natural rate of interest

Archive for the 'natural rate of interest' Category

Rules vs. Discretion Historically Contemplated

Here is a new concluding section which I have just written for my paper “Rules versus Discretion in Monetary Policy: Historically Contemplated” which I spoke about last September at the Mercatus Confernce on Monetary Rules in a Post-Crisis World. I have been working a lot on the paper over the past month or so and I hope to post a draft soon on SSRN and it is now under review for publication. I apologize for having written very little in past month and for having failed to respond to any comments on my previous posts. I simply have been too busy with work and life to have any energy left for blogging. I look forward to being more involved in the blog over the next few months and expect to be posting some sections of a couple of papers I am going to be writing. But I’m offering no guarantees. It is gratifying to know that people are still visiting the blog and reading some of my old posts.

Although recognition of a need for some rule to govern the conduct of the monetary authority originated in the perceived incentive of the authority to opportunistically abuse its privileged position, the expectations of the public (including that small, but modestly influential, segment consisting of amateur and professional economists) about what monetary rules might actually accomplish have evolved and expanded over the course of the past two centuries. As Laidler (“Economic Ideas, the Monetary Order, and the Uneasy Case for Monetary Rules”) shows, that evolution has been driven by both the evolution of economic and monetary institutions and the evolution of economic and monetary doctrines about how those institutions work.

I distinguish between two types of rules: price rules and quantity rules. The simplest price rule involved setting the price of a commodity – usually gold or silver – in terms of a monetary unit whose supply was controlled by the monetary authority or defining a monetary unit as a specific quantity of a particular commodity. Under the classical gold standard, for example, the monetary authority stood ready to buy or sell gold on demand at legally determined price of gold in terms of the monetary unit. Thus, the fixed price of gold under the gold standard was originally thought to serve as both the policy target of the rule and the operational instrument for implementing the rule.

However, as monetary institutions and theories evolved, it became apparent that there were policy objectives other than simply maintaining the convertibility of the monetary unit into the standard commodity that required the attention of the monetary authority. The first attempt to impose an additional policy goal on a monetary authority was the Bank Charter Act of 1844 which specified a quantity target – the aggregate of banknotes in circulation in Britain – which the monetary authority — the Bank of England – was required to reach by following a simple mechanical rule. By imposing a 100-percent marginal gold-reserve requirement on the notes issued by the Bank of England, the Bank Charter Act made the quantity of banknotes issued by the Bank of England both the target of the quantity rule and the instrument by which the rule was implemented.

Owing to deficiencies in the monetary theory on the basis of which the Act was designed and to the evolution of British monetary practices and institution, the conceptual elegance of the Bank Charter Act was not matched by its efficacy in practice. But despite, or, more likely, because of, the ultimate failure of Bank Charter Act, the gold standard, surviving recurring financial crises in Great Britain in the middle third of the nineteenth century, was eventually adopted by many other countries in the 1870s, becoming the de facto international monetary system from the late 1870s until the start of World War I. Operation of the gold standard was defined by, and depended on, the observance of a single price rule in which the value of a currency was defined by its legal gold content, so that corresponding to each gold-standard currency, there was an official gold price at which the monetary authority was obligated to buy or sell gold on demand.

The value – the purchasing power — of gold was relatively stable in the 35 or so years of the gold standard era, but that stability could not survive the upheavals associated with World War I, and so the problem of reconstructing the postwar monetary system was what kind of monetary rule to adopt to govern the post-war economy. Was it enough merely to restore the old currency parities – perhaps adjusted for differences in the extent of wartime and postwar currency depreciation — that governed the classical gold standard, or was it necessary to take into account other factors, e.g., the purchasing power of gold, in restoring the gold standard? This basic conundrum was never satisfactorily answered, and the failure to do so undoubtedly was a contributing, and perhaps dominant, factor in the economic collapse that began at the end of 1929, ultimately leading to the abandonment of the gold standard.

Searching for a new monetary regime to replace the failed gold standard, but to some extent inspired by the Bank Charter Act of the previous century, Henry Simons and ten fellow University of Chicago economists devised a totally new monetary system based on 100-percent reserve banking. The original Chicago proposal for 100-percent reserve banking proposed a monetary rule for stabilizing the purchasing power of fiat money. The 100-percent banking proposal would give the monetary authority complete control over the quantity of money, thereby enhancing the power of the monetary authority to achieve its price-level target. The Chicago proposal was thus inspired by a desire to increase the likelihood that the monetary authority could successfully implement the desired price rule. The price level was the target, and the quantity of money was the instrument. But as long as private fractional-reserve banks remained in operation, the monetary authority would lack effective control over the instrument. That was the rationale for replacing fractional reserve banks with 100-percent reserve banks.

But Simons eventually decided in his paper (“Rules versus Authorities in Monetary Policy”) that a price-level target was undesirable in principle, because allowing the monetary authority to choose which price level to stabilize, thereby favoring some groups at the expense of others, would grant too much discretion to the monetary authority. Rejecting price-level stabilization as monetary rule, Simons concluded that the exercise of discretion could be avoided only if the quantity of money was the target as well as the instrument of a monetary rule. Simons’s ideal monetary rule was therefore to keep the quantity of money in the economy constant — forever. But having found the ideal rule, Simons immediately rejected it, because he realized that the reforms in the financial and monetary systems necessary to make such a rule viable over the long run would never be adopted. And so he reluctantly and unhappily reverted back to the price-level stabilization rule that he and his Chicago colleagues had proposed in 1933.

Simons’s student Milton Friedman continued to espouse his teacher’s opposition to discretion, and as late as 1959 (A Program for Monetary Stability) he continued to advocate 100-percent reserve banking. But in the early 1960s, he adopted his k-percent rule and gave up his support for 100-percent banking. But despite giving up on 100-percent banking, Friedman continued to argue that the k-percent rule was less discretionary than the gold standard or a price-level rule, because neither the gold standard nor a price-level rule eliminated the exercise of discretion by the monetary authority in its implementation of policy, failing to acknowledge that, under any of the definitions that he used (usually M1 and sometimes M2), the quantity of money was a target, not an instrument. Of course, Friedman did eventually abandon his k-percent rule, but that acknowledgment came at least a decade after almost everyone else had recognized its unsuitability as a guide for conducting monetary policy, let alone as a legally binding rule, and long after Friedman’s repeated predictions that rapid growth of the monetary aggregates in the 1980s presaged the return of near-double-digit inflation.

However, the work of Kydland and Prescott (“Rules Rather than Discretion: The Inconsistency of Optimal Plans”) on time inconsistency has provided an alternative basis on which argue against discretion: that the lack of commitment to a long-run policy would lead to self-defeating short-term attempts to deviate from the optimal long-term policy.[1]

It is now I think generally understood that a monetary authority has available to it four primary instruments in conducting monetary policy, the quantity of base money, the lending rate it charges to banks, the deposit rate it pays banks on reserves, and an exchange rate against some other currency or some asset. A variety of goals remain available as well, nominal goals like inflation, the price level, or nominal income, or even an index of stock prices, as well as real goals like real GDP and employment.

Ever since Friedman and Phelps independently argued that the long-run Phillips Curve is vertical, a consensus has developed that countercyclical monetary policy is basically ineffectual, because the effects of countercyclical policy will be anticipated so that the only long-run effect of countercyclical policy is to raise the average rate of inflation without affecting output and employment in the long run. Because the reasoning that generates this result is essentially that money is neutral in the long run, the reasoning is not as compelling as the professional consensus in its favor would suggest. The monetary neutrality result only applies under the very special assumptions of a comparative static exercise comparing an initial equilibrium with a final equilibrium. But the whole point of countercyclical policy is to speed the adjustment from a disequilbrium with high unemployment back to a low-unemployment equilibrium. A comparative-statics exercise provides no theoretical, much less empirical, support for the proposition that anticipated monetary policy cannot have real effects.

So the range of possible targets and the range of possible instruments now provide considerable latitude to supporters of monetary rules to recommend alternative monetary rules incorporating many different combinations of alternative instruments and alternative targets. As of now, we have arrived at few solid theoretical conclusions about the relative effectiveness of alternative rules and even less empirical evidence about their effectiveness. But at least we know that, to be viable, a monetary rule will almost certainly have to be expressed in terms of one or more targets while allowing the monetary authority at least some discretion to adjust its control over its chosen instruments in order to effectively achieve its target (McCallum 1987, 1988). That does not seem like a great deal of progress to have made in the two centuries since economists began puzzling over how to construct an appropriate rule to govern the behavior of the monetary authority, but it is progress nonetheless. And, if we are so inclined, we can at least take some comfort in knowing that earlier generations have left us a lot of room for improvement.

Footnote:

[1] Friedman in fact recognized the point in his writings, but he emphasized the dangers of allowing discretion in the choice of instruments rather than the time-inconsistency policy, because it was only former argument that provided a basis for preferring his quantity rule over price rules.

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: Brad Delong, Paul Krugman

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.

John Cochrane Explains Neo-Fisherism

Published November 12, 2014 Fisher equation , John Cochrane , Knut Wicksell , natural rate of interest , Neo-Fisherism 13 Comments
Tags: Cantillon Effects, Hayek, Henry Thornton, Law of Reflux, Nick Rowe

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.

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.

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.

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.

A New Version of my Paper (with Paul Zimmerman) on the Hayek-Sraffa Debate Is Available on SSRN

Published July 7, 2014 expectations , Hayek , intertemporal equilibrium , Irving Fisher , Keynes , natural rate of interest , own rate of interest , Piero Sraffa 12 Comments
Tags: Fisher, Hayek, Keynes, Sraffa

One of the good things about having a blog (which I launched July 5, 2011) is that I get comments about what I am writing about from a lot of people that I don’t know. One of my most popular posts – it’s about the sixteenth most visited — was one I wrote, just a couple of months after starting the blog, about the Hayek-Sraffa debate on the natural rate of interest. Unlike many popular posts, to which visitors are initially drawn from very popular blogs that linked to those posts, but don’t continue to drawing a lot of visitors, this post initially had only modest popularity, but still keeps on drawing visitors.

That post also led to a collaboration between me and my FTC colleague Paul Zimmerman on a paper “The Sraffa-Hayek Debate on the Natural Rate of Interest” which I presented two years ago at the History of Economics Society conference. We have now finished our revisions of the version we wrote for the conference, and I have just posted the new version on SSRN and will be submitting it for publication later this week.

Here’s the abstract posted on the SSRN site:

Hayek’s Prices and Production, based on his hugely successful lectures at LSE in 1931, was the first English presentation of Austrian business-cycle theory, and established Hayek as a leading business-cycle theorist. Sraffa’s 1932 review of Prices and Production seems to have been instrumental in turning opinion against Hayek and the Austrian theory. A key element of Sraffa’s attack was that Hayek’s idea of a natural rate of interest, reflecting underlying real relationships, undisturbed by monetary factors, was, even from Hayek’s own perspective, incoherent, because, without money, there is a multiplicity of own rates, none of which can be uniquely identified as the natural rate of interest. Although Hayek’s response failed to counter Sraffa’s argument, Ludwig Lachmann later observed that Keynes’s treatment of own rates in Chapter 17 of the General Theory (itself a generalization of Fisher’s (1896) distinction between the real and nominal rates of interest) undercut Sraffa’s criticism. Own rates, Keynes showed, cannot deviate from each other by more than expected price appreciation plus the cost of storage and the commodity service flow, so that anticipated asset yields are equalized in intertemporal equilibrium. Thus, on Keynes’s analysis in the General Theory, the natural rate of interest is indeed well-defined. However, Keynes’s revision of Sraffa’s own-rate analysis provides only a partial rehabilitation of Hayek’s natural rate. There being no unique price level or rate of inflation in a barter system, no unique money natural rate of interest can be specified. Hayek implicitly was reasoning in terms of a constant nominal value of GDP, but barter relationships cannot identify any path for nominal GDP, let alone a constant one, as uniquely compatible with intertemporal equilibrium.

Aside from clarifying the conceptual basis of the natural-rate analysis and its relationship to Sraffa’s own-rate analysis, the paper also highlights the connection (usually overlooked but mentioned by Harald Hagemann in his 2008 article on the own rate of interest for the International Encyclopedia of the Social Sciences) between the own-rate analysis, in either its Sraffian or Keynesian versions, and Fisher’s early distinction between the real and nominal rates of interest. The conceptual identity between Fisher’s real and nominal distinction and Keynes’s own-rate analysis in the General Theory only magnifies the mystery associated with Keynes’s attack in chapter 13 of the General Theory on Fisher’s distinction between the real and the nominal rates of interest.

I also feel that the following discussion of Hayek’s role in developing the concept of intertemporal equilibrium, though tangential to the main topic of the paper, makes an important point about how to think about intertemporal equilibrium.

Perhaps the key analytical concept developed by Hayek in his early work on monetary theory and business cycles was the idea of an intertemporal equilibrium. Before Hayek, the idea of equilibrium had been reserved for a static, unchanging, state in which economic agents continue doing what they have been doing. Equilibrium is the end state in which all adjustments to a set of initial conditions have been fully worked out. Hayek attempted to generalize this narrow equilibrium concept to make it applicable to the study of economic fluctuations – business cycles – in which he was engaged. Hayek chose to formulate a generalized equilibrium concept. He did not do so, as many have done, by simply adding a steady-state rate of growth to factor supplies and technology. Nor did Hayek define equilibrium in terms of any objective or measurable magnitudes. Rather, Hayek defined equilibrium as the mutual consistency of the independent plans of individual economic agents.

The potential consistency of such plans may be conceived of even if economic magnitudes do not remain constant or grow at a constant rate. Even if the magnitudes fluctuate, equilibrium is conceivable if the fluctuations are correctly foreseen. Correct foresight is not the same as perfect foresight. Perfect foresight is necessarily correct; correct foresight is only contingently correct. All that is necessary for equilibrium is that fluctuations (as reflected in future prices) be foreseen. It is not even necessary, as Hayek (1937) pointed out, that future price changes be foreseen correctly, provided that individual agents agree in their anticipations of future prices. If all agents agree in their expectations of future prices, then the individual plans formulated on the basis of those anticipations are, at least momentarily, equilibrium plans, conditional on the realization of those expectations, because the realization of those expectations would allow the plans formulated on the basis of those expectations to be executed without need for revision. What is required for intertemporal equilibrium is therefore a contingently correct anticipation by future agents of future prices, a contingent anticipation not the result of perfect foresight, but of contingently, even fortuitously, correct foresight. The seminal statement of this concept was given by Hayek in his classic 1937 paper, and the idea was restated by J. R. Hicks (1939), with no mention of Hayek, two years later in Value and Capital.

I made the following comment in a footnote to the penultimate sentence of the quotation:

By defining correct foresight as a contingent outcome rather than as an essential property of economic agents, Hayek elegantly avoided the problems that confounded Oskar Morgenstern ([1935] 1976) in his discussion of the meaning of equilibrium.

I look forward to reading your comments.

Hawtrey’s Good and Bad Trade, Part III: Banking and Interest Rates

Published October 1, 2013 Hawtrey , monetary theory , natural rate of interest 11 Comments
Tags: Henry Thornton, Knut Wicksell

In my previous installment in this series, I began discussing Hawtrey’s analysis of a banking system that creates credit money convertible into a pure fiat money. I noted what seem to me to be defects in Hawtrey’s analysis, mainly related to his incomplete recognition of all the incentives governing banks when deciding how much money to create by making loans. Nevertheless, it is worth following Hawtrey, even with the gap, as he works his way through his analysis .

But, before we try to follow Hawtrey, it will be helpful to think about where he is heading. In his analysis of a pure fiat money system, all — actually not quite all, but almost all — of the analytical work was done by considering how a difference between the amount of fiat money people want to hold and the greater or lesser amount that they actually do hold is resolved. If they hold less money than they want, total spending decreases as people try (unsuccessfully in the aggregate) to build up their cash balances, and if they hold more money than they want, spending increases as people try (unsuccessfully in the aggregate) to part with their excess cash hoaldings. Reaching a new equilibrium entails an adjustment of the ratio of total spending to the stock of fiat money that characterized the initial equilibrium. There may be an interest rate in such an economy, but a change in the interest rate plays no part in the adjustment process that restores equilibrium after a monetary shock (i.e., a change in the stock of fiat money). Hawtrey aims to compare (and contrast) this adjustment process with the adjustment process to a change in the quantity of fiat money when not all money is fiat money — when there is also credit money (created by banks and convertible into fiat money) circulating along with fiat money.

In analyzing a monetary disturbance to a credit-money system, Hawtrey takes as his starting point a banking system in equilibrium, with banks and individuals holding just the amount of currency, reserves and deposits that they want to hold. He then posits a reduction in the total stock of currency.

The first effect of the contraction of the currency is that the working balance of cash in the hands of individual members of the community will be diminished. The precise proportion in which this diminution is shared between bankers and other people does not matter, for those who have banking accounts will quickly draw out enough cash to restore their working balances. As soon as this process is completed we have two effects; first, that the greater part, indeed practically the whole, of the currency withdrawn comes out of the banks’ reserves, and secondly, that the total amount of purchasing power in the community (i.e., currency in circulation plus bank balances) is diminished by the amount of currency withdrawn. One consequence of the existence of a banking system is that a given diminution in the stock of currency produces at this stage much less than a proportional diminution in the total of purchasing power. (pp. 58-59)

Hawtrey goes on to explain this point with a numerical example. Suppose total purchasing power (i.e., the sum of currency plus deposits) were £1 billion of which £250 million were currency and £750 million deposits. If the stock of currency were reduced by 10%, the amount of currency would fall to £225 million, with total stock of purchasing power falling to £975 million. (Note by the way, that Hawtrey’s figure for total purchasing power, or the total stock of money, does not correspond to the usual definition of the money stock in which only currency held by the public, not by the banking system, are counted.) At any rate, the key point for Hawtrey is that under a fiat currency with a banking system, the percentage decrease (10%) in the stock of currency is not equal to the percentage decrease in the total stock of money (2.5%), so that a 10% reduction in the stock of currency, unlike the pure fiat currency case, would not force down the price level by 10% (at least, not without introducing other variables into the picture). Having replenished their holdings of currency by converting deposits into currency, the total cash holdings of the public are only slightly (2.5%) less than the amount they would like to hold, so that only a 2.5% reduction in total spending would seem to be necessary to restore the kind of monetary equilibrium on which Hawtrey was focused in discussing the pure fiat money case. A different sort of disequilibrium involving a different adjustment process had to be added to his analytical landscape.

The new disequilibrium introduced by Hawtrey was that between the amount of currency held by the banks as reserves against their liabilities (deposits) and the amount of currency that they are actually holding. Thus, even though banks met the demands of their depositors to replenish the fiat currency that, by assumption, had been taken from their existing cash balances, that response by the banks, while (largely) eliminating one disequilibrium, also created another one: the banks now find that their reserves, given the amount of liabilities (deposits) on their balance sheets, are less than they would like them to be. Hawtrey is thus positing the existence of a demand function by the banks to hold reserves, a function that depends on the amount of liabilities that they create. (Like most banking theorists, Hawtrey assumes that the functional relationship between bank deposits and banks’ desired reserves is proportional, but there are obviously economies of scale in holding reserves, so that the relationship between bank deposits and desired reserves is certainly less than proportional.) The means by which banks can replenish their reserves, according to Hawtrey, again following traditional banking theory, is to raise the interest rate that they charge borrowers. Here, again, Hawtrey was not quite on the mark, overlooking the possibility that banks could offer to pay interest (or to increase the rate that they were already paying on deposits) as a way of reducing the tendency of depositors to withdraw deposits in exchange for currency.

The special insight brought by Hawtrey to this analysis is that a particular group of entrepreneurs (traders and merchants), whose largest expense is the interest paid on advances from banks to finance their holdings of inventories, are highly sensitive to variations in the bank lending rate, and adjust the size of their inventories accordingly. And since it is the manufacturers to whom traders and merchants are placing orders, the output of factories is necessarily sensitive to the size of the inventories that merchants and traders are trying to hold. Thus, if banks, desiring to replenish their depleted reserves held against deposits, raise interest rates on loans, it will immediately reduce the size of inventories that merchants and traders want to hold, causing them to diminish their orders to manufacturers. But as manufacturers reduce output in response to diminished orders from merchants, the incomes of employees and others providing services and materials to the manufacturers will also fall, so that traders and merchants will find that they are accumulating inventories because their sales to dealers and retailers are slackening, offsetting the effect of their diminished orders to manufacturers, and, in turn, causing merchants and traders to reduce further their orders from manufacturers.

As this process works itself out, prices and output will tend to fall (at least relative to trend), so that traders and merchants will gradually succeed in reducing their indebtedness to the banks, implying that the total deposits created by the banking system will decrease. As their deposit liabilities decline, the amount of reserves that the banks would like to hold declines as well, so that gradually this adjustment process will restore an equilibrium between the total quantity of reserves demanded by the banking system and the total quantity of reserves that is made available to the banks (i.e., the total quantity of currency minus the amount of currency that the public chooses to hold as cash). However, the story does not end with the restoration of equilibrium for the banking system. Despite equilibrium in the banking system, total spending, output, and employment will have fallen from their original equilibrium levels. Full equilibrium will not be restored until prices and wages fall enough to make total spending consistent with a stock of currency 10% less than it was in the original equilibrium. Thus, in the end, it turns out that a 10% reduction in the quantity of currency in a monetary system with both fiat money and credit money will cause a 10% reduction in the price level when a new equilibrium is reached. However, the adjustment process by which a new equilibrium is reached, involving changes not only in absolute prices and wages, but in interest rates, is more complicated than the adjustment process in a pure fiat money system.

Hawtrey summed up his analysis in terms of three interest rates. First, the natural rate “which represented the actual labour-saving value of capital at the level of capitalisation reached by industry. This ratio of labour saved per annum to labour expended on first cost is a physical property of the capital actually in use, and under perfectly stable monetary conditions is equal to the market rate of interest.” Second the market rate which “diverges from the natural rate according to the tendency of prices. When prices are rising them market rate is higher, and when falling lower, than the natural rate, and this divergence is due to the fat that the actual profits of business show under those conditions corresponding movements.” Third, there is the profit rate, “which represents the true profits of business prevailing for the time being,” and does not necessarily coincide with the market rate.

The market rate is in fact the bankers’ rate, and is greater or less than the profit rate, according as the bankers wish to discourage or encourage borrowing. . . .

Consequently, for the banker’s purposes, a “high” rate of interest is one which is above the profit rate, and it is only when the rate of interest is equal to the profit rate that there is no tendency towards either an increase or decrease in temporary borrowing. In any of the three cases the rate of interest may be either above or below the natural rate. If the natural rate is 4% and the profit rate in consequence is only 2%, a market rate of 3% is “high,” and will result in a curtailment of borrowing. If prices are rising and the profit rate is 6%, a market rate of 5% is “low,” and will be compatible with an increased borrowing.

In the case we are now considering we assumed the disturbance to be a departure from perfectly stable conditions, in which the market rate of interest would be identical with the “natural” rate. On the contraction of the currency occurring the bankers raised the market rate above the natural rate. But at the same time the fall of prices began, and there must consequently be a fall of the profit rate below the natural rate. As we now see, the market rate may actually fall below the natural rate, and so long as it remains above the profit rate it will still be a “high” rate of interest.

When the restoration of the bank reserves is completed the market rate will drop down to equality with the profit rate, and they will remain equal to one another and below the natural rate until the fall of prices has gone far enough to re-establish equilibrium. (pp. 66-67)

Although it seems to me that Hawtrey, in focusing exclusively on the short-term lending rate of banks to explain the adjustment of the banking system to a disturbance, missed an important aspect of the overall picture (i.e., the deposit rate), Hawtrey did explain the efficacy of a traditional tool of monetary policy, the short-term lending rate of the banking system (the idea of a central bank having not yet been introduced at this stage of Hawtrey’s exposition). And he did so while avoiding the logical gap in the standard version of the natural-rate-market-rate theory as developed by both Thornton and Wicksell (see section 3 of my paper on Ricardo and Thornton here) explaining why changes in the bank rate could affect aggregate demand without assuming, as do conventional descriptions of the adjustment process, that the system was adjusting to an excess demand for or an excess supply of bank deposits.

Hawtrey’s Good and Bad Trade: Part II

Published September 24, 2013 Hawtrey , James Tobin , John Fullarton , Knut Wicksell , monetary theory , natural rate of interest 21 Comments
Tags: effective demand, Irving Fisher, Keynes

Here I am again back at you finally with another installment in my series on Hawtrey’s Good and Bad Trade. In my first installment I provided some background on Hawtrey and a quick overview of the book, including a mention of the interesting fact (brought to my attention by David Laidler) that Hawtrey used the term “effective demand” in pretty much the same way that Keynes, some 20 years later, would use it in the General Theory.

In this post, I want to discuss what I consider the highlights of the first six chapters. The first chapter is a general introduction to the entire volume laying out the basic premise of the book, which is that the business cycle, understood as recurring fluctuations in the level of employment, is the result of monetary disturbances that lead to alternating phases of expansion and contraction. It is relatively easy for workers to find employment in expansions, but more difficult to do so in contractions. From the standpoint of the theory of economic equilibrium, the close correlation between employment and nominal income over the business cycle is somewhat paradoxical, because, according to the equilibrium theory, the allocation of resources is governed by relative, not absolute, prices. In the theory of equilibrium, a proportional increase or decrease in all prices should have no effect on employment. To explain the paradox, Hawtrey relies on the rigidity of some prices, and especially wages, an empirical fact that, Hawtrey believed, was an essential aspect of any economic system, and a necessary condition for the cyclicality of output and employment.

In Hawtrey’s view, economic expansions and contractions are caused by variations in effective demand, which he defines as total money income. (For reasons I discussed about a year and a half ago, I prefer to define “effective demand” as total money expenditure.) What determines effective demand, according to Hawtrey, is the relationship between the amount of money people are holding and the amount that they would, on average over time, like to hold. The way to think about the amount of money that people would like to hold is to imagine that there is some proportion of their annual income that people aim to hold in the form of cash.

The relationship between the amount of cash being held and the amount that people would like to hold depends on the nature of the monetary system. Hawtrey considers two types of monetary system: one type (discussed in chapter 2) is a pure fiat money system in which all money is issued by government; the other (discussed in chapter 3) is a credit system in which money is also created by banks by promising to redeem, on demand, their obligations (either deposits or negotiable banknotes) for fiat money. Credit money is issued by banks in exchange for a variety of assets, usually the untraded IOUs of borrowers.

In a pure fiat money system, effective demand depends chiefly on the amount of fiat money that people want to hold and on the amount of fiat money created by the government, fiat money being the only money available. A pure fiat money system, Hawtrey understood, was just the sort of system in which the propositions of the quantity theory of money would obtain at least in the medium to long run.

[I]f the adjustment [to a reduction in the quantity of money] could be made entirely by a suitable diminution of wages and salaries, accompanied by a corresponding diminution of prices, the commercial community could be placed forthwith in a new position of equilibrium, in which the output would continue unchanged, and distribution would only be modified by the apportionment of a somewhat larger share of the national product to the possessors of interest, rent, and other kinds of fixed incomes. In fact, the change in the circulating medium is merely a change in the machinery of distribution, and a change, moreover, which, once made, does not impair the effectiveness of that machinery. If the habits of the community are adapted without delay to the change, the production of wealth will continue unabated. If customary prices resist the change, the adjustment, which is bound to come sooner or later, will only be forced upon the people by the pressure of distress. (p. 41)

In a fiat money system, if the public have less money than they would like to hold their only recourse is to attempt to reduce their expenditures relative to their receipts, either offering more in exchange, which tends to depress prices or reducing their purchases, making it that much more difficult for anyone to increase sales except by reducing prices. The problem is that in a fiat system the amount of money is what it is, so that if one person manages to increase his holdings of money by increasing sales relative to purchases, his increase in cash balances must have be gained at the expense of someone else. With a fixed amount of fiat money in existence, the public as a whole cannot increase their holdings of cash, so equilibrium can be restored only by reducing the quantity of money demanded. But the reduction in the amount of money that people want to hold cannot occur unless income in money terms goes down. Money income can go down only if total output in real terms, or if the price level, falls. With nominal income down, people, wanting to hold some particular share of their nominal income in the form of money, will be content with a smaller cash balance than they were before, and will stop trying to increase their cash balances by cutting their expenditure. Because some prices — and especially wages — tend to be sticky, Hawtrey felt that it was inevitable that the adjustment to reduction in the amount of fiat money would cause both real income and prices to fall.

Although Hawtrey correctly perceived that the simple quantity theory would not, even in theory, hold precisely for a credit system, his analysis of the credit system was incomplete inasmuch as he did not fully take into account the factors governing the public’s choice between holding credit money as opposed to fiat money or the incentives of the banking system to create credit money. That theory was not worked out till James Tobin did so 50 years later (another important anniversary worthy of note), though John Fullarton made an impressive start in his great work on the subject in 1844, a work Hawtrey must have been familiar with, but, to my knowledge, never discussed in detail.

In such a banking system there is no necessary connexion between the total of the deposits and the amount of coin which has been paid to the banks. A banker may at any time grant a customer a loan by simply adding to the balance standing to the customer’s credit in the books of the bank. No cash passes, but the customer acquires the right, during the currency of the loan, to draw cheques on the bank up to the amount lent. When the period of the loan expires, if the customer has a large enough balance to his credit, the loan can be repaid without any cash being employed, the amount of the loan being simply deducted from the balance. So long as the loan is outstanding it represents a clear addition to the available stock of “money,” in the sense of purchasing power. It is “money” in the the sense which will play, in a community possessing banks, the same part as money in the stricter sense of legal tender currency would play in the fictitious bankless community whose commercial conditions we previously have been considering. This is the most distinctive feature of the banking system, that between the stock of legal tender currency and the trading community there is interposed an intermediary, the banker, who can, if he wishes, create money out of nothing. (PP. 56-57)

This formulation is incomplete, inasmuch as it leaves the decision of the banker about how much money to create unconstrained by the usual forces of marginal revenue and marginal cost that supposedly determine the decisions of other profit-seeking businessmen. Hawtrey is not oblivious to the problem, but does not advance the analysis as far as he might have.

We have now to find out how this functionary uses his power and under what limitations he works. Something has already been said of the contingencies for which he must provide. Whenever he grants a loan and thereby creates money, he must expect a certain portion of this money to be applied sooner or later, to purposes for which legal tender currency is necessary. Sums will be drawn out from time to time to be spent either in wages or in small purchases, and the currency so applied will take a little time to find its way back to the banks. Large purchases will be paid for by cheque, involving a mere transfer of credit from one banking account to another, but the recipient of the cheque may wish to apply it ot the payment of wages, etc. Thus the principal limitation upon the banker’s freedom to create money is that he must have a reserve to meet the fresh demands for cash to which the creation of new money may lead. (Id.)

This is a very narrow view, apparently assuming that there is but one banker and that the only drain on the reserves of the banker is the withdrawal of currency by depositors. The possibility that recipients of cheques drawn on one bank may prefer to hold those funds in a different bank so that the bank must pay a competitive rate of interest on its deposits to induce its deposits to be held rather than those of another bank is not considered.

In trade a seller encourages or discourages buyers by lowering or raising his prices. So a banker encourages or discourages borrowers by lowering or raising the rate of interest. (p.58)

Again, Hawtrey only saw half the picture. The banker is setting two rates: the rate that he charges borrowers and the rate that he pays to depositors. It is the spread between those two rates that determines the marginal revenue from creating another dollar of deposits. Given that marginal revenue, the banker must form some estimate of the likely cost associated with creating another dollar of deposits (an estimate that depends to a large degree on expectations that may or may not be turn out to be correct), and it is the comparison between the marginal revenue from creating additional deposits with the expected cost of creating additional deposits that determines whether a bank wants to expand or contract its deposits.

Of course, the incomplete analysis of the decision making of the banker is not just Hawtrey’s, it is characteristic of all Wicksellian natural-rate theories. However, in contrast to other versions of the natural-rate genre, Hawtrey managed to avoid the logical gap in those theories: the failure to see that it is the spread between the lending and the deposit rates, not the difference between the lending rate and the natural rate, that determines whether banks are trying to expand or contract. But that is a point that I will have to come back to in the next installment in this series in which I will try to follow through the main steps of Hawtrey’s argument about how a banking system adjusts to a reduction in the quantity of fiat money (aka legal tender currency or base money) is reduced. That analysis, which hinges on the role of merchants and traders whose holding of inventories of goods is financed by borrowing from the banks, was a critical intellectual innovation of Hawtrey’s and was the key to his avoidance of the Wicksellian explanatory gap.

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: Earl Thompson, Fisher equation, Fisher inequality, Wicksell

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: Allin Cottrell, expected inflation, Miles Kimball

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.

Who Sets the Real Rate of Interest?

Published July 3, 2013 expectations , Federal Reserve , Irving Fisher , Martin Feldstein , Milton Friedman , natural rate of interest , natural rate of unemployment , real interest rates , Uncategorized , Wall Street Journal 49 Comments
Tags: Fisher equation, John Taylor, Martin Feldstein, Milton Friedman, Wall Street Journal

Understanding economics requires, among other things, understanding the distinction between real and nominal variables. Confusion between real and nominal variables is pervasive, constantly presenting barriers to clear thinking, and snares and delusions for the mentally lazy. In this post, I want to talk about the distinction between the real rate of interest and the nominal rate of interest. That distinction has been recognized for at least a couple of centuries, Henry Thornton having mentioned it early in the nineteenth century. But the importance of the distinction wasn’t really fully understood until Irving Fisher made the distinction between the real and nominal rates of interest a key element of his theory of interest and his theory of money, expressing the relationship in algebraic form — what we now call the Fisher equation. Notation varies, but the Fisher equation can be written more or less as follows:

i = r + dP/dt,

where i is the nominal rate, r is the real rate, and dP/dt is the rate of inflation. It is important to bear in mind that the Fisher equation can be understood in two very different ways. It can either represent an ex ante relationship, with dP/dt referring to expected inflation, or it can represent an ex post relationship, with dP/dt referring to actual inflation.

What I want to discuss in this post is the tacit assumption that usually underlies our understanding, and our application, of the ex ante version of the Fisher equation. There are three distinct variables in the Fisher equation: the real and the nominal rates of interest and the rate of inflation. If we think of the Fisher equation as an ex post relationship, it holds identically, because the unobservable ex post real rate is defined as the difference between the nominal rate and the inflation rate. The ex post, or the realized, real rate has no independent existence; it is merely a semantic convention. But if we consider the more interesting interpretation of the Fisher equation as an ex ante relationship, the real interest rate, though still unobservable, is not just a semantic convention. It becomes the theoretically fundamental interest rate of capital theory — the market rate of intertemporal exchange, reflecting, as Fisher masterfully explained in his canonical renderings of the theory of capital and interest, the “fundamental” forces of time preference and the productivity of capital. Because it is determined by economic “fundamentals,” economists of a certain mindset naturally assume that the real interest rate is independent of monetary forces, except insofar as monetary factors are incorporated in inflation expectations. But if money is neutral, at least in the long run, then the real rate has to be independent of monetary factors, at least in the long run. So in most expositions of the Fisher equation, it is tacitly assumed that the real rate can be treated as a parameter determined, outside the model, by the “fundamentals.” With r determined exogenously, fluctuations in i are correlated with, and reflect, changes in expected inflation.

Now there’s an obvious problem with the Fisher equation, which is that in many, if not most, monetary models, going back to Thornton and Wicksell in the nineteenth century, and to Hawtrey and Keynes in the twentieth, and in today’s modern New Keynesian models, it is precisely by way of changes in its lending rate to the banking system that the central bank controls the rate of inflation. And in this framework, the nominal interest rate is negatively correlated with inflation, not positively correlated, as implied by the usual understanding of the Fisher equation. Raising the nominal interest rate reduces inflation, and reducing the nominal interest rate raises inflation. The conventional resolution of this anomaly is that the change in the nominal interest rate is just temporary, so that, after the economy adjusts to the policy of the central bank, the nominal interest rate also adjusts to a level consistent with the exogenous real rate and to the rate of inflation implied by the policy of the central bank. The Fisher equation is thus an equilibrium relationship, while central-bank policy operates by creating a short-term disequilibrium. But the short-term disequilibrium imposed by the central bank cannot be sustained, because the economy inevitably begins an adjustment process that restores the equilibrium real interest rate, a rate determined by fundamental forces that eventually override any nominal interest rate set by the central bank if that rate is inconsistent with the equilibrium real interest rate and the expected rate of inflation.

It was just this analogy between the powerlessness of the central bank to hold the nominal interest rate below the sum of the exogenously determined equilibrium real rate and the expected rate of inflation that led Milton Friedman to the idea of a “natural rate of unemployment” when he argued that monetary policy could not keep the unemployment rate below the “natural rate ground out by the Walrasian system of general equilibrium equations.” Having been used by Wicksell as a synonym for the Fisherian equilibrium real rate, the term “natural rate” was undoubtedly adopted by Friedman, because monetarily induced deviations between the actual rate of unemployment and the natural rate of unemployment set in motion an adjustment process that restores unemployment to its “natural” level, just as any deviation between the nominal interest rate and the sum of the equilibrium real rate and expected inflation triggers an adjustment process that restores equality between the nominal rate and the sum of the equilibrium real rate and expected inflation.

So, if the ability of the central bank to use its power over the nominal rate to control the real rate of interest is as limited as the conventional interpretation of the Fisher equation suggests, here’s my question: When critics of monetary stimulus accuse the Fed of rigging interest rates, using the Fed’s power to keep interest rates “artificially low,” taking bread out of the mouths of widows, orphans and millionaires, what exactly are they talking about? The Fed has no legal power to set interest rates; it can only announce what interest rate it will lend at, and it can buy and sell assets in the market. It has an advantage because it can create the money with which to buy assets. But if you believe that the Fed cannot reduce the rate of unemployment below the “natural rate of unemployment” by printing money, why would you believe that the Fed can reduce the real rate of interest below the “natural rate of interest” by printing money? Martin Feldstein and the Wall Street Journal believe that the Fed is unable to do one, but perfectly able to do the other. Sorry, but I just don’t get it.

Look at the accompanying chart. It tracks the three variables in the Fisher equation (the nominal interest rate, the real interest rate, and expected inflation) from October 1, 2007 to July 2, 2013. To measure the nominal interest rate, I use the yield on 10-year Treasury bonds; to measure the real interest rate, I use the yield on 10-year TIPS; to measure expected inflation, I use the 10-year breakeven TIPS spread. The yield on the 10-year TIPS is an imperfect measure of the real rate, and the 10-year TIPS spread is an imperfect measure of inflation expectations, especially during financial crises, when the rates on TIPS are distorted by illiquidity in the TIPS market. Those aren’t the only problems with identifying the TIPS yield with the real rate and the TIPS spread with inflation expectations, but those variables usually do provide a decent approximation of what is happening to real rates and to inflation expectations over time.

Before getting to the main point, I want to make a couple of preliminary observations about the behavior of the real rate over time. First, notice that the real rate declined steadily, with a few small blips, from October 2007 to March 2008, when the Fed was reducing the Fed Funds target rate from 4.75 to 3% as the economy was sliding into a recession that officially began in December 2007. The Fed reduced the Fed Funds target to 2% at the end of April, but real interest rates had already started climbing in early March, so the failure of the FOMC to reduce the Fed Funds target again till October 2008, three weeks after the onset of the financial crisis, clearly meant that there was at least a passive tightening of monetary policy throughout the second and third quarters, helping create the conditions that precipitated the crisis in September. The rapid reduction in the Fed Funds target from 2% in October to 0.25% in December 2008 brought real interest rates down, but, despite the low Fed Funds rate, a lack of liquidity caused a severe tightening of monetary conditions in early 2009, forcing real interest rates to rise sharply until the Fed announced its first QE program in March 2009.

I won’t go into more detail about ups and downs in the real rate since March 2009. Let’s just focus on the overall trend. From that time forward, what we see is a steady decline in real interest rates from over 2% at the start of the initial QE program till real rates bottomed out in early 2012 at just over -1%. So, over a period of three years, there was a steady 3% decline in real interest rates. This was no temporary phenomenon; it was a sustained trend. I have yet to hear anyone explain how the Fed could have single-handedly produced a steady downward trend in real interest rates by way of monetary expansion over a period of three years. To claim that decline in real interest rates was caused by monetary expansion on the part of the Fed flatly contradicts everything that we think we know about the determination of real interest rates. Maybe what we think we know is all wrong. But if it is, people who blame the Fed for a three-year decline in real interest rates that few reputable economists – and certainly no economists that Fed critics pay any attention to — ever thought was achievable by monetary policy ought to provide an explanation for how the Fed suddenly got new and unimagined powers to determine real interest rates. Until they come forward with such an explanation, Fed critics have a major credibility problem.

So please – please — Wall Street Journal editorial page, Martin Feldstein, John Taylor, et al., enlighten us. We’re waiting.

PS Of course, there is a perfectly obvious explanation for the three-year long decline in real interest rates, but not one very attractive to critics of QE. Either the equilibrium real interest rate has been falling since 2009, or the equilibrium real interest rate fell before 2009, but nominal rates adjusted slowly to the reduced real rate. The real interest rate might have adjusted more rapidly to the reduced equilibrium rate, but that would have required expected inflation to have risen. What that means is that sometimes it is the real interest rate, not, as is usually assumed, the nominal rate, that adjusts to the expected rate of inflation. My next post will discuss that alternative understanding of the implicit dynamics of the Fisher equation.

That Oh So Elusive Natural Rate of Interest

Published February 28, 2013 expectations , Hayek , Irving Fisher , Keynes , Ludwig Lachmann , natural rate of interest , Piero Sraffa 13 Comments
Tags: Bob Murphy, Fisher, Hayek, Keynes, Sraffa

Last week, I did a short post linking to the new draft of my paper with Paul Zimmerman about the Sraffa-Hayek exchange on the natural rate of interest. In the paper, we attempt to assess Sraffa’s criticism in his 1932 review of Prices and Production of Hayek’s use of the idea of a natural rate of interest as well as Hayek’s response, or, perhaps, his lack of response, to Sraffa’s criticism. The issues raised by Sraffa are devilishly tricky, especially because he introduced the unfamiliar terminology of own-rates of interest, later adopted Keynes in chapter 17 of the General Theory in order to express his criticism. The consensus about this debate is that Sraffa got the best of Hayek in this exchange – the natural rate of interest was just one of the issues Sraffa raised, and, in the process, he took Hayek down a peg or two after the startling success that Hayek enjoyed upon his arrival in England, and publication of Prices and Production. In a comment to my post, Greg Ransom questions this conventional version of the exchange, but that’s my story and I’m sticking to it.

What Paul and I do in the paper is to try to understand Sraffa’s criticism of Hayek. It seems to us that the stridency of Sraffa’s attack on Hayek suggests that Sraffa was arguing that Hayek’s conception of a natural rate of interest was somehow incoherent in a barter economy in which there is growth and investment and, thus, changes in relative prices over time, implying that commodity own rates of interest would have differ. If, in a barter economy with growth and savings and investment, there are many own-rates, Sraffa seemed to be saying, it is impossible to identify any one of them as the natural rate of interest. In a later account of the exchange between Sraffa and Hayek, Ludwig Lachmann, a pupil of Hayek, pointed out that, even if there are many own rates in a barter economy, the own rates must, in an intertemporal equilibrium, stand in a unique relationship to each other: the expected net return from holding any asset cannot differ from the expected net return on holding any other asset. That is a condition of equilibrium. If so, it is possible, at least conceptually, to infer a unique real interest rate. That unique real interest rate could be identified with Hayek’s natural rate of interest.

In fact, as we point out in our paper, Irving Fisher in his classic Appreciation and Interest (1896) had demonstrated precisely this point, theoretically extracting the real rate from the different nominal rates of interest corresponding to loans contracted in terms of different assets with different expected rates of price appreciation. Thus, Sraffa did not demonstrate that there was no natural rate of interest. There is a unique real rate of interest in intertemporal equilibrium which corresponds to the Hayekian natural rate. However, what Sraffa could have demonstrated — though had he done so, he would still have been 35 years behind Irving Fisher – is that the unique real rate is consistent with an infinite number of nominal rates provided that those nominal rates reflected corresponding anticipated rate of price appreciation. But, instead, Sraffa argued that there is no unique real rate in intertemporal equilibrium. That was a mistake.

Another interesting (at least to us) point in our paper is that Keynes who, as editor of the Economic Journal, asked Sraffa to review Prices and Production, borrowed Sraffa’s own-rate terminology in chapter 17 of the General Theory, but, instead of following Sraffa’s analysis and arguing that there is no natural rate of interest, Keynes proceeded to derive, using (without acknowledgment) a generalized version of Fisher’s argument of 1896, a unique relationship between commodity own rates, adjusted for expected price changes, and net service yields, such that the expected net returns on all assets would be equalized. From this, Keynes did not conclude, as had Sraffa, that there is no natural rate of interest. Rather, he made a very different argument: that the natural rate of interest is a useless concept, because there are many natural rates each corresponding to a different the level of income and employment, a consideration that Hayek, and presumably Fisher, had avoided by assuming full intertemporal equilibrium. But Keynes never disputed that for any given level of income and employment, there would be a unique real rate to which all commodity own rates had to correspond. Thus, Keynes turned Sraffa’s analysis on its head. And the final point of interest is that even though Keynes, in chapter 17, presented essentially the same analysis of own rates, though in more general terms, that Fisher had presented 40 years earlier, Keynes in chapter 13 explicitly rejected Fisher’s distinction between the real and nominal rates of interest. Go figure.

Bob Murphy wrote a nice paper on the Sraffa-Hayek debate, which I have referred to before on this blog. However, I disagree with him that Sraffa’s criticism of Hayek was correct. In a post earlier this week, he infers, from our statement that, as long as price expectations are correct, any nominal rate is consistent with the unique real natural rate, that we must agree with him that Sraffa was right and Hayek was wrong about the natural rate. I think that Bob is in error on the pure theory here. There is a unique real natural rate in intertemporal equilibrium, and, in principle, the monetary authority could set a money rate equal to that real rate, provided that that nominal rate was consistent with the price expectations held by the public. However, intertemporal equilibrium could be achieved by any nominal interest rate selected by the monetary authority, again provided that the nominal rate chosen was consistent with the price expectations held by the public. In practice, either formulation is very damaging to Hayek’s policy criterion of setting the nominal interest rate equal to the real natural rate. But contrary to Sraffa’s charge, the policy criterion is not incoherent. It is just unworkable, as Hayek formulated it, and, on Hayek’s own theory, the criterion is unnecessary to avoid distorting malinvestments.

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

Uneasy Money