Wednesday, September 1, 2010

Liquidity Traps and Deflation Traps

Krugman posted a 1998 paper here., which goes some way to explaining what he might be thinking about here. The 1998 Krugman and I apparently think alike. The example he used in his paper is exactly the same one I used here. If anyone doubts the existence of liquidity traps, it is clear that we can produce these in essentially any mainstream, precise, dynamic general equilibrium monetary model. The liquidity trap that Krugman produces is one where you fix monetary policy in the future, ask what it takes in terms of monetary policy to drive the nominal interest rate to zero in the present, then ask what happens if you go further. Once the nominal interest rate is at zero in the present, if the central bank injects more money at the margin, this is irrelevant. In an earlier version of a paper I am currently revising, I included an example that looked almost identical, in a Lagos-Wright construct, but you can do the same with cash-in-advance, as Krugman does. Krugman's 1998 paper then gets into some hand-waving about insufficient demand, real interest rates that are too low (he's describing Japan at the time), etc., that I did not find so useful, but we'll leave that aside for now.

Krugman's 1998 example, which is a temporary liquidity trap, works in exactly the same fashion as phenomena that occur in essentially all monetary models at the Friedman rule. The Friedman rule is a rule for monetary policy that implies a zero nominal interest rate forever. At the Friedman rule, there is always a liquidity trap. Another way to think of this is that there are many paths for the money stock that are consistent with having a zero nominal interest rate forever. If, for example, negative money growth of -4% per year with an initial money stock M implies that the nominal interest rate is zero forever, then -4% per year money growth with an initial money stock xM also implies the nominal interest rate is zero forever, where x > 1. Further, the path for price level in the first case is also an equilibrium in the second case. Note that this is not just standard neutrality of money as the quantities and the prices are the same in both cases. However, it's not any money stock path that will support the Friedman rule. What Ricardo Lagos shows here (and this is related to work done long ago by Charles Wilson) is that, roughly, the money stock has to go to zero in the limit. This is all about the long run, and the forward looking behavior of economic agents. If we do not anticipate that the money stock will be decreasing at a sufficient rate indefinitely, this cannot happen.

Now, Krugman and others seem to associate liquidity traps with deflation. That is certainly the standard Friedman-rule logic, and it could be that when Krugman says "deflation trap" he means "liquidity trap." In the paper I'm revising (see these slides) you can show that liquidity traps can occur for any inflation rate, with monetary policy set appropriately, and the trap can persist forever. The liquidity trap arises in taking full account of the role of banks. What happens is that, if private assets used in financial exchange are sufficiently scarce (e.g. in a financial crisis), and cash is sufficiently plentiful, then the nominal interest rate can be zero, potentially even with a positive rate of inflation. There is nothing particularly weird going on here - no funny equilibria or disequilibria.

Note that there are other liquidity trap phenomena, related to current policy. For example, under current conditions with a positive level of excess reserves, and interest paid on those reserves, a swap by the central bank of reserves for T-bills is essentially irrelevant, for the same reasons you get a standard liquidity trap. The central bank is just swapping one interest bearing asset for another that is essentially identical.

What's the bottom line? First, the conditions required to support sustained deflation in standard models seem hard to fulfill in practice given what we understand about commitment by the Fed to future policy. Second, it is possible to have a sustained liquidity trap without sustained deflation. These are just more reasons why we should not be too worried about deflation.

18 comments:

  1. "These are just more reasons why we should not be too worried about deflation."

    But should we be worried about just LOW inflation? As this can greatly limit the Fed.s ability to fight a demand deficit which causes higher than necessary unemployment and lower than necessary GDP. Plus, it can hurt real wage adjustment due to excessive resistance to nominal wage cuts, that I think there is good empirical evidence for.

    If you're going to claim that all of the employment is just structural and none of it is due to a demand crunch, what do you think of this:

    http://voices.washingtonpost.com/ezra-klein/2010/09/where_the_job_losses_are_in_on.html

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  2. 1. "But should we be worried about just LOW inflation?" That's not clear. If you take a strong position that the inflation rate should be 2%, then it's currently too low. You would have to tell me why 2% is better than 1%, for example.
    2. "Demand deficit" means absolutely nothing to me. That's some old language. Modern macroeconomoists don't find that notion useful.
    3. In the link you talk about, they try to dismiss the idea of mismatch due to sectoral reallocation across industries. But note that they have a lot to say about geography. The key observations are the labor market observations about unemployment and vacancies. It would be useful to know where the vacancies are, and where the unemployment is, both in terms of geography and occupations. We seem to have some inkling that the dispersion across "sectors" (geographical, occupational, and by industry) is high, slowing the recovery. By the way, you should ditch these old notions of "structural" vs. cyclical (what you call "demand crunch") unemployment. Unemployment is unemployment. It's people we observe searching for work. Don't think of this working like a competitive auction market with a fixed wage.

    By the way, you're off topic. I was trying to focus this on deflation without thinking about the real implications - not that these things aren't an important part of the larger problem.

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  3. I'm trying to get my head around this.

    "Further, the path for price level in the first case is also an equilibrium in the second case."

    OK. I think I've got this. It's because the level of intermediation is indeterminate? Over a wide range of equilibria, people don't care whether they hold capital directly, or hold bank money and let the banks hold the capital? So all the nominal and real things are the same, comparing across equilibrium paths, but more capital is intermediated into money on one path than one another? Is that right? It's a sort of Modigliani-Miller theorem?

    But results like that (a continuum of real equilibria) are usually very "fragile", in the sense that a tiny change in the assumptions of the model will destroy all but one of those equilibria.

    "In the paper I'm revising (see these slides) you can show that liquidity traps can occur for any inflation rate, ...."

    That's what I can't get.

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  4. For "banks" in the above, you can read "government plus central bank", perhaps.

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  5. If "money" pays interest, I have no problem with seeing that liquidity traps can occur at any inflation rate. Start in one liquidity trap, increase inflation by 10%, increase the interest on money by 10%, and you are back in another liquidity trap. Is that what's happening?

    If not, then I can't think why the MRS between money and other assets could stay equal to the return differential when you raise inflation and lower the real return on holding money.

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  6. Start in one liquidity trap. Increase the inflation rate (which pushes nominal interest rates on bonds up), and also increase the demand for government bonds relative to real capital at the same time (which pushes the nominal interest rates on bonds back down again). That can put you back in a liquidity trap. OK. I can see that. And that increased demand for bonds, relative to capital, a large part of what got us into the current liquidity trap (falling expected inflation, and falling natural rate, did the rest).

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  7. Nick:

    You say:
    "OK. I think I've got this. It's because the level of intermediation is indeterminate? Over a wide range of equilibria, people don't care whether they hold capital directly, or hold bank money and let the banks hold the capital? So all the nominal and real things are the same, comparing across equilibrium paths, but more capital is intermediated into money on one path than one another? Is that right? It's a sort of Modigliani-Miller theorem?"

    It's more or less standard liquidity trap. People use currency and bank deposits in transactions. The banks hold reserves, government bonds, and loans. In the liquidity trap equilibrium the nominal interest rate is zero and banks are holding excess reserves. Now conduct a one-time open market purchase of bonds. The banks are happy to hold the reserves rather than the bonds, all the transactions are executed using the same media of exchange, all prices and quantities are unchanged.

    "For "banks" in the above, you can read "government plus central bank", perhaps."

    Yes, the central bank is in there too. When I say "banks" that's a catch-all. What's in the model represents all the financial intermediaries out there.

    "If "money" pays interest, I have no problem with seeing that liquidity traps can occur at any inflation rate. Start in one liquidity trap, increase inflation by 10%, increase the interest on money by 10%, and you are back in another liquidity trap. Is that what's happening?"

    No. You can get this without interest on reserves. Note that the equilibrium with a liquidity trap has a nominal interest rate of zero.

    "But results like that (a continuum of real equilibria) are usually very "fragile", in the sense that a tiny change in the assumptions of the model will destroy all but one of those equilibria."

    No, it's not a continuum of equilibria. There are many equilibria (it's a monetary model), but I'm just looking at the stationary ones. There can be a unique liquidity trap equilibrium. Change exogenous policy, and you get the same equilibrium.

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  8. In my Wicksellian way of thinking, you can get a liquidity trap at a positive inflation rate if the risk-adjusted marginal product of capital is negative, which can happen if risk aversion is high enough and physical capital is plentiful enough. I think it could persist forever, too, if people have sufficient motivation to save at a negative real interest rate (thus replenishing the capital stock and keeping the marginal product of capital low). Does this bear any relation to what's happening in your model?

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  9. '"Demand deficit" means absolutely nothing to me. That's some old language. Modern macroeconomoists don't find that notion useful.'

    I have your Macroeconomics textbook (2008 edition). What pages explain your view of the causes of recessions, or big jumps in unemployment? Or if not in that edition, your new edition, or some other summarizing writing.

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  10. Andy,

    Yes, it's actually not so far off. The real interest rate can be low, essentially because there is a scarcity of "liquid" assets - liquidity associated with how useful it is in financial transactions. That's when you get the liquidity trap. What is it that makes the marginal product of capital low in your Wicksellian framework? Of course the usual Keynesian notion is that the real rate is too high when there is a liquidity trap. You would like the nominal rate to be lower, but you're stuck at the zero lower bound.

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  11. Richard,

    You're looking at the 3rd edition, right, with the road and the tree on the front? Chapters 11 and 12 give the standard views on sources of business cycles. I do 4 theories:

    1. Real business cycle model (basically Prescott for undergraduates)
    2. Segmented markets model (gives you a nonneutrality of money in an equilibrium model)
    3. Keynesian coordination failure model (Keynes in equilibrium)
    4. Standard IS-LM AD-AS (Chapter 12).

    This goes through each theory, explains something about how the theory matches the data, and goes through criticisms. I try to be fair about it. I like the most recent edition (4th edition) better, in terms of what I do with the Keynesian economics. I do a sticky price model (essentially Woodford for undergrads) and it fits in better with the rest of the stuff and is much simpler. I want students to understand all of these things and think independently. If you say "demand deficiency," that assumes something in particular about what you think is causing the downturn, and what you should do about it. I tell my students that business cycles have many causes, all of these theories potentially have something to say, and the policymaking involves figuring out what factors are at play and what to do in specific circumstances. Chapters 11 and 12 do not address anything relating to unemployment - it's all employment determination (except of course with the sticky wage in Chapter 12, 3rd edition, which is very conventional). Unemployment is in Chapter 16, where I do search and efficiency wages.

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  12. Thanks,

    I'll order a copy of the 4th and eventually read those chapters.

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  13. Shameless advertising: Yes, the 4th edition has financial crisis stuff in it. I expand on credit markets - some things with frictions associated with information and collateral. As well, I integrate some of the current policy issues into the presentation, among other things.

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  14. Just browsed Wright-Lagos 2005. Why do they assume a positive price level? Isn't the whole point of essentialist models to describe why fiat money is valued in the first place?

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  15. JP: No, that's not an assumption. There is always an equilibrium where money is not valued. We take that as being well-known, and focus on equilibria where money is valued.

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  16. "I tell my students that business cycles have many causes"
    I seem to recall John Bryant saying that business cycles are always at bottom co-ordination failures. That's the unifying theme. You can talk about what lies behind the failure, but I think its a nice way to frame it.
    So I wouldn't have it as a separate theory, its a meta-narrative for all the others....

    pe

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  17. But sometimes there doesn't seem to be a failure, which is what Prescott was getting at. As well, if we think the early 1980s recession was about monetary policy (and we could debate that), that has to be some short-run nonneutrality of money. I wouldn't call that a coordination failure.

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