Saturday, July 7, 2012

Interest Rates and (In)elastic Expectations

[Apologies to any non-econ readers, this is even more obscure than usual.]

Brad DeLong observed last week that one of the most surprising things about the Great Recession is how far long-term interest rates have followed short rates toward zero.
I have gotten three significant pieces of the past four years wrong. Three things surprised and still surprise me: (1.) The failure of central banks to adopt a rule like nominal GDP targeting, or it's equivalent. (2.) The failure of wage inflation in the North Atlantic to fall even farther than it has--toward, even if not to, zero. (3.) The failure of the yield curve to sharply steepen: federal funds rates at zero I expected, but 30-Year U.S. Treasury bond nominal rates at 2.7% I did not. 
... The third... may be most interesting. 
Back in March 2009, the University of Chicago's Robert Lucas confidently predicted that within three years the U.S. economy would be back to normal. A normal U.S. economy has a short-term nominal interest rate of 4%. Since the 10-Year U.S. Treasury bond rate tends to be one percentage point more than the average of expected future short-term interest rates over the next decade, even five expected years of a deeply depressed economy with essentially zero short-term interest rates should not push the 10-Year Treasury rate below 3%. (And, indeed, the Treasury rate fluctuated around 3 to 3.5% for the most part from late 2008 through mid 2011.) But in July of 2011 the 10-Year U.S. Treasury bond rate crashed to 2%, and at the start of June it was below 1.5%.  [
The possible conclusions are stark: either those investing in financial markets expect ... [the] current global depressed economy to endure in more-or-less its current state for perhaps a decade, perhaps more; or ... the ability of financial markets to do their job and sensibly price relative risks and returns at a rational level has been broken at a deep and severe level... Neither alternative is something I would have or did predict, or even imagine.
I also am surprised by this, and for similar reasons to DeLong. But I think the fact that it's surprising has some important implications, which he does not draw out.

Here's a picture:
The dotted black line is the Federal Funds rate, set, of course, by the central bank. The red line is the 10-year Treasury; it's the dip at the far right in that one that surprises DeLong (and me). The green line is the 30-year Treasury, which behaves similarly but has fallen by less. Finally, the blue line is the BAA bond rate, a reasonable proxy for the interest rate faced by large business borrowers; the 2008 financial crisis is clearly visible. (All rates are nominal.) While the Treasury rates are most relevant for the expectations story, it's the interest rates faced by private borrowers that matter for policy.

The recent fall in 10-year treasuries is striking. But it's at least as striking how slowly and incompletely they, and corporate bonds, respond to changes in Fed policy, especially recently. It's hard to look at this picture and not feel a twinge of doubt about the extent to which the Fed "sets" "the" interest rate in any economically meaningful sense. As I've mentioned here before, when Keynes referred to the "liquidity trap," he didn't mean the technical zero lower bound to policy rates, but its delinking from the economically-important long rates. Clearly, it makes no difference whether or not you can set a policy rate below zero if there's reason to think that longer rates wouldn't follow it down in any case. And I think there is reason to think that.

The snapping of the link between monetary policy and other rates was written about years ago by Benjamin Friedman, as a potential; it figured in my comrade Hasan Comert's dissertation more recently, as an actuality. Both of them attribute the disconnect to institutional and regulatory changes in the financial system. And I agree, that's very important. But after reading Leijonhufvud's On Keynesian Economics and the Economics of Keynes [1], I think there may be a deeper structural explanation.

As DeLong says, in general we think that long interest rates should be equal to the average expected short rates over their term, perhaps plus a premium. [2] So what can we say about interest rate expectations? One obvious question is, are they elastic or inelastic? Elastic expectations change easily; in particular, unit-elastic expectations mean that whatever the current short rate is, it's expected to continue indefinitely. Inelastic expectations change less easily; in the extreme case of perfectly inelastic interest rate expectations, your prediction for short-term interest rates several years from now is completely independent of what they are now.

Inelastic interest-rate expectations are central to Keynes' vision of the economy. (Far more so than, for instance, sticky wages.) They are what limit the effectiveness of monetary policy in a depression or recession, with the liquidity trap simply the extreme case of the general phenomenon. [3] His own exposition is a little hard to follow, but the simplest way to look at it is to recall that when interest rates fall, bond prices rise, and vice versa. (In fact they are just two ways of describing the same thing.) So if you expect a rise in interest rates in the future that means you'll expect a capital loss if you hold long-duration bonds, and if you expect a fall in interest rates you'll expect a capital gain.  So the more likely it seems that short-term interest rates will revert to some normal level in the future, the less long rates should follow short ones.

This effect gets stronger as we consider longer maturities. In the limiting case of a perpetuity -- a bond that makes a fixed dollar period every period forever -- the value of the bond is just p/i, where p is the payment in each period and i is the interest rate. So when you consider buying a bond, you have to consider not just the current yield, but the possibility that interest rates will change in the future. Because if they do, the value of the bonds you own will rise or fall, and you will experience a capital gain or loss. Of course future interest rates are never really known. But Keynes argued that there is almost always a strong convention about the normal or "safe" level of interest.

Note that the logic above means that the relationship between short and long rates will be different when rates are relatively high vs. when they are relatively low. The lower are rates, the greater the capital loss from an increase in rates. As long rates approach zero, the potential capital loss from an increase approaches infinity.

Let's make this concrete. If we write i_s for the short interest rate and i_l for the long interest rate, B for the current price of long bonds, and BE for the expected price of long bonds a year from now, then for all assets to be willing held it must be the case that i_l = i_s - (BE/B - 1), that is, interest on the long bond will need to be just enough higher (or lower) than the short rate to cancel out the capital loss (or gain) expected from holding the long bond. If bondholders expect the long run value of bond prices to be the same as the current value, then long and short rates should be the same. [*] Now for simplicity let's assume we are talking about perpetuities (the behavior of long but finite bonds will be qualitatively similar), so B is just 1/i_l. [4] Then we can ask the question, how much do short rates have to fall to produce a one point fall in long rates.

Obviously, the answer will depend on expectations. The standard economist's approach to expectations is to say they are true predictions of the future state of the world, an approach with some obvious disadvantages for those of us without functioning time machines. A simpler, and more empirically relevant, way of framing the question, is to ask how expectations change based on changes in the current state of the world -- which unlike the future, we can observe. Perfectly inelastic expectations mean that your best guess about interest rates at some future date is not affected at all by the current level of interest rates; unit-elastic expectations mean that your best guess changes one for one with the current level. An of course there are all the possibilities in between. Let's quantify this as the subjective annual probability that a departure of interest rates from their current or "normal" level will subsequently be reversed. Now we can calculate the exact answer to the question posed above, as shown in the next figure.

For instance, suppose short rates are initially at 6 percent, and suppose this is considered the "normal" level, in the sense that the marginal participant in the bond market regards an increase or decrease as equally likely. Then the long rate will also be 6 percent. Now we want to get the long rate down to 5 percent. Suppose interest rate expectations are a bit less than unit elastic -- i.e. when market rates change, people adjust their views of normal rates by almost but not quite as much. Concretely, say that the balance of expectations is that there is net 5 percent annual chance that rates will return to their old normal level. If the long rate does rise back to 6 percent, people who bought bonds at 5 percent will suffer a capital loss of 20 percent. A 5 percent chance of a 20 percent loss equals an expected annual loss of 1 percent, so long rates will need to be one point higher than short rates for people to hold them. [5] So from a starting point of equality, for long rates to fall by one point, short rates must fall by two points. You can see that on the blue line on the graph. You can also see that if expectations are more than a little inelastic, the change in short rates required for a one-point change in long rates is impossibly large unless rates are initially very high.

It's easy enough to do these calculations; the point is that unless expectations are perfectly elastic, we should always expect long rates to change less than one for one with short rates; the longer the rates considered, the more inelastic expectations, and the lower initial rates, the less responsive long rates will be. At the longest end of the term structure -- the limiting case of a perpetuity -- it is literally impossible for interest rates to reach zero, since that would imply an infinite price.

This dynamic is what Keynes was talking about when he wrote:
If . . . the rate of interest is already as low as 2 percent, the running yield will only offset a rise in it of as little as 0.04 percent per annum. This, indeed, is perhaps the chief obstacle to a fall in the rate of interest to a very low level . . . [A] long-term rate of interest of (say) 2 percent leaves more to fear than to hope, and offers, at the same time, a running yield which is only sufficient to offset a very small measure of fear.
Respectable economists like DeLong believe that there is a true future path of interest rates out there, which current rates should reflect; either the best current-information prediction is of government policy so bad that the optimal interest rate will continue to be zero for many years to come, or else financial markets have completely broken down. I'm glad the second possibility is acknowledged, but there is a third option: There is no true future course of "natural" rates out there, so markets adopt a convention for normal interest rates based on past experience. Given the need to take forward-looking actions without true knowledge of the future, this is perfectly rational in the plain-English sense, if not in the economist's.

A final point: For Keynes -- a point made more clearly in the Treatise than in the General Theory -- the effectivness of monetary policy depends critically on the fact that there are normally market participants with differing expectations about future interest rates. What this means is that when interest rates rise, people who think the normal or long-run rate of interest is relatively low ("bulls") can sell bonds to people who think the normal rate is high ("bears"), and similarly when interest rates fall the bears can sell to the bulls. Thus the marginal bond will be held held by someone who thinks the current rate of interest is the normal one, and so does not require a premium for expected capital gains or losses. This is the same as saying that the market as a whole behaves as if expectations are unit-elastic, even though this is not the case for individual participants. [6] But when interest rates move too far, there will no longer be enough people who think the new rate is normal to willingly hold the stock of bonds without an interest-rate risk premium. In other words, you run out of bulls or bears. Keynes was particularly concerned that an excess of bear speculators relative to bulls could keep long interest rates permanently above the level compatible with full employment. The long rate, he warned,
may fluctuate for decades about a level which is chronically too high for full employment; – particularly if it is the prevailing opinion that the rate of interest is self-adjusting, so that the level established by convention is thought to be rooted in objective grounds much stronger than convention, the failure of employment to attain an optimum level being in no way associated, in the minds either of the public or of authority, with the prevalence of an inappropriate range of rates of interest’.
If the belief that interest rates cannot fall below a certain level is sufficiently widespread, it becomes self-fulfilling. If people believe that long-term interest rates can never persistently fall below, say, 3 percent, then anyone who buys long bonds much below that is likely to lose money. And, as Keynes says, this kind of self-stabilizing convention is more likely to the extent that people believe that it's not just a convention, but that there is some "natural rate of interest" fixed by non-monetary fundamentals.

So what does all this mean concretely?

1. It's easy to see inelastic interest-rate expectations in the data. Long rates consistently lag behind short rates. During the 1960s and 1970s, when rates were secularly rising, long rates were often well below the Federal Funds rate, especially during tightening episodes; during the period of secularly falling rates since 1980, this has almost never happened, but very large term spreads have become more common, especially during loosening episodes.

2. For the central bank to move long rates, it must persuade markets that changes in policy are permanent, or at least very persistent; this is especially true when rates are low. (This is the main point of this post.) The central bank can change rates on 30-year bonds, say, only by persuading markets that average rates over the next 30 years will be different than previously believed. Over small ranges, the existence of varying beliefs in the bond market makes this not too difficult (since the central bank doesn't actually have to change any individual's expectations if bond sales mean the marginal bondholder is now a bull rather than a bear, or vice versa) but for larger changes it is more difficult. And it becomes extremely difficult to the extent that economic theory has taught people that there is a long run "natural" rate of interest that depends only on technology and time preferences, which monetary policy cannot affect.

Now, the obvious question is, how sure are we that long rates are what matters? I've been treating a perpetual bond as an approximation of the ultimate target of monetary policy, but is that reasonable? Well, one point on which Keynes and today's mainstream agree is that the effect of interest rates on the economy comes through demand for long-lived assets -- capital goods and housing. [7] According to the BEA, the average current-cost age of private fixed assets in the US is a bit over 21 years, which implies that the expected lifetime of a new fixed asset must be quite a bit more than that. For Keynes (Leijonhufvud stresses this point; it's not so obvious in the original texts) the main effect of interest rates is not on the financing conditions for new fixed assets, as most mainstream and heterodox writers both assume, but on the discount rate used  of the assets. In that case the maturity of assets is what matters. On the more common view, it's the maturity of the debt used to finance them, which may be a bit less; but the maturity of debt is usually matched to the maturity of assets, so the conclusion is roughly the same. The relevant time horizon for fixed assets is long enough that perpetuities are a reasonable first approximation. [8]

3. So if long rates are finally falling now, it's only because an environment of low rates is being established as new normal. There's a great deal of resistance to this, since if interest rates do return to their old normal levels, the capital losses to bondholders will be enormous. So to get long rates down, the Fed has to overcome intense resistance from bear speculators. Only after a great deal of money has been lost betting on a return of interest rates to old levels will market participants begin to accept that ultra-low rates are the new normal. The recent experience of Bill Gross of PIMCO (the country's largest bond fund) is a perfect example of this story. In late 2010, he declared that interest rates could absolutely fall no further; it was the end of the 30-year bull market in bonds. A year later, he put his money where his mouth was and sold all his holdings of Treasuries. As it turned out, this was just before bond prices rose by 30 percent (the flipside of the fall in rates), a misjudgment that cost his investors billions. But Gross and the other "bears" had to suffer those kinds of losses for the recent fall in long rates to be possible. (It is also significant that they have not only resisted in the market, but politically as well.) The point is, outside a narrow range, changes in monetary policy are only effective when they cease to be perceived as just countercyclical, but as carrying information about "the new normal." Zero only matters if it's permanent zero.

4. An implication of this is that in a world where the lifespan of assets is much longer than the scale of business-cycle fluctuations, we cannot expect interest rates to be stationary if monetary policy is the main stabilization tool. Unless expectations are very elastic, effective monetary policy require secular drift in interest rates, since each short-term stabilization episode will result in a permanent change in interest rates. [9] You can see this historically: the fall in long rates in the 1990 and 2000 loosenings both look about equal to the permanent components of those changes. This is a problem for two reasons: First, because it means that monetary policy must be persistent enough to convince speculators that it does represent a permanent change, which means that it will act slower, and require larger changes in short rates (with the distortions those entail) than in the unit-elastic expectations case. And second, because if there is some reason to prefer one long-ru level of interest rates to another (either because you believe in a "natural" rate, or because of the effects on income distribution, asset price stability, etc.) it would seem that maintaining that rate is incompatible with the use of monetary policy for short-run stabilization. And of course the problem is worse, the lower interest rates are.

5. One way of reading this is that monetary policy works better when interest rates are relatively high, implying that if we want to stabilize the economy with the policy tools we have, we should avoid persistently low interest rates. Perhaps surprisingly, given what I've written elsewhere, I think there is some truth to this. If "we" are social-welfare-maximizing managers of a capitalist economy, and we are reliant on monetary policy for short-run stabilization, then we should want full employment to occur in the vicinity of nominal rates around 10 percent, versus five percent. (One intuitive way of seeing this: Higher interest rates are equivalent to attaching a low value to events in the future, while low interest rates are equivalent to a high value on those events. Given the fundamental uncertainty about the far future, choices in the present will be more stable if they don't depend much on far-off outcomes.) In particular -- I think it is a special case of the logic I've been outlining here, though one would have to think it through -- very low interest rates are likely to be associated with asset bubbles. But the conclusion, then, is not to accept a depressed real economy as the price of stable interest rates and asset prices, but rather to "tune" aggregate demand to a higher level of nominal interest rates. One way to do this, of course, is higher inflation; the other is a higher level of autonomous demand, either for business investment (the actual difference between the pre-1980 period and today, I think), or government spending.

[1] The most invigorating economics book I've read in years. It'll be the subject of many posts here in the future, probably.

[2] Why there should be a pure term premium is seldom discussed but actually not straightforward. It's usually explained in terms of liquidity preference of lenders, but this invites the questions of (1) why liquidity preference outweighs "solidity preference"; and (2) why lenders' preferences should outweigh borrowers'. Leijonhufvud's answer, closely related to the argument of this post, is that the "excessively long" lifespan of physical capital creates chronic excess supply at the long end of the asset market. In any case, for the purpose of this post, we will ignore the pure premium and assume that long rates are simply the average of expected short rates.

[3] Keynes did not, as is sometimes suggested by MMTers and other left Keynesians, reject the effectiveness of monetary policy in general. But he did believe that it was much more effective at stabilizing full employment than at restoring full employment from a depressed state

[4] I will do up these equations properly once the post is done.

[5] I anticipate an objection to reasoning on the basis of an equilibrium condition in asset markets. I could just say, Keynes does it. But I do think it's legitimate, despite my rejection of the equilibrium methodology more generally. I don't think there's any sense that human behavior can be described as maximizing some quantity called utility," not even as a rough approximation; but I do think that capitalist enterprises can be usefully described as maximizing profit. I don't think that expectations in financial markets are "rational" in the usual economists' sense, but I do think that one should be able to describe asset prices in terms of some set of expectations.

[6] We were talking a little while ago with Roger Farmer, Rajiv Sethi, and others about the desirability of limiting economic analysis to equilibria, i.e. states where all expectations are fulfilled. This implies, among other things, that all expectations must be identical. Keynes' argument for why long rates are more responsive to short rates within some "normal" range of variation is -- whether you think it's right or not -- an example of something you just can't say within Farmer's preferred framework.

[7] Despite this consensus, this may not be entirely the case; and in fact to the extent that monetary policy is effective in the real world, other channels, like income distribution, may be important. But let's assume for now that demand for long-lived assets is what matters.

[8] Hicks had an interesting take on this, according to Leijonhufvud. Since the production process is an integrated whole, "capital" does not consist of particular goods but of a claim on the output of the process as a whole. Since this process can be expected to continue indefinitely, capital should be generally assumed to be infinitely-lived. When you consider how much of business investment is motivated by maintaining the firm's competitive position -- market share, up to date technology, etc. -- it does seem reasonable to see investment as buying not a particular capital good but more of the firm as a whole.

[9] There's an obvious parallel with the permanent inflation-temporary employment tradeoff of mainstream theory. Except, I think mine is correct!


  1. You are rocking! But what is the difference between this duration based argument and Mankiw's sticky expectations model?

    I recommend crediting Jan Kregel in this post somewhere, as he's prominently made this argument in heterodox circles.

    1. By diverse means we arrive at the same end, no?

      Personally I first encountered this geenral line of argument studying with Bob Pollin -- endogenous money and the whole structuralist vs. accomodationist debate. Then later reading Lance Taylor, which clarified what JMK meant by liquidity trap -- the presentation in the GT was hard sledding when I first read it. And most recently reading Leijonhufvud. But yes, Kregel should be mentioned -- do you have a particular paper in mind?

      As I understand Mankiw, that's a model specifically of inflation expectations. If you're a mainstream person, you tend to think the long-run real interest rate is fixed by fundamentals, which means you don't need to to talk about backward-looking expectations at all. They do that only for prices/inflation and for exchange rates. (In somewhat ad hoc and inconsistent ways, IMO.) But maybe I'm wrong? Does Mankiw talk about sticky expectations of interest rates or asset prices specifically?

      It's funny that there is some acceptance of destabilizing speculation in mainstream stuff -- asset bubbles, self-fulfilling exchange rate crises, etc. -- but much less interest in stabilizing speculation, as in Keynes story of the long rate.

  2. Forcing Bill Gross to lose billions in slow motion is a crazy way to get to full employment.

    1. I agree!

      I wrote this post mainly to clarify my own thinking, not to make any policy or political argument. But obviously the argument that comes out of this is that while monetary policy can help stabilize demand, it's very weak at restoring demand once it's fallen - and not just because short rates can't go below zero, or because central banks are choosing the wrong target. (Although it is certainly true, and important, that central bankers are not really trying to reduce unemployment.)

      Another, related but more straightforward explanation of this, also stressed by Leijonufvud, is that expectations of returns on investment are also conventional and moderately elastic. Once demand has fallen - and especially if it has remained depressed for a while - expected returns on investment fall, so the interest rate that would have been low enough to prevent the fall in activity is no longer low enough to reverse it. This is why

    2. you temporarily need lower rates than you will want when the economy recovers. But the expectation of long rates returning to their old level will prevent them from falling in the first place. This is why monetary policy can't work in a situation like this without Bill Gross losing a billion dollars - that's the only way you force him to change his expectations. Much simpler to prove the pessimistic expectations of entrepreneurs wrong by raising demand directly. But that takes fiscal policy.

      These endogenous shifts in expectations are behind the whole logic of "pump priming." But as far as I can tell they are almost entirely ignored by macro economists - heterodox as well as mainstream - presumably because they can't be modeled as an equilibrium. Well and also because of the disinterest - again, I'm afraid, among most heterodox approaches as well - in cyclical dynamics in general.

      I guess that's not entirely fair - people are interested in asset bubbles and so on. But if you're looking for an analysis of cycles that is not 100% financial, it's surprisingly hard to find.

  3. I have some problem with the idea that, when interest rises, value of older bonds falls exactly in the same proportion.
    For example suppose that today I buy 100$ of new bonds at ten years at 1%/year. this means that, at maturity, I'll get 110$.
    Suppose that after five years I need liquidity and I sell them but in the meanwile interest become 2%/year. From the point of view of the buyer my asset is simply something that will become 110$ in five years, regardless of how much I payd it in the first place, so it is equivalent to a newly issued bond with 5 years of maturity with 100$ of principal and 2% interest, so I can sell it for 100$. in this example I just lost 5$ of foregone interest in the pasr five years, that is 5% and not 50%.

  4. The exact inverse relationship only holds for perpetuities (bonds with an infinite maturity, where the principle is never repaid.) if you think that the importance of interest rates is primarily for the valuation (rather than the financing) of capital goods, and you think that capital goods are effectively infinitely lived, then this is the correct way to think about it. I think both assumptions are defensible; Keynes seems to have held both of them.

    Otherwise, if you are thinking in terms of financing conditions for long but not infinitely lived assets, the perpetuity is only an approximation, but for long maturities it's not an unreasonable one. For example, a 30 year bond loses 14% of its value when interest rates rise from 5% to 6%, compared with a 20% loss for a perpetuity. But qualitatively the story here will hold as long as the interest rates that matter are much longer than the timescale of business cycles. In your example, the term is 10 years and the fluctuation lasts five years. That's not a big difference in timescales for the argument to work. But I think my case is more realistic - capital goods typically last much more than 10 years and recessions less than 5.

  5. I get confused when you map Keynes's "interest rate" abstraction to the bond market. Bill Gross made a bearish bet on interest rates, but that's a bullish bet on the economy. Holding (safe) bonds is a more bearish bet on the economy than holding cash.

    1. I am using bull and bear in Keynes's sense: bullish and bearish about bond prices.

    2. I thought that "bonds" were the only asset in Keynes's model. That makes it hard to talk about the current situation, where bullish on bonds means bearish on real assets.

      Suppose the Fed eliminated the zero bound tomorrow. Is that bullish for bonds? No! Bond investors are counting on Fed paralysis.

    3. Interesting issue. The GT model has labor, consumption goods, short assets (money and short bonds), and long assets (long bonds and physical capital.) The postwar mainstream used a different aggregation structure, with all bonds grouped together and with long physical assets grouped with short physical assets. In that model, the story I'm telling would not make much sense. Which is the better model? You'll have to judge for yourself.

    4. I mean, with long physical assets grouped with consumption goods -- i.e. all current production is aggregated.

  6. Check out the euro dollar futures which show expected future fed rate settings (plus/minus a fed funds-libor basis)out ten years?

    Also, maybe low rates are deflationary/contractionary, all else equal? via the interest income channels? The govt is a net payer of interest, so lower rates reduce that 'fiscal channel of interest rates' (bernanke sacks reinhart 2004) and, also, this time around savers rates fell more than borrower's, with the difference going to lenders net interest margins where there is a 0 propensity to consume? QE mainly just a tax? The fed's turning over 80 billion to the tsy each year that would have otherwise been earned by the private sector? the spectrum is from positive rates which are a gov subsidy to the economy, to negative rates which are a tax?

    How hard is it for a CB to inflate? The Fed has been trying as hard as it can for 4 years with no success, Japan going on two decades?

    Warren Mosler

    1. Hi Warren.

      Delighted to see that you're reading this. You are central in the conversation this blog hopes to contribute to.

      You are right that one important way to develop this argument, is to look for empirical evidence on interest rate expectations. Hopefully I will be able to do this at some point.

      I touch on the possibly procyclical rather than countercyclical effects of monetary policy in the followup to this post I am just finishing writing. My own sense is that low rates are almost certainly inflationary/expansionary on balance -- the distributional effect points in the same direction as the conventional incentive effect, and the share of short rates in marginal costs is too low to overcome that. But I'm certainly open to being persuaded otherwise.

      The final point you make is exactly the point of this post. Even with all the will in the world, a central bank may have very little capacity to reflate the economy once depression-appropriate expectations have solidified.

  7. With regards to P/i, the assumption is that i is the rate throughout the length of the console. If we assume EH, then when i(n) is changing, then the i in P/i would be the average i.

    That means, for a perpetual, if investors believe that "long term", the rate of interest will be 4%, then even a 20 or 100 year period of interest rates at 0% will not cause i to change at all. The console price wont budge one bit as a result of short rates changing, because the limit as n-> infinity of Average(i(n)) will be 4% even if finitely many of the i(n)'s are zero. All that matters is the tail of the sequence.

    So "new normal" is not just for a decade, or even ten decades. New normal has to mean forever. And there is good reason to view capital as a console because even if the life of a piece of capital equipment is finite, investors own the firm, and firms re-invest and maintain the capital base with no apparent end-in-sight. Even when firms are de-listed, they are typically absorbed by other firms, with investors in the old firm becoming shareholders of the newer firm. Only in the special case of bankruptcy that wipes out shareholders fully and permanently (e.g. no possibility of in-the-money warrants) would you ascribe a terminus to the firm. Although that probability is non-zero, it would nevertheless point to a long life of the firm.

    This is also in line with the returns on capital as measured by the BEA:

    The returns don't seem to move a whole lot even as nominal rates thrash about.

    A similar picture is painted with implied rental yields: They do not move in line with changes in the interest rate, not even changes in long dated bonds.

    1. Exactly. Exactly.

      The only point I want to push back on is, given fundamental uncertainty, it is possible for expectations of the the interest rate over the next forever to change, even as a result of monetary policy. Tho again, Bill Gross has to lose his billions first.

      (An interesting corollary, which I'm sure has occurred to you, is that if there is a single annuity anywhere in the world, the "natural" rate of interest can never be negative.)

    2. (I actually meant to mention that Keynes was specifically considering the case of equity finance, which is the obvious real-world case of a perpetuity. I didn't because in practice equity is not a major source of finance in modern economies, apart from special circumstances like the late 90s tech boom.)

    3. Yes, I agree with your points. But I would say that equity *is* the major source of finance. Most firms are not large enough to be able to tap the bond markets, and in most nations, bond markets are not that deep. Bond markets are basically for governments and pseudo-government institutions such as banks.

      In the U.S., which has the deepest bond markets of the world, half of firms are privately held and are funded solely via equity. Even for those firms that can access the credit markets, they prefer to finance themselves via re-invested earnings, which I would consider equity finance.

      I think the reason for this is credit constraints. Because banks are leveraged, they are able to extend credit only when it is super-collaterilized, and in that case they want land, not produced capital, to act as collateral. Really, they want something that is stable in value and will continue to have a stable value even should the firm be mismanaged or lose money. Therefore they do not want to lend against anything that is responsible for adding value. Banks generally lend to households against real estate and tend not to be big players in uncollaterallized lending. There is very little uncollaterilized lending going on, globally. I would say exceptions to the above tend to be in nations with financial repression in which the government promises to absorb bank losses on a routine basis. In that case, banks will venture and lend against speculative enterprises other than land.

    4. I think that is the key point. Monetary policy appears has to feed into the economy via super long term investments that are sensitive to interest rates. Those are the only things where the interest rates matters sufficiently to be considered.

      That and businesses where extremely poor profit margins have to be super-leveraged to get anything that is worth putting equity into. A system that absolutely requires super cheap money to be operational.

      So monetary policy interest rate targeting approaches appear to require property speculation and hedge funds with a constant rise in the private debt to gdp ratio to gain any traction.

  8. This is just fantastic. There are many many good ideas, and this all resonates extremely well since I've been reading Leijonhufvud as well.

    The new normal is precisely what SRW has been talking about in the negative unnatural rate of interest. Or Iza Kaminska in her reflections on the age of post-scarcity and negative carry.

    One thing I wish to do is to add some Mehrling to Leijonhufvud. Note how close your footnote on Hicks is to Fischer Black's finance-view of the economy. Far too many people are attached to the view of capital as buildings and factories, whether they realise it or not. With capital, it is hard to distinguish between prices and quantities, at least in the aggregate. The effect of asset prices goes beyond just Tobin's q - which as you have demonstrated is anyway not empirically borne out.

    A decline in asset prices is a supply shock. (This is Cowen's we are not as wealthy as we thought we were) This is the reason why we don't see deflation, merely disinflation. The dominance of asset price re-valuations over real flows as the primary result of monetary policy is one reason why consumer prices/ wages are so stable. Greenspan managed to achieve low unemployment and low inflation together precisely through the Greenspan put. It's *great* short-run stabilization policy, but it breeds financialization, the increasing correlation of presumably risky assets and severe fragility underneath the stability.

    These are just some random thoughts. I'm trying to put together the many themes that I read about everyday.

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