Tuesday, August 31, 2010

Deflation Traps

Here's a Krugman post about deflation. Early on he says this:
Now, at this point any Taylor rule fitted to past Fed behavior says that the Fed funds rate should be something like minus 5 or 6 right now, but you can’t do that, so we’re stuck with an interest rate that’s too high given low inflation and very high unemployment.
I wish people would stop making the argument this way. If your model is a New Keynesian one, as seems to be the case here, and you are thinking about policy in terms of a Taylor rule, you better take account of the fact that there is a zero lower bound on the nominal interest rate. If the rule is telling you that the fed funds rate should be minus 5 or 6, you have the wrong rule.

Roughly, the rest of Krugman's argument hangs on this:
The crucial thing to understand about this position is that it’s not self-correcting. On the contrary, as inflation falls over time and possibly goes to actual deflation, we sink deeper into the trap.
Now he's just making it up. "As inflation falls over time..." Why? How? Then he qualifies it ("...possibly goes to actual deflation"). Is that high probability or low probability? Can you put a point estimate on that, with a confidence interval? Why do you get trapped? If Krugman knows, he should lay this out for the rest of us so we can evaluate it.

A crucial element in this is what happens to the quantities, in particular the ones on the Fed's balance sheet, as this process unfolds. New Keynesians wanted to ditch monetary quantities from their models, in part because this made things simple, and so they could focus on what they thought was important, principally the welfare losses from sticky price frictions. Contributing to that was the failure of Old Monetarism, principally due to instabilities (over virtually any horizon) in "money demand" functions.

However, the financial crisis caught many people with their pants down, unfortunately. The New Keynesians are trying to rectify that by getting monetary quantities and financial factors back in their models. Of course the Real Business Cycle people had their pants down too - it's as dangerous to put all your eggs in the TFP basket as it is to put them all in the sticky price basket.

Here, I construct what I think is a plausible future scenario for future Fed policy, and I can't convince myself that sustained deflation can happen. If you think it is likely, you need to explain (carefully) why financial institutions, and everyday Joes and Marthas, will continue to hold $2.3 trillion in outside money which is appreciating in real terms, and not somehow use the stuff in transactions, thus causing inflation. And the answer can't be "Japan."


  1. Maybe we can use the TR - the negative reading - to deduce how much the Treasury yield curve must be pulled down, and therefore how much QE is needed (...assuming that QE actually works).


  2. Can anyone explain what the cross in the Krugman's post means? It seems our Nobel prize winner thinks he can draw any two lines with any sexy name he likes. Ignore me if you could follow Krugman's analysis with his fancy picture.

  3. Anonymous 1:

    That logic is something like what Rudebusch argues here:


    However, I don't buy it. It seems to me you need a model to capture the quantitative easing, so you can work that into the analysis. The model is wrong, so you have to fix it.

    Anonymous 2:

    There's a related picture in Bullard's paper here:


    He argues that the full blown analysis behind the picture is in a paper by Benhabib and coauthors, concerning bad properties of the Taylor rule. If you read Benhabib et. al. and look at their examples, note that when you converge to the deflationary equilibrium (for example a Friedman rule), this requires a particular behavior of the money stock. I can give you more details if you want.

  4. I agree completely that the *answer* can't be Japan, but wouldn't it be desirable for it (doesn't it have) to be part of the question? As in: "... our model can also explain Japan's deflation ... "? I'd like to turn the challenge around to the pioneer of "new monetarism" (I just read the "desiderata" for it, and found it fascinating, btw): if you think sustained deflation, as in Japan, can't happen- what are the essential factors distinguishing this situation and theirs? And the answer cannot be "because they're different".

  5. Catesby,

    Yes, good point. I know a little bit about Japan, but not enough to be very confident about the comparison. I think it's a mis-characterization, though, to say that the Japanese deflation has been "sustained." The banking system is obviously quite different, and the central bank has behaved in different ways. Can you give me a good reference that puts the key observations on Japanese time series and the whole financial and central banking history for the last 20 years or so in one place (or a few places)?

  6. Thanks for the reference (here is anonymous #2 & #3). But Krugman's picture still fails.

    The dynamics other than the intersection one is explosive, so there are 3 possibilities: (1) explose to infinite inflation and interest rate; (2) converge zero bound of interest rate, as what Krugman main described as "the trap"; (3) steady state at the intersection.

    Since both inflation rate and interest rate are jump variables, the economy should jump to intersection immediately, which is the only perfect foresight eqm. It is not the case ONLY when the slopes of line reversed, so there are continuum of eqm paths converging to the intersection. I think it is the indeterminacy suggested by Benhabib et al. But even in this case, the zero bound never hit.

    The trap is possible only when is (a) the slopes of line reversed and (b) the intersection is below the x-axis. If we have (a) but not (b), then no trap is ever hit on any eqm path; if (b) but not (a) then the dynamics is explosive and moving away from the trap.

    It seems our Nobel prize winner has everything wrong

  7. "Since both inflation rate and interest rate are jump variables, the economy should jump to intersection immediately, which is the only perfect foresight eqm..."

    Assuming I could play basketball like LeBron James I'd be doing commercials for Nike.

    When the conclusion is extremely sensitive to the relaxation of ludicrously unrealistic assumptions don't you think that should be taken into account in your inferences from the model to reality? Or you should rely a lot more heavily on models which don't critically depend on fairy land assumptions?

  8. I'm sorry, I can't get the LeBron James example. What happens to Kobe Bryant too?

    When the analysis of Prof Krugman is extremely sensitive to the arbitrary assumptions don't you think that should be taken into account in your inferences from the model to consistency? Or you should rely a lot more heavily on models which don't critically depend on anything-you-can-say assumptions?

  9. Yes, Richard. Try harder. You're not making sense so far.

  10. anonymous: I replied in the subsequent post. Thought I would just write this thing down.

  11. Perfectly instantly flexible prices and perfect foresight and perfect rational expectations for everyone are assumptions that are far from reality, or extremely far, and the models that use them like with Ricardian equivalence are very sensitive to the relaxation of these assumptions, and that should be taken into account in the inferences that people draw from these models to reality, rather than making literal, or highly literal, inferences from these models to reality.

  12. The solution to the deflation trap is obvious: we must simply follow the Kocherlakota-Williamson logic and increase the fed funds rate to a level above the long-run real interest rate.

    Obviously, the market will realize that such a nominal rate can only be consistent with inflation, because we know from the Fisher equation that i=r+pi, so if i>r we must have pi>0. Hence agents will expect positive inflation (despite the fact that the money supply would be falling) and we will move effortlessly to a new equilibrium with positive inflation.

  13. Anonymous:

    Here's where your story falls down, and where you have demonstrated that you have not yet understood the whole debate:

    "Hence agents will expect positive inflation (despite the fact that the money supply would be falling)"

    The way you support a particular nominal interest rate path (typically - there are some complications due to the the large positive supply of excess reserves in existence) is with a particular money supply path. If the money supply is falling that's not going to support what you are proposing as a long-run nominal interest rate.

    Don't put words in the mouths of others, or attribute thoughts that aren't there. Give us your own thoughts.

  14. If the money supply is falling that's not going to support what you are proposing as a long-run nominal interest rate.

    That's exactly the flaw in Kocherlakota's argument. He claims that keeping rates low leads to deflation, but the only way the Fed could achieve this is by continually increasing the money supply.

    So, I'm not putting words in the mouth of others, I'm using their ideas in a different context to illustrate why they were mistaken.

    My own thoughts on deflation are pretty much "old" Monetarist: if the Fed can engineer a sufficient growth in the money supply (M2 say) then deflation can be averted. I don't see (anticipated) deflation as a problem in any case.

    I think you're being a bit harsh on Krugman, though. He's explained his views quite clearly in various articles on the liquidity trap, and they make sense up to a point.

  15. I don't know of any *good* lost decade Japan references for anything (monetary/fiscal/banking policy), though I've not dug very far. The most accessible stuff that everyone cites as proof of whatever position they are plugging (e.g. Krugman citing Posen's "Fiscal Policy works when it is tried"), strikes me as resting on weak theoretical foundations.

    On banking specifically, would you say there is a gap to be filled with a comparative study of policy in the aftermath of banking crises- "800 years of financial clean-ups", if you will? Promising dissertation material, perhaps?

  16. Yes, plenty of work here to do. Lucas said once (or something like this) that once he started thinking about growth he couldn't think about anything else. Don't you find it's that way with this stuff?

  17. Let's put it this way: it isn't my field, and I've got a stack of real work to do, but instead I'm spending sleepless nights sifting through blogs, ploughing through papers, and pouring over balance sheets.

    If one were to start a project along the lines I mentioned above, any ideas about useful theoretical starting points?

  18. That's hard to say. I'm not sure about the specifics of what you want to do.

  19. It's an open-ended question, and I understand if you don't have time to answer, but I guess I'm asking:

    If you needed facts about changes in financial intermediation in the wake of crises to incorporate into or inform a new monetarist model, what sort of things would you most want to know?

  20. 1. How does the structure of bank supervision and regulation matter?
    2. What about systems dominated by a few large banks (e.g. Canada) vs. systems with a lot of small banks and some large ones too (e.g. US)?
    3. What about too-big-to-fail? How has this affected incentives and behavior of banks? Do banks get large because of economies of scale or the protections of too-big-to-fail, or both?
    4. When crisis happen and there are massive injections of liquidity by central banks, where does it go? What motivates banks to hold reserves, sometimes in very large quantities? How do capital requirements come into play?
    5. What is quantitative easing about? Why does it matter?

    How is that?

    Takeo Hoshi, Anil K Kashyap
    Working Paper 14401

    seems to have useful data and references on the Japan's banking crisis.