrium"? For the record, yes, I think you and Krugman are saying the same thing, but the reason I am unsure is that he has communicated very well and you have not. If you are going to surpass him in that respect, you still have a long row to hoe: Krugman's diagrams make clear that there is not a second equilibrium point, merely a metastable locus of points. You, on the other hand, have confusingly drawn a second intersection point but corrected yourself in the text.

Of course it is true, as you say, that Krugman's premises are not necessarily correct; being a good communicator is no guarantee of being right. But his argument is valid, even if it is not sound.

I think talking about it in equilibrium terms confuses things. Just about how the dynamic adjustment will play out. (I don't believe general equilibrium is a practical concept anyway.) In this case I think the liquidity is caused ultimately by neo-mercantilism and so is a disequilibrium situtation.

vjk: In the 1960's economists believed that the Phillips Curve was downward-sloping. Friedman and Phelps said in 1968 the LRPC should be vertical according to theory, even though the SRPC would slope down. The 1970's. 80's. and 90's data, when the trade-off disappeared, led nearly all economists to change their minds and say that Phelps and Friedman were basically right. Though maybe not at very low inflation rates. Paul Krugman is basically reflecting standard opinion here. Whether standard opinion is correct is another matter. The data is just too shotgun to say. But the data don't contradict the standard theoretical view, is the best we can say.

Phil: If you found PK's original post clear, that's fine. I didn't. I needed to superimpose his two diagrams to see it more clearly. Reading comments on other blogs suggested a lot of people found it hard to follow. Whether they will find mine any easier is another question. But I'm going to give it a try.

An "unstable" equilibrium is like a ball on top of a curved hill. If it moves a little bit away from the top, it won't come back. There are lots of fancier definitions.

If the central bank holds the nominal interest rate constant, then the good equilibrium is unstable. That is standard macro. That's what I've drawn in my picture. The Fed can only make it stable by moving the nominal rate, and doing so quickly, in response to deviations from that equilibrium. But if the Fed does this (follows the Taylor Principle), the equilibrium is not metastable; it's stable (given standard assumptions). That's why I prefer my way of drawing it to PK's.

Here’s what I thought he was saying:

You only get (real) inflation if you have full employment. Therefore, in order to get any inflation, you have to promise enough inflation to get full employment; if you promise less, you won’t get any inflation.

" So if the Fed promises 4% inflation, and people believe the Fed, the economy moves to the good equilibrium. "

Translation: I drew some nice curves between pressure, volume, and temperature, and decided that if the CB lowers volume by squeezing on a balloon, then the temperature of the gas inside will drop. This must be true because there is solid statistical data for the curves.

adjacent/q: yep. But you have to draw the curves to see why.

RSJ: I don't think it's as bad as that. Economists do have some sort of theory behind the Phillips Curve and IS curve. Certainly nothing anywhere near as good as the ideal gas laws. But not just statistical correlations.

Nick, I know that, but you see the pitfall with just doing an equilibrium analysis?

Suppose the phillips curve is 100% right -- an iron law. Suppose the IS curve is an iron law. Then you draw two equilibria, high inflation/high employment and low inflation/low employment.

That still does not mean that you can move from the bad to the good by changing inflation. It could well be that only by changing employment can you generate high inflation, and if the CB tries to generate inflation by buying bonds, it will fail. I.e. the existence of two equilibria does not mean you can get from one to the other however you want.

No statistical analysis will help you, since we agree on the correlation but disagree on the causation.

On the other hand if, the government buys goods, then someone must be hired to produce those goods -- they do not just appear out of the sky -- so with enough goods purchases, employment must fall and regardless of what the phillips relation actually is, we are in a low unemployment environment. What is the downside of the government spending too much by purchasing goods? That the price of goods goes up? That people save and repair their balance sheets? Certainly the government can purchase as many goods as are available for sale, and also place orders for even more goods to be delivered later. The government can pay in advance. Buying goods is the one thing that *must* lower unemployment, since goods are the only thing that require labor to produce. It does not require labor to save the proceeds of a helicopter drop and no labor is employed to sell a bond to the CB.

This is where I get frustrated when you on the one hard redefine monetary policy to include the purchase of goods -- in defiance of all accepted language and laws -- and then on the other hand say that fiscal policy is less effective than monetary policy. The combination of these two beliefs is a type of impotent stagnation, where in principle we can solve the problem by buying goods, and we know we can solve the problem, but when it comes time to act, we always buy bonds, not goods, because buying bonds is "more effective". Then we are surprised that the CB managed to buy a lot of bonds without anyone becoming employed.

And so we remain stuck.

Nick:

I sometimes wonder about theories of inflation that put so much stock in the Phillips curve. Krugman says: "But how do you get inflation? Only by having a full-employment economy." What is this? A theorem of some sort? A claim relating to the evidence (I can provide plenty of examples of economies experiencing high inflation with less than "full" employment)?

It seems to me that there is evidently still a huge worldwide demand for USD/UST out there. To me, this seems likely to the proximate source of disinflation pressure. I'm not sure how/why domestic unemployment should matter for U.S. inflation (the inverse real rate of return on an asset held widely in wealth portfolios around the world). Anyway, just a thought.

RSJ: "I.e. the existence of two equilibria does not mean you can get from one to the other however you want."

Agreed. But there's something I missed from that diagram. probably should have made it explicit. The IS curve is drawn as a function of *expected* inflation. The Phillips Curve is drawn as a function of *actual* inflation. *If* (you will say it's a big "if") you can change expected inflation, and the IS is an iron law, that will create jobs, and create the actual inflation to ratify those expectations.

That's one way in which equilibria in economics may be different from those in the natural sciences. Expectations matter.

This weekend the Canadian government will sacrifice a goat. And nearly all Canadians will change their real behaviour in response. The goat is called Daylight Savings Time. (My next post)

David. I part way agree with you. For starters, it's missing the "expectations" bit of the expectations-augmented Phillips Curve.

But I still wonder if that's enough. I'm thinking of those hilarious slides on your blog, about a month back. Plus the UK, where I can't understand why inflation is so high. And underlying it all is the element of truth in your and Steve's complaints about sticky price (non) theory.

But the excess demand for USD ought to be the flip-side of the excess supply for everything else, including labour, but not exclusively labour.

"But if the Fed does this (follows the Taylor Principle), the equilibrium is not metastable; it's stable ..."

That is the first time in my life I have heard a stochastically controlled process described as "stable." No wonder you find Krugman hard to understand!

OK, but what statistical evidence is there that inflation expectations can be controlled by CB bond purchases in the current climate?

Statistics only gives you the correlation, but it doesn't tell you which variable can be tweaked by government, or under what circumstances.

For that you need a really robust model of behavior that includes, say, ponzi borrowing and that distinguishes explicitly between short term riskless rates and long term risky rates. If the NK models can't/don't do this, then why would you think that the expectations channels work as you would expect, or that the policy prescriptions that worked in the past will work today.

I vaguely recall a different "iron law" phillips curve relation that worked for about 20 years. How do you know that monetarism hasn't just enjoyed a similar run, and will need to be replaced in the same way that hydraulic Keynesianism was replaced?

P.S. I think your graph was fine, and am surprised that you have such a tough crowd complaining about axis and asymptotes. Your explanation was much better than Krugman's IMO. Am cranky due to the general state of affairs in the U.S. at present.

Phil: Really? A bicycle is a stochastic controlled process. I would describe the bike itself as in an unstable equilibrium (if it's upright), but a bike+rider combination as a stable equilibrium (within limits, if the rider is competent).

Is my usage there idiosyncratic? (That's a genuine question.)

Because the bike+rider is an OK metaphor for any central bank trying to target inflation by varying the nominal rate of interest.

RSJ: "OK, but what statistical evidence is there that inflation expectations can be controlled by CB bond purchases in the current climate?"

Since the current climate is fairly unique, really damn all, unfortunately (unless the very recent data counts). We're all relying on whatever theory we can cobble together, and whatever data we think might be vaguely relevant.

"For that you need a really robust model of behavior that includes,..."

Stop right there! We don't have one. Now, what was it you wanted to include?

Yep, your general points are very much like the old 1975 "Lucas Critique", of which the old Phillips Curve is a classic example. It's why we need theory, not just correlations.

Thanks for saying you liked my presentation.

Without getting into politics....the US has pulled out from much worse in the past. It will do so again.

RSJ/Nick:

P.S. I think your graph was fine, and am surprised that you have such a tough crowd complaining about axis and asymptotes

The vertical part seems unlikely, physically not economically, speaking.

I wonder, still, whether there is empirical corroboration of the vertical part.

Not criticizing for the sake of criticism or anything of this sort.

vjk: It is hard to corroborate, empirically, the hypothesis that a line is vertical. All you can do is fail to prove that it's not vertical.

You may find this post by David Andolfatto both informative and amusing: http://andolfatto.blogspot.com/2010/09/classroom-lesson-phillips-curve.html

If I approached that data without a theoretical prior, I confess that I would draw a Long Run PC sloping the "wrong" way.

Why do you say it's unlikely, "physically"? Do you mean that in interdependent systems, coefficients of zero are implausible, a priori?

Nick:

It is hard to corroborate, empirically, the hypothesis that a line is vertical

Well, that bothers me.

Why do you say it's unlikely, "physically"?
There is no known mechanical process that would be described by a non differentiable function similar to Phillips curve. Therefore, intuitively, it seems rather unlikely that an arguably inertial unemployment/inflation dynamics could be described by something like that: when "marginal" inflation jumps from say 1% to infinity at whatever level of unemployment such jump may occur.

Rowe:

As QE moves us up the phillips curve, the additional real growth (and lower unemployment) shift the "IS" curve to the left. The gap between the two equilibriums gets smaller.

Why does it move to the left? Because with lower unemployment and higher real growth it takes a lower inflation rate to get real interest rates sufficently negative to get people to spend.

Further, since QE involves buying longer term bonds, rather than just the zero nominal rate short term bonds, this also moves the "IS" curve to the left. If you think about lowering short term rates as reducing the level of all rates, then having the Fed take on the risk of buying the long ones bonds, and not just reducing long bonds by lowering the yield on short bonds, then if we are treating the short rate as "the" interest rate, then you are raising (making less negative) the level of the short rate needed to generate the unemployment rate.

And that is why Krugman is wrong. He is ignoring the effect of expecations of real growth on real interest rates (the normal IS curve shifts to the right) and he continues to assume that the central bank only buys the very same securities that have a zero nominal yield.

The only effect he is accepting is higher expected inflation, lower real interest rate, constant IS curve.

Bill: Yep. Whether you agree or disagree with PK, his ability to make clear simple arguments one can look at and critique is very worthwhile. (That's why I got so frustrated with this particular post that I decided to re-write it for myself, or anyone else).

Your first two paragraphs I would describe as making the IS flatter, rather than shifting it left (or right in normal space). I'm still enough of an Old Keynesian in some ways to want to build the multiplier into the IS curve. But whether it makes it flatter or shifts it left depend on whether you want to talk about the effects of *current* or *expected future* unemployment (output). It comes to the same thing, really.

The Phillips Curve is also worrisome. I want to put something closer to the standard expectations-augmented Phillips Curve in there. Sure, the SRPC may be very flat at present, and so it takes a long time for expectations to adjust and for the SRPC to shift down. But if the Fed credibly announced higher inflation, my guess is it would shift up.

vjk: according to standard theory, if you push unemployment below the "natural rate", and try to hold it there forever, it's not so much that inflation immediately jumps to infinity, but that it will rise, and accelerate, and accelerate at a faster and faster pace, without limit. It's not discontinuous. It's just that the derivatives of the price level with respect to time are all positive. First, second, maybe third, and we lose count after that. We prefer to invert the function to talk about it. "The unemployment rate is independent of the inflation rate in the long run". "We cannot keep unemployment permanently below the natural rate without ever-accelerating inflation". There just doesn't exist any permanent monetary equilibrium out there.

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