Archive for the 'Fisher equation' Category

The Well-Defined, but Nearly Useless, Natural Rate of Interest

Published November 5, 2015 David Davidson , Fisher equation , Hayek , Irving Fisher , Keynes , Knut Wicksell , Milton Friedman , natural rate of interest , Piero Sraffa , Tyler Cowen 16 Comments
Tags: ,

Tyler Cowen recently posted a diatribe against the idea monetary policy should be conducted by setting the interest rate target of the central bank at or near the natural rate of interest. Tyler’s post elicited critical responses from Brad DeLong and Paul Krugman among others. I sympathize with Tyler’s impatience with the natural rate of interest as a guide to policy, but I think the scattershot approach he took in listing, seemingly at random, seven complaints against the natural rate of interest was not the best way to register dissatisfaction with the natural rate. Here’s Tyler’s list of seven complaints.

1 Knut Wicksell, inventor of the term “natural rate of interest,” argued that if the central bank set its target rate equal to the natural rate, it would avoid inflation and deflation and tame the business cycle. Wicksell’s argument was criticized by his friend and countryman David Davidson who pointed out that, with rising productivity, price stability would not result without monetary expansion, which would require the monetary authority to reduce its target rate of interest below the natural rate to induce enough investment to be financed by monetary expansion. Thus, when productivity is rising, setting the target rate of interest equal to the natural rate leads not to price stability, but to deflation.

2 Keynes rejected the natural rate as a criterion for monetary policy, because the natural rate is not unique. The natural rate varies with the level of income and employment.

3 Early Keynesians like Hicks, Hansen, and Modigliani rejected the natural rate as well.

4 The meaning of the natural rate has changed; it was once the rate that would result in a stable price level; now it’s the rate that results in a stable rate of inflation.

5 Friedman also rejected the natural rate because there is no guarantee that setting the target rate equal to the natural rate will result in the rate of money growth that Freidman believed was desirable.

6 Sraffa debunked the natural rate in his 1932 review of Hayek’s Prices and Production.

7 It seems implausible that the natural rate is now negative, as many exponents of the natural rate concept now claim, even though the economy is growing and the marginal productivity of capital is positive.

Let me try to tidy all this up a bit.

The first thing you need to know when thinking about the natural rate is that, like so much else in economics, you will become hopelessly confused if you don’t keep the Fisher equation, which decomposes the nominal rate of interest into the real rate of interest and the expected rate of inflation, in clear sight. Once you begin thinking about the natural rate in the context of the Fisher equation, it becomes obvious that the natural rate can be thought of coherently as either a real rate or a nominal rate, but the moment you are unclear about whether you are talking about a real natural rate or a nominal natural rate, you’re finished.

Thus, Wicksell was implicitly thinking about a situation in which expected inflation is zero so that the real and nominal natural rates coincide. If the rate of inflation is correctly expected to be zero, and the increase in productivity is also correctly expected, the increase in the quantity of money required to sustain a constant price level can be induced by the payment of interest on cash balances. Alternatively, if the payment of interest on cash balances is ruled out, the rate of capital accumulation (forced savings) could be increased sufficiently to cause the real natural interest rate under a constant price level to fall below the real natural interest rate under deflation.

In the Sraffa-Hayek episode, as Paul Zimmerman and I have shown in our paper on that topic, Sraffa failed to understand that the multiplicity of own rates of interest in a pure barter economy did not mean that there was not a unique real natural rate toward which arbitrage would force all the individual own rates to converge. At any moment, therefore, there is a unique real natural rate in a barter economy if arbitrage is operating to equalize the cost of borrowing in terms of every commodity. Moreover, even Sraffa did not dispute that, under Wicksell’s definition of the natural rate as the rate consistent with a stable price level, there is a unique natural rate. Sraffa’s quarrel was only with Hayek’s use of the natural rate, inasmuch as Hayek maintained that the natural rate did not imply a stable price level. Of course, Hayek was caught in a contradiction that Sraffa overlooked, because he identified the real natural rate with an equal nominal rate, so that he was implicitly assuming a constant expected price level even as he was arguing that the neutral monetary policy corresponding to setting the market interest rate equal to the natural rate would imply deflation when productivity was increasing.

I am inclined to be critical Milton Friedman about many aspects of his monetary thought, but one of his virtues as a monetary economist was that he consistently emphasized Fisher’s  distinction between real and nominal interest rates. The point that Friedman was making in the passage quoted by Tyler was that the monetary authority is able to peg nominal variables, prices, inflation, exchange rates, but not real variables, like employment, output, or interest rates. Even pegging the nominal natural rate is impossible, because inasmuch as the goal of targeting a nominal natural rate is to stabilize the rate of inflation, targeting the nominal natural rate also means targeting the real natural rate. But targeting the real natural rate is not possible, and trying to do so will just get you into trouble.

So Tyler should not be complaining about the change in the meaning of the natural rate; that change simply reflects the gradual penetration of the Fisher equation into the consciousness of the economics profession. We now realize that, given the real natural rate, there is, for every expected rate of inflation, a corresponding nominal natural rate.

Keynes made a very different contribution to our understanding of the natural rate. He was that there is no reason to assume that the real natural rate of interest is unique. True, at any moment there is some real natural rate toward which arbitrage is forcing all nominal rates to converge. But that real natural rate is a function of the prevailing economic conditions. Keynes believed that there are multiple equilibria, each corresponding to a different level of employment, and that associated with each of those equilibria there could be a different real natural rate. Nowadays, we are less inclined than was Keynes to call an underemployment situation an equilibrium, but there is still no reason to assume that the real natural rate that serves as an attractor for all nominal rates is independent of the state of the economy. If the real natural rate for an underperforming economy is less than the real natural rate that would be associated with the economy if it were in the neighborhood of an optimal equilibrium, there is no reason why either the real natural rate corresponding to an optimal equilibrium or the real natural rate corresponding to the current sub-optimal state of economy should be the policy rate that the monetary authority chooses as its target.

Finally, what can be said about Tyler’s point that it is implausible to suggest that the real natural rate is negative when the economy is growing (even slowly) and the marginal productivity of capital is positive? Two points.

First, the marginal productivity of gold is very close to zero. If gold is held as bullion, it is being held for expected appreciation over and above the cost of storage. So the ratio of the future price of gold to the spot price of gold should equal one plus the real rate of interest. If you look at futures prices for gold you will see that they are virtually the same as the spot price. However, storing gold is not costless. According to this article on Bloomberg.com, storage costs for gold range between 0.5 to 1% of the value of gold, implying that expected rate of return to holding gold is now less than -0.5% a year, which means that the marginal productivity of real capital is negative. Sure there are plenty of investments out there that are generating positive returns, but those are inframarginal investments. Those inframarginal investments are generating some net gain in productivity, and overall economic growth is positive, but that doesn’t mean that the return on investment at the margin is positive. At the margin, the yield on real capital seems to be negative.

If, as appears likely, our economy is underperforming, estimates of the real natural rate of interest are not necessarily an appropriate guide for the monetary authority in choosing its target rate of interest. If the aim of monetary policy is to nudge the economy onto a feasible growth path that is above the sub-optimal path along which it is currently moving, it might well be that the appropriate interest-rate target, as long as the economy remains below its optimal growth path, would be less than the natural rate corresponding to the current sub-optimal growth path.

Forget the Monetary Base and Just Pay Attention to the Price Level

Published December 23, 2014 David Beckworth , Fisher equation , intertemporal equilibrium , Jack Hirshleifer , Milton Friedman , Paul Krugman , quantity theory of money , zero lower bound 19 Comments
Tags: ,

Kudos to David Beckworth for eliciting a welcome concession or clarification from Paul Krugman that monetary policy is not necessarily ineffectual at the zero lower bound. The clarification is welcome because Krugman and Simon Wren Lewis seemed to be making a big deal about insisting that monetary policy at the zero lower bound is useless if it affects only the current, but not the future, money supply, and touting the discovery as if it were a point that was not already well understood.

Now it’s true that Krugman is entitled to take credit for having come up with an elegant way of showing the difference between a permanent and a temporary increase in the monetary base, but it’s a point that, WADR, was understood even before Krugman. See, for example, the discussion in chapter 5 of Jack Hirshleifer’s textbook on capital theory (published in 1970), Investment, Interest and Capital, showing that the Fisher equation follows straightforwardly in an intertemporal equilibrium model, so that the nominal interest rate can be decomposed into a real component and an expected-inflation component. If holding money is costless, then the nominal rate of interest cannot be negative, and expected deflation cannot exceed the equilibrium real rate of interest. This implies that, at the zero lower bound, the current price level cannot be raised without raising the future price level proportionately. That is all Krugman was saying in asserting that monetary policy is ineffective at the zero lower bound, even though he couched the analysis in terms of the current and future money supplies rather than in terms of the current and future price levels. But the entire argument is implicit in the Fisher equation. And contrary to Krugman, the IS-LM model (with which I am certainly willing to coexist) offers no unique insight into this proposition; it would be remarkable if it did, because the IS-LM model in essence is a static model that has to be re-engineered to be used in an intertemporal setting.

Here is how Hirshleifer concludes his discussion:

The simple two-period model of choice between dated consumptive goods and dated real liquidities has been shown to be sufficiently comprehensive as to display both the quantity theorists’ and the Keynesian theorists’ predicted results consequent upon “changes in the money supply.” The seeming contradiction is resolved by noting that one result or the other follows, or possibly some mixture of the two, depending upon the precise meaning of the phrase “changes in the quantity of money.” More exactly, the result follows from the assumption made about changes in the time-distributed endowments of money and consumption goods.  pp. 150-51

Another passage from Hirshleifer is also worth quoting:

Imagine a financial “panic.” Current money is very scarce relative to future money – and so monetary interest rates are very high. The monetary authorities might then provide an increment [to the money stock] while announcing that an equal aggregate amount of money would be retired at some date thereafter. Such a change making current money relatively more plentiful (or less scarce) than before in comparison with future money, would clearly tend to reduce the monetary rate of interest. (p. 149)

In this passage Hirshleifer accurately describes the objective of Fed policy since the crisis: provide as much liquidity as needed to prevent a panic, but without even trying to generate a substantial increase in aggregate demand by increasing inflation or expected inflation. The refusal to increase aggregate demand was implicit in the Fed’s refusal to increase its inflation target.

However, I do want to make explicit a point of disagreement between me and Hirshleifer, Krugman and Beckworth. The point is more conceptual than analytical, by which I mean that although the analysis of monetary policy can formally be carried out either in terms of current and future money supplies, as Hirshleifer, Krugman and Beckworth do, or in terms of price levels, as I prefer to do so in terms of price levels. For one thing, reasoning in terms of price levels immediately puts you in the framework of the Fisher equation, while thinking in terms of current and future money supplies puts you in the framework of the quantity theory, which I always prefer to avoid.

The problem with the quantity theory framework is that it assumes that quantity of money is a policy variable over which a monetary authority can exercise effective control, a mistake — imprinted in our economic intuition by two or three centuries of quantity-theorizing, regrettably reinforced in the second-half of the twentieth century by the preposterous theoretical detour of monomaniacal Friedmanian Monetarism, as if there were no such thing as an identification problem. Thus, to analyze monetary policy by doing thought experiments that change the quantity of money is likely to mislead or confuse.

I can’t think of an effective monetary policy that was ever implemented by targeting a monetary aggregate. The optimal time path of a monetary aggregate can never be specified in advance, so that trying to target any monetary aggregate will inevitably fail, thereby undermining the credibility of the monetary authority. Effective monetary policies have instead tried to target some nominal price while allowing monetary aggregates to adjust automatically given that price. Sometimes the price being targeted has been the conversion price of money into a real asset, as was the case under the gold standard, or an exchange rate between one currency and another, as the Swiss National Bank is now doing with the franc/euro exchange rate. Monetary policies aimed at stabilizing a single price are easy to implement and can therefore be highly credible, but they are vulnerable to sudden changes with highly deflationary or inflationary implications. Nineteenth century bimetallism was an attempt to avoid or at least mitigate such risks. We now prefer inflation targeting, but we have learned (or at least we should have) from the Fed’s focus on inflation in 2008 that inflation targeting can also lead to disastrous consequences.

I emphasize the distinction between targeting monetary aggregates and targeting the price level, because David Beckworth in his post is so focused on showing 1) that the expansion of the Fed’s balance sheet under QE has been temoprary and 2) that to have been effective in raising aggregate demand at the zero lower bound, the increase in the monetary base needed to be permanent. And I say: both of the facts cited by David are implied by the fact that the Fed did not raise its inflation target or, preferably, replace its inflation target with a sufficiently high price-level target. With a higher inflation target or a suitable price-level target, the monetary base would have taken care of itself.

PS If your name is Scott Sumner, you have my permission to insert “NGDP” wherever “price level” appears in this post.

John Cochrane Explains Neo-Fisherism

Published November 12, 2014 Fisher equation , John Cochrane , Knut Wicksell , natural rate of interest , Neo-Fisherism 13 Comments
Tags: , , , ,

In a recent post, John Cochrane, responding to an earlier post by Nick Rowe about Neo-Fisherism, has tried to explain why raising interest rates could plausibly cause inflation to rise and reducing interest rates could plausibly cause inflation to fall, even though almost everyone, including central bankers, seems to think that when central banks raise interest rates, inflation falls, and when they reduce interest rates, inflation goes up.

In his explanation, Cochrane concedes that there is an immediate short-term tendency for increased interest rates to reduce inflation and for reduced interest rates to raise inflation, but he also argues that these effects (liquidity effects in Keynesian terminology) are transitory and would be dominated by the Fisher effects if the central bank committed itself to a permanent change in its interest-rate target. Of course, the proviso that the central bank commit itself to a permanent interest-rate peg is a pretty important qualification to the Neo-Fisherian position, because few central banks have ever committed themselves to a permanent interest-rate peg, the most famous attempt (by the Fed after World War II) to peg an interest rate having led to accelerating inflation during the Korean War, thereby forcing the peg to be abandoned, in apparent contradiction of the Neo-Fisherian view.

However, Cochrane does try to reconcile the Neo-Fisherian view with the standard view that raising interest rates reduces inflation and reducing interest rates increases inflation. He suggests that the standard view is strictly a short-run relationship and that the way to target inflation over the long-run is simply to target an interest rate consistent with the desired rate of inflation, and to rely on the Fisher equation to generate the actual and expected rate of inflation corresponding to that nominal rate. Here’s how Cochrane puts it:

We can put the issue more generally as, if the central bank does nothing to interest rates, is the economy stable or unstable following a shock to inflation?

For the next set of graphs, I imagine a shock to inflation, illustrated as the little upward sloping arrow on the left. Usually, the Fed responds by raising interest rates. What if it doesn’t?  A pure neo-Fisherian view would say inflation will come back on its own.

cochrane1

Again, we don’t have to be that pure.

The milder view allows there may be some short run dynamics; the lower real rates might lead to some persistence in inflation. But even if the Fed does nothing, eventually real interest rates have to settle down to their “natural” level, and inflation will come back. Mabye not as fast as it would if the Fed had aggressively tamed it, but eventually.

cochrane2

By contrast, the standard view says that inflation is unstable. If the Fed does not raise rates, inflation will eventually careen off following the shock.

cochrane3

Now this really confuses me. What does a shock to inflation mean? From the context, Cochrane seems to be thinking that something happens to raise the rate of inflation in the short run, but the persistence of increased inflation somehow depends on an underlying assumption about whether the economy is stable or unstable. Cochrane doesn’t tell us what kind of shock to inflation he is talking about, and I can imagine only two possibilities, either a nominal shock or a real shock.

Let’s say it’s a nominal shock. What kind of nominal shock might Cochrane have in mind? An increase in the money supply? Well, presumably an increase in the money supply would cause an increase in the price level, and a temporary increase in the rate of inflation, but if the increase in the money supply is a once-and-for-all increase, the system must revert, after a temporary increase, back to the old rate of inflation. Or maybe, Cochrane is thinking of a permanent increase in the rate of growth in the money supply. But in that case, why would the rate of inflation come back on its own as Cochrane suggests it would? Well, maybe it’s not the money supply but money demand that’s changing. But again, one would normally assume that an appropriate change in central-bank policy could cope with such a scenario and stabilize the rate of inflation.

Alright, then, let’s say it’s a real shock. Suppose some real event happens that raises the rate of inflation. Well, like what? A supply shock? That raises the rate of inflation, but since when is the standard view that the appropriate response by the central bank to a negative supply shock is to raise the interest-rate target? Perhaps Cochrane is talking about a real shock that reduces the real rate of interest. Well, in that case, the rate of inflation would certainly rise if the central bank maintained its nominal-interest-rate target, but the increase in inflation would not be temporary unless the real shock was temporary. If the real shock is temporary, it is not clear why the standard view would recommend that the central bank raise its target rate of interest. So, I am sorry, but I am still confused.

Now, the standard view that Cochrane is disputing is actually derived from Wicksell, and Wicksell’s cycle theory is in fact based on the assumption that the central bank keeps its target interest rate fixed while the natural rate fluctuates. (This, by the way, was also Hayek’s assumption in his first exposition of his theory in Monetary Theory and the Trade Cycle.) When the natural rate rises above the central bank’s target rate, a cumulative inflationary process starts, because borrowing from the banking system to finance investment is profitable as long as the expected return on investment exceeds the interest rate on loans charged by the banks. (This is where Hayek departed from Wicksell, focusing on Cantillon Effects instead of price-level effects.) Cochrane avoids that messy scenario, as far as I can tell, by assuming that the initial position is one in which the Fisher equation holds with the nominal rate equal to the real plus the expected rate of inflation and with expected inflation equal to actual inflation, and then positing an (as far as I can tell) unexplained inflation shock, with no change to the real rate (meaning, in Cochrane’s terminology, that the economy is stable). If the unexplained inflation shock goes away, the system must return to its initial equilibrium with expected inflation equal to actual inflation and the nominal rate equal to the real rate plus inflation.

In contrast, the Wicksellian assumption is that the real rate fluctuates with the nominal rate and expected inflation unchanged. Unless the central bank raises the nominal rate, the difference between the profit rate anticipated by entrepreneurs and the rate at which they can borrow causes the rate of inflation to increase. So it does not seem to me that Cochrane has in any way reconciled the Neo-Fisherian view with the standard view (or at least the Wicksellian version of the standard view).

PS I would just note that I have explained in my paper on Ricardo and Thornton why the Wicksellian analysis (anticipated almost a century before Wicksell by Henry Thornton) is defective (basically because he failed to take into account the law of reflux), but Cochrane, as far as I can tell, seems to be making a completely different point in his discussion.

Monetary Theory on the Neo-Fisherite Edge

Published May 6, 2014 Earl Thompson , expectations , Fischer Black , Fisher equation , gold standard , Stephen Williamson 31 Comments
Tags: , , , , , , , , , ,

The week before last, Noah Smith wrote a post “The Neo-Fisherite Rebellion” discussing, rather sympathetically I thought, the contrarian school of monetary thought emerging from the Great American Heartland, according to which, notwithstanding everything monetary economists since Henry Thornton have taught, high interest rates are inflationary and low interest rates deflationary. This view of the relationship between interest rates and inflation was advanced (but later retracted) by Narayana Kocherlakota, President of the Minneapolis Fed in a 2010 lecture, and was embraced and expounded with increased steadfastness by Stephen Williamson of Washington University in St. Louis and the St. Louis Fed in at least one working paper and in a series of posts over the past five or six months (e.g. here, here and here). And John Cochrane of the University of Chicago has picked up on the idea as well in two recent blog posts (here and here). Others seem to be joining the upstart school as well.

The new argument seems simple: given the Fisher equation, in which the nominal interest rate equals the real interest rate plus the (expected) rate of inflation, a central bank can meet its inflation target by setting a fixed nominal interest rate target consistent with its inflation target and keeping it there. Once the central bank sets its target, the long-run neutrality of money, implying that the real interest rate is independent of the nominal targets set by the central bank, ensures that inflation expectations must converge on rates consistent with the nominal interest rate target and the independently determined real interest rate (i.e., the real yield curve), so that the actual and expected rates of inflation adjust to ensure that the Fisher equation is satisfied. If the promise of the central bank to maintain a particular nominal rate over time is believed, the promise will induce a rate of inflation consistent with the nominal interest-rate target and the exogenous real rate.

The novelty of this way of thinking about monetary policy is that monetary theorists have generally assumed that the actual adjustment of the price level or inflation rate depends on whether the target interest rate is greater or less than the real rate plus the expected rate. When the target rate is greater than the real rate plus expected inflation, inflation goes down, and when it is less than the real rate plus expected inflation, inflation goes up. In the conventional treatment, the expected rate of inflation is momentarily fixed, and the (expected) real rate variable. In the Neo-Fisherite school, the (expected) real rate is fixed, and the expected inflation rate is variable. (Just as an aside, I would observe that the idea that expectations about the real rate of interest and the inflation rate cannot occur simultaneously in the short run is not derived from the limited cognitive capacity of economic agents; it can only be derived from the limited intellectual capacity of economic theorists.)

The heretical views expressed by Williamson and Cochrane and earlier by Kocherlakota have understandably elicited scorn and derision from conventional monetary theorists, whether Keynesian, New Keynesian, Monetarist or Market Monetarist. (Williamson having appropriated for himself the New Monetarist label, I regrettably could not preserve an appropriate symmetry in my list of labels for monetary theorists.) As a matter of fact, I wrote a post last December challenging Williamson’s reasoning in arguing that QE had caused a decline in inflation, though in his initial foray into uncharted territory, Williamson was actually making a narrower argument than the more general thesis that he has more recently expounded.

Although deep down, I have no great sympathy for Williamson’s argument, the counterarguments I have seen leave me feeling a bit, shall we say, underwhelmed. That’s not to say that I am becoming a convert to New Monetarism, but I am feeling that we have reached a point at which certain underlying gaps in monetary theory can’t be concealed any longer. To explain what I mean by that remark, let me start by reviewing the historical context in which the ruling doctrine governing central-bank operations via adjustments in the central-bank lending rate evolved. The primary (though historically not the first) source of the doctrine is Henry Thornton in his classic volume The Nature and Effects of the Paper Credit of Great Britain.

Even though Thornton focused on the policy of the Bank of England during the Napoleonic Wars, when Bank of England notes, not gold, were legal tender, his discussion was still in the context of a monetary system in which paper money was generally convertible into either gold or silver. Inconvertible banknotes – aka fiat money — were the exception not the rule. Gold and silver were what Nick Rowe would call alpha money. All other moneys were evaluated in terms of gold and silver, not in terms of a general price level (not yet a widely accepted concept). Even though Bank of England notes became an alternative alpha money during the restriction period of inconvertibility, that situation was generally viewed as temporary, the restoration of convertibility being expected after the war. The value of the paper pound was tracked by the sterling price of gold on the Hamburg exchange. Thus, Ricardo’s first published work was entitled The High Price of Bullion, in which he blamed the high sterling price of bullion at Hamburg on an overissue of banknotes by the Bank of England.

But to get back to Thornton, who was far more concerned with the mechanics of monetary policy than Ricardo, his great contribution was to show that the Bank of England could control the amount of lending (and money creation) by adjusting the interest rate charged to borrowers. If banknotes were depreciating relative to gold, the Bank of England could increase the value of their notes by raising the rate of interest charged on loans.

The point is that if you are a central banker and are trying to target the exchange rate of your currency with respect to an alpha currency, you can do so by adjusting the interest rate that you charge borrowers. Raising the interest rate will cause the exchange value of your currency to rise and reducing the interest rate will cause the exchange value to fall. And if you are operating under strict convertibility, so that you are committed to keep the exchange rate between your currency and an alpha currency at a specified par value, raising that interest rate will cause you to accumulate reserves payable in terms of the alpha currency, and reducing that interest rate will cause you to emit reserves payable in terms of the alpha currency.

So the idea that an increase in the central-bank interest rate tends to increase the exchange value of its currency, or, under a fixed-exchange rate regime, an increase in the foreign exchange reserves of the bank, has a history at least two centuries old, though the doctrine has not exactly been free of misunderstanding or confusion in the course of those two centuries. One of those misunderstandings was about the effect of a change in the central-bank interest rate, under a fixed-exchange rate regime. In fact, as long as the central bank is maintaining a fixed exchange rate between its currency and an alpha currency, changes in the central-bank interest rate don’t affect (at least as a first approximation) either the domestic money supply or the domestic price level; all that changes in the central-bank interest rate can accomplish is to change the bank’s holdings of alpha-currency reserves.

It seems to me that this long well-documented historical association between changes in the central-bank interest rates and the exchange value of currencies and the level of private spending is the basis for the widespread theoretical presumption that raising the central-bank interest rate target is deflationary and reducing it is inflationary. However, the old central-bank doctrine of the Bank Rate was conceived in a world in which gold and silver were the alpha moneys, and central banks – even central banks operating with inconvertible currencies – were beta banks, because the value of a central-bank currency was still reckoned, like the value of inconvertible Bank of England notes in the Napoleonic Wars, in terms of gold and silver.

In the Neo-Fisherite world, central banks rarely peg exchange rates against each other, and there is no longer any outside standard of value to which central banks even nominally commit themselves. In a world without the metallic standard of value in which the conventional theory of central banking developed, do the propositions about the effects of central-bank interest-rate setting still obtain? I am not so sure that they do, not with the analytical tools that we normally deploy when thinking about the effects of central-bank policies. Why not? Because, in a Neo-Fisherite world in which all central banks are alpha banks, I am not so sure that we really know what determines the value of this thing called fiat money. And if we don’t really know what determines the value of a fiat money, how can we really be sure that interest-rate policy works the same way in a Neo-Fisherite world that it used to work when the value of money was determined in relation to a metallic standard? (Just to avoid misunderstanding, I am not – repeat NOT — arguing for restoring the gold standard.)

Why do I say that we don’t know what determines the value of fiat money in a Neo-Fisherite world? Well, consider this. Almost three weeks ago I wrote a post in which I suggested that Bitcoins could be a massive bubble. My explanation for why Bitcoins could be a bubble is that they provide no real (i.e., non-monetary) service, so that their value is totally contingent on, and derived from (or so it seems to me, though I admit that my understanding of Bitcoins is partial and imperfect), the expectation of a positive future resale value. However, it seems certain that the resale value of Bitcoins must eventually fall to zero, so that backward induction implies that Bitcoins, inasmuch as they provide no real service, cannot retain a positive value in the present. On this reasoning, any observed value of a Bitcoin seems inexplicable except as an irrational bubble phenomenon.

Most of the comments I received about that post challenged the relevance of the backward-induction argument. The challenges were mainly of two types: a) the end state, when everyone will certainly stop accepting a Bitcoin in exchange, is very, very far into the future and its date is unknown, and b) the backward-induction argument applies equally to every fiat currency, so my own reasoning, according to my critics, implies that the value of every fiat currency is just as much a bubble phenomenon as the value of a Bitcoin.

My response to the first objection is that even if the strict logic of the backward-induction argument is inconclusive, because of the long and uncertain duration of the time elapse between now and the end state, the argument nevertheless suggests that the value of a Bitcoin is potentially very unsteady and vulnerable to sudden collapse. Those are not generally thought to be desirable attributes in a medium of exchange.

My response to the second objection is that fiat currencies are actually quite different from Bitcoins, because fiat currencies are accepted by governments in discharging the tax liabilities due to them. The discharge of a tax liability is a real (i.e. non-monetary) service, creating a distinct non-monetary demand for fiat currencies, thereby ensuring that fiat currencies retain value, even apart from being accepted as a medium of exchange.

That, at any rate, is my view, which I first heard from Earl Thompson (see his unpublished paper, “A Reformulation of Macroeconomic Theory” pp. 23-25 for a derivation of the value of fiat money when tax liability is a fixed proportion of income). Some other pretty good economists have also held that view, like Abba Lerner, P. H. Wicksteed, and Adam Smith. Georg Friedrich Knapp also held that view, and, in his day, he was certainly well known, but I am unable to pass judgment on whether he was or wasn’t a good economist. But I do know that his views about money were famously misrepresented and caricatured by Ludwig von Mises. However, there are other good economists (Hal Varian for one), apparently unaware of, or untroubled by, the backward induction argument, who don’t think that acceptability in discharging tax liability is required to explain the value of fiat money.

Nor do I think that Thompson’s tax-acceptability theory of the value of money can stand entirely on its own, because it implies a kind of saw-tooth time profile of the price level, so that a fiat currency, earning no liquidity premium, would actually be appreciating between peak tax collection dates, and depreciating immediately following those dates, a pattern not obviously consistent with observed price data, though I do recall that Thompson used to claim that there is a lot of evidence that prices fall just before peak tax-collection dates. I don’t think that anyone has ever tried to combine the tax-acceptability theory with the empirical premise that currency (or base money) does in fact provide significant liquidity services. That, it seems to me, would be a worthwhile endeavor for any eager young researcher to undertake.

What does all of this have to do with the Neo-Fisherite Rebellion? Well, if we don’t have a satisfactory theory of the value of fiat money at hand, which is what another very smart economist Fischer Black – who, to my knowledge never mentioned the tax-liability theory — thought, then the only explanation of the value of fiat money is that, like the value of a Bitcoin, it is whatever people expect it to be. And the rate of inflation is equally inexplicable, being just whatever it is expected to be. So in a Neo-Fisherite world, if the central bank announces that it is reducing its interest-rate target, the effect of the announcement depends entirely on what “the market” reads into the announcement. And that is exactly what Fischer Black believed. See his paper “Active and Passive Monetary Policy in a Neoclassical Model.”

I don’t say that Williamson and his Neo-Fisherite colleagues are correct. Nor have they, to my knowledge, related their arguments to Fischer Black’s work. What I do say (indeed this is a problem I raised almost three years ago in one of my first posts on this blog) is that existing monetary theories of the price level are unable to rule out his result, because the behavior of the price level and inflation seems to depend, more than anything else, on expectations. And it is far from clear to me that there are any fundamentals in which these expectations can be grounded. If you impose the rational expectations assumption, which is almost certainly wrong empirically, maybe you can argue that the central bank provides a focal point for expectations to converge on. The problem, of course, is that in the real world, expectations are all over the place, there being no fundamentals to force the convergence of expectations to a stable equilibrium value.

In other words, it’s just a mess, a bloody mess, and I do not like it, not one little bit.

The Internal Contradiction of Quantitative Easing

Published November 18, 2013 Federal Reserve , Fisher equation , Paul Krugman , real interest rates , Scott Sumner 22 Comments
Tags: , ,

Last week I was struggling to cut and paste my 11-part series on Hawtrey’s Good and Bad Trade into the paper on that topic that I am scheduled to present next week at the Southern Economic Association meetings in Tampa Florida, completing the task just before coming down with a cold which has kept me from doing anything useful since last Thursday. But I was at least sufficiently aware of my surroundings to notice another flurry of interest in quantitative easing, presumably coinciding with Janet Yellen’s testimony at the hearings conducted by the Senate Banking Committee about her nomination to succeed Ben Bernanke as Chairman of Federal Reserve Board.

In my cursory reading of the latest discussions, I didn’t find a lot that has not already been said, so I will take that as an opportunity to restate some points that I have previously made on this blog. But before I do that, I can’t help observing (not for the first time either) that the two main arguments made by critics of QE do not exactly coexist harmoniously with each other. First, QE is ineffective; second it is dangerous. To be sure, the tension between these two claims about QE does not prove that both can’t be true, and certainly doesn’t prove that both are wrong. But the tension might at least have given a moment’s pause to those crying that Quantitative Easing, having failed for five years to accomplish anything besides enriching Wall Street and taking bread from the mouths of struggling retirees, is going to cause the sky to fall any minute.

Nor, come to think of it, does the faux populism of the attack on a rising stock market and of the crocodile tears for helpless retirees living off the interest on their CDs coexist harmoniously with the support by many of the same characters opposing QE (e.g., Freedomworks, CATO, the Heritage Foundation, and the Wall Street Journal editorial page) for privatizing social security via private investment accounts to be invested in the stock market, the argument being that the rate of return on investing in stocks has historically been greater than the rate of return on payments into the social security system. I am also waiting for an explanation of why abused pensioners unhappy with the returns on their CDs can’t cash in the CDs and buy dividend-paying-stocks? In which charter of the inalienable rights of Americans, I wonder, does one find it written that a perfectly secure real rate of interest of not less than 2% on any debt instrument issued by the US government shall always be guaranteed?

Now there is no denying that what is characterized as a massive program of asset purchases by the Federal Reserve System has failed to stimulate a recovery comparable in strength to almost every recovery since World War II. However, not even the opponents of QE are suggesting that the recovery has been weak as a direct result of QE — that would be a bridge too far even for the hard money caucus — only that whatever benefits may have been generated by QE are too paltry to justify its supposedly bad side-effects (present or future inflation, reduced real wages, asset bubbles, harm to savers, enabling of deficit-spending, among others). But to draw any conclusion about the effects of QE, you need some kind of a baseline of comparison. QE opponents therefore like to use previous US recoveries, without the benefit of QE, as their baseline.

But that is not the only baseline available for purposes of comparison. There is also the Eurozone, which has avoided QE and until recently kept interest rates higher than in the US, though to be sure not as high as US opponents of QE (and defenders of the natural rights of savers) would have liked. Compared to the Eurozone, where nominal GDP has barely risen since 2010, and real GDP and employment have shrunk, QE, which has been associated with nearly 4% annual growth in US nominal GDP and slightly more than 2% annual growth in US real GDP, has clearly outperformed the eurozone.

Now maybe you don’t like the Eurozone, as it includes all those dysfunctional debt-ridden southern European countries, as a baseline for comparison. OK, then let’s just do a straight, head-to-head matchup between the inflation-addicted US and solid, budget-balancing, inflation-hating Germany. Well that comparison shows (see the chart below) that since 2011 US real GDP has increased by about 5% while German real GDP has increased by less than 2%.

US_Germany_RGDP

So it does seem possible that, after all, QE and low interest rates may well have made things measurably better than they would have otherwise been. But don’t expect to opponents of QE to acknowledge that possibility.

Of course that still leaves the question on the table, why has this recovery been so weak? Well, Paul Krugman, channeling Larry Summers, offered a demographic hypothesis in his column Monday: that with declining population growth, there have been diminishing investment opportunities, which, together with an aging population, trying to save enough to support themselves in their old age, causes the supply of savings to outstrip the available investment opportunities, driving the real interest rate down to zero. As real interest rates fall, the ability of the economy to tolerate deflation — or even very low inflation — declines. That is a straightforward, and inescapable, implication of the Fisher equation (see my paper “The Fisher Effect Under Deflationary Expectations”).

So, if Summers and Krugman are right – and the trend of real interest rates for the past three decades is not inconsistent with their position – then we need to rethink revise upwards our estimates of what rate of inflation is too low. I will note parenthetically, that Samuel Brittan, who has been for decades just about the most sensible economic journalist in the world, needs to figure out that too little inflation may indeed be a bad thing.

But this brings me back to the puzzling question that causes so many people to assume that monetary policy is useless. Why have trillions of dollars of asset purchases not generated the inflation that other monetary expansions have generated? And if all those assets now on the Fed balance sheet haven’t generated inflation, what reason is there to think that the Fed could increase the rate of inflation if that is what is necessary to avoid chronic (secular) stagnation?

The answer, it seems to me is the following. If everyone believes that the Fed is committed to its inflation target — and not even the supposedly dovish Janet Yellen, bless her heart, has given the slightest indication that she favors raising the Fed’s inflation target, a target that, recent experience shows, the Fed is far more willing to undershoot than to overshoot – then Fed purchases of assets with currency are not going to stimulate additional private spending. Private spending, at or near the zero lower bound, are determined largely by expectations of future income and prices. The quantity of money in private hands, being almost costless to hold, is no longer a hot potato. So if there is no desire to reduce excess cash holdings, the only mechanism by which monetary policy can affect private spending is through expectations. But the Fed, having succeeded in anchoring inflation expectations at 2%, has succeeded in unilaterally disarming itself. So economic expansion is constrained by the combination of a zero real interest rate and expected inflation held at or below 2% by a political consensus that the Fed, even if it were inclined to, is effectively powerless to challenge.

Scott Sumner calls this monetary offset. I don’t think that we disagree much on the economic analysis, but it seems to me that he overestimates the amount of discretion that the Fed can actually exercise over monetary policy. Except at the margins, the Fed is completely boxed in by a political consensus it dares not question. FDR came into office in 1933, and was able to effect a revolution in monetary policy within his first month in office, thereby saving the country and Western Civilization. Perhaps Obama had an opportunity to do something similar early in his first term, but not any more. We are stuck at 2%, but it is no solution.

Keynes on the Fisher Equation and Real Interest Rates

Published September 2, 2013 Fisher equation , Irving Fisher , Keynes , monetary policy , monetary theory , natural rate of interest , real interest rates , Uncategorized , zero lower bound 27 Comments
Tags: , , ,

Almost two months ago, I wrote a post (“Who Sets the Real Rate of Interest?”) about the Fisher equation, questioning the idea that the Fed can, at will, reduce the real rate of interest by printing money, an idea espoused by a lot of people who also deny that the Fed has the power to reduce the rate of unemployment by printing money. A few weeks later, I wrote another post (“On a Difficult Passage in the General Theory“) in which I pointed out the inconsistency between Keynes’s attack on the Fisher equation in chapter 11 of the General Theory and his analysis in chapter 17 of the liquidity premium and the conditions for asset-market equilibrium, an analysis that led Keynes to write down what is actually a generalized version of the Fisher equation. In both of those posts I promised a future post about how to understand the dynamic implications of the Fisher equation and the relationship between Fisher equation and the Keynesian analysis. This post is an attempt to make good on those promises.

As I observed in my earlier post, the Fisher equation is best understood as a property of equilibrium. If the Fisher equation does not hold, then it is reasonable to attribute the failure to some sort of disequilibrium. The most obvious, but not the only, source of disequilibrium is incorrectly expected inflation. Other sources of disequilibrium could be a general economic disorder, the entire economic system being (seriously) out of equilibrium, implying that the real rate of interest is somehow different from the “equilibrium” rate, or, as Milton Friedman might put it, that the real rate is different from the rate that would be ground out by the system of Walrasian (or Casselian or Paretian or Fisherian) equations.

Still a third possibility is that there is more than one equilibrium (i.e., more than one solution to whichever system of equations we are trying to solve). If so, as an economy moves from one equilibrium path to another through time, the nominal (and hence the real) rate of that economy could be changing independently of changes in expected inflation, thereby nullifying the empirical relationship implied (under the assumption of a unique equilibrium) by the Fisher equation.

Now in the canonical Fisherian theory of interest, there is, at any moment of time, a unique equilibrium rate of interest (actually a unique structure of equilibrium rates for all possible combinations of time periods), increasing thrift tending to reduce rates and increasing productivity of capital tending to raise them. While uniqueness of the interest rate cannot easily be derived outside a one-commodity model, the assumption did not seem all that implausible in the context of the canonical Fisherian model with a given technology and given endowments of present and future resources. In the real world, however, the future is unknown, so the future exists now only in our imagination, which means that, fundamentally, the determination of real interest rates cannot be independent of our expectations of the future. There is no unique set of expectations that is consistent with “fundamentals.” Fundamentals and expectations interact to create the future; expectations can be self-fulfilling. One of the reasons why expectations can be self-fulfilling is that often it is the case that individual expectations can only be realized if they are congruent with the expectations of others; expectations are subject to network effects. That was the valid insight in Keynes’s “beauty contest” theory of the stock market in chapter 12 of the GT.

There simply is no reason why there would be only one possible equilibrium time path. Actually, the idea that there is just one possible equilibrium time path seems incredible to me. It seems infinitely more likely that there are many potential equilibrium time paths, each path conditional on a corresponding set of individual expectations. To be sure, not all expectations can be realized. Expectations that can’t be realized produce bubbles. But just because expectations are not realized doesn’t mean that the observed price paths were bubbles; as long as it was possible, under conditions that could possibly have obtained, that the expectations could have been realized, the observed price paths were not bubbles.

Keynes was not the first economist to attribute economic fluctuations to shifts in expectations; J. S. Mill, Stanley Jevons, and A. C. Pigou, among others, emphasized recurrent waves of optimism and pessimism as the key source of cyclical fluctuations. The concept of the marginal efficiency of capital was used by Keynes to show the dependence of the desired capital stock, and hence the amount of investment, on the state of entrepreneurial expectations, but Keynes, just before criticizing the Fisher equation, explicitly identified the MEC with the Fisherian concept of “the rate of return over cost.” At a formal level, at any rate, Keynes was not attacking the Fisherian theory of interest.

So what I want to suggest is that, in attacking the Fisher equation, Keynes was really questioning the idea that a change in inflation expectations operates strictly on the nominal rate of interest without affecting the real rate. In a world in which there is a unique equilibrium real rate, and in which the world is moving along a time-path in the neighborhood of that equilibrium, a change in inflation expectations may operate strictly on the nominal rate and leave the real rate unchanged. In chapter 11, Keynes tried to argue the opposite: that the entire adjustment to a change in expected inflation is concentrated on real rate with the nominal rate unchanged. This idea seems completely unfounded. However, if the equilibrium real rate is not unique, why assume, as the standard renditions of the Fisher equation usually do, that a change in expected inflation affects only the nominal rate? Indeed, even if there is a unique real rate – remember that “unique real rate” in this context refers to a unique yield curve – the assumption that the real rate is invariant with respect to expected inflation may not be true in an appropriate comparative-statics exercise, such as the 1950s-1960s literature on inflation and growth, which recognized the possibility that inflation could induce a shift from holding cash to holding real assets, thereby increasing the rate of capital accumulation and growth, and, consequently, reducing the equilibrium real rate. That literature was flawed, or at least incomplete, in its analysis of inflation, but it was motivated by a valid insight.

In chapter 17, after deriving his generalized version of the Fisher equation, Keynes came back to this point when explaining why he had now abandoned the Wicksellian natural-rate analysis of the Treatise on Money. The natural-rate analysis, Keynes pointed out, presumes the existence of a unique natural rate of interest, but having come to believe that there could be an equilibrium associated with any level of employment, Keynes now concluded that there is actually a natural rate of interest corresponding to each level of employment. What Keynes failed to do in this discussion was to specify the relationship between natural rates of interest and levels of employment, leaving a major gap in his theoretical structure. Had he specified the relationship, we would have an explicit Keynesian IS curve, which might well differ from the downward-sloping Hicksian IS curve. As Earl Thompson, and perhaps others, pointed out about 40 years ago, the Hicksian IS curve is inconsistent with the standard neoclassical theory of production, which Keynes seems (provisionally at least) to have accepted when arguing that, with a given technology and capital stock, increased employment is possible only at a reduced real wage.

But if the Keynesian IS curve is upward-sloping, then Keynes’s criticism of the Fisher equation in chapter 11 is even harder to make sense of than it seems at first sight, because an increase in expected inflation would tend to raise, not (as Keynes implicitly assumed) reduce, the real rate of interest. In other words, for an economy operating at less than full employment, with all expectations except the rate of expected inflation held constant, an increase in the expected rate of inflation, by raising the marginal efficiency of capital, and thereby increasing the expected return on investment, ought to be associated with increased nominal and real rates of interest. If we further assume that entrepreneurial expectations are positively related to the state of the economy, then the positive correlation between inflation expectations and real interest rates would be enhanced. On this interpretation, Keynes’s criticism of the Fisher equation in chapter 11 seems indefensible.

That is one way of looking at the relationship between inflation expectations and the real rate of interest. But there is also another way.

The Fisher equation tells us that, in equilibrium, the nominal rate equals the sum of the prospective real rate and the expected rate of inflation. Usually that’s not a problem, because the prospective real rate tends to be positive, and inflation (at least since about 1938) is almost always positive. That’s the normal case. But there’s also an abnormal (even pathological) case, where the sum of expected inflation and the prospective real rate of interest is less than zero. We know right away that such a situation is abnormal, because it is incompatible with equilibrium. Who would lend money at a negative rate when it’s possible to hold the money and get a zero return? The nominal rate of interest can’t be negative. So if the sum of the prospective real rate (the expected yield on real capital) and the expected inflation rate (the negative of the expected yield on money with a zero nominal interest rate) is negative, then the return to holding money exceeds the yield on real capital, and the Fisher equation breaks down.

In other words, if r + dP/dt < 0, where r is the real rate of interest and dP/dt is the expected rate of inflation, then r < –dP/dt. But since i, the nominal rate of interest, cannot be less than zero, the Fisher equation does not hold, and must be replaced by the Fisher inequality

i > r + dP/dt.

If the Fisher equation can’t be satisfied, all hell breaks loose. Asset prices start crashing as asset owners try to unload their real assets for cash. (Note that I have not specified the time period over which the sum of expected inflation and the prospective yield on real capital are negative. Presumably the duration of that period is not indefinitely long. If it were, the system might implode.)

That’s what was happening in the autumn of 2008, when short-term inflation expectations turned negative in a contracting economy in which the short-term prospects for investment were really lousy and getting worse. The prices of real assets had to fall enough to raise the prospective yield on real assets above the expected yield from holding cash. However, falling asset prices don’t necessary restore equilibrium, because, once a panic starts it can become contagious, with falling asset prices reinforcing the expectation that asset prices will fall, depressing the prospective yield on real capital, so that, rather than bottoming out, the downward spiral feeds on itself.

Thus, for an economy at the zero lower bound, with the expected yield from holding money greater than the prospective yield on real capital, a crash in asset prices may not stabilize itself. If so, something else has to happen to stop the crash: the expected yield from holding money must be forced below the prospective yield on real capital. With the prospective yield on real capital already negative, forcing down the expected yield on money below the prospective yield on capital requires raising expected inflation above the absolute value of the prospective yield on real capital. Thus, if the prospective yield on real capital is -5%, then, to stop the crash, expected inflation would have to be raised to over 5%.

But there is a further practical problem. At the zero lower bound, not only is the prospective real rate not observable, it can’t even be inferred from the Fisher equation, the Fisher equation having become an inequality. All that can be said is that r < –dP/dt.

So, at the zero lower bound, achieving a recovery requires raising expected inflation. But how does raising expected inflation affect the nominal rate of interest? If r + dP/dt < 0, then increasing expected inflation will not increase the nominal rate of interest unless dP/dt increases enough to make r + dP/dt greater than zero. That’s what Keynes seemed to be saying in chapter 11, raising expected inflation won’t affect the nominal rate of interest, just the real rate. So Keynes’s criticism of the Fisher equation seems valid only in the pathological case when the Fisher equation is replaced by the Fisher inequality.

In my paper “The Fisher Effect Under Deflationary Expectations,” I found that a strongly positive correlation between inflation expectations (approximated by the breakeven TIPS spread on 10-year Treasuries) and asset prices (approximated by S&P 500) over the time period from spring 2008 through the end of 2010, while finding no such correlation over the period from 2003 to 2008. (Extending the data set through 2012 showed the relationship persisted through 2012 but may have broken down in 2013.) This empirical finding seems consistent with the notion that there has been something pathological about the period since 2008. Perhaps one way to think about the nature of the pathology is that the Fisher equation has been replaced by the Fisher inequality, a world in which changes in inflation expectations are reflected in changes in real interest rates instead of changes in nominal rates, the most peculiar kind of world described by Keynes in chapter 11 of the General Theory.

On a Difficult Passage in the General Theory

Published July 25, 2013 Earl Thompson , expectations , Fisher equation , inflation , Irving Fisher , Keynes , natural rate of interest 32 Comments
Tags: , ,

Keynes’s General Theory is not, in my estimation, an easy read. The terminology is often unfamiliar, and, so even after learning one of his definitions, I have trouble remembering what the term means the next time it’s used.. And his prose style, though powerful and very impressive, is not always clear, so you can spend a long time reading and rereading a sentence or a paragraph before you can figure out exactly what he is trying to say. I am not trying to be critical, just to point out that the General Theory is a very challenging book to read, which is one, but not the only, reason why it is subject to a lot of conflicting interpretations. And, as Harry Johnson once pointed out, there is an optimum level of difficulty for a book with revolutionary aspirations. If it’s too simple, it won’t be taken seriously. And if it’s too hard, no one will understand it. Optimally, a revolutionary book should be hard enough so that younger readers will be able to figure it out, and too difficult for the older guys to understand or to make the investment in effort to understand.

In this post, which is, in a certain sense, a follow-up to an earlier post about what, or who, determines the real rate of interest, I want to consider an especially perplexing passage in the General Theory about the Fisher equation. It is perplexing taken in isolation, and it is even more perplexing when compared to other passages in both the General Theory itself and in Keynes’s other writings. Here’s the passage that I am interested in.

The expectation of a fall in the value of money stimulates investment, and hence employment generally, because it raises the schedule of the marginal efficiency of capital, i.e., the investment demand-schedule; and the expectation of a rise in the value of money is depressing, because it lowers the schedule of the marginal efficiency of capital. This is the truth which lies behind Professor Irving Fisher’s theory of what he originally called “Appreciation and Interest” – the distinction between the money rate of interest and the real rate of interest where the latter is equal to the former after correction for changes in the value of money. It is difficult to make sense of this theory as stated, because it is not clear whether the change in the value of money is or is not assumed to be foreseen. There is no escape from the dilemma that, if it is not foreseen, there will be no effect on current affairs; whilst, if it is foreseen, the prices of exiting goods will be forthwith so adjusted that the advantages of holding money and of holding goods are again equalized, and it will be too late for holders of money to gain or to suffer a change in the rate of interest which will offset the prospective change during the period of the loan in the value of the money lent. For the dilemma is not successfully escaped by Professor Pigou’s expedient of supposing that the prospective change in the value of money is foreseen by one set of people but not foreseen by another. (p. 142)

The statement is problematic on just about every level, and one hardly knows where to begin in discussing it. But just for starters, it is amazing that Keynes seems (or, for rhetorical purposes, pretends) to be in doubt whether Fisher is talking about anticipated or unanticipated inflation, because Fisher himself explicitly distinguished between anticipated and unanticipated inflation, and Keynes could hardly have been unaware that Fisher was explicitly speaking about anticipated inflation. So the implication that the Fisher equation involves some confusion on Fisher’s part between anticipated and unanticipated inflation was both unwarranted and unseemly.

What’s even more puzzling is that in his Tract on Monetary Reform, Keynes expounded the covered interest arbitrage principle that the nominal-interest-rate-differential between two currencies corresponds to the difference between the spot and forward rates, which is simply an extension of Fisher’s uncovered interest arbitrage condition (alluded to by Keynes in referring to “Appreciation and Interest”). So when Keynes found Fisher’s distinction between the nominal and real rates of interest to be incoherent, did he really mean to exempt his own covered interest arbitrage condition from the charge?

But it gets worse, because if we flip some pages from chapter 11, where the above quotation is found, to chapter 17, we see on page 224, the following passage in which Keynes extends the idea of a commodity or “own rate of interest” to different currencies.

It may be added that, just as there are differing commodity-rates of interest at any time, so also exchange dealers are familiar with the fact that the rate of interest is not even the same in terms of two different moneys, e.g. sterling and dollars. For here also the difference between the “spot” and “future” contracts for a foreign money in terms of sterling are not, as a rule, the same for different foreign moneys. . . .

If no change is expected in the relative value of two alternative standards, then the marginal efficiency of a capital-asset will be the same in whichever of the two standards it is measured, since the numerator and denominator of the fraction which leads up to the marginal efficiency will be changed in the same proportion. If, however, one of the alternative standards is expected to change in value in terms of the other, the marginal efficiencies of capital-assets will be changed by the same percentage, according to which standard they are measured in. To illustrate this let us take the simplest case where wheat, one of the alternative standards, is expected to appreciate at a steady rate of a percent per annum in terms of money; the marginal efficiency of an asset, which is x percent in terms of money, will then be x – a percent in terms of wheat. Since the marginal efficiencies of all capital assets will be altered by the same amount, it follows that their order of magnitude will be the same irrespective of the standard which is selected.

So Keynes in chapter 17 explicitly allows for the nominal rate of interest to be adjusted to reflect changes in the expected value of the asset (whether a money or a commodity) in terms of which the interest rate is being calculated. Mr. Keynes, please meet Mr. Keynes.

I think that one source of Keynes’s confusion in attacking the Fisher equation was his attempt to force the analysis of a change in inflation expectations, clearly a disequilibrium, into an equilibrium framework. In other words, Keynes is trying to analyze what happens when there has been a change in inflation expectations as if the change had been foreseen. But any change in inflation expectations, by definition, cannot have been foreseen, because to say that an expectation has changed means that the expectation is different from what it was before. Perhaps that is why Keynes tied himself into knots trying to figure out whether Fisher was talking about a change in the value of money that was foreseen or not foreseen. In any equilibrium, the change in the value of money is foreseen, but in the transition from one equilibrium to another, the change is not foreseen. When an unforeseen change occurs in expected inflation, leading to a once-and-for-all change in the value of money relative to other assets, the new equilibrium will be reestablished given the new value of money relative to other assets.

But I think that something else is also going on here, which is that Keynes was implicitly assuming that a change in inflation expectations would alter the real rate of interest. This is a point that Keynes makes in the paragraph following the one I quoted above.

The mistake lies in supposing that it is the rate of interest on which prospective changes in the value of money will directly react, instead of the marginal efficiency of a given stock of capital. The prices of existing assets will always adjust themselves to changes in expectation concerning the prospective value of money. The significance of such changes in expectation lies in their effect on the readiness to produce new assets through their reaction on the marginal efficiency of capital. The stimulating effect of the expectation of higher prices is due, not to its raising the rate of interest (that would be a paradoxical way of stimulating output – insofar as the rate of interest rises, the stimulating effect is to that extent offset) but to its raising the marginal efficiency of a given stock of capital. If the rate of interest were to rise pari passu with the marginal efficiency of capital, there would be no stimulating effect from the expectation of rising prices. For the stimulating effect depends on the marginal efficiency of capital rising relativevly to the rate of interest. Indeed Professor Fisher’s theory could best be rewritten in terms of a “real rate of interest” defined as being the rate of interest which would have to rule, consequently on change in the state of expectation as to the future value of money, in order that this change should have no effect on current output. (pp. 142-43)

Keynes’s mistake lies in supposing that an increase in inflation expectations could not have a stimulating effect except as it raises the marginal efficiency of capital relative to the rate of interest. However, the increase in the value of real assets relative to money will increase the incentive to produce new assets. It is the rise in the value of existing assets relative to money that raises the marginal efficiency of those assets, creating an incentive to produce new assets even if the nominal interest rate were to rise by as much as the rise in expected inflation.

Keynes comes back to this point at the end of chapter 17, making it more forcefully than he did the first time.

In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest – namely, the rate of interest which, in the terminology of my Treatise, preserved equality between the rate of saving (as there defined) and the rate of investment. I believed this to be a development and clarification of of Wicksell’s “natural rate of interest,” which was, according to him, the rate which would preserve the stability of some, not quite clearly specified, price-level.

I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus, it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value for the rate of interest irrespective of the level of employment. . . .

If there is any such rate of interest, which is unique and significant, it must be the rate which we might term the neutral rate of interest, namely, the natural rate in the above sense which is consistent with full employment, given the other parameters of the system; though this rate might be better described, perhaps, as the optimum rate. (pp. 242-43)

So what Keynes is saying, I think, is this. Consider an economy with a given fixed marginal efficiency of capital (MEC) schedule. There is some interest rate that will induce sufficient investment expenditure to generate enough spending to generate full employment. That interest rate Keynes calls the “neutral” rate of interest. If the nominal rate of interest is more than the neutral rate, the amount of investment will be less than the amount necessary to generate full employment. In such a situation an expectation that the price level will rise will shift up the MEC schedule by the amount of the expected increase in inflation, thereby generating additional investment spending. However, because the MEC schedule is downward-sloping, the upward shift in the MEC schedule that induces increased investment spending will correspond to an increase in the rate of interest that is less than the increase in expected inflation, the upward shift in the MEC schedule being partially offset by the downward movement along the MEC schedule. In other words, the increase in expected inflation raises the nominal rate of interest by less than increase in expected inflation by inducing additional investment that is undertaken only because the real rate of interest has fallen.

However, for an economy already operating at full employment, an increase in expected inflation would not increase employment, so whether there was any effect on the real rate of interest would depend on the extent to which there was a shift from holding money to holding real capital assets in order to avoid the inflation tax.

Before closing, I will just make two side comments. First, my interpretation of Keynes’s take on the Fisher equation is similar to that of Allin Cottrell in his 1994 paper “Keynes and the Keynesians on the Fisher Effect.” Second, I would point out that the Keynesian analysis violates the standard neoclassical assumption that, in a two-factor production function, the factors are complementary, which implies that an increase in employment raises the MEC schedule. The IS curve is not downward-sloping, but upward sloping. This is point, as I have explained previously (here and here), was made a long time ago by Earl Thompson, and it has been made recently by Nick Rowe and Miles Kimball.

I hope in a future post to work out in more detail the relationship between the Keynesian and the Fisherian analyses of real and nominal interest rates.

What Gives? Has the Market Stopped Loving Inflation?

Published June 7, 2013 expectations , Fisher equation , inflation , monetary policy , QE 15 Comments
Tags:

One of my few, and not very compelling, claims to fame is a (still unpublished) paper (“The Fisher Effect Under Deflationary Expectations“) that I wrote in late 2010 in which I used the Fisher Equation relating the real and nominal rates of interest via the expected rate of inflation to explain what happens in a financial panic. I pointed out that the usual understanding that the nominal rate of interest and the expected rate of inflation move in the same direction, and possibly even by the same amount, cannot be valid when the expected rate of inflation is negative and the real rate is less than expected deflation. In those perilous conditions, the normal equilibrating process, by which the nominal rate adjusts to reflect changes in inflation expectations, becomes inoperative, because the nominal rate gets stuck at zero. In that unstable environment, the only avenue for adjustment is in the market for assets. In particular, when the expected yield from holding money (the expected rate of deflation) approaches or exceeds the expected yield on real capital, asset prices crash as asset owners all try to sell at the same time, the crash continuing until the expected yield on holding assets is no longer less than the expected yield from holding money. Of course, even that adjustment mechanism will restore an equilibrium only if the economy does not collapse entirely before a new equilibrium of asset prices and expected yields can be attained, a contingency not necessarily as unlikely as one might hope.

I therefore hypothesized that while there is not much reason, in a well-behaved economy, for asset prices to be very sensitive to changes in expected inflation, when expected inflation approaches, or exceeds, the expected return on capital assets (the real rate of interest), changes in expected inflation are likely to have large effects on asset values. This possibility that the relationship between expected inflation and asset prices could differ depending on the prevalent macroeconomic environment suggested an empirical study of the relationship between expected inflation (as approximated by the TIPS spread on 10-year Treasuries) and the S&P 500 stock index. My results were fairly remarkable, showing that, since early 2008 (just after the start of the downturn in late 2007), there was a consistently strong positive correlation between expected inflation and the S&P 500. However, from 2003 to 2008, no statistically significant correlation between expected inflation and asset prices showed up in the data.

Ever since then, I have used this study (and subsequent informal follow-ups that have consistently generated similar results) as the basis for my oft-repeated claim that the stock market loves inflation. But now, guess what? The correlation between inflation expectations and the S&P 500 has recently vanished. The first of the two attached charts plots both expected inflation, as measured by the 10-year TIPS spread, and the S&P 500 (normalized to 1 on March 2, 2009). It is obvious that two series are highly correlated. However, you can see that over the last few months it looks as if the correlation has been reversed, with inflation expectations falling even as the S&P 500 has been regularly reaching new all-time highs.

TIPS_S&P500_new

Here is a second chart that provides a closer look at the behavior of the S&P 500 and the TIPS spread since the beginning of March.

TIPS_S&P500_new_2

So what’s going on? I wish I knew. But here is one possibility. Maybe the economy is finally emerging from its malaise, and, after four years of an almost imperceptible recovery, perhaps the overall economic outlook has improved enough so that, even if we haven’t yet returned to normalcy, we are at least within shouting distance of it. If so, maybe asset prices are no longer as sensitive to inflation expectations as they were from 2008 to 2012. But then the natural question becomes: what caused the economy to reach a kind of tipping point into normalcy in March? I just don’t know.

And if we really are back to normal, then why is the real rate implied by the TIPS negative? True, the TIPS yield is not really the real rate in the Fisher equation, but a negative yield on a 10-year TIPS does not strike me as characteristic of a normal state of affairs. Nevertheless, the real yield on the 10-year TIPS has risen by about 50 basis points since March and by 75 basis points since December, so something noteworthy seems to have happened. And a fairly sharp rise in real rates suggests that recent increases in stock prices have been associated with expectations of increasing real cash flows and a strengthening economy. Increasing optimism about real economic growth, given that there has been no real change in monetary policy since last September when QE3 was announced, may themselves have contributed to declining inflation expectations.

What does this mean for policy? The empirical correlation between inflation expectations and asset prices is subject to an identification problem. Just because recent developments may have caused the observed correlation between inflation expectations and stock prices to disappear, one can’t conclude that, in the “true” structural model, the effect of a monetary policy that raised inflation expectations would not be to raise asset prices. The current semi-normal is not necessarily a true normal.

So my cautionary message is: Don’t use the recent disappearance of the correlation between inflation expectations and asset prices to conclude that it’s safe to abandon QE.

My Paper (co-authored with Paul Zimmerman) on Hayek and Sraffa

Published February 20, 2013 Alchian , Austrian Business-Cycle Theory , Fisher equation , Hayek , Irving Fisher , Keynes , Piero Sraffa , Uncategorized 13 Comments
Tags: , , , ,

I have just uploaded to the SSRN website a new draft of the paper (co-authored with Paul Zimmerman) on Hayek and Sraffa and the natural rate of interest, presented last June at the History of Economics Society conference at Brock University. The paper evolved from an early post on this blog in September 2011. I also wrote about the Hayek-Sraffa controversy in a post in June 2012 just after the HES conference.

One interesting wrinkle that occurred to me just as I was making revisions in the paper this week is that Keynes’s treatment of own rates in chapter 17 of the General Theory, which was in an important sense inspired by Sraffa, but, in my view, came to a very different conclusion from Sraffa’s, was actually nothing more than a generalization of Irving Fisher’s analysis of the real and nominal rates of interest, first presented in Fisher’s 1896 book Appreciation and Interest. In his Tract on Monetary Reform, Keynes extended Fisher’s analysis into his theory of covered interest rate arbitrage. What is really surprising is that, despite his reliance on Fisher’s analysis in the Tract and also in the Treatise on Money, Keynes sharply criticized Fisher’s analysis of the nominal and real rates of interest in chapter 13 of the General Theory. (I discussed that difficult passage in the General Theory in this post).  That is certainly surprising. But what is astonishing to me is that, after trashing Fisher in chapter 13 of the GT, Keynes goes back to Fisher in chapter 17, giving a generalized restatement of Fisher’s analysis in his discussion of own rates. Am I the first person to have noticed Keynes’s schizophrenic treatment of Fisher in the General Theory?

PS: My revered teacher, the great Armen Alchian passed away yesterday at the age of 98. There have been many tributes to him, such as this one by David Henderson, also a student of Alchian’s, in the Wall Street Journal. I have written about Alchian in the past (here, here, here, here, and here), and I hope to write about Alchian again in the near future. There was none like him; he will be missed terribly.

The Wisdom of David Laidler

Published September 11, 2012 David Laidler , expectations , Fisher equation , Friedman , Monetarism , monetary policy , monetary theory 24 Comments

Michael Woodford’s paper for the Jackson Hole Symposium on Monetary Policy wasn’t the only important paper on monetary economics to be posted on the internet last month. David Laidler, perhaps the world’s greatest expert on the history of monetary theory and macroeconomics since the time of Adam Smith, has written an important paper with the somewhat cryptic title, “Two Crises, Two Ideas, and One Question.” Most people will figure out pretty quickly which two crises Laidler is referring to, but you will have to read the paper in order to figure out which two ideas and which question, Laidler has on his mind. Actually, you won’t have to read the paper if you keep reading this post, because I am about to tell you. The two ideas are what Laidler calls the “Fisher relation” between real and nominal interest rates, and the idea of a lender of last resort. The question is whether a market economy is inherently stable or unstable.

How does one weave these threads into a coherent narrative? Well, to really understand that you really will just have to read Laidler’s paper, but this snippet from the introduction will give you some sense of what he is up to.

These two particular ideas are especially interesting, because in the 1960s and ’70s, between our two crises, they feature prominently in the Monetarist reassessment of the Great Depression, which helped to establish the dominance in macroeconomic thought of the view that, far from being a manifestation of deep flaws in the very structure of the market economy, as it had at first been taken to be, this crisis was the consequence of serious policy errors visited upon an otherwise robustly self-stabilizing system. The crisis that began in 2007 has re-opened this question.

The Monetarist counterargument to the Keynesian view that the market economy is inherently subject to wide fluctuations and has no strong tendency toward full employment was that the Great Depression was caused primarily by a policy shock, the failure of the Fed to fulfill its duty to act as a lender of last resort during the US financial crisis of 1930-31. Originally, the Fisher relation did not figure prominently in this argument, but it eventually came to dominate Monetarism and the post-Monetarist/New Keynesian orthodoxy in which the job of monetary policy was viewed as setting a nominal interest rate (via a Taylor rule) that would be consistent with expectations of an almost negligible rate of inflation of about 2%.

This comfortable state of affairs – Monetarism without money is how Laidler describes it — in which an inherently stable economy would glide along its long-run growth path with low inflation, only rarely interrupted by short, shallow recessions, was unpleasantly overturned by the housing bubble and the subsequent financial crisis, producing the steepest downturn since 1937-38. That downturn has posed a challenge to Monetarist orthodoxy inasmuch as the sudden collapse, more or less out of nowhere in 2008, seemed to suggest that the market economy is indeed subject to a profound instability, as the Keynesians of old used to maintain. In the Great Depression, Monetarists could argue, it was all, or almost all, the fault of the Federal Reserve for not taking prompt action to save failing banks and for not expanding the money supply sufficiently to avoid deflation. But in 2008, the Fed provided massive support to banks, and even to non-banks like AIG, to prevent a financial meltdown, and then embarked on an aggressive program of open-market purchases that prevented an incipient deflation from taking hold.

As a result, self-identifying Monetarists have split into two camps. I will call one camp the Market Monetarists, with whom I identify even though I am much less of a fan of Milton Friedman, the father of Monetarism, than most Market Monetarists, and, borrowing terminology adopted in the last twenty years or so by political conservatives in the US to distinguish between old-fashioned conservatives and neoconservatives, I will call the old-style Monetarists, paleo-Monetarists. The paelo-Monetarists are those like Alan Meltzer, the late Anna Schwartz, Thomas Humphrey, and John Taylor (a late-comer to Monetarism who has learned quite well how to talk to the Monetarist talk). For the paleo-Monetarists, in the absence of deflation, the extension of Fed support to non-banking institutions and the massive expansion of the Fed’s balance sheet cannot be justified. But this poses a dilemma for them. If there is no deflation, why is an inherently stable economy not recovering? It seems to me that it is this conundrum which has led paleo-Monetarists into taking the dubious position that the extreme weakness of the economic recovery is a consequence of fiscal and monetary-policy uncertainty, the passage of interventionist legislation like the Affordable Health Care Act and the Dodd-Frank Bill, and the imposition of various other forms of interventionist regulations by the Obama administration.

Market Monetarists, on the other hand, have all along looked to monetary policy as the ultimate cause of both the downturn in 2008 and the lack of a recovery subsequently. So, on this interpretation, what separates paleo-Monetarists from Market Monetarists is whether you need outright deflation in order to precipitate a serious malfunction in a market economy, or whether something less drastic can suffice. Paleo-Monetarists agree that Japan in the 1990s and even early in the 2000s was suffering from a deflationary monetary policy, a policy requiring extraordinary measures to counteract. But the annual rate of deflation in Japan was never more than about 1% a year, a far cry from the 10% annual rate of deflation in the US between late 1929 and early 1933. Paleo-Monetarists must therefore explain why there is a radical difference between 1% inflation and 1% deflation. Market Monetarists also have a problem in explaining why a positive rate of inflation, albeit less than the 2% rate that is generally preferred, is not adequate to sustain a real recovery from starting more than four years after the original downturn. Or, if you prefer, the question could be restated as why a 3 to 4% rate of increase in NGDP is not adequate to sustain a real recovery, especially given the assumption, shared by paleo-Monetarists and Market Monetarists, that a market economy is generally stable and tends to move toward a full-employment equilibrium.

Here is where I think Laidler’s focus on the Fisher relation is critically important, though Laidler doesn’t explicitly address the argument that I am about to make. This argument, which I originally made in my paper “The Fisher Effect under Deflationary Expectations,” and have repeated in several subsequent blog posts (e.g., here) is that there is no specific rate of deflation that necessarily results in a contracting economy. There is plenty of historical experience, as George Selgin and others have demonstrated, that deflation is consistent with strong economic growth and full employment. In a certain sense, deflation can be a healthy manifestation of growth, allowing that growth, i.e., increasing productivity of some or all factors of production, to be translated into falling output prices. However, deflation is only healthy in an economy that is growing because of productivity gains. If productivity is flagging, there is no space for healthy (productivity-driven) deflation.

The Fisher relation between the nominal interest rate, the real interest rate and the expected rate of deflation basically tells us how much room there is for healthy deflation. If we take the real interest rate as given, that rate constitutes the upper bound on healthy deflation. Why, because deflation greater than real rate of interest implies a nominal rate of interest less than zero. But the nominal rate of interest has a lower bound at zero. So what happens if the expected rate of deflation is greater than the real rate of interest? Fisher doesn’t tell us, because in equilibrium it isn’t possible for the rate of deflation to exceed the real rate of interest. But that doesn’t mean that there can’t be a disequilibrium in which the expected rate of deflation is greater than the real rate of interest. We (or I) can’t exactly model that disequilibrium process, but whatever it is, it’s ugly. Really ugly. Most investment stops, the rate of return on cash (i.e., expected rate of deflation) being greater than the rate of return on real capital. Because the expected yield on holding cash exceeds the expected yield on holding real capital, holders of real capital try to sell their assets for cash. The only problem is that no one wants to buy real capital with cash. The result is a collapse of asset values. At some point, asset values having fallen, and the stock of real capital having worn out without being replaced, a new equilibrium may be reached at which the real rate will again exceed the expected rate of deflation. But that is an optimistic scenario, because the adjustment process of falling asset values and a declining stock of real capital may itself feed pessimistic expectations about the future value of real capital so that there literally might not be a floor to the downward spiral, at least not unless there is some exogenous force that can reverse the downward spiral, e.g., by changing price-level expectations.  Given the riskiness of allowing the rate of deflation to come too close to the real interest rate, it seems prudent to keep deflation below the real rate of interest by a couple of points, so that the nominal interest rate doesn’t fall below 2%.

But notice that this cumulative downward process doesn’t really require actual deflation. The same process could take place even if the expected rate of inflation were positive in an economy with a negative real interest rate. Real interest rates have been steadily falling for over a year, and are now negative even at maturities up to 10 years. What that suggests is that ceiling on tolerable deflation is negative. Negative deflation is the same as inflation, which means that there is a lower bound to tolerable inflation.  When the economy is operating in an environment of very low or negative real rates of interest, the economy can’t recover unless the rate of inflation is above the lower bound of tolerable inflation. We are not in the critical situation that we were in four years ago, when the expected yield on cash was greater than the expected yield on real capital, but it is a close call. Why are businesses, despite high earnings, holding so much cash rather than using it to purchase real capital assets? My interpretation is that with real interest rates negative, businesses do not see a sufficient number of profitable investment projects to invest in. Raising the expected price level would increase the number of investment projects that appear profitable, thereby inducing additional investment spending, finally inducing businesses to draw down, rather than add to, their cash holdings.

So it seems to me that paleo-Monetarists have been misled by a false criterion, one not implied by the Fisher relation that has become central to Monetarist and Post-Monetarist policy orthodoxy. The mere fact that we have not had deflation since 2009 does not mean that monetary policy has not been contractionary, or, at any rate, insufficiently expansionary. So someone committed to the proposition that a market economy is inherently stable is not obliged, as the paleo-Monetarists seem to think, to take the position that monetary policy could not have been responsible for the failure of the feeble recovery since 2009 to bring us back to full employment. Whether it even makes sense to think about an economy as being inherently stable or unstable is a whole other question that I will leave for another day.

HT:  Lars Christensen

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner

Archives

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 3,261 other subscribers
Follow Uneasy Money on WordPress.com