Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Sunday, November 21, 2010

A Wile E. Coyote Moment

Paul Krugman has teamed up with NY Fed economist Gauti Eggertsson to produce a new working paper: Debt, Deleveraging, and the Liquidity Trap. Krugman provides a bit of background about this project on his blog. I see that at least a couple of people have already commented on paper; e.g., Nick Rowe and Steve Williamson. I thought that I'd join in on the fun.

And fun it is. Eggertsson and Krugman (henceforth, EK) certainly have a way with words. The imagery is splendid; my favorite, of course, being the Wile E. Coyote moment (or the Minsky moment) as reflecting the shock that unexpectedly slips the rug out from underneath the financial system.

O.K., so it's fun. But is it progress? I think it is. In particular, it's encouraging to see that the authors (Krugman, in particular, I suppose) are starting to take seriously the notion that agent heterogeneity and financial market frictions may be important elements to include in a theory of the business cycle. It should go without saying these latter two properties are the sine quibus non of modern macroeconomic modeling methodology.  As EK say in their abstract: "Making some agents debt-constrained is a surprisingly powerful assumption...". Yep, it's a real eye-opener alright. (For a few other surprises relating to the power of this assumption, see my entry here).

I want to keep this post reasonably short, so I limit myself to one (albeit important) aspect of the EK paper: the financial market friction, in the form of a debt constraint. Let me explain take a moment to explain the gist of it (for those who may be unfamiliar).

The key friction giving rise to this constraint is limited commitment (or limited enforcement). In lay terms, think about this as the unwillingness  to make good on one's promises. Taking out a loan would be no problem at all -- if debtors could be relied upon to honor their debt, in particular, by servicing it and paying it off out of their future earnings. But if debt default is a relatively low-cost proposition, then debtors may be tempted to exercise the option. To the extent that creditors anticipate these future default incentives, they are likely to restrict credit supply. The result is that people may not be able to get credit even if they are, in principle, able to pay it off.

As an aside, most people probably think of debt constraints as the consequence of "market failure" leading to an inefficiency. But as I explain here (A theory of inalienable property rights), legally imposed debt constraints might be the solution to a social problem when financial markets work too well. I mention this here because the social problem I highlight stems from heterogeneous time-discount factors, which is also a property of the EK model. In the absence of a debt-constraint, the impatient mortgage their future and embark on consumption trajectory that takes them to hell. Unfortunately for the rest of us, it is a hell that they share with the rest of society (a negative externality, in my model); so we prevent them from doing this.

Alright, back to the main story. So they have two types of agents in their model: patient and impatient. In an unfettered financial market, the latter are eventually enslaved to the former. But an exogenously imposed debt constraint prevents this extreme case from happening. Instead, the impatient hit their debt ceiling and then roll their debt over forever, paying interest to the creditors (the patient). If we call the patient agents "China" and the impatient agents "USA," we might start talking about "global imbalances." But let's not go there (though, if you're interested, you might want to go here).

And now for the Minsky moment: an unanticipated drop in the exogenous debt limit. The shock appears to be modeled as permanent. Imagine that a debtor is servicing a constant stock of $100 of debt (he'd like to borrow more, but creditors cannot secure themselves beyond $100). Following the Minsky moment, his debt limit is dropped to $75 (forever). Creditors are now worried that they cannot secure themselves beyond $75. So how does our debtor respond?

It seems to me that he will respond by defaulting on that portion of the debt he is able to; i.e., $25. I mean, why wouldn't he? It is not like he is committed to paying back debt; after all, the debt limit is rationalized in the first place by the limited commitment/enforcement friction.

And so, following a Minsky moment, we would expect a significant redistribution in wealth away from creditors toward debtors. Now that debtors have a lower cost of debt service, we can expect their consumption to increase (they are still debt-constrained, after all).

This is not, however, what happens in the EK model. Why not? Well, because following the Minsky moment, they impose the following behavioral assumption on debtors: "Suppose furthermore that the debtor must move quickly to bring debt within the new, lower, limit, and must therefore deleverage to the new borrowing constraint." [pg. 7]. Of course, this is what I assumed too. The difference is that EK assume that the deleveraging process does not entail default. Somehow, despite an implicit limited commitment friction, debtors are committed to deleveraging by paying down their debt. And, of course, paying down their debt means reducing consumption.

Is it not interesting how one is able to derive such polar opposite predictions from two plausible views of how debt is discharged following an unexpected financial market shock? Naturally, I am biased toward my view--not necessarily because it is descriptively more accurate (though we obviously do see defaults in the data) -- but because it appears logically more consistent with the frictions underlying the debt constraint in the model. If a prescribed behavior is inconsistent with the model environment, then (in my view) even more than the usual amount of caution is warranted in weighing the model's predictions and interpretation of events. (This is not to say that internal consistency is the only desired criterion of a model, of course.)

It would be interesting to explore the robustness of the EK results in the context of a model that takes the source of the debt limit (and its propensity to change) more seriously. (Not that the other shortcuts they take deserve any less attention.)  All in all, I like the paper because it at least makes at some attempt to formalize a popular interpretation of recent economic events. It's a small step forward and should, I think, spur a lively debate and future refinements...which is what our science is all about.


  1. Hi David:

    Suppose the debt limit is cut from $100 to $75. How will this affect the natural rate of interest?

    Under the EG/PK assumption (that the impatient have to pay back the $25 immediately) it will cause a very big drop in the natural rate of interest. Because the impatient are suddenly forced to save, and so forced to act like ultra-patient people.

    Suppose instead we run with your assumption: there's a forgiveness/default on the $25 excess debt. I think that would leave the natural rate of interest unchanged. Because the new debt limit is binding, just like the old debt limit, so the impatient half of the population are shut out of the loanable funds market, and the rate of interest will be determined by the time-preference of the patient.

    But suppose instead there's a continuum of agents, from the very patient to the very impatient (maybe some sort of multi-period OLG model). The lower is the debt limit, the greater the fraction of the population that is borrowing constrained, and the lower the natural rate of interest. So even if a cut in the debt limit from $100 to $75 leads to a default/forgiveness of the $25 for those who were already over the new limit, we would still see a reduction in the natural rate of interest.

  2. The model assumes the change in the debt limit happens faster than the credit market can adapt, so the model first shows overshoot and undershoot. But it still damps out eventually. The impatient sell some inventory, and refinance under new rates. The impatient are marginally poorer because they bet that the limit would stay high.

    How does one get to a deflation spiral? Borrowers have to be more inept at downsizing then lenders such that they fall farther away from equilibrium.

  3. I'm not going to read the paper, but I will comment on one aspect. If what Matt says about the change in the debt limit being faster than the credit market can adapt is so, then the researchers get this aspect backwards in at least some cases.

    Banks were rolling over their short-term financing pretty much daily. The refi rates started to up before the real estate crash, not after. It appears that those institutions lending to the banks (i.e. other banks) were adjusting the cost of credit based on new information about asset quality (MBS for most part).

  4. "It seems to me that he will respond by defaulting on that portion of the debt he is able to"

    [I haven't read the paper yet but ...] is there potentially something in here about banking? As I understand it, the paper does not feature banks, but banks try to deleverage by selling assets as opposed to defaulting, because they are trying to avoid declaring themselves bankrupt. Then when that becomes unavoidable, the government steps in to pay off bank creditors, assume (de facto) ownership of bank assets and again attempts to avoid default.

    Might this justify the behavioural assumption they use?

  5. What the bond market lacks is the ability to bet the future GDP, short money, as Scott Sumner points out. If the bond market is unable to bet the negative direction as easily as bet the positive, then we can get the persistent asymmetry, bond holders finding their power over lenders increasing in a downturn, hence a cause of the debt spiral.

    My point was that we need a persistent, increasing force to spiral, setting initial conditions is not enough.

  6. Suppose the exogenous debt restriction drops, as in this example, from $100 to $75. Debtors default on $25 of their debt.

    But what if that debt restriction is not exogenous, but endogenous, and that the default causes the debt restriction to fall again? Isn't the logical outcome default on 100% of the debts? And what does that--the continuous threat of complete defaults--do to the credit system?

  7. This is a really good post I think.

    However, as a regular Krugman defender I'm of course thinking of how to reconcile things in his favour, I'm struggling though. How's this for a try...

    Perhaps all the debt is short term and fully collateralized with some sort of long term assets (don't be a smartass and ask me what assets or where they come from, they are an endowment). The debt lasts one period and has to be refinanced each period.

    Now, the value of the assets falls from 100 to 75 so the debtor can't roll all the debt (again, don't ask me how, say negative productivity shock). However, there is no seniority so all creditors have equal claim meaning that the debtor can only declare bankruptcy and have all the assets seized, it is not possible to default on only 25% of the debt. Thus, bankruptcy means that the (former) debtor is left with no assets and thus can never borrow again.

    Now at least there is a (potentially large) cost to the debtor of default which means that he may well choose to have a period of extremely low consumption that allows him to continue financing the $75 worth of borrowing instead of being shut out of the debt market forever.

    What say you?

  8. PS: of course, keeping access to the debt markets is only valuable if there is some chance that the asset value, and hence borrowing capacity, will increase again in future.

    So, if we like the negative productivity shock interpretation then we just have to allow for the possibility of positive shocks as well.

  9. I think Adam's on the right track. For example, Mendoza (AER forthcoming) and Mendoza and Quadrini (JME 2010) have borrowing constraints of the form b_t <= psi P_t k_t, where psi is a parameter that captures the degree of the enforcement problem.

    We can think of this kind of constraint arising endogenously (in a limited, superficial way) from an enforcement problem in which the lender can only recover a fraction 1-psi of the borrower's collateral in the case of default. Importantly, this kind of constraint precludes default in equilibrium by restricting the set of contracts to those that are enforceable. The borrower will never default because the value of his collateral is at least as high as his required debt service.

    It's worth taking a look at the two papers I mentioned. They generate debt-deflation mechanics without sticky prices or any notion of nominal prices at all. It comes purely from general equilibrium. These papers are far better than E&K's in terms of explaining this phenomenon. The real contribution that E&K make (at least in my opinion) is the point that fiscal policy can loosen borrowing constraints of this form and dampen the financial accelerator effects that generate debt-deflation.

  10. Nick: I think any way we slice it, the real rate of interest will be lower (this is a standard property of neoclassical models with debt constraints, is it not?). Of course, having to deleverage by paying down debt quickly will cause the short-term real interest rate to spike down more sharply, before recovering to its (lower) steady-state level. But in any case, with lower interest rates and a good chunck of debt discharged, won't this mean more purchasing power for the impatient?

    Luis Enrique: There is nothing in their model about "banking" per se, or collateralized lending, or distressed asset sales, for that matter. In any case, I'm sure that one can come up with many stories to justify their behavioral assumption on debt discharge. But stories are not a perfect substitute for explicit modeling.

    doc: I think that Nick Rowe made a similar point in his review.

    Adam P: Yes, I am following your story and it may indeed be one way to rationalize what EK have in mind. You take a lot of things as given, however (not a criticism, just a fact). You speak of collateralized debt, of seniority (a lack of), punishment for default, etc. These are all things that should be modeled explicitly, I think.

    Joe: I presume there is no default in those models because agents understand beforehand that default incentives can vary with the state of the world. This is not the case in the EK paper; the Minsky moment is completely I imagine that default should occur. Oh, and thanks for the references!

  11. Actually, in Mendoza's JME paper with Quadrini the shock in question is completely unanticipated. The constraint there is slightly different (the borrower can divert a fraction psi of his capital plus output at tomorrow's prices) but basically the same. They get away with it because the transition dynamics after the shock are deterministic so future prices are always known.

    I agree that the theoretical justification for this kind of constraint is a bit weak. It works fine in a deterministic world when we know the price of capital tomorrow with certainty, but if something unexpected happens that makes my debt obligations larger than the assets I can divert, I should default. I guess my point is simply that it's a common modeling choice even among "serious" (in PK's terminology) macro researchers.

  12. David: "I think any way we slice it, the real rate of interest will be lower (this is a standard property of neoclassical models with debt constraints, is it not?)"

    Yes, I think so.

    "But in any case, with lower interest rates and a good chunck of debt discharged, won't this mean more purchasing power for the impatient?"

    The way I see it, the default on the debt causes a transfer of wealth (purchasing power) from creditor to debtor. And the lower interest rate also causes an income effect of the opposite sign for creditor and debtor. To a first approximation, these transfers and income effects cancel out at the aggregate level.

    By the way, I second what Adam said. You have put your finger on some crucial assumptions of the model.

  13. David,

    yes, I am leaving tons out of course. If I saw a simple interpretation in the context of the model as they wrote it there'd have been no struggle:)

  14. the patient agents "China" and the impatient agents "USA," we might start talking about "global imbalances." China outsourcing