Friday, April 12, 2013

Liquidity Traps and Low Real Rates

Not much time for blogging these days, but I thought I would contribute to this discussion by David Andolfatto, Tyler Cowen, Paul Krugman, and Brad DeLong.

Here are the facts: (i) The short-term nominal interest rate is essentially at the zero lower bound (ZLB); (ii) real bond yields (of all maturities) are very low relative to history. People have a hard time explaining those facts with Keynesian models. In a typical sticky price New Keynesian model, the problem that the ZLB can present for monetary policy is that the real rate of interest is too high, and there is no way to lower it. But if one thinks that history is a guide to what is right, then it looks like what is wrong is that the real rate is too low, not too high.

How do New Keynesians deal with this? If you read Ivan Werning's paper, for example, you'll see that he sidesteps the question. In Werning's model, the central bank wants to be at the ZLB because there is a negative shock to the natural rate of interest, and he analyzes how policy should deal with that problem. But what's a natural rate shock? I don't think we want to think of the financial crisis as a change in preferences, with everyone becoming contagiously more patient, any more than we would want to think of the Great Depression as a contagious attack of laziness.

If you press New Keynesians on this question, they will say that the natural rate shock - or preference shock - stands in for something that is going on in another type of model. One explanation I have heard appeals to incomplete markets frameworks. In such models, if exogenous debt limits for individuals fall, then the real interest rate will go down. In those models, the real rate is always below the "natural rate," which is the rate of time preference, and the gap between the natural rate and the actual real rate depends on how tight borrowing constraints are. There's something like this going on in Eggertsson and Krugman's paper.

But carry that one step further. Why would borrowing constraints be tighter in the world we're living in now? One explanation could be that collateral has become more scarce. The financial crisis essentially destroyed a large quantity of privately-produced collateral, which took the form of asset-backed securities. Government debt is a substitute for privately-produced collateral, and with a lot of sovereign debt in the world looking very dodgy, the world demand for the debt of the US government is very high. Assets that are used in financial exchange, and which serve the role of collateral in credit transactions carry a liquidity premium. The prices of those assets are higher than their "fundamental," where the fundamental price is what would be justified purely by the future payoffs on the assets and risk. The more scarce the assets are, the higher the liquidity premia, and the higher the prices. Higher asset prices is the same thing as low real interest rates. Simple.

Thus, the explanation is not a drop in "natural" rates of interest. It's the scarcity of safe assets for use as collateral and for exchange in financial markets.

I've been thinking about this a lot lately, and think I have come up with something interesting. I'm presenting some preliminary work on this on Monday at this conference. I'll tell you more later when I have the bugs worked out.


  1. Two questions:

    1. If your and Krugman's policy implications are the same ( more government debt as tepmorary replacement for private debt ), it looks like you and Krugman are describing the same thing with words that seem opposite because you are simply doing comparisons in the same model between the different interest rates. So it is just a definitional, not substantive difference?

    2. Suppose technological innovation would allow us to reduce the interest rates below zero. Could you briefly describe the intuition about the optimal course of action in this case. Is it better to cut rates below zero, or is it better to expand the supply of government debt?

    1. At zero rate in a deflationary economic environment, the real amount of money held increases over time, but the owner pays nothing for this free 'service'. That's unfair and unbalanced.

      So the interest rate should be negative such that his pile stays at the same real value or maybe marginally more more or marginally less, depending on other factors.

      The interest rate can be different for different sums of money or asset classes. So zero for low deposits and higher for higher deposits.

    2. Money Demand:

      1. No. The model is different, and policy works in a different way.

      2. What "technological innovation" do you have in mind. You understand that the ZLB is just an arbitrage condition?

    3. It isn't "just" an arbitrage condition; it's an arbitrage condition made possible by the behavior of a monopolist market manipulator (the Fed, which makes this arbitrage possible by promising to use its monopoly power to maintain the real value of money). Or it's made possible by sticky prices -- if one believes in such things. If you unstick prices and/or use the Fed's monopoly power in a different way, then you can remove the arbitrage condition and thereby remove the ZLB. Miles Kimball has a proposal to do this by establishing a crawling peg between paper currency and bank money, with the Fed promising to maintain the value of bank money but having paper currency deliberately depreciate. This would break the arbitrage, and banks (and the Fed in particular) could offer a negative interest rate (provided it wasn't larger than the depreciation rate of paper currency, which we assume is large enough that this wouldn't be an issue).

      So suppose we did have such a system. Under what circumstances would it then be preferable to increase the supply of safe assets rather than cutting interest rates?

      Or else just suppose the target inflation rate were higher than it is. If expected inflation were 3%, would cutting the interest rate to zero from 1% be a good idea in circumstances like the present? And/or would it be preferable to increase the supply of safe assets?

      And suppose the natural real interest rate were -2% under the current inflation target. When would it be better to increase the supply of safe assets and raise the interest rate above zero, and when would it be better just to keep the interest rate at zero?

      Now that I think about it, the answers to those questions are pretty straightforward. There is a welfare loss due to liquidity constraints, which is reduced by increasing the supply of safe assets. There is presumably some cost to creating those safe assets (for example, the deadweight loss of future taxation, if the assets are government bonds that need to be serviced). You produce safe assets until the marginal cost equals the marginal benefit. In the absence of a zero bound, this is straightforward. In the presence of a zero bound, it's a little more complicated, because there is an additional benefit in avoiding the zero bound. But in principle it's a separate issue.

    4. The way you describe Kimball's proposal, it makes not sense to me at all. Can you give me a link?

    5. This is his main article, though the idea has been fleshed out more in Twitter discussions and commentary elsewhere, I think.

    6. An odd way of looking at it. Some people view the problem as trying to create inflation by pushing on a string. Once we hit the zero lower bound, we can't tighten in the usual sense. But if we could charge negative interest on reserves - i.e. tax the reserves, then we solve the problem. Holding outside money (reserves plus currency) becomes less desirable, and the price level has to rise. Kimball wants to tax currency. I think we can all understand that this is impractical. But it's not a new idea. See this Marvin Goodfriend paper:

  2. The market is trying to make interest rates negative which would rebalance the economy more quickly, but we do not allow this for fear of capital flight.

    But we could allow it by having more than one interest rate. One zero bound for low amounts, say under $100 000 and others negative for higher amounts. Its equivalent to haircuts in many ways.

  3. Stephen,

    I think that sounds roughly like how I think of it. The relevant rate is the borrowing rate between unconstrained and constrained households, made up of the real (risk free) rate plus a "representative" credit spreads. When credit spreads are high, presumably the optimal cost of borrowing will rise less than the credit spread, the equilibrium total borrowing rate being contained by borrowing demand. So the natural (risk free) rate drops. If the credit spread is high enough the natural rate can go arbitrarily negative.

    So what to do about it? Issuing enough government debt would probably do the trick, probably via devaluation causing reflation and a consequent drop in the real rate at the ZLB. Maybe we could use the money for a sovereign wealth fund, but perhaps Wallace irrelevance would mean that this would not cause the desired devaluation. Perhaps we have to spend it or heli drop it, especially on constrained consumers.

    I do notice a bit of cognitive dissonance among some commenters. Yes, issuing more debt could raise the natural rate, which would be a good thing. But some seem to confuse the real rate and the natural rate. If the CB raises the real rate that is absolutely a *disquilibrium* dynamic. The CB *sets* the real rate wherever it wants to and the natural rate doesn't follow at all. As Krugman says, the Fed's job is to get the real rate as close as absolutely possible to the natural rate. That definitely doesn't mean raising it. Unless the Fed can do something about credit spreads, I don't see any other relevant option than forward rate guidance.

    1. "Yes, issuing more debt could raise the natural rate, which would be a good thing."

      All this natural rate talk is confusing things. Think of the natural rate as the real interest rate if policy is optimal, within the class of feasible policies. The way I'm thinking about it, the natural rate hasn't changed, and we're below it.

  4. Ultimately, the best way to escape the liquidity trap (short of limiting issuance of currency and putting the policy rate negative) is to put unsustainable upward pressure on demand thus causing inflation. Issuing debt *in and of itself* doesn't do anything because you have to issue it in exchange for something. If that something is capital assets, then Wallace neutrality probably kills you. The only alternatives are spend it (including e.g. "investing" it in public goods that can't be reversed by Ricardian private agents) or heli drop it. If you heli drop on unconstrained balance sheets then Ricardian equivalence kills you. So you have to drop it on poor people or fairly indiscriminately since most people are probably fairly constrained.

    If most people are already paying high borrowing costs then a heli drop is a no brainer from an aggregated balance sheet perspective. Government leverages up at a 0% rate, and levered consumers pay off credit card debt costing 20% or worse. The personal debt relief massively outweighs the government debt in the global intertemporal optimization.

    (Yes, I've hand waved a bit, replacing the representative household with the typical household. Given the current wealth distribution, I think the number of people that would be harmed by a heli drop is small. And I'm not that concerned for them.)

  5. Stephen,

    I don't view the 2 points of view as conflicting. The natural rate of interest is negative for whatever reason, so in order to keep inflation and the output gap in line, we need to lower the nominal rate (which we can't because of the ZLB). Increasing G or increasing the expected inflation will increase the natural rate of interest and provide another way. Whether doing this would also solve the safe asset shortage is a different matter, but my view is that it probably will.

    Second of all, if you assume the CB is following some Taylor rule or NGDP targeting, increasing expected inflation, would increase the long term nominal rate and usually by more than just the expected inflation so that it would increase the long term real rate. So a liquidity trap is causing the long term real rate to be low, which would answer your initial question.

    Hope that makes sense?

  6. Stephen,
    I'm not sure what you mean by, "collateral used for financial exchange".

    If I am a corporate Treasurer, I can place funds on deposit at JP Morgan for probably 10bp -- less than the 20bp I might get from a repo. Are you saying real rates are negative because corporate Treasurers want to earn an extra 10bp? Or are they negative because corporate Treasurers mistrust JP Morgan?

    Also, why were real rates positive in Japan during their banking crisis? Why didn't they experience a "collateral shortage"? Perhaps for structural reasons, agents continued to trust their banks.

  7. Stephen,

    To me, the natural rate is the optimal real rate for any given policy choice. I don't think that's confusing at all. Think of the CB as always moving last in response to whatever happens in fiscal policy. The natural rate is already defined by the fiscal policy choice when the Fed has to choose its policy real rate setting.

    Anyways, what is the benefit of your definition? Is there some complex policy choice available to the Fed that involves the Fed hiking the real rate to the new "optimal real rate" (natural rate!) I don't understand how the CB is supposed to issue debt with non-trivial effects unless they are spending or heli dropping on constrained households. What is this "optimal real rate" (natural rate!) policy of which you speak?

  8. Steve, quick question: What do you mean by "history is a guide to what's right"?

    1. Noah,

      I am so glad you asked that question and I hope he answers it.

      As for this post, I don't understand why the natural rate thing is so hard for Mr. Williamson to catch on to. It's about a shock to aggregate demand. As for why the natural rate does not rise quickly, there is some disturbing mechanism, which may vary by circumstances. In the current depression, it seems to have been that it is a balance sheet recession which, for a while exemplified a temporary debt deflation pattern. That has come to an end, but people are still attempting to repair their balance sheets (not everyone as Krugman-Eggertson have pointed out). The savings rate is higher for individuals, but the government has not filled the gap and private investors apparently realized that there would be a prolonged depression, so are averse to investment in productive capacity they may not have need to use. This results in low demand for savings. Savings up, investment down => disequilibrium in the credit market in the form of a liquidity trap. I hope I got all that right and my explanation can be followed.

    2. Julian, I don't want to respond on Steve's behalf, but I think you take too much for given. Example:
      "Savings up, investment down => disequilibrium in the credit market"

      But why would such a disequilibrium exist? What kind of assumptions about human behavior or market frictions does one need to make to get such an outcome? These are important questions that the simple story you told does not answer. Eggertsson and Krugman's paper does try to answer some of these questions. I think Steve is simply trying to take the analysis deeper. He is trying to emphasize the role that safe assets play as collateral that facilitates transactions, and study what happens when such assets become scarce. I think this is probably part of the story, but not the whole story. But I am more sympathetic to behavioral explanations than he is.

    3. Zero lower bound?! What we are talki g about is that the natural interest rate is not reachable unless market participants expect higher inflation than prevails (in this scenario). Paul Krugman's Japan liquidity trap paper discusses this conundrum, as does Mike Woodford. The essential thing is to cause market participants to expect higher inflation OR to shift the New Keynesian IS curve to the right, because the natural rate is otherwise well out of reach.

    4. But first you need to answer how consumers make saving decisions. It is easy to draw a supply and demand curve for loanable funds, show that they intersect where the real interest rate is negative, and say, gee, the zero lower bound is preventing us from getting there. However, it would also be bad science, since it is ad hoc.

      Think of the natural interest rate as the rate at which consumers are indifferent between consuming an extra dollar now versus saving it and consuming that dollar plus interest in the future. Given that people value present consumption more than they value future consumption, that rate needs to be positive to compensate them for postponing consumption. Otherwise, people would borrow against their future income to consume more now. So here is the issue. Despite the big drop in the real rate of interest, people are not doing that. So what is going on? Is it because people have become so much more patient than they used to be (a drop in the natural rate, as defined), or because they are they facing more stringent borrowing constraints? If the latter is true, is it because of a drop in the availability of collateral? These are important questions both from a theory and a policy perspective, and cannot be addressed with a simple IS-MP framework. Yes, I use it to teach undergrads (though I am planning to switch to Steve's book next semester) but the truth is that it is very superficial, and therefore very limited in terms of its use for policy.

    5. Read my first comment and homework: read Krugman-Eggertson's discussion of deleveraging on VOX (just search for Krugman Eggertsson vox). Absorb its meaning. It holds some of the keys to this. I'm just writing this for your convenience and because I am unable to go too deep into this right now (family, work, etc.).

    6. Boy Steve really attracts the crackpots doesn't he? From Guam, no less.

    7. Julian, you are trying really hard to miss my point, aren't you. I have read Krugman and Eggersson's (E&K) actual paper, though not the discussion on VOX. As I said in a previous comment, the paper goes way beyond the simple IS-MP story you laid out, and I gave them credit for it. Krugman likes to frame things in IS-MP terms, perhaps because he thinks readers are more familiar with this framework, but in my opinion he is doing a disservice to the paper.

      But looking at the details of the model also raises questions. Here are three important details:
      1) In the model, there are two types of consumers. Given the rate of interest, the patient consumers are indifferent between consuming now or later, but the impatient ones are not. Impatient consumers would rather consume more now, but the debt limit prevents them from doing so.
      2) As a result, these consumers end up cutting consumption involuntary when someone (who, we are not told) forces them to pay off some of their debt. This is imposed exogenously by the authors in what they call a "Minsky moment".
      3) Patient consumers actually do increase current consumption in response to the drop in the real interest rate, but under certain conditions the increase is not enough to offset the drop in the consumption of impatient consumers, unless the interest rate becomes negative (zero lower bound).

      Now, maybe it is because I do mostly empirical work, but there are a few things I am uncomfortable with.
      A) Did banks really start calling back loans? Were people truly forced to pay back their debt? I personally have not heard many such stories. So it would be nice if E&K could provide some evidence that the reduction in consumption was indeed forced upon consumers.
      B) Did the consumption of households not facing borrowing constraints really increase? I have not looked at the data, but this proposition contradicts my general impression that the drop in consumption was rather widespread.
      C) Of course, it could be that I am taking the model too literally. The authors claim that we can think of the drop in the debt limit "as corresponding to a sudden realization that assets were overvalued and that peoples’ collateral constraints were too lax." But is the shock in their model equivalent to a drop in the value of collateral? I am not sure. In E&K a drop in the price level is bad because the debt is in nominal terms but the debt limit is in real terms, which means that impatient consumers must cut consumption more if prices are falling. But if the true shock is a drop in the nominal price of a class of assets that serve as collateral, then a drop in the price level of consumer goods will prevent the relative price of that asset from falling as much as it otherwise would have. This Pigou effect is absent from their model, which has no real assets: any saving by patient consumers is used to finance the consumption of impatient consumers. In my opinion, this is a serious drawback!

      Of course, once again, the IS-MP story has nothing to say about all of this!

    8. It's "if history is a guide to what is right..."

      It's an assumption: If we assume that the average real rate prior to the financial crisis is roughly optimal, then the current real rate must be too low.

      Of course I don't know what is optimal withoout a good quantitative theory.

  9. Steve, it would be really helpful if you could briefly and clearly answer Andy's question:
    "Or else just suppose the target inflation rate were higher than it is. If expected inflation were 3%, would cutting the interest rate to zero from 1% be a good idea in circumstances like the present? And/or would it be preferable to increase the supply of safe assets?"

    Most of your readers here do not have time to study your model, so a brief answer that illustrates the main intuition would be really helpful.

  10. I'll second The Money Demand's request for an answer to Andy's question.

    Also, what does it mean to increase the supply of safe assets? Would you issue bonds in exchange for

    A) reserves?
    B) capital assets?
    C) goods and services?
    D) nothing (heli drops)?
    E) something else?

    It's well and good to speak about the optimal rate over some given policy space. But I can't figure out what policy space you are talking about. "Create more safe assets" is not well defined.

  11. "I don't think we want to think of the financial crisis as a change in preferences, with everyone becoming contagiously more patient, any more than we would want to think of the Great Depression as a contagious attack of laziness."

    What an amazing juxtaposition of strange assertions.

    In a financial crisis, when the world is collapsing around us, finanace-heavy balance sheets are based on incorrect valuations, and no one trusts anyone anymore, _obviously_ everyone becomes contagiously more safety-seeking. What you call "patience" is a patience/safety tradeoff.

    We'd be happy to think of the Great Depression as a contagious attack of laziness _if there were lots of examples of out of work people happy to be out of work._ We're not happy to think of the GD that way because people being happy to be out of work were in short supply then, as always.

    1. No, what you are proposing is in effect a rise in risk aversion, and it would affect the risk premium and not the risk-free rate. Fail.

  12. First the stuff about how high interest rates lead to inflation, now the stuff about the real rate being below the natural rate. Fair is foul and foul is fair.

  13. Steve, interesting analysis. I will be waiting to see the paper. I still cannot decide how much of the problem is due to borrowing constraints versus buyers' remorse. The supply of financial assets was driven by households demand for homes, equipment for these homes, and so on. At some point buyers found out that they had vastly overpaid. So what if people decided to pay off some of the debt they shouldn't have taken in the first place and examine whether they are overpaying for other assets also, including education? ( I wouldn't call this reaction an increase in patience, but in the model one could treat its impact as if it was caused by an increase in patience. No?

  14. the collateral scarcity point makes perfect sense but couldn't I take that as an argument that QE works?

    I know you think QE is irrelevant but as far as I understand this is because you don't think it changes asset prices.

    Suppose that due to some sort of market segmentation, or whatever else, the Fed is able to raise asset prices with its purchases and that QE thus increases the nominal stock of available collateral.

    Wouldn't that imply that QE is effective?

  15. Polymath more right:
    "I don't think we want to think of the financial crisis as a change in preferences, with everyone becoming contagiously more patient, "
    Most consumers' largest savings "account" was their house equity.
    Their daily consumption was based on a loose Lifetime Consumption model in which their Net Worth and their Expected Net Worth were prominent variables.
    For most individuals, a higher expected net worth, based on higher house prices, caused higher current consumption.

    The house price bubble pop caused a revaluation of net worth, and a realization that the net worth was worth a LOT LESS than in their previous pre 2007 consumption calculations.

    If an individual consumes C+(10% of 200,000) when he has 200k of Net worth, and only C+(5% of 100,000) with 100k of Net Worth, such a 15k drop in consumption is not a change in preferences, it's a change in Net Worth.

    Ag Demand models should include Net Worth variables, but I'm not seeing Net Worth discussed much among monetarists.

    A heli-drop of $100 000 to the above individual might be the only policy which would have him consuming C+(10% of 200,000).

    The gov't should borrow less and really just print the "money", at least until inflation is closer to the unemployment rate.

    On the fiscal side, more tax cuts are better for increasing the deficit and increasing taxpayer consumption than more gov't spending -- plus with far higher average personal rates of return.

    1. You're really not familiar with the last 30 years of macroeconomics, are you? The permanent income/life cycle model of consumption, in which wealth is the central determinant of consumption, is the basic building block of all models. Crackpots rejoice, you have another member!

    2. Crackpot indeed.
      Empirical evidence suggests that people consume about 1/2 out of current and the other half out of permanent income.

  16. Who are you, CA?