Even Worse than Paul Krugman Imagines?

Reading Karl Smith’s comment on my previous entry, I started to think about the implications of rational expectations in the context of potential deflation. I’m thinking of a model like “Rational Expectations meets Calvo Pricing meets the Keynesian Multiplier meets the Mundell-Tobin Effect.” It goes something like this:

Start out imagining that prices are stable. Then introduce the expectation of an output gap (like the output gap that the CBO expects). An output gap implies that actual (sticky) prices are above equilibrium (flexible) prices. As more cohorts adjust their prices toward equilibrium levels, actual prices will fall. If you expect actual prices to fall, you have a disincentive from investing, because you have to pay today’s sticky prices for your capital goods, but you will only be able to sell your product at tomorrow’s (lower) flexible prices. So investment will be lower than it otherwise would be. And because of the multiplier effect, consumption will be lower than it otherwise would be.

So overall demand will be significantly lower than it otherwise would be. Therefore equilibrium prices will be even lower. Therefore we have to anticipate an even greater rate of deflation. Therefore we have to anticipate an even larger disincentive from investment, which implies an even lower level of investment, which implies an even lower level of consumption, which implies even less demand, which implies even lower equilibrium prices, which implies even faster deflation, which implies an even greater disincentive from investment, and so on. And all the “so on” is something that, if we have rational expectations, we will immediately anticipate.

Without actually writing down a model (which I’m not going to do), I can’t say for sure whether there will be an equilibrium, but if there is one, I’m pretty sure it is really, really, really ugly. My intuition says that, in an economy without a public sector or a foreign sector, there will normally be no equilibrium, and all production will simply cease.

If you throw in a government, then you can presumably have an equilibrium even without any private investment, so the economy won’t grind completely to a halt, but it will sure look pretty awful. Although I wonder: if the process of selling requires holding inventories, then it requires some investment. (Technically, it requires a level of investment that may not be positive but that can still be reduced if there are incentives to reduce it.) If the disincentive to investment rises without bound, then there will be no incentive to hold inventories, and production will still cease, even with public sector demand.

I would guess that someone has already done this sort of model more rigorously, and I don’t know what the conclusions were. But I would guess that they were quite unpleasant.

What happens to the inflation when the output gap is zero?

In a blog post a couple of weeks ago, Paul Krugman presents a scatterplot of the change in the inflation rate (y) as a function of the output gap (x), with the following regression line:

y = 0.5228 x - 0.4739

I'm puzzled as to why he includes a constant term in this regression. (Maybe he was using graphics software that won't do a no-constant fit?) If you take the regression line at face value, it means that the inflation rate is predicted to fall by almost half a percentage point each year when the output gap is zero. It also means that the economy must run nearly a full percentage point above potential in order to prevent the inflation rate from falling. That doesn't make any sense.

The sensible way to do the fit is to constrain the constant term to zero (which makes the math a lot easier if you're doing the fit by hand, but some software insists on doing things the hard way even when it doesn't make sense).

It turns out it doesn't make much difference in the conclusion: the slope of the line is still approximately 0.5, and in the relevant region (with output gap above 6 percent) the intercept is not of much relative consequence. But I would have found the whole thing more convincing if the plot had displayed a reasonable regression line to begin with. When you show a line that implies that the inflation rate declines even under normal conditions, it's not that impressive when you conclude that it will decline too much under unusual conditions.


UPDATE: Paul Krugman responds. His main point is that the IMF's definition of potential output doesn't require that the inflation rate be constant when actual output equals potential (i.e. when the gap is zero). So now I understand that the IMF's construction doesn't have that property. But I'm having trouble understanding the theoretical meaning of that construction. Doesn't the IMF's filter amount to an empirical way of making a guess at a concept that still should have that property theoretically?

I suppose I can understand that you don't want to force a constraint on the guess after it has already been made. (See Prof. Kurgman's point about circular reasoning.) But the chart still doesn't look right to me. Since the CBO's potential output concept does imply stable inflation at the zero point, how can you plug the CBO's gap forecast into the IMF's gap equation and get a meaningful result? (Well, OK, the result is meaningful for our purposes, because the fitted line passes close enough to the origin to give approximately the right result, to at least the level of precision necessary for the original point about deflation risk, and because the two methods for estimating the output gap lead to reasonably similar results for the US historically -- again, given that we don't really need much precision.) Under the circumstances, since we're mixing two different concepts anyhow, it's an arbitrary decision whether to impose the zero constraint, and I think the chart would look prettier if the line went through the origin. (I suppose that's a matter of personal taste.)

I also don't like the idea of using a filter that needs to know the whole series before it can do the smoothing (which IIRC is the case with the Hodrick-Prescott filter used by the IMF). It seems to me there is still a bit of circular reasoning involved, or at least, that you're constructing a fake data series that can't necessarily be expected to have the same properties in real time as it does with benefit of hindsight. I suppose if I were doing this, and if I wanted to keep the T's crossed &c., I would avoid the CBO's gap forecasts entirely and just use raw GDP. Then I could determine historical potential output by putting the data through a one-directional filter which I could then apply to the CBO's forecasts. But it's still unclear whether the fitted line should be constrained to have a zero intercept. It seems to me, the only reason to interpret the fitted relationship as a structural one is that we have a theory wherein such a relationship exists. And in the theory, as I understand it, the line does have to pass through the origin.

Pork is Essential for Good Health

Yeah, it's not just "good for you"

Here's how things stand: the stimulus bill is way too small, it's floundering in the Senate, and we stand possibly on the edge of a deflationary abyss.

Solution: find, say, the 5 most wavering Republican senators and offer them each $100 billion worth of pork. (2 isn't enough because 1 or 2 might defect and some Democrats might defect also -- although it's kind of hard to imagine a Democrat joining a Republican filibuster under the circumstances),

That solves both problems: the stimulus bill will be big enough (if perhaps less evenly distributed in its impact than one might hope -- but multiplier effects will spread out over space), and it will survive a cloture vote.

Problem solved. No depression. Happy days are here again.

Of course, it ain't gonna happen, so I still like long Treasuries.

Time for a Price Level Target, and a Damned High One!

If you believe in a NAIRU, or anything remotely like a NAIRU or an accelerationist Phillips curve, the prognosis for prices is looking increasingly ugly. For those who believe confidently in such a Phillips curve and accept historical estimates of the parameters, deflation is now a certainty, and severe deflation is a strong possibility. Even among those who don't believe in a Phillips curve, deflation should be considered at least a serious possibility, and the danger of a deflationary spiral should not be ignored.

It's time to stop worrying about policies that "may cause inflation in the long run" and to embrace such policies specifically because they may -- and hopefully will -- cause inflation. Markets are desperately in need of "shock and awe," and the Fed can provide that shock by setting a long-run price level target much higher than anything previously considered reasonable. I would recommend a target representing an average rate of inflation of 6% over the next 5 years and 5% over the subsequent 5 years. The Fed could also set longer range price targets that represent lower inflation rates thereafter (assuming the earlier targets are achieved): say 4% from 2019 to 2024 and 3% thereafter. (Experience has now made clear that 2% was too low -- too close to zero -- for a long-run target during normal times.)

The point of using price level targets is that, the worse things get, the more inflation the Fed will promise for the future. And the more inflation it promises for the future (assuming markets believe those promises), the lower will be longer term real interest rates at any give level of nominal rates. If the Fed can induce such an expectation, it will then be able to provide a more dramatic stimulus at just the right time by setting real rates that are significantly negative. (If necessary, the Fed can set longer-term real rates by buying sufficient quantities of longer term securities, or by having the Treasury retire such securities.)

Again, "dangerous policies" that "may be highly inflationary in the long run" are just the policies that our leaders should be embracing at this moment, precisely because those policies may -- and hopefully will -- be inflationary in the long run. So if the Fed buys lower quality securities on which it risks having to take losses, let it say, "It is our great hope, in the event that economic weakness prevents the price level from approaching our target, that we may have the opportunity to take large losses on these securities and to make up those losses by creating more base money. Only by taking such losses can we implement the 'helicopter drop' that may be necessary." And if the Fed should expand the monetary base dramatically in the hope of encouraging bank lending, and detractors should argue that this policy is reckless because the Fed will need to withdraw that money later to prevent inflation and may not be willing to do so, let the Fed respond, "It is not our intention to withdraw that money later, unless the price level should threaten to rise significantly above our target. Should the inflation rate over the next few years prove too low, it is our intention to resist steadfastly any pressure to avoid the very high inflation rates that will then be necessary to achieve our target."

Let's be quite clear about the arithmetic here. If the average inflation rate over the next 5 years should be zero -- which in the absence of policies such as those I advocate above, would be a very reasonable forecast, and in the presence of such policies would still not be an unreasonable one -- the Fed will of course miss its 5-year target by a dramatic margin. But the 10-year target will remain. The arithmetic would then require an 11% inflation rate over those next 5 years, in order to meet that target. That is the promise that the Fed must make for the future in order to achieve the vital goal of producing very low real interest rates today. And as for those who say that 11% is too much, even if they be 99% of the population, to my mind they are all traitors, enemies of the United States and of the world, and if I had my way, they would all be hanged!

Their intentions are good, perhaps, but we must not let such foolishness lead us down the road to Hell.