Friday, February 17, 2012

What is the Liquidity Trap?

In the common usage, popularized by Krugman, a liquidity trap is just a situation where the interest rate set by the central bank has reached zero. Since it can't go below that (the Zero Lower Bound), if more expansionary policy is needed it will have to take the form of fiscal policy or unconventional monetary policy -- quantitative easing and so on. But if there were some technical fix (a tax on excess reserves, say, or abolishing cash) that allowed central banks to make the policy rate negative, there would be no limit to the capacity of monetary policy to overcome any shortfall in demand. The idea -- expressed by modern monetarists in the form of the negative natural rate -- is that there are so few investment opportunities with positive expected returns that if investment rose enough to equal desired saving at full employment, the expected return on the marginal new unit of capital would be negative. So you'd need a negative cost of capital to get businesses to undertake it.

That makes sense, I guess. But it's not what Keynes meant by liquidity trap. And Keynes' version, I think, is more relevant to our current predicament.

Keynes himself doesn't use the term, and his explanation of the phenomenon, in chapters 13 and 15 of the General Theory, is rather confusing. (Lance Taylor has a much clearer statement of it in Reconstructing Macroeconomics, which I may add a summary or excerpt of to this post when I get home tonight and have the book.) So rather than quote chapter and verse, I'm just going to lay out what I understand the argument to be.

Interest, says Keynes, is not, as the classical economists said, the price of consuming in the future relative to the consuming in the present. It is the price of holding an illiquid rather than a liquid asset today. (This is one of the main points of the book.) The cost of holding an illiquid asset (a bond, let's say) is the inconvenience that it can't be used for transaction purposes, but also the opportunity cost of not being able to buy a bond later, if interest rates rise. Another way of saying the same thing: The risk of holding a bond is not just that you won't have access to means of payment when you need it; it is also the capital loss you will suffer if interest rates rise while you are holding the bond. (Remember, the price of an existing bond always moves inversely with the interest rate.)

This last factor isn't so important in normal times, when opinions about the future rates of bonds vary; if the supply of liquidity rises, there will be somebody who finds themselves more liquid than they need to be and who doesn't expect a rise in interest rates in the near future, who will purchase bonds, driving up their price and driving the interest rate down. The problem arises when there is a consensus about the future level of interest rates. At that point, anyone who holds a bond yielding below that level will be anxious to sell it, to avoid the capital loss when interest rates inevitably rise. (Or equivalently, to be able to purchase a higher yield bond when they do.) This effect is strongest at low interest rates, since bondholders not only are more likely to expect a capital loss in the future, but are getting very little interest in the present to compensate them for it. Or as Keynes says,
Nevertheless, circumstances can develop in which even a large increase in the quantity of money may exert a comparatively small influence on the rate of interest. For ... opinion about the future of the rate of interest may be so unanimous that a small [decrease] in present rates may cause a mass movement into cash. It is interesting that the stability of the system and its sensitiveness to changes in the quantity of money should be so dependent on the existence of a variety of opinion about what is uncertain. Best of all that we should know the future. But if not, then, if we are to control the activity of the economic system by changing the quantity of money, it is important that opinions should differ.
In other words, the essence of the liquidity trap is a convention about the normal level of interest rates. It's important to note that this convention is self-stabilizing -- if everyone believes that interest rates on a particular class of bond cannot be below 3 percent, say, for any extended period of time, then anyone who finds themselves holding a bond yield less than 3 percent will be anxious to sell it. And their efforts to do so will push the price of the bonds down, which itself will increase their yield back to 3 percent, so that the people who did not share the convention are the ones who end up suffering the loss.

This probably seems confusing and tedious to most readers (and tediously familiar to most of the rest.) Maybe it will be clearer and more interesting with some pictures:

10-Year Treasury Rate and the Federal Funds Rate


BAA Bond Rates and the Federal Funds Rate

The horizontal axis of this scatterplot is the Federal Funds rate. The vertical axis shows a market interest rate -- the 10-year Treasury bond rate in the first one, and the BAA corporate bond rate in the second. The heavy black diagonal corresponds to a market rate equal to the Fed Funds rate. In both cases, there's a clear positive relationship over normal ranges of policy rates -- 3 percent to 8 percent or so. But outside of this range, particularly at the bottom end, the relationship breaks down. The floor on Treasuries is a hard 3 percent or so, while the floor on BAA bonds varies from time to time but also doesn't go below 3 percent. [1] This is Keynes' liquidity trap. [2] And when you look at it, it becomes much less clear that the inability to extend the black line past the origin -- Krugman's liquidity trap -- is the problem here. What good would it do, if market rates stop following the policy rate well before that?


UPDATE: A smart, skeptical comment by Bruce Wilder leads me to reformulate the argument in a hopefully clearer way.

The necessary and sufficient condition for a liquidity trap is a consensus among market participants that nominal interest rates are more likely to rise than to fall over the relevant time horizon. Obviously, one basis for such a consensus might be that it is literally impossible for short rates to fall any further. [3] In this sense the ZLB liquidity trap is a special case of the Keynesian liquidity trap. But the Keynesian concept is broader, because conventions about the floor of interest rates can be strongly self-stabilizing, especially where they are backed up by the political power of rentiers.


[1] "The most stable, and the least easily shifted, element in our contemporary economy has been hitherto, and may prove to be in future, the minimum rate of interest acceptable to the generality of wealth-owners. If a tolerable level of employment requires a rate of interest much below the average rates which ruled in the nineteenth century, it is most doubtful whether it can be achieved merely by manipulating the quantity of money. ... Cf. the nineteenth-century saying, quoted by Bagehot, that 'John Bull can stand many things, but he cannot stand 2 per cent.'"

[2] It also, not coincidentally, looks like the textbook LM curve. The replacement of LM with an central bank-determined interest rate curve in newer textbooks, is not progress.

[3] Note that it is not in fact the case that nominal interests cannot be negative, because in the real world cash has substantial carrying costs.

11 comments:

  1. Despite your rather self-deprecating tag, this post does make a serious run at greatness. The graphs are particularly helpful, and put the liquidity trap in a different light.

    Cheers!
    JzB

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  2. If you look at the 'real yield' on the 30-year TIPS, it's clear that investors are accepting very low returns on investments without economic risk (but plenty of interest rate risk). So I don't see any evidence of a liquidity trap as Keynes defined it.

    What we see is not a fear of interest rate risk, but rather a fear of a repeat of 2008 where the bottom falls out of the economy. Junk bonds have a high default rate priced in, and the expected return on stocks relative to bonds is high.

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  3. According to Keynes the Fed has to increase the variability of opinions about future interest rate and not to decrease it.

    And the second point is that the interest rate risk stays largely with the financial sector and not with investors (by which I do not mean financial so called investors). They would not care less as long as they see demand coming. Whether interest rates are at 3% or at 3.5% on a 10y investment loan is pretty much a rounding mistake in their investment plans.

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  4. Hey JW want to post about this post. What is each point? A quarter, month, year? What's the range of years being sampled here? Thx.

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  5. I'm not sure I understand how Krugman's short-hand differs from Keynes's account. You seem to want Keynes' floor to be a social convention, akin to driving on the left or the right, but the floor is, itself, a function of the zero-bound. Do you really not see that? Or, am I missing something else?

    I do see how the new monetarists have a view different from Keynes, so maybe I am not completely missing the point. Do you think Krugman is straddling the divide between an institutionalist/structuralist/operational model of interest rates and investment, and a purely analytic model turning on a Wicksellian natural rate? Is Keynes?

    It seems to me that Keynes, at pains to escape the paralysis of institutionalists of his day, never really draws a sharp enough line between analytic theory and operational understanding. With Hicks (and Hansen and Samuelson) the theorists took the ball and ran with it, and someone like Krugman just naturally is drawn to analytic "insight" over the kind of operational and institutionalist understanding Keynes could apply. So, in that sense, Krugman has a decidedly neoclassical-synthesis (aka analytic) framework, which leaves some operational understanding sadly out of account. Still, I do not think Krugman thinks in terms of a Wicksellian "natural" rate, but maybe I'm mistaken.

    Keynes seems to me, to be struggling to work out an operational model of money and financial markets as a response to genuine uncertainty. This would be money as an institutional mechanism, and the liquidity trap is a malfunction of the mechanism. Krugman is no institutionalist, but he does offer an analytic insight into a fundamental limitation on the mechanism, which is the same fundamental limitation, which Keynes is pointing to.

    If this comment/question seems opaque, just say so, and I'll backup a bit.

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  6. Max-

    Interesting point. You are right, TIPS rates don't show anything like the same floor as conventional bonds. So what are we to make of that?

    One interpretation would be that Keynes' liquidity-trap dynamic, which you could describe as a discontinuous upward jump in interest-rate risk when rates fall below a conventional floor, is not what's holding up long rates. Rather, there has been an increase in inflation expectations which just happens to offset the fall in the Fed Funds rate. (Note that the story you suggest of increasing default risk is *not* what's going on here, since the same floor behavior is seen in Treasuries as well as in private bonds.) Logically that's certainly possible, but I don't think it's what's going on here.

    I think it's simpler to say that given that the TIPS market is *much* smaller than the Treasury market, it's a new instrument without enough history to rally solidify conventions, and expected returns depend not only on expectations about interest rates but also expected inflation, which isn't subject to the same kind of stabilizing speculation -- for all these reasons, there isn't a conventional floor in that market the way there is for regular Treasuries. Also, because the market is so small, it may be dominated by a relatively small number of investors with very high inflation expectations. There certainly are a nontrivial number of asset owners who believe inflation will be much higher in the relatively near future (and remember, to buy a TIPS at their current extremely high prices (implying a large negative return if inflation doesn't rise), you don't have to believe yourself that inflation will rise, or even way to hedge against the possibility; you just have to be confident that someone else does. There is no equivalent group of asset owners who expect much lower bond yields, I don't think.

    But those are just preliminary thoughts. Worth exploring more.

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  7. Steve,

    They are monthly observations, from the earliest available on FRED (1/1962 for 10-year Treasuries, 4/1971 for mortgages) to October 2011, which is when I made the graphs. I used them to explain the liquidity trap to my students last fall; not sure how well it worked.

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  8. You seem to want Keynes' floor to be a social convention, akin to driving on the left or the right, but the floor is, itself, a function of the zero-bound. Do you really not see that?

    Bruce,

    I disagree. I think the perception that short rates cannot go below zero is does help support the convention, but is neither a necessary nor sufficient condition for it.

    Do you think Krugman is straddling the divide between an institutionalist/structuralist/operational model of interest rates and investment, and a purely analytic model turning on a Wicksellian natural rate? Is Keynes?

    Keynes pretty clearly believes that (a) the natural rate is not really a meaningful concept, since it is based on a decision to allocate a fixed lifetime income between present and future, when income itself is endogenous to expenditure decisions; and even if something like it is calculable in principle, it is never relevant in practice since the market rate will always be well above it. "The investment market can become congested through a shortage of cash. It can never become congested through a shortage of saving." I'm honestly not sure what Krugman's underlying view here is.

    Keynes seems to me, to be struggling to work out an operational model of money and financial markets as a response to genuine uncertainty.

    Yes. By the way, this is where I think a lot of Post Keynesian analysis (Davidson, Shackle, etc.) goes off the rails. They want to draw a direct line between "we simply do not know" and the demand for liquidity, but obviously pure uncertainty in that sense can't justify any course of action over any other. So then they bring in a meta-convention that says if you don't have any other solid basis for action, hold money. Which is certainly a reasonable description of how economic actors often behave; but at that point all the work is being done by the behavioral rule and might as well have skipped the whole philosophical excursion into non-ergodicity, etc.

    Anyway, I'd be extremely interested in hearing you develop your thoughts on this further. I'm sure I've missed some of that you're saying here.

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    Replies
    1. I should add, I say "perception that short rates cannot go below zero" because, you know, they actually can.

      The idea of the ZLB is based on the assumption that the carrying costs of cash are zero, but this is obviously far from the case. And given that cash does have substantial carrying costs (security, etc.), and that -- contrary to naive theory -- large transactions are preferentially settled with credit rather than cash, reserves are actually *more* liquid the cash, which means that there is no reason they can't carry a negative interest rate. And in fact, we do observe negative interest rates "in the wild," both on various short-dated government bonds and in the form of an excess-reserve tax, as adopted e.g. in Sweden. So another reason the ZLB can't explain the liquidity trap, is that it doesn't actually exist.

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  9. the interest rate risk stays largely with the financial sector and not with investors (by which I do not mean financial so called investors). They would not care less as long as they see demand coming. Whether interest rates are at 3% or at 3.5% on a 10y investment loan is pretty much a rounding mistake in their investment plans.

    Quite true. Thee's a second slip between the cup and lip, which is that even if the Fed can move the whole broad interest-rate complex, and not just the policy rate and a few other short rates, this may not have a big effect on real activity, especially in a slump. "You can't push on a string," etc. In fact -- a good subject for another post -- there's a very convincing argument that for some time now the main channel of monetary policy has been through fluctuations in asset values and not through any effect on the cot of borrowing directly.

    But that's a separate argument; the liquidity trap is an explanation for why you don't even get to the point of worrying about that, because long rates don't move anyway.

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